Progress in Energy and Combustion Science 59 (2016) 79 162
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Progress in Energy and Combustion Science
journal homepage: www.elsevier.com/locate/pecs
Progress in dynamic simulation of thermal power plants
FalahTagedPD15XX Alobaid*D16XX, NicolasD17XX Mertens,D18XXRalfD19XX Starkloff,D20XXThomasD21XX Lanz,D2XXChristianD23XX Heinze,D24XXBerndD25XX EppleD26XX
TechnischeTagedP Universitat€ Darmstadt, Institute for Energy Systems and Technology, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany
ARTICLETAGEDP INFO ABSTRACTTAGEDP
Article History: While the conventional design of thermal power plants is mainly focused on high process efficiency, market Received 29 March 2016 requirements increasingly target operating flexibility due to the continuing shift towards renewables. Dynamic Accepted 10 November 2016 simulation is a cost-ef0X3DX ficient tool for improving the flexibility of dispatchable power generation in transient Available online xxx operation1X3DXsuch as load changes and start-up procedures. Specific applications include the optimisation of con- trol structures, stress assessment for critical components and plant safety analysis in malfunction cases. This Keywords:TagedP work is2X3DXa comprehensive review of dynamic simulation, its development and application to various thermal Dynamic simulation power plants. The required mathematical models and various components for description the basic process, Thermal power generation Flexibility automation and electrical systems of thermal power plants are explained with the support of practical example fl Transient operation models. The underlying ow models and their fundamental assumptions are discussed, complemented by an Load changes overview of commonly used simulation codes. Relevant studies are summarised and placed in context for dif- Start-up procedures ferent thermal power plant technologies: combined-cycle power, coal-fired power, nuclear power, concen- Flow models trated solar power, geothermal power, municipal waste incineration and thermal desalination. Particular Combined-cycle power attention is given to those studies that include measurement validation in order to analyse the influence of fi Coal- red power model simplifications on simulation results. In conclusion, the study highlights current research efforts and Nuclear power future development potential of dynamic simulation in the field of thermal power generation. Concentrated solar power © 2016 The Authors. Published by Elsevier Ltd. Geothermal power Municipal waste incineration This is an open access article article under the CC BY-NC-ND license Thermal desalination (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction ...... 4 1.1. Flexible power generation ...... 4 1.2. Structure...... 5 2. Mathematical modelling ...... 5 2.1. Overview...... 6 2.2. Thermal hydraulic models ...... 6 2.2.1. Mixture flowmodel...... 7 2.2.2. Two-fluidmodel...... 10 2.2.2.1. Four-equation model...... 11 2.2.2.2. Five-equation model ...... 11 2.2.2.3. Six-equation model...... 11 2.2.2.4. Seven-equation model ...... 14 2.2.3. Solution method ...... 15 2.2.4. Comparison...... 15 2.3. Process components ...... 17 2.3.1. Connection point ...... 17 2.3.2. Thin-walled tube ...... 17 2.3.2.1. Pipe ...... 18 2.3.2.2. Valve...... 18 2.3.2.3. Attemperator/desuperheater ...... 19
* Corresponding author:D27XFalahX Alobaid ([email protected]). Tel.: +49 (0) 6151/16 23004; fax: +49 (0) 6151/16 22690.D29XX E-mail address: [email protected] (F. Alobaid), [email protected] (N. Mertens), [email protected] (R. Starkloff), [email protected] (T. Lanz), [email protected] (C. Heinze), [email protected] (B. Epple). http://dx.doi.org/10.1016/j.pecs.2016.11.001 0360-1285/© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 80 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
2.3.2.4. Heat exchanger ...... 19 2.3.3. Thick-walled tube ...... 19 2.3.3.1. Header...... 20 2.3.3.2. Drum ...... 20 2.3.3.3. Separator...... 21 2.3.3.4. Feedwater storage tank ...... 21 2.3.4. Turbomachines ...... 21 2.3.4.1. Compressor...... 22 2.3.4.2. Fan ...... 23 2.3.4.3. Blower...... 23 2.3.4.4. Pump ...... 23 2.3.4.5. Steam turbine...... 23 2.3.4.6. Gas turbine ...... 24 2.3.5. Additional components ...... 24 2.3.5.1. Combustion chamber ...... 25 2.3.5.2. Fluidized bed...... 25 2.3.5.3. Fuel cell ...... 25 2.3.5.4. Weather...... 25 2.3.5.5. Mill...... 26 2.3.5.6. Flue gas control...... 26 2.3.6. Examples ...... 26 2.4. Automation system...... 27 2.4.1. Measurement modules...... 27 2.4.2. Analogue modules...... 27 2.4.2.1. Basic modules...... 27 2.4.2.2. Static modules ...... 29 2.4.2.3. Dynamic modules...... 30 2.4.3. Binary modules ...... 31 2.4.3.1. Basic modules...... 31 2.4.3.2. Advanced modules...... 31 2.4.4. Signal source modules...... 32 2.4.5. Controller modules...... 33 2.4.6. Examples ...... 33 2.5. Electrical system ...... 34 2.5.1. Basic modules ...... 36 2.5.1.1. Electrical node ...... 36 2.5.1.2. Electrical line...... 36 2.5.1.3. Switch ...... 37 2.5.1.4. Load...... 37 2.5.2. Current sources modules ...... 37 2.5.2.1. Generator ...... 37 2.5.2.2. Battery...... 37 2.5.2.3. Solar photovoltaic...... 38 2.5.3. DC and AC modules ...... 38 2.5.3.1. DC/AC inverter...... 38 2.5.3.2. AC/DC converter...... 38 2.5.3.3. AC/AC transformer...... 39 2.5.3.4. DC/DC converter...... 39 2.5.4. Examples ...... 40 3. Combined-cycle power...... 40 3.1. Loadchange...... 41 3.2. Start-up procedure ...... 44 3.2.1. Simulation ...... 44 3.2.2. Optimisation ...... 46 3.3. Additional studies ...... 48 3.3.1. Island operation ...... 49 3.3.2. Compressed-air energy storage ...... 49 3.3.3. Integrated gasification combined-cycle...... 50 4. Coal-firedpower...... 50 4.1. Response to disturbances ...... 52 4.2. Start-up procedures ...... 53 4.3. Flexibility increase ...... 53 4.4. Oxyfuel concept...... 55 5. Nuclearpower ...... 56 5.1. Specificfeatures...... 57 5.1.1. Basic principle...... 58 5.1.2. Reactor pressure vessel and reactor core ...... 58 5.1.3. Cooling circuits and auxiliary systems ...... 59 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 81
5.2. Safety analysis...... 60 5.2.1. Validation experiments ...... 60 5.2.2. Statistical accident analyses...... 61 5.3. Load cycling...... 63 5.3.1. Experience with load following ...... 63 5.3.2. Thermal hydraulic-neutronic instabilities...... 64 6. Concentrated solar power ...... 65 6.1. Development ...... 66 6.2. Specificfeatures...... 66 6.2.1. Solar field ...... 66 6.2.2. Power block...... 69 6.2.3. Energy storage and back-up system ...... 69 6.3. Dynamic studies ...... 69 7. Additional thermal power technologies ...... 70 7.1. Geothermal power ...... 70 7.2. Municipal waste incineration ...... 71 7.3. Seawater desalination ...... 77 8. Conclusion and future prospects ...... 78 Acknowledgments ...... 79 References ...... 79
Abbreviation IT intermediate temperature ITF integral test facility LB-LOCA large break loss-of-coolant accident AC alternating current LCOE levelised costs of energy AFS auxiliary feedwater system LHV lower heating value AIS accumulator injection system LOCA loss of coolant accidents BFP boiler feed pump LP low pressure BPCV bypass control valve LPIS low pressure injection system BWR boiling water reactor LT low temperature CAES compressed-air energy storage MCFC molten carbonate fuel cell CCPP combined-cycle power plant MED multiple-effect distillation CHP combined heat and power MPC model-predictive control CCS carbon capture and storage MSCV main steam control valve CFB circulating fluidized bed MSF multi-stage flash desalination CFD computational fluid dynamics NPP nuclear power plant CP circulation pump PAFC phosphoric acid fuel cell CSP concentrated solar power PEM proton exchange membrane DAEs differential-algebraic equation systems PI proportional-integral controller DBA design basis accident PH preheater DC device control, direct current PT parabolic trough DFGD dry flue gas desulfurization PV photovoltaic cell DNI direct normal irradiance PWR pressurized water reactor DSG direct steam generation RH reheater ECCS emergency core cooling system RO reverse osmosis ECO economiser RP recirculation pump EVA evaporator RPV reactor pressure vessel FG flue gas SCR selective catalytic reduction FEL following electric load SETF separate effect test facility FTL following thermal load SG steam generation FVM finite volume method SH superheater FW feedwater SNCR selective non-catalytic reduction GT gas turbine SOFC solid oxide fuel cell HP high pressure ST steam turbine HPIS high pressure injection system TES thermal energy storage HRSG heat recovery steam generator TIT turbine inlet temperature HTF heat transfer fluid TOC total organic carbon IAEA international atomic energy agency TOT turbine outlet temperature IAM incidence angle modifier TVC thermal vapour compression IGCC integrated gasification combined-cycle US NRC United States nuclear regulatory commission IGV inlet guide vanes WENRA Western European nuclear regulators association IP intermediate pressure WFGD wet flue gas desulfurization IS injection system WS water/steam ISCC integrated solar combined-cycle 82 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
TagedP fl 1. Introduction 40 years). The operating exibility of thermal power plants is limited by technical constraints such as ramp rates and mini- fi TheTagedP expansion of intermittent electricity generation, in particular mum load limit. Existing power plants can be retro tted with wind power and photovoltaics, can lead to the seemingly paradox optimised components and control circuits to mitigate these fl situation of negative electricity prices at times of low power demand constraints and to meet enhanced exibility requirements. and/or high renewable power supply. The main reason isD3XX the relative Highly dispatchable generating units such as combined-cycle inflexibility of dispatchable power generation such as coal and power plants and gas engines are also available to replace out- D41XX nuclear power, which send a negative price signal in order to avoid a dated plants. cost-intensive unit shutdown. Five major approaches to maintain security of supply and to improve flexibility of the future electricity InTagedP this work, the approach of flexibly dispatchable power genera- system can be distinguished in general [1]: (i) expansion of high- tion (v) is reviewed based on the scientific literature dedicated to voltage transmission infrastructure, (ii) enrollment of demand dynamic simulation of thermal power plants. response, (iii) modification to system operations, (iv) large-scale energy storage and (v) flexibly dispatchable power generation. The 1.1. Flexible power generation authors are convinced that the future electricity system will com- prise all of these concepts, to varying degrees and with the possible ATagedP thermal power plant ideally operates at steady state design addition of value-adding processes beyond electricity (e.g. power- load, but it is also required to operate on so-called off-design load to-fuels). However, the conceptsD34XXdiffer in their potential impact, conditions due to the fluctuations of supply and demand as well as technological maturity and economic viability. The latter aspect is the increased penetration of renewable energy sources. In Europe, especially important, considering that there is often no direct reim- these requirements translate into new operating challenges that can bursement to a market participant for providing flexibility (with the be divided in three categories. Firstly, higher load gradients for both exception of participation in the limited balancing energy market). positive and negative load changes are required. Furthermore, the dynamic of start-up and shut-down procedures should also be opti- i.TagedP The adequate addition of high-voltage transmission infrastruc- mised in response to a sudden load change in the grid. Secondly, the ture in combination with smart power electronics is essential technical operating range of thermal power plants has to be to accommodate the growing renewable capacity and ensures extended by re-evaluating the minimum load limit. Lower minimal security of supply. By increasing the number of interconnec- load potentially reduces the number of shut-down/start-up proce- tions between major load centres, the transmission capacity dures and thus lifetime consumption of thermally stressed compo- and robustness of the electricity grid can be greatly improved. nents. A complete shut-down is often not an option for combined For sufficient flexibility of the overall system, the grid expan- heat and power generation unless sufficient thermal storage capac- sion must be complemented by additional measures. Environ- ity is installed. Thirdly, high efficiency at part load is relevant since mental and political challenges are common causes for the the thermal power plants that were originally operated almost con- protractedD35XexpansionX of grid infrastructure. tinuously at nominal load should now run in load-following opera- ii.TagedP Demand response is the ability of end users to adjust load tion. Here, a thermo-economic optimisation at different base loads demand (could be reduce or increase)D36XXaccording to price signals and off-design load conditions is necessary. A thermal power plant or dispatch rules. This measure can be applied to mitigate or that meets these new requirements will have a competitive advan- counteract short-term grid imbalances. tage in the electricity market. iii.TagedP The average forecast errors of regional wind and solar power OperatingTagedP flexibility of thermal power plants is therefore an generation typically range from 3% to 6% one hour-ahead and essential factor for reliable grid stability as well as for economic 6% to 8% a day-ahead (based on rated capacity) [2]. Improved operation. Dynamic simulation offers an effective toolD42XforX optimising forecasting decreases the uncertainty in residual load, resulting the power plant performance and control structures as well as for in reduced utilisation of expensive peaking capacity and a assessing capabilities and limitations of the system with regard to cost-effective modification of system operations. Both (ii) and process, materials, emissions or economics. This implies strong (iii) are support measures under development with the poten- requirements on both model accuracy and efficiency of the numeri- tial to effectively reduce costs associated with the transforma- cal solver. Modern simulation programmes provide user interfaces,D43XX tion of the electricityD39Xsystem.X solution algorithms and component libraries for full-scale modelling iv.TagedP Large-scale energy storage, also called grid-energy storage, can and simulation of the dynamic processes. These simulation codes be charged or discharged flexibly to allow for high shares of are based on different thermal hydraulic models that are described renewable electricity feed-in. Grid-energy storage is, in theory, with the governing conservation equations for mass, momentum, ideally suited to balance intermittent power supply and energy and empirical correlations for friction and heat transfer. For demand. Pumped hydroelectric storage is commonly used, but modelling of thermal power plants, different process components it is limited to suitable geographical conditions. Other technolo- such as pipe, heat exchanger, drum and pump etc. are required. In gies in various stages of development include battery energy addition to process components, a thermal power plant includes storage, flywheel energy storage, compressed air energy stor- several automation and electrical systems. The accurate description age, power-to-gas and thermal energy storage. Despite recent of automation structures and control devices are essential in order advances in battery storage driven by the automotive industry, to obtain a realisticD4XXdynamic response. The consideration of electri- the specific costs of these storage systems still limit their use to cal components in the dynamic simulation is necessary to compute small-scale applications and there is currently no economically the electrical power consumption and to study malfunction cases viable storage technology available for the required order of with loss of electricity supply. capacityD40X(TWhX rather than MWh). MostTagedP power plant processes are based on the generation of v.TagedP The most economic option for increasing system flexibility is to superheated steam at high pressure, driving a steam turbine coupled improve the existing infrastructure of electricity supply. In with an electrical generator. In water/steam evaporator circuits, many countries without abundant natural resources suitable two-phase flows are generally present. As this flow type is compli- for large hydro or geothermal energy, power generation is cated and shows diverse flow patterns, a number of two-phase mod- mainly based on thermal power plants (and will continue to do els with various levels of complexity were proposed in literature. so in the foreseeable future, considering plant lifetimes of up to There are typically two categories of two-phase flow models: In the F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 83
TagedPfirst category, the two-phase flow is considered as mixture and areTagedP reviewed. Furthermore, the response of the numerical models to treated as single-phase flow with fairly complex thermodynamic disturbances is discussed, which is a common approach to verify the properties. The water and steam phases are assumed to be in ther- model performance when operational data is missing. The relevant modynamic equilibrium with equal velocity, pressure and tempera- investigations of start-up procedures, stress in thick-walled compo- ture. The second category of two-phase flow models treats each nents and power plant optimisation are introduced. The finalD50XsectionX phase as a fluid and accordingly, separate sets of conservation equa- of this chapter focuses on oxyfuel coal-fired power plants for carbon tions for gas and liquid phase are formulated. In addition to the capture and storage (CCS). conservation equations, adequate constitutive equations and experi- ChapterTagedP 5 offers an overview of dynamic process simulation for mental correlations are required. These can be tables for thermody- nuclear power plants (NPPs). For this purpose, the differences namic and transport properties or relations for heat transfer between nuclear power plants and conventional thermal power coefficients. The classic six-equation version of the two-fluid model plants are addressed. The chapter gives a description of the unique is a single pressure model. Here, both phases are in mechanical equi- and thorough validation process that is used in the field of nuclear librium, but not in chemical and thermal equilibrium. The seven- safety analysis and refers to further studies in that field. In this con- equation flow model considers separate phases and does not text, the statistical approach to safety analysis is presented as well. assume, by contrast to the six-equation flow model, pressure equi- The topic of load-following operation and its challenges regarding librium of phases. The five-equation and four-equation versions of nuclear power plants is discussed, including the special issue of neu- the two-fluid model assume mechanical and thermal equilibrium, tronic-thermal hydraulic instability.D51XX but not chemical equilibrium. ChapterTagedP 6 is dedicated to concentrated solar power (CSP) technol- ogy. CSP is a renewable technology that is characterized by simple 1.2. Structure integration of energy storage. It uses mirrors, lenses or a combina- tion of both to concentrate solar rays on a receiver, heating a work- ThisTagedP review is divided in two main parts:Inthe5X4DX firstpart(Chapter ing fluid that directly or indirectly runs a thermodynamic process to 2), the mathematical background for modelling of thermal power generate electricity. Currently, levelised costs of energy (LCOE) are plants is described, including an overview of simulation programmes relatively high. However, recent technical improvement and operat- that are applied to predict the behaviour of these systems in steady ing experience show potential for efficiency increase, standardisa- state and during transients. The mixture flow model and the two- tion and cost reduction. The review lists recent studies that were phase fluid models (four-equation, five-equation, six-equation and conducted to analyse dynamic behaviour of whole CSP plants and seven-equation flow model) are explained. Process, automation and single sub-systems such as solar field, thermal energy storage and electrical components required for the dynamic simulation of thermal power block. Results and scope of these studies are presented and power plants are also described, supported by model examples. future areas of investigation are derived. TheTagedP second part of this manuscript (chapters 3 to 7) is dedicated ChapterTagedP 7 offersD52XXinsight into several technologies that are less to the relevant body of literature, focusing on the application of frequently considered in dynamic studies, namely geothermal dynamic simulation to specific energy system technologies: com- power, municipal waste incineration and seawater desalination. bined-cycle power, coal-fired power, nuclear power, concentrated Geothermal power plants use heat released from the earth's solar power, geothermal power, municipal waste incineration and crust to drive a Rankine cycle. Until now, a little work has been thermal desalination. Most of these technologies can also supply done to explore the dynamic behaviour of these plants. Munici- useful thermal energy for industrial processes, district heating and pal solid waste incineration is used to significantly decrease other applications, increasing the power plant flexibility and waste volume as well as to produce stable and odourless residue. decreasing the total fuel consumption. This approach is known as Although municipal waste incineration has been applied com- combined heat and power (CHP) and relevant studies are referenced mercially for many decades in industrialised countries, the in the correspondingD46XXchapters. The dynamic studies on CHP fre- dynamic behaviour has not yet been investigated in the litera- quently address the optimal operating strategy for a given use case, ture. Calculation results for the start-up procedure of a waste which may be selected among following electric load (FEL), follow- incineration plant are shown in this review for the first time. ing thermal load (FTL) or a specific mixture thereof. Industrial thermal desalination processes such as multi-stage ChapterTagedP 3 is a survey of publications on dynamic simulation flash and multiple-effect desalination are very energy-intensive applied to gas-turbine based power plants, with particular regard to and cost-intensive processes that ensure a stable and sustainable combined-cycle power plants. In the field of power generation, com- source of drinking water in arid regions with sea access. The bined-cycle power plants (CCCP) are widely recognized for high chapter includesD53XXan explanation of the working principle of ther- efficiency, fast start-up capability and comparatively lowD47XXenviron- mal seawater desalination and an overview of numerical studies. mental impact. The technology also supports increasing shares of InTagedP the conclusion of this work, the results of the literature review renewable feed-in due to flexible unit dispatch. After a summary of and current developments are summarised. Furthermore, recom- general CCPP development,D48XXSection 3.1 introduces the reader to mendations for further research effort in the field of dynamic simu- basic plant dynamics by considering parameter variations and load lation of thermal power plants are given. changes. TheD49XX studies on simulation and optimisation of CCPP start- up procedures are covered in Section 3.2. The start-up transient has 2. Mathematical modelling a distinct position among operating transients, which is also reflected in the literature. Finally, Section 3.3 is a brief overview of ModernTagedP thermal power plants have to be designed for maxi- complementary works on dynamic simulation in the broader con- mum efficiency, low emissions and high flexibility with regard to text of gas-turbine based technology, including numerical studies of load changes, start-ups and shutdowns. In complementing the compressed-air energy storage and integrated gasification com- experimental works, mathematical models contribute to a better bined-cycle. understanding of the processes, their capabilities and limitations ChapterTagedP 4 gives an overview of publications that investigate the and play an important role for increasing the efficiency and flexi- transient operation of coal-fired power plants. With regard to bility of thermal power plantsD54X.X Generally, design and optimisation installed capacity, coal-fired power plants are the most important of energy systems start with steady state modelling. Here, it is generating units in many countries. Following a short description of assumed that the power plant operates continuously at its design the working principle of the coal-fired plant, the dynamic models base load. The steady state models do not require control 84 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 structuresTagedP and are mathematically based on mass, momentum, TagedP In case of zero-dimensional modelling, the local discretisation is species and energy balances. Using steady state simulation tools, not considered. The modelling of thermal power plant compo- analyses of the thermodynamic properties of the working fluid, nents such as heat exchanger, pump, condenser, turbine, etc., mass and energy flowsaswellasprocessefficiency can be con- results in an algebraic system of equations with the inputs and ducted for a series of operating points. However, steady state sim- output parameters of the components (pressure, enthalpy, mass ulation tools do not allow any information about transient flow rate and concentration). operations. The relevant next step is therefore the process analy- TagedP In case of one-dimensional modelling, the thermal power plant sis with dynamic models during transients, load changes and mal- components are discretised between the inlet and outlet along function cases. Dynamic simulation is preferred for the proposal the flow in finite objects, resulting in so called numerical grid. stage of a power plant project, e.g. to check whether or not the The partial differential equations obtained are thus approxi- load changes according to specificcustomerrequirementsarefea- mated by an algebraic system of equations. Finally, the state vari- sible without unacceptable lifetime consumption in thick-walled ables such as temperature, enthalpy and pressure at each components. However, investigation into the dynamic perfor- discrete location can be determined. mance of thermal power plants requires detailed information of TagedP In case of two-dimensional or three-dimensional modelling, local the process. The inherent complexity of the governing differential discretisation of the additional coordinates is required, resulting conservation equations and the numerical solution methods make in more detailed and computationally more expensive calcula- the dynamic simulation codes very sophisticated computer soft- tion of the thermal power plant components. ware with long development periods. TheTagedP knowledge of the steady state data of process components is 2.1. Overview sufficient in many practical engineering applications. Design calcula- tions at different loads are also conducted with such steady state TheTagedP first simulation program for thermal power plants dates back simulation models. Dynamic simulation allows investigation into to the 1960s. In the early 1970s, a method was developed, in which a the transient behaviour of the entire thermal power plant with its water/steam circuit was solved numerically. Here, the circuit was related control structures. Furthermore, the dynamic behaviour after constructed using individual components connected through lines. accidents in case of nuclear power plants is of major relevance for The main components of the water/steam circuit as well as the con- safe operation. Despite the advantages that dynamic simulation nection lines were systematised in code, so the entire circuit can be offers, the programming effort and computational time is consider- defined as a sequence of numbers and interpreted by the computer. ably higher compared to steady state calculations. This representation (selecting from the library and building compo- SeveralTagedP in-house developed codes and commercial software pro- nent by component) has been widely maintained in most simulation grammes for steady state and dynamic process simulation of ther- programmes since. Based on this methodology, for example, Stama- mal power plants are available, e.g. EBSILON Professional, APROS telopoulo [3] developed in 1995 an in-house code in the frame of a and ASPEN Plus DYNAMICS. Some programmes provide specialised steady state simulation project of thermal power plants. In line with component libraries for steady state and time-dependent simulation increasing interest on dynamic simulation, Stamatelopoulo and his of energy systems, including combined-cycle, simple cycle plants successors [4] presented a transient simulation program (known as and many others. Other programmes such as MATLAB/SIMULINK ENBIPRO) based on the finite volume method (FVM), which was fur- offer the researcher an open interface for modelling of non-standard ther extended by other researchers. Today, modern simulation pro- components. Using the non-proprietary object-oriented, equation- grammes combine a graphical user interface with detailed models based language (MODELICA), complex physical systems with for flow, thermodynamics and heat transfer. The calculations enable mechanical and control subcomponents can be modelled. Based on rapid assessment of: MODELICA, different non-commercial and commercial simulation environments are also available such as DYMOLA, JModelica.org and TagedP New plant design. SimulationX. In nuclear technology, dynamic simulation codes cal- TagedP Process modifications and retrofitting of existing plants. culate the complex multi-phase phenomena in regular operation TagedP Plant optimisation. and in accident situations. Such programmes were developed in TagedP Plant security and safety. many countries that designed nuclear reactors, e.g. RELAP in the US, TagedP Operating behaviour at base loads, off-design loads, start-up and CATHARE in France and ATHLET in Germany. shut-down procedures. TheTagedP above mentioned programmes differ in terms of function and TagedP Operating behaviour during malfunctions. areas of application. Since the development of the programs is ongo- ing, no details about scope of application can be given. The steady TheTagedP mathematical background of these programmes is based on state simulation programmes listed in Table 1 and the dynamic sim- the balance equations of mass, momentum, species and energy. The ulation programmes listed in Table 2 are the result of long-term complexity of these equations and the required numerical solution development by companies or universities and are usually not freely algorithms depends on, firstly whether the flow problem is steady accessible. The lists are non-exhaustive and restricted to widely state, quasi-steady or dynamic: known programmes, which are both used in industrial practice and scientific research. The cited references, among others, are matched TagedP In steady state simulation, the time derivatives are eliminated with the corresponding simulation code and give the reader an ori- from the conservation equations. entation for the application fields of each program. The fact that no TagedP In dynamic simulation, the time derivatives must be taken into study is listed for a certain application does not imply that the simu- consideration. lation code is unable to cover it. TagedP In quasi-steady simulation, the time derivative of certain compo- nents is not relevant and it can be consequently neglected in the 2.2. Thermal hydraulic models conservation equations, which in return simplifies the system of equations significantly. TheTagedP state of the art in modelling the thermal hydraulic of thermal power plants differs in the fundamental physical models. Here, various and secondly on the dimension of flow problem (zero-dimensional, formulations (conservative or non-conservative) have been suggested one-dimensional, two-dimensional or three-dimensional): and different numerical methods for compressible and incompressible F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 85
Table 1 mixture.TagedP Due to its simplicity and applicability to a wide range of In-house codes and commercial software programmes for steady state process two-phase flow regimes, this model is of considerable relevance simulation. since the response of the total mixture and not of each constituent Program Developer phase is often sufficient. The two-fluid models become, however, more appropriate for special applications since they offer the possi- EBSILON Professional STEAG Commercial bility to include non-equilibrium thermodynamic situations into the https://www.steag-systemtechnologies.com formulation. Furthermore, the two-fluid models allow the treatment of the conservation equations and thus the description of phase GATECYCLE GE Energy Commercial boundaries in an easier way. This problem can clearly be observed in http://www.ge-energy.com the mixture flow model that uses many closure models, resulting in approximate solutions and accordingly accuracy restrictions for cer- IPSEpro SimTech Simulation Commercial tain applications. www.simtechnology.com TheTagedP steady state and dynamic behaviour of thermal power plants can also be described using the lumped parameter model that also KRAWAL Siemens In-house code known as the lumped element model. Here, the description of the http://www.siemens.com physical system is simplified by mean of discrete control volumes (zones or lumps) that are connected each other by means of thermal KPRO Fichtner IT Consulting AG resistors and capacitors with the assumption of a small temperature Commercial http://www.kpro-fichtner.de difference inside each lump. The equivalent thermal network con- sists of thermal resistance, thermal capacitances and power losses NOWA Vienna University of Technology, inside the system. The lumped parameter model can be applied to Institute for Thermodynamic and Energy Conversion electrical and mechanical systems, heat transfer processes and ther- In-house code mal hydraulic analysis of conventional thermal power plants includ- http://www.tuwien.ac.at/tuwien_home ing nuclear reactors. The application of the lumped parameter fi PEPSE, PMAX, etc. SCIENTECH, Inc. model is suitable, when a simpli ed formulation of the transient Commercial behaviour of the process is required. The advantage of such an http://scientech.cwfc.com approach lies in the reduced computational cost, but it does not offer
PROATES POWERGEN, Power Technology the same accuracy of more complex numerical methods such as mix- In-house code ture and two-fluid models. The lumped element model is outside the http://www.osti.gov/scitech scope of this review and further information can be found for exam-
PROSIM Endat Ltd ple in [162]. Commercial InTagedP the following sections, the mixture flow model and the differ- http://www.endat.fi ent two-fluid models are explained in detail.
Thermoflow (GT PRO, Thermoflow GT MASTER, STEAM PRO, Commercial 2.2.1.TagedP Mixture flow model THERMOFLEX, etc.) http://www.thermoflow.com TheTagedP one-dimensional mixture flow model (also known as homo- fl VALI Belsim S.A. geneous or three-equation ow model) assumes thermodynamic Commercial equilibrium between phases. The mixture flow model is represented http://www.belsim.com/vali by three-partial differential equations for mass, momentum and energy that describe the steady state and dynamic behaviour of the characteristic variables. For single phase flow components (e.g. TagedPflows were investigated. The complexity of the process is explained by superheater, reheater, turbine section and economiser), the three theoccurrenceofseveraltwo-phaseflow regimes, heat conduction in characteristic fluid variables are the local pressure, the total mass solid structures, heat transfer between fluidandsolidstructures,heat flux and the fluid temperature or the fluid enthalpy for subcooled and mass transfer between gas and liquid. water or superheated steam. In case of two-phase flow components TheTagedP thermal hydraulic models describe the steady state and (e.g. evaporator and condenser), the three variables are comple- dynamic behaviour of a single phase flow or a two-phase flow. Many mented by the void fraction. The void fraction can be computed by approaches can be found in the literature in order to model the two- adding a fourth additive constitutive equation. The latter is a drift- phase flow in a thermal power plant such as mixture flow model or flux correlation that describes an adequate relation between differ- two-fluid models, including four-equation, five-equation, six-equa- ent two-phase parameters, e.g. a relation between the steam quality tion and even seven-equation flow models. In the two-fluid models, or steam mass flux and steam void fraction. The drift-flux closure two sets of conservation equations are formulated, governing the laws that allow a slip relation between phases are based on theoreti- mass, momentum and energy balance for each phase. This formula- cal, empirical or semi-empirical approaches. Several studies have tion presents considerable difficulty by reason of mathematical com- been carried out, resulting in numerous void fraction experiments plexity and the uncertainty in modelling the interaction between and different drift-flux correlations, which show significant devia- phases at the interphase boundary. Generally, these relations cannot tions. Bhagwat and Ghajar [163] evaluated the correlations available be derived from fundamental physical laws and in most cases are in the literature and observed that the tested correlations, although based on empirical assumptions. Solving the resulting differential predicting the void fraction with desired accuracy at a certain point, equations requires higher computational effort and entails parame- were inaccurate for a broad range of operating conditions. Further- ters that may cause numerical instability, especially due to improper more, the correlations that predict the void fraction accurately for selection of interfacial terms. The difficulties associated with the vertical pipe orientation fail in case of inclined pipe orientations. two-fluid models can be significantly reduced by formulating the According to Bhagwat and Ghajar [164], the recommended correla- two-phase flow in terms of the mixture flow model. Here, three tions by the above mentioned studies lose their accuracy at higher characteristic fluid variables are computed, including local pressure, pressure, large pipe diameter and for fluids with higher dynamic vis- total mass flux and temperature or enthalpy, represented by three cosity than water. In conclusion, there is no closure relation that reli- conservation equations (mass, momentum and energy) of the ably predicts the void fraction for a suitable range of flow patterns, 86 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Table 2 Programmes for the dynamic process simulation of thermal power plants.
Program Developer Application
Combined-cycle Coal-fired Nuclear Concentrated Municipal waste Thermal power power power solar power incineration desalination, Geothermal power
ATHLET, ATLAS, Gesellschaft fur€ Anlagen- und Reaktorsi- xx[5 10] [11] xx COCOSYS, etc. cherheit (GRS) In-house code http://www.grs.de/en
Advanced Process Technical Research Center of Finland [12 19] [20 28] [29,30] [31 36] x [37] Simulation Soft- (VTT) ware (APROS) Commercial http://www.apros.fi/en
Advanced System Aspen Technology, Inc. [15,17,38,39] [40 44] x [45,46] x [47] for Process Engi- Commercial neering (ASPEN https://www.aspentech.com Plus DYNAMICS, ASPEN HYSYS, etc.)
CATHARE CATHARE team xx[48 51] xx x In-house code http://www-cathare.cea.fr
ClaRa (based on Das Projekt Dyncap x [52 54] xx x x Modelica In-house code language) http://www.claralib.com
Dynamic Boiler Vienna University of Technology, Insti- [55 57] xx x x x Simulation (DBS) tute for Thermodynamic and Energy Conversion In-house code http://www.tuwien.ac.at/tuwien_home
Dynamic Network Technical University of Denmark [58 61] [62 64] xx x x Analysis (DNA) Thermal Energy, Department of Mechanical Engineering In-house code http://www.dtu.dk/english
DYMOLA (based on Dassault Systemes [65 70] [71 73] [74] [75 83] xx Modelica Commercial language) http://www.3ds.com
DYNAPLANT Siemens [84 87] xx x x x In-house code http://www.siemens.com
ENBIPRO Technische Universitat€ Braunschweig, [88,89] [90 93] xx x x Institute of Energy and Process Sys- tems Engineering In-house code https://www.tu-braunschweig.de/ines/ research/enbipro
gPROMS Platform Process Systems Enterprise Limited [94,95] [64,96 98] xx x [99 101] Commercial http://www.psenterprise.com
JModelica.org Modelon AB [86,102,103] [104] x [105] xx (based on Model- Open-source code ica language) http://www.jmodelica.org/
MATHEMATICA Wolfram Research xxx[106] xx Commercial https://www.wolfram.com/ mathematica
MISTRAL Technische Universitat€ Darmstadt, [87,107 109] xx x x x Department of Energy Systems and Technology In-house code http://www.tu-darmstadt.de
(continued) F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 87
Table 2 (Continued)
Program Developer Application
Combined-cycle Coal-fired Nuclear Concentrated Municipal waste Thermal power power power solar power incineration desalination, Geothermal power
SIMULINK The MathWorks, Inc. [110 113] [114 118] [119 121] [122,123] [124] [125 127] Commercial https://www.mathworks.com
Power Plant Simula- KED GmbH [128 130] [130] [130] [129] xx tor & Designer Commercial (PPSD) http://www.ked.de/index.html?&LD1
ProTRAX Software TRAX Energy Solutions [131 135] xx x x x Commercial https://energy.traxintl.com
EASY5, etc. MSC Software [136,137] [138] [139] xx x Commercial http://www.mscsoftware.com
EcosimPro, PROO- Empresarios Agrupados A.I.E x [140] [141] xx x SIS, etc. Commercial http://www.ecosimpro.com
SimSci, DYNSIM, Schneider Electric Software xxxxx[142] etc. Commercial http://software.schneider-electric.com
SimulationX ITI GmbH xxxxxx Commercial https://www.simulationx.com
RELAP Idaho National Laboratory xx[9,143 146] [147,148] xx Commercial http://energy.gov
Transient System University of Wisconsin xxx[149 153] x [154] Simulation Tool Commercial (TRNSYS) http://sel.me.wisc.edu/trnsys
UniSim Design Honeywell [155,156] [157,158] xx x x (acquired by Commercial Aspen) https://www.honeywellprocess.com
3-Key Master Western Services Corporation xxx[159 161] xx Commercial https://www.ws-corp.com
voidTagedP fractions, diameters, orientations of pipe and particularly fluid kineticTagedP energy of the flow. In the mass equation, the source term can properties. contain additional mass flows into the system, or vice versa. The TheTagedP dynamic behaviour of three characteristic fluid variables, pressure derivative term appears in the energy equation due to the including the local pressure, the total mass flux and the temperature fact that the total enthalpy is used instead of the internal energy U. or the enthalpy is described by three conservation equations of the @U @h @p mixture. D 0 ¡ ð2:4Þ @t @t @t TheTagedP mass conservation is expressed as: InTagedP thick-walled tubes (e.g. drum and feedwater storage tank), the @r @ðÞru C D S ð2:1Þ lower part is pure water and the upper part is pure steam. Here, the @t @z composition of the outflowing fluid from the tank is determined by TheTagedP momentum conservation is written as: the water level and the connected branch height. Generally, the number of connected branches to the tank is not limited. The branch @ðÞru @ ru2 @p C D¡ C F C F C fðÞð val C form C pu 2:2Þ inlet height must, however, be in the height range of the tank. When @t @z @z gra wal the water level is below the branch height, the flow consists of TagedP The energy conservation is: steam, while it consists of water if the water level is above the @ðÞrh @ðÞruh @p branch height. In between, there is a transition region, where the 0 C 0 D C q ð2:3Þ @t @z @t wal composition of the leaving fluid is gradually changing from water to steam. InTagedP these equations, Fgra is the gravitational acceleration force per InTagedP case of two-phase systems, the formulation of the mixture volume, Fwal and qwal represent the friction force per volume and the flow model is the fundamental physical laws for the conservation of heat flow through walls per volume. The symbols rD5XXand u refer to the density and longitudinal velocity of fluid, respectively. The func- mass, momentum and energy with the movement between the two phase flow using drift-flux correlations. In this model, the four char- tion f considers the pressure losses due to valve and form frictions as fl fl well as the hydrostatic pressure differences and the pressure force acteristic uid variables are the local pressure, the total mass ux, the temperature or enthalpy and the void fraction. The mixture of a pump. The total enthalpy h0 is the static enthalpy including the 88 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 continuityTagedP equation is expressed as: TagedPthe momentum equation of the mixture complemented by a kine- @ðÞ@ðÞ matic equation specifying the relative motion between phases and rm rmum C D Sm ð2:5Þ the two-fluid models (see the following section), where the velocity @t @z of each phase is solved separately. TheTagedP symbols rmD56XX, um and Sm represent the density, the fluid veloc- ity and the injection or leakage of the mixture, respectively. The 2.2.2.TagedP Two-fluid model momentum equation of the mixture by neglecting the effect of sur- TheTagedP two-fluid models, also known as heterogeneous or face tension is written as: Euler Euler flow model, formulate separate conservation equa- @ðr u Þ @ðr u2 Þ @ xr r tions of mass, momentum and energy for gas and liquid phase. m m C m m C gas liq V2 ð2:6Þ @ @ @ ðÞ¡ gas;j The two-fluid models describe the two-phase flow more accu- t z z 1 x rm @ rately than the mixture flow model, but the definition of the D¡ p C C C ðÞC C Fgra Fwal f val form pu fi @z interaction terms between phases is dif cult. This is due to the fact that the interaction terms cannot be determined from physi- Here,TagedP the symbol xD57XXis the void fraction of the gas phase, rD58XX and gas cal laws and are generally obtained from experiments under sev- rD59XX denote the density of gas and liquid phase, respectively. The liq eral artificial assumptions. Here, careful study of the interfacial symbol V is the drift velocity of the gas phase with respect to the gas, j constitutive equations is required, since the improper selections volumetric centre of the mixture. The energy equation of the mix- of these terms may result in numerical instability. Due to the ture is defined as: increased number of differential equations and closure relations, @ð Þ @ð Þ @ xr r @ rmh0;m C rmumh0;m C gas liq ¡ D p C ð : Þ the two-fluid models, in contrast to mixture flow model, are @ @ @ Vgas;j h0;gas h0;liq @ qwal 2 7 t z z rm t relatedtohighercomputationalcostandaresuitableforthermo- ZuberTagedP and Findlay [165] proposed the following relation for dynamic non-equilibrium applications. Accordingly, the complex fl Vgas, j: and time-consuming two- uid models are only implemented in few simulation programmes such as APROS and RELAP. V ; D u ¡C j ð2:8Þ gas j gas 0 InTagedP the two-fluid models, the velocities and temperatures of fi where j is the super cial velocity and C0 represents the distribution each phase are independent, as opposed to the mixture flow parameter: model with drift-flux correlations, where there is only one 〈xj〉 momentum equation and one energy equation of mixture. The C D ð2:9Þ 0 〈x〉〈j〉 four-equation or five-equation model assumes mechanical and thermal equilibrium, but not chemical equilibrium. In the six- TagedP 〈〉 The expression within the angle brackets ( ) indicate the equation version of the two-fluid models, the phases are in fl cross-sectional averaged ow properties. The Eq. (2.9) can be written mechanical equilibrium (they are at the same pressure), but not as: in chemical and thermal equilibrium. The seven-equation version jgas of the two-fluidmodelallowsthephasestobecompletelyin V ; D ¡ j ¡j ð2:10Þ gas j x gas liq non-equilibrium state. In the latter, each phase has its own pres- sure, own velocity and temperature. According to Stuhmiller TheTagedP superficial velocity of gas or liquid is an artificial velocity, [166], the seven-equation flow model avoids the non-hyperbolic- determined by assuming that only a given phase is flowing in a cer- ity of the six-equation flow model that can lead to ill-posed tain cross-sectional area. It can be determined as: Cauchy problems. Mathematically, a hyperbolic partial differen- _ V tial equation of order n has a well-posed initial value problem j D k ð2:11Þ k A for the first n ¡ 1 derivatives, i.e. the Cauchy problem is solved TagedP _ fl locally for certain initial data of any non-characteristic hypersur- Here, the subscript k is either gas or liquid, Vk is the volume ow rate of the phase and A is the cross-sectional area. Using drift-flux face [167].Inalltwo-fluid models (excepting the seven-equation correlations, the drift velocity and void fraction can be defined, model), the void fraction is generally determined by the interfa- cial drag. The latter is calculated based on drift-flux correlations which in turn can be used to obtain the velocity of gas phase ugas and for the distribution parameter and void-weighted area-averaged liquid phase uliq as: drift velocity. rliq u D u C V ; Non-condensableTagedP gases may affect the dynamic behaviour of gas m r gas j m ð2:12Þ thermal power plants, particularly nuclear power plants. The x rgas u D u ¡ V ; non-condensable gases can be nitrogen, oxygen, helium or liq m 1¡x r gas j m hydrogen that are mixed with steam phase or dissolved in liquid with the mixture density rmD60XX: phase. These gases can also be transferred from one phase to another. For example, when the nuclear power plant operates at r D xr C ðÞ1¡x r ð2:13Þ m gas liq normal operation for long period, the nitrogen that is used to InTagedP conclusion, the formulation of the homogenous flow model is pressurise the hydro-accumulators and other systems is dis- based on the mixture balance equations. In two-phase flow regions, solved into the liquid phase. In case of primary circuit breaks, the relative motion between phases is taken into account by a kine- the accumulator water is injected into the primary circuit, caus- matic constitutive equation. The constitutive equations are, gener- ing lower pressure and accordingly the release of dissolved ally, derived by considering interfacial geometry, body-force field, nitrogen from liquid to gas phase [168].Furthermore,dissolved shear stresses and interfacial momentum transfer. Due to its sim- oxygen, carbon dioxide and other gases in feedwater leads to plicity and applicability to a wide range of two-phase flow, the mix- serious corrosion damages in the steam generator components ture flow model with drift-flux correlations is often used when the and should therefore be removed using a deaerator system. response of the total mixture and not of each constituent phase is Accordingly, the treatment of non-condensable gases has to be required. Therefore, this flow model can be found in most of simula- taken into account the simulation programmes that are used in tion programmes such as APROS, ASPEN Plus DYNMICS and PPSD. safety analysis work. Generally, the modelling of non-condens- However, one should distinguish between the drift-flux models, able gases can be considered in the formulation of the two-fluid where it is assumed that the two-phase flow can be expressed by models. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 89
InTagedP the following sections, the different versions of the two-fluid TagedP models, including four-equation, five-equation, six-equation and G ; C G ; D 0 ð2:20Þ seven-equation flow model are described in detail. gas liq liq gas TheTagedP gas momentum balance equation is defined as: @ðxr u Þ @ðxr u2 Þ @ @ 2.2.2.1.TagedP Four-equation model. TagedPThe four-equation model assumes gas gas C gas gas D C C ¡ p C pext ð : Þ Fgra;gas Fwal;gas Fliq;gas x 2 21 instantaneous phase change and equilibrium of the two phases. @t @z @z @z This version of two-fluid model contains one mixture mass equa- TheTagedP liquid momentum balance equation is expressed as: tion, one mixture energy equation and two momentum equa- @ ðÞ¡ @ ðÞ¡ 2 tions for gas and liquid phase. Therefore, the phase velocities are 1 x rliquliq 1 x rliquliq C ð2:22Þ independent from each other, in contrast to the mixture flow @ @ t z fl model with drift- ux correlations that uses one momentum @p @pext D F ; C F ; C F ; ¡ðÞ1¡x C equation for the mixture. The four conservation equations, gra liq wal liq gas liq @z @z describing the physical properties of mixture (pressure and tem- TheTagedP term inside the time derivative expresses the temporal perature) as well as gas and liquid velocities, are expressed as: change of gas or liquid flow rate. The term inside the space @ C ðÞ¡ @ C ðÞ¡ fl xrgas 1 x rliq xrgasugas 1 x rliquliq derivative is equal to the changes of ow momentum along the C D S ð2:14Þ integration axis z. The last term on the right-hand side of the @t @z momentum equation describes the influence of pressure on the @ð Þ @ð 2 Þ xrgasugas xrgasugas @p @pext momentum conservation due to the axial pressure distribution C D F ; C F ; C F ; ¡x C ð2:15Þ @t @z gra gas wal gas liq gas @z @z and external pressure forces such as pump or losses due to valve and form friction. @ðÞ¡ @ðÞ¡ 2 1 x r uliq 1 x rliqu TheTagedP energy balance equation for the gas-liquid mixture is written liq C liq ð2:16Þ @ @ as: t z @ @ hi D C C ¡ðÞ¡ p C pext @ Fgra;liq Fwal;liq Fgas;liq 1 x xr h ; C ðÞ1¡x r h ; ð2:23Þ @z @z @t gas 0 gas liq 0 liq hi hi @ @ @ C C ðÞ¡ D p C xrgasugash0;gas 1 x rliquliqh0;liq qwal xr h0;gas C ðÞ1¡x r h ; ð2:17Þ @z @t @t gas liq 0 liq hi TagedP fi fl @ @p In the second version of the ve-equation model (with draft ux C xr u h ; C ðÞ1¡x r u h ; D C q @z gas gas 0 gas liq liq 0 liq @t wal correlation), the phase velocities are coupled by a functional rela- tion. The mass and energy conservation equations are solved for gas InTagedP these equations, the subscripts gas and liq refer to the gas and and liquid separately, while the momentum equation is only solved liquid phase. The forces F ,F and F account for gravitation, wall gra wal ik for gas-liquid mixture. Here, the summation of gas and liquid friction and interfacial friction per volume, respectively. The sub- momentum (Eqs. (2.21) and (2.22)) results in the mixture momen- script ext refers to an external pressure source/sink such as pump fi tum conservation equation: and losses due to valve and component-speci c friction. The symbol q denotes the wall heat flow per volume. @r u @r u2 @p @p wal m m C m m D F C F ¡ C ext ð2:24Þ @t @z gra wal @z @z 2.2.2.2.TagedP Five-equation model. TagedPIn the five-equation model, mass bal- where rmD61XXis the mixture density and um is the mixture velocity. The ances for each phase are required instead of a mass equation of mix- drift-flux model describes the superficial velocity of gas u as a fl fi gas ture in the four-equation ow model. The ve-equation model can function of superficial mixture velocity j, void fraction x, drift-flux either be formulated with thermal equilibrium or with drift-flux cor- velocity Vgas, j and distribution parameter C0. relation. ForTagedP the gas phase, the energy balance equation is expressed as: TheTagedP first version of the five-equation model assumes mechan- @ðxr h ; Þ @ðxr u h ; Þ @ ical and thermal equilibrium between phases (pressure and tem- gas 0 gas C gas gas 0 gas D p C G C C ð : Þ @ @ x @ h0;liq;gas qwal;gas qliq;gas 2 25 perature are kept equal), but the phases will generally not be in t z t chemical equilibrium. Here, mass and momentum conservation and for the liquid phase as: equations are solved for gas and liquid separately, while the @ hi@ hi fi ðÞð1¡x r h ; Þ C ðÞð1¡x r u h ; Þ ð2:26Þ energy equation is only solved for gas-liquid mixture. The ve @t liq 0 liq @z liq liq 0 liq fl transient, partial differential equations of two-phase ow can be @p D ðÞ1¡x ¡Gh ; ; C q ; C q ; formulated as below. @t 0 gas liq wal liq gas liq TheTagedP mass balance in an Eulerian form by neglecting the diffusion TheTagedP heat flows per volume on the right-hand side of the energy term is written for the gas phase as: equations are defined separately for the heat transfer from wall to @ @ gas q , wall to liquid q and between phases (q and xrgas xrgasugas wal,gas wal,liq liq,gas C D Sgas C G ; ð2:18Þ q ). @t @z liq gas gas,liq and for the liquid phase as: TagedP TagedP fl 2.2.2.3. Six-equation model. The six-equation ow model, in contrast fi @ðÞ¡ @ ðÞ1¡x r u to the four-equation model and the ve-equation model, has 1 x rliq liq liq C D S C G ; ð2:19Þ attracted more attention in the scientific literature. This flow model @t @z liq gas liq allows chemical and thermal non equilibrium (velocity and temper- TagedP The terms Sgas and Sliq represent the injection and leakage of gas ature disequilibrium between phases), but assumes mechanical G and liquid phase. The interfacial mass transfer of gas liq,gas describes equilibrium (the phases are at the same pressure at all time). The G the evaporation and the interfacial mass transfer of liquid gas,liq six-equation flow model is suitable for water/steam mixture with considers condensation. The sum of interfacial mass transfer of dominating mass and heat transfer between phases. It is character- liquid and gas is zero: ised by separate conservation equations of mass, momentum and 90 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
energyTagedP for gas and liquid phase. However, the formulation of two TagedPcalculated with the Lee-Ryley correlation, if hgas < hgas,sat (vapour is complete sets of conservation equations presents considerable diffi- subcooled, condensation) [170]: culty by reason of mathematical complexity and modelling uncer- = = 61ðÞ¡ λ 2 C 0:74Re1 2 Pr1 3 tainty of the interaction terms between phases. The six-equation x gas dro gas K ; D ð2:33Þ model is therefore more prone to numerical instability, in particular i gas 2 ddrocp;gas vis-a-vis the mixture flow model. ThisTagedP section describes the six-equation flow model, as imple- fl with the Reynolds number of droplet ow Redro, the Prandtl number mented in the advanced process simulation software (APROS) [169]. of the gas phase Prgas, the thermal conductivity of the gas phase λgas fl The solution of the six-equation ow model is based on the one- and the heat capacity of the gas phase cp,gas. The droplet dimensional six partial differential equations, from which the pres- diameter ddro that describes the interface size of the two phases has sure, the void fractions, the phase velocities and enthalpies are a considerable influence on the calculation of the interfacial heat solved. As previously mentioned, the application of the six-equation transfer coefficient as well as the interfacial friction force. It is deter- flow model requires the knowledge of mass, momentum and energy mined as: 0 1 transfer between phases. These interaction terms can be determined vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fl u using the ow parameters and their derivatives coupled with empir- B 8s u s C d D min@ ; 1:73t A ð2:34Þ ical correlations for various gas/liquid flow regimes. If the two-phase dro D 2 rgas uik g r ¡r flow also includes non-condensable gases, additional conservation liq gas equations, describing the behaviour of the non-condensable gases TheTagedP term Duik represents the relative velocity between phases, sD62XX are required. is the surface tension, rD63XX and rD64XXdenote the density of the gas and TagedP gas liq The mass conservation equation for phase k is written as: the liquid, respectively. The droplet Reynolds number is calculated @ð Þ @ð Þ as follows: xkrk C xkrkuk D G ð : Þ ik 2 27 @t @z D rgas uikddro TagedP Re D ð2:35Þ The momentum conservation equation for phase k is formulated dro h as: gas TagedP D65XX @ð Þ @ð 2Þ @ Here, the symbol hgas represents the dynamic gas viscosity. If hgas xkrkuk xkrkuk p C D¡x C G u C F ; C F ; C F ð2:28Þ h (evaporation), the interfacial heat transfer coefficient of gas @t @z k @z ik ik gra k wal k ik gas,sat is reduced by multiplying the Eq. (2.33) by the variable a: C ðÞC C fk val form pu 1 a D ð2:36Þ TagedP ðÞ¡ The energy conservation equation is expressed as: C Tgas Tgas;sat 1 1000 @ð Þ @ð Þ @ xkrkh0;k xkrkukh0;k p C D x C G h ; C q C q ; C F u ð2:29Þ TagedP fi @t @z k @t ik 0 ik ik wal k ik ik The interfacial heat transfer coef cient of the liquid phase Ki,liq is calculated during vaporization (h > h ) as follows: TheTagedP subscript k refers to l D liquid or g D gas. The subscript ik liq liq,sat ¡ refers to the interface between two phases and the subscript wal, k 1:2 ¢ 10 8r2 u2 ¢ expðÞ 4:5x D liq liq ð : Þ denotes the interface between one phase and the wall. The term G is Ki;liq 2 37 hliq Prliq the mass exchange rate between phases. The function f considers k TagedP D6XX the effects of valves, pumps and friction on the flow. The terms Fand Here, the term uliq represents liquid phase velocity, Prliq and hliq q represent to the average friction force per volume and the heat are the Prandtl number and the dynamic viscosity of the liquid flow per volume, respectively. In the energy equation, the symbol h phase. During condensation (hliq hliq,sat), the interfacial heat trans- 0 fi fl is the total enthalpy including the kinetic energy. In the six-equation fer coef cient of liquid increases and is calculated in droplet ow flow model, the wall friction F , the interfacial friction F , the according to Shah correlation [171]: wal,k ik "# fl fl : : : interfacial heat ow qik and wall heat ow qwal,k are modelled by 0:092Re0 8 Pr0 4λ 0 38 D dro liq liq ðÞ¡ 0:8 C : 0:79ðÞ¡ 0:04 pcri ð : Þ means of empirical correlations. Ki;liq 2 1 x 3 8x 1 x 2 38 D c ; p TagedP H p liq The gravitation force per volume is determined using the follow- 61ðÞ¡x λ C liq ing relation: E 2 ddrocp;liq D Q ð : Þ Fgra;k xkrkg cos 2 30 TheTagedP symbol DH is the hydraulic diameter of the flow channel, λ where the symbol Q is the inclination angle and g denotes the stan- Prliq, liq and cp,liq represent the Prandtl number, the thermal conduc- dard gravity. tivity and the heat capacity of the liquid phase, respectively. The TheTagedP mass exchange rate (interfacial mass transfer) G is obtained terms E and x are the rate of entrainment and the liquid concentra- fl by forming the energy balance for the phase boundary as follows: tion in the ow. The critical pressure of the steam/water mixture pcri is equal to 22.06 MPa. q C q ; ¡q G D¡G D¡ i;liq i gas wal;i ð : Þ TheTagedP wall heat flow q is determined depending on the heat ik ki ¡ 2 31 wal.k hgas;sat hliq;sat transfer zone. Generally, three heat transfer zones can be distin-
TheTagedP symbols hgas,sat and hliq,sat represent the saturation enthalpies guished: wetted wall, dry wall and a transition zone between of gas and liquid. The interfacial heat flow is calculated separately wetted wall and dry wall. When the wall temperature is lower for the liquid and gas phases as: than the saturation temperature of the liquid, single phase flow is assumed to be in contact with the wall. During this stage, the q ; D¡K ; ðh ¡h ; Þ i gas i gas gas gas sat ð : Þ heat flux rises with increasing wall temperature. If the heat flux D¡ ð ¡ Þ 2 32 qi;liq Ki;liq hliq hliq;sat has exceeded the critical heat flux, the wall starts drying out and
Here,TagedP the terms hgas and hliq are the static enthalpies of gas and accordingly the heat transfer decreases sharply. The transition liquid, respectively. Separate heat transfer correlations are required zone ranges from the critical heat flux temperature to the mini- for evaporation and condensation. The interfacial heat transfer coef- mum film boiling temperature. Above this temperature, the dry
ficients Ki,gas and Ki,liq depend strongly on both phase flow velocities wall zone stars. Here, only the gas phase touches the wall and and void fraction. The interfacial heat transfer coefficient of gas is the heat flux begins to increase again. The critical heat flux and F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 91 theTagedP minimum film boiling temperature are used for the selection relation:TagedP of the heat transfer zone. 0 1¡0:5 ¡ TheTagedP heat flux on a wetted wall can be defined according to several 1 rliq rgas d D @ C gA ð2:46Þ correlations, e.g. the Dittus Boelter correlation for forced convec- bub 2 2 DH f s tion and the Thom correlation for nucleate boiling [172]. The nucle- ate boiling starts when the wall temperature exceeds the saturation with the variable f that depends on the void fraction: temperature of the liquid. The heat flow is expressed as follows 8 < 1:3 C 15:7x3ðÞ256¡768x case x < 0:25 [173]: f D ð2:47Þ 8 : > λ 17 case x 0:25 > liq : 0:8 0:4 ¡ > 0 023Re Pr Twal Tliq case Twal Tliq;sat < D2 liq liq D |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}H ð : Þ and the variable fdD69XXthat relies on the bubble diameter and the qwal;liq 2 39 > A fl > hi hydraulic diameter of the ow channel: : C ¢ : ¢ ¡7 ¡ 2 > A 1971 exp 2 3 10 p Twal Tliq case Twal Tliq;sat 5 dbub 5dbub fd D 2:81 C 34 6¡ ð2:48Þ DH DH IfTagedP the wall temperature is higher than the minimum film boiling TheTagedP viscosity factor Fh,D70XliqX of the liquid phase is expressed as fol- temperature, the heat transfer correlations of a dry wall are used. lows: fl The heat ow between a dry wall and the gas phase is calculated 2 30:25 according to Bestion as follows [174]: g r ¡r 4 liq gas 5 F ; D h ð2:49Þ D 1 ; 2 ; 3 ; 4 ¡ ð : Þ h liq liq 2 3 qwal;gas max Kwal;gas Kwal;gas Kwal;gas Kwal;gas hwal hgas 2 40 rliqs
fi 1 InTagedP the annular flow regime, the interfacial friction force per vol- with the Berenson coef cient for pool boiling Kwal;gas. The heat trans- fi 2 3 ume is determined according to [175] as follows: fer coef cients Kwal;gas and Kwal;gas denote to laminar and turbulent 4 fi forced convection, while K ; is the heat transfer coef cient of 0:01½ 1 C 75ðÞ 1¡x r Du jDu j wal gas D gas ik ik ð : Þ natural convection. Fik;ann 2 50 DH InTagedP the transition zone between the wetted wall and the dry wall, TagedP fl the heat flow is interpolated between the heat flow of the dry In the droplet ow regime, the interfacial friction force per vol- D71XX zone and the critical heat flow. The latter is calculated using the ume is calculated as a function of the droplet diameter ddro [174]: Zuber Griffith correlation for lower mass flow density and the Biasi 0:75ðÞ 1¡x f r Du jDu j D dro gas ik ik ð : Þ correlation for higher mass flow density [172]. Fik;dro 2 51 ddro TheTagedP friction force between the single phase (gas or liquid) and the with the friction coefficient f of the droplet flow: wall of the flow channel is computed with the relation: dro : : ¡ j j D 24 C 3 6 C 0 42 ð : Þ 2fwal;krkuk uk fdro : ¡ : 2 52 F ; D ð2:41Þ Re 0 313 C : ¢ 4 ¢ 1 16 wal k dro Redro 1 4 25 10 Re DH dro ForTagedP specific cases, non-condensable gases can be modelled and TheTagedP phase friction coefficients are calculated employing the Bla- therefore additional equations may be required. This can be a non- sius correlations and laminar formula. The phase friction coefficients condensable gas in steam phase or a dissolved component in liquid are then determined depending on the void fraction, for the gas phase. Assuming that non-condensable gas and steam form a homo- phase as: geneous mixture, then the steam and the non-condensable gas have the same temperature and velocity. Thus, only one additional partial D 16 5; : ¡0:25 5 ð : Þ differential equation for the density of the non-condensable gas is fwal;gas max x 0 079Regas x 2 42 Regas required: and for the liquid phase as: @ðÞ@ xr u xrNC C NC gas D ð : Þ @ @ SNC 2 53 D 16 ¡ 5 ; : ¡0:25 ¡ 5 ð : Þ t z fwal;liq max 1 x 0 079Reliq 1 x 2 43 Reliq TheTagedP subscript NC refers to the non-condensable gas. The term SNC describes dissolving/release of non-condensable gas in the steam TheTagedP interfacial friction force Fik (the friction between liquid and gas phases) is highly relied on the flow regime. Generally, it can be (positive for formation and negative for reduction). TagedP distinguished between stratified and non-stratified flow, including The dissolved gas in liquid phase is modelled by a mass transport bubbly, annular and droplet flow regimes. Based on the void fraction equation of the dissolved gas as: hihi xD67XXand the rate of entrainment E, the interfacial friction force is for- @ @ ðÞ1¡x r X C ðÞ1¡x r u X ; D S ð2:54Þ mulated as: @t liq NC @z liq liq NC dis NC ÂÃ D ðÞ¡ ðÞ½ ¡ C C ð : Þ Here,TagedP the symbol X is the molar fraction of the dissolved gas. Fik 1 E 1 x Fik;bub xFik;ann EFik;dro 2 44 NC,dis ItTagedP should be mentioned here that the massive existence of non- TagedP fl The interfacial friction of bubbly ow Fik,bub is determined accord- condensable gas must also be considered in the conservation equa- ing to [174]: fi ! tions of the gas phase. The total gas enthalpy is then de ned as: 0:25 29r f F ; r gas d h liq liq 3 h0;gas D ðÞ1¡XNC hNC C XNCh0;gas ð2:55Þ F ; D C xðÞ1¡x Du jDu jð2:45Þ ik bub d D ik ik bub H Furthermore,TagedP the total gas density is calculated as a sum of where Duik represents the relative velocity between phases. The steam partial density and non-condensable gas partial density. bubble diameter dD68XbubX can be estimated using the following Similar to gas density, the total pressure is the sum of partial 92 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 pressures.TagedP The heat and mass transfers between wall and gas, TheTagedP momentum balances for gas and liquid phases are written: wall and liquid, gas and liquid must also include additional @ @ 2 C fl xrgasugasA rgasu pgas xA terms in order to consider the in uence of non-condensable C gas gases. @t @z @ @ D x C A C ¡ C G TagedP TagedP fl pintA xpgas Ab uliq ugas AintAuint 2.2.2.4. Seven-equation model. The two-phase six-equation ow |fflfflfflfflffl{zfflfflfflfflffl}@z |fflfflfflfflffl{zfflfflfflfflffl}@z |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} fi Interfacial mass model accounts for signi cant non-equilibrium of phases, but still Volume fraction term Pressure term Velocity relaxation rate assumes pressure equilibrium. The seven-equation model (also transfer ð2:59Þ known as two-pressure flow model) allows the phases to be ¡ ¡ 2ðÞ0:5 ¡1 ¡ 2 0:5 fl fwal;gasrgasx ugas uwal pA fintrgas ugas uint Aint totally independent of each other. It solves the uid dynamic |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}2 fl interface problems and the two-phase ow system simulta- Wall drag Interfacial viscous drag neously, resulting in separate pressure, velocity, temperature and C xr gA chemical potential for both phases. The model has two sets of |fflfflfflfflffl{zfflfflfflfflffl}gas mass, momentum and energy conservation equations as well as Gravitational term one volume fraction evolution equation that describes how the fl @ ðÞ¡ @ 2 C ðÞ¡ uid composition changes with time. Although the seven-equa- 1 x rliquliqA rliquliq pliq 1 x A fl fl C tion ow model is different from the six-equation ow model, @t @z many of the closure models in the six-equation flow model can @ðÞ¡ @ D 1 x C ðÞ¡ A also be implemented here. The closure laws are determined from pintA @ 1 x pliq @ z z the flow parameters and their derivatives, coupled with empirical 2 0:5 C Ab ugas¡u ¡GA Au ¡f ; r ðÞ1¡x u ¡u ðÞpA correlations, describing all regimes of the two-phase flow [176]. liq int int wal liq liq liq wal 1 InTagedP the process simulation of thermal power plants and espe- ¡ f r u ¡u 2A0:5 C ðÞ1¡x r gA 2 int liq liq int int liq cially nuclear power plant, it is actually more common to apply ð2:60Þ the two-fluid model with pressure equilibrium. The partial-dif- ferential equation system related to the pressure equilibrium TheTagedP energy equations are: suffers, however, from improper mathematical properties. The @ xr h0;gasA @ r h0;gas C pgas xugasA eigenvalues of the Jacobian matrix are not always real and may gas C gas assumecomplexvalues,whichinturnleadtoanill-posed @t @z @x p Cauchy problem. The seven-equation model systematically D p u A ¡ int Ap ¡p C u bAu ¡u int int @ gas liq |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}int liq gas allows seven real eigenvalues and is shown to have a well- |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}z |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}h Velocity relaxation term posed basis of eigenvectors, particularly in the context of com- Volume fraction term Pressure relaxation term pressible two-phase flows. In comparison to models using a ð : Þ pint 0:5 2 61 pressure equilibrium assumption, the unconditionally hyper- ¡GA A ¡h ; ; C K ; T ¡T A int 0 gas int |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}int gas int gas int bolic property makes the two-pressure seven-equation model |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}rint Interfacial heat transfer very attractive. Recently, this flow model has gained interest for Interfacial mass heat transfer "# modelling of a wide range of applications, including non-equi- 0:5 @ 2 fl fl fl fl A librium dispersive two- uid ow, free-surface two- uid ow C xK ; T ¡T 4pA C C xr gu A wal gas wal gas @x |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}gas gas under the influence of gravity, boiling and flashing of super- |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Gravitational term heated liquid as well as the bubble collapse in light water reac- Wall heat transfer tor. However, the seven-equation model also suffers from fi @ ðÞ¡ @ C ðÞ¡ several dif culties such as the model complexity and the pres- 1 x rliqh0;liqA rliqh0;liq pliq 1 x uliqA @ðÞ1¡x C D pintuintA ¡ ence of neoconservative products, i.e. the model cannot be @t @z @z equivalently recast in full conservative form. These neoconser- pint ¡ C ¡ ¡G pint ¡ Apliq pgas uintbAugas uliq AintA h0;liq;int h rint ð2:62Þ vative products naturally disappear, when the void fraction is "# : @ 2 0 5 0:5 A locally constant in space and the model corresponds to two C K ; T ¡T A C ðÞ1¡ K ; T ¡T 4 A C int liq int liq int x wal liq wal liq p @ decoupled gas dynamic systems. x C ðÞ¡ ThisTagedP section describes the seven-equation model, as imple- 1 x rliqguliqA mented in the RELAP software [177]. The seven-equation flow model MostTagedP of the two-phase nomenclatures used in these sets of equa- for one-dimensional two-phase flow presents full mechanical and tions have already been mentioned. The interfacial mass transfer G thermodynamic non-equilibrium and consists of the following con- is here has the unit kg/m5s, while it is kg/m3s in other two-fluid mod- servation equations. els. The symbols A and A represent the flow cross-sectional area TagedP int The volume fraction evolution is expressed as: fi and the speci c interfacial area between phases (gas and liquid) per ¡ @ðÞxA @ðÞxuintA pgas pliq GAintA unit volume. The terms pgas and pliq denote the gas pressure and the C D A C ð2:56Þ D72XX @t @z h pint liquid pressure. The symbol b refers to the interphase momentum |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |fflfflffl{zfflfflffl} transfer coefficient (resistance coefficient). The terms pint and uint Pressure relaxation rate Interfacial mass transfer represent the interfacial pressure and the interfacial velocity that TheTagedP mass balances for gas and liquid phases are formulated as: exerted on the surface of a two-phase control volume, where the volume fraction gradients exist. These interfacial variables are @ @ xrgasA xrgasugasA expressed as: C D GAintA ð2:57Þ @t @z @ðÞ¡ p ¡p |fflfflffl{zfflfflffl} D C 1 x gas liq ð : Þ uint uint sgn @ C 2 63 Interfacial mass transfer z Zgas Zliq @ ðÞ¡ @ ðÞ¡ ZgasZliq @ðÞ1¡x 1 x rliqA 1 x rliquliqA p D p C sgn u ¡u ð2:64Þ C D¡GA A ð2:58Þ int int Z C Z @z gas liq @t @z int gas liq F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 93 withTagedP the phasic relation: TagedP The physical values of working fluid in a control volume such as mass flow, energy flow and separate substance are determined. Z D r c ð2:65Þ k k k TagedP The outputs of automation and electrical components are speci- TagedP Here, k denotes liquid or gas and the symbol ck is the phasic fied. sound speed. The average values of interfacial pressure and velocity can be defined as follows: 2.2.4.TagedP Comparison Z u C Z u D gas gas liq liq ð : Þ InTagedP the previous sections, different thermal hydraulic models uint C 2 66 Zgas Zliq are presented such as the mixture flow model and the two-fluid models. The selection of the appropriate flow model depends on Z p C Z p D gas liq liq gas ð : Þ computational effort and desired level of accuracy. Although pint C 2 67 Zgas Zliq the mixture flow model entails a less accurate description of SimilarTagedP to the six-equation flow model, the non-condensable two-phase flow phenomena, in many cases it presents the most gases can be included in the framework of the seven-equation efficient approach for the dynamic simulation of thermal flow model. The non-condensable gases can be a part of the gas powerplants.Foramoredetailedconsideration of components phase or dissolved in the liquid phase. In this case, additional such as evaporator or condenser, a two-phase flow model partial differential equations are expressed for non-condensable should be selected. In this section, two examples from the sci- gases in the gas phase (e.g. nitrogen, helium and hydrogen in the entific literature are presented, showing the mixture flow model steam) and for dissolved components in the liquid phase (e.g. and the two-fluidmodelsindirectcomparisonwithmeasure- nitrogen, helium, hydrogen and even boron dissolved in water). ment data. The first study applied an in-house code, while the second study used two different commercial simulation pro- 2.2.3.TagedP Solution method grammes. InTagedP order to solve the one-dimensional partial differential equations, WippelTagedP [178] developed a dynamic simulation code (AHKSIM, the finite difference solution method or the finite volume solution latter known as MISTRAL) with different thermal hydraulic method is, generally, applied. The partial differential equations are dis- models, i.e. mixture flow model and six-equation flow model. In cretised with respect to space and time and the non-linear terms are order to determine the volumetric void fraction, the drift- linearised. In the space discretisation (integration over the correspond- flow model according to Zuber and Findlay [165] was imple- ing element length), several discretisation schemes such as the first- mented. order upwind scheme, the second-order central differencing scheme = x rg andthequadraticupwindinterpolation are available. For time discreti- x D ð2:68Þ x C 1¡x C Vgas;j C0 _ = sation, the implicit method is usually employed. The physical proper- rg rl m A ties such as pressure, velocity and enthalpy in the model can finally be TheTagedP distribution parameter C0 and average drift velocity of the calculated using the discretised conservation equations, the parame- gas phase V were computed using Rouhani and Chexal Lellouche fl gas,j tersforinletandoutlet ows and the thermodynamic properties. correlations. TagedP fi According to the software APROS [169] that uses the nite vol- TwoTagedP heat recovery steam generator (HRSG) models were built ume solution method to solve the one-dimensional partial differen- based on the mixture flow model and the six-equation flow model. tial equations, the solution method includes: The investigated power plant is a simple single-pressure HRSG with- out reheat. A breakdown case, in which the live steam valve was TagedP The conservation equations for mass, momentum and energy are suddenly opened, was simulated and the results obtained from both applied to the control volumes. HRSG models were compared to measurement. After opening the TagedP fl fl Single phase ows, homogeneously mixed two phase ows, non- live steam valve, the pressure in the system drops sharply and the fl equilibrium separate phase ows as well as laminar, turbulent or steam mass flow rate increases considerably. Since the heat input to fl critical ows can be considered. Furthermore, radiation, convec- the HRSG remains constant, the steam temperature decreases by tion and diffusion as well as relevant heat transfer correlations reason of increased mass flow rate. In Fig. 1, the comparison can be applied. Relevant chemical reactions can be assigned to between the measurement values and numerical results of mixture the control volumes in consideration. flow model and six-equation flow model is illustrated. It can be TagedP Material property libraries can be called with regard to relevant observed that the two-fluid model reproduces the system behaviour fi parameters such as pressure, speci c enthalpy and mass fraction. with better accuracy compared to mixture flow model. Minor TagedP For valid application range, empirical correlations are used. differences can be noted between Rouhani correlation and Chex- TagedP The control system element models such as controllers, logical al Lellouche correlation, where the latter is slightly more favour- signals and operations as well as sequential automation blocks able. can be included functionality in the simulation model. AlobaidTagedP et al.D74XX[15,17] investigated into the capability of differ- TagedP The electrical components such as generator, electric motors, ent commercial simulation codes to predict the real behaviour of electrical bus bars, network elements and converters can be a combined-cycle power plant during part loads, off-design oper- included functionality in the simulation model. ation and start-up. The combined-cycle power plant with a TagedP The resulting one-dimensional partial differential equations are three-pressure heat recovery steam generator and a single reheat discretised with respect to space. This can be performed using is built with the process simulation software tools ASPEN Plus different interpolation methods such as upwind interpolation, DYNAMICS using the mixture flow model and APROS using the linear interpolation, quadratic upwind interpolation and high- six-equation flow model. D73XX order schemes. InTagedP Fig. 2, the dynamic simulation results of the intermediate TagedP fl For unsteady ows, the time should be discretised, considering pressure circuit including feedwater and steam mass flow rates, relevant state variables and selected time steps. In order to pressure as well as the superheated steam temperature are pre- obtain the time dependent solution, initial conditions and bound- sented for off-design operation. The intermediate pressure (IP) fi ary conditions that can also depend on time must be de ned. feedwater mass flow rate obtained numerically agrees well with TagedP At the end of each time-step and for each control volume, mass measurement. Similar to the IP feedwater mass flow rate, the errors are checked and non-linearity errors are iteratively corrected. simulated superheated steam mass flow rate follows accurately 94 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 theTagedP measured data. However, a slight deviation that lasted for TheTagedP steam temperature computed by the mixture flow model 30 min can be detected between the numerical models and the shows acceptable agreement. Although the temperature jump real power plant in the period of time between t D 90 min and preceded the measured data by 20 min, the simulated gradient t D 120 min. From t D 120 min on, both models show high accu- is close to the real plant with a relative error of approximately racy with a maximum relative error of approximately 2%. The 15%. From t D 75 min, the calculation of the steam temperature superheated steam temperature calculated with the mixture is close to the measurement. Compared to the three-equation flow model overestimates the measured one, while the simulated model, the six-equation model shows quantitative agreement temperature in the six-equation model underestimates the mea- with measurement. Prior to start-up, the LP drum level in the surement. The numerical models reproduce qualitatively the six-equation model and experiment is equal to 2.3 m, while it is dynamic behaviour of the IP pressure. Compared to the mixture 2.22 m in the three-equation model. The level of the LP drum flow model, the six-equation model simulates the dynamic pres- obtained numerically by both models agrees very well with sure change with higher accuracy, especially in time period experiment. However, the numerical models failed to simulate between t D 150 min and t D 400 min. Here, the six-equation the oscillations in the drum level in the period of time model and the three-equation model show maximum relative between t D 20 min and t D 120 min. The three-equation model errors of about 3% and 7%, respectively. shows an almost smooth development of the LP drum level, TheTagedP dynamic behaviour of the low pressure (LP) system while the six-equation model predicts the level oscillations during start-up procedure is presented in Fig. 3.Thecalculated more accurately. feedwater mass flow rate matches very well with measurement. InTagedP this comparative study between the three-equation flow However, the considerable oscillations in the measured feed- model and the six-equation flow model, the following conclusions water mass flow rate with average amplitude of 75 kg/s are not are drawn: predicted by the numerical models. Starting from t D 150 min, the simulated feedwater mass flow rate lies marginally above TagedP1. In steady state, both three-equation flow model and six-equa- the measured data with a relative error of 2%. The computed tion flow model can quantitatively reproduce the process steam mass flow rate exiting from the LP superheater is in good parameters of a real power plant. The relative error for mass agreement with the real power plant. At t D 36 min, the timing flow rate, temperature and pressure are all within 5%, while of first steam generation is accurately predicted by the six- several parameters are captured with a relative error of less equation model, in contrast to the three-equation model. For than 1%. the latter, the steam production starts about 15 min earlier than 2.TagedP During off-design operation and start-up procedure, higher dis- measurement. From t D 75 min, qualitative agreement between crepancy is observed. Both three-equation and six-equation flow simulation and experiment can be observed. models can qualitatively follow the measurements with a
Fig. 1. Experimental and numerically obtained steam temperature, pressure and steam mass flow rate during a breakdown case (reproduced from reference [178]). F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 95
TagedP maximum relative error of approximately 12%. Several parame- flTagedPow and one outlet flow. The following mass and energy balances ters are captured with a relative error of less than 5%. can be expressed: 3.TagedP For the given case, the six-equation flow model describes the Xi D k Xi D j behaviour of the real power plant during off-design operation m_ ; D m_ ; ð2:69Þ and start-up procedure more accurately compared to the three- inl i out i i D 1 i D 1 equation flow model. The correct time prediction of first steam generation and temperature gradients as well as the better Xi D k Xi D j _ D _ ð : Þ reproduction of the measured parameter oscillations are advan- minl;ihinl;i mout;ihout;i 2 70 tages of the six-equation flow model, at the cost of increased i D 1 i D 1 computational effort. TheTagedP subscripts k and j represent the number of inlet flows and outlet flows. In case of mixing two fluids with different compositions 2.3. Process components such as natural gas and air, the materials balances of the individual species must be computed and the mixture enthalpies calculated Basically,TagedP a conventional thermal power plant consists of a accordingly. The pressure of all outlet flows involved is assumed to flue gas side and a water/steam side. In the flue gas side, flows be equal. of various reactants are injected into the combustion chamber, where the reactions between oxidiser and hydrocarbon take 2.3.2.TagedP Thin-walled tube place. The released heat is transferred through radiation and Thin-walledTagedP tubes are used as a representation of several differ- convection to the water/steam side, converting feedwater into ent structures in a power plant like pipes, valves and heat exchang- superheated steam. The latter expands in the steam turbine, pro- ers. The thin-walled tubes incorporate a heat transfer model ducing mechanical energy. Using an electrical generator, the between wall and fluid, heat storage and a pressure loss of the flow. mechanical energy is then converted into electrical energy that The wall temperature of thin-walled tubes can be modelled with a is transmitted to the grid. The process components required for constant temperature in the radial direction for simplification. the modelling of a thermal power plant include points, thin- Berndt [179] calculated the wall temperature of thin-walled tubes, walled tubes, thick-walled tubes, turbomachines etc. The tubes formulating the wall energy balance under the assumption of infi- of the economisers, evaporator and superheater heat exchangers nite thermal conductivity in the radial direction and negligible ther- as well as the connecting pipes and valves belong to the thin- mal conductivity i;n the axial and tangential directions as follows: walled tubes, while other components such as drum and header @ belong to thick-walled tubes. The turbo-machines are rotating D D ¡ C _ ð : Þ Awal x rwalcp;walTwal aAin Tfl Twal Q 2 71 devices that extract energy from or transfer energy to the work- @t ing fluid. In this work, the term working fluid refers to water/ Here,TagedP the symbol Awal is the cross-section surface of the wall, rwalD75XX steam, flue gas, organic working fluids, etc. and cP,wal represent the density and the heat capacity of the wall _ material, Q is the heat flow, a denotes the heat transfer coefficient,
2.3.1.TagedP Connection point Ain is the inner surface area of the wall, Tfl and Twal are the tempera- TheTagedP point or node component is the most basic process compo- ture of the working fluid and the wall, respectively. In order to nent used in process simulation. It has no actual real process compo- reduce the computational cost, it can be assumed that the physical nent as a counterpart and is used to connect different kinds of characteristics of wall material such as density and heat capacity are process components together. The point may have at least one inlet not subject to major change during the transient.
Fig. 2. Experimental and numerically obtained IP feedwater mass flow rates, IP steam mass flow rate, IP steam temperature and IP pressure during the off-design operation (reproduced from reference [15] with permission of authors and Elsevier). 96 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 3. Experimental and numerically obtained LP feedwater mass flow, LP steam mass flow, LP steam temperature and LP drum level during start-up procedure (reproduced from reference [17] with permission of authors and Elsevier).
TagedP fl 2.3.2.1.TagedP Pipe. TheTagedP working fluid, other gaseous and liquid fluids can correlation between the mass ow rate and the valve position. fl be transported using pipes that entail pressure drop of the flow. Typically, the characteristic curves are linear (mass ow Numerically, the pipe component that is defined between two con- increases linearly with valve travel) or equal percentage (mass fl nection points is applied to calculate the fluid flow (e.g. velocity). ow increases exponentially with valve travel). In special cases, Here, the shape and dimensions of pipes need to be specified. When different kind of curve types such as parabolic, hyperbolic or it is necessary, the heat storage into the pipe material or the heat square root can also be considered. The position of the control flow rate out from the pipe can be taken into account. In some appli- valve is controlled by the automation system. The valve model cations (e.g. evaporator with natural circulation operation), the den- receives the new setpoint and computes valve movement during sity differences at inlet and outlet have to be considered and are the the time step, taking into account the driving time of the valve. fi main driving force for the fluid. The driving time of the valve is de ned as the time required by TheTagedP pressure drop of the flow in the pipe can be expressed as: the valve actuator to open the valve from the fully closed position to the fully opened position or vice versa. Large valves in thermal r u2 D D L k k ð : Þ power plants use hydraulic pressure or electricity, allowing typi- ppip fk 2 72 D 2 cal driving times between 10 s and 30 s. Moreover, the process
TheTagedP symbol fk represents the friction coefficient, rkD76XXand uk are the simulation can incorporate loss of electrical energy supply. In density and the velocity of the fluid, L and D denote the length and this case, there are three possible modes of valve operation: to diameter of the pipe. open, to close or to stay at the same position. TagedP The shut-off valves include different types such as butterfly 2.3.2.2.TagedP Valve. TagedPIn a thermal power plant, the main task of a valve is to valve, flap valve and conical seat valve. The characteristic curve achieve desired fluid flow rates. In the process simulation, the valve of a shut-off valve is usually not known, but the driving time and model is considered as flow resistance. The pressure drop over the the flow resistance coefficient of a fully open valve are required. valve can be computed as a sum of the pressure drop due to friction However, there are generic characteristic curves of the flow resis- coefficient fk and the pressure drop due to flow resistance coefficient tance coefficient as a function of the valve position for each valve of the valve fval: type. In contrast to the control valves, the binary signals TRUE or FALSE control the shut-off valve. If the signal is TRUE, the valve L r u2 Dp D f C f k k ð2:73Þ starts opening and the valve begins to close, when the signal is val val k D 2 FALSE. In break down cases (electrical power is lost), the shut-off TheTagedP valve is controlled using automation components and can valve either stays in its current position, starts closing or opening also be connected to electrical components to simulate its behaviour depending on the valve configuration. during the loss of electricity. In thermal power plants, there are dif- TagedP The check valve, also known as non-return valve or one-way ferent kinds of valves used such as control valve, shut-off valve, valve allows the fluid to flow through it in only one direction. It check valve and safety valve. is either fully open or fully closed. If the pressure difference over the valve is positive, i.e. the pressure at the valve inlet is higher TagedP For control valve, the flow resistance is calculated as a function of than the pressure at the valve outlet, the valve is open. If the the valve position that is a non-dimensional value between 0 and pressure difference over the valve is negative, the check valve is 1. The valve is fully closed, when the valve position is 0 and is closed. fully opened, when the valve position is 1. The control valve is TagedP A safety valve has the function of increasing the safety of thermal specified by a so-called characteristic curve that describes the power plants by limiting pressure in pressure vessels. Here, the F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 97
TagedPfl uid is automatically discharged from a drum or other compo- balanceTagedP has to be solved for the tube wall, describing the heat fi nents when the pressure exceeds the speci ed limit. In a pres- transport from the flue gas to the tube wall and from the tube sure safety valve, the opening position is linked to the pressure. wall to the water/steam flow. In a tube bundle heat exchanger for example, the heat flows to the tube wall from the flue gas 2.3.2.3.TagedP Attemperator/desuperheater. TheTagedP attemperator (injection (through convection and thermal radiation) and from an optional cooler) limits the steam temperature to the setpoint value. In ther- flame-radiation zone of a combustion chamber. Then, the heat is mal power plants, the attemperators are installed at superheater transferred from the tube wall to the working fluid. Fig. 4 illus- and reheater surfaces to control the temperature at the inlet of the trates the discretised structure of a counter-flow tube bundle high and intermediate pressure turbines. The attemperators use heat exchanger as an example. The flue gas path and water/steam water directly from the boiler feedwater pumps. The injected mass tubes are discretised in equally-spaced control volumes with one flow rate is adjusted by a control circuit that controls the valve posi- calculation node in the centre and a calculation branch between tion. While the attemperator controls the steam temperature, a two adjacent nodes. Here, each control volume consists of a hori- desuperheater removes the superheating of the steam and reduces zontal pipe pass. To reduce the computational cost, each control the temperature of the steam to a range between 10 °C and 50 °C volume may consist of many horizontal pipes in parallel. The flue above saturation temperature. Desuperheaters are found e.g. in the gas path and the water/steam side are coupled by the heat flows bypass system of the high pressure turbine, which routes the high through the tube walls. pressure steam not admitted by the turbine into the cold reheater or condenser. Here, a desuperheater is installed that reduces the steam TagedP temperature to approximately 50 °C above the saturated steam tem- 2.3.3. Thick-walled tube TagedP perature. The assumption of constant temperature in the radial direction of thin-walled components is acceptable for purposes of simplification. 2.3.2.4.TagedP Heat exchanger. TagedPIn thermal power plants, heat exchangers In the case of thick-walled components that are usually not posi- fl are used, where heat transfer between one or more fluids takes tioned in the ue gas path such as drum and header, this assumption place. Based on the requirements, a variety of different heat is non-permissible and can lead to errors, especially by calculating fi exchangers has been developed. Basically, the heat exchangers are the heat storage in the walls. The temperature pro le in a thick- designed as regenerator and recuperator. In regenerators, the heat walled component can be calculated by solving Fourier's differential fl fi equation: transfer between uids is carried out in two steps. In the rst step, fl @ @ @ the heat ow is transferred to a storage mass and in the second step Twal r c ; T D λ ð2:74Þ the energy stored is emitted to the heat-absorbing fluid after a time @t wal p wal wal @r wal @r delay. The charge/discharge cycle can be discontinuous or continu- Here,TagedP the character λ is the thermal conductivity of the wall. To ous. An example of regenerators is the thermal wheel, also known as wal simplify the problem, the wall can be divided into individual circular a rotary air preheater. In recuperators, by contrast, the heat is trans- ring elements and the differential equation is solved numerically for ferred continuously between fluids through a solid wall. They repre- each segment. This discretisation is valid, if the thermal conduction sent the most commonly-used type of heat exchangers, including in the axial direction is negligible and the temperature distribution double-pipe heat exchangers, plate heat exchangers, shell and tube is radially-symmetric [180]. bundle heat exchangers etc. Depending on the flow configuration of DuringTagedP start-up procedures of the thermal power plant, espe- the fluids, it can be distinguished between co-current flow, counter- cially cold start-ups, the generated steam can condense on the current flow, cross-flow or hybrid flow arrangements. If phase- still-cool wall surface of thick-walled components. The heat change occurs in any of the fluids, the heat exchanger is referred to transfer coefficient of the condensate is much higher than the as phase-change heat exchanger; otherwise it is a sensible heat heat transfer coefficients of the steam and the boiling water in exchanger. In thermal power plants, the heat exchangers used are thelowerpartofthedrum,whichinturnleadstodifferentheat listed as follows: fluxes along the wall. Accordingly, heat is transported in the tan- gential direction of the drum wall. In order to consider heat TagedP Shell and tube bundle heat exchangers (economizer, evaporator, transport in radial and tangential direction, 2D calculation of the superheater and reheater): This type of heat exchanger transfers heat conduction in the drum wall is required. In contrast, during heat from the flue gas path to the water/steam circuit. It consists hot and even warm start-ups no condensation is present and of numerous, equally long, heated tubes installed in parallel. The only small temperature differences between the upper and the bundle of tubes is connected to one another by a header. The lower part of the drum occur. Therefore, the heat transfer in working fluid flows through the tubes, while the flue gas flows thick-walled hollow cylinders can be reduced to heat conduction over the tubes, transferring heat between the two fluids. in the radial direction. TagedP Membrane wall heat exchanger (evaporator): This type of heat InTagedP thick-walled components, the rate of temperature change is exchanger is installed on the combustion chamber walls of coal- usually required to calculate thermal stresses and thus to prove the fired boilers. safety of operation during start-up and shutdown procedures of TagedP Feedwater preheater: This type of heat exchanger heats the feed- boilers. Material stresses are calculated based on the recorded pres- water mass flow, before entering the steam generator using sure and temperature history. The thermal stresses are proportional steam extractions form the high and low pressure turbines. the difference between integral average wall temperature and inner TagedP Condenser: This type of heat exchanger condensates the turbine wall temperature: exhaust steam by means of cooling water or cooling air, depend- ing on site conditions. D aT blinEs ðÞ¡ ðÞ; ð : Þ sth Twal t Twal;in r t 2 75 TagedP Air and gas preheaters: These types of heat exchangers heat air or 1¡v fl natural gas for combustion using the heat of ue gas or process TheTagedP linear thermal expansion coefficient blinD7XX, the modulus of elas- steam. ticity Es and Poisson's number v are material characteristics. The stress concentration factor aTD78XXtakes into account weakening of the TheTagedP transport equations required to model the heat exchanger cylinder wall due to connected tubes, i.e. this factor is strongly used in thermal power plants are mass, momentum and energy dependent on the geometry and weld joints. The average wall tem- balances for flue gas flow and water/steam flow. Only the energy perature of a thick-walled component with a volume V can be 98 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 4. Counter-flow heat exchanger of a low pressure economiser of a HRSG; (a) real geometry (24 rows with 105 tubes per row) and (b) discretisation structure of the investi- gated heat exchanger.
calculatedTagedP according to the following relation: deTagedP flection boxes. The saturated steam leaves the drum apex through Z a steam dryer (demister) that enhances the removal of liquid drop- 1 T D T dV ð2:76Þ lets entrained in the vapour stream. However, the saturated steam wal V wal V flowing into the superheaters may include a small amount of water TagedP In case of a hollow cylinder, this relation takes the form: droplets. The water remains in the drum bottom and flows through Z 2 rout the downcomers to the evaporator. Pre-warmed feedwater is fed to T ðÞt D T ðÞr; t rdr ð2:77Þ wal 2 ¡ 2 wal the drum through economisers with a certain degree of subcooling rout rin rin and mixed with the saturated water in the drum. The content of salts TagedP Here, the symbols rin and rout are the inner and outer radius of the in the pre-warmed feedwater cannot leave with the saturated steam hollow cylinder. From Eq. (2.77), it can be observed that the thermal and remains in the evaporator system. Accordingly, a specific stresses are a quadratic function of the wall thickness, which in turn amount of water is constantly discharged from the drum to the increases with the design pressure. blow-down tank, limiting the concentration of salts in the evapora- TagedP In the following sections, the thick-walled tubes used in thermal tion system. The mathematical model that describes the physical power plants will be explained, including header, drum, separator processes in the drum, by contrast to the header model, are and feedwater storage tank. extremely complex. This is due to the fact that the separation of the two-phase flow takes place under highly-turbulent flow regime. A TagedP TagedP 2.3.3.1. Header. The header is a thick wall pipe with large diameter schematic of the drum model with all variables is presented in Fig. 6. connected to a large number of heating surface tubes with relatively InTagedP the drum model, it can be assumed that the momentum trans- small diameter (see Fig. 5). The headers are arranged at the inlet and ported into the drum with the inlet flows is completely dissipated, outlet of tube-bundle heat exchangers. The function of the inlet but it builds up again at the pipes, when the working fluid leaves the header is to distribute the working fluid as uniformly as possible in drum. For the definition of the drum, the volume Vdru, the height the tubes of the heat exchanger. The outlet header collects and H and the cross-sectional area A are required. The mass of the fl dru dru homogenises the working uid from the tubes and feeds it to inter- water and the steam in the drum can be expressed as: connecting pipes. As described above, the thick walls of headers can D store or release the heat from or to the working fluid during transi- mliq;dru rliq;druAliq;druldru ð : Þ ents. Furthermore, the temperature gradients in the header walls 2 78 m ; D r A ðÞH ¡l result in material and thermal stresses. Therefore, the headers used st dru st;dru dru dru dru in thermal power plants are designed with stringent requirements Here,TagedP the symbol Aliq,dru denotes the cross-sectional area of the for strength, corrosion and creep properties. The high mechanical drum filled with water, rliq,druD79XX and rst,druD80XX are the densities of water properties of the header are required on the one hand due to the and steam in saturation state. A feedwater control valve is used to operation under harsh conditions, e.g. high temperature and pres- regulate the level of the water in the drum ldru by adjusting the feed- sure, high rate of temperature and pressure changes, and on the water mass flow rate entering into the drum (see Fig. 15). According other hand due to the large number of connected tubes that contrib- to mass and energy flows at inlet and outlet of the drum, the follow- ute to cross-sectional weakening. ing unsteady balance equations of mass:
Xi D k Xi D j Xi D n dmliq;dru dmst;dru 2.3.3.2.TagedP Drum. TagedPThe drum is a horizontal, cylindrical shaped tank C D m_ ; C m_ ; ¡ m_ ; ¡m_ ¡m_ ð2:79Þ dt dt fw i riser i down i blow st with comparatively thick walls. In natural or forced circulation ther- i D 1 i D 1 i D 1 mal power plants, the drum represents the core of the evaporator and energy: system and has a variety of functions. It is used as link between the dm ; h ; ; dm ; h ; ; downcomers and the risers, enabling the circulation of the working liq dru 0 liq dru C st dru 0 st dru fluid through evaporators. Furthermore, the drum separates steam dt dt Xi D k Xi D j Xi D n from the water/steam mixture by force of gravity using the density D _ C _ ¡ _ ð : Þ mfw;ih0;fw;i mriser;ih0;riser;i mdown;ih0;down;i 2 80 difference between gaseous and liquid phase. The separation of the i D 1 i D 1 i D 1 two-phase mixture can be improved with different types of separa- dpdru ¡m_ h ; ¡m_ h ; C V tors using centrifugal force, e.g. cyclone separators or simply blow 0 blow st 0 st dru dt F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 99
Fig. 5. Header; (a) outlet header and (b) inlet header. canbeapplied.Intheequations,thesubscriptsTagedP k, j, n represent tankTagedP stores the feedwater in order to decouple the feedwater mass the number of the feedwater pipes, the number of the risers and flow rate from the build-up of condensate. Generally, the storage the number of downcommers that are connected to the drum, capacity is designed to cover a few minutes of full-load operation of respectively. The inlet mass flows are the feedwater mass flow the boiler. This stored energy can be used effectively in order to yield _ fl from economisers mfw and water/steam mixture mass ow from a rapid increase of the electrical power output (condensate throt- _ the riser mriser.Theoutletmassflows are the water mass flow to tling method). Here, the steam extraction valves to the low pressure _ fl downcomers mdown andthewatermass ow to blow-down tank preheaters and the condensate valve to the feedwater tank are tem- _ fl _ mblow as well as the steam mass ow leaving at the drum apex mst. porarily throttled or even closed. Accordingly, the extraction steam Thepressurederivativeappearsintheenergyequation,sincethe passes through the last turbine stages, resulting in a sudden increase internal energy of the water or the steam is replaced with the cor- in the electrical power output (up to 5% within 30 s) that can lasts responding total enthalpy h0. The time derivatives in the mass and for a few minutes depending on the volume of the feedwater storage energy balance equations can be approximated by using a suitable tank and/or the condenser tank. The condensate throttling method, numerical solution method. although it has no impact on the main steam pressure, has compli- cated dynamic behaviour, since it results in the variations of extrac- 2.3.3.3.TagedP Separator. TagedPThe separator (generally called as cyclone) is a tion steam flows as well as the level change of the feedwater storage vertical, cylindrical shaped tank with a relative small diameter and tank. high wall thickness (see Fig. 7). It is located at the evaporator outlet InTagedP thermal power plants, the feedwater storage tank is equipped of once-through boilers with part load recirculation or with super- with a deaerator that removes the dissolved oxygen, carbon dioxide imposed circulation. The once-through boilers can be operated at and other gases from the feedwater. Dissolved oxygen in feedwater subcritical and supercritical pressures and offer a higher degree of reacts with metallic walls and forms oxides (rust). This in turn leads operational flexibility. In the once-through boiler with superim- to serious corrosion damages in the steam generator components. If posed circulation, the circulation number amounts to around 1.3 carbon dioxide is also present, then it combines with water to form 1.7 and therefore the separator is used to separate the water from carbonic acid that causes additional corrosion. The feedwater stor- the water/steam mixture during operation. In the once-through age tank and deaerator are modelled as hydraulic accumulators. In boiler with part load recirculation, the working fluid is forced to steady state modelling, the mass balance of the storage is simplified flow through all heat exchangers in a single pass. Here, the separator to equalisation of the inflow and the outflow. In transient case, the is used to remove the water droplets within the steam flow and mass balance of the storage can be expressed as: to separate the water from the water/steam mixture only during dm sto D _ ¡ _ ð : Þ start-up procedures and at low part loads. If the boiler is operated at minl mout 2 83 supercritical pressure, no phase separation can take place. The work- dt ing principle of the separator is that the two-phase mixture enters TheTagedP energy balance of the storage is written as: tangentially into the separator, leading to a spiral flow of the gas dmstoh0;sto D m_ h ; ¡m_ h ; ð2:84Þ phase. The water droplets in the stream are centrifuged to the sepa- dt inl 0 inl out 0 out rator wall, where they move downwards and are collected in the separator storage tank. The clean steam leaves through the upper part of the cyclone. Based on the drum model, the following applies 2.3.4.TagedP Turbomachines for the mass balance: TurbomachinesTagedP are a vital part of every energy system. They Xi D k transfer energy between a rotor and a fluid (gas or liquid). The dm ; dm liq dru C st;dru D _ ¡ _ ¡ _ ð : Þ mheader;i mst mliq 2 81 energy transfer can take place from rotor to fluid (e.g. compressor, dt dt i D 1 fan and pump) or from fluid to rotor (e.g. steam and gas turbines). Modern turbomachines have smaller gaps between rotor and hous- and for energy balance: ing for minimising the leakage loss. In the pump, the pressure of an dm ; h ; ; dm ; h ; ; incompressible fluid is increased to a higher level, while the pressure liq dru 0 liq dru C st dru 0 st dru ð2:82Þ dt dt of a compressible fluid is increased using the compressor. According Xi D k to ASME, fans differ from blowers and compressors by the pressure D _ ¡ _ ¡ _ C dpdru mheader;ih0;header;i msth0;st mliqh0;liq Vdru ratio that can be achieved (up to 1.1 for fans, from 1.11 to 1.2 for D dt i 1 blowers and more than 1.2 for compressors). In a steam turbine, the Here,TagedP the subscript k denotes to number of the header pipes that superheated or reheated steam expands, resulting in mechanical are connected to the wall of the separator. work. The gas turbine with its combustion chamber is a combustion system, converting natural gas or liquid fuels to mechanical energy. 2.3.3.4.TagedP Feedwater storage tank. TagedPThe feedwater pumped into the In process simulation, turbomachines are integrated into the water/ steam generator is typically supplied from a heated container with steam cycle, the electrical system and in the automation system. thick walls known as feedwater storage tank. The feedwater storage This allows designer to evaluate their electric power consumption/ 100 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 6. Drum and the connected tubes (adapted from reference [201] with permission of author). generationTagedP during transients and to assess their behaviour during thereforeTagedP the mass balance is expressed as: breakdown cases and when electricity is lost (blackout). Further m_ D m_ ð2:85Þ information regarding the specific turbomachines is presented in inl out the following sections. TheTagedP energy balance is defined as: _ D _ C ð : Þ minlhinl mouthout P 2 86 2.3.4.1.TagedP Compressor. TheTagedP compressor is a turbomachine that TagedP increases the pressure and the enthalpy of compressible, low The following equation can be used to calculate the required per- density fluids. The pressure increase is characterised by the com- formance: pressor pressure ratio that describes the ratio of the outlet pres- D _ ðÞ V ð : Þ P mcp T Tinl comp 2 87 sure (discharge pressure) to the inlet pressure (suction pressure). Here,TagedP c is the air specific heat capacity at the average tempera- Compressors are classified according to two different types, p ture. It can be determined simply as: namely intermittent flow (positive displacement) and continuous fl fl ow (rotor dynamic). The intermittent ow compressors include ðÞT C Tout T D inl ð2:88Þ rotary compressor and reciprocating compressor, while the con- 2 tinuous flow compressors include centrifugal compressor and TheTagedP dimensionless ratio can be expressed as: axial compressor. Rotary compressors consist of two rotors k h ; within a casing. The reciprocating compressors increase the pres- Vcomp D P pol comp ¡1 ð2:89Þ sure by reducing the volume of the working fluid. This can be Here,TagedP the term k is the isentropic exponent. The optimum pressure carried out by a piston within a cylinder as the compressing and P displacing element, achieving high compression ratios. The cen- ratio depends on the selected thermodynamic process and should fi trifugal compressors convert angular momentum transferred by provide the maximum ef ciency of combined gas and steam processes. a set of rotating impeller blades (dynamic displacement) to the For the Joule process, the design pressure ratio for modern gas turbines working fluid. The axial compressors use arrays of aerofoils to is approximately 18 20 and in case of reheat gas turbines is up to 38. fi 2X8DX compress the working fluid. An axial air compressor is one of the The polytropic compressor ef ciency hpol, comp is computed as: main components ofD81XXthe combined-cycle power plant. It com- P D ln ð : Þ hpol;comp k k 2 90 presses and supplies the fresh atmospheric air to the combustion P ¡1 C ln h 1 chamber of the gas turbine. Relevant input data for the compres- isen;comp sor model include the dimensions of components, design point with the isentropic efficiency hisen,compD83XX : values for pressure and temperature before compressor, pressure ¡ fi D hout hinl ð : Þ ratio, rotation speed, characteristic curve and ef ciency. Basically, hisen;comp 2 91 h ; ¡h the compressor model has one inlet flow and one outlet flow and out isen inl F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 101
combustionTagedP chamber and the cooler ambient air. Without the induced-draft fan, excess pressure may prevail in the combustion chamber, which should generally be prevented for safety reason due to the flue gas leakage. InTagedP the fan models, the input data of the fan such as geometry, dimension, characteristic curve, mechanical coupling must be speci- fied. Furthermore, the automation and electrical systems for starting and stopping the motor as well as for controlling the inlet guide vanes can be modeled, if necessary.
2.3.4.3.TagedP Blower. TheTagedP blower is used instead of the fan, when higher pressure ratio (approximately 1.11 1.2) is required. In process sim- ulation, the mathematical model of the fan can be used for the blower.
2.3.4.4.TagedP Pump. WhileTagedP the compressor is designed for compressible low density flow such as air or gas, a pump is designed to increase the pressure of incompressible fluids such as water or oil. In the pump, the mechanical energy of the shaft is trans- formed into kinetic and potential energy of the flow. At several locations in the thermal power plant, the pumps are used to transport the working fluid from one location to another. For example,thecondensatepumpsmovethecondensatewater through the low pressure preheaters into the feedwater storage tank. The boiler feedwater pump forces the water from the feed- water tank to flowthroughhighpressurepreheatersbefore entering the steam generator. TheTagedP pump model can include mechanical coupling, motor and busbar. The automation system adjusts the rotation speed of the pump by frequency control or directly by aid of the mechanical cou- pling. The steady state operation of a pump is computed as a func- fl _ tion of the actual volumetric ow rate Vliq and the rotation speed w as: 0 !1 _ 2 V 2 D @ ¡ðÞ¡ liq A w ð : Þ H Hmax Hmax Hnom _ 2 93 V ; wnom Fig. 7. Separator; (a) side view and (b) front view. liq nom TheTagedP initial values required for the pump model are maximum
pump head Hmax, nominal pump head Hnom, nominal volumetric _ flow rate Vnom and nominal rotation speed wnom. The rotation speed TheTagedP symbol hinl is the state enthalpy at the inlet of the compres- of the pump can be controlled by automation and electrical systems. sor, while hout,isen and hout denote the state enthalpy at the compres- If electricity is lost, the pump is coast-down according to the follow- sor outlet for the isentropic process and for the real process, ing relation: respectively. The discharge temperature of the compressor is calcu- Dt lated with the following formula: w D w0 1¡ ð2:94Þ tstop D C V ð : Þ Tout 1 comp Tinl 2 92 Here,TagedP the symbol w0 represents the rotation speed of the pump at old time step, Dt is the time step and tstop denotes to the coast-down 2.3.4.2.TagedP Fan. ATagedP fan generates a pressure difference, allowing for a time of the pump. large mass flow rate of air or gas to overcome a flow resistance. The drive power required is supplied by a rotating shaft (generally an 2.3.4.5.TagedP Steam turbine. TagedPThe steam turbine transforms enthalpy of electric motor). Basically, it can be distinguished between centrifugal steam to mechanical energy. The model of the steam turbine flow and axial flow fans. In the axial fan, the fluid flows axially along calculates the enthalpy after the turbine module using the the fan shaft without any change in the flow direction. In the centrif- enthalpy before the turbine, the efficiency and the nominal val- ugal fan, the fluid changes its direction relative to the shaft (forward ues. The mechanical power produced by the turbine is com- curved, backward curved or radial). puted and transferred to the generator model. The steam InTagedP thermal power plants, the fans used are forced-draft and turbine model may describe the turbine either with a single tur- induced-draft fans. The forced-draft fan is located at the inlet of bine stage or with many stages in order to consider the steam the flue gas path, while the induced-draft fan is located at the extractions. outlet of the flue gas path. The forced-draft fan supplies fresh air TheTagedP pressure and enthalpy drops over the turbine are added as for the combustion chamber via air preheaters. The induced-draft source terms in momentum and energy equations. The pressure fan creates a certain amount of negative pressure in the combus- change in the turbine stage is specified at nominal load and com- tion chamber (the pressure is below atmospheric pressure) by puted using the Stodola equation at part loads. The pressure drop is fl _ sucking the ue gas through the stack into the atmosphere. For a function of nominal mass flow rate mnom, the nominal pressure at this purpose, old thermal power plants use only the stack draft, the turbine inlet pinl,nom and the nominal pressure at the turbine out- fl i.e. the density difference between the hot ue gas in the let pout,nom: 102 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
TagedP TagedP vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi "# u h u n C 1 z n pout pout D D ¡ ¡ ¡ ð : Þ u ¡ hturb;dro xhinl;st href hinl;st href 2 106 p u 1 p _ D _ inl u inl ð : Þ pinl m mnom t n C 1 2 95 pinl;nom p ; n 1¡ out nom C ðÞ1¡x hpðÞ ¡hpðÞ pinl;nom inl;dro out;dro with: are obtained. Here, the subscripts st and dro refer to steam and water droplets, inl to the state before the turbine and out to the state after p ln out the turbine. The quantities x and hD84XXare the steam mass fraction and D pinl ð : Þ n 2 96 the polytropic expansion efficiency, respectively. The notation h(p) ln pout ¡ ln Tout pinl Tinl refers to the enthalpy in saturation state. TheTagedP mechanical power produced by the steam turbine can be cal- where m_ represents the mass flow rate, p is the pressure before the inl culated by knowing the mass flow through turbine and the enthalpy steam turbine, p is the pressure after the steam turbine, T out inl drop: and Tout denote the temperatures at inlet and outlet of the steam tur- bine. Xi D k D D _ ð : Þ TheTagedP enthalpy drop over the steam turbine is determined with the Pmech hturb;imi 2 107 D expansion efficiency. Generally, the processes are not purely isentro- i 1 TagedP _ pic or isothermal but a function of the exponent. The expansion Here, the subscript k is number of the turbine stages and mi is the equation is obtained from: mass flow rate that flows into the turbine stage i. 1 @h D ð : Þ 2.3.4.6.TagedP Gas turbine. InTagedP addition to compressor, combustion chamber h @ 2 97 v p and steam generator, the gas turbine represents the core element of IfTagedP the specific volume v is solved from Eq. (2.97) and introduced a combined-cycle power plant (CCPP). The gas turbine (GT) converts in Johanson‘s equation: flue gas enthalpy to mechanical energy, driving an electrical genera- tor that produces electrical energy. Using a heat recovery steam gen- h pv D ð2:98Þ erator (HRSG), the waste heat of the gas turbine can be used to z generate steam and drive a steam turbine. Typically, gas turbines can be operated with different fuels, including nature gas, crude oil the following equation is obtained: and biogas. They can extend their fuel range to cover biomass and @h h @p coal through the application of integrated gasification combined- D ð2:99Þ h z p cycle (IGCC). Modern gas turbines can reach their nominal load within 20 min, while 70% of the nominal flue gas temperature and D g Where z g¡1 and g is the isentropic exponent. By integrating the 60% of the nominal flue gas mass flow are already achieved approxi- right side term of Eq. (2.99) from hout to hinl and left side from pout to mately 7 min after the start. pinl, the following relation is obatined: ByTagedP contrast to steam turbines, heavy-duty gas turbines with high h inlet temperature require cooling of the first blade rows. If the cool- h p z inl D inl ð2:100Þ ing is not required, the mathematical model of the gas turbine is hout pout similar to the steam turbine. In case of air cooling, the entire gas tur- TheTagedP enthalpy is defined with regard to the reference enthalpy bine has to be divided into many stages. The cooling air of one stage href: is mixed with the combustion gases and can be considered in the h mass balance equation of the turbine stage. Based on empirical data, ¡ z hinl href p Wang and Leithner [181] developed an formula to calculate the cool- D inl ð2:101Þ ¡ fl hout href pout ing air mass ow required at nominal load: ¡ Eq.TagedP (2.101) can be written as: m_ D m_ 3:1817 ¢ 10 4T ¡0:2454 ð2:108Þ "# cool air inl h p z TagedP _ fl ¡ D ¡ out ð : Þ The symbol mair represents the total air mass ow rate and Tinl is hout href hinl href 2 102 pinl the inlet temperature in degree Celsius. At part loads, the following TagedP fi equation is proposed by Palmer and Erbes [182]: The speci c enthalpy drop over a turbine section is determined rffiffiffiffiffiffiffiffiffiffi fl fi using different models. When the uid is steam, the speci c p Tnom m_ D m_ ; ð2:109Þ enthalpy drop over a turbine is calculated as: cool cool nom p T nom D D ¡ ¡ ¡ ð : Þ hturb;st hinl;st href hout;st href 2 103 TheTagedP subscript nom refers to the nominal state. IfTagedP the fluid contains water droplets, the specific enthalpy drop can be computed with the following formula: 2.3.5.TagedP Additional components ÂÃ TagedP D D ¡ ¡ ¡ ð : Þ Detailed modelling of conventional thermal power plants hturb;dro xhinl;st href hout;st href 2 104 requires, besides the above mentioned process components, addi- C ðÞ¡ ðÞ ¡ ðÞ tional components such as different firing systems, mills and flue 1 x hpinl;dro hpout;dro gas clearing devices, e.g. electrostatic precipitator and selective cata- IntroducingTagedP the Eq. (2.102) in Eqs. (2.103) and (2.104), the follow- lytic reduction unit. Furthermore, there is an increased attention on ing Equations: hybrid power plants that combine different technologies to produce h electrical power. As a result, the dynamic simulation programmes z D D ¡ ¡ ¡ pout ð : Þ hturb;st hinl;st href hinl;st href 2 105 must extend their existing libraries with new models for wind tur- pinl bines, solar and fuel cells applications. Examples of hybrid systems F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 103 areTagedP the integrated solar combined-cycle power plant (ISCC) and the TagedPvolume fraction of solid is constant, while the volume fraction of hybrid fuel cell/gas turbine power plant. solid in the lean region decreases exponentially with height.
2.3.5.1.TagedP Combustion chamber. TagedPThe combustion of the fossil fuel takes 2.3.5.3.TagedP Fuel cell. ATagedP fuel cell converts chemical energy into electricity place in the combustion chamber. The combustion chamber model and forms water. The fuel cell has two electrodes, namely anode and has oxidiser inlet (generally air or oxygen), fuel inlet (such as coal, cathode. Generally, hydrogen is the basic fuel, but fuel cells can also oil or gas) and flue gas outlet. Compared to combustion process of extend their fuel range to cover methane. There are four different liquid or gaseous fuels, the combustion of solid fuels (coal, biomass types of fuel cells, including molten carbonate (MCFC), solid oxide or municipal solid waste) is more complex, including three major (SOFC), phosphoric acid (PAFC) and proton exchange membrane mechanisms: drying, pyrolysis and oxidation. The flue gas formed (PEM). The selection of the fuel cell type depends on the specific during combustion consists generally of O2,N2,CO2,H2O, SO2 and application; whether large or small scale, stationary or mobile. Ar. The combustion calculation that predicts the composition of the TheTagedP modelling of a fuel cell requires the consideration of chemi- flue gas requires the type of fossil fuel, the fuel mass flow rate, the cal reactions and additional components involved. For example, the Air/fuel ratio, temperature etc. Determining the exact composition is simulation model of a solid oxide fuel cell includes a natural gas of high relevance for defining the material properties of the flue gas. reformer and a sulphur removal unit. The fuel cell model is con- The mass flow balance in the combustion chamber can be expressed nected on the one hand to the process components such as pipe or as: valve, supplying it with reactants such as air and fuel and discharg- ing products such as water. On the other hand, it is connected to the m_ ; D m_ ; C m_ ; ð2:110Þ out fg inl air inl fuel electrical system (electrical source). The voltage of the fuel cell is and accordingly the energy balance is written as: used as boundary condition for the electrical system, while the elec- _ D _ C _ ð : Þ tric current of the electrical network is transferred to the fuel cell mout;fghout;fg minl;airhinl;air minl;fuelLHVfuel 2 111 calculation and applied as input. Further information regarding the TagedP fl Here, the subscript fg refers to ue gas and the term LHV is the dynamic modelling of fuel cells can be found in the literature, for lower heating value of the fuel. In addition to the mass and energy example in [190,191]. balances, a balance equation for each substance is solved. Usually, the combustion chamber is operated under atmospheric pressure 2.3.5.4.TagedP Weather. AmongTagedP renewable energy sources, solar energy like in pulverised coal and incineration power plants. On the con- offers a promising option for electricity generation in the countries trary, the combustion chamber of a gas turbine is pressurised. with high solar radiation. Solar technologies can be divided into con- centrating solar power (CSP) and photovoltaic cells (PV). In the lat- TagedP TagedP fl 2.3.5.2. Fluidized bed. The uidized bed is a bulk of solid particles ter, the sunlight is directly converted into electrical energy using fl located in a vertical vessel and the gas or liquid ows from the bot- semiconducting materials. In CSP, the sunlight of a large area is con- fl tom via a porous plate or nozzles. The gas-solid uidized bed is char- centrated using mirrors or lenses onto absorber tubes, through acterised by several advantages such as high heat and mass transfer which a heat transfer fluid (generally oil or water) passes. The ther- rates, resulting in uniform temperature gradients in the bed even mal energy stored in the heat transfer fluid is used as a heat source with highly exothermic or endothermic reactions. Practical applica- for a power generation system. This should not be confused with fl tions of uidized bed reactors include CO2 capture in thermal power concentrator photovoltaics, a technology that directs concentrated plants by chemical or carbonate looping process as well as solid fuels sunlight to photovoltaic cells. Concentrated solar power plants are fi conversion, including gasi cation and combustion of coal, biomass showing increasing interest in field of research and application, fi fl and even fuel mixtures. Depending on the super cial uidization mostly as parabolic trough collectors and solar tower collectors. This fi velocity, it can basically be distinguished between xed bed, station- is due to the fact that the CSP technology can easily be coupled with fl fl fl ary uidized bed and circulating uidized bed. The uidized bed can, thermal energy storage and with fossil fuel combustion system, generally, be divided into a dense phase zone and a lean zone. In the increasing the plant availability, especially during low radiation dense zone, there is a higher concentration of solids near the air dis- periods. However, the daily and monthly variation of the solar radia- tributor plate. It can be differentiated here between two phases: the tion is a main drawback. emulsion phase (uniform mixing of gas and solids) and the bubble TheTagedP solar radiation module considers the variation of solar radia- phase (only gas). The dense zone is followed with the lean zone, in tion at different periods of day. It calculates the solar position and fl which the concentration of solids decreases sharply as the ow both beam and diffusive irradiation on the horizontal surface accord- moves upwards. ing to input parameters such as geometric coordinates of the field, TagedP Basically, there are two different numerical approaches for the time, elevation from sea level and clear sky index. The data from fl fl representation of gas solid ow in the uidized bed (Euler Euler solar radiation module can be used to determine the total amount of and Euler Lagrange). In the Euler Euler method, also known as irradiation that is passed to different types of surfaces with different fl two uid method, each phase is regarded as a continuum and is angles of inclination. The direct irradiance received per unit area by mathematically calculated by solving the balance equations. The a surface normal to the sun is defined as direct normal irradiance Euler Lagrange approach combines the continuum descriptions of (DNI). Using DNI values obtained from weather stations at the loca- fl uid phase with the Lagrange representation of dispersed phase on tion, the absorbed solar energy by an absorber tube can be computed the basis of Newton's transport equations. Although these numerical as follows: models described here are already implemented in 3D simulation D ðÞðÞ ð : Þ programmes such as ANSYS-FLUENT (among others publications Sabsorb DNI cos u AaperhoptEtrackfdustfcleanfrow;shadfend¡losskIAM 2 112
[183,184]), OpenFOAM and CPFD-BARRACUDA (among others publi- with the mirror aperture area Aaper and the incidence angle u.D85XX The cations [185 188]), they are not suitable for 1D process pro- symbol hoptD86XX represents the optical efficiency and Etrack is a tracking grammes used to simulate the entire thermal power plant system. error. The reduction in the absorption energy due to several factors Therefore, semi-empirical models such as Kunii and Levenspiel can also be considered, including dust on the absorber glass cover
[189] are preferred by reason of low computational cost. In this fdust, mirror cleanliness fclean, row shadowing frow,shad and end-losses fl model, the uidized bed is divided into two regions (dense and lean fend ¡ loss caused by spacing between solar collector elements, spacing regions), interacting each other based on several assumptions. The between solar collector assembly as well as the non-zero incidence dense region describes the lower part of the rector, where the angle. When the angle of incidence increases, losses that can arise 104 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 dueTagedP to additional reflection and absorption by the glass envelope are twoTagedP strategies can be generally applied, either the use of low sulphur corrected by the incidence angle modifier (IAM).D87XX coal or installing scrubbers. Commercialised technologies for sul- phur scrubbing include wet, semidry and dry processes. For thermal 2.3.5.5.TagedP Mill. MillsTagedP are mechanical devices used to break different power plants, the technology of choice is the wet flue gas desulfuri- types of solid materials in small pieces by grinding, crushing or cut- zation (WFGD) scrubber and in case of lower sulphur oxides emis- ting. In pulverised coal-fired power plants, a pulveriser coal mill sions is the dry flue gas desulfurization (DFGD). grinds the raw coal into a combustible dust. Here, the coal particles ATagedP promising method to reduce CO2 emissionsisthecarboncap- are dried by flue gas or hot air and milled to fine size, so that stable ture and storage (CCS). Depending on the manner of CO2 capture combustion and complete burn-out of pulverised coal can be and the oxidation of fuel, it is distinguished between three CO2 cap- achieved in the combustion chamber. The coal properties such as ture methods, namely pre-combustion, post-combustion and oxy- volatile components, ash content, hardness, humidity and grinding fuel. In the pre-combustion approach, the carbon dioxide is fineness are the decisive factor for selecting the required mill. Basi- separated before the combustion process. The coal is gasified in a cally, coal pulverisers can be divided into three assembly groups, first step at higher pressure levels and the syngas consists essen- impact mills, gravity-force mills and external force mills. The impact tially of carbon monoxide and hydrogen. In a subsequent water-gas mills such as hammer and beater wheel mills are classified as high shift reaction, the carbon monoxide reacts under the supply of speed mills. While the hammer mill is suitable for lignite and hard steam to carbon dioxide and additional hydrogen. The flue gas in coal, the beater wheel mill is preferred for lignite, but can be used the post combustion process, which is basically consists of nitro- conditionally for hard coal. The gravity-force mills are low speed gen, oxygen, carbon dioxide and steam, is further treated. Here, dif- mills and well suited for wet and hard coal. Due to their construc- ferent concepts are developed such as the chemical scrubbing of tion, they are identified as tube mills. When considering the design flue gas (among others, Diao et al.D8XX[195]) and the carbonate loop- of external force mills, different constructions are well-known such ing process (among others, Strohle€ et al.D89X[196]X ). In the third method as bowl mill and roller mill. In such medium speed mills, the grind- (the oxyfuel process), the coal is combusted with pure oxygen. ing bowl is rotated by a gearbox, while the grinding parts are pressed After cleaning the flue gas from pollutants and separation of the by external force either by springs or hydraulic cylinders against the steam by a condensation process, the fluegasconsistsofpureCO2 grinding track. The external force mills are suitable for harder coals, that can be compressed for transport and storage. Due to the provi- showing different advantages such as high grinding performance, sion of the pure oxygen using an air separation unit, there is an low wear and low power consumption. enormous loss of overall efficiency of 8 14 percentage points AlthoughTagedP the dynamic of the mill has a significant influence on [197]. The combustion of solid fuels by means of the chemi- dynamic behaviour of the entire coal-fired power plant, the mill is, cal looping process, a new combustion concept, enables a CO2 cap- generally, modelled as a mixing point of the coal and the primary air ture with low energy input. Here, air and fuel are kept separate, and for purposes of simplification. In this mixing point, the water content the oxygen is transferred from the air to the fuel by use of an oxy- of the coal is evaporated under the assumption that no combustion gen carrier material. Generally, particles containing a suitable will take place. If it is required, complex pulveriser models, e.g. metal oxide are used as oxygen carriers and these particles are [192 194] can also be applied to achieve accurate dynamic behav- moved between two coupled, circulated gas solid fluidized beds iour of pulverised coal-fired power plants. (air reactor and fuel reactor). In an ideal case, the flue gas at the
fuel reactor outlet consists of CO2 and H2O. The latter can be easily 2.3.5.6.TagedP Flue gas control. ParticulateTagedP matter, nitrogen oxides (NOx), removed by condensation [198,199]. sulphur oxides (SOx) and carbon dioxide (CO2) emissions emitted by ForTagedP the modelling of flue gas cleaning devices (dust removal, NOx the combustion of fossil fuels contribute to global climate change removal, SOx removal and CO2 capture), the standard library compo- and might present a hazard for health and environment. The energy nents of dynamic simulation programmes are generally insufficient system in terms of conversion of fossil fuels as a major emission apart from a few exceptions (e.g. ASPEN Plus DYNAMICS). Therefore, source is in the focus of attention. Flue gas cleaning systems are simple numerical models are used, in which the flue gas cleaning therefore considered as an essential part of modern thermal power systems such as electrostatic precipitator and selective catalytic plants. reduction unit are modelled as pressure drops and thermal masses. FossilTagedP fuels, except natural gas, contain non-combustibles that Thus, detailed models of flue gas cleaning components should be the form the majority of the particulate in the flue gas such as ash and subject of further research. some amount of unburned carbon. Particulate control equipment is therefore required to remove particulate, keep the particulate from 2.3.6.TagedP Examples re-entering the flue gas and discharge the collected material. Differ- InTagedP the previous sections, different process components such as ent types of particulate control equipment are available, including thin-walled and thick-walled tubes as well as turbomachines are electrostatic precipitators, fabric filters, mechanical collectors and presented. Base modelling of thermal power plants is carried out by venturi scrubbers. selecting the process components and combining them to generate a
TheTagedP term NOx denotes cumulative emissions of nitric oxide (NO), model of an existing system and/or a new process for research. nitrogen dioxide (NO2) and other nitrogen-bearing species. In ther- Although the building of a model is generally limited by the program mal power plants, there are three principal mechanisms of NOx for- libraries, a specific component may be modelled by combining vari- mation, namely thermal NOx, fuel-bound NOx and prompt NOx.A ous existing process components. All necessary specifications can be reduction in NOx emissions can be achieved using primary and sec- inserted in the components that are linked by flows of either mate- ondary techniques. The primary measures for NOx aim to reduce rial, energy or heat properties to finish construction. Here, two dif- both peak temperature and residence time at peak temperature, ferent examples are selected from the scientific literature, showing including fuel/air staging, over fire air, less excess air, flue gas recir- detailed dynamic models of a combined-cycle power plant built in culation and combustion optimisation. The secondary techniques ASPEN PLUS DYNAMICS [38] and a pulverised coal-fired power plant are based on chemical reduction of NOx such as selective catalytic built in APROS and in MODELICA [21,53]. reduction (SCR) and selective non-catalytic reduction (SNCR). InTagedP Fig. 8, a combined-cycle power plant model that comprises a MostTagedP sulphur emitted to the atmosphere oxidizes slowly to sul- gas turbine connected to a vertical gas path is illustrated. The heat phur dioxide (SO2) that is a reactive and acid gas. In the combustion recovery steam generator that is arranged downstream of the gas of fossil fuels, large quantities of SO2 are emitted. For SO2 control, turbine is unfired. The water/steam circuit is a three-pressure-stage F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 105 withTagedP forced circulation in the HP, IP and LP evaporator paths and InTagedP the air/flue gas system, the primary air is supplied by two reheater section after the high pressure turbine. Process components speed controlled radial fans and flows through the regenerative used to build the model are: heat exchangers, drums, pumps, tur- air preheater into the mill (pulverizer). The coal dust is entrained bines, pipes, valves and attemperator. Furthermore, different con- with air, fed into the furnace and burned. The secondary air is trollers and electrical components are used. The LP feedwater supplied by two parallel forced draft fans, which are specified as directed to the LP economiser is supplied by the condensate pump. axial fans with variable blade angle. Afterwards the secondary air A control valve for the LP drum level is located between the LP econ- passes a steam coil air preheater and the regenerative air omiser outlet and the LP drum and the heated water flows into the preheater, before entering the furnace. In order to consider the LP drum. In the LP drum, the water circulates through the LP evapo- false air, which is impossible to avoid in a balanced-draft system, rator tube bundle, where it is heated by the gas turbine exhaust gas ambient air is introduced at the hopper of the steam generator and converted into saturated steam. The saturated water in the LP and adjusted for the nominal case. After exiting the steam genera- drum is separated and a significant portion of the flow is directed tor, the now 350 400 °C hot flue gas flows through the selective into the HP and IP circuits via high and intermediate boiler feed catalytic reduction, the regenerative air preheater, the electro- pumps (HP BFP and IP BFP). The dry steam exits the LP drum and static precipitator and the induced draft fan that keeps the fur- flows through the LP superheater. After leaving the superheater, the nace at a slight negative pressure. superheated steam enters the LP turbine. Process water is extracted from the LP circuit for fuel gas preheating, before it is returned to 2.4. Automation system the condenser. TheTagedP feedwater flows into the HP drum via the HP economisers. InTagedP dynamic simulation, the selection of suitable control structures The water in the HP drum circulates through the HP evaporator with is essential in order to accurately describe the behaviour of thermal the help of the forced circulation pump (HP RP). The recirculated power plants during transients. The automation components, water is heated by the flue gas and converted into saturated steam explained below according to Refs. [169,200,201], include measuring in the HP drum. While the liquid stays in the drum and mixes with devices, analogue and binary modules, signal sources and control- water coming from the HP economisers, the steam exits the drum lers. and flows to the HP superheaters. The steam flows through the high pressure superheaters, where it absorbs additional heat from the 2.4.1.TagedP Measurement modules flue gas. The HP superheated steam exits the HRSG and enters the MeasuringTagedP devices collect data on the physical properties and HP turbine section. A high pressure attemperator is provided at the transmit them in analogue signals. The output signal of a measuring inlet of the last superheater to control the temperature at the inlet of device can be used as an input signal for a control structure or for the HP turbine. The water for the HP attemperator is taken from the other purposes such as operation monitoring or data recording. Mea- high pressure feedwater pump. The high pressure feedwater mass suring values from thermal power plants include but are not limited flow is controlled by the HP drum level control valve that is located to pressures, temperatures, mass flow rates and levels. upstream of the HP economisers. Generally, the analogue structure TheTagedP pressure and temperature measurement modules can be applies to the IP circuit. applied to record the pressure and temperature of different process InTagedP Fig. 9, a pulverised coal-fired power plant is modelled using components such as points, tanks, headers, pipes, etc. two dynamic simulation programmes APROS and MODELICA. The yp D yp power plant consists of an air/flue gas system and a water/steam out inp ð : Þ system. In the steam generator, the chemically bond energy of the 2 113 yT D yT coal is converted into heat that is transferred from the flue gas side out inp to the water/steam circuit and used to generate steam for a Rankine TheTagedP flow measurement module can be used to record the mass cycle. flow rate through pipes, channels and valves. InTagedP the water/steam system, the feedwater enters the economiser y _ D y _ ð2:114Þ (ECO) at the top of the steam generator. The water is then directed outm inpm to the membrane wall evaporator, where the evaporation takes TheTagedP level measurement module can be applied to record the level place. Due the once-through design the evaporation zone is not in different components such as tanks and condensers. defined and the two-phase region is load dependent. For low part yL D yL ð2:115Þ load operation, during start-up or shut-down, a forced circulation is out inp in operation. A cyclone is installed to separate the water droplets ItTagedP should be mentioned that measurements devices may cause a within the steam flow and a separator storage tank is used for phase pressure drop in the flow. This pressure drop is typically not consid- separation. The circulation is forced by a circulation pump (CP) and ered in measurement modules and can be considered separately, if the level is controlled by a circulation control valve. The circulated required. mass flow re-enters the steam generator at the economiser inlet. The produced steam, saturated or partly superheated, enters the 2.4.2.TagedP Analogue modules steam cooled supporting tube system (superheater 1) of the con- AnalogueTagedP modules are used to modify analogue signals. In these vective heat exchangers and flows downwards to the super- modules, the output signal is always analogue, but in addition to the heater 2 (platen superheater). After the platen superheater, the analogue input signal, a binary signal may be found for controlling steam flows through superheaters 3 and 4. In between the super- tasks. The analogue modules can be divided in three groups, namely heaters, three attemperator stages are arranged for steam tem- basic, static and dynamic modules. These are explained in detail in perature control. The reheater is divided into two heat the following sections. exchangers and has one attemperator. The steam leaves the once-through steam generator and flows through the high pres- 2.4.2.1.TagedP Basic modules. TagedPAnalog basic modules are adder, multiplier, sure turbine before re-entering the steam generator via the divider, mean value, setpoint and signal splitter (see Fig. 10). The reheater. Afterwards the steam fully expands in one intermediate adder module is applied to add or subtract the signals yinl,1,yinl,2 and turbine and two low pressure turbines to condenser pressure. yinl, i. The output signal yout is calculated according to the equation: The condensed water is fed through seven feedwater preheaters y D§y ; § y ; § ... § y ; ð2:116Þ back to the steam generator. out inl 1 inl 2 inl i 106 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 8. Combined-cycle power plant modelled in ASPEN PLUS DYNAMICS (adapted from reference [38] with permission of authors and Elsevier).
TheTagedP multiplier module can be used for a multiplication of ana- TheTagedP divider is a module that can be used for a division of logue signals. The output signal is calculated using the following two analogue signals. The value of the output signal is calculated equation: as: y D y ; y ; ... y ; ð2:117Þ ynum out inl 1 inl 2 inl i y D ð2:119Þ out y AnTagedP amplifier is a special case of the multiplier module and used to den TagedP amplify the input signal yinl by a factor KP. The result is yout: The value of the denominator signal must not be equal to zero. TagedP D ð : Þ The mean value module calculates the average value of analogue yout kP yinl 2 118 input signals. The output signal yout is expressed as: F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 107
Fig. 9. Pulverised coal-fired power plant; (a) modelled in APROS and (b) modelled in MODELICA (reproduced from references [21,53] with permission of authors, Elsevier and Cre- ative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/).
TagedP TagedP 8 y ; C y ; C ... C y ; < y D inl 1 inl 2 inl i ð2:120Þ 0 case t T out ðÞD ð : Þ N yout t : 2 122 ðÞ¡ > TheTagedP symbol N represents the number of input signals. yinl t T case t T TheTagedP term “setpoint” refers to the target value of a variable. The set- TheTagedP memory module is used as memory for an analogue signal point module may have two operation modes (normal and tracking). value. The module has an analogue input signal, an analogue output In normal operation, the output signal is constant. For example, the signal and a binary input signal. If the binary input signal has the control system of the boiler aims to maintain the steam temperature value FALSE, the output signal value is equal to the input signal at inlet of the steam turbine at a constant temperature setpoint. In the value. If the binary input value is changed to TRUE, the value of the tracking operation, the output signal is not constant and follows the output signal is fixed and remains independent of the input signal value of the input signal either immediately or with a given gradient. value changes. TheTagedP signal splitter divides the same signal in two information TheTagedP switch module can be considered as selector between two fl ows. The input signal is yinl and the outlet signals areyout,1 and yout,2. analogue signals. It has two analogue input signals, a binary input D D ð : Þ signal and an analogue output signal. The output signal follows the yout;1 yout;2 yinl 2 121 first input signal, if the binary input is TRUE and follows the second input signal, if the binary input is FALSE. This can be described math- TagedP TagedP 2.4.2.2. Static modules. Analogue static modules include delay, ematically with the help of the following equation: memory, switch, dead band, hysteresis, limiter, Max and Min selec- 8 D tor, polyline and square root (see Fig. 11). Some of the static modules < yinl;1 case ybin 0 D ð : Þ such as dead band and limiter are a source of discontinuity, which in yout : 2 123 D return may result in numerical instability of the simulation. yinl;2 casey bin 1
ATagedP delay module shifts the given value of an input signal yinl by a TheTagedP dead band module has an analogue input signal and an ana- time constant T. The outlet signal yout is expressed as: logue output signal. When the absolute value of the input signal is 108 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 10. Analogue basic modules; (a) adder, (b) multiplier, (c) divider, (d) mean value and (e) setpoint.
smallerTagedP than the defined dead band value (DB), the output signal is forTagedP two input signal is: 8 equal to zero. If the input signal value is bigger than DB, the output < yinl;1 case yinl;1 yinl;2 signal is the input signal value minus the dead band value. If the D ð : Þ yout : 2 126 input signal value is less than the negative dead band value (¡DB), < yinl;2 case yinl;1 yinl;2 the output value is then the sum of the input signal value and the TagedP dead band value. These relations are expressed by the following The equation for minimum value selection for two input signal is equation: expressed as: ( 8 j j < yinl;1 case yinl;1 yinl;2 > 0 case yinl DB <> yout D ð2:127Þ > D ð : Þ yinl;2 case yinl;1 yinl;2 yout y ¡DB case y DB 2 124 > inl inl :> TheTagedP function module can be used to form a polyline (n-point C < ¡ yinl DB case yinl DB cross line curve) between two variables. The value of the output TheTagedP hysteresis module is used to form a hysteresis effect to an signal is a function of the input signal and the given polyline. analogue signal. The value of the output signal will follow the input Thepolylinewillbedefined by a set of (x, y)coordinatepairs.If signal, so long as the value of the input signal is changing to the the input signal value is out of the range of the defined x coordi- same direction. If the direction changes, then the value of the output nates, the value of the output signal equals the function value of signal is held constant as long as the total change to that new direc- the last x coordinate. tion is smaller than the defined hysteresis value. TheTagedP square root module returns a square root of an input signal
ATagedP limiter limits the signal yinl within a predefined range using a value. The output signal is expressed as: highD90XXlimit value LD91XX and a low limit value L . If the value of the pffiffiffiffiffiffiffiffiffiffi high low y D jy j ð2:128Þ input signal is between the given limits, the value of the output sig- out inl nal follows the value of the input signal. These can be expressed as: 8 TagedP TagedP 2.4.2.3. Dynamic modules. Analogue dynamic modules include gra- > yinl case Llow yinl Lhigh <> dient, integrator, differentiator, derivator and filter. y ¼ L case y < L ð2:125Þ TheTagedP gradient module limits the rate of variation for a variable. out > low inl low :> The rate of variation can be limited separately for increase and for L case y > L high inl high decrease direction. The value of the output signal follows the TheTagedP Max and Min modules are signal selectors. The value of the changes of the input signal considering the defined gradient limits. output signal is equal to the highest value of the input signals in case The value of the output signal is the same as the input, if the change of a Max operator and is the smallest value of the input signals in in the input signal is slower than the defined gradient or the input case of a Min operator. The equation for maximum value selection signal does not change.
Fig. 11. Analogue static modules; (a) delay, (b) memory, (c) switch, (d) dead band, (e) hysteresis, (f) limiter, (g and h) max and min selector, (i) polyline and (j) square root. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 109
TheTagedP integrator and differentiator modules are simple control com- isTagedP in TRUE state. The output signal is only FALSE, if all input signals ponents. The output value of an integrator module can be expressed as: are in FALSE state. 8 Zt < D D 0 case yinl;1 0 and yinl;2 0 1 D ð : Þ yout ðÞt D y ðÞt dt ð2:129Þ yout 2 132 T inl : D D int 1 case yinl;1 1oryinl;2 1 0 TheTagedP rate of change of the output value is determined according to UsingTagedP the logical operator “NOT”, the state of the binary input sig- the given integration time Tint and the value of the input signal. If nal can be inverted. It has only one input signal and one output sig- the input signal is positive, the output value is increasing. If the value nal. ( of the input signal is negative, the output value is decreasing. The D 0 case yinl 1 output value remains constant, when the input value is zero. For yout D ð2:133Þ D example, if the integration time is set to 60 s and the input signal is 1 case yinl 0 1.0, the output value will increase to 1.0 within 1 min. TagedP fi The differentiator module can be represented as rst-order ordi- 2.4.3.2.TagedP Advanced modules. TagedPThe advanced binary modules include, nary differential equation. The rate of change of the output value is among others, delay, switch, n/m selector, flip-flop, limit value calculated according to the given derivation time Tder and the value checker, button, alarm and timer (see Fig. 13). of the input signal yinl as: TheTagedP delay module shifts a binary signal in time. It has one binary dy input signal and one binary output signal. The output signal will fol- y D T inl ð2:130Þ out der dt low the input signal after a given delay time, which can be constant or varied by an analogue signal. Mathematically, this relation can be TheTagedP derivator module defines the rapid changes of a variable. written as follows: The output signal of the derivator depends on the derivation time ; D ðÞ D ¡D ðÞ ð : Þ and the derivation gain. The latter calculates the height of the yout t Tt yinl t Tt 2 134 impulse, while the derivation time determines the duration of the TheTagedP switch module is a selector between two binary signals. It impulse. Using these parameters, it is possible to define the step has two input binary signals, an output binary signal and an input response of the derivator module. If the value of the input signal binary control signal. The state of the output signal follows the state does not change (steady state case), the value of the output signal of either of the two input signals depending on the control signal. is zero. ( D TheTagedP filter module performs a filtering operation on an analogue yinl;1 case ycon 1 D ð : Þ signal. The value of the output signal is determined according to the yout 2 135 y ; case y D 0 input signal value and the filter parameters. The simplest filter is a inl 2 con moving average filter. The only parameter in this case is the time TheTagedP n/m selector is a logical selector module for binary signals. constant of the filter Tfil. The symbol m denotes the number of input signals, while the symbol n is a given positive integer. The output signal is TRUE, when at least n number of input signals are in TRUE state. Otherwise, the output TagedP 2.4.3. Binary modules signal is in FALSE state. TagedP Binary modules (Boolean logic elements) are required for TheTagedP flip-flop is a bistable element, i.e. it has two stable states. The selection purposes in many control circuits. In such modules, the flip-flop module can be used as a memory in logical circuits. The input can be binary or/and analogue signals, while the output is state of the output only can be changed with a TRUE input signal, always binary. Therefore, when an expression is evaluated by either SET or RESET signal. The output signal is: binary modules, the output signal is ether zero or unity (zero means FALSE and unity means TRUE). The most relevant binary TagedP FALSE, if both input signals (SET and RESET) are in FALSE state. modules used in the dynamic simulation of thermal power plants TagedP FALSE, if the RESET input only is in TRUE state. are explained below. TagedP FALSE, if both inputs are in TRUE state and the RESET input is dominating. 2.4.3.1.TagedP Basic modules. InTagedP Fig. 12, basic binary modules (AND, OR and TagedP TRUE, if the SET input is in TRUE state. NOT) are depicted. The logical operator “AND” is applied in order to TagedP TRUE, if both inputs are in TRUE state and the RESET input is not perform a logical operation AND for binary signals. The output signal dominating. is TRUE, when all input signals are in TRUE state. If one of the input signals is in FALSE state, the output signal is FALSE. ( TagedP D D The limit value checker compares the analogue input value to a 0 case yinl;1 0 or yinl;2 0 given limit value LV, resulting in the following output signal: yout D ð2:131Þ D D 1 case yinl;1 1 and yinl;2 1 TagedP TheTagedP operator “OR” is used to perform a logical operation OR for FALSE, if the value of the analogue input signal is greater than the binary signals. The output signal is TRUE, if any of the input signals given limit value.
Fig. 12. Basic binary modules; (a) AND, (b) OR and (c) NOT. 110 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 13. Advanced binary modules; (a) delay, (b) switch, (c) n/m selector, (d) flip-flop, (e) limit value checker, (f) button, (g) alarm and (h) timer.
TagedP TRUE, if the value of the analogue input signal is smaller than the comparesTagedP it to a given max time value. The output signal is in FALSE given limit value. state, so long as the max time value is not reached. When the max time value is reached, the output signal is in TRUE state. The timer ThisTagedP relation can be expressed mathematically using the follow- module can also be used as an analogue module. In this case, the ing equation: time is given as analogue output value. Moreover, the timer can be ( reset via a RESET signal. 0 case yinl LV yout D ð2:136Þ < 1 case yinl LV 2.4.4.TagedP Signal source modules TagedP fi TheTagedP limit value checker module can also form a hysteresis effect The signal source modules can be applied to de ne transient set- to an analogue signal. In this case, an additional hysteresis value HV points or to generate binary or analogue signals. These include pulse, has to be given. The output signal is: noise, sine or cosine wave, square wave and triangular wav genera- tor (see Fig. 14). The mean value of the output signals for analogue TagedP FALSE, if the analogue input signal is bigger than the given limit signal generators is zero. In the signal source modules, the output value plus the half of the hysteresis value. signal is a function of time: TagedP TRUE, if the analogue input signal is smaller than the given limit yout D f ðtÞ ð2:139Þ value minus the half of the hysteresis value. TheTagedP pulse generator module generates binary pluses. The module has a binary input signal, an analogue input signal and a binary out- Accordingly,TagedP the following equation can be formulated: 8 put signal. When the input signal is FALSE, the output signal is > 0 case y LV C HV=2 always in FALSE state. If the input signal is changing from FALSE to <> inl TRUE, the module will generate pulses. Each pulse lasts for half of y D ¡ = < C = ð2:137Þ out > constant case LV HV 2 yinl LV HV 2 fi :> the de ned period time, which can be constant or varied according < ¡ = 1 case yinl LV HV 2 to the analogue input signal. TheTagedP noise generator module generates random signal with a ATagedP cold junction is a special case of the limit value checker. Here, constant power spectral density. The module has a binary input the analogue signal is compared to another analogue signal, instead signal that is used to switch off the generator, an analogue input of the limit value in case of the conventional module. The output signal that is used to define a given variance and an analogue value is then: output signal. When the binary input is in FALSE state, the value of the output signal will be zero. If the generator is switched on, TagedP FALSE, if the value of the first analogue input signal is bigger than themodulewillgeneratenormallydistributedwhitenoiseofa the value of the second analogue input signal. given variance. TagedP TRUE, if the value of the first analogue input signal is smaller than TheTagedP sine wave generator module generates a sine wave. The the value of the second analogue input signal. amplitude and the time period of the sine wave can be constant or varied depending on analogue input signals. A cosine wave has a Mathematically,TagedP this relation can be written as: ( shape identical to that of a sine wave, with a phase-shift of p/2 radi- 0 case yinl;1 yinl;2 ans. D ð : Þ yout 2 138 TheTagedP square wave generator module generates square waves. It 1 case y ; < y ; inl 1 inl 2 has one binary input, two analogue inputs for amplitude and the TheTagedP button module has only an output signal. When the button is time period of the generated wave and one analogue output. The pushed, the output is in TRUE state. After a certain period of time output of the module is zero, if the binary input is in FALSE defined by user, the output value returns to FALSE. state. When the generator is switched on, the module will gener- TheTagedP alarm module provides alarms triggered by logical signals. If ate square waves according to the given amplitude and the time the input signal shows the desired value (TRUE or FALSE), the mod- period that can be constant or varied following the analogue ule sends an alarm message. input signals. TheTagedP timer module has an inlet and an output signal. When the TheTagedP triangular wave generator module generates triangular inlet signal is set to TURE, the timer starts counting the time and waves and can be switched on/off by a binary input signal. The F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 111
Fig. 14. Signal source modules; (a) pulse generator, (b) noise generator, (c) sine and cosine wave generator, (d) square wave generator, and (e) triangular wave generator.
TagedP TagedP FF amplitude and the time period of generated triangular waves can be controller and yout is the output of the feedforward (FF) part of the defined by two analogue inputs. controller. TheTagedP transient equation of a PID controller is expressed as: 2.4.5.TagedP Controller modules Z KP dyinl TheTagedP well-known control schemes in process and energy systems yout D K y C y dt C K T ð2:141Þ P inl T inl P D dt are explained briefly below. These include feedback control, feedfor- I TagedP ward control, feedforward plus feedback control, cascade control The parameters KP,TI,TD represent gain, integration time and der- and cascade plus feedforward control [202]: ivation time of the controller, respectively. In order to obtain a PD or a PI controller, TI !1 or TD D0 can be specified. In the control schemes of thermal power plants, the controllers applied are PI and TagedP Feedback control scheme: A feedback control system represents PID controller. For the determination of controller parameters, sev- the simplest form of closed loop control scheme. The error signal eral tuning methods can be found in the literature, namely stereo- resulting from the comparison between the process output and typical tuning methods and intelligent methods. The stereotypical the setpoint is used as a means for the controller. tuning methods include Ziegler Nichols, relay auto-tuning, pole TagedP Feedforward control scheme: A feedforward control responses to placement and internal model control [204]. The intelligent methods the moment when the disturbance occurs. The process variable use fuzzy logic, genetic algorithms, artificial neutral networks and adjustment is therefore based on the knowledge of the process particle swarm optimization for finding the controller parameters using mathematical model and measurement disturbances with- [205]. out having to wait for a deviation in the process variable. Due to WhichTagedP control scheme is more appropriate to control a process, it modeling errors and unmeasured disturbances, a flawless feed- cannot be completely stated. For example, feedforward control may forward control is not possible and is, generally, used in combi- show in some cases better performance than feedback control or nation with a feedback control. cascade control. A detailed understanding of the invistagted process TagedP Feedforward plus feedback control scheme: In this control sys- and the control theory are therefore required in order to obtain a tem, the roll of the feedforward controller is to decrease or elimi- physically meaningful operation. Further information can be found nate the effect of outer disturbances, while the feedback for example in [206,207]. controller will respond to setpoint variations. Compared to a feedback control system, this combined control technique can significantly give better response to a disturbance that can be 2.4.6.TagedP Examples measured, before it affects the process output. TheTagedP control structures consist of various components such as TagedP Cascade control with and without feedforward control schemes: controllers, analogue and binary components, which are combined The cascade control consists of two loops, namely an inner loop in order to satisfy certain control requirements. In this section, dif- and an outer loop. This control scheme leads to the benefits ferent control structures used in thermal power plants, including required, only when the inner loop has faster dynamics as com- drum level, steam bypass and feedwater control circuits [14,38] are pared to the outer loop [203]. The cascade control is frequently explained as examples. used within the control circuits of thermal power plants. A com- TheTagedP three-element level controller is used to adjust the water bination of cascade and feed-forward control is achieved, in level in different power plant components such as feedwater storage which the primary and the secondary processes are controlled by tank, feedwater preheater and drum. In Fig. 15, the three-element a cascade control, while the disturbance rejection is obtained level controller of the drum in a heat recovery steam generator is using a feedforward control. illustrated. The controller adjusts the feedwater mass flow rate by controlling the feedwater valve, which is located between the boiler feedwater pump and the economisers. The operation algorithm of TypicalTagedP variants of controller used in these control schemes the drum level controller is described as follows: on the one hand, are P-controller, I-controller, PI-controller, PD-controller, and the difference between the feedwater mass flow rate and the steam fl _ PID-controller. The output of the controller yout is determined mass ow rate dm is measured. On the other hand, the difference according to the control deviation of the controller and to possi- between the drum level setpoint and the actual value dL is measured. ble feedforward input. The deviation of these two paths (dm_ , dL) affects a PI-controller. The PI-controller commands the continuous device control (DC) that oper- y D yP C yI C yD C yFF ð2:140Þ out out out out out ates the drum level valve. If the pressure in the drum exceeds a certain TagedP P _ Here, the term yout represents the output of the proportional (P) value, the deviation (dm, dL) will be replaced by the pressure difference I part of the controller, yout is output of the integral (I) part of the con- between the drum and the maximum pressure setpoint in order to pre- D troller, yout denotes the output of the derivative (D) part of the vent further increase of the drum pressure. 112 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
TagedP TheTagedP high pressure bypass control circuit used in a combined- HPBPCV controls the high pressure to reach the pressure level, cycle power plant is depicted in Fig. 16. It routes the high pressure which was existent before the steam turbine trip. Holding the steam, which is not accepted by the high pressure turbine into the pressure at high level has the advantage that the HRSG is already cold reheater. This control circuit is in operation during the power prepared to the hot restart. TagedP plant start-up, as long as the high pressure steam quality has not In case of gas turbine load rejection, the gas turbine exhaust tem- D92XX matched the high pressure turbine requirements. Furthermore, the perature drops very fast to low level. In order to prevent the con- high pressure bypass system is used during the steam turbine trip at densation in the high pressure superheater, the HPBPCV will any load. A desuperheater has been installed, which cools the steam open to reduce the high pressure to its saturation temperature behind the high pressure bypass control valve to 50 °C above the sat- below the gas turbine exhaust temperature. urated steam temperature, before it enters the cold reheater system. The injection water is delivered from the high pressure feedwater ATagedP schematic representation of the high pressure feedwater pump. The main tasks of the high pressure bypass controller are to control structure used in a Benson HRSG is illustrated in Fig. 17. insure a smooth build-up of the high pressure during the start-up, to This control circuit offers the possibility to operate the high pres- prevent the high pressure from decreasing during the turbine trip sure system in level mode (nature circulation) or Benson mode and to prevent the condensation in the high pressure superheater in (once-through). Furthermore, it provides a save operation for case of a gas turbine load rejection. The principle of the work is as heat recovery steam generator during GT transients and fast follows: start-up procedures. The idea behind the feedwater mass flow controller is based on the heat of the flue gas that can be TagedP During the start-up procedure, both HP bypass valve (HPBPCV) absorbed by HP evaporators (DhFG, EVA) as well as the enthalpies and HP main steam valve (HPMSCV) are initially closed. This pro- of the working fluidatinletandoutletofHPevaporators(DhWS, cedure enables the pressure in the high pressure circuit to EVA). The obtained value is then corrected by the attemperators increase rapidly. When the minimum pressure setpoint is met, mass flowsasfunctionofthefeedwatermassflow, by the deriva- the HP bypass valve starts opening to counteract further rising of tive element for considering additional heat output of the metal the pressure. Due to the continuous pressure increasing, the masses of the evaporator (Kmetal,EVA), by the derivative element HPBPCV is forward opened. for considering mass storage process of the working fluid in the TagedP After the HP bypass valve is fully open, the steam pressure rises economizer (DrWS,ECO),bythedegreeofsub-coolingattheevapo- due to the steam generation increasing. At this stage, the auto- rator inlet (Dsub),bythedegreeofsuperheatingincaseofBenson matic setpoint adjuster is activated. It tracks the bypassed pres- mode (Dsup) or the steam quality in case of level mode (DxD93X)atX sure at interval about 1 bar below the high pressure. the evaporator outlet. Depending on the operation mode (level or TagedP fi When a speci ed high pressure is reached, the HPBPCV is throt- Benson), a further correction is also performed. While in level tled to intermediate start position (circa 70%). This process mode, the water level within the HP separator should be kept at fi ensures the high pressure to reach the xed pressure setpoint a fixed level independent from the HRSG load, the enthalpy at fi faster. After the xed pressure is met, the HP bypass valve limita- the outlet of the HP separator in Benson mode should meet the fi tion is switched off to hold the pressure at the xed value by fur- load dependent enthalpy setpoint. ther opening of the HPBPCV. TagedP When the main steam control valve starts opening, the HP bypass 2.5. Electrical system valve starts closing in the same attitude. If the HPMSCV is fully opened, then the HPBPCV is closed. The high pressure bypass InTagedP addition to process and automation components, a thermal valve could be again opened, if the pressure in the high pressure power plant contains several electrical modules that are vital for the fi circuit is increased over a de ned setpoint (the nominal pressure power plant operation. The consideration of electrical components pulse delta p) in order to discharge the high pressure. in dynamic simulation of thermal power plants is of high relevance TagedP In case of the steam turbine trip, the HP bypass control circuit is to calculate the electrical power consumption at base loads and put in operation. While the HPMSCV is immediately closed, the make sure that process and automation components get the needed
Fig. 15. Control circuit of the drum water level (extended from reference [38] with permission of authors and Elsevier). F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 113
Fig. 16. High pressure steam bypass control circuit; (a) schematic representation and (b) modelled in APROS (extended from reference [14] with permission of authors and Elsevier).
electricTagedP power during transients. Furthermore, electrical compo- blackout.TagedP In the latter, the electricity supply is lost and accordingly nents are used to evaluate the effect of possible failures in the elec- all motor driven components trip. The passive system should direct trical network on automation and process components and to study the power plant to a safe operation point, which can be assessed the power plant behaviour at severe break down cases such as using dynamic simulation models. 114 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 17. Control circuit of the feedwater mass flow rate in a heat recover steam generator (adapted from reference [14] with permission of authors and Elsevier).
TheTagedP electrical components required for the dynamic simula- lineTagedP represented by a resistance (Fig. 18-(a)and(b))oranACelec- tion of thermal power plants consist of node, line, switch, load, trical line with a pi equivalent circuit (Fig. 18-(c)). Each electrical generator, transformer, direct current source, battery, inverter, linehasaninputandanoutputconnectionnode,defining the alternating current/direct current converter and direct current/ positive direction of line from the input node to the output node. direct current converter. The node, switch, line and load compo- The type of the electrical line is automatically defined according nents can be applied to both alternating current (AC) and direct to the type of the connection nodes (both connection nodes must current (DC) electrical circuits. The battery and DC/DC converter be either DC or AC nodes). The electrical line has a built-in mea- are direct current modules, while the inverter and AC/DC con- surement for current, active power and reactive power. Transmis- verter connect direct current and alternating current circuits. sion electrical lines become transmission networks, when The generator and transformer can be used only in the alternat- interconnected with each other. ing current system. The electrical modules described below are InTagedP direct current electrical circuits, the power is always active explained as implemented in the process simulation software power in steady state. Furthermore, the capacitance or induc- (APROS) [169]. tance elements are generally not considered. The reactive power only exists considering transient cases. The impedance of a DC 2.5.1.TagedP Basic modules electrical line contains only an active part, while the reactive InTagedP an electrical system model, the basic electrical components are part is zero. The current in a DC electrical line has a homoge- node, line, switch and load. neous distribution over the cross-section A. Accordingly, the resistance per length l can be described by the following equa- 2.5.1.1.TagedP Electrical node. TagedPThe main function of the electrical node is to tion: connect other electrical modules to each other. It can be applied for l both alternating current and direct current electrical circuits (for R D r ð2:142Þ el A example, see Fig. 18). Here,TagedP the character relD94XXis the electrical resistivity that also known fi 2.5.1.2.TagedP Electrical line. TagedPThe electrical line is a component for as speci c electrical resistance or volume resistivity. The electrical modelling bulk transfer of electrical energy via the electrical resistivity is an intrinsic property, describing how strongly the mate- fl transmission line. The module can be a one phase DC electrical rial resists the ow of an electric current. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 115
Fig. 18. Models of a battery and a generator at a defined time during (a) discharging and (b) charging; (c) model of a direct current source followed by a DC/AC inverter.
2.5.1.3.TagedP Switch. TagedPThe switch is located between two electrical nodes circuitsTagedP (see Fig. 19). The generator is connected to one node. The and can be applied to direct or alternating current electrical circuits. electrical power produced by the generator is the mechanical power The order of nodes is insignificant, but they have to be same type, multiplied by the efficiency. The generator has built-in regulators for either DC (Fig. 18-(a) and (b)) or AC nodes (Fig. 18-(c)). The switch is frequency, voltage and power. controlled by a logical input. If the input signal is in TRUE state, the switch is closed. In this case, the switch is a kind of a transparent 2.5.2.2.TagedP Battery. TagedPA battery is an electric device, converting the module type, i.e. the electrical nodes on both sides of the switch stored chemical energy into electrical energy. The battery mod- have the same voltage. If the input signal is in FALSE state, the switch ulecanbeappliedtostoretheenergyoftheone-phasedirect is open and there is no connection through this module to another current or to supply current to the DC electrical circuits. The bat- node. tery is represented as a direct current source, variable initial resistor and energy charging level counter. The operation modes 2.5.1.4.TagedP Load. TagedPThe load module models the power consumption in of the battery include charge, discharge and stand-by. The alternating current or direct current electrical circuits. The charge/discharge processes of the battery depend on the voltage load is connected to one node by either a DC node (Fig. 18-(a) level of the direct current system and the remaining capacity of and(b))oranACnode(Fig. 18-(c)). The load has a built-in mea- the battery. surement for current, active power and reactive power. The reac- TheTagedP operating characteristics during the discharge of a battery tive power is zero, if the load is connected to a direct current depend on discharge capacity and voltage. The discharge capacity node. is a function of discharge current (loading), ambient temperature and long term warehousing, while the voltage is dependent on 2.5.2.TagedP Current sources modules discharging current and state of energy storage (loading time). TheTagedP current sources modules are power generation devices. It can The discharge capacity Q can be described by Peukert exponen- be distinguished between alternating current generators such as tial equation: electrical generator and direct current sources such as battery and QIðÞD CI1¡n ð2:143Þ solar photovoltaic. Here,TagedP the symbol I is the discharge current, n denotes the Peukert 2.5.2.1.TagedP Generator. TagedPThe generator module is applied to model the exponent with default value of 1.4 and C represents a factor that is production of electrical power in alternating current electrical calculated at the nominal point of the battery: 116 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 19. Model of a thermal power plant connected to a power grid.
TagedP
C D In t ð2:144Þ byTagedP the solar panel module are dependent on the consumption of TheTagedP discharge capacity decrease during a simulation time step Dt electricity in the electrical circuit and the I-V curve of the solar is calculated as: panel. D D D n 1¡n t ð : Þ 2.5.3.TagedP DC and AC modules Q I Inom 2 145 3600 TheTagedP DC and AC modules required to simulate the electrical net- TagedP The symbol Inom is the nominal current. The voltage is determined work include DC/AC inverter, AC/DC converter, AC/AC transformer with the formula: and DC/DC converter.
U D K1K2Unom ð2:146Þ 2.5.3.1.TagedP DC/AC inverter. TheTagedP inverter is an electrical device, convert- TagedP Here, Unom represents the nominal voltage, the factors K1 and K2 ing the voltage from direct current to alternating current. It can be are dependent on discharge current and discharge time. The dis- applied to convert DC electricity from solar panels, batteries or fuel charge current is determined by the electricity consumption of the cells to AC for the electrical grid. The DC/AC inverter is usually not DC system. The discharge capacity of a battery decreases for reduced suitable for inductive AC and sensitive electronic devices that can be ambient temperature, during long term warehousing or stand-by damaged by poor waveforms. without recharging. TheTagedP inverter module has two connection nodes and simulates TagedP The charging current can be expressed as a function of capacity: the transformation of DC electric power into three-phase AC Q¡0:6Q max : electric power (see Fig. 18-(c)). The input electrical node is a DC I D Inome 0 5Inom ð2:147Þ node, while the output node is an AC type. The DC/AC inverter where Qmax is the maximum capacity of battery and Inom represents module is represented as one electrical line ending in a node the nominal charging current. The internal resistance of the battery with a high base admittance (nearly zero voltage) to the DC cir- can be changed to control the charging current. cuit, in addition to an AC three-phase generator for supplying TheTagedP self-discharge process is simulated by decreasing the power to the AC circuit. The connection between the DC circuit capacity of the battery by a small amount during each time step. and AC circuit is arranged in such a way that the AC voltage is The dependent on the DC voltage and the AC apparent power is self-discharge of a battery can be considered in all operation equal to the power losses of the DC side resistance. As a result, modes (discharge, charge and stand-by). The self-discharge time the AC load is transferred into the DC supply side. of the battery depends mainly on the ambient temperature. For TheTagedP inverter component can either control the voltage of the AC example, at 40 °C, the capacity of the battery is assumed to circuit or supply the required power. In the power supply mode, the change from the maximum capacity to zero in 9 months. The power of the AC circuit is controlled according to the active power self-discharge time is 21 months at 30 °C, while it is 32 months setpoint. In the voltage control mode, the inverter controls the volt- at 20 °C. age of the second connection node according to the nominal DC volt-
age and voltage. Generally, the single phase DC voltage UDC of the 2.5.2.3.TagedP Solar photovoltaic. TagedPThe solar photovoltaic system, also inverter is higher than the required three-phase (phase to phase) known as solar panel, is a module type for production of DC electri- voltage UAC (approximately UDC D1.634UAc). cal power (see Fig. 20). The solar panel module is represented as DC current source with variable internal resistance and is connected to a weather component. The ideal DC source has constant internal 2.5.3.2.TagedP AC/DC converter. TagedPThe AC/DC converter is an electrical device, resistance, while the internal resistance of the solar panel changes converting the voltage from alternating current to direct current. non-linearly with solar radiation. The current and voltage generated This device can be found in several electrical circuits (e.g. charging F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 117
Fig. 20. Model of a solar panel with a battery and a load; (a) during the day and (b) during the night. batteries),TagedP but is characterised by poor current overload capacity and lines.TagedP Increasing the voltage by a step-up transformer at the gen- expensive automatic regulators. erating side of the power network decreases the capital cost and TheTagedP AC/DC converter module models the transformation of three- improves the voltage regulation of the system. With the help of phase AC electric power into a DC electric power (see Fig. 18-(b)). step-down transformer at the receiving end, the high voltage is This is represented as one electrical line ending in a node with a high reduced to the desired level for distribution to the consumers base admittance (nearly zero voltage) to the AC circuit and a direct (see Fig. 19). The transformer consists basically of two or more current source, supplying the voltage or power to the DC node. The coils that are electrically isolated from each other, but wrapped connection between AC and DC circuits is arranged to transfer the together around a closed magnetic iron circuit (core), allowing DC power loss into the AC supply side. In order to achieve that, the the electrical power to be transferred from one coil to other by DC voltage should be a function of the AC voltage and the DC appar- induction. ent power is equal to the power losses of the AC side resistance. TheTagedP transformer is represented as one electrical line ending in a SimilarTagedP to DC/AC inverter, the AC/DC converter can either control node with a high base admittance to the primary circuit and an alter- the voltage of the DC circuit or supply the required power. In voltage nating current generator for supplying the voltage or power to the control mode, the conversion is based on a model of ideal diode secondary circuit (output node). This module has a primary and sec- bridge under the assumption that the ratio of AC and DC voltages is ondary connection node. Both connection nodes have to be alternat- constant. The single phase DC voltage of the AC/DC converter is ing current nodes and the order of the nodes is important. higher than the three-phase AC voltage (approximately
UDC D1.35UAc). If the AC voltage is lower, then the DC voltage shows 2.5.3.4.TagedP DC/DC converter. SimilarTagedP to the transformer that transforms a reduced amplitude. the voltage level between two AC circuits, the DC/DC converter is a module type for modelling voltage changes in DC electrical circuits 2.5.3.3.TagedP AC/AC transformer. TagedPThe generated electricity with low (see Fig. 20). The DC/DC converter can either control the voltage of level voltage must be transformed to higher voltage for efficient the secondary circuit or supply the required power. In the voltage electrical power transmission. In this case, the electrical current control mode, the ratio of primary and secondary voltages is decreases, which in turn results in a reduction in the ohmic assumed to be constant. The converter is represented as one electri- losses and a reduction in cross-sectional area of the electrical cal line ending in a node with a high base admittance to the primary 118 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 circuitTagedP and a direct current source for supplying the voltage or power steamTagedP side. Today a 1 C 1 arrangement of GT and ST units in combi- to the secondary circuit (output node). The connection between the nation with a triple-pressure reheat (3PRH) HRSG is state of the art, primary and secondary circuits is arranged in such a way that the as shown in Fig. 22. Considering TOTs in the order of 600 °C, supple- secondary voltage is dependent on the primary voltage and the sec- mentary firing is widely omitted and nominal efficiency of the pro- ondary apparent power is equal to the power losses of the primary cess can reach up to 60%. Also, combined-cycle power plants with side resistance. Accordingly, the secondary circuit load is transferred efficiency levels greater than 60% are now running, for example to the primary circuit supply side. Irsching 4 plant that is located in Irsching, Germany. A more detailed introduction to the technical characteristics of the combined-cycle 2.5.4.TagedP Examples process is offered in Kehlhofer et al.D95XX[210]. Combined-cycle power UsingTagedP the described electrical components, the impact of possible plants can also supply useful thermal energy for district heating, failures in the electrical network on the energy system can be evalu- decreasing the total fuel consumption and reaching high efficiencies ated. Furthermore, the power consumption of process components [211]. can be calculated at steady state and in transient operation cases. InTagedP contrast to other thermal power plants, beside higher effi- The Figures below show different modelling examples of electrical ciency combined-cycle power plants are also characterized by flexi- networks. ble unit dispatch, see Lu and Shahidehpour [212]. Fast response InTagedP Fig. 18-(a) and (b), the dynamic model of a battery is illustrated capability is a prerequisite for increasing shares of renewable feed- during the charge and discharge processes. In addition to the battery, in and thus represents a competitive advantage for the operator in a various electrical components, including node, line, AC/DC con- changing market environment. Three criteria are typically consid- verter, generator and load are also modelled. In Fig. 18-(c), a DC ered to assess the practical flexibility of a power plant: start-up source (either a battery or a solar panel) with DC/AC inverter, switch time, maximum load gradient (positive and negative) and minimum and AC load is shown. load. Only 10 min are required for starting a simple-cycle gas tur- TheTagedP example of an entire thermal power plant model connected bine, irrespective of its initial temperature. CCPP load transients are, to the power grid is depicted in Fig. 19. The thermal power plant however, limited by thermal stresses in the thick-walled compo- generates superheated steam that enters the steam turbine section. nents of the bottoming steam cycle, namely ST rotor, ST casing, high The mechanical power obtained by the steam turbine is transferred pressure (HP) drum and outlet manifolds of HP superheater and final to the generator via a shaft. The electric power produced is fed to the reheater. A modern CCPP can complete the start-up procedure in less power grid in addition to other generating units. Part of the electric than 30 min after an overnight shutdown and sustain challenging power is used to cover the own electricity demand of the power load gradients up to § 60%/min, as e.g. stipulated by the Great Brit- plant. ain Grid Code for primary frequency response. The minimum load of TheTagedP dynamic model of a solar panel with battery and load is pre- a combined-cycle is mainly determined by the gas turbine, where sented in Fig. 20. During the day, part of the electricity generated by stable combustion as well as CO and NOx levels in compliance with the solar panel is consumed by the load and the remaining part is emission regulations must be preserved. Consequently, the corre- used to charge the battery (Fig. 20-(a)). In the night, the direct nor- sponding operating point is dependent on the specific type of gas mal irradiance becomes zero and accordingly the battery starts dis- turbine and possibly country-specific regulation. The operating load charging (Fig. 20-(b)). can be decreased to 40 50% of nominal load for typical gas turbines. This level may be further reduced to 20% if a sequential-combustion 3. Combined-cycle power design is used, so that one GT combustor can be shut down entirely. Minimum load is relevant to flexible operation since it defines the Gas-TagedP fired power generation accounted for 22% total share in 2012 lower boundary for negative load changes. If frequent cycling is worldwide electricity generation according to IEA [208], dominated anticipated, a CCPP capable of operation at low minimum load may by combined-cycle power plants (CCPP). The modern concept of the also be an economically viable option to reduce the number of start- combined-cycle is the result of an evolutionary process in the second ups and shutdowns. half of last century, mainly driven by increasing performance of the CalculationTagedP and optimisation of the transient system behaviour gas turbine. As early attempts to combine a gas turbine (GT) and a are an integral part of the CCPP design process with particular steam cycle, the GT was installed to enhance the efficiency of exist- regard to control design. This ensures that the actual power plant ing large-scale steam power plants by using the hot exhaust gas for meets the contractual guarantees and regulatory requirements in feedwater preheating instead of steam extractions or as a supply of all states of operation. According to Radin et al.D96XX[213],dynamic hot combustion air to the fully-fired steam generator. Korneuburg A power station, commissioned 1960 in Austria, is considered to be the first CCPP according to the modern definition of combined-cycle. The general idea is that the waste heat of a gas turbine is absorbed by a heat recovery steam generator (HRSG) installed downstream in the flue gas path (see Fig. 21). The generated steam is used in a Ran- kine bottoming cycle, which generates additional power in the steam turbine (ST). Jeffs [209] reports that despite the sound approach, process efficiency of Korneuburg CCPP did not exceed 32.5%. The GT operating temperatures at the time were as low as 620 °C at the turbine inlet (TIT) and 310 °C at the turbine outlet (TOT), so that supplementary firing was still required to support the steam cycle. Major technological developments including high tem- perature resistant materials and thermal barrier coatings, low-NOx combustion and innovative cooling methods significantly improved GT performance since. Whereas early CCPP configurations only used simple single-pressure HRSGs, additional pressure stages were introduced over time in order to increase steam parameters and to reduce the temperature mismatch between flue gas and water/ Fig. 21. Schematic of a combined-cycle power plant. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 119
Fig. 22. Detailed example flow chart of a triple-pressure bottoming cycle with reheat (extended from reference [18] with permission of authors and Elsevier). simulationTagedP is also a cost-efficient tool to support unit commis- 3.1. Load change sioning and regular operation by estimating component lifetime and directing maintenance. For verification of the overall plant OneTagedP of the basic tasks for dynamic simulation in the field of ther- design and control concept, a sophisticated simulation model is mal power plants is to calculate the response of the physical system required that can be considered a virtual representation of all the and the control circuits to a change in load demand. While load essential systems for plant dynamics. The complexity of these changes are rather simple procedures both in terms of practical exe- simulation models, based on differential equation systems and cution and numerical study, they are still useful to gain insight into numerical solution procedures, entails a computational effort that the transient system behaviour of a combined-cycle power plant. is unsuitable for optimisation purposes. Therefore, a reduced sys- ForTagedP the purpose of describing CCPP dynamics, the gas turbine can tem model must be developed, which captures the dynamic typically be treated as quasi-static component since the GT system behaviour and makes the problem accessible to mathematical inertia and characteristic time scale of GT response are negligibly techniques such as optimal control. The results are then verified small in comparison to the bottoming cycle. This statement does not by applying the optimised solution to the original simulation hold if there is integration of gas turbine and bottoming cycle that model and e.g. checking if boundary conditions are violated. prevents a separate analysis of the two, such as GT steam cooling. ThisTagedP chapter gives an overview of the published studies on Detailed gas turbine modelling is not covered in this chapter: For dynamic simulation applied to gas-turbine based power plants, system-level considerations, describing GT exhaust mass flow focusing on combined-cycles. Due to its considerable inertia and (including flue gas composition) and exhaust temperature as simple delayed system response, the bulk of the studies are dedicated to functions of load is often sufficient. Constant GT exhaust tempera- HRSG modelling and simulation. Section 3.1 introduces the reader to ture is typically maintained in the range between full load and the dynamic behaviour of the CCPP by considering basic parameter approximately 50% load whereas the GT exhaust mass flow shows a variations and load changes. In Section 3.2, the simulation of start- linear variation due to the changing position of the inlet guide vanes up procedures and the numerous investigations dedicated to start- (IGV). Below this load range, the IGV remain at closed position and up optimisation are covered. Section 3.3 is a brief overview of com- flue gas temperature is proportional to GT load. Thus a load change plementary works on dynamic simulation in the broader context of directly translates to a corresponding change of GT exhaust mass gas-turbine based power plants, including numerical studies of com- flow and/or flue gas temperature. pressed-air energy storage and integrated gasification combined- FromTagedP a mathematical point of view, this is a perturbation of the cycle. initial system in steady state to which the bottoming cycle responds 120 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 dynamically.TagedP Dechamps [214] suggested four time constants of a sin- gle HRSG heat exchanger as measure of the time to reach equilib- rium in response to a perturbation:
TagedPt1 - governing the enthalpy exchange for the flue gas, TagedPt2 - governing the external heat transfer of the tube wall, TagedPt3 - governing the internal heat transfer of the tube wall, TagedPt4 - governing the enthalpy exchange for water/steam.
PracticalTagedP calculations show that the time constants for enthalpy exchange processes are comparatively small (t1 » 0.1 s and t4 » 1s) and that the overall time constant of the single heat exchanger is typically controlled by external gas-side heat transfer (t2 » 100 s): mc t2 D ð3:1Þ a0A0 Fig. 23. Increase of time constants for warm start-up response of selected heat TheTagedP time constant is therefore defined as the thermal capacitance exchangers. (For interpretation of the references to colour in the text, the reader is of the heat exchanger mc divided by the rate of convective heat referred to the web version of this article.) transfer a0D97XXA0. However,TagedP the HRSG is a complex arrangement of several heat exchangers positioned in the flue gas channel according to the tem- perature profile. In order to take into account the thermal capaci- tance of the components (jD1...i¡1) between the given component and the perturbation, Gulen€ and Kim [215] state that the time con- stant of a component ti can be approximated with sufficient accuracy by a simple summation of all single time constants:
Xi ti D tj ð3:2Þ j D 1 TheTagedP heat exchanger closest to GT exhaust, typically the final HP superheater, directly faces the perturbation in gas enthalpy. It is con- sequently the first to respond and eventually reach steady state. In contrast, the response of the next heat exchanger is delayed since part of the perturbation is absorbed upstream. The time constant of the individual heat exchanger in the HRSG thus increases in propor- tion to its distance from the source of the perturbation whereas the fraction of the heat input available to the heat exchanger decreases (see Fig. 23). ShinTagedP et al.D98X[216]X studied the system response of a simple 2P HRSG to rapid changes and sinusoidal variations of GT load. The HRSG was modelled forming unsteady conservation equations of mass and energy for bulk heat exchangers. Fig. 24 illustrates the characteristic time scales of the gas turbine, high pressure (HP) and low pressure (LP) circuits using 10% load increase as example. The authors assume that GT load is controlled by the fuel mass flow in order to yield a step-like temperature increase, which explains the constant exhaust mass flow. From top to bottom, the figures show the responses of the GT system, HP and LP drum pressures as well as HP steam tem- perature and flue gas outlet temperature (the latter is closely linked to the temperature variation of the LP economiser). It can be observed that the gas turbine reaches stable operation after (tGT D4 s), which is negligible in relation to the time constants of the HP and
LP circuits (tHP D200 s and tLP D2000 s) and confirms that the quasi- static assumption is justified. The delayed response of the LP circuit in comparison to the HP circuit due to the accumulated thermal capacitance of the upstream heat exchangers is also reflected. PletlTagedP [87] conducted transient experiments supported by numerical simulation for a single-pressure once-through HRSG at the combined heat and power plants of TU Munich, where the gas turbine was simulated by a duct burner. Fig. 25 shows the mea- sured and calculated fluegastemperaturesasfunctionoftimefor different tube layers between flue gas inlet and the stack in a rewetting experiment. The system is initially characterised by a deliberate lack of feedwater supply for the given, constant heat input. The steam is completely superheated already when enter- Fig. 24. Gas turbine load increase and response of the double-pressure HRSG (repro- ing the heat exchangers and no additional heat from the flue gas duced from reference [216] with permission of Elsevier). F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 121 isTagedP absorbed. Therefore, the flue gas temperatures for tube layers WeißTagedP [219] and Rieger [19] investigated HRSG test configurations 36 and 40 are equal at t D 0. For 0 t 70, a linear increase of the at the same plant in order to improve the performance of once- feedwater mass flow to the nominal value is conducted. Since the through feedwater mass flow control in response to rapid load function of heat exchangers in a once-through steam generator is changes. Weiß distinguishes between load changes with variation of variable, the zone of evaporation is shifted downstream and addi- the flue gas mass flow (upper load range) and load changes with vari- tional mass is injected in the HRSG. This entails a reduction of the ation of the flue gas temperature (lower load range). The former type water/steam temperature to saturation temperature for some is controlled with relative ease since all HRSG components are influ- tube layers that initially contained superheated steam, so that all enced at the same time and the temperature profile along the flue heat exchangers contribute to heat transfer in steady state. The gas path remains largely unchanged. In contrast, for the latter type transient between the two operating points is governed by heat strong thermal charging and discharging processes of the storage discharge of tube walls and structural material. The simulation masses are present that dampen load following behaviour of the bot- results presented in the figure clearly show that neglecting ther- toming cycle. The author therefore suggests a modification of the mal inertia in the HRSG model results in a significant underesti- mass flow controller that introduces a source term for heat storage in mation of time constants and an inaccurate prediction of system the calculation of the mass flow setpoint. Based on measurement response. The author also reports that compared to the consider- data, the current energy content of steel and water/steam inventory ation of thermal storage masses, replacing the standard homoge- is estimated and compared with the fictional energy content in steady neous model with the more sophisticated slip flow model yields state for the current boundary conditions. The difference is used for only a minor improvement of simulation results. A plausible adjustment of the feedwater mass flow, considering a desired transi- explanation is that the 180 ° tube baffles between the tube layers tion time [219]. Rieger studied the capability of different control con- allow for momentum exchange between water and steam phase cepts for once-through HRSG to handle rapid load changes from full [87].Itshouldfinally be noted that the effect of thermal inertia is load to 38% and vice versa. In level control mode, the separator level more pronounced in this example vis-a-vis a commercial plant is the controlled variable while steam enthalpy at the evaporator out- due to the relatively large amount of liner and structural material let is used for once-through control mode. Due to the long distance in the scaled down HRSG system. between control valve and measuring point, both control concepts KimTagedP and Edgar [217,218] developed a mixed-integer nonlinear are initially characterised by a slow response that allows controlling a programming approach and applied it to a combined heat and power maximum load gradient of § 7%/min.InanapproachsimilartoWeiß, plant. The power plant completely covers the utility's changing by considering thermal storage in the HRSG material the permitted demands of power, heat and cooling throughout the year. The devel- load gradients in the test plant could be increased to 30%/min for oped model aims to maximise the net income of the power plant by level mode and 14%/min for once-through mode [19]. selling surplus power to the grid. The results show that the devel- WhileTagedP level-based control is typical for drum-type evaporators, oped algorithm is an effective methodology with reasonable compu- this concept is not applicable for once-through evaporators after the tation time of few hours to determine the optimal operation in 24 h initial start-up phase since the separator is run dry. Alobaid et al.D9XX ahead. [14] developed a sophisticated mass flow controller for once- TheTagedP dynamic behaviour of uncontrolled HRSG is usually not through HRSGs that covers all states of CCPP operation (see Fig. 17). encountered in practical applications. Commercial CCPP use hierarchi- The controller switches from level control mode to once-through cal plant control that is structured according to high-level unit control, control mode when a sufficient degree of steam superheating is system control and component control. As the basic control circuit of a reached at the evaporator outlet. The control principle is derived transient HRSG model, feedwater control is addressed in the follow- from the available heat input absorbed from the flue gas, which is ing. However, it must be complemented by several additional control corrected by thermal energy storage of the evaporator mass and circuits e.g. for live steam attemperation and ST bypass stations in divided by the desired enthalpy increase in the evaporator. Further order to describe the transient behaviour of the overall CCPP system. corrections account for fluid-side mass storage in the evaporator,
Fig. 25. Boundary conditions for rewetting experiment (left), comparison of calculated and measured flue gas temperatures (right) (reproduced from reference [87]). (For inter- pretation of the references to colour in the text, the reader is referred to the web version of this article.) 122 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
TagedP theTagedP degree of subcooling at the inlet and the degree of superheating admission from ST bypass valves to the ST control valve is con- fi at the outlet to calculate the current mass flow setpoint [14]. ducted in parallel. According to the common OEM de nition, the start-up sequence is completed when all bypass valves are fully 3.2. Start-up procedure closed and the total steam generation is admitted to the ST. This point corresponds to approximately 90% of nominal load for a FastTagedP start-up capability is the key benchmark for flexibility of a start-up to full load, so that the load may still increase after start- power generation unit and distinguishes CCPP from other conven- up completion. tional power plant technologies. The accurate calculation of com- bined-cycle start-up procedures and the reduction of start-up time ThisTagedP step-by-step start-up sequence is conservative in the sense with various optimisation methods therefore receive considerable that the procedure limits thermal stresses due to a gradual increase attention in the literature. Start-up procedures are classified as hot of metal temperatures in thick-walled components. Kehlhofer et al.D10XX starts after overnight shutdown, warm starts after weekend shut- [210] specify conventional start-up times in case of a 400 MW sin- down and cold starts after a shutdown of several days. However, gle-shaft CCPP as 155 min for cold start, 105 min for warm start and these categories are too broad for practical purposes. Operating tran- 47 min for hot start. Recently, dynamic simulation was used to sients are in fact determined as function of initial “cold” metal tem- design fast start-up schemes for warm and hot start-ups that shorten peratures of the thick-walled components, in particular ST rotor, ST or omit steam temperature matching by applying measures such as casing and HP drum. A conventional CCPP start-up sequence, as sophisticated stress control, flexible header design and cascaded HP shown in Fig. 26, is conducted as follows: steam bypass. The start-up time for hot starts can thus be reduced to less than 30 min, see Ruchti et al.D10X[220]X . The following section is ded- TagedP Purging: The GT is accelerated to approximately 25% of nominal icated to publications on start-up simulation and the comparison of speed using the generator as motor or with an auxiliary starter. simulation results with measurement data. The balance between This speed is maintained for some minutes until the gas duct vol- combined-cycle start-up time and lifetime consumption of the criti- ume has been exchanged with air several times to remove any cally stressed components is the determining factor for start-up residual hydrocarbons. Condenser vacuum is established by a optimisation, as described in Section 3.2.2. vacuum pump or ejector. TagedP Ignition and synchronisation: The burners are ignited, which 3.2.1.TagedP Simulation marks the actual beginning of the start-up (t D 0). The GT quickly InterestTagedP in CCPP dynamic simulation sparked in the early 1990s accelerates to nominal speed corresponding to the grid frequency, primarily in Europe and Asian-Pacific countries, owing to the success after which it is automatically synchronised. Up to this point, the of combined-cycle in the recently liberalised electricity markets and sequence is independent of the initial metal temperatures. the rapid progress in digital computing. TagedP Steam temperature matching: The GT is loaded to minimum load InTagedP an early study, Dechamps [214] described an approach to (IGV in closed position) and held until the required parameters model the complex geometry of HRSG finned-tube bundles with an for steam admission to the ST (approximately 50% of nominal equivalent one-dimensional heat exchanger. The unsteady energy pressure and a sufficient degree of superheating) are met. Mean- conservation equations for flue gas, metal and working fluid are dis- while initial steam generation is accommodated by the ST bypass cretised by finite-volume method and solved with an explicit inte- system so that HP pressure is increased in a controlled manner. gration scheme. The latter uses a constant time step and a density The hold time increases with the duration of the preceding shut- correction for numerical stability and reduced computational effort. down. Once steam quality is confirmed, the ST control valve is Complemented by PID drum level controllers, the method is applied opened and first steam is admitted to the ST. to reproduce the cold start of a 2P HRSG. The comparison with mea- TagedP Loading: The GT is loaded to the given load setpoint by gradually surement, in particular the timing of first steam generation and the shifting the IGV to open position; the permitted load gradient is a accurate jump of drum level, suggests that the system inertia and function of the selected start-up mode. The switchover of steam swelling effect are well described. Temperature results are not pre- sented in the work, however. KimTagedP et al.D102XX[221] investigated the effect of CCPP cold start-up with a flue gas bypass on thermal stress in the drum of a 1P HRSG. Using the lumped capacitance method, heat exchangers are modeled as bulk heat exchangers and not discretised in space. The drum is assumed to reach thermal equilibrium after each time step, yielding a quasi-static problem formulation. The authors show that operation of the flue gas bypass can be scheduled to mitigate thermal stress peaks at the inner drum surface. Despite the simplifications and although the use of such bypass stacks has been widely omitted since, the study is one of the first to consider thermal stress in com- bined-cycle operation. AlobaidTagedP et al.D103XX[12] presented the model of a commercial-scale 3PRH HRSG, based on the six-equation flow model of the thermal hydraulic process simulator Apros as well as detailed geometry and heat balance data. The gas turbine is simplified as time-dependent boundary condition of exhaust gas mass flow and temperature. Fig. 27 shows part of the presented results for a warm start-up sequence, which are in close agreement with measurement data. The devia- tions of initial pressure level as well as steam flow during the switchover from ST bypass valve to ST control valve reflect unavail- able information with regard to valve characteristics. Fig. 26. Warm start-up curve for single-shaft combined-cycle power plant (repro- MeinkeTagedP [65] developed the process model of a 3PRH CCPP duced from reference [210]). with a homogeneous flow model, using DYMOLA/MODELICA. In F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 123 contrastTagedP to the previously described studies, the model also ofTagedP the current CCPP that translate into a minimum load of 40% includes the GT system and the associated control circuits such and a permissible load gradient of 4.8%/min are also considered. as exhaust temperature control by IGV and GT power control. The study concludes that the share of lifetime consumption This requires proprietary information such as the detailed char- attributed to warm and hot starts of the plant is predominant acteristics of GT compressor mass flow as function of pressure and that the rate of lifetime consumption is nearly doubled in ratio and IGV position. The model is validated with measurement the future due to the higher frequency of warm starts [65]. data of a hot start to 54% load and results show generally good WhileTagedP researchers usually close the differential equation system agreement, part of which are depicted in Fig. 28.Atypicalprob- with empirical correlations, Sindareh-Esfahani et al.D104XX[113] used a lem is the determination of the exhaust mass flow, which is not Genetic Algorithm function of MATLAB/SIMULINK to identify measured in the real plant but calculated indirectly via the resid- unknown parameters for heat transfer. Two separate sets of experi- ual oxygen content. This entails significant uncertainty particu- mental data gathered during HRSG cold start-up were required, one larly at low load. Based on the validated model, lifetime for training and one for model validation. consumption of thick-walled components in the natural-circula- HackTagedP et al.D105XX[131] presented a methodology for adaptation of tion HRSG under a future scenario is estimated. This scenario HRSG design to cycling operation. Dynamic simulation of the attempts to reflect the German electricity market in 2023, which CCPP system for cold and warm start-up is conducted in a first is characterised by the complete abandonment of nuclear power step, where the natural-circulation HP evaporator loop is consid- and a high share of renewable feed-in. Flexibility improvements ered in particular detail. Secondly, the calculated steam
Fig. 27. Boundary conditions during warm start (a), measured and simulated response of the high pressure circuit (b) (reproduced from reference [12] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) 124 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 28. Calculated and measured parameters during the hot start-up of a gas turbine (reproduced from reference [65]). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) temperatureTagedP and pressure transients as well as the heat transfer underestimatedTagedP in the model. The sudden pressure drop after shut- coefficients are applied as boundary conditions for detailed down, which is not explained by the simulation, is attributed to finite-element analysis of the drum-riser connection (see Fig. manual venting of the superheater in order to prevent condensation 29). The obtained thermal stresses combined with pressure during extended standstill. stresses are used to analyse the material fatigue caused by start- GTagedPulen€ and Kim [215] developed an independent concept, up and shutdown cycles. Discontinuities such as weld connec- using the time constant of individual heat exchangers to model tions and surface irregularities are accounted for by a conserva- transient processes with simplified arithmetic equations rather tive reduction factor for fatigue strength. The authors summarize than differential equations. Experience-based steam admission that there is significant potential for start-up time reduction logic and practical assumptions are presented to complement while maintaining acceptable component life. the approach. For 3PRH HRSGs in combination with F-Class GT, MertensTagedP et al.D106X[16]X compared the dynamic behaviour of two 3PRH theproposedmethodisshownto reproduce the published HRSG models - drum-type and once-through with equal steady results of sophisticated codes with good qualitative agreement. state output for cold, warm and hot start-up procedures using Apros. As most researchers use complex simulation codes, which inher-
Thermal stress sthD107XXis generally proportional the difference between ently impairs full transparency of the underlying methods and average wall temperature Tave and inner wall temperature Tin, which the possibility of reproducing results, their approach is a notable is negative for start-up processes: exception among the cited studies.
D blinEs ðÞ¡ ð : Þ sth aT ¡ Tave Tin 3 3 1 v 3.2.2.TagedP Optimisation Fig.TagedP 30 shows the temperature responses in the wall of the HP ConsideringTagedP a given simulation model that can successfully drum vis-a-vis the wall of the once-through separator bottle, indi- reproduce the transient behaviour of the real power plant, it is cating smaller temperature peaks and comparatively fast tempera- straightforward to take one further step and investigate the poten- ture adjustment for the separator. The study concludes that the tial for optimisation. For instance, existing CCPPs can generate addi- once-through HRSG is favourable for combined-cycle plants with tional revenue by faster start-up procedures if the additional costs enhanced flexibility requirements, at the cost of slightly increased for maintenance and replacement are appropriately taken into heat exchanger surface of the HP circuit (approximately 9% in the account [222]. This increase of lifetime consumption can be miti- given case). gated by incorporating rigorous start-up optimisation in the design Recently,TagedP Mertens et al.D108XX[18] studied the dynamic behaviour of a of the CCPP, more precisely the minimisation of start-up time sub- commercial 3PRH CCPP for a start-up and shutdown operating cycle ject to operating restrictions such as thermal stress. Some recent with Apros. The measured and calculated responses for the HP cir- efforts are dedicated to introducing Model-Predictive Control (MPC) cuit of the bottoming cycle are compared in Fig. 31, showing gener- in power plant systems, which offers performance advantages com- ally good agreement. However, the premature occurrences of the pared to conventional PID control, in particular for highly dynamic initial temperature ramp in the HP superheater and of first steam systems and systems with delayed response. In MPC the control generation indicate that the thermal inertia of the real plant is input is computed by solving an optimisation problem for the F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 125
Fig. 29. FEM analysis of local temperature and stress distribution at the high pressure drum-riser connection during a cold start-up (reproduced from reference [131]). dynamicTagedP plant model over a receding time horizon. The control is InTagedP this notation xD10XisX the state vector, uD1XisX the control vector and tD12XisX only applied during a small part of the considered time before the the time. The reader is referred to Bryson and Ho [224] for in-depth calculation is repeated with a new set of states, so that future states discussion on the necessary conditions for optimality. For the pur- of the system are taken into account. pose of this chapter and the specific application to CCPP start-up, it BausaTagedP and Tsatsaronis [223] found that numerical solution meth- is sufficient to state that numerical methods are required to solve ods for large-scale dynamic optimisation problems, which assume nonlinear optimal control problems and that direct collocation the general form of differential-algebraic equation systems (DAEs), methods have shown to be an efficient approach for large-size opti- are available from optimal control problems in chemical engineer- misation. The general idea of collocation is to discretise the state and ing. The standard form of an optimal control problem is to minimise control variables over time and to substitute these variables as well the cost functional JD109XXsubject to the state equation a, algebraic con- as the cost function with polynomial approximations (see Fig. straints b and initial condition x0: 32). Polynomial coefficients are treated as variables of the opti- R misation process that need to satisfy the system equations at tf minutðÞJ D LxðÞ; u; t dt C f xt ; ut ; t s:t: t0 f f f discrete points in the time domain, also known as collocation ð3:4Þ points. The discretised parameter optimisation problem can e.g. _ D ðÞ; ; ; ðÞ; ; ; D ðÞ x axu t 0 bxu t x0 xt0 be solved by sequential-quadratic programming algorithms. In
Fig. 30. Temperature gradients in the separator wall (left) and in the drum wall (right) during hot, warm and cold start-ups (reproduced from reference [16] permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) 126 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 31. Boundary conditions for a hot start-up and a shutdown procedure (a), dynamic response of high pressure circuit (b) (solid line: measurement and dashed line: simulation) (reproduced from reference [18] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) theTagedP second part of the study [225], Bausa and Tsatsaronis illus- MatsumotoTagedP et al.D13XX[226] improved the start-up schedule with a trate the method by comparing unconstrained and constrained combination of fuzzy reasoning and neural networks in an early optimisation of a load change from 50% to 75% for a simplified work. Expert knowledge is incorporated in fuzzy logic rules, which single-pressure CCPP model. direct the optimisation qualitatively towards the optimum point. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 127
Fig.32. Discretisation according to Runge Kutta method (left) and backward-difference scheme (right) (reproduced from reference [223] with permission of ASME).
TheTagedP neural network is trained in parallel, using start-up schedules peakTagedP is located at the beginning of ST loading phase and that both and operating parameters as inputs and schedule modification rates peak stress and start-up time can be significantly reduced with obtained by fuzzy logic as outputs. During the optimisation, the regard to the reference procedure, despite the fact that the optimisa- actual schedule modification is gradually shifted from fuzzy logic to tion process is described as “trial-and-error” rather than an optimal- the neural network for fine adaptation e.g. to ambient temperature ity-based method. and humidity. Constraints such as thermal stress in the ST rotor, AlbanesiTagedP et al.D15XX[228] optimised the cold start-up procedure for temperature gradient in the HP drum and NOx emissions were different stress constraints of the ST rotor, using the variations of GT imposed. The authors report a reduction in start-up time and fuel load and of valve position for ST admission as control variables. The consumption by 35.6% and 26.3%, respectively. result shows that the required start-up time is reduced by 20% for a ShirakawaTagedP et al.D14XX[227] conducted start-up optimisation of a vali- conservative stress constraint and 48% for a standard stress con- dated 3PRH HRSG model by sequential quadratic programming. The straint; however, the presented reference procedure is rather nonlinear optimisation problem is formulated to reduce start-up lengthy (340 min). time, using control inputs bound by upper and lower boundaries FailleTagedP and Davelaar [112] decomposed the start-up transient in and operational constraints such as ST rotor stress, temperature gra- four phases and optimised steam temperature matching phase and dient in the HP drum and NOx emissions. Compared to conventional GT loading phase with MATLAB/SIMULINK. As the resulting start-up optimisation based on the practitioner's experience, start-up time is sequence satisfies all operating constraints for the reduced model reduced by another 22% while satisfying the specified constraints. but exceeds one constraint for the detailed simulation model, their CasellaTagedP and Pretolani [66] presented the simplified model of a study demonstrates that the model to be optimised must accurately 3PRH CCPP in DYMOLA/MODELICA for optimisation purposes, in capture the original system dynamics despite the reduction in com- which the LP system is largely neglected. The radial temperature dis- plexity. tribution in the ST rotor is calculated by Fourier's equation, discre- TicaTagedP et al.D16XX[69] derived a reduced model from the simulation tised with finite differences. Results show that the thermal stress model by Casella and Pretolani [66] in DYMOLA/MODELICA in order
Fig.33. Switchover from grid operation to island operation, responses of generating unit (left) and frequency (right) (reproduced from reference [230] with permission of ASME). 128 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
researchTagedP is dedicated to state estimation of the energy system required for on-line implementation.
3.3. Additional studies
InTagedP the following a brief overview of complementary works on dynamic simulation in the broader context of combined-cycle power plants is offered, including alternative concepts for GT-based power plants.
3.3.1.TagedP Island operation ATagedP case that rarely occurs in practice is the so-called island opera- tion, i.e. power plant operation disconnected from the grid. Both Ahluwalia and Domenichini [229] and Maderni et al.D19XX[230] studied the transient behaviour of a 60 MW CCPP at Mirafiori, Italy, including the switchover from regular grid operation to island operation. Fig. 33 shows the simulation results for opening of the circuit breaker, yielding a rapid drop from full load to the load level currently demanded by the local manufacturing plant. The authors also report an effort to control high-frequency and high-amplitude load disturbances in island mode, related to Fig. 34. Schematic of a compressed-air energy storage plant (simplified). welding stations.
3.3.2.TagedP Compressed-air energy storage TagedP to make it accessible to gradient-based optimisation methods. These TheTagedP basic idea of compressed-air energy storage (CAES) is to com- methods require continuously differentiable equations so that possi- bine a simple-cycle gas turbine process with storage for pressurised ble sources of discontinuity in the reference model, such as condi- air (see Fig. 34). Operation of the plant is therefore inherently tional functions, case distinctions and lookup tables, must be dynamic: In storage mode, the storage cavern is loaded with pres- replaced with smooth approximations. Small deviation from the surised air when excess electrical energy is available. In generation reduced model is reported when the computed solution of the mini- mode, the air is used for combustion of natural gas in the GT during mum-time optimal control problem is re-applied to the reference peak electricity demand. The gas turbine with compressed air energy model. In conclusion, the authors state that the proposed method is storage can be started without additional energy from the power able to convert nonlinear simulation models based on MODELICA grid and reaches 100% of its nominal load in approximately 6 min. into reduced optimisation models suitable for MPC. For the purpose of comparison, new gas turbines (without com- TagedP In an effort to close the gap between physical modelling on the pressed air energy storage) can be run up to full load within 20 min, D17XX one hand and optimisation on the other hand, Larsson et al. [102] while the half of the generated power is used to drive the compres- extended the open-source platform JModelica.org as interface to sor. The fast start-up of CAES power plants is of high relevance as a numerical optimisation algorithms. The nonlinear MPC optimisation standby power plant for case of electrical network failure and even problem is formulated with the Optimica extension of MODELICA to stabilize variances of fluctuating energy sources such as wind and solved by direct collocation methods and automatic differentia- energy etc. For CAES a large, well-explored and pressure-tight stor- tion. A case study of a warm combined-cycle start-up with MPC is age cavern is required, resulting in a limited number of suitable sites. D18XX presented using the same reference model [66] as Tica et al. It is con- Two plants currently exist in the world: Huntorf in Germany cluded that the proposed framework can be successfully applied to (290 MW, hD120XDX42%) and McIntosh in the USA (110 MW, hD12XDX54%). The fi nonlinear MPC in the eld of power generation, and that further latter is more efficient since exhaust heat is recovered for preheating
Fig. 35. Simplified flow chart of an integrated gasification combined-cycle process. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 129
Fig. 36. Overview of a hard-coal fired power plant (reproduced from reference [233] with permission of Springer).
ofTagedP the combustion air. Based on dynamic simulation of the cyclic TagedPmodel of an entrained-flow gasifier to an existing CCPP model for operation, Yoshimoto and Nanahara [231] combined CAES with a system-level control studies. Limited validation of the gasifier model water/steam bottoming cycle for increased efficiency. Nielsen and is conducted with steady state reference data of an operating IGCC. Leithner [88] further improved the concept by means of a thermal Bauersfeld [68] developed a modular MODELICA library of IGCC storage that absorbs heat from the hot compressed air in storage components, focusing on the chemical systems for syngas treatment. mode for combustion air preheating in generation mode. In addition Lee et al.D123XX[232] conducted dynamic simulations with the detailed the study proposes the use of a brine shuttle pond at the surface con- model of a Shell entrained flow gasifier, partially validated by steady nected to the cavern, which in contrast to conventional CAES allows state data. Najmi et al.D124XX[95] investigated different control strategies almost isobaric discharging by varying the storage volume (for for IGCC load change in gPROMS. A buffer tank between sorption- details, see Nielsen [89]). enhanced water gas shift and GT is used in order to reduce the fluc- tuations in mass flow and composition of fuel gas. The authors state 3.3.3.TagedP Integrated gasification combined-cycle that smooth operation during load changes can be maintained if the TheTagedP integrated gasification combined-cycle (IGCC) is a promis- load ramp of the gasifier is initiated ahead of the GT, which follows a ing concept to make the high-efficiency combined-cycle process sequence of multiple small load changes and intermediate waiting available to solid fuels such as coal by means of a chemical gasi- times. fication and syngas treatment plant installed upstream (see Fig. 35). The distinct advantage of IGCC is the possibility to efficiently 4. Coal-fired power integrate pre-combustion capture of carbon dioxide. Only a small number of IGCC plants without carbon capture were commis- Coal-TagedP fired power plant plays a major role for the global electricity sioned hitherto due to the substantial complexity of the process, supply at present and in the foreseeable future. The specific contri- which drives investment costs and heavily affects practical avail- bution varies from country to country and depends on several ability. Operating experience of these plants also shows that impact factors such as coal and gas prices, political framework, local dynamic operation is a challenge, motivating several recent pub- resources and access to the world market. In Fig. 36, the flow sche- lications on the subject. matic of a modern hard-coal fired power plant is presented. The SeparateTagedP component models and their control circuits were pre- main component is the steam generator, where pulverised coal sented by Seliger et al.D12XX[111] for the cryogenic air separation unit in entrained with the primary air flow is burned, releasing the thermal
MATLAB/SIMULINK and by Robinson and Luyben [39] for H2S energy stored in chemical bounds. The obtained heat is transferred absorber unit, water-gas shift reactors and CO2 stripping unit in to the working fluid in economiser, evaporator and superheater in Aspen Dynamics. Casella and Colonna [67] coupled the MODELICA order to generate steam for the Rankine cycle. Modern coal-fired 130 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 powerTagedP plants use single reheat and several low pressure and high simulations.TagedP The general approach of the model was unconventional pressure feedwater preheaters, resulting in an increase of the ther- for time and gave an idea for whole scope of dynamic power plant mal process efficiency. The flue gas leaves the steam generator and simulation. Today, the computational resources are sufficient and the remaining heat is applied to preheat the combustion air using an the numerical models of coal-fired power plants are becoming more air preheater. The flue gas may pass different cleaning devices like detailed, driven by increasing market pressure for high efficiency, selective catalytic reduction system, a particulate collector and a operating flexibility and emissions compliance. Since the response desulphurisation unit. The size of a coal-fired power plant has a of pulverised coal flow to a change of the raw fuel feed is of great range from small industrial units to large utility power plants with importance for the dynamic behaviour of a coal-fired plant, different up to 1300 MW per unit [233]. mathematical models were developed. For the description of ver- EvenTagedP though all coal-fired power plants are working on the same tical pulveriser, several models are proposed over the last deca- principle, every power plant is individually engineered, which des (among others: Lee [236],Fan[237],Zhouetal.D126XX[193] or leads to different operation modes and different dynamic behaviour. Niemczyk et al.D127XX[238]). Others models developed for tube-balls Criteria that define the specific design are listed in the following (Wei D128XetX al. [239]) or for beater mills used in lignite coal-fired points: power plant like the model of Debelikovic et al.D129XXpresented in their work [240]. In general, the pulveriser models have different TagedP Coal composition: The coal composition has the most important parameters that must be adjusted to the specifictypeofpulver- influence on pulverisers, burners, furnace, heat exchangers, foul- iser,sincefactorslikesizeorgeometryhaveaninfluence on the ing and size of flue gas cleaning devices. Here, the content ash, dynamics of the power plant. The pulveriser model of Fan [237] sulphur, volatiles, water and fixed carbon lead to specific require- has been validated with operational data of a vertical spindle ments for each component. The list of fuel categories is long and mill in Australia, but for other pulveriser types the available data varies from country to country and reaches from (meta-) anthra- is limited. cite over bituminous and subbituminous coal to lignite [234]. InTagedP this section, the dynamic models of coal-fired power plants TagedP Fuel handling and firing concepts: Normally, pulverised coal- from the literature are categorised in different sections correspond- fired plants are equipped with a direct firing system. Here, the ing to the published simulation results. raw coal is pulverised in the mill and transported by primary air directly to the burners. Depending on coal composition, different 4.1. Response to disturbances mills like ball tube, ball, roller, beater mills can be used. The respond of the pulverised coal flow to a change of the raw coal AtTagedP the beginning, researches and engineers tried using feed or the primary air has a significant impact on the dynamic dynamic simulation models to understand the response of the and transient behaviour. In power plants with circulating fluid- coal-fired power plant during a disturbance [241].Themathe- ized bed (CFB) combustion, different dynamic responses are matical model of a 200 MW drum-type steam generator was one occurring. of the first detailed models published by Kwan and Anderson in TagedP Emissions limits: The local emission regulation limits define how 1970 [242]. In order to describe the system, 109 equations have large the flue gas cleaning devices have to be designed and been developed and linearized. In the 1970s, the dynamic pro- weather to be applied at all. cess simulation was at the beginning of its development and lim- TagedP Water/steam cycle: While power plants with supercritical steam ited by the computational resources and powerful tools. parameters are always designed for once-through operation, Nevertheless, the illustrated results show the impact of a step plants with sub-critical steam parameters may also be equipped change of the governor valve, fuel, air flow or feedwater supply with a natural or a forced circulation. Even though one reheater to the rest of the power plant. With the aid of the dynamic sim- stage is state of the art, some plants are equipped with a second ulation tools, the qualitative and quantitative behaviours after a reheater stage. step disturbance became a well-known scenario. Therefore, the TagedP Reheater temperature control: The usage of water extracted from simulation of a step disturbance is often used as an indicator for the feedwater pump in attemperators is the most common way the model quality of large and complex models when operational for temperature control of coal-fired power plants. If other data is missing. Lu [117] introduced a model of 677 MW unit reheater control concepts like flue gas recirculation, tilting burn- located at Castle Peak B power plant in Hong Kong, China using ers, flue gas dampers or internal heat exchangers in the water/ MATLAB/SIMULINK. The model itself has a general purpose steam cycle are applied, other controls are necessary and the reaching from optimisation to personal training. The used equa- dynamic behaviour may differ. tions are described and offer the reader a very good overview of the mathematical structure. However, the numerical results DynamicTagedP models of coal-fired power plants are developed for dif- obtained from dynamic simulations lack validation towards ferent reasons. At early stages, the models were often restricted by experimental data. The model quality is checked via the response the computational time and therefore limited to smaller subsections to step changes, namely a change in the main pressure step of the power plant. Here, the models were generally divided into change and a sudden position change of the main steam valve. small subsystems like turbine or boiler systems. One of the most The given results indicate a reasonable response of modelled detailed model of a fossil-fired plant of the first two decades of physics and control systems. Recently, an entire coal-fired power dynamic plant simulation was published by Armor et al.D125XX[235] in plant model of one 500 MW unit at the Didcot power station 1982. The authors used the tool, so-called modular modelling system was presented by Oko and Wang [243]. The developed model in order to create a model of the Mystic Unit 7 power plant describes the steam generator and the complete water/steam (550 MW). Although the developed model was very complex, but side without the mills and the gas side. Unlike other transient the used fuel in the steam generator is oil. Apart from the missing models, it is validated with steady state plant measurements at pulverisers and the additional flue gas recirculation, the power plant 70%, 80%, 94.4% and 100% load. The numerical results obtained is similar to other coal-fired power plants of the time. The authors from the model shows a good agreement for those four steady described the modelling process and gave an interesting overview of state points. Nevertheless, no transient validation has been per- the occurring problems. For a quality check of the power plant formed due to the lack of experimental data. The quality of the model, several simulation tests have been performed, showing a transient behaviour is uncertain; however the calculated step promising match between the measured data and the predicted load changes have reasonable characteristics. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 131
Fig. 37. Comparison of a classic start-up (left) and an optimised start-up (right) (reproduced from reference [168]).
4.2. Start-up procedures whileTagedP keeping the thermal stresses within the required borders. On the base of this drum steam generator, Franke et al.D13XX[247] extended TheTagedP stress in the thick-walled components like headers or drums the generic model for the on-line application in a commercial ther- is induced by the change of pressure and temperature during a tran- mal power plant. sient. These components (see Section 2.3.3) are expensive and dam- MeinkeTagedP et al.D132XX[71] developed a detailed model of the 508 MW ages can lead to crucial economic losses for the operator. In coal- hard coal-fired plant located in Rostock, Germany, which includes fired power plants, the most crucial operation is the start-up when all relevant plant components and control schemes. For the model- high gradients in the metal structure occur. Since the stresses in the ling process, the simulation platform MODELICA and the non-com- drum or headers limit the absolute start-up time, they are of special mercial library ThermoPower [248] was used. The focuses in this interest. In the past, start-up curves of thermal power plants often study were the additional developed components like two-phase designed on operational experience and conservative assumptions. tanks and the gas side of the steam generator. In order to evaluate The use of dynamic simulations tools offered the possibility of opti- the quality of this model, a comparison of a start-up from 0 to 90% misation of the start-up progress by limiting the stresses in the after 37 h shut down period between the model and operational thick-walled components. Kruger€ et al.D130XX[244,245] published an opti- data was performed. The given results show a high accuracy of the mised control concept for the start-up procedure of a drum boiler. 240 min long start-up procedure. Fig. 38 illustrates the mass flow The model is an extended version of the well-known drum boiler rates and temperatures at the inlet and the outlet of the steam gen- model of Astroem and Bell [246], including economiser, evaporator, erator as well as the pressure and temperature at the outlet of SH1. drum, superheater, attemperators and bypass system. The main At the beginning of the simulation, the steam generator operates at focus was the stress reduction in the thick-walled components. The part load recirculation mode and a constant mass flow into the high authors give a very good overview of the start-up procedure as well pressure system is maintained. It is visible that the developed model as the initial conditions and show the results of standard classic and its corresponding control schemes calculate correctly. Only in start-up and a stress-optimised start-up. In Fig. 37, both start-up the life steam production between 20 and 40 min, larger differences procedures are compared. Due an optimised fuel supply and bypass occur. The authors used this model to investigate the stress in the control, it was possible to shorten the start-up time significantly, thick-walled components during start-ups and load changes. 132 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 38. Experimental and numerically obtained mass flow rates and temperatures at the inlet and the outlet of the steam generator as well as the pressure and temperature at the outlet of SH1 during start-up procedure (reproduced from reference [71], Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creati vecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Fig. 39. Results of electrical load, main stem pressure, main steam temperature and drum level during transient response for load ramp from 55% to 95% load at 5%/min (top) and transient response for load ramp from 75% to 95% at 20%/min (bottom) (reproduced from reference [249]). F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 133
Fig. 40. Experimental and numerically obtained steam mass flow rate and temperature during a load change (reproduced from reference [118]). (For interpretation of the referen- ces to colour in the text, the reader is referred to the web version of this article.)
4.3. Flexibility increase ofTagedP the load change, the simulation shows that the steam tempera- tures can be kept within reasonable limits. Zehtner et al.D136XX[24] devel- ModiTagedP fications of existing coal-fired power plants are driven by oped a model of the 450 MW hard coal thermal power plant Zolling, different reasons and dynamic models can help to investigate new Germany in 2008 using the commercial simulation tool APROS. Even innovations. Here, detailed models are often used for complete sys- though the need for flexibility improvement of existing power plants tem integration of a new control concept or component. A good in Germany was not key motivation for this study, the model was example is the work of Roth et al.D13XXin 2005 [23] reported of the waste one of the first large detailed models that are used to investigate the heat integration into the feedwater preheating system. The authors dynamic response of the hard coal thermal power plant. The model employed the simulation software APROS for the modelling of the describes the water/steam side in detail, while the gas side is not 392 MW coal-fired power plant. The model itself is comprehensive modelled in detail as in later published studies [71,21]. The model of and separates into 500 components. The simulation results show Zehtner et al.D137X[24]X used to evaluate the power plant response for sec- how fast an additional amount of heat could be converted into elec- ondary frequency control applying different condensate throttling tricity. Other models are used for the new control concepts like the variants and feedwater oversteering. Here, the standard condensate drum boiler model introduced by Peet and Leung [249]. It takes the throttling procedure of the thermal power plant, simulated with the boiler, the turbines and the feedwater track into account. The study model, shows a good agreement with the operational data (see Fig. includes a good overview of the main steam temperature and the 41). The model also includes a stress and fatigue calculation of the unit control. The reheat temperature is controlled by dampers in the thick-walled components. A more detailed description of the numer- second pass of the boiler. With the non-validated model, several ical model and the corresponding simulation results are given in simulation have been performed, including load changes [25]. (100 95 100%, 55 95% and 75 95%) with different load change TheTagedP recently published study by Starkloff et al.D138X[21]X of a large hard rates and a load rejection calculation. The results for a load change once-through coal-fired power plant in Germany focused on the from 55% to 95% at 5%/min and 75 to 95% at 20% /min are presented model description and the validation of the numerical model with in Fig. 39. The numerical results show that the implemented controls operational data. Therefore, a negative load change from 100% to can maintain pressure, steam temperature and drum level after the 27.5% is presented, e.g. live steam pressure during the load change fast load change. Here, a classic advantage of dynamic simulation and the O2 content in the flue gas downstream of the regenerative tools is visible, i.e. the investigation of the plant response during a air preheater (see Fig. 42). Unlike most other models in scientific lit- load change with 20%/min with a numerical model has much less erature, the different firing levels in the steam generator are mod- risks. InTagedP order to optimise the control strategy of a 600 MW supercriti- cal pulverized coal-fired power plant, Mohmand et al.D134XX[118] used a MATLAB/SIMULINK model with fuel, feedwater and main steam position as input parameters. The focus is on the water/steam side leaving the gas side completely out of the model by converting the fuel flow directly into heat. The reported results, like the main steam mass flow rate and temperature during a load change from 350 to 600 MW in Fig. 40, look promising. The results and the operational data during this specific load change have very little derivations and the implemented control circuits behave like the original ones. Sev- eral assumptions for model simplification have been applied, which limit the model for other or more complex purposes. TheTagedP model published by Meinke et al.D135XX[71] was extended in order to evaluate faster load change rates [65]. Here, the regular load change rate (2%/min) was doubled (4%/min) and the corresponding steam temperatures and the induced thermal stresses were ana- lysed. In Ref. [65], it was shown clearly that a load change from 37% Fig. 41. Simulation of a condensate throttling and the comparison with operational fl to 100% with a doubled change rate results in unfavourable uctua- data (reproduced from reference [25]). (For interpretation of the references to colour tion in the steam temperatures. With an optimised control strategy in the text, the reader is referred to the web version of this article.) 134 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 42. Measured and simulated steam pressure and O2 content during a load change (reproduced from reference [21] with permission of authors and Elsevier). (For interpreta- tion of the references to colour in the text, the reader is referred to the web version of this article.)
elled,TagedP which offer the possibility of shutting individual levels off. 4.4. Oxyfuel concept Since the model was developed for flexibility increase in general, it is modelled with minimal boundary conditions and realistic control InTagedP the last decade, the carbon capture and storage (CCS) technol- schemes. The validated model is prepared to investigate most think- ogy, which has a significant CO2 reduction potential, moved into the able flexibility increasing measures. focus of scientist and industry [252,253]. One of the CCS technolo- RichterTagedP et al.D139X[250]X used the simulation tool MODELICA for flexibi- gies is the combustion of a fuel with a nitrogen-free oxidant. Air is lisation of coal-fired power plants. By contrast to the study in [71], therefore separated into nitrogen and 95% pure oxygen, employing the ClaRa library is applied. The described unit and the fuel are not an air separation unit. The oxygen enriched air is burned together specified. The structure of the water/steam side and the steam gen- with recirculated flue gas in order to keep the flame temperature in erator is detailed and comparable to [71] or [21]. However, the dif- the range of conventional power plants. A challenge for the design ferent firing levels are not discretised. The dynamic behaviour is and operation of an oxyfuel coal-fired power plant is the flue gas validated with operational data during a load change from 60 to 90 side with its complex recirculation path, the air separation and the to 75% within 100 min of an unknown unit (see Fig. 43). Even though gas processing unit. Unfortunately, the design and operation experi- the simulation and the experimental data show a good agreement, ences of large conventional thermal power plants can be only partly some derivations are visible. The authors explained them due to the applied since whole structure of the gas side is quite different. Fur- fact of simplification of the unit control, where the developed model thermore, the experiences of oxyfuel pilot facilities can be only is used to evaluate an energy storage system within the water/steam partly adopted for large-scale power plants due to test plants charac- cycle. The shown concept gives an idea of the future role of thermal ter and inadequate knowledge of the real process. Therefore, one- energy storage systems in the power plant process. dimensional dynamic process simulation offers the possibilities to TheTagedP supercritical model developed by Zindler et al.D140XX[251] was evaluate different scenarios and to develop control strategies for the generated in order investigate the British grid code. In the non-com- new process. There are different designs for commercial large-scale mercial software Enbipro, a very simplified model of the steam gen- oxyfuel coal-fired power plants; nevertheless the basic structure of erator and the water/stem side has been generated. Unfortunately, the recirculation path is basically similar. The proposed models are there is no validation of the model performance at all. mostly complex and reasonable detailed. Most works concentrate
Fig. 43. Measured and simulated power output and temperatures during an off-design operation (reproduced from reference [250], Creative Commons Attribution-NonCommer- cial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 135
Fig. 44. Flue gas composition and temperatures during a switch over from air to oxygen firing at 100% load (reproduced from reference [256] with permission of Elsevier). moreTagedP on the model itself than on the results like in [254], where very (malfunctionTagedP of the coal feed, low oxygen purity or wrong oxygen detailed model of an 800 MW oxyfuel coal-fired power plant was measurement) is evaluated. The authors reported relevant observa- presented. Here, the oxygen boiler is coupled with an air separation tions, showing the model performance. An oxygen content measure- unit and the gas processing unit. However, no results of an air to ment in a power plant with an error of 10% may lead to serious oxygen switch were given. problems since the recirculation of the flue gas amplifies the effect Recently,TagedP Jin et al.D14XX[255,256] described a dynamic model of drastically. The oxygen content in the flue gas and the oxidant are of 600 MW oxyfuel power plant using ASPEN Plus DYNAMICS. The high importance for the safe of operation of such a power plant and model is very detailed on the gas side and the water/steam side, a high quality of control is required. Under safety aspects, a well- respectively. A various number of simulations carried out like engineered numerical model is tool with a high potential. Safety responses to disturbances in coal feed or oxygen purity. The pro- aspects are also in the work of Postler et al.,D145XX who discussed in [27] posed switch over from air to oxygen and vice versa occurs at the the design of a planned 250 MW plant at Jaenschwalde, Germany. nominal load of 100%. The proposed procedure is capable to switch They presented a load change and the impact of a recirculation fan from air to oxygen firing within 17 min at recycle ratio of 0.7. In their trip followed by a master fuel trip of the power plant. Interactions of work, the responses of the products SO2,SO3, CO, NO, NO2 are illus- the fans, the behaviour furnace pressure and the corresponding trated, which may peak like NOx during the switch over procedure.D142X3X mass flow rate are visualized in Fig. 45 (top). Starkloff et al.D146XX[26] Here, the chemical background and the good database of chemical extended the Postler et al.D147XXmodel [27] and simulated a total blackout reaction parameters of ASPEN Plus DYNAMICS is very supportive. auf the power plant (see Fig. 45 (bottom)). The dynamic simulations The results also indicate the changing of the flue gas composition of malfunctions can help to evaluate and design controls and safety and the higher heat capacity that leads to lower gas temperatures at mechanisms for this new process. Damper position, driving time or the end of the switch over (see Fig. 44). However, it is not reported, safety sequences can be optimised. Postler [28] described the switch if the dynamic behaviour of the gas temperatures has an impact on from air to oxygen operation at 50% boiler load using the software the steam parameters. APROS. The procedure needs around 30 min, which is comparable to ApartTagedP from oxyfuel coal-fired power plants with pulverised coal [256] and [258]. furnace, the circulated fluidized bed boiler is another option for a TheTagedP air separation unit and the gas processing unit are often large-scale application of an oxyfuel power plant. Consequently, modelled as a boundary condition for the oxyfuel power plant, e.g. dynamic models of CFB plants were developed [257,258]. Complex [27,28,256,258]. The dynamic performance of these air separation models of air fired CFB models are given in [259,260]. The study of a units can be the limiting factor of the overall dynamic performance. large CFB power plant published by Lappalainen et al.D14XX[258] gives The integration of air separation unit with its control system in the several CFB specific aspects in an oxyfuel environment. The simula- entire oxyfuel power plant model is of high interest. Pottmann et al.D148XX tion software APROS is used to model and investigate the air to oxy- [158] used the commercial software UniSim and the in-house tool gen switch. In addition to switch over from air to oxygen and from OPTISIM in order to model the gas processing unit and the air sepa- oxygen to air, the sensitivity of the mode switching to disturbances ration unit, respectively. The presented results give a good 136 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
compartmentsTagedP around the cooling circuit play a major role and are modelled as well. AnotherTagedP typical application of dynamic simulation tools in the context of nuclear power plants is the training of the licensed staff for normal operation as well as unexpected plant transients. These trainings are usually conducted in life-size replicates of the control rooms allowing for a very realistic training environ- ment with the possibility of recreating a broad variety of scenar- ios. ThisTagedP chapter of the review delves into dynamic simulation applied to NPPs, namely the analysis of load changes and the safety analysis. Typical computer codes used for those tasks are presented and exemplary results are shown and discussed. Moreover, this chapter gives an overview of upcoming developments in the field of dynamic simulation of nuclear power plants.
5.1. Specific features
Firstly,TagedP a short introduction to the unique aspects of nuclear power plants compared to conventional thermal power plants is offered. This includes the basic principle of nuclear fission as well as the design features of the most common plant types.
5.1.1.TagedP Basic principle Fig. 45. Gas dynamics after a trip of the recycle fan (top) and gas dynamics after total TagedP blackout of the power plant (bottom) (reproduced from references [26,27] with per- The underlying principle for every nuclear power plant is the 235 mission of authors and Elsevier). nuclear fission of heavy elements. In Fig. 46, this is shown for Uas fuel. The uranium nucleus reacts, in the case of 235U, with a thermal neutron and is split into two smaller nuclei and about 2 to 3 new fast neutrons. At the same time, a considerable amount of energy impressionTagedP how the numerical models may be used for the develop- (about 200 MeV) is released. The fast neurons have to be decelerated ment of control and operation strategies. by a moderator to be able to initiate the next fission reaction. Other fuels that use thermal neutrons for the reaction are 239Pu and 233Th. 5. Nuclear power Both are artificially produced in so-called breeder reactors. A fuel that uses fast neutrons for the reaction is 238U. In this case no moder- TheTagedP first commercial nuclear power plants (NPPs) came into ator is needed. operation in the 1950s. The two oil crises in 1973 and 1979 led to SeveralTagedP different types of nuclear power plants have been the demand of an oil-independent and cheap energy source, which designed and built based on the principle described above. They dif- spiked the number of newly built NPPs worldwide. Since then NPPs fer in the type of coolant (e.g. water, helium, CO2,sodium),mod- have become a major source of power generation. To date over 430 erator (e.g. light water, heavy water, graphite and none in case commercial nuclear power reactors operate in 31 countries with an of fast breeder reactors) and the number of cooling circuits. The installed power of about 370 GW, providing more than 2400 TWh of most common reactor types are light water reactors, namely the electricity per year. This equals roughly 11% of the annual consump- boiling water reactor (BWR) with one cooling circuit and the tion in electricity worldwide [261]. Today, new plants are still pressurized water reactor (PWR) with two cooling circuits. Fur- designed, planned and built. Two main driving forces behind those thermore the designs of BWR and PWR concepts vary from one projects can be identified. Firstly, in regard of global warming manufacturer to another. nuclear power is considered as one of the possible measure to signif- InTagedP addition more uncommon reactor types, like the Canadian icantly decrease the amount of emitted carbon dioxide. Secondly, heavy water reactor or the French sodium cooled fast breeder reac- nuclear power is a relatively import-independent power source tor Superphenix, exist. The former one uses natural uranium omit- since comparably cheap and little amounts of fuel are needed, which ting the need for the highly complex enrichment process. The latter are available in a number of regions all over the world and not used one is able to make use of the 238U that which is accounts for 99.3% in any competing sector [262]. The second factor is closely linked to of the isotopes in natural uranium. Due to the predominance in the very low marginal cost of nuclear power, which in turn usually power generation this review focuses on BWR and PWR power puts NPPs to the far left of the merit order. Therefore, NPPs are plants. generally used as base load plants without the need for regular load changes. Only in a few countries, e.g. France and Germany, 5.1.2.TagedP Reactor pressure vessel and reactor core NPPs are extensively used for load following. This led to a low TheTagedP reactor core is the central part of the power plant. There the demand of dynamic process simulation of NPPs during load nuclear fission takes place and the energy stored in the fuel is changes [263,264]. released. The layout is similar for PWR and BWR and therefore is NeverthelessTagedP nuclear safety is a main topic during design and described jointly. In light water reactors the core is located in the operation since the erection of the first commercial plants. The mat- reactor pressure vessel. It is made up from fuel assemblies which in ter became increasingly important over time and first computational turn consist of a set of fuel rods filled with sintered UO2 pellets. In analyses of the dynamic behaviour of the plants during accident con- between the fuel assemblies control rods, made of neutron absorb- ditions were conducted very early. Today, several sophisticated pro- ers, can be moved in and out in order to control the neutron flux and gram codes for nuclear power plants exist, which can model the hence the reactor power. transient behaviour of the cooling circuits and the reactor core. Espe- InTagedP Fig. 47, typical layouts of a PWR reactor pressure vessel (RPV) cially for loss of coolant accidents (LOCA) the interactions of and a BWR RPV are depicted. The control rod drives are installed on F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 137
Fig. 46. Nuclear fission of Uranium (reproduced from reference [328], Creative Commons Attribution 4.0 International (CC BY 4.0), License: https://creativecommons.org/licenses/ by/4.0/).
Fig. 47. Reactor pressure vessel of a pressurized water reactor (a) and a boiling water reactor (b) (reproduced from reference [329]). 138 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
itTagedP rises through the core and evaporates. Above the core in the steam separator the liquid is diverted to the downcomer, while the satu- rated steam leaves the RPV at the top. TheTagedP power of a nuclear reactor is controlled via the neutron flux. In light water reactors an inherent control mechanism exists because of a temperature feedback loop. With higher temperatures, the density and therefore the moderation of water decreases. At the same time, the construction materials and the fuel pellets absorb more neutrons. Both effects reduce the thermal neutron flux and hence reactor power. BeyondTagedP that mechanism the power is controlled by the control rod position and the boron concentration in PWR. In BWR no boron is used in the coolant and the power is controlled mainly with the recirculation pumps. At higher throughputs, the void is reduced, resulting in better moderation and increased reactor power.
5.1.3.TagedP Cooling circuits and auxiliary systems TheTagedP PWR concept is used in most of the nuclear power plants in the world. It is a light water reactor with two cooling circuits. The main components of the primary circuit are the RPV with the reactor core, the main coolant loops, each with their own steam generator and main coolant pump, and a pressurizer (see Fig. 48). The number of loops varies from two to four. Typical pressure levels for the pri- mary circuit are around 16 MPa. TheTagedP steam generators produce saturated steam at about 7 MPa for the secondary circuit. The layout is similar to any other steam power process (see Fig. 49) with a few variations. Firstly, because of the comparably low pressure there are only two turbine Fig. 48. Primary circuit of a pressurized water reactor (reproduced from reference stages. Secondly, the superheater is powered by the main steam. [330]). This actually lowers the plant efficiency but is necessary to limit the steam moisture to an acceptable level for the low pressure topTagedP of the RPV. The main coolant is injected through inlet nozzles, turbine. flows through the downcomer to the bottom of the core and rises SeveralTagedP safety and auxiliary systems are integrated in the stan- through the core. There, the heat from the fuel assemblies is dard PWR concepts. The actual design, the purposes and the names absorbed. The coolant leaves the RPV through the outlet nozzles. In differ between plant manufacturers. To give an overview only the contrast to the PWR, the control rod drives are located below the most important systems are explained in the following. Several RPV. The feedwater is injected above the core. With recirculation safety systems are subsumed under the name Emergency Core Cool- pumps, the water is pumped down to the lower plenum from, where ing System (ECCS). They are used to remove the decay heat of the
Fig. 49. Secondary circuit of a pressurized water reactor. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 139 reactorTagedP core both after regular shut down as well as reactor scram reactor,TagedP in case of reactor transients and the interactions with the under accident conditions. It is therefore designed as a highly reli- surrounding building and compartments (containment codes), in able and redundant system with emergency power supply. The ECCS case of loss of coolant accidents. This is achieved either by incorpo- is connected to the primary circuit. Typical safety systems of the rating additional simulation modules or by linking the software to ECCS are the High Pressure Injection System (HPIS), the Accumulator external simulation programs. Injection System (AIS), and the Low Pressure Injection System (LPIS). TheTagedP simulation of the surrounding building with its compart- The HPIS and the LPIS are both pump driven systems, which supply ments is done with very simplified models or with very simplified coolant at different pressure levels of the primary reactor. The AIS discretisation, nevertheless validated with numerous experiments. depends on pressurized accumulators, which release the inventory An example of an external program for containment simulation is through a check valve into the primary circuit. COCOSYS [274], typically linked to ATHLET. Other examples are TheTagedP emergency feedwater or auxiliary feedwater system (AFS) is GOTHIC and CONTAIN. The thermal hydraulic is usually described connected to the secondary circuit and supplies feedwater to the with a so-called lumped-parameter model. The containment of the steam generators if the main feedwater pumps are inoperable. This plant is subdivided into control volumes with the thermodynamic can be the case during regular start-up and shut-down procedures state defined only by temperature and mass of the specified compo- as well as accident conditions. nents. Typically different zone models are available. For instance, in TheTagedP boiling water reactor is the second most common reactor COCOSYS equilibrium and non-equilibrium (two-phase)D156XX zones and type. In contrast to the PWR, it consists only of one circuit. Here, the special zones for the pressure suppression pool in BWR or the jet reactor pressure vessel also acts as a steam generator and supplies vortex condenser in the Russian WWER-440 PWR can be selected. the main steam directly to the turbine. The layout of the cooling cir- cuit is almost identical to the secondary circuit of a PWR. Also the 5.2.1.TagedP Validation experiments pressure level of approximately 7 MPa is similar. TheTagedP validation of the nuclear reactor simulation codes is based on InTagedP BWR, the ECCS typically consists of a HPIS and a LPIS. Further- separate effect tests, integral system tests and transients in commer- more, BWR plants contain a pressure control and relief system. It is cial plants. In 1983, a program was initiated by the OECD to compile used to release the pressure form the RPV in accident scenarios to code validation matrices. Phenomena were identified that are avoid a plant of condition of a high pressure core meltdown at all expected to occur during transients in BWR and PWR. The integral cost. The steam is lead to a condensation chamber, also called pres- test facilities (ITF) and separate effect test facilities (SETF) were built sure suppression pool, where it is condensed. This system is also and experiments, useful to characterize the phenomena identified, used in case of breaks to reduce the pressure in the containment were conducted. The results of several tens of ITF experiments and [265]. about a thousand SETF experiments are compiled in [275,276]. Vali- dation results of containment codes are summarized in [277,278]. 5.2. Safety analysis TheTagedP reports provide a general overview of accident progression for light water and also heavy water reactors. The main focuses are TheTagedP build and operation of NPPs is strongly regulated by the the phenomena and safety systems employed in these reactor types authorities in any country and the safety regulations usually exceed and to highlight the differences. For example, in the report for the the regulations for conventional thermal power plants by far. containment code validation approximately 120 phenomena in the Despite the fact that several standards exist basic safety philosophy categories of containment thermal hydraulic, hydrogen behaviour, and requirements are similar. Examples for safety requirements are aerosol and fission products, iodine chemistry, core melt distribution the German “Sicherheitsanforderungen an Kernkraftwerke” [266], and system behaviour are identified and a synopsis of more than 200 the US NRC Requirements, the IAEA Safety Standards [267] and the experiments for those six categories are included. yet to be passed European WENRA Reference Levels. AnTagedP example for a cross reference matrix is shown in Table 3.It TwoTagedP general approaches for safety analyses are differentiated in allows identifying what phenomena are covered by which test and the safety standards, the probabilistic approach and the determin- are suitable for code assessment, in this case for large break LOCAs istic approach. In the probabilistic approach, initiating events are in PWR. The actual validation is then conducted with pre test and defined and the accident sequences are analysed respecting the fault post test calculations that are compared to the experiment results. probability of the plant systems. Hereby, an initiating event is any Since the compilation of these reference matrices, more phenomena incident that requires an automatic or operator action to bring the were marked as important and additional experiments were con- plant into a safe and steady state condition [268]. The final result of ducted. the calculation is a core damage frequency. In the deterministic ReventTagedP os et al.D157XX[280] illustrated the general approach in code approach, a set of design-basis accidents as well as beyond-design- validation, where some parameters are determined with a basis accidents is examined and the event sequence is determined parameter study and then the experiments results are compared under conservative boundary conditions [269]. Typical scenarios to the simulation results. Here, the result of one of the OECD- that are investigated in the deterministic approach are loss of cool- SETH experiments is compared to the results of ATHLET and dif- ant accidents (LOCA), loss of offsite power and earthquakes. ferent RELAP versions. The OECD-SETH program is aimed at InTagedP both cases, probabilistic and deterministic approach, an exten- investigating issues that are relevant to accident prevention and sively tested and validated simulation tool is needed for the simula- started in 2001. The experiment in question deals with the topic tion of the accident sequence in order to convince the surveyors and ofborondilutiononresumptionofnaturalcirculationinthe the regulatory authorities of compliance with the regulations. There- steam generators following a small break LOCA. This scenario fore, only few dynamic simulation programs, which are specifically constitutes a challenge to analytical methods. The water evapo- validated for these use cases, are used in the supervisory procedures. rates within the core and condenses on the primary side of the Common codes are ATHLET [270], CATHARE [271] and RELAP steam generators. In this so called reflux condenser mode the [272,273]. boron is mainly retained in the liquid phase, so that the vapour AllTagedP these codes share the two-phaseD15XX heterogeneous flow model phaseandthecondensatearealmostboronfree.Theborondilu- with the addition of non-condensable gases transport equations and tion is an important phenomenon because D158XrecriticalityX can occur 1D-discretisation. Moreover, the application in the field of safety if the diluted plug enters the core. analysis not only requires the simulation of the water/steam process TheTagedP experiment was conducted in the integral test facility PKL but also the interactions with the neutron kinetics of the nuclear (see Fig. 50), which is operated at the Technical Center of AREVA and 140 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Table 3 Cross reference matrix for large breaks in PWRs [279].
isTagedP a mock-up of a 1300 MW class PWR [280,281]. The test facility 5.2.2.TagedP Statistical accident analyses simulates the entire primary side with four loops and the essential TheTagedP accident scenarios that need to be analysed in order to parts of the secondary side. The elevations correspond to the eleva- receive an operating license are called design basis accidents tions in an actual plant and the volumina and power are scaled (DBA). Usually these are divided into two groups, loss of coolant 1:145. accidents (LOCA) and accidents or transients without loss of TheTagedP analyses were performed by six working groups from differ- coolant. For both it has to be proven, that certain criteria would ent countries using different codes. The aim of this paper was to not be exceeded. both show and compare the results obtained by different working ThisTagedP is typically done in a deterministic analysis by setting groups in their simulation of the experiment and to analyse the main conservative values for the boundary conditions like reactor parameters involved in order to draw conclusions on improvements power, reactor pressure and burn-up of the fuel (higher burn-up that can be made in the analytical approach to such tests. All the par- yields higher decay heat). The calculations are performed ticipants managed to successfully predict the overall thermal hydrau- with the validated codes that are best-estimate codes, i.e. the lic system behaviour. Vessel fill-up together with slug build-up by model parameters are not chosen in a way that necessarily reflux-condensation (see Fig. 51) up to 3000 s after start of the tran- yields conservative results but are set to match the validation sient are phenomena that were correctly predicted, whereas simula- experiments. Due to the choice of conservative boundary condi- tion of natural circulation restart and transport of low-borated water tions, the calculated result is nevertheless assumed to be a cov- slugs (see Fig. 52) were identified as areas for improvement. ering or conservative result for the respective performance InTagedP conclusion, the validation of nuclear system codes is a very criteria. broad and well discussed topic. The validation matrices allow for InTagedP a more recent approach that is propagated in the USA Code of a thorough test of new and changed codes and ongoing Federal Regulation and the German Sicherheitsanforderungen, the researches ensure that newly identified phenomena are consid- boundary conditions are no longer set to values considered ered and experiments are added. conservative but are given as probability distributions. The F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 141
Fig. 50. PKL facility, volume: 1:145, elevations: 1:1, max. pressure: 45 bar, max. power 2.5 MW (reproduced from reference [280,281] with permission of Elsevier and Creative Commons Attribution 3.0 Unported (CC BY 3.0), License: https://creativecommons.org/licenses/by/3.0/).
sameTagedP is done for model parameters like heat transfer coeffi- boundaryTagedP conditions only uses one calculation whereas for a cients, since these are not known with complete certainty and result covering 95% of the possible results with a confidence of in some cases even the choice of a conservative value would be 95% at least 59 calculations are required according to Wilk's for- non-trivial. This approach yields a result distribution from mula. Usually 93 or 124 calculations are performed to be able to which the confidence level that the maximum code result will omit one or two outliers respectively. On the other hand, the not be exceeded with a certain probability can be obtained results of the probabilistic method are more realistic and allow [282]. for an assessment of result's uncertainties. Additionally the influ- OnTagedP the one hand, the statistical approach requires a much ence of model parameters with a fixed but inaccurately known higher calculation effort. The method with conservative value is reflected in the result. The difference between the two
Fig. 51. RPV level (left) and mass flow in intact loop 3 (right) (reproduced from reference [280] with permission of Elsevier). 142 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 52. Mass flow rate after natural circulation restart (left) and boron concentration in loop 3 (right) (reproduced from reference [280] with permission of Elsevier).
Fig. 53. Consideration of discrete values (left) or of input parameter value distributions instead (right) (reproduced from reference [282], Creative Commons Attribution 3.0 Unported (CC BY 3.0), License: https://creativecommons.org/licenses/by/3.0/). approachesTagedP is depicted in Fig. 53 with the conservative boundary ThisTagedP emphasizes the advantages of the statistical analysis in com- conditions on the left and the statistical method on the right plex systems, where the interactions between different input param- [282]. eters are hard to predict. Therefore, the reviewers suggest a transfer ArkomaTagedP et al.D159XX[30] analysed a large break loss-of-coolant accident of the knowledge in statistical transient analysis from the nuclear (LB-LOCA) in EPR-type nuclear power plants using the described sta- energy branch into other fields of study with dynamic simulations. tistical method. The best-estimate code used is APROS coupled with the fuel-performance code FRAPTRAN-GENFLO. The goal of the anal- ysis was to show that the maximum number of failing fuel rods in the reactor core in the transient is lower than the performance crite- rion of 10% of failed rods. The failing of the fuel rods is mainly deter- mined by the cladding temperature of the fuel rod. TheTagedP 59 results for the maximum fuel cladding temperature are plotted in Fig. 54 together with six additional curves: the highest and lowest temperatures in black, the average temperature in blue, and the median in turquoise for each time step as well as the results of two extra calculations with the nominal and conservative values for the model parameters and boundary conditions in green and red respectively. The lowest and highest temperatures at each time step are represented with the black lines. ATagedP clear reason why certain calculations gave high and low extreme values could not be found. More over the conservative case inD160XXwhich conservative input values were chosen based on engineer- ing judgement did not lead to the absolute highest cladding temperatures. Several other paper on the topic of statistical accident analysis also draw the conclusion, that parameter combina- Fig. 54. Maximum cladding temperatures (reproduced from reference [30] with per- tions considered conservative do not necessarily lead to a conserva- mission of Elsevier). (For interpretation of the references to colour in the text, the tive result. reader is referred to the web version of this article.) F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 143
5.3. Load cycling
AsTagedP briefly described in the introduction, load cycling has not yet played a major role for nuclear power plants since NPPs are gener- ally used as base load plants. The reasons are manifold and include technical as well as economical aspects. Therefore, no dynamical simulations of the power generation process during normal opera- tion are known to the authors. Nevertheless, experience with load following exist.
5.3.1.TagedP Experience with load following ATagedP comprehensive overview on the experience with load follow- ing in France, Germany, USA and Sweden as well as on the technical aspects of load changes in BWR and PWR is given by Persson et al.D16XX [283]. The goal of the report was to elicit the capability to comple- fl Fig. 56. Schematic characteristic curve for recirculation control in a German BWR ment the uctuating power supply of renewable energies with the (reproduced from reference [284] with permission of AREVA NP GmbH). NPPs in Sweden. In order toD162XXachieve this goal, technical aspects that were regarded important for load following, were investigated. These include: InTagedP Fig. 56, the recirculation control curve in a BWR is depicted for constant control rod position. Recirculation control is per- TagedP Thermal stress on the components, leading to increased plant fectly suitable for load cycling in the upper power range from wear, about 60% to 100% of the rated electrical output. Hereby the fi TagedP The limit in neutron flux control, usually caused by limited con- power distribution is not signi cantly affected minimizing the trol rod drive speed, stress on the reactor components. For lower power output, the TagedP The requirements for the in-core instrumentation, control rod manoeuvring sequence has to be optimised. Under TagedP Risk of fuel damage caused be different thermal expansion coeffi- these conditions load-following operation between 20% and cients for the fuel pellets and the surrounding fuel rod, 100% is expected to be feasible. TagedP TagedP The so called xenon peak that occurs a few hours after a load Both studies draw the conclusion that in principle there are no reduction and prevents the return to the nominal power, technical obstacles to use the nuclear power plants in Sweden and fl TagedP Increased risk of incidents leaving normal operation, and Germany for exible power generation in load following with mini- TagedP The effect on the fuel economy. mum load of 65% and 50% respectively. Both reports also suggest that higher rates and ranges are possible with suitable changes like LudwigTagedP et al.D163XX[284] conducted a comparable study for German optimised fuel management, optimised control rod manoeuvring NPPs only. The motivation for this paper was the decision of the Ger- and predictive operating strategies [283,284]. man government in favour of a lifetime extension for the German AnTagedP exemplary overview on the maximum load change rate and NPPs and the question if those plants can readily react to changes in on the load cycling range for some of the current light water reactor load demand. The authors identified similar fields of interest to designs is given in Table 4. investigate the fast response capabilities. Additionally, the part-load characteristics of German PWR and BWR are explained. 5.3.2.TagedP Thermal hydraulic-neutronic instabilities InTagedP Fig. 55, a schematic part load diagram of a PWR is shown. For a TheTagedP aforementioned studies as well as similar works (Pouret et al.D164XX reactor power from 0 to 40% of the nominal power, the average cool- [263], Stein and Griffith [290]) omit the topic of coupled thermal ant temperature rises. Here a load following would yield high ther- hydraulic-neutronic instabilities that can occur in boiling water mal stress on the components in the primary circuit. Between 40% reactors. In most power plants, provisions are taken against these by and 100% of the nominal reactor power, the average coolant temper- prohibiting certain combinations of control rod position and low ature in the reactor is constant. This is therefore the typical range for recirculation pump speed and thus limit the load cycling range. This load following.
Table 4 Load following capabilities of different reactor designs.
Design Reactor type Maximum load Load cycling change rate range
ABWR [285] BWR 60%/min 65% 100% AP1000 [286] PWR 5%/min 15% 100% EPR [287] PWR 5%/min 60% 100% 2.5%/min 25% 60% ESBWR [288] BWR N/A 50% 100% Konvoi [283, 289] PWR 2%/min 20% 100% 5.2%/min 50% 100% 10%/min 80% 100% SWR 69 [283] BWR 3.8%/min 60% 100% 10%/min 90% 100% SWR 72 [283] BWR 4.6%/min 60% 100% 10%/min 90% 100% Vor-Konvoi [283] PWR 4.4%/min 50% 100% 10%/min 80% 100% VVER-1000/1200 (V-392 PWR 5%/min 50% 100% Fig. 55. Schematic part load diagram of a German PWR (reproduced from reference and V-491) [287] 10%/min §20% [284] with permission of AREVA NP GmbH). 144 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
AsTagedP several in-depth reviews on the topic of thermal hydraulic instabilities exist (e.g. March-Leuba and Rey [291], Prasad et al.D165XX [292], Ruspini et al.D16X[293]X ), no further details are given. Nevertheless, as load following is becoming more relevant with the addition of fluctuating renewable energy sources, thermal hydraulic instabilities during reactor transients should not be neglected.
6. Concentrated solar power
InTagedP concentrated solar power (CSP) plants, solar rays are concen- trated by means of mirrors or lenses or a combination of both to heat a working fluid, which then directly or indirectly drives a ther- modynamic process in order to generate electric power. In this chap- ter, only concentrated solar thermal power is discussed, while concentrated photovoltaics (CPV) and plants with non-concentrating collectors are out of scope. TheTagedP overall efficiency of a CSP plant (see Fig. 59) is determined by Fig. 57. Instability region in the power-flow map for the Leibstadt NPP (reproduced the optical efficiency of the reflector, the efficiency of the receiver from reference [331]). (absorber tube), the thermal losses during fluid transport, thermal energy storage efficiency (optional) and the efficiency of energy con- TagedP is shown in Fig. 57 for the NPP Leibstadt in Switzerland. The effect of version in the power block [294]. thermal hydraulic-neutronic instabilities is widely known since the D ð : Þ 1980s when such instabilities were observed at the Caorso plant in hCSP hopt hrec htra hsto hcon 6 1 Italy. TheTagedP heat transfer fluid (HTF) is usually a synthetic oil. The size of TagedP fl The basic mechanism causing ow instabilities in BWRs is the the solar field determines the amount of electric output. As the solar fl density wave. The coolant in BWRs ows in the upward direction field roughly accounts for half of the capital expenditure for a CSP through the core. Thus, variations in the density, caused by dif- plant, current research efforts are focused on increasing electric con- fl ferent steam void fractions, travel upwards with the ow. In version efficiency by higher process temperatures in order to down- fl two-phase ow regimes, the local pressure drop is very sensitive size the solar field and decrease the levelised cost of electricity fi to the local void fraction and a signi cant part of a pressure (LCOE). This requires application of working fluids that remain stable drop is delayed with respect to the original perturbation. If the at high temperatures, such as molten salt or demineralised water, i.e. fl inlet ow is perturbed at certain frequencies, the pressure drop direct steam generation (DSG). can decrease with increasing flow and a self-sustained oscillation can occur [291]. 6.1. Development InTagedP addition, in BWRs the power generation is directly linked to the fl neutron ux which is a function of the reactivity feedback and there- InTagedP the beginning of the 20th century, household solar water heat- fore depends on the void fraction. Thus a density or pressure oscilla- ers were commercialised in South West USA and the North-Ameri- tion respectively is necessarily accompanied by a power or neutron can Frank Shuman successfully completed a parabolic trough plant fl ux oscillation. The feedback paths are illustrated in Fig. 58 [291]. for powering an irrigation system in Meadi, Egypt, in 1913. The
Fig. 58. Block diagram of the feedback paths for the coupled neutronics-thermal hydraulics instability type (reproduced from reference [291] with permission of Elsevier). F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 145
Fig. 59. Typical setup of a concentrated solar power plant (parabolic through) with thermal storage.
ItalianTagedP Giovanni Francia designed and built the first linear Fresnel TagedPinstalled in 2013 and a total of 5.5 TWh solar thermal energy collector in Genoa, Italy, in 1964 and the first solar tower plant in were generated. Spain leads the world in solar thermal energy Sant'Ilario, Italy, in 1965. As of 2011, 29 CSP plants have been in with 2.3 GW of cumulative CSP capacity. Close to 2% of annual operation worldwide with around 1220 MWel installed capacity electricity in Spain is generated by CSP plants. This is the highest [106]. It can be seen in Fig. 60 that the large majority of the solar share of all countries in the world. The U.S. ranks second with thermal capacity is installed in Spain and the U.S. Furthermore, para- 900 MW CSP capacity installed at the end of 2013. However, bolic trough CSP plants are the most widely deployed technology, deployment of CSP grows at a high pace in the U.S. with followed by tower, linear Fresnel and Stirling dish CSP plants with 400 MW being added in 2013 and over 600 MW in early 2014 huge distance. Growth of installed CSP capacity started in 2009, [295]. The Ivanpah central receiver plant in California, consisting mainly in Spain (see Fig. 61). At the end of 2013, the total installed of three distinct towers with each operating its own power CSP capacity amounted to 3.6 GW. About 900 MW were newly block, is the largest CSP plant with respect to installed capacity
Australia Fresnel (0.2%) (0.7%) Italy Germany Tower Stirling dish (0.4%) (0.1%) (3.0%) (0.1%) Iran (1.4%)
USA (40.1%) Spain Parabolic trough (57.9%) (96.3%)
Fig. 60. Solar thermal power plant projects in operation in the world (March 2011). Left: installed power by country. Right: installed power by technology (reproduced from refer- ence [106] with permission of Elsevier). 146 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 61. Global cumulative growth of the solar thermal electricity capacity as of 2013 (reproduced from reference [296], (C)D1XX OECD/IEA 2014 Technology Roadmap, Solar Thermal Electricity, IEA Publishing. License: www.iea.org/t&c).
TagedP soTagedP far. It was completed in February 2014 and is totalling a net receiver (see Fig. 62-(b)). This technology emerged as major alter- power output of 377 MW [296]. native to the parabolic dish technology, since it is characterized by high theoretical efficiency as well as high potential for future cost 6.2. Specific features reduction. The high concentration ratios compared to linear focus- ing systems allow the receiver to operate at higher temperatures fl CSPTagedP plants generally consist of a solar field, an energy storage sys- with reduced losses [294]. The capacity is limited by the heat ux tem (optional) and a power block as described in the following sec- that can be absorbed by the receiver surface and transferred to fl tions. the heat transfer uid, without overheating receiver walls and heat transfer fluid [299]. As already stated, the thermal efficiency 6.2.1.TagedP Solar field of central receiver systems is relatively high. Operating tempera- ThereTagedP are different CSP technologies that are mainly distin- tures range from 300 °C to 2000 °C with concentration ratios guished by concentrator and receiver systems, see Fig. 62. Parabolic between 150 and 1500. Double-axes tracking of the heliostats is trough and linear Fresnel reflectors concentrate direct sunlight on a common. Overall, the technology is still relatively immature, fi line (line focus), whereas parabolic dish and solar tower technolo- implying high speci ccosts[298]. TagedP fl gies concentrate light on a point (point focus) [106]. Furthermore, Linear Fresnel re ector (LFR): Linear Fresnel CSP plants use mul- linear Fresnel and the solar tower technology have in common that tiple mirrors moving on one axis. These mirrors focus the solar fi the receiver is fixed and does not move together with the concentra- rays on a downward facing xed linear receiver (see Fig. 62-(c)). tor device. This reduces the effort of HTF transport to the power All commercial LFR plants currently in operation use DSG. There block. In contrast, the receiver of parabolic trough and parabolic dish is one 30 MW LFR plant operating in Spain since early 2012 and technology is mobile. In general, a mobile receiver allows collecting one 125 MW commercial LFR plant operating in India since 2014. more energy compared to a fixed receiver [296]. The technology is characterized through a simple design but low overall optical and thermal efficiency [294], especially when the TagedP Parabolic trough (PT) collectors: This technology focuses solar sun is low in the sky in early morning and late afternoons and rays through parabolic trough-shaped mirrors on linear receiver during winter [296]. Operating temperatures range from 50 to tubes along the parabola's focal line (see Fig. 62-(a)). These 300 °C with concentration ratios between 10 and 40. Single-axis receiver tubes are isolated in evacuated glass envelopes. Oil is tracking of the reflectors is common. Overall, the technological heated inside the tubes and further transferred to a power block. maturity can be considered as moderate. However, relative costs The parabolic trough technology was used in the first commercial are the lowest due to its simple design [298]. plants built in California and is still most widely deployed [294]. TagedP Parabolic dish reflector: This technology uses an array of para- In addition to synthetic oil as heat transfer fluid, more recent bolic dish-shaped mirrors to focus solar energy on a receiver projects investigate the deployment of direct steam generation located at the common focal point of the dish mirrors [299].A (DSG) collectors to improve performance and reduce costs [297]. heat-to-electricity engine, such as a Stirling motor or micro-tur- One small parabolic trough plant with DSG technology is cur- bine connected to a generator, is located at the common focal rently operating in Thailand [296]. The thermal efficiency of par- point (see Fig. 62-(d)). Parabolic dish technology is characterized abolic trough collectors is relatively low. Operating temperatures by the highest efficiency potential for solar energy conversion of range from 50 °C to 400 °C with concentration ratios between 15 all CSP technologies (no cosine losses [294]), low start-up losses and 45 [298]. Single-axis tracking is common. However, double- and favourable modularity, so that the dish can be easily installed axes tracking could increase the amount of collected solar energy in remote areas to meet the local power requirements. The tech- by up to 46% compared to a fixed surface (experimental investi- nology requires three-dimensional tracking, rendering systems gation by Bakos) [299]. The overall technology maturity can be more complex and reducing tracking accuracy [299]. However, considered as advanced with relatively low costs [298]. very high costs and risks caused the parabolic dishes to disappear TagedP Heliostat field collector (Central receiver system CRS / solar almost completely from the commercial energy landscape [296]. tower): Multiple heliostat field collectors (large mirrors with dou- Recently, parabolic dish resurrected as option for future CSP con- ble-axes tracking) focus solar rays to a fixed tower mounted cepts. Operating temperatures range from 150 °C to 1500 °C with F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 147
(a) Parabolic trough (b) Central receiver
Solartower
Reflector Absorber tube Solar field piping
Heliostats
(c) Linear Fresnel reflector (d) Parabolic dish
Curved mirrors Receiver, engine
Reflector Absorber tube and reconcentrator
Fig. 62. Classification of reflectors (reproduced from reference [296], (C)2XDX OECD/IEA 2014 Technology Roadmap, Solar Thermal Electricity, IEA Publishing, License: www.iea.org/t&c).
TagedP concentration ratios between 100 and 1000. Overall, the technol- asTagedP much as 47% to levels over 70% on a sunny day [303]. The relative ogy maturity is low [298]. ease of thermal energy storage for high dispatchability is the main competitive advantage of CSP vis-a-vis photovoltaics. 6.2.2.TagedP Power block InTagedP most applications, the thermal energy storage medium stores DependingTagedP on the CSP reflector type with its characteristic oper- thermal energy in form of sensible heat (heating and cooling a mate- ating temperature, the layout and the specific dispatchability rial without change of phase), for instance in synthetic oil and molten requirements, CSP plants are equipped with one of the following salt. However, systems that utilize latent heat (melting and freezing power block types: of suitable high-temperature phase-change materials), thermochemi- cal (reversible chemical reactions usedtostoreanddischargeenergy) TagedP Rankine cycle (steam cycle). and other sensible heat materials are the subject of ongoing research TagedP Organic Rankine cycle ORC (low-temperature steam cycle). [302]. Furthermore, energy can be stored in steam accumulators. The TagedP Stirling engines (heat-to-electricity engine). energy density is low for sensible heat storage, whereas the density TagedP Brayton (Joule) cycle (gas turbine cycle). increases with latent heat storage, sorption and thermochemical stor- TagedP Combined-cycle (Brayton combined with Rankine as bottoming age. As yet, the maturity level of these storage technologies is in cycle) as described in [300,301]. opposite correlation to their prospective power density. TechnicalTagedP aspects to be considered when evaluating thermal 6.2.3.TagedP Energy storage and back-up system energy storage technologies are: AsTagedP solar irradiation is limited to daytime and depending on the clearance of the sky, CSP is generally not dispatchable. However, ther- TagedP High thermal storage capacity, mal energy storage (TES) can be integrated in a CSP plant (see Fig. TagedP Good heat transfer rate between heat storage material and heat 59), making it highly dispatchable. TES also enables CSP plants to con- transfer fluid, vert the intermittent solar energy source to a constant power output. TagedP Good stability of heat storage material to avoid chemical and Round-trip efficiencies above 97% were reported for TES units consist- mechanical degradation after a certain number of thermal cycles, ing of two-tanks with hot and cold salt [302]. Furthermore, a storage TagedP Compatibility between heat transfer fluid, heat exchanger mate- can increase the solar share (fraction of energy provided by solar) by rial, and storage material, 148 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
TagedP Reversibility to achieve large numbers of charging and discharg- areTagedP no studies in the field of dynamic simulation for parabolic dish ing cycles, systems so far. Table 5 provides an overview about recent publica- TagedP Low level of thermal losses, tions on dynamic simulation of CSP systems. TagedP Ease of control [299]. InTagedP the following, some recent studies that include measurement validation are selected for detailed description. Garcia et al.D17XX[106]
AmongTagedP the total installed capacity at the end of 2013, roughly were the first researchers to develop a model based on the 50 MWel 2.3 GW do not include storage, while approximately 1.3 GW contain solar thermal power plant Andasol II in Granada, Spain, where the a thermal energy storage system. However, among the expected collected heat is transferred using synthetic oil as heat transfer fluid. capacity to be added until 2020, about 80% will likely incorporate Their simulation is conducted using Wolfram's MATHEMATICA 7 storage capability [295]. software. The model aims to be flexible in order to analyse different InTagedP addition to thermal energy storage, back-up systems with fos- characteristics of any trough plant. Hence, it is anticipated to use sil fuel or biomass fired auxiliary boilers make CSP plants fully dis- this model for designing new plants and to optimise operation strat- patchable, which makes the technology more attractive for utilities. egies with respect to maximizing electricity output. Fig. 63 compares Furthermore, the back-up system can compensate for thermal stor- validation results with measurement data of the reference plant for age losses during the night, prevent freezing and accelerate the partly cloudy days. start-up process in the morning. Almost all CSP plants use some fos- TheTagedP most recent studies were conducted by Al-Maliki et al.8X71DX[35,36], sil fuel as back-up, most commonly natural gas. As the power block in which the 50 MWel Andasol II plant is also modelled, including all already exists, the additional costs for an auxiliary boiler are rela- required control circuits. However, the authors used the thermal tively low and they are outweighed by the operational benefits of a hydraulic simulation code APROS. The model includes a two-tank back-up system. thermal energy storage operated with molten salt and a detailed Finally,TagedP several full-hybrid setups are conceivable. These dynamic model of the power block. After achieving convincing valida- hybrid systems routinely use a fuel together with solar energy. tion results, it is found that the thermal energy storage enables the For example, small solar fields can be added to a fossil-fired plant to deliver an almost constant power output despite small fluctu- thermal power plant (even as re-powering). These integrated ations in DNI. Furthermore, the plant is capable of sustained power solar combined-cycle (ISCC) plants use solar energy to evaporate generation for 7.5 h after sunset due to the storage. Comparison steam for the bottoming cycle. Furthermore, solar boosters for between measurement and simulation for a day with strong coal plants replace the economisers that are heated by extraction cloudy periods (see Fig. 64) shows good agreement in the period flows from the steam turbine. Hence, more steam can be between 10:00 and 17:00. The discrepancies after this period are expanded in the turbine so that power output is boosted [296]. related to unknown operator behaviour in particular. With an Since the conventional part typically plays the major role in optimised operation strategy, the time of electrical power output these systems and the solar part is the auxiliary support, full- can be increased by about 26% compared to the reference case. hybrid systems are not further discussed in this work. LiuTagedP et al.D179XX[122] analysed the dynamic behaviour of a TES system
implemented in the 1 MWel central receiver direct steam generation 6.3. Dynamic studies plant Badaling. The thermal energy storage consists of an oil-oper- ated cold and hot tankD180XXas well as a steam accumulator. The complete DynamicTagedP simulation of CSP plants is conducted as the technology plant is modelled in DYMOLA by means of the MODELICA library relies on direct solar radiation, which in fact is dynamic in nature. “ThermoSysPro”. A two-level control loop is designed in MATLAB/ Clouding, the angle of irradiation depending on day-time and season SIMULINK and connected to the simulation model. Fig. 65 shows the as well as the geographic location of a plant influence the amount of results after a dynamic perturbation of DNI. The drum pressure energy that can be collected. Dynamic simulation aims to study the increases instantaneously when DNI rises. At a certain drum pres- performance of CSP plants under different solar irradiance condi- sure, the system switches to storage mode and the storage steam tions. Furthermore, plant start-up procedures, the capacity and valve opens in order to limit the pressure in the drum. The steam dynamics of TES charge and discharge cycles as well as the annual mass flow to the turbine is stabilized with constant drum pressure. power output respectively the capacity factor can be analysed. Two The pressure in the steam accumulator increases as steam is different types of studies can be distinguished, which either simulate injected. Not shown in the diagrams is an increase in feedwater sup- based on half to one hour time steps and treat most thermal compo- ply to the drum in order to maintain a constant drum level. As the nents as quasi-static or which attempt to track short duration cloud results illustrate, coupling of the two-level control system modelled and thermal transients using more fundamental approaches. Key in MATLAB/SIMULINK with the DYMOLA process model is successful. inputs for system performance forecasting include direct normal The authors aim to use the model for prospective studies of further irradiation (DNI) time series data, combined with the local ambient control solutions in the future. temperature, humidity and wind speed [294]. MitterhoferTagedP and Orosz [81] modelled a low-cost 3 kWel micro-CSP CommercialTagedP software for energy system modelling used in solar with a rock-bed TES system in DYMOLA. The solar-thermal loop is thermal applications includes: IPSEpro, EBSILON Professional, Eco- represented by a dynamic model, whereas the model of the Organic SimPro, TRNSYS, GATECYCLE, DYMOLA, MATHEMATICA and ASPEN. Rankine Cycle is steady state. The model is validated with experi- A free, but closed-source package is the System Advisor Model (SAM) mental data from a test site at Eckerd College in St. Petersburg, Flor- from the National Renewable Energy Laboratory (NREL), which is ida. Results show a possible net electricity generation of 4.08 MWh/ based on the well-known TRNSYS simulation engine. An example for annum at an average power output of 2.5 kW and a capacity factor a free open-source system model is SOLERGY (Lovegrove and Stein) of 18.8%. Operation of the ORC condenser can be optimised by apply- [294]. Recent studies also used the APROS simulation code to model ing a control strategy that allows for a variable pinch point, which and simulate a parabolic trough CSP plant (see [35] and [36]). A results in an increase of annual net electricity generation by 14% in detailed overview of codes applicable to CSP technologies is given in comparison to a constant condensation pinch point (see Fig. 66). Ho [304]. As parabolic trough CSP plants are most widely deployed, this technology offers the most reliable base of operating data and is 7. Additional thermal power technologies commonly used to validate dynamic simulation models. Some other studies investigated the dynamics of central receiver and linear Fres- ThereTagedP are several further thermal power technologies, in addition nel reflector systems. However, to the authors’ best knowledge there to the above-described, that are rarely considered in the dynamic F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 149
Table 5 Recent publications dealing with dynamic simulation of CSP systems.
Publication CSP type Comments
Al-Maliki et al.D3X[35]X Parabolic trough 50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and detailed power block; APROS; model validation; clear days and slight cloudy periods.
Al-Maliki et al.D4X[36]X Parabolic trough 50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and detailed power block; APROS; model validation and optimisation of operation strategy; strong cloudy periods in summer days.
El Hefni and Soler [79] Central receiver 145 MWel molten salt central receiver power system; including two-tank TES system and power block; DYMOLA; model validation, checking performance and design, and prediction of yearly electricity production; simulation with yearly DNI.
Liu et al. [122]D5XX Central receiver 1 MWel DSG solar tower power plant; including two-tank oil TES system, steam accumulator, and power block; DYMOLA, coupled with MATLAB/SIMULINK; simulate heat transfer performance and storage charging and releasing procedure, test of two-level control design; artificial DNI transient.
Luo et al.D6X[305]X Parabolic trough Synthetic oil parabolic trough solar field; including hot oil storage tank, w/o power block; own dynamic mathematical collector model; model validation, optimisation of solar field layout; diverse irradiation conditions.
Mitterhofer and Orosz [81] Parabolic trough 3 kWel micro-CSP plant; including rock bed TES system and ORC (steady state model); DYMOLA and Engineering Equation Solver (EES); model validation, optimisation, and prediction of annual net electricity generation; different DNI profiles during one year.
Diendorfer et al.D7X[306]X Parabolic trough Floating offshore parabolic trough collectors; w/o TES and power block; model validation; analy- ses of optical performance as a function of time and location; different offshore DNI profiles.
El Hefni [80] Parabolic trough / Synthetic oil parabolic trough solar power plant and DSG linear Fresnel hybrid CCPP; DYMOLA; linear Fresnel model validation and prediction of yearly electricity production; simulation with yearly DNI.
Falchetta and Rossi [307] Parabolic trough 9 MWel molten salt parabolic trough plant; including two-tank TES system; ISAAC Dynamics; analyses of draining operations.
€ Osterholm and Palssonb [82] Parabolic trough 50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and simplified Rankine cycle; DYMOLA; model validation; clear summer day and partly clouded day.
Rodat et al.D8X[83]X Linear Fresnel Synthetic oil and DSG linear Fresnel CSP plant; w/o (oil) and including (DSG) TES, including power block (simplified by a heat sink for oil as HTF and turbine by orifice for DSG); DYMOLA; model validation, investigation of control scheme and response on DNI perturbations; DNI profiles for a sunny and a partly cloudy day.
Russo [147] Parabolic trough Molten salt parabolic trough CSP plant; including direct storage system, w/o power block; modified RELAP5 code; model validation, analysing thermal-hydraulic behaviour, filling and draining procedures.
Wagner and Wittmann [308] Parabolic trough 125 MWel molten salt parabolic trough CSP plant; including direct two-tank TES system, auxiliary heater, and power block (pseudo-transient); EBSILON Professional with add-ons; analyses of different operation strategies; DNI profiles from NREL.
Zhang et al.D9X[78]X Central receiver 1 MWel DSG power tower plant; including and w/o two-tank oil TES system and steam accumulator, including power block; DYMOLA; model validation; measured DNI profile from test campaign.
Manenti and Ravaghi-Ardebili [309] Parabolic trough 4.7 MWel molten salt parabolic trough CSP plant; including direct two-tank TES system; own mathematical model of economiser; dynamic modelling of economiser and whole plant.
Powell and Edgar [303] Parabolic trough 1 MWth direct parabolic trough CSP plant; including two-tank TES system, boiler, and fossil fuel back-up; analyses of interaction between storage and other components to control power out- put and collector outlet temperature, comparison between systems with and w/o storage; DNI profile of a clear and a cloudy day.
Xu et al.D10X[310]X Central receiver 1 MW DSG solar power tower plant; including two-tank oil TES system and steam accumulator, w/o power block; own mathematical model; analyses of recharge and discharge process of TES system, response of dynamic steam flow disturbances.
Garcia et al.D1X[106]X Parabolic trough 50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system; Wolfram's Mathematica 7; model validation; different DNI profiles.
Larrain et al.D12X[311]X Parabolic trough 100 MW DSG parabolic trough plant with fossil-fueld auxiliary heater; w/o TES; Engineering Equation Solver (EES); estimate required back-up fraction for different plant locations; different DNI profiles during one month.
Eck and Hirch [76] Parabolic trough DSG parabolic trough collector loop; w/o TES and power block; MODELICA; model validation, investi- gation of different feed water control systems; overall and local shadings of collector loop.
Stuetzle et al.D13X[312]X Parabolic trough 30 MWel synthetic oil parabolic trough solar electric generating system; w/o TES, including simpli- fied Rankine cycle (steady state model); model validation and development of a linear model predictive controller; summer and winter day.
Jones et al.D14X[149]X Parabolic trough 30 MWel synthetic oil parabolic trough solar electric generating system; w/o TES, including power block (steady state); TRNSYS; model validation; simulations on daily basis with DNI profiles for sunny and cloudy days. 150 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 63. Comparison of measured data and simulated results. Left: mostly clear and sunny days. Right: days with slight cloudy periods (reproduced from reference [106] with per- mission of Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) simulationTagedP studies. These technologies include geothermal 7.1. Geothermal power power, municipal waste incineration and seawater desalination. The general lack of in-depth studies for those technologies is TheTagedP geothermal power plants use heat generated by radioac- mainly linked to the economics that strongly favour steady state tive decay in the earth, which is removed by accessing natural operation or to the comparatively small market penetration. In hot water reservoirs or by the so called hot-dry-rock process, this chapter, the available research on these technologies in the where an artificial circulation system between the heat source literature is reviewed. and the plant is generated by injecting water into the ground. F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 151
1000 500
800 400 Sim.
2 600 300
400 200 DNI [W/m ] Exp.
200 HTF temperature [°C] 100
0 0 0 5 10 15 20 0 5 10 15 20 Time [h] Time [h] 150 1200 h 1000 t 100 800
600
400 50 Thermal power [MW ] 200 Total HTF mass flow rate [kg/s] Total 0 0 0 5 10 15 20 0 5 10 15 20 Time [h] Time [h] 200 60
50 el th 150 40 r [MW ]
100 30
20 50 Storage energy [MW ] Electrical powe 10
0 0 0 5 10 15 20 0 5 10 15 20 Time [h] Time [h]
Fig. 64. Comparison of measured data and simulated results for a day with strong cloudy periods (reproduced from reference [36] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
TheTagedP retrieved hot water than can either be flashed directly to temperatureTagedP geothermal resources in the range between 90 °C driveaRankineprocessortheheatistransferredtoasecondary and 150 °C and low temperature geothermal resources (below circuit using a working fluid with more favourable evaporation 90 °C) are preferably applied to direct uses. Several novel designs characteristics. Generally, high temperature geothermal resour- are proposed recently to generate electricity from moderate or ces above 150 °C are applied to D18XpowerX generation. Moderate low temperature resources geothermal resources economically, 152 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
Fig. 65. Dynamic response of thermal storage system on DNI perturbation (reproduced from reference [122], Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.) butTagedP these are not efficient like power generation from high tem- dynamicTagedP model of the plant is generated. Other recent studies perature geothermal resources [313]. can be found in [47,154]. DueTagedP to the near-zero marginal cost for geothermal power, the power plants are mostly used for base-load demand and there is 7.2. Municipal waste incineration little motivation to investigate transient operation. On the other hand, a number of studies on the dynamic storage behaviour of InTagedP the last few decades and due to the rapid development of the wells/reservoirs exist, which are typically the limiting factor national economies, continued urbanisation and improvement of liv- for those types of power plants. For example, Casella [314] con- ing standard, the solid waste output is constantly increasing. In order ducted a study on the modelling, control and optimization of a to effectively dispose of solid waste, different solutions have been double-flashgeothermalplantusingProcSim,anin-housecode suggested such as recycling, reduction of waste generation and land- from Laboratory of the Politecnico di Milano. Within this study, fills. A proven approach for the large-scale disposal of municipal modelling approaches for components unique to geothermal solid waste is the thermal treatment in grate systems. Municipal power plants, e.g. the stripper columns, are presented and a waste incineration is characterised by several advantages such as F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 153
Fig. 66. Net electricity generation and comparison of the accumulated power output for two different control strategies (reproduced from reference [81] with permission of ASME). theTagedP cost reduction of residual landfill due to the lower volume of end combustionTagedP on the grate, a post-combustion zone, in which the products (10% of the original volume) and decreasing the total secondary air is injected and a zone with auxiliary burners. The organic carbon (TOC) of waste, resulting in inert residues unable to auxiliary burners are required on the one hand for plant start-up produce landfill gas. The heat released in waste combustion can be and on the other hand for supporting the combustion tempera- recovered by a water/steam circuit for the supply of electricity and ture, when the calorific value of waste is insufficient. On the district heating. Accordingly, the residual waste can be used as sub- grate, the incineration of waste takes place in different zones stitute fuel for the conventional fossil fuels. using primary air (air/fuel ratio between 0.4 and 1.3). The ther- ATagedP municipal waste incineration power plant, shown in Fig. 67,con- mal process steps are drying, pyrolysis, combustion of volatile sists basically of water/steam side, flue gas path and flue gas cleaning matters and burn out of char. During the pyrolysis, the products devices. In a waste bunker, the delivered raw waste is classified and of char, tar, gases (e.g. carbon monoxide, carbon dioxide and treated. Here, bulky components are crushed and incombustible nitrogen) and volatile organic compounds are basically formed, materials are discharged. Using a crane, the waste is transported to which are released in different proportions. The char is the the firing system. The combustion system is composed of a primary remaining solid that almost consists of pure carbon. In the post-
Fig. 67. Schematic of a municipal waste incineration (TREA Leuna) (reproduced from reference [332]). 154 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162
To horizontal pass HTS_09 +32 m
Water/steam HTS_14 HTS_10
HTS_08
HTS_13 HTS_11 HTS_07
HTS_06
HTS_05 HTS_12
HTS_04
Air +18.4 m
HTS_03 Light fuel
Auxiliary burners secondary air
+15 m
HTS_02
Flue gas Heat exchanger Flue gas pipe HTS_01 Water Control valve Point
+13 m Heat flow Boundary condition
Primary combustion zone
Fig. 68. Municipal waste incineration modelled in APROS. combustionTagedP zone, the remaining combustible species are burned destroyedTagedP by the combustion, the waste incinerators can emit with excess secondary air (approximately 1.5 air/fuel ratio). The high quantities of solid residues (particulate matter), heavy met- exhaust gas flows into the fluegaspaththatiscomposedofver- als, acid gases and nitrogen oxides. Therefore, complex flue gas tical radiation passes and a horizontal pass, in which shell and treatment is required, see Section 2.3.5.6.Thethermalenergy tube heat exchangers are installed. Although most pollutants are released from waste combustion (heating value: approximately F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 155
Fig. 69. Temperature profile within the vertical passes at full load operation.
10TagedP MJ/kg) is transferred to the water/steam circuit via membrane wall evaporators, superheaters and economisers. MunicipalTagedP waste incinerations can also be used to remove the sewage sludge, which denote the residual by-product of industrial and municipal wastewater treatment. The dry sewage sludge con- Fig. 70. Dynamic behaviour of a waste incineration power plant during start-up proce- tains up to 70% organic components and the remaining 30% are com- dure: (top) pressure, (bottom) steam mass flow rate (red line, first axis) and gross elec- posed of, among others, silicates, phosphates, phosphor and heavy trical output of the steam turbine (blue line, second axis). (For interpretation of the metals. With a heating value of 9 to 12 MJ /kg (dried), more than half references to colour in the text, the reader is referred to the web version of this article.) of the sewage sludge in Germany was incinerated in 2010 with the aim of full thermal treatment in the current decade. TheTagedP availability and operation efficiency of a municipal waste incineration can be improved using numerical simulations that can TagedPtemperature decreases sharply due to secondary air supply. The flue be divided in one-dimensional process simulation and three-dimen- gas enters the second vertical pass at h D 32 m and the third vertical sional computational fluid dynamics (CFD). While 3D simulations pass at h D 18 m. Along the flow path, the flue gas temperature are often used for individual components to visualize flow patterns, decreases to approximately 700 °C, before the horizontal pass. The 1D process simulations can model the entire power plant. In the sci- comparison between numerical results and design data shows high entific literature, numerical studies of waste incinerator using CFD consistency. and steady state process simulation were frequently reported. In Pressure,TagedP steam mass flow rate and the gross electrical output of contrast, no publication on 1D dynamic simulation of a municipal the steam turbine during start-up procedure of the municipal waste waste incineration exists to the authors’ knowledge. For the first incineration are depicted in Fig. 70. Approximately 20 min after igni- time, dynamic simulation results for a 60 MWth municipal waste tion, the steam pressure reaches a fixed holding point at 15 bar. The incineration built in Tampere, Finland, are presented in the follow- bypass valve to condenser opens in order to counteract any further ing. The plant burns 5.7 kg/s of waste with an ideal LHV of 10.5 MJ/ pressure rise. Subsequently, the steam mass flow increases sharply kg and discharges 36.3 kg/s of flue gas at 160 °C as well as 0.7 kg/s of within minutes to 15 kg/s. Between t D 120 min and t D 180 min, the slag at 450 °C. The primary air is fed to the grate through 5 zones at heat input starts increasing, resulting in higher steam production 150 °C, while the secondary air that equates to about 30% of the total rate and thus pressure increase. At t D 145 min, the main steam con- air mass flow rate is then supplied through a series of jets on the trol valve to steam turbine starts opening and the bypass valve to sidewalls of the post-combustion zone at 225 °C. The water/steam condenser closes in reverse. As a result, the electrical output of the circuit consists of 4 economisers, 7 superheaters and 5 evaporators steam turbine increases to its nominal value of about 16 MWel. The with natural circulation. At full load, the superheated steam mass LHV variation of the solid waste is reflected by fluctuations of the flow rate at turbine inlet amounts to 20.5 kg/s at 400 °C and 45 bar. steam mass flow. The gross electrical output of the steam turbine is approximately
16 MWel, which yields an electrical gross efficiency of 26.5%. The 7.3. Seawater desalination dynamic model of the municipal waste incineration was generated using APROS. The influence of waste heating value variations on the InTagedP emerging economies especially, the growing population plant efficiency as well as the dynamic behaviour for both part loads together with improved living standard is accompanied by a rapid and start-up procedures were investigated. In Fig. 68, the flue gas increase in clean water demand. Recent studies unanimously expect vertical passes including post-combustion zone, auxiliary burners that in the future, stress on water availability will rise even more and membrane wall heat exchangers are displayed. due to global warming and agricultural irrigation. Desalination of Fig.TagedP 69 shows the temperature profile within the vertical passes seawater is an essential part in providing drinking water in arid of the municipal waste incineration at full load operation. The y-axis regions around the world. In the Gulf Arab states for example, where refers to the height above ground and the x-axis represents the tem- drinking water has always been a scarce and precious resource, perature. At the outlet of the primary combustion zone (h D 14 m), most of the fresh water is produced with seawater desalination the flue gas temperature is around 1200 °C. In the height range plants. Generally, desalination processes can be divided into thermal between h D 14 m and h D 15 m, the temperature of the flue gas processes and membrane processes. decreases due to the heat transfer to the water-cooled combustion TheTagedP separation technology using membrane is a purely physi- chamber walls. In the post-combustion zone, the combustion cal process without heating. For practical application, reverse 156 F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 osmosisTagedP (RO) that uses a semipermeable membrane is especially 8. Conclusion and future prospects relevant. In reverse osmosis, an external pressure considerably higher than the osmotic pressure (seawater: 23 bar) is applied OperatingTagedP flexibility of thermal power plants is essential in order on the side of seawater with high salt concentration. While the to compensate the intermittency of renewable energy sources such membrane allows the solvent to pass to the other side, it keeps as wind or photovoltaics. Enhanced flexibility requirements for the solute on the pressurized side. Reverse osmosis desalination power plants translate, among others, into high load gradients, process utilizes electrical power generated by thermal power reducing the minimum load limit and minimising start-up duration.D184XX plants, e.g. combined-cycle, nuclear power plant and recently This study is a review of dynamic simulation for design, optimisation renewable energy sources [315]. Since the large-scale electricity and the development of novel thermal power plants, including storage is now related to technical challenges, modern operation hybrid concepts that integrate renewables in conventional power concept of RO desalination offers the ability to use the excess plants. generation capacity at times of reduced grid demand and/or AnTagedP overview of dynamic simulation programmes widely used for increased renawable generation to produce clean water that can scientific and industrial application is presented, supported by be easily stored in containers [316,317]. example models for different simulation codes such as ASPEN PLUS InTagedP thermal processes or distillation processes, part of the sea- DYNAMICS, DYMOLA and APROS. The simulation codes are generally water is evaporated, so that brine with high salt concentration based on the governing conservation equations of mass, momentum, remains. After condensing the vapour and adding calcium bicar- species and energy. The specific mathematical formulation of the bonate and other mineral nutrients to the pure distillate, drink- balance equations depends on the underlying flow model. Many ing water is obtained. The thermal processes include multi-stage approaches can be found in the literature such as mixture flow flash, multiple-effect evaporation possibly combined with ther- model or two-fluid models, which in turn can be divided into four- mal vapour compression. In multi-stage flash desalination (MSF), equation, five-equation, six-equation and seven-equation flow mod- the seawater is heated to a maximum temperature of about els. Due to its relative simplicity and suitability for a range of practi- 115 °C and then passes through a series of pressure stages. In cal applications, the mixture flow model is of considerable relevance each chamber a lower pressure thaninthepreviousoneprevails, since the calculation of average mixture properties is often suffi- so that part of the salty seawater is spontaneously flashed to ciently accurate for system-level analysis. The two-fluid model offers steam in order to reach the local saturation state. The multiple- the possibility to consider thermodynamic non-equilibrium phe- effect distillation (MED) consists of multiple stages. In each nomena. It is thus more suitable for detailed analysis of specific com- stage, the seawater flows on horizontal pipes in the direction of ponents and application cases characterised by intense mass and gravity, forming seawater films on the surface of pipes. The hori- heat transfer between phases. The resulting partial differential equa- zontal pipes are internally heated by a steam flow. Accordingly, tion system is discretised and typically closed with empirical corre- part of the seawater is vaporized, collected and directed into the lations, which are selected according to the prevailing flow regime. horizontal pipes of the next stage. There, the vapour condenses; Basic process components required for modelling thermal power releasing its condensation heat to another seawater film and the plants such as tubes, flow valves, heat exchangers, turbomachines process is repeated. For large applications, multi-effect distilla- etc. are discussed, complemented by automation and electrical mod- tion is often used together with vapour compression in order to ules vital for power plant control. The latter include analogue and recover low temperature heat, resulting in an efficiency increase binary modules, signal sources, controllers, generator, transformer, of the MED process. The thermal desalination processes (based inverter and others. on enthalpy of evaporation) are, in contrast to membrane pro- RelevantTagedP publications on dynamic simulation are discussed for cesses, an energy-intensive. However, the membranes are sensi- the different technologies of combined-cycle power, coal-fired tive to chlorine or organic components, so that an additional power, nuclear power, concentrated solar power, geothermal power, pre-treatment of the seawater is essential. municipal waste incineration and thermal desalination in the indi- TheTagedP thermal desalination processes require heating steam that is, vidual chapters. The results can be summarised as follows: generally, produced by a combined heat and power plant or a nuclear reactor. The thermal desalinations are operated at their Combined-cycleTagedP power: Since the gas turbine is an inherently flexi- nominal base loads (stable regimes) and therefore steady state simu- ble component, studies in the literature are largely focused on the lation models are adequate. However, a few studies on the dynamic dynamic response of the water/steam bottoming cycle, in particular simulations of desalination plants can be found in the literature. For the heat recovery steam generator. Detailed modelling and calcula- example, Agha et al.D182XX[37] developed the dynamic simulation model tion of CCPP start-up transients are conducted rather frequently, as of a thermal desalination process (MSF-TVC) using APROS. The well as dynamic optimisation under thermal stress restraints. In con- model was evaluated towards the design data of an industrial desali- trast, system-level dynamics of the IGCC process and the interaction nation plant in Tripoli-Libya with 1200 m3/day production capacity. of syngas path components are not well understood and should be Furthermore, detailed models of thermal desalination units (MED the subject of further study. By deriving reduced models for real- and MSF) coupled with nuclear reactors are presented. Al-Fulaij et time computation from the detailed simulation models, the prospec- al.D183XX[99,100] developed lumped parameter dynamic models for once- tive use of model-predictive control in power engineering applica- through MSF and brine circulation MSF using gPROMS. The gener- tions can be envisaged. Some recent studies are dedicated to shift ated models were in good agreement with measurement data the field of dynamic simulation and optimisation away from com- obtained from existing MSF plants with relative error below 1.5% in mercial codes towards more openly accessible models and software steady state and dynamic conditions. Among others, further publica- tools, a promising approach that the authors would encourage other tions on the dynamic simulation of desalination plants are researchers to follow in the interest of scientific progress. [126,142,318 324]. Recently, new technologies are developed to desalinate seawater using renewable energy sources [325], espe- PulverisedTagedP coal power: In many countries, coal-fired power genera- cially solar energy [326] or even municipal solid waste [327]. These tion remains indispensable in the foreseeable future in order to cover intermittent energy sources (e.g. cloudy day in case of solar energy base load demand. While all coal-fired power plants have the same and variation in heating value of municipal solid waste) require an working principle, each power plant is unique engineered, leading to understanding of the transient process behaviour, which in turn can individual dynamic behaviour. Here, the load change and start-up be evaluated using dynamic simulation. behaviour by increasing flexibility requirements are in the focus of F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79 162 157 interest.TagedP The lack of available data for validation of the developed studiesTagedP regarding the dynamic behaviour of thermal desalination models is a major problem. Although the technology of coal-fired plants (e.g. MSF and MED). The absence of detailed analysis of desali- power is well known, there is still potential for further improvement nation process dynamics, in addition to the missing validation with regarding load gradients, minimal load limit and start-up procedure, plant data should be covered with future studies. Furthermore, there which can be explored using dynamic simulation. Furthermore, the is an interest in developing new desalination technologies using combustion of coal with a nitrogen-free oxidant (oxyfuel concept) renewable energy sources, which increases the need for dynamic has recently received attention. Dynamic simulation can contribute simulation. to this field of research, since design and operation experiences from conventional coal power plants can only be applied to a limited D185XX degree. TheTagedPD19XX desirable expansion of renewable energy sources in many countries around the world is drastically altering the traditional TagedP Nuclear power: The topic of dynamic simulation for nuclear power landscape of power generation, which is required to ensure security plants is broadly discussed and thorough work has already been of supply. Intermittent energy sources such as wind and solar lead to fi done, in the eld of accident analyses in particular. The amount of increasing market demand for control energy in order to maintain research on NPP load-following capability is limited but not a likely grid stability. However, this does not compensate for the decline in focus for further study due to both economic and technical reasons. wholesale electricity prices that impairs the economic viability of The statistical analysis of transient system behaviour is an approach thermal power plants. A number of measures are introduced by only used for NPPs as yet. The existing body of literature shows that power plant operators in response to the new market environment the classic approach of selecting conservative boundary conditions such as retrofitting existing power plants for higher load gradients has its downsides for complex systems. Therefore, statistical analysis and reduced minimum load. Thus, the accurate prediction of should be considered as option for other applications where operat- dynamic system behaviour becomes an integral part of design and D186XX ing safety is paramount.. operation of thermal power plants. Furthermore, process optimisa- tion, which is not always feasible in the real plant due to economic TagedP Concentrated solar power: Due to the inherently dynamic nature of andD192XX safety reasons, is numerically possible. Dynamic simulation is a fi CSP operation, a signi cant number of studies are available in the lit- valuable tool for both the researcher and the practitioner in order to erature. Most studies focus on system-level plant dynamics consid- gain valuable insight and understanding of the system. ering transient solar radiation. Some other studies investigate the dynamic behaviour of sub-systems such as thermal energy storage, InTagedP closing: “Static is simple, but the universe is dynamic”. considering stable power output and improvement of capacity fac- fl tor. In case of molten salt as heat transfer uid, detailed analyses of Acknowledgments filling and draining procedures are conducted. Optimised operation strategies are frequently reported. The considered time horizons TheTagedP authors would like to thank both Institute for Energy Systems vary from operating transients of several minutes up to the predic- & Technology and TU Darmstadt Energy Center for financial support, tion of annual performance data. A certain emphasis lies on mathe- enabling open-access publication of this review. Mr.D193XX Mertens and fi fi matical models for the solar eld. 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