UPTEC ES 19036 Examensarbete 30 hp December 2019

Techno-Economic Analysis of Organic Rankine Cycles for a Boiler Station Energy system modeling and simulation optimization

Jamel Hudson Abstract Techno-Economic Analysis of Organic Rankine Cycles for a Boiler Station Jamel Hudson

Teknisk- naturvetenskaplig fakultet UTH-enheten The Organic Rankine Cycle (ORC) may be the superior cycle for power generation using low temperature and low power heat sources due to Besöksadress: the utilization of high molecular mass fluids with low boiling Ångströmlaboratoriet Lägerhyddsvägen 1 points. They are flexible, simple, easy to operate and maintain, and Hus 4, Plan 0 offer many possible areas of application including waste heat recovery, biomass power, geothermal power and solar power. Therefore, Postadress: they may prove to be of significant importance in the reduction of Box 536 751 21 Uppsala global greenhouse gas emissions and the mitigation of climate change.

Telefon: In this thesis, the technical feasibility and economic profitability 018 – 471 30 03 of implementing an ORC in a district heating boiler station is

Telefax: investigated. A model of the ORC connected to the hot water circuit 018 – 471 30 00 of a biomass boiler is simulated. The achieved evaporation temperature is estimated to 135°C and the condensation temperature is Hemsida: found to vary in the range of 70-100°C. The results show that it is http://www.teknat.uu.se/student both possible and profitable to implement an ORC in the studied boiler station. A maximum net present value of 2.3 MSEK is achieved for a 400 kW system and a maximum internal rate of return of 8.5%, equivalent to a payback period of 9.5 years, is achieved for a 300 kW system. Furthermore, the investment is found to be most sensitive to changes in electricity price, net electric efficiency and capital expenditure cost.

Handledare: Marcus Guldstrand Ämnesgranskare: Ali Al-Adili Examinator: Petra Jönsson ISSN: 1650-8300, UPTEC ES 19036 Acknowledgements

The idea of the thesis originated from my passion for sustainable energy technology and from Claes Nyl´en,manager at WSP, who was able to find a suitable project in cooperation with Alings˚as Energi.

I would therefore like to thank Claes Nyl´en,for his help to initiate the thesis, in addition to the management of Alings˚asEnergi, in particular manager Einar Str¨om. Thank you.

I also thank my supervisor Marcus Guldstrand for his support, expertise, and tough questions, which helped the analysis progress in the right direction. Without Marcus the technical level of the thesis would not be what it is. Thank you.

Furthermore, I give thanks to my subject reviewer Ali Al-Adili who has thoroughly reviewed the report and provided constructive feedback. Without Ali the standard of the report would not be what it is. Thank you.

Bj¨ornSamuelsson of Svenska Rotor Maskiner AB and Elin Ledskog of Againity AB have both been helpful in providing me with insights and details regarding the workings of commercial ORC systems. The talks and study visits have been helpful, interesting, and enjoyable. Therefore, I give thanks to both Bj¨ornand Elin. Thank you.

i Popul¨arvetenskaplig sammanfattning

Klimatf¨or¨andringartill f¨oljdav m¨anniskans anv¨andningav fossila br¨anslen ¨arallvarliga och n˚agotvi b¨orf¨ors¨oka undvika. F¨oratt lyckas med det beh¨over vi minska v˚aranv¨andningav fossila br¨anslen, fr¨amstolja, kol och naturgas som i dagsl¨agetanv¨andsf¨oratt producera elektricitet. Elektriciteten produceras genom att br¨ansletsf¨orbr¨annsmed syfte att koka och f¨or˚angavatten under ett h¨ogt tryck, varefter vatten˚angantrycks genom en turbin vilket ger upphov till en rotationsr¨orelse.Tur- binens rotationenergi omvandlas sedan till en elektrisk effekt med hj¨alpav en generator. Majoriteten av v¨arldenselektricitet produceras p˚aett s˚adant s¨att,och det leder till stora v¨axthusgasutsl¨app.

F¨oratt minska utsl¨appen av v¨atxhusgaser beh¨over vi d¨armedbyta ut fossilbaserad elproduktion- skapacitet mot f¨ornybar s˚adan.Men hur ska vi g¨oradet? Fritt fl¨odande energi, i form av fr¨amst sol- och vindenergi, p˚ast˚asav m˚angavara l¨osningp˚amorgondagens energif¨ors¨orjning— men vad g¨orvi n¨arvarken solen skiner eller vinden bl˚aser?Man kan t¨anka sig att anv¨andandet av batterier

¨arl¨osningen,men en storskalig reglering av v¨arldenseln¨atenbart med battrier ¨arvarken h˚allbar eller tekniskt m¨ojligmed dagens batteriteknologi. Allra helst skulle vi vilja ha en f¨ornybar baskraft, som kan producera elektricitet kontinuerligt, dygnet runt.

Organiska rankinecykler ¨arv¨armemaskiner baserade p˚aorganiska fluider med l¨agrekokpunkt ¨an vatten. De till˚aterelproduktion med v¨armek¨allorav l˚agtemperatur (l¨agre¨an400 °C) samt ¨aven av l˚ageffekt (l¨agre¨an10 MW), f¨orvilka vanliga ˚angkraftverk ¨arotillr¨ackliga. Det ¨arav stor betydelse eftersom mycket av den tillg¨anligav¨armeeffekten,s˚asom spillv¨armei industrier och geotermisk v¨arme,ofta karakt¨ariseras av att vara av l˚agtemperatur och men ¨aven av l˚ageffekt. Av den anled- ningen kan organiska Rankinecykeler spela en viss roll i begr¨ansningenav klimatf¨or¨andringarna.

I det h¨ararbetet studeras b˚adeden tekniska genomf¨orbarhetenoch ekonomiska l¨onsamhetenav att implementera en organisk rankinecykel i ett fj¨arrv¨armeverk i s¨odraSverige. F¨ordelenmed att till¨ampaorganiska rankinecykler i just fj¨arrv¨armeverk ¨aratt det medf¨oren h¨ogenergiverkningsgrad, till f¨ojd av att den v¨armeenergisom inte omvandlas till elektricitet kan tas omhand om och anv¨andas i fj¨arrv¨armen¨atet.F¨oratt bed¨omaden organiska rankinecykelns p˚averkan p˚afj¨arrv¨armeverket, och l¨onsamheten,skapas en modell av fj¨arrv¨armeverket med v¨armemaskinenintegrerad i systemet.

ii Modellen simuleras med befintlig produktionsdata och l¨onsamhetenbest¨ams. Resultatet visar p˚a att det ¨arfullt m¨ojligtoch l¨onsamt att implementera organiska Rankinecykler i fj¨arrv¨armeverk.

Dock s˚avisar det sig att l¨onsamheten ¨arstarkt kopplad till systemets nominella effekt, elpriset och kapitalkostnaderna. Dessutom s˚ap˚avisasatt l¨onsamheten ¨arstarkt kopplad till fj¨arrv¨armever- kets returtemperatur, och att h¨ogrel¨onsamhet d¨armed kan n˚asgivet att returtemperaturen s¨anks.

Studiens resultat kan anv¨andassom underlag f¨orbeslutsfattare som funderar p˚aatt implementera organiska rankinecykler i deras fj¨arrv¨armeverk. Studien ¨ar¨aven av nytta f¨orandra till¨ampning- somr˚aden¨anjust fj¨arrv¨armeverk eftersom en generell metod f¨oratt modellera organiska rankinecyk- ler utvecklas och beskrivs.

iii Executive Summary

Introduction

ORCs may contribute to renewable electricity generation and thus play a role in the mitigation of climate change. The technical feasibility and economic profitability of implementing an ORC at S¨avelundsverket is therefore studied, with the aim of finding the optimal power rating and plant operation.

The effects of a) lowering the DHS supply and return temperatures and b) connecting an ORC to the hot water circuits of all three boilers is also investigated.

Method

The chosen ORC system integration into the plant is illustrated in figure 4.15.

Figure 1: Model of the boiler station with an ORC integrated.

The boiler plant with the ORC model, connected after the flue gas condenser belonging to the boiler of line C, is modeled and simulated. This is chosen as the best location due to the high temperature of the hot water circuit belonging to boiler C, and it is placed after the flue gas condenser such that the power output of the flue gas condenser is unaffected. The electric power output of the ORC depends on the pressure difference over the expander, which is determined by the temperature difference of the heat source and the cooling flow. More precisely, the condenser

iv pressure is determined by the exit temperature of the cooling flow through the condenser; a low temperature cooling flow results in a low condenser pressure which is desirable. However, the exit temperature of the cooling flow depends on the thermal power output and the net electric efficiency of the ORC. Therefore an iterative approach is used in order to model and simulate the system.

The ORC is modeled with the parameters listed in table1, and the profitability is determined using the parameters listed in table2.

Table 1 List of parameters of the ORC model

Parameter Value

Fluid R1233ZD(E) [C3ClF3H2] Expander isentropic efficiency 80% Pump isentropic efficiency 80% Generator electric efficiency 95% Condenser HX TTD 10 °C Evaporator HX TTD 10 °C Evaporation temperature 135 °C Energy losses Neglected Piping pressure losses Neglected Maximum allowable thermal power input 10 · PRAT ED Part load performance Accounted for by correction factor

Table 2 List of economic parameters

Parameter Value Discount rate 5% [60] Economic lifetime 20 years [4][53][55] Electricity price 0.45 SEK⁄MWh Electricity certificate price 0.05 SEK⁄MWh [61] Electricity distribution cost 0.05 SEK/kW h [60] Power charge fee 172 SEK⁄kW [60] High load power charge fee 256 SEK⁄kW [60] Fuel price 0.200 SEK⁄MWh [60] ORC unit cost 10-30 kSEK⁄kW [4][53][55] Installation cost 20% of ORC unit cost Operation and maintenance cost 2% of ORC unit cost [4][53][55]

v Results

Simulating the model, a maximum net present value (NPV) of 2.3 MSEK for a 400 kW machine and internal rate of return (IRR) of 8.5% for a 300 kW machine is found. A sensitivity analysis show that the profitability of the investment is very sensitive to changes in electricity price, net electric efficiency and capital expenditure cost.

Figure 2: Net present value as a function of power rating and electricity price.

vi Key insights

I Integrating an ORC into the HWC of a boiler in a heat-only boiler station is both possible and profitable.

I It is better to connect the ORC after the flue gas condenser belonging to FPC. This limits the flow rate available to the ORC but leaves the heat recovery capability of the flue gas condenser unaffected.

I To increase the profitability of the investment, shift as much of the load of boilers A and B to boiler C in order to both maximize the cooling mass flow rate available to the condenser of the ORC and the thermal power available to the evaporator of the ORC.

I The ORC reduces the power charge fee and distribution costs, which together constitute a substantial share of the total revenues of the investment.

I A maximum electricity production of about 3 200 000 kWh is achieved for a 1000 kWel machine. For system power ratings exceeding 1000 kWel, the yearly electricity production decreases.

I Reducing the supply and return temperature of the power station greatly increases the prof- itability of the investment.

I Aggregating the boiler powers such that more thermal power is made available to the ORC does not increase the profitability of the investment much at all. This is due to a limitation in cooling mass flow rate available to the ORC condenser. Implementing a larger machine to make it possible to utilize a larger thermal input would increase the condenser outlet temperature so much so that the net electric efficiency is severely decreased.

vii Nomenclature

List of Symbols

Greek Letters ∆ Difference - η Efficiency ∈ (0 − 1) ψ Working condition ∈ (0 − 1)

Roman Letters J C Heat capacity K E Energy J H Enthalpy J m Mass kg P Pressure P a P Power W Q Thermal energy J J S Entropy K T Temperature °C U Internal energy J V Volume m3 W Work J

Subscripts b boundary el electric gen generator p pressure, at constant pressure p pump s isentropic, zero entropy generation t turbine th thermal v volume, at constant volume wf working fluid

viii List of Abbreviations

BWR Back Work Ratio CHP Combined Heat and Power HX Heat Exchanger HTF Heat Transfer Fluid HWC Hot Water Circuit FPA Biomass Boiler of Line A FPB Biomass Boiler of Line B FPC Biomass Boiler of Line C FGC Flue Gas Condenser IRR Internal Rate of Return NPV Net Present Value ORC Organic Rankine Cycle TIP Turbine Inlet Pressure WHR Waste Heat Recovery

ix List of Technical Expressions

Enthalpy A thermodynamic property defined as the sum of the internal energy and the product of the volume and pressure of the system. Entropy A statistical property describing the unorderedness of a thermo- dynamic system. It is related to the number of possible micro- scopic configurations in which the system can be arranged. Some entropy generating processes incur unrecoverable losses due to en- ergy spent on unproductive unordering of matter. Heat Capacity A physical material property defined as the amount of thermal energy that needs to be supplied to a mass of 1 kg to increase its temperature by 1 °C. Critical Point The end point of the pressure-temperature curve, above which phase boundaries vanish and the fluid exists in a supercritical state wherein distinct gas and liquid phases do not exist. Internal Energy The energy contained within the system, described as the random kinetic energy energy of the microscopic particles due to their translations, rotations and vibrations. Irreversibility Energy loss due to unproductive entropy generation and unorder- ing of matter. Isentropic Efficiency A performance metric describing how closely a component approx- imates the corresponding ideal component. For an expander it is the fraction of actual work output to the isentropic work output i.e. the work output if the expansion process would take place without irreversibilities. Organic Rankine Cycle A thermodynamic power cycle using an organic fluid and a liquid- vapor phase change for the conversion of heat energy to electricity. Terminal Temperature Difference An indicator of the performance of a heat exchanger, measured as the temperature difference of the hot fluid upon entering the heat exchanger and the colder fluid when exiting the heat exchanger.

x Contents

1 Introduction 1 1.1 Aim...... 3 1.2 Scope...... 3 1.3 Structure and overview...... 3 1.4 Background...... 4 1.4.1 District Heating Systems...... 4 1.4.2 The Electricity Market of Sweden...... 5 1.4.3 S¨avelundsverket Heat-Only Boiler Station...... 6 1.4.4 Organic Rankine Cycle Market Overview...... 9 1.4.5 Manufacturers of Interest to S¨avelundsverket...... 12

2 Theory 13 2.1 Fundamentals of Thermodynamics...... 13 2.1.1 Work, Pressure and Heat...... 13 2.1.2 Internal Energy...... 14 2.1.3 Enthalpy...... 15 2.1.4 Entropy...... 15 2.1.5 Thermodynamics Laws...... 16 2.1.6 State functions...... 18 2.2 Thermodynamic Power Cycles...... 18 2.2.1 Carnot Cycle...... 18 2.2.2 Rankine Cycle...... 21 2.2.3 Combined Heat and Power (CHP)...... 26 2.3 Organic Rankine Cycle Systems...... 26 2.3.1 Working Fluids...... 26 2.3.2 Expanders...... 30 2.3.3 Heat Exchangers...... 31

xi 2.4 Flue-gas Condensation...... 35 2.5 Financial Investment Analysis...... 35 2.5.1 Net Present Value...... 35 2.5.2 Discount Rate...... 36 2.5.3 Internal Rate of Return...... 38

3 Method 39 3.1 Data received on S¨avelundsverket...... 39 3.2 System Integration...... 40 3.3 Model Input Data...... 41 3.4 Modeling the Organic Rankine Cycle...... 42 3.5 Modeling and Simulating the System...... 46 3.6 Financial Modeling...... 48 3.6.1 Electricity network subscription...... 48 3.6.2 Modeling costs...... 49 3.6.3 Modeling benefits...... 51 3.7 Sensitivity Analysis...... 52 3.8 Scenario Analysis...... 53

4 Results 54 4.1 Boiler Power, DHS Temperature and Mass Flow...... 54 4.2 Investment Cost Estimation...... 56 4.3 Organic Rankine Cycle Model...... 57 4.3.1 Comparison of working fluids...... 59 4.3.2 Thermal efficiency and condensation temperature...... 63 4.3.3 Net electric efficiency during part-load operation...... 65 4.4 Flue Gas Condenser Model...... 67 4.5 Simulating the system...... 68 4.6 Profitability Analysis...... 73 4.7 Sensitivity Analysis...... 76 4.8 Scenario Analysis...... 78 4.8.1 Scenario 1: Aggregating the boiler powers...... 78 4.8.2 Scenario 2: Lowering the DHS supply and return temperature...... 80

5 Discussion 84

6 Conclusion 86

References 87

xii Appendices 92 A.1 Received plant data...... 93 A.2 Flowchart of the simulation algorithm...... 95 A.3 System output during the year with an ORC integrated...... 96 A.4 Model verification...... 96 A.5 Validation of Results...... 100 A.5.1 Svenska Rotor Maskiner...... 100 A.5.2 Againity...... 101 A.6 Code: Constructing model input data...... 102 A.7 Code: Flue gas condenser model...... 103 A.8 Code: ORC model...... 104 A.9 Code: Run ORC function...... 105 A.10 Code: T-s plot...... 107 A.11 Code: p-h plot...... 108 A.12 Code: Boiler station model with an ORC integrated...... 109 A.13 Code: Boiler station model with an ORC integrated – for Scenario 1...... 114 A.14 Code: Financial investment valuation model...... 119 A.15 Code: Find max P...... 120

xiii List of Figures

1 Model of the boiler station with an ORC integrated...... iv 2 Net present value as a function of power rating and electricity price...... vi

1.1 The District Heating Network of Alings˚asEnergi [19]...... 7 1.2 Simplified layout of the boiler station...... 8 1.3 Total installed capacity per application and per manufacturer [20]...... 10 1.4 Market share per application and per manufacturer [20]...... 10 1.5 Evolution of installed capacity over time, per application [20]...... 11 1.6 Market share per application and per manufacturer [20]...... 11

2.1 Carnot cycle illustrated on a PV diagram...... 20 2.2 Carnot cycle illustrated on a T-s diagram...... 20 2.3 Temperature-Entropy diagram of a saturated water/steam Rankine cycle...... 24 2.4 Temperature-Entropy diagram of a superheated water/steam Rankine cycle...... 24 2.5 Temperature-Entropy diagram of a reheated water/steam Rankine cycle...... 25 2.6 Temperature-Entropy diagrams of saturated Rankine cycles for three different work- ing fluids of different molecular complexity [4]...... 27 2.7 Twin screw expander [40]...... 30 2.8 Off-design expander isentropic efficiency and thermal efficiency of ORC [47]...... 31 2.9 Off-design component isentropic efficiency and thermal efficiency of ORC [48]..... 31 2.10 Shell and tube heat exchanger [49]...... 32 2.11 Heat Exchanger Terminal Temperature Difference...... 34

3.1 Model of the boiler station with an ORC integrated...... 40 3.2 Model of the ORC part-load performance...... 44 3.3 T-s diagram of the modeled power cycle...... 45 3.4 Flowchart of the computation algorithm...... 47

4.1 Constructed FPC boiler power profile...... 54

xiv 4.2 DHS Return and Supply Temperature...... 55 4.3 Calculated DHS mass flow rate...... 55 4.4 System cost as a function of power rating...... 56 4.5 ORC model T-s diagram...... 57 4.6 ORC model P-h diagram...... 58 4.7 Fluids illustrated in a T-s diagram...... 60 4.8 Organic fluids illustrated in a T-s diagram...... 61 4.9 Sulfur dioxide T-s diagram...... 62 4.10 R1233ZD(E) T-s diagram...... 62 4.11 Thermal efficiency vs condensation temperature...... 64 4.12 ORC part-load correction factor...... 65 4.13 ORC surface of net electric efficiency...... 66 4.14 Flue gas condenser surface of power output...... 67 4.15 Layout of the simulated boiler station with the integrated ORC model...... 68

4.16 Resulting DHS supply temperature for a 1000 kWel ORC...... 69

4.17 Resulting DHS supply temperature for a 1400 kWel ORC...... 69

4.18 Boiler power load profile for a 1000 kWel ORC...... 70

4.19 Simulated system temperatures and mass flow rates for a 1000 kWel ORC...... 71 4.20 Simulated power generation for a 1000 kW ORC...... 72 4.21 Net present value of ORC´systems as a function of electric power rating and electri- city price...... 74 4.22 Internal rate of return of ORC systems as a function of electric power rating and electricity price...... 75 4.23 Payback period of ORC systems as a function of electric power rating and electricity price...... 75 4.24 NPV sensitivity plot...... 77 4.25 Aggregated boiler power profile...... 78 4.26 NPV and IRR for scenario 1: Aggregated boiler power...... 79 4.27 DHS Return and Supply Temperature for scenario 2a: Slightly reduced DHS supply and return temperature...... 80 4.28 NPV and IRR for scenario 2a: Slightly reduced DHS supply and return temperature. 81 4.29 DHS Return and Supply Temperature for scenario 2b: 4th generation DHS supply and return temperature...... 82 4.30 NPV and IRR for scenario 2b: 4th generation DHS supply and return temperature. 83

1 FPC boiler power during 2018...... 93 2 FPB boiler power during 2018...... 93

xv 3 FPA boiler power during 2018...... 94 4 Return and supply temperature during 2018...... 94 5 Flowchart of the computation algorithm...... 95 6 System output for a 800 kW ORC...... 96 7 Estimated production for a 1000 kW system by SRM [55]...... 100 8 Estimated production for a 385 kW system by Againity [53]...... 101

xvi List of Tables

1 List of parameters of the ORC model...... v 2 List of economic parameters...... v

1.1 List of ORC manufacturers, with number of installed units and total installed capa- city before Dec 31st, 2016 [20]...... 9

2.1 Description of technical terms relating to thermodynamic processes...... 19

3.1 List of provided plant data...... 39 3.2 List of restraints...... 39 3.3 List of parameters of the ORC model...... 45 3.4 List of model input variables...... 46 3.5 List of economic parameters...... 51

4.1 Description of states...... 57 4.2 ORC parameters...... 59 4.3 Table of fluid properties and thermal efficiencies...... 60

4.4 Financial analysis of a 500 kWel ORC...... 73 4.5 Sensitivity of the NPV with respect to certain variables...... 76

1 Parameter inputs...... 97 2 Parameter outputs for the 20th iteration...... 97 3 Parameter used for the manual computation...... 98 4 Validation of results, SRM...... 100 5 Validation of results, Againity...... 101

xvii Chapter 1

Introduction

Antrophogenic climate change due to the widespread use of fossil fuels, and the subsequent emissions of green house gases, is a real concern and a matter to be taken seriously [1]. To solve this problem the world must shift away from oil, gas and coal and develop renewable means of electricity generation. Solar and wind energy is most prominently championed by policy-makers, and laymen, as the future of clean electricity generation. But, what should we do when the sun doesn’t shine and the wind doesn’t blow?” Many might suggest that the solution is that we store enough energy in batteries and further improve the interconnectedness of the power networks of the world, however there are some issues with that idea. Altough perhaps possible in the future, stabilizing the entire electricity network using the battery technology of today is neither possible nor sustainable, due to technical and resource constraints, in addition to being very expensive [2][3]. It is clear that a renewable, or low emitting, means of continuously generating electricity is needed. Furthermore, ways to improve the energy efficiency, and thus reduce the fuel consumption, of already existing industrial processes and vehicle using fossil fuels, needs to be developed as well. Today, gas and steam power cycles are used to generate most of the electricity in the world, however there are many energy sources for which both gas and steam cycles do not offer viable energy conversion solutions, due to technical infeasibility or unfavourable economics [4]. Such energy sources are either characterized by being of low temperature, low power (below 10 MWel), or a combination of the two. Organic Rankine cycles are, in contrast to gas and steam power cycles, well suited for low power and low temperate heat source applications, such as electricity production from biomass combustion, industrial waste heat and geothermal heat to name a few [4]. The technology is simple, compact and easy to implement: the boiler pressures are relatively low, the turbines can be single stage, the operation is simple and the low maintenance requirements result in high reliability, high availability and long life times [4]. The Organic Rankine Cycle is also well suited for both continuous and variable power generation, and offers good power generation performance during low partial thermal loading [4].

1 Goldschmidt [5] assessed the profitability of applying ORC systems in boiler stations utilizing hot oil boilers, and found organic Rankine cycles superior to steam/water Rankine cycles in the range of 0.5-2.0 MWel [5]. However the study does not thermodynamically model the system as a whole, so the more practical effects of integrating an ORC system into the station is not investigated. Furthermore, the economic analysis is based on several assumptions, such as an arbitrary 5000 hours full-load operation per year with a fixed net electricity production. In a slightly more recent study, Sundberg et al. (2011) assessed the feasibility of different cogeneration technologies and for different applications [6]. This was done based on a master thesis by performed by Svensson (2011) in which a model of the system was developed in Matlab and simulated using hourly-data [7]. Using the model, several case studies were investigated one of which was the feasibility of applying an ORC system in a small local heating network. The results of the study found that it would not be profitable based on the prevailing economic conditions and due to limitations in available thermal demand resulting in a very small ORC system and thus higher investment costs per kWel. Eriksson (2009) evaluated several different thermal power technologies applied to Swedish conditions of which one was the organic Rankine cycle [8]. Of the assessed technologies, the organic Rankine cycle, applied in a district heating boiler station, was showed to be the most feasible. However none of the technologies were found to be profitability during the prevailing economic conditions. Nazaar and Lundkvist (2018) evaluated the profitability of rebuilding a district heating pipeline and a subsequent installation of a small (<50 kWel) ORC system in boiler station in Sweden [9]. The proposed ORC was modeled as being integrated between the supply- and return temperature allowing for a temperature differential of 50 °C at most. Due to this, a low net electric efficiency of roughly 2.2 % was achieved, resulting in a non-profitable investment. Lind (2015) investigated the electricity generation and profitability of combined ORC and heat pump integrated into a district heating system [10]. It is a certain type of ORC system which can be reversed and act as a heat pump, by some adjustments, allowing for the generation of electricity during the summer and heat during the winter. The proposed integration is similar to the one modeled by Nazaar and Lundkvist [9] in which the system is integrated between the district heating system suppy and return temperature. The results of the study show a very profitable investment, with a payback period of less then two years. This may be due to the fact than an arbitrary net electric efficiency of 5% is used, much higher than what was found by Nazaar and Lundkvist [9].

2 1.1 Aim

In this thesis, the technical feasibility and economic profitability of implementing an ORC in the heat-only boiler plant S¨avelundsverket, located in Alings˚as,Sweden, is investigated. The research questions asked, in order to fulfil to aim of the thesis, are:

• How, technically, can an Organic Rankine Cycle system best be implemented in S¨avelunds- verket in order to maximize the profitability of the investment?

• How should the plant best be operated in order to maximize the profitability of the investment?

• What is the optimal system sizing, i.e. installed nominal power, which maximizes the profit- ability of the investment?

1.2 Scope

The scope of the thesis comprises technical modeling and simulation of the boiler station with an Organic Rankine Cycle system integrated into the plant. The thermodynamic modeling of the boiler station and the ORC is done in a steady state manner, neglecting transient phenomena. Heat and pressure losses are also neglected due to their relatively small significance in this application. The results from the technical simulation is then used in a financial model to assess the profitability of the investment. The simulation of the model and financial investment analysis is performed for an economic default case scenario which most closely resembles the economic reality of today. The profitability at different electricity prices is also studied, since it is unlikely that the electricity price of the future will remain what it is today. Sensitivity analyses are also conducted in order to illustrate how changes, or uncertainty, in input parameters affect the valuation of the project as a whole. A few scenario analysis are performed in order to investigate the effects of different scenarios.

1.3 Structure and overview

Chapter 1, Introduction, introduces the topic and provides a background to district heating systems, the electricity market of Sweden and the boiler station S¨avelundsverket. Furthermore an overview of the ORC world market and some interesting ORC manufacturers is provided. Chapter 2, Theory, provides the fundamental thermodynamic theory necessary to understand the physics of the thesis, covering fundamental thermodynamic concepts such as entropy and enthalpy, in addition to thermodynamic power cycles. Flue gas condensation and heat exchanger theory, as

3 well as theory on financial investment valuation, is also described. Chapter 3, Method, describes the method used to fulfil the aim of the thesis. Data provided for by the management of S¨avelundsverket and the data used in the model is described. Also, the method used to model and simulate the components of the system and the system as a whole and evaluate the profitability of the investment is described in detail. Additionally, a couple of hypothetical scenarios of interest to be investigated are also also described. Chapter 4, Results, presents the result of the performed technical- och economic analysis. The result of the performed scenario analyses and sensitivity analyses is also presented. In Chapter 5, Discussion, the underlining meaning, or significance, of the work is explored and the major findings are discussed. In Chapter 6, Conclusion, the key findings of the thesis are summarised.

1.4 Background

1.4.1 District Heating Systems

District heating systems (DHS) were first introduced for commercial purposes in the United States, in Lockport and New York, in the late 1800s and first in Europe in the 1920s in Germany [11]. Major district heating networks now exist in several of the major cities: Moscow, Beijing, Berlin and Stockholm to name a few, and it is estimated that there are 6000 district heating systems in Europe and 80’000 globally [12]. Globally and in the EU, less heat is supplied by use of district heating than by use of electricity, however DHS are common in the Nordic and Baltic countries where high implementation rates exist [13].

District heating systems most commonly supply heat to districts by means of transporting hot water through a network of pipes directly to end consumers which absorb some of the heat. The water, now cooled and at a lower temperature, is then transported back to a central heating facility to be re-heated and sent out into the district heating network again. In Sweden, the district heating facilities consists of one, or several, boilers in which primarily biofuels or waste is burned. However, fossil fuels still dominate the district heating fuel supply in many parts of the world.

District heating systems offer a variety of benefits of the local community and society in general. E.g. it allows for a flexibility in choosing the heat sources, reduced fuel consumption and fuel costs, reduced emissions and greater ability to control emissions [14]. Some drawbacks are that the systems require substantial initial investments and it is very costly to supply heat to geographically dispersed communities due to high connection fees and increased thermal losses [14].

Globally, the main users of district heating are large buildings and industrial facilities; the service sector only represents a smaller share of the total district heat consumption. Single family homes

4 are not often connected due to high energy distribution losses resulting in high distribution costs, and as a result not more than 2% of European single family homes are connected [15].

The vast majority, 98%, of the worlds electricity is generated using steam turbines which have efficiencies of around 40% meaning that 60% of the heat energy is wasted [4]. Furthermore, many industries generate heat as a by product which is also wasted. This unused potential in heat energy provides a strong argument for the implementation of district heating systems. By cooling the condenser of the power plant against the district heating network, i.e. simultaneously generating useful heat and electricity, the otherwise wasted heat may be salvaged, increasing the total energy efficiency of the process vastly. The simultaneous generation of electric and useful thermal energy, named cogeneration or combined heat and power (CHP) generation, is often used when the primary requirement is heat.

1.4.2 The Electricity Market of Sweden

The Swedish electricity network can be divided into three main areas: (1) transmission network (2) regional networks and (3) local network. The transmission network is used to transmit electric energy over large distances and is thus operated at a high voltage level to reduce the required current and the subsequent transmission losses. The regional network is in turn used to transmit power from the transmission networks to the local networks, into which end-use consumers, such as households, are connected. In total, the power cabling of the entire Swedish electricity network comprises about 570 000 km in length which is roughly 360 times the length of Sweden, and about two thirds of the total cabling length is buried underground [16].

Svenska kraftn¨at is a state-owned public utility company owning and operating the transmission network (stamn¨atet)and is responsible for maintaining the power balance and operational reliability in the Swedish power grid. The frequency of the Swedish electricity grid is to be maintained close to 50 Hz. Whenever there is a mismatch between the power fed into the grid by the generators and the power consumed by the loads, the frequency of the grid either increases or decreases. However, it is quite challenging to constantly maintain the grid frequency in a safe operating the range of 49.9-50.1 Hz, independent on the fluctuations of the power demand and supply. In order to do so, the power generation is rapidly increased at times when the frequency starts to increase, and by decreasing the power generation at times when the frequency starts to decrease.

The regional and local networks are maintained by local and regional utility companies which are responsible for ensuring that their networks are maintained enough such that the reliability of the supply can be guaranteed [16].

The Swedish electricity network, as a whole, is a regulated monopoly and its the Energy Market Inspectorate (Ei) that is tasked with assessing the utilities revenues and making sure that the price

5 increases placed on consumers are reasonable [16].

The trading of electricity takes place on Nord Pool, a power exchange founded in 1996 by Sweden and Denmark. Nord Pool provides marketplaces for [17]:

1. Day-ahead market. A market for trading power products to be delivered 24 hours in advance, offered in the Nordics, Baltics, Central Western Europe and the UK.

2. Intraday market. A market for hourly, or sub-hourly, trading of power products within 13 markets, encompassing the Nordic, Baltic, German, Luxembourg, French, Dutch, Belgian and Austrian markets.

3. Futures market A market for the future delivery of power products.

During 2018 a total of 524 TWh of power was traded through Nord Pool, of which 396 TWh was traded in the Nordic and Baltic day-ahead market, 120 TWh in the day-ahead market and 8.3 TWh in the intraday markets [17]. The average system price was 43.99 EUR/MWh, or around 0.469 SEK/kWh [17].

Sweden is a very oblong country with a lot of electricity production in the north, due to the natural occurrence of cheap hydropower. However, most of the people live in the southern part of Sweden, implying the need of electricity transport from the north of Sweden to the south of Sweden. This results in ”bottle necks” in the distribution capacity of the longitudinal power lines going from north to south. To amend this, the electricity network was split into four electricity price areas in 2011.

1.4.3 S¨avelundsverket Heat-Only Boiler Station

Alings˚asEnergi is an energy concern owned by the municipality of Alings˚as.Their product portfolio includes a district heating network and a heat production facility, providing the municipality of Alings˚aswith their district heating demand. The heating demand of the municipality is provided for almost solely by S¨avelundsverket, with a small part of the heat demand supplied using biogas in another facility [19]. Currently the annual district heating demand of Alings˚asamounts to 145 GWh, which is expected to rise to 170 GWh before year 2040 [19]. The DHS network is almost 160 km long with 670 houses and 400 apartment buildings, consisting of 6550 apartments, connected. The heating network is shown in figure 1.1[19].

6 Figure 1.1: The District Heating Network of Alings˚asEnergi [19].

7 S¨avelundsverket comprises three solid fuel burners, of which two are rated for 14 MWth and one for 7 MWth, in addition to an 12 MWth oil boiler, a 0.5 MWth landfill gas boiler and two flue gas condensers of 8 MWth each. It is primarily their new 14 MWth boiler FPC that is of interest for

ORC application, and secondarily the boilers FPB and FPA of 7 MWth and 14 MWth respectively. A simplified layout of the plant, neglecting the oil boiler and landfill gas boiler, is illustrated in figure 1.2.

Figure 1.2: Simplified layout of the boiler station.

Component Description FPC Boiler of line C FPB Boiler of line B FPA Boiler of line A FGC Flue Gas Condenser HX Heat Exchanger

8 1.4.4 Organic Rankine Cycle Market Overview

A nearly exhaustive world overview of the Organic Rankine Cycle market at the industrial level up until the year of 2017 is shown in table 1.1[20]. The sum of 706 projects and 1754 installed ORC units up until 2017 amounts to a total installed capacity of 2701 MW, which is comparable to the installed capacity of around 2 large nuclear reactors or 900 medium-sized wind turbines.

Table 1.1 List of ORC manufacturers, with number of installed units and total installed capacity before Dec 31st, 2016 [20].

9 Geothermal power generation is the most prevalent ORC application is terms of installed capacity, constituting 74.8 of total installed ORC capacity in the world. Waste heat recovery (WHR) is noted to be an emerging field of interesting potential for various ORC unit sizes, contrary to the geothermal power generation field which is dominated by a few large players due to high barriers of entry as a result of large investment cost requirements [20], as is shown in figure 1.3. Furthermore, biomass applications amount to 11% of total installed capacity. Italian Turboden dominates the biomass ORC arena with large share of installed power and installed plants. Concentrated solar power applications are as of end of 2016 negligible primarily due to the high investment cost of the field of solar receivers which make them more expensive than photovoltaic and battery system solutions [20]. In conclusion, aggregated over all areas of ORC applications, the American company ORMAT is found to be the world leader with 62.9% of of the total installed capacity, followed by the Italian companies Turboden (13.4%) and Exergy (11.1%) [20].

Figure 1.3: Total installed capacity per application and per manufacturer [20].

Figure 1.4: Market share per application and per manufacturer [20].

The evolution of installed capacity over time, per application is shown in figure 1.5. Geothermal is noted to be the initial application ORC application with the first plants developed in the 1980s [20]. Biomass ORC:s emerged in the early 2000s and solar just recently. The growth of the biomass market has been stable due to the possibility of applying the same standardized, off-the-shelf, ORC units [20]. It has partly also been by driven by political financial

10 incentives in central Europe [20]. The average biomass ORC plant is ≈ 1.5 MW, with the largest reaching ≈ 8 MW and there has been a market trend towards increased average unit size yet also a market trend towards increased diversity in unit size with more and more small units as well [20].

Figure 1.5: Evolution of installed capacity over time, per application [20].

A geographical market breakdown shows that USA constitute the largest share of installed capacity overall, and Germany, followed by Italy, Canada and Austria has the largest shares of installed capacities for biomass application. Also there are many ORC systems under construction in Europe, whereas for geothermal applications the growth in the near future is shown to be more geographically dispersed [20].

Figure 1.6: Market share per application and per manufacturer [20].

11 1.4.5 Manufacturers of Interest to S¨avelundsverket

In this section ORC manufacturers meeting certain criteria, making them of interest to S¨avelunds- verket. are briefly described. The criteria considered are geographical proximity and the provision of ORC systems of at least 200 kWel nominal power suitable for heat source temperatures up to 170°C.

Againity

Againity, with headquarters in Norrk¨oping,Sweden, offers Organic Rankine Cycles in the range of

50-2500 kWel. The systems are able to work with heat source temperatures as low as 90°C due to their own developed axial-flow turbine [21]. Their ORC systems are standardized, modular, and have low down-times, with availabilities exceeding 97%, and short installation times.

Svenska Rotor Maskiner

Svenska Rotor Maskiner (previously Opcon) is a Swedish company dating back to 1908. In the 1920s they invented the famous and widely used air preheater which increased the thermal efficiency of many industrial processes [22]. Currently their product range and expertise is within the areas of industrial WHR, geothermal heat recovery, industrial refrigeration compressors, air systems for use in fuel cell applications, screw compressors and screw expanders [23]. Their ORC solution, named the SRM Powerbox, can utilize heat sources as low as 55°C and uses a twin-screw expander [24].

ECT Power

ECT Power is a Swedish company is in the process of developing a unique ORC concept, which they name the ORC 2.0. They don’t have a commercial system yet, but are working on realizing their concept and taking it to market [25]. The technology utilizes a multi-pressure pump and turbine system that will supposedly increase the thermal efficiency vastly.

12 Chapter 2

Theory

2.1 Fundamentals of Thermodynamics

The behaviour of thermodynamic systems follows the four laws of thermodynamics and the workings of thermodynamic systems may be described in either a macroscopic view, by classical thermody- namic theory, or in a microscopic view, by statistical mechanics theory. The classical view is sufficient for thermodynamic computation of power cycles, however in this theory chapter some statistical descriptions are included for sake of completion and to facilitate the understanding of some key concepts.

2.1.1 Work, Pressure and Heat

In thermodynamics the work exerted, or performed, by a system is equal to the energy transferred by the system to its surrounding. Similarly, work can be exerted from the surrounding on the system by the transfer of energy.

The pressure-volume work, or simply PV work, occurs when the volume of a system changes due to the pressure exerted on the system boundary. It is also named moving boundary work since it is associating with moving the system boundary. For a closed system the infinitesimal amount of work performed by the system is found as [33]

∂Wb = F · ds = PA · ds = P · dV (2.1)

13 The total work is then found as the closed surface integral of the pressure exerted on the system boundary during an expansion, or compression, from an initial volume V1 to a final volume V2 [33].

I V2 Wb = P · dV (2.2) V1

2.1.2 Internal Energy

The energy of a system contained within its boundary is named the internal energy. It does not include the kinetic energy of the movement of the system as a whole nor any potential energy due to external force fields [33].

The internal energy of any given state is constructed by adding up the macroscopic transfers of energy that prepared it from the reference state to the current state. It can be expressed as

U = ∆U + Uref (2.3) where ∆U is the change in internal energy formed as the summation of the energies required to transform the previous reference state to the new state, i.e.

X ∆U = i (2.4) i

In a classical view, the internal energy can be seen as the sum of motion of the particle’s contained within the system boundaries, with respect to the center-of-mass of the system. Therefore the internal energy may be divided into microscopic potential and kinetic energy components and expressed as

U = Upot,micro + Ukin,micro (2.5)

In a statistical view, each particle contained within the system has exists in its own microstate of energy, i, and with a certain probability, pi. The internal energy of the system as a whole is then found as the expected values of all the individual microstates, i.e. [34]

N X U = pii (2.6) i=1

The internal energy of the system can be increased by increasing the mass of the system, i.e. by increasing the number of particles, by the supply of heat or by doing thermodynamic work on the system.

In practise it is difficult, if not impossible, to accurately measure the internal energy of any given state. However, engineering thermodynamics is only concerned with the changes in internal energy,

14 and not with the absolute value. The changes in internal energy can be deduced from knowledge of certain extensive properties of the system, such as the entropy of the system, when it is prepared from its initial state to a new state by means thermodynamic processes or thermodynamic opera- tions.

For a closed system, such as for the Rankine power cycle, changes in the internal energy of the system are solely due to heat and work performed since there is no transfer of mass through the system boundary. It can be expressed as

dU = ∂Q + ∂Wb + ∂Wisochoric (2.7) where ∂Wisochoric is the work which do not alter the volume of the system, such as frictional work.

2.1.3 Enthalpy

Enthalpy, derived from the Greek word ’thalpos’ meaning ’heat’, or ’warmth’, was originally used to describe the heat content of a system; however the original interpretation is now obsolete and a bit misleading. It is a combination property consisting of the internal energy of the system and the product of the pressure and volume of the system [33].

H = U + PV (2.8)

It is an extensive property, i.e. dependent on the mass of the system. The equivalent intensive specific enthalpy is often used, simply defined as [33]

H h = (2.9) m

It is a very useful property for analyzing power cycles because for closed processes occuring under constant pressure, the heat absorbed or released equals the enthalpy change of the system. And for an isentropic expansion process, the change in enthalpy equals the work performed by the system on its boundary.

2.1.4 Entropy

Entropy, after the greek word for ’transformation’, can be interpreted as a measure of a systems un- certainty, or unorderedness, which remains after observable macroscopic properties such as volume, pressure and temperature have been accounted for. It has to do with the number of possible mi- croscopic configurations that the system can assume.

In the 1850s and 1860s, before any statistical mechanical interpretation of the topic existed, Rudolf

15 Clausius described entropy as the dissipative (unproductive) energy use of a system during a change state [35]. E.g., when usable heat is used to produced work in thermodynamic power cycle, a ’trans- formational’ energy content is ’lost’ as generated frictional heat.

In a classical thermodynamics view the microscopic details of the system are not considered, and the entropy of a system is defined from its empirical relations to certain thermodynamic variables such as temperature, pressure and heat capacity. It only depends on the current state of the sys- tem, independent of how that state came to be. Thus, if state variables such as the pressure and temperature of the system are known, the entropy of the system may be determined. Formally, it is defined as [33] ∂Q dS = rev (2.10) T where Qrev represents the heat gain, or loss, for a internally reversible (ideal) process and T the temperature of the system boundary. So, for any process, reversible or not, if the energy of the system is reduces by ∂E and the entropy of the system is reduced by dS, the system must release thermal energy not less than T dS to the environment. The greater the irreversibilites in the process, the more heat energy released for the same entropy loss.

Later, during the 1870s, Boltzmann, Gibbs and Maxwell later gave entropy its statistical basis. In statistical mechanics, it is seen a measure of the number of ways in which a system can be arranged and is thus proportional to the number of individual atoms and molecules of the system. It is a measure of the number of states with significant probability of occupation

X S = −Kb pi · log(pi) (2.11) i where Kb is the Boltzmann constant and pi is the probability that the i:th state is occupied [34].

2.1.5 Thermodynamics Laws

Zeroth Law of Thermodynamics

The zeroth law, although evident, is included for sake of completion. It simply states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other [33].

First Law of Thermodynamics

The first law of thermodynamics, also known as the conservation of energy principle, states that energy can neither be created nor destroyed during a process; it can only be transformed [33]. For an isolated system, i.e. a system enclosed with walls through which neither mass nor energy can

16 pass, the total energy of the system is therefore constant due to the fact that energy is always conserved over time. Furthermore, for closed systems, the first law implies that the change in internal energy of the system is equal to the difference of the heat supplied to the system and the work performed by the system energy can neither be created nor destroyed during a process; it can only be transformed [33]. ∆U = Q − W (2.12)

Second Law of Thermodynamics

The second law of thermodynamics can be formulated in many different, yet equivalent, ways. The important implication of the statements is that the entropy of a closed system may never decrease with time [33]. The entropy of a closed system and its surrounding may remain constant in cases where equilibrium exists, or if a fictive ”reversible” (non-entropy generating) process is taking place [33]. However, for all real world processes the total entropy of the system and the surroundings increase, and are thus irreversible. The entropy generation accounts of the irreversibility of the process - and therefore the term ”irreversibility” has become synonymous with ”entropy generating” or ”inefficiency” when relating to thermodynamic processes.

For a idealized reversible process in a closed system the incremental entropy generation exactly equals, per definition, the incremental change in heat energy of the system divided by the boundary temperature of the system [33]. ∂Q dS = (2.13) T However for an irreversible process in a closed system the entropy generation will always be larger than the ’ideal’, or reversible, entropy generation [33].

∂Q dS > (2.14) T

Third Law of Thermodynamics

The third law, although less relevant for engineering thermodynamics relating to power cycles, is included for sake of completion. It provides an absolute reference point for the determination of the entropy of a system, which is extremely important for analyzing chemical reactions [33]. The third law states that the entropy of a system approaches a minimum, constant, value as the temperature of the system approaches zero, independent on other variables such as the pressure or applied magnetic field upon the system. The minimum value is the lowest-energy state possible and known as the zero-point energy of the system. For a perfect crystal there exists only one possible lattice configuration at absolute zero, and thus the ground state is 0 K [33]. However for every other system the zero-point energy will always be greater than 0 K.

17 2.1.6 State functions

Thermodynamic state functions, or functions of state, describe system properties as a function of one, or several, state variables which only depend on the current state of the system and not on the path by which the system came to be [36]. A non-exhaustive list of common state functions used in engineering thermodynamics are: energy, internal energy, exergy, enthalpy, entropy, pressure, temperature and volume. The function of state are solely dependent on certain state variables; state variables which in turn also may themselves be state functions dependent on a certain set of state variables.

For properties of interest, we have that

H =f(p, T, S) S =f(p, T, H) T =f(p, H, S) p =f(T,H,S) however knowing only two state variables is enough to determine the state function. In some cases, when interested in the saturation pressure or saturation temperature of a fluid, the state function can be determined by knowledge of the temperature, or the pressure, solely.

2.2 Thermodynamic Power Cycles

A thermodynamic cycle consists of a sequence of thermodynamic processes involving heat and work transfer through the system boundary, while state variables such as pressure and temperature are varied. They are most often used to transform heat energy to useful work, and are thus heat engines by definition. Thermodynamic cycles may also be reversed such that they transfers heat energy from the cold source to the hot source, and are thereby named heat pumps.

The cycles may be closed or open. A closed system may exchange energy with its environment but not matter, and an open system may exchange both energy and matter. Thermal power plants utilize closed power cycles; there is no mass transfer crossing the system boundary from or into the environment, if everything is working as it should. A list of technical terms relation to thermodynamic processes is detailed in table 2.1.

2.2.1 Carnot Cycle

Sadi Carnot proposed an ideal theoretical power cycle in 1824 which was later named after him [37]. The cycle is reversible and extracts heat from a hot reservoir, produces some maximum amount of

18 Table 2.1 Description of technical terms relating to thermodynamic processes

Adiabatic No heat transfer Isothermal Constant temperature Isobaric Constant pressure Isochoric Constant volume Isentropic Constant entropy Isenthalpic Constant specific enthalpy Polytropic pV n = Constant Reversible process Zero entropy generation work, and deposits the remaining heat to the cold reservoir.

The Carnot cycle consists of four processes, occuring in the following order [33]:

(1) −→ (2) Isothermal expansion. Heat is transfered from the hot source into the system at constant pressure whereby the volume of the system increases and work is performed by the system on its boundary.

(2) −→ (3) Reversible adiabatic expansion. The system is continuing to expand but now during a state of reduced pressure, but constant temperature. The system boundary is increasing in volume and work is being performed by the system on its boundary.

(3) −→ (4) Reversible Isothermal compression. The surroundings do work on the system boundary, increasing the pressure. The system is rejecting heat into the cold source, at constant pressure while it is being compressed.

(4) −→ (1) Reversible adiabatic compression. The surroundings continue to do work on the system, compressing it further resulting in a pressure and temperature increase of the system.

A pressure-volume diagram can be used to illustrate the changes in volume and pressure of a system, shown in figure 2.1. For cyclic processes, the work output can be estimated as the area enclosed by the curve when travelling through the sequence of processes. The temperature-entropy diagram is another common diagram to visualize the cycle, shown in figure 2.2. The work output of during one cycle can thus be found by integrating the pressure over the volume. By knowing that the internal energy of the system is the same after one cycle, i.e. that H dU = 0, the work is

I I I I W = P · dV = (dQ − dU) = (T · dS − dU) = T · dS = (Th − Tc)∆S

Reasoning using the second law of thermodynamics the work output may also be found. From the hot source an amount of energy amount equivalent to TH ∆S is extracted and into the cold source

TH ∆S is deposited. From this the maximum amount of work output is found as the difference

19 Figure 2.1: Carnot cycle illustrated on a PV diagram.

Figure 2.2: Carnot cycle illustrated on a T-s diagram.

20 (TH − TC )∆S. The thermal efficiency thus depends solely on the temperature difference between the two reservoirs.

QH = TH ∆S

QC = TC ∆S W Q − Q T η = = H C = 1 − C QH QH TH

The Carnot cycle is useful when analyzing the potential of a power cycle because it provides an upper limit of achievable thermodynamic efficiency, and is therefore often used as a benchmark. Actual power cycles efficiencies are often quoted as a percentage of the Carnot efficiency, denoted as Fraction of Carnot (FoC) [4].

2.2.2 Rankine Cycle

Thermal power plants, which are used to generate the vast majority of the worlds electricity, are based on the Rankine cycle, which is an idealized heat engine for conversion of heat energy into mechanical energy. Water/steam is predominantly used as the working fluid. However real power plants are non-ideal and undergo thermodynamic processes with losses. The losses, or irreversiblities arise due to real world conditions and imperfect machinery. They include friction, mixing of two fluids, heat transfer through a finite temperature difference, electric resistance, inelastic deformation of solids and chemical reactions [33]. When modeling an actual power plant, the efficiency of its components, primarily the expander and pump, needs to be discounted by their isentropic efficiencies to account for the losses in the components.

The Rankine cycle consists of four processes which are [33]:

(1) −→ (2) Isentropic pressurization of liquid water in a pump. The pressure of the water is increased by a pump, named the boiler feed water pump because it feeds the water into the boiler. In the ideal case the pump work is found as the pressure-volume work, which is equal to the enthalpy increase of the fluid [33]

W˙ P =m ˙ wf · v1 · (P2 − P1) (2.15)

W˙ P =m ˙ wf · (h2 − h1) (2.16)

21 However, in reality the work input to the pump exceeds the enthalpy increase due to irreversibilities, such as friction, and we have that [33]

h2s − h1 ηp = (2.17) h2 − h1 h2s − h1 h2 = h1 + (2.18) ηp

W˙ p =m ˙ wf · (h2 − h1) (2.19)

For Rankine cycles using steam as the working fluid, the pump work in relation to the turbine work is small, and often neglected in calculations. However for Rankine cycles using organic fluids, the ratio of pump work to turbine work (BWR) can reach 16% [38].

(2) −→ (3) Isobaric heat addition in the boiler. The pressurized water is heated and vaporized in the boiler. The heat input which is absorbed by the water equals the product of the mass flow rate of the water and the difference of the specific enthalpies of the water, before and after the boiler. The governing equation for the heat addition into the cycle is [33]

Q˙ in =m ˙ wf · (h3 − h2) (2.20)

(3) −→ (4) Isentropic expansion in the turbine. The water, now in vaporized form as steam, is expanding through the turbine, giving off a part of its energy as work to the turbine blades resulting in a rotational motion of the turbine around its shaft. The rotational, mechanical, energy of the rotating shaft is then converted into electrical energy by use of a electrical generator. In the ideal case the work output is given as

W˙ T =m ˙ wf · (h3 − h4) (2.21)

However, in reality the enthalpy drop over the expander (most often an axial turbine) is reduced due to irreversibilites. This is accounted for by the isentropic efficiency of the expander.

h3 − h4 ηT = h3 − h4s

h4 = h3 − ηT · (h3 − h4s)

W˙ T =m ˙ wf · (h3 − h4)

(4) −→ (1) Isobaric heat rejection in the condenser. After the turbine the fluid exists as a liquid-vapor mixture. The vapor content of the mixture is

22 liquefied using a condensing heat exchanger. The thermal power output is given as [33]

Q˙ out =m ˙ wf · (h4 − h1) (2.22)

The mass fraction of the fluid in relation to the total mass is named the vapor qualitiy, x. In general, vapor qualities below 90% is undesirable.

m x = vapor (2.23) mtotal y − y x = f (2.24) yg − yf

yf = Property in saturated liquid state (2.25)

yg = Property in saturated vapor state (2.26) y = Specific enthalpy, entropy or volume (2.27)

The thermal and electric efficiencies of the power plant is

W˙ out,net W˙ t − W˙ p (h3 − h4) − (h2 − h1) ηth = = = (2.28) Q˙ in Q˙ in (h3 − h2)

ηel = ηth · ηgen (2.29) where ηgen is the efficiency of the electric generator.

The Rankine cycle is often visualized using the T-s diagram. For a saturated cycle, as shown in figure 2.3, the expansion process over the turbine begins in the saturated phase and ends up deep inside the two-phase region. This is highly undesirable because liquid water damages the turbine blades. In order to prevent this from happening, superheating of the steam upon entry in the turbine is often used [33], as shown in figure 2.4. Often, this superheating process is repeated several times by expanding the steam in the turbine in several stages and reheating it before entry [33], as shown in figure 2.5.

23 Figure 2.3: Temperature-Entropy diagram of a saturated water/steam Rankine cycle.

Figure 2.4: Temperature-Entropy diagram of a superheated water/steam Rankine cycle.

24 Figure 2.5: Temperature-Entropy diagram of a reheated water/steam Rankine cycle.

25 2.2.3 Combined Heat and Power (CHP)

Combined heat and power(CHP), or cogeneration, plants simultaneously generate both electricity and useful heat. Instead of rejecting the excess heat from the power cycle into the environment, it is utilized as e.g. process heat or supplied to a district heating network. This results in a greatly increased energy utilization factor, or energy efficiency, of the process as a whole [33]. The energy utilization factor is found as [33]

W˙ net + Q˙ u u = (2.30) Q˙ in

Qu = Useful heat generated (2.31)

2.3 Organic Rankine Cycle Systems

Organic Rankine Cycle rely on the same principle as conventional steam Rankine cycles but use organic fluids instead of water, making them more suitable for utilization of low-temperature heat sources [4].

2.3.1 Working Fluids

The choice of working fluid is the most important design choice of an ORC system since it affects the thermodynamic cycle, the performance and cost of components, the plant layout and the safety requirements [4]. Furthermore it is the single criteria which separate ordinary steam/water power cycles from their organic counterparts – in this case it is the fluid that makes the machine.

Substituting water, a simple molecule consisting of 3 atoms, with a more molecularly complex fluid have substantial effects. The heat capacity of the fluid is increased due to a greater phonon contri- bution to the heat capacity. The phenomena is explained by the phonon theory of thermodynamics wherein the heat capacity of the fluid is largely described as arising from atomic vibrations, named phonons [39]. Increasing the specific heat capacity of the fluid will have three major effects on the power cycle [4]: (1) Alter the slope of the saturated vapor curve as commonly depicted in the Temperature-Entropy diagram, (2) Increase the importance of the liquid preheating phase with respect to the evaporation phase and (3) Increase the importance of the desuperheating phase of the heat-rejection process.

The influence of the fluids molecular complexity, on the power cycle is illustrated for three fluids of varying molecular complexity: Water [H2O], Benzene [C6H6] and MDM [C8H24O2Si3][4].

26 Figure 2.6: Temperature-Entropy diagrams of saturated Rankine cycles for three different working fluids of different molecular complexity [4].

Firstly, the saturated vapor curve is altered in such a way that the slope of the curve to the right of the critical point is vertical, or positive. This results in a completely dry expansion phase, without liquid formation in the expander, in contrast to a steam/water power cycle which suffers from liquid formation in the last stages of the turbine. For this reason organic Rankine cycles do not, at least when utilizing dry or isentropic fluids, require superheating. This is important since substantial superheating is not possible when utilizing a low temperature heat source; there simply does not exist a second, higher temperature, heat source with which to superheat the vapor with.

Secondly, due to the altered characteristics of the saturated vapor curve, a larger part of the heat addition takes place in the liquid fluid state, with respect to the vaporization phase, for power cycles utilizing organic fluids. This is shown by the ”shape” of the power cycle, depicted in the Temperature-Entropy diagrams for Benzene and MDM in figure 2.6[4].

Thirdly, as is also depicted by the saturation curves of Benzene and MDM in figure 2.6, the tem- perature drop across the expander is lower for organic fluids than for water, resulting in a higher turbine outlet temperature. This will have the affect that the heat released during the process occurs over a larger temperature difference and with a larger amount of heat being released during the desuperheating phase for organic power cycles than for a steam/water power cycles [4].

Categorization of working fluids

As previously described and shown by the ”shape” of the power cycle in the Temperature-Entropy diagram, the characteristics of organic working fluids differ from water. Due to this the organic working fluids are commonly categorized into three types [4]:

1. Wet fluids with negative saturation vapor curves

27 2. Isentropic fluids have vertical saturation vapor curves

3. Dry fluids have positive saturation vapor curves

For organic Rankine cycles it is primarily dry and isentropic fluids that are of interest since wet fluids can give rise to liquid drop formation in the expander which in turn can result in erosion and corrosion of the expander.

Thermal Stability

Organic fluids most often deteriorate when heated to high temperatures. The thermal stability of a working fluid is its ”heat resistance”,i.e. the capability of all its physical properties to remain unchanged when heated. It is an important characteristics since it determines the temperature at which the fluid can be heated to, as well as the maximum temperature at which the fluid can be used in a thermodynamic cycle. Thermal degradation is caused due to the breaking of the molecular bonds of the working fluid, resulting in the forming of new compounds with different boiling points, which is highly undesirable for the overall heat transfer process. Thermal degradation always occurs after a threshold temperature, the Thermal Stability Limit, and it increases exponentially as a function of temperature after that limit [4]. For most organic working fluids the thermal stability limit is around 350-400°C[4].

Constant Temperature Heat Sources

It is shown that for constant heat sources, the best real cycle solution is always a satured cycle [4]. However for variable temperature heat sources it is not a clear cut case and various config- urations must be considered [4]. Furthermore, for constant temperature heat sources, as is more or less present in S¨avelundsverket, the fluid properties which, to the greatest extent, influence the performance of the saturated Rankine are [4]

1. the molecular complexity, i.e. the number of atoms

2. the critical temperature

3. the molecular mass

It is also shown that organic Rankine cycles utilizing both simple and complex working fluids should, in theory, be able to reach ideal cycle efficiencies of 85% of the Carnot efficiencies. Accounting for the irreversibilites of a real power cycle, the limit reduces to about 65-70%, nonetheless still impressive [4]. However, cycles utilizing highly complex working fluids incur heavy efficiency penalties and as a result have a higher need for a recuperator to decrease those efficiency penalties [4].

28 Desirable characteristics of working fluids

Several considerations must be made when selecting an approriate working fluid, some more evident than others. Ideally, a working fluid should be [4]:

1. Commercially available and inexpensive. A cheap working fluid is increasingly important for larger plants. Fortunately the global HVAC industry places much of the same requirements on its working fluids and produces them in large quantities and cheap.

2. Nonflammable. Flammable hydrocarbon, e.g. ethanol, are sometimes used which in turn brings additional precautionaries and costs.

3. Nontoxic and compatible with materials. Ideally the fluid is non-toxic in reasonable quantities and works with the materials of the system (e.g. the lubrication, piping etc.).

4. Environmentally harmless. The harmfulness of organic working fluids are quantified by two measures, (1) Ozone depletion potential (ODP) and (2) Global warming potential (GWP), and is ideally low in both measures.

5. Isentropic or dry. Because the occurrence of liquid drop formation during the expansion phase is undesirable, and since substantial superheating in order to avoid this is inappropriate for low temperature heat sources, a fluid with a vertical or positive saturation curve slope is desirable.

6. Sufficiently high thermal stability limit. A thermal stability limit above the temperature of the heat source is desirable to avoid thermal degradation of the fluid.

7. Acceptable pressure. Different fluids have different saturation pressures at different temperat- ures. Ideally we want the pressure over the turbine to be high, i.e a high boiler pressure and a low condensation pressure. A too high condensation pressure not only reduces the efficiency of the cycle but also results in a more costly design of the condenser.

8. High specific enthalpy of vaporization and density. By using a fluid with a high specific enthalpy of vaporization and density the same amount of fluid absorbs more heat in the vaporization process, thus less of the fluid needs to be circulated throughout the system to transport the same amount of heat. The result is a system with a reduced flow rate and reduced pump-to-turbine back work ratio.

However no working fluid lives up to all of these requirements, so there is always a compromise [4].

29 2.3.2 Expanders

The expander is the most important component in terms of determining the performance of an ORC system [4]. Many different types of expanders exist, such as axial-flow turbines, radial-inflow turbines, radial-outflow turbines and positive displacement (”volumetric”) expanders [4]. Since both axial inflow and radial inflow turbines are well known and comparatively easier to visualize, a twin-screw positive displacement expander is illustrated in figure 2.7. However, the axial inflow

Figure 2.7: Twin screw expander [40]. turbine is by far the most common turbine in general, with over 90% of the worlds electricity being generated with axial-flow turbines [4], and often used for ORC applications as well. Due to the characteristics of the working fluid, efficient two-stage or even single-stage turbine designs are made possible, allowing for a more compact turbine. The performance of expanders, in general, primarily depends on the design of the expander, the actual size of the expander and the extent to which it is operating at off-design conditions [4]. At partial thermal loading, the working fluid mass flow evaporated is reduced which in turn reduces the mass flow through the expander. The result is that the enthalpy drop over the expander is reduced. A literature review shows that expander isentropic efficiencies of 65% [41], 75% [42], 80% [43], 86% [44] and 87% [45] are used when modeling and simulating ORC systems. A study using finite element analysis to determine the efficiency of an actual turbine used for ORC application found a turbine efficiency in the range of 80-85% [46]. Furthermore, the partial load performance of a biomass CHP ORC system has been studied by Erhart et al.[47]. They found that the turbine efficiency decreases with the mass flow rate, and that the thermal efficiency decreases exponentially with the reduction of thermal input, shown in

30 figure 2.8.

Figure 2.8: Off-design expander isentropic efficiency and thermal efficiency of ORC [47].

Wang et al. (2016) studied the performance of an ORC system with a variable heat source tem- perature and mass flow rate [48]. They found that the turbine efficiency and thermal efficiency behaved similarly to the findings in [47], shown in figure 2.9.

Figure 2.9: Off-design component isentropic efficiency and thermal efficiency of ORC [48].

2.3.3 Heat Exchangers

Heat exchangers (HXs) are systems facilitating heat transfer between two, or more, both used for heating and cooling purposes. An example of a HX found in most homes is a space heater. Industrial HXs are most often used for cooling purposes and a condenser is a common example of such a HX. The HX design depends on the purpose and requirements on the heat transfer process, and for that reason there are many different types of HXs. One of the most common types found

31 Figure 2.10: Shell and tube heat exchanger [49]. in industry is the shell and tube HX, shown in figure 2.10. Other common types of HXs are plate HXs and Tube-in-Tube HXs.

Thermal conduction is the primary mechanism by which the heat transfer in a heat exchanger, from one fluid to the other, occurs. In general, thermal energy is transfered through the material by disorganized microscopic collisions of particles and movements of electrons within the material. In solids, conduction is mediated by the combinations of the vibrations, propagation and diffusion of molecules, phonons and electrons. Metals are therefore good thermal conductors, and often used in heat exchangers, due to their metallic bonds which allow for the free movement of electrons within the material.

Fourier’s law describes the rate of heat transfer as proportional to the negative temperature gradient across the surface. It is given as q˙ = −k∇T (2.32)

∂ ∂ ∂ where ∇ is the nabla operator ( ∂x , ∂y , ∂z ) and k is the conductivity of the material which may be seen as constant in certain temperature ranges, depending on the material.

Differentiating across the entire surface, S, of a material the heat transfer is found as the closed surface integral ∂Q I = −k ∇T · dS (2.33) ∂t where the dS represents the differential surface element. In the one-dimensional case, e.g. through a plane surface, the equation [2.33] simplifies to

dT Q˙ = −k (2.34) dx

32 ˙ dQ where Q = dx . In heat exchangers, and other flow systems, the temperature driving force of the heat transfer process is often described by the logarithmic mean temperature difference (LMTD). For a heat exchanger with two ends, named A and B, the LMTD is

∆T − ∆T LMT D = A B (2.35) ln ∆TA ∆TB and can be used to determine the heat transfer in the heat exchanger, i.e. the heat exchanged, as

Q˙ = U · A · LMT D (2.36) U = Heat transfer coefficient (2.37) A = Area (2.38)

The performance of a heat exchanger is often measured by the terminal temperature difference (TTD) of the fluid flows passing through the heat exchanger. The higher temperature fluid gives of thermal energy and exits the HX at a lower temperature, whereas the lower temperature fluid enters the HX at a higher temperature.

Considering a counter-flow HX, if the temperature of the hot fluid entering the HX is named Th1 and the exit temperature of the colder fluid is named Tc2, then the TTD is given as Th1 −Tc2. For a counter-flow HX the TTD, with the same notation of temperature flows, is illustrated in figure 2.11. The saturation temperature, and thus condenser pressure, depends on the TTD. When modeling organic Rankine cycles, TTD values of 6 °C is observed to be used by some authors [50][51].

33 Figure 2.11: Heat Exchanger Terminal Temperature Difference.

34 2.4 Flue-gas Condensation

Flue gas condensation is a heat recovery process in which the flue gas from the water is cooled down below its dew-point, resulting in liquid water formation. The energy content of the condensed water is then recovered as low grade heat.

Tdp = Tsat(Pv) (2.39)

Pv = Partial pressure of water vapor (2.40)

When the flue gas is condensed, the mass content of the dry gases remains unchanged; it is only the mass content of the wet content, the water, that is reduced.

The energy balance over the condenser is

Q˙ RGK FPC = H˙ in − H˙ out = H˙ flue gas,in − H˙ flue gas,out − H˙ cond (2.41)

Enthalpy of the inflow depends on the mass fractions of the different molecules in the flue gas, which depends on the chemical composition of the used fuel.

˙ Hin =m ˙ in,H2O · hin,H2O + (m ˙ N2 · hN2 +m ˙ CO2 · hCO2 +m ˙ O2 · hO2 ) (2.42)

Enthalpy of the outflow is

H˙ out = H˙ out,flue gases + H˙ out,condensate (2.43) ˙ Hout, flue gases =m ˙ out,H2O · hout,H2O + (m ˙ N2 · hN2 +m ˙ CO2 · hCO2 +m ˙ O2 · hO2 ) (2.44) ˙ Hout,condensate = (m ˙ in,H2O − m˙ out,H2O) · hcondensate,H2O (2.45) (2.46)

2.5 Financial Investment Analysis

For many financial decisions, costs and benefits occur at different points in time and since a unit of currency to be paid (or spent) in the future is worth less than that same unit of currency today, there is a need of implementing life cycle costing analysis when analyzing financial projects. This is true even if there is no inflation since the same unit of cash can be invested and generate interest.

2.5.1 Net Present Value

The net present value (NPV) is used as a measure of economic value when comparing different investment, or project, options. It is determined as the difference between the present value (PV)

35 of the benefits and costs of the project, i.e.

NPV = PV(Benefits) − PV(Costs) (2.47)

If positive cash flows are used to represent benefits and negative cash flows are used to represent costs the NPV can also be expressed as

NPV = PV(All project cash flows) (2.48)

The present value of a future cash flow, C, n years forward in time using a discount rate of r, is calculated as C PV = (2.49) (1 + r)n Incorporating inflation, i, in the PV expression we have that

 1 + i n PV = C (2.50) 1 + r

If we define C as the net cash flow occuring during year n, the NPV of the project is determined as

N X  1 + i n NPV = · C (2.51) s 1 + r n=0

It can be shown that for a constant net cash flow, C, the NPV reduces to a finite geometric series with the value [52] 1+i
n+1 ! 1 − 1+r NPV = C · 1+i
, r 6= 0 (2.52) 1 − 1+r

2.5.2 Discount Rate

The rate used to discount future cash flows to the present value, referred to as the discount rate, r, is an important parameter of the NPV and must be chosen carefully. Often the discount rate is set equal to the companies weighted average cost of capital (WACC), which is the average cost of capital the firm must pay to all of its investors to compensate them for the risk of holding the firm’s debt and equity together. Another alternative is set to the discount rate equal to the interest rate which the company can expect to return from alternative, competing projects. This would allow for a direct comparison of the alternatives.

The WACC, for a company financed only by debt and equity, is formulated as

D E WACC = · C + · C · (1 − T ) (2.53) D + E d D + E e

36 where D is the total debt, E the total equity, Cd the cost of debt, Ce the cost of equity and T is the corporate tax rate [52].

The cost of debt is, in the general case, determined as

Cd = (Rf + credit risk rate)(1 − T ) (2.54) where Rf is the interest rate of a risk-free bond with a duration matching the term structure of the corporate debt [52]. The cost of debt is a measure on the amount of money that is spent on debts and can also be determined as the sum of interests being paid on all debts divided by the total amount of debt, i.e. P diri Cd = P (2.55) di

The cost of equity is determined by the risk free rate, Rf , the risk premium of the market determined as the difference in the historical return on the market and the risk free rate, and by the sensitivity of the asset to market risk [52].

Ce = Rf + β(Rm − Rf ) (2.56)

The sensitivity of to market risk β, is determined by the covariance (Cov) between the asset and the market as well as by the variance (Var) of the market [52]. In this case the asset would be the present value of future revenues generated from the electricity production of the ORC.

Cov(r, r ) β = m (2.57) V ar(rm)

However if we assume that the present value of future cash flows arising from the electricity pro- duction only depends solely on the electricity price, the expression of the WACC can be further simplified. Since the electricity price is fairly insensitive to stock market fluctuations, the β of the electricity production can be assumed very low and set to 0. The cost of equity is equal to the risk free rate and the WACC is then expressed as

D E WACC = · C + · R (1 − t) (2.58) D + E d D + E f

The NPV Decision Rule

Since NPV is expressed in terms of cash today the equivalent of the NPV is the value, or wealth, that the project adds to the company today. Therefore, when deciding between projects, one should choose the project with the highest NPV. Furthermore, when deciding whether to accept or reject a project, one should accept projects with positive NPV and reject projects with negative NPV.

37 2.5.3 Internal Rate of Return

The IRR is a metric used to assess the relative profitability of investments [52]. It is defined as the interest rate for which the net present value of all cash flows of the investment, or project, is equal to zero [52]. The definition of the IRR relies on the same formulas as the NPV, i.e. discounted cash flow (DCF) analysis, and yields the return of the project.

IRR = Value of discount rate such that the NPV equals zero (2.59)

It can also be expressed as

N X  1 + i n IRR = NPV = (S − C) + C = 0 (2.60) s 1 + r 0 n=1

The strength of the IRR method is that it yields the investments profitability in relative terms, which is useful for comparison of various investments, or projects, of different size.

38 Chapter 3

Method

3.1 Data received on S¨avelundsverket

Production data, relating to the boilers and system temperatures of S¨avelundsverket, is provided for by the management of the plant. It includes data on the boiler powers and the return temperature. Data on the supply temperature is hard to obtain and for that reason a realistic, estimated, data series is provided by the management of the plant. The format of the data is presented in table 3.1, and the data is viualized in appendix A1. Some limitations relating to the plant is also provided for, shown in table 3.2

Table 3.1 List of provided plant data

Data Format Unit Electric power consumption Hourly average values W DHS return temperature Daily average values °C DHS supply temperature Daily average values °C FPC boiler power Daily average values W FPB boiler power Daily average values W FPC boiler power Daily average values W

Table 3.2 List of restraints

Restraint Limit

Minimum boiler downtime 30 days/year Minimum boiler runtime 7 consecutive days Maximum DHS supply temperature drop 5 °C Maximum DHS temperature in plant 115 °C

39 3.2 System Integration

The chosen ORC system integration into the plant is illustrated in figure 4.15. The boilers FPA and FPB are modeled as an aggregate boiler FPAB.

Figure 3.1: Model of the boiler station with an ORC integrated.

An Organic Rankine cycle system can be integrated into the boiler station in several ways, however in order to maximize the electricity production, and the revenues therefrom, it is desirable that:

1. The temperature of the heat transfer fluid mass flow (water) through the evaporative heat exchanger is high

2. The temperature of the heat transfer fluid mass flow (water) through the condensing heat exchanger is low

3. The mass flow rate of the heat transfer fluid mass flow (water) through the condensing heat exchanger is high

By having a high temperature mass flow through the evaporative heat exchanger the maximum allowable boiler pressure, and turbine inlet pressure, is increased. Similarly, a low temperature cooling flow through the condenser in combination with a high mass flow results in a low condenser pressure. The pressure difference over the turbine is thus increased by a high temperature difference, which is desirable.

Since the hot water circuit temperature of boiler FPC is greater than the HWC temperatures of

40 boilers FPB and FPA, due to the higher pressure rating of boiler C, a model of the system with the evaporator, the ”hot side”, of the ORC connected to the hot water circuit of boiler FPC is created. In practise, the physical connection is made with pipes, and the flow rate can be controlled by use of three-way valves. Ideally, we would want to maximize the mass flow rate through the condenser and thus connect it to the DHS return flow just upon arrival at the plant, before it has been split up into smaller mass flows within the plant. However, connecting into a point before the fluegas condenser belonging to FPC would raise the temperature of the incoming flow to the flue gas condenser and reduce its power output as a result. Therefore, the condenser is connected just after FGC-FPC.

By connecting the evaporator outflow to the return circuit of the FPC HWC, i.e. by connecting in parallel across HX-FPC, the temperature into HX FPC is unaffected. This is desirable since it leaves the temperature difference, ∆T , between HX FPC and the DHS flow unaffected. A reduction in ∆T would in result in a reduced HX heat transfer performance. Due to the fact that the condenser of ORC system is cooled against the return flow, approximately all of the heat output QORC,OUT is recovered in the process. This results in a high, almost 100% total energy efficiency, independent on the electric efficiency which may be 10% or less. Also, due to this, the net power output from the process as a whole (the aggregation of the boiler and flue gas condenser power) is approximately equal to the electric power output, which has the resulting effect that the DHS return temperature is lowered by a fraction relating to the electric power output.

3.3 Model Input Data

The available thermal power which may be fed to the ORC is limited by the power of boiler FPC and the rated thermal power input. From the obtained production data it can be seen that FPC is not operated at its maximum capacity, so the input data to the model is adjusted such that as much as possible of the DHS demand is provided for by FPC. However the boiler cannot operate year round, a minimum downtime of 30 days per year is required. An algorithm that finds the 30 day period with the lowest thermal power demand of the DHS network and shifts that load from FPC to FPA and FPA is implemented, resulting in the maximal power loading of the FPC. Another limitation, which is also adjusted for by another algorithm, is the fact that any boiler may not operate for shorter than 7 consecutive days.

Neglecting the biogas boiler and peak-load oil boiler, and distribution losses, the DHS demand can be approximated as the sum of the boiler powers and fluegas condenser powers.

Q˙ DHS = Q˙ FPC + Q˙ FPB + Q˙ FPA + Q˙ FGC,FPC + Q˙ FGC,FPAB (3.1)

41 From the aggregation of the boiler powers and fluegas condenser powers the DHS mass flow rate is found as Q˙ DHS m˙ DHS = (3.2) CPTe − CpTa

3.4 Modeling the Organic Rankine Cycle

The thermodynamic state of the working fluid as it passes through the power cycle can be determ- ined using a table of fluid properties. The C++ library CoolProp with equations of state (EOS) and transport properties of 122 fluids is used (Coolprop, 2019). It is supported by Python and many other programming languages, however not by MATLAB directly. This can be solved by either running a Python program in MATLAB or by approximating the function by a polynomial and evaluating the polynomial in MATLAB. In this work the latter option is chosen.

On the choice of preheating

Commercial ORC systems, especially smaller systems below 10 MWel, rarely preheat the working fluid in a separate heat exchanger since it would require an additional heat exchanger, in excess of the evaporative heat exchanger. The increased thermal efficiency, and additional revenues therefrom, do not make up for the incurred costs. Therefore, a power cycle without preheating is modeled.

On the choice of superheating

Furthermore, the working fluids used in commercial fluids are often dry, allowing for a dry expansion phase with no, or very limited, liquid drop formation. The resulting benefit is that there is no need to superheat the fluid, which would require an additional, costly, heat exchanger. Also, for a constant temperature heat source the optimal cycle is shown to be saturated [4]; using superheating would not result in any benefits just additional costs.

Evaporation temperature

The evaporation temperature is limited by the temperature of the HTF (hot water) at the exit of the evaporative HX, T2, and by the TTD of the HTF and the organic working fluid. Furthermore,

T2, depends on the HTF inlet temperature, T1 and mass flow rate,m ˙ 1. However, it is desirable that T2 is controlled such that it is fixed at the temperature of the mass flow returning to the FPC-HX, which is currently 145°C, year round. The boiler circuit of FPC is rated at a pressure of 10 bar, resulting in a maximum HTF saturation temperature of 179.9°C. Currently the boiler is operated such that the HTF temperature is in the range of 160-168°C. However, since the HTF will not start evaporating until it reaches the saturation temperature at the HWC pressure of 10 bar, the temperature of the HWC can be increased to a higher temperature.. Therefore, T1 is set to

42 170°C, year round; roughly 10°C below the saturation temperature for safety reasons. The resulting evaporation temperature of the ORC working fluid depends on T2 and the TTD.

T1 = 170°C (3.3)

T2 = 145°C (3.4)

Tevap,max = T2 − TTDevap (3.5)

Condensation temperature

The condensation temperature depends on the DHS mass flow temperature exiting the condensing

HX, T4 and the TTD. However, T4 in turn depends on the mass flow ratem ˙ orc and the heat rejection by the condensing HX and resulting heat addition to the mass flowm ˙ orc.

Tcond = T4 + TTDcond (3.6)

On the choice of working fluid

Different isentropic and dry working fluids are evaluated and compared. The most suitable working fluid will be used in the default model, i.e the fluid which most closely resembles the working fluid(s) of the ORC manufacturers of interest to S¨avelundsverket.

Component efficiencies

From discussions with manufacturers of ORC systems, and from the conducted literature review on the matter, realistic design-point expander and pump isentropic efficiencies are in the range of 70-85%, depending on type of expander and the build-quality. The expander and pump efficiencies are both set to 80% during nominal working conditions. The electric efficiency of the generator is modeled as being 95% and constant. This is a reasonable assumption it should be slightly more than 95% during nominal operation and be slightly less than 95% during off-design operation. The terminal temperature difference of the evaporator and condenser is set to be 10°C, and fix, not- varying with the LMTD. Although lower values of 6°C are observed in literature, [50][51], a higher value is used as a precautionary measure due to the scarcity of sources in literature modeling actual, commercial, systems.

Partial load performance

The performance off the system during off-design conditions is accounted for by multiplying the η nominal thermal efficiency with a correction factor, ψ. From [47] and [48], ψ = th/ηth,nominal, is estimated and shown in figure 4.12. ψ is further estimated by a third degree least-squares estimate,

43 with coefficients [-0.5323 0.0643 1.4592 -0.0010]. From ψ the thermal efficiency is determined as

ηth = ψ · ηth,nominal (3.7) 3 2 1 ηth = (−0.5323)ψ + (0.0643)ψ + (1.4592)ψ + (−0.0010) (3.8)

Figure 3.2: Model of the ORC part-load performance.

To conclude, the resulting cycle being modeled is a simple, saturated cycle without the utilization of superheating or preheating. The cycle consists of one pump, one evaporative heat exchanger, one expander and one condensing heat exchanger. The power cycle shape using the refrigerant

R1233ZD(E) [C3ClF3H2], used by the company Againity for this type of application, is illustrated in figure 3.3 in order to illustrate the general shape of the cycle. A list of the ORC parameters used in the model is presented in table 3.3.

44 Figure 3.3: T-s diagram of the modeled power cycle

Table 3.3 List of parameters of the ORC model

Parameter Value Fluid R1233ZD(E) Expander isentropic efficiency 80% Pump isentropic efficiency 80% Generator electric efficiency 95% Condenser HX TTD 10 °C Evaporator HX TTD 10 °C Evaporation temperature 135 °C Energy losses Neglected Piping pressure losses Neglected Maximum allowable thermal power input 10 · PRAT ED Part load performance Accounted for by correction factor

45 3.5 Modeling and Simulating the System

A model of the boiler station with the Organic Rankine Cycle is constructed. The model inputs are shown in table 3.4.

Table 3.4 List of model input variables

Variable Description Unit

Ta Return temperature °C Te Supply temperature °C m˙ DHS DHS mass flow W Q˙ FPC FPC thermal power W Q˙ F P AB FPAB thermal power W PRAT ED System electric power rating W ˙ QORC,RAT ED Maximum thermal power input °C Q˙ ORC,IN Thermal power supplied to the system W

The workings of the algorithm is illustrated in figure5. Given the inputs, the algorithm first computes the minimum mass flowm ˙ ab such that the temperature of the mass flow out of the HX of FPAB precisely equals the limit temperature of 115 °C. The resulting mass flowm ˙ is computed asm ˙ DHS minusm ˙ ab. Subsequently, Tb is computed from the mass flowm ˙ and the FGC-FPC power, which depends on the return temperature and the FPC power. The ORC condenser outlet temperature T4, and as result also Tc, depends on the thermal power output which in turn depends on the thermal input fed to the ORC and the electric efficiency. However the electric efficiency in turn depends on T4. Thus, in order to initialize first the computation, T4 is arbitrarily set to 60°C for the computation to proceed. Td is also set to an arbitrary number, in this case to the desired

Te which is preferable because it is close to what it will end up being. This is due to the fact that an initial ansatz close to the actual values increases the rate of convergence.

Next, with an ansatz of T4 = 60°C, the electric efficiency of the ORC is determined. Then, from the electric efficiency, the electric power and thermal power output of the ORC is determined, from which T4 is computed. Tc depends on T4 and the fraction of mass flow which does not go through the ORC condenser, however since we want T4 to be as low as possible, all of the available mass

flow is taken through the condenser, i.e.m ˙ orc =m ˙ , resulting in Tc = T4.

Then, the power fed to the HX of FPC is determined and Td is computed. If Td has changed since the last iteration, the electric efficiency of the ORC, and the subsequent power flows and temperatures, are computed anew. When Td has stabilized, the algorithm computes the delivered supply temperature Te given the boiler power of FPAB. For the first iterations the resulting supply temperature will always be slightly less than the desired supply temperature due to the power output of the ORC, which needs to be compensated for. If possible, the boiler power of FPC is first

46 increased, and secondly the boiler power of FPAB. Thereafter the procedure is repeated until the resulting supply temperature reaches the desired one. During some special days for which the FPC boiler is run close to its maximum capacity and FPAB is turned off the desired supply temperature is not reached, due to the fact that FPAB cannot be turned on for a period less than a week. In these cases the supply temperature is left as is, as along as it is not more than 5°C less than the desired temperature. The maximum allowable drop in return temperature is around 5°C.

Figure 3.4: Flowchart of the computation algorithm.

47 3.6 Financial Modeling

In order to determine the profitability of the project, costs and benefits during the system life-time must be determined and discounted.

3.6.1 Electricity network subscription

The electricity network cost consists of five parts:

1. Network subscription cost. For the year of 2020 it is 25 000 SEK/year.

2. Distribution cost. For the year of 2020 it is 0.05 SEK/kW h. It is calculated from the amount of electricity purchased from the electricity network.

3. Yearly power charge fee of 172 SEK/kW . It is calculated as the mean of the two highest measured hourly power consumption values, occuring in separate months, multiplied with the power charge fee. However, it may not less than the product of power charge fee and the current power subscription of 700 kW.

4. High load power charge fee of 256 SEK/year. It is calculated as the mean of the two highest measured hourly power consumption values, occuring in separate months during the high load period of November to March, multiplied with the power charge fee.

5. Penalty charge fee. Power consumption above 700 kW is charged with an additional 100%, and if this consumption occurs during the high load period an additional 150% is charged.

As an example, if the two highest measured power consumption values during the year, occuring in separate months, is 800 kW during an hour in January and 900 kW during an hour in February, then the total power charge fee for the year is

800 + 900 Power charge fee = · 172 = 146 200 SEK/year (3.9) 2 800 + 900 High load power charge fee = · 256 = 217 600 SEK/year (3.10) 2 Total power charge fee = 146 200 + 217 600 = 363 800 SEK/year (3.11)

Network subscription cost Electricity produced with an ORC will not affect the network subscription cost since it is fixed. However, the distribution cost and power charge fees are reduced.

Distribution cost Generating electricity will reduce the amount of electricity purchased from the electricity network, and reduce the distribution cost accordingly.

48 Power charge fees The power generation will reduce the maximum power consumption of the plant during the year, and reduce both the yearly power charge fee and the high load power charge fee accordingly. The power charge fees with an power generated ORC is calculated as from the mean the two hours with highest measured power consumption, with an ORC integrated. The power charge fees with and without an ORC can then be compared and a cost reduction found. However, the ORC will generate maximum power during the winter, which is also the period with the highest plant power consumption. Because of this, the power charge fees will be reduced by approximately the mean of the power generation during the winter. Therefore, the reduction is estimated as

Power charge cost reduction = mean(Pgen(Nov-Mar)) · (172 + 256) (3.12)

Penalty charges

During consumption above the power subscription limit of 700 kWel, an additional 100% is charged. If this occurs during the high load period, an additional 150% is charged. The effects of the ORC in terms of reducing these penalty costs are neglected in the analysis.

Energy tax

There is an energy tax in Sweden of levied on the consumption of electricity. It is only paid by the electricity consumer, and since implementing an ORC does not affect the total power consumption of the plant considerable, the tax will not influence the profitability of the project. The energy tax does therefore not need not be included in the analysis.

Inflation and price escalation

The electricity price is assumed to increase with inflation, 1:1. Therefore, inflation does not need to be considered when calculating the costs and benefits of the project. This is a modest estimation, since many believe the electricity price, an revenues therefrom, to increase at a faster rate than inflation in years to come.

3.6.2 Modeling costs

The most important costs are the unit cost of the ORC, the installation cost (piping and electrical), the maintenance cost and the fuel cost. The unit costs depends on the power rating of the system and large systems are relatively cheaper, in terms of SEK/kW ; it ranges from about 30 kSEK/kW for kSEK smaller systems in the range of 50-100 kWel down to about 10 /kW for systems above 1000 kWel. To account for this when modeling ORC systems of different power ratings, the unit cost is modeled

49 by an exponential function, and the installation and maintenance is set to vary in proportion to the unit cost. The exponential unit cost curve is derived from commercial ORC unit prices obtained from contact with manufacturers, and is further verified in literature [63]. Together, the unit and installation cost constitute the total capital expenditure (CAPEX) cost. It is calculated as

CCAPEX = CU + CI (3.13)

6 P [W] 6 0.7 CU = 12 · 10 [SEK] · ( RATED /10 ) (3.14)

CI = CU · 20% (3.15) where CU is the unit cost and CI is the installation cost.

The fuel cost is determined as the amount of fuel used up in the heat addition process. It is determined as the amount electricity generated by the ORC, while taking into account the electric efficiency of the generator. The additional fuel use will equal the amount of additional power the boilers need to supply in order to deliver the correct supply temperature and power to the grid, but it is more convenient to calculate it according to eq. 3.16

Egen CF = QF · pF = · pF (3.16) ηgen where QF fuel consumption, CF is the fuel cost, pF is the fuel price, Egen is the amount of generated electricity and ηgen is the electric efficiency of the generator.

The maintenance cost is estimated to be in the range of 1.5-2% of the ORC unit cost, per year, [4][53][55]. However it is important to note that the maintenance costs are difficult to accurately estimate and may easily escalate. Also, something quite interesting to note, is that the maintenance costs should vary inversely with the number of starts and stops of the machine. The result is the maintenance costs of a machine operating at e.g. 7000 hours per year may be less than for a machine operating at e.g. 3500 hours per year.

To conclude, the total operational expenditure costs are thus estimated as

COPEX = CF + CM (3.17)

Egen CF = · pF (3.18) ηgen

CM = CU · 2% (3.19)

Egen Q∆ = (3.20) ηgen

50 The total costs are then modeled as

CTOTAL = CCAPEX + COPEX (3.21)

= CU + CI + CF + CM (3.22)

3.6.3 Modeling benefits

The revenues of the investment arise from the generated electricity, which is then sold to the grid or consumed locally in S¨avelundsverket. In addition to the value of electricity sold, or self-consumed, additional revenues arise from the renewable electricity certificate system. Renewable electricity production is subsidized in Sweden by the mechanism of the electricity certificate system. Producers of renewable electricity are allotted precisely 1 certificate per 1 MWh electricity produced, which the electricity consumers then are required to buy in an open market.

The revenues are calculated as

Revenue = Egen · (pel + pcert) + Eself-consumed · pdist + ∆Power charge fee (3.23) where pel is the electricity price, pdist is the distribution cost and pcert is the electricity certificate price. The economic parameters used when calculating the costs and benefits of the investment are presented in table 3.5.

Table 3.5 List of economic parameters

Parameter Value Discount rate, r 5% [60] Economic lifetime, τ 20 years [4][53][55] SEK Electricity price, pe 0.45 ⁄MWh Electricity certificate price 0.05 SEK⁄MWh [61] Electricity distribution cost 0.05 SEK/kW h [60] Power charge fee 172 SEK⁄kW [60] High load power charge fee 256 SEK⁄kW [60] SEK Fuel price, pf 0.200 ⁄MWh [60] ORC unit cost 10-30 kSEK⁄kW [4][53][55] Installation cost 20% of ORC unit cost Operation and maintenance cost 2% of ORC unit cost [4][53][55]

51 3.7 Sensitivity Analysis

Sensitivity analyses of the thermodynamic and economic models are performed in order to study how the most important output variables depend on uncertainties of the input parameters. Thus, the aim of the sensitivity analyses is to reveal how sensitive the output variables, primarily NPV and IRR, are to varying input parameters.

The sensitivity analysis is performed using the one-at-a-time (OAT) method in which input factors are changed one-at-a-time, while the rest are kept at their baseline values. The observed changes in output results can then be directly linked to the change in a variable.

The sensitivity is calculated as

Percentage change in output variable Sensitivity = (3.24) Percentage change in input variable

However, this approach doesn’t fully explore the input space and does not take into account the simultaneous interaction of two, or more, variables. Hence, the OAT method is unable to detect possible interactions between input variables.

If the model response is linear with respect to individual input variables, the sensitivity can meas- ured by fitting a linear regression model to the model response. This is the case, at least for small deviations in the input parameters.

52 3.8 Scenario Analysis

A few possible future scenarios which are of interest are analysed. However the profitability as a function of certain economic variables, e.g. the electricity price, is also evaluated but is not seen as a different scenario all together.

Aggregating the boiler powers

A scenario that is evaluated is the possibility of connecting the ORC evaporator to the HWCs of all three boiler such that the avaialable thermal power for the ORC is increased. To evaluate this scenario, the developed model of S¨avelundsverket, shown in figure 4.15, is adjusted. The adjusted code is presented in appendix A.13.

Reducing the supply and return temperatures

The effect of lowering the return och supply temperature is also explored. The key benefit of a decreased supply temperature is a resulting decrease in return temperature and a subsequent increase in the thermal efficiency of the ORC. However, while it is true that reducing the supply temperature decreases the received ∆T of the HXs of the DHS load consumers this should not be a major issue for a minor change in ∆T . Therefore a sub-scenario in which the supply- and return is decreased slightly, by 10°C, is evaluated. A future trend towards very low temperature DHS, named 4th generation, is shown to be plausible [57][58][59]. The lowest possible mean supply and return temperatures for such a scenario is around 50 and 20 °C[58][59]. However, it is quite uncertain exactly how the temperature would vary over the year. In order to simulate this scenario the return temperature profile is set to be constant throughout the year and the supply temperature is set to vary between 50-65°C; 50°C during the summer and 65°C during the winter.

53 Chapter 4

Results

4.1 Boiler Power, DHS Temperature and Mass Flow

The constructed boiler profile of FPC is shown in figure 4.1. The boiler power is maximized and the minimum no-load period of the boiler is chosen to occur when DHS demand is at its lowest, in order to maximize the available thermal power to the ORC. That is the reason why the power is zero for days 192-222, as seen in figure 4.1. The constructed power load profile can be compared to the original boiler power, shown in appendix A1.

Figure 4.1: Constructed FPC boiler power profile.

54 The DHS supply and return temperature during the year of 2018 which is used as model input is shown in figure 4.2

Figure 4.2: DHS Return and Supply Temperature.

The DHS mass flow rate, calculated from the boiler powers, the flue gas condenser powers and the temperature difference of the supply and return temperature, is shown in figure 4.3.

Figure 4.3: Calculated DHS mass flow rate.

55 4.2 Investment Cost Estimation

The unit cost of ORC systems are in the range of 30000 - 10000 kSEK/kW , depending on the power rating of the system [63]. This is confirmed by a few ORC manufacturers, however the exact pricing of their systems is confidential and therefore not disclosed. Furthermore the maintenance cost is estimated to be 2% of the unit cost, per year, and set to 2% in the calculation. The installation cost depends on the location and system power rating, and is difficult to estimate. From discussions with the management of S¨avelundsverket and the supervisor of the thesis a value of 20% of the unit cost is taken as a reasonable assumption.

CCAP EX = Cunit + Cinstallation (4.1)

6 P [W] 6 0.7 Cunit = 12 · 10 [SEK] · ( RAT ED /10 ) (4.2)

Cinstallation = Cunit · 20% (4.3)

From equations 4.1:4.3, the specific cost curve illustrated in figure 4.4 is derived. The total CAPEX system cost, directly derived from the specific cost curve, is also shown in figure 4.4.

Figure 4.4: System cost as a function of power rating

56 4.3 Organic Rankine Cycle Model

The ORC power cycle model is shown in figure 4.5. The evaporation temperature is seen to be bounded exactly TTD°C below the exit temperature of the HTF (water) outlet temperature out of the evaporative HX. Similarly, the condensing temperature is bounded exactly TTD°C above the outlet temperature of the DHS mass flow through the condensing HX. The cycle is also visualized on a p-h diagram, shown in figure 4.6. The thermodynamic states 1-5 are described in 4.1.

Table 4.1 Description of states

State Description 1 Saturated liquid, just before evaporation 2 Saturated vapor, just before expander inlet 3 Vapor, just after expander outlet 4 Saturated vapor, just before condensation 4b Saturated liquid, just after condensation 5 Pressurized liquid, just after pump outlet

Figure 4.5: ORC model T-s diagram.

57 Figure 4.6: ORC model P-h diagram.

58 4.3.1 Comparison of working fluids

Several candidate working fluids, more than 30 in total, are studied using the parameters listed in table 4.2. The most promising fluids, in terms of yielding high thermal efficiencies, are presented in table 4.3. Note that the condenser inlet and outlet temperatures listed in table 4.3 are only used for the comparison of the fluids. When modeling the ORC integrated into the boiler station, the condenser inlet and outlet temperature will vary.

Table 4.2 ORC parameters

Parameter Value Evaporator HTF inlet temperature 170° Evaporator HTF outlet temperature 145°C Evaporator TTD 10°C Evaporation temperature 135°C Condenser HTF inlet temperature 50°C Condenser HTF outlet temperature 70°C Condenser TTD 10°C Condensing temperature 80°C Expander isentropic efficiency 80% Pump isentropic efficiency 80% Working condition, ψ 100% Superheating none Preheating none

The Carnot efficiency is calculated from the heat soucre and heat sink (cold source) temperatures, since all of the heat exchange for a Carnot cycle takes place at those temperatures. The fraction of carnot efficiency (FoC) is then found as

η F oC = th (4.4) ηC Condensation inlet HTF Temperature [K] η = 1 − = 27.1% (4.5) C Evaporator inlet HTF temperature [K]

However, the FoC may be seen as a bit misleading due to the fact that the temperature different available to the ORC system, after taking into account the temperature drops in the HXs and the TTDs, is only 135 − 80 = 55°C and not 170 − 50 = 120°C. Nonetheless, the result shows that thermal efficiencies in the range of about 8 to 9.3% are found. This yields FoCs in the range of 29.7 to 34.4%. The cycle utilizing Sulfur dioxide exhibits the highest BWR, 13.8%, while the cycle utilizing Ethylene oxide exhibits the lowest BWR, 5.97%. This further confirms the work done in [38] which found BWRs up to about 16%, and the notion that the pump work when modeling ORCs ought not to be neglected.

59 Table 4.3 Table of fluid properties and thermal efficiencies

Fluid Chemical form. Tcrit [° C] Pevap [bar] Pcond [bar] wexp [kJ/kg] wpump [kJ/kg] BWR [%] ηth [%] FoC [%] R1233ZD(E) C3ClF3H2 166.45 22.94 0.01650 16.99 1.605 9.451 8.390 30.99 R1234ZE(Z) C3F4H2 150.12 26.897 0.01575 16.670 2.153 12.92 8.043 29.70 R245CA C3F5H3 174.42 19.40 0.01587 18.70 1.381 7.385 8.40 30.10 R11 CCl3F 197.91 16.32702 0.013735 17.20 1.038 6.033 9.067 33.48 R141b C2Cl2FH3 204.4 13.78 0.01491 21.89 1.067 4.875 9.048 33.41 R21 CCl2FH 178.3 25.77 0.0144576 20.16257 1.757 8.714 8.948 33.04 SulfurDioxide SO2 157.49 54.890 0.006619 27.168 3.7485 13.80 8.71 32.18 n-Butane C4H10 152.0 28.67 0.02102 31.47 4.613 14.66 7.915 29.23 cis-2-Butene C4H8 162.6 26.98 0.009696 34.57 4.0587 11.74 8.385 30.96 EthyleneOxide C2H4O 195.77 27.35 0.008035 50.35 3.005 5.97 9.314 34.39

The saturation curves of the fluids investigated are shown in figure 4.7, while water illustrated as a reference. As can be seen in figure 4.7, the critical temperatures of the organic fluids are

Figure 4.7: Fluids illustrated in a T-s diagram.

substantially lower than the critical temeprature of water. Furthermore, many of them exhibit dry, or isentropic, behaviour during expansion. It can be noted that sulfur dioxide and Ethylene oxide are wet. Furthermore, sulfur dioxide would be promising for ORC application, if it were not extremely toxic and deadly.

60 Figure 4.8: Organic fluids illustrated in a T-s diagram.

Taking a closer look at the power cycle shape of a Sulfur dioxide, in figure 4.9, we see that the expansion phase ends in the two-phase region. The vapor quality at the expander outlet is 85%, which may be tolerable, depending on expander. In comparison to the power ”shape” of R1233ZD(E), shown in figure 4.10, the state of Sulfur dioxide at the turbine outlet is a two-phase mixture, and not a slightly superheated vapor.

61 Figure 4.9: Sulfur dioxide T-s diagram

Figure 4.10: R1233ZD(E) T-s diagram.

62 The fluid R1233ZD(E) is used by Againity for this type of application, whereas SRM uses R1234ZE(Z). They are both similar in terms of chemical composition and achieve comparable thermal efficien- cies. Since the measures of efficiency are derived from simulating the cycle using fixed expander isentropic efficiencies, it may be slightly misleading due to the fact that the characteristics of the fluids also influence the design of the expander and its maximum achievable isentropic efficiency. Againity uses an axial-flow turbine whereas SRM uses a volumetric twin-screw expander; and the choice of expander type undoubtedly affects the cost and efficiency of the system.

The reason why water is unsuitable for this type of application has to do with the requirements it places on the expander. Designing a compact expander (few stages) utilizing water is currently not possible, and may not be possible at all. If it were, the thermal efficiency in this application would be 10.3%, and with an acceptable expander outlet vapor quality of 93%.

Going forwards, the fluid R1233ZD(E) which is used by Againity will be used when simulating the integrated ORC system, due to its higher thermal efficiency.

4.3.2 Thermal efficiency and condensation temperature

The condensation temperature affects the condensation pressure and thus the turbine outlet pres- sure. The condenser pressure if often said to affect the ”back pressure” experienced by the expander, however this terminology is a bit misleading since pressure is a scalar quantity and therefore not directed in any direction.

Lowering the temperature of the cooling flow will reduce the condensation pressure and increase the pressure drop over the expander, yielding higher thermal efficiencies. The thermal efficiency as a function of condensation temperatures in the range of 20-120°C is shown in figure 4.11. The thermal efficiency at a condensation temperature of 20°C, which is 16.6%, is roughly twice the efficiency at 80°C. However since the DHS return temperature is about 40°C, and the ORC is connected after FGC-FPC, the condenser inlet temperature will always be more than 40°C. The resulting condensation temperature will therefore always be more than at least 50°C, accounting for the 10°C TTD of the condensing HX. Therefore the maximum attainable thermal efficiency is limited to no more than 12%, for this type of fluid, heat source temperature and HX TTD.

63 Figure 4.11: Thermal efficiency vs condensation temperature.

64 4.3.3 Net electric efficiency during part-load operation

The ORC will sometimes operate at off-design conditions. It might be rated at e.g. 1 MWel, and a maximum HX thermal input of 10 MWth, however the available thermal input will be substantially less than that during some days of the year, most often during summer time. Therefore, the part- load performance is modeled. A polynomial is approximated to measured data of ORC off-design performance presented in [47] and [48]. The resulting correction factor is shown in figure 4.12.

Figure 4.12: ORC part-load correction factor.

65 Varying the condensation temperature and correction factor, ψ, a 3D surface diagram visualizing the off-design efficiency of the ORC system is constructed, and presented in figure 4.13. The electric efficiency of the generator is set to 95%, independent of ψ.

Figure 4.13: ORC surface of net electric efficiency.

66 4.4 Flue Gas Condenser Model

Although not a result of this thesis, the flue gas condenser model is presented in this section, in figure 4.14. The same model was used for both FGC-FPC and FGC-FPAB. The 3D surface was created using a few isolines of constant return temperature [62]. The output power is shown to be very sensitive to changes in return temperature, and it was for this reason that the ORC model is connected after FGC-FPC.

Figure 4.14: Flue gas condenser surface of power output.

67 4.5 Simulating the system

The system being simulated is illustrated again, in figure 4.15. To clarify, the chosen ORC integra- tion is after the FGC-FPC. The evaporator outlet is connected such that the HWC heat transfer fluid (HTF) is circulated to the lower temperature HWC of FPC.

Figure 4.15: Layout of the simulated boiler station with the integrated ORC model.

Supply temperature

A 1000 kWel system is simulated, and the resulting supply temperature is shown in figure 4.16. The mean deviation is 0.0707°C, the maximum deviation is 2.24°C and the cumulative deviation is

25.7°C, over the entire year. For a 1400 kWel system, the maximum deviation from desired supply temperature is 2.57°C, and the mean deviation is 0.056°C. The cumulative deviation, summed up over the entire year, is thus 20.4°C.

68 Figure 4.16: Resulting DHS supply temperature for a 1000 kWel ORC.

Figure 4.17: Resulting DHS supply temperature for a 1400 kWel ORC.

69 The simulated boiler power load profile for a 1000 kWel ORC system is illustrated in figure 4.18. The additional boiler power needed to adjust for the net thermal power consumption of the ORC, i.e. the difference of QORC,IN − QORC,OUT , is not much at all. The additional power power is seen as the distance between the blue dotted line (constructed data) to the red solid line (simulated result). The mean power increase of FPC, for the time that FPC is in operation, is 0.53 MWth.

For FPAB the corresponding increase is 0.40 MWth.

Figure 4.18: Boiler power load profile for a 1000 kWel ORC.

70 A closer look of the boiler plant system temperatures for the same 1000 kWel system is shown in figure 4.19. In figure 4.19 (a) the system mass flows are shown. Not all of the incoming DHS mass flow can be used to cool the ORC condenser, because a part of it is split before the ORC and fed to the HXs of boilers FPA and FPAB. The limit temperature Tab = 115°C sets the minimum possible mass flow ratem ˙ ab, and subsequently the maximum possible mass flow ratem ˙ . In figure 4.19 (b) it can be seen that the heat rejection of the ORC increases the temperature of the mass flow by 30.6°C on average. If the mass flow ratem ˙ could be increased, the resulting condenser outlet temperature would be reduced and the net electric efficiency of the ORC increased. The temperature after the HX of FPC, shown in figure 4.19 (c). During the winter, when the DHS demand is high, the resulting supply temperature is met by the additional power of boiler A och B. However, when A and B is not operated because the DHS demand is low, boiler C solely regulates towards the desired supply temperature, neglecting the accumulator (heat battery) which is not included in the model. That explains the appearance of the Td curve; during high load times it is more rough and during low load times it is controlled such that Td = Te,desired. In figure 4.19 (d) the outlet temperature of the HX of boiler AB is shown. Tab = 115°C when the boiler is operated and Tab = 0°C.

Figure 4.19: Simulated system temperatures and mass flow rates for a 1000 kWel ORC.

71 The resulting efficiency and power generation for the same 1000 kWel system is shown in figure 4.20. As can be seen in (a) and (b), the thermal input to the ORC is limited by the FPC power. During times when the FPC power is below the rated thermal input power of the ORC, all of the available power is fed to the ORC. The net electric efficiency is in the range of 3-6%, yielding a power generation in the range of 300-600 kWel. This limited power generation is due to the high condenser outlet temperature shown in figure 4.19 (b). In turn, the high condenser outlet temperature is because of the limited mass flow through the condenser; some of the mass flow needs to be split and taken through the HX of FPA and FPB, shown in 4.19 (a).

Figure 4.20: Simulated power generation for a 1000 kW ORC.

72 4.6 Profitability Analysis

A smaller, 500 kWel, system is simulated and the results of the financial analysis is shown in table 4.4. A total generation of 2.63 GW h/year is achieved. It amounts to an average power generation of 328 kW during the operational period of the year, which is 333 consecutive days in total. Almost all of the generated electricity is self-consumed locally at the plant, yielding a electricity saving of 1080 kSEK⁄year. The reduction in distribution cost and reduction in power charge fee together together consitute a significant share of the total revenues, 120 kSEK/year and 164 kSEK/year respectively.

Parameter Value Power rating 500 kWel CAPEX Unit cost 7.39 MSEK Installation cost 1.48 MSEK OPEX Maintenance cost 147 kSEK⁄year Fuel cost 552 kSEK⁄year Power generation Electricity generation 2.63 GWh⁄year Electricity, self-consumed 2.40 GWh⁄year Electricity, sold 0.23 GWh⁄year Revenues Revenue electricity sold 99.2 kSEK⁄year Revenue electricity self-consumed 1080 kSEK⁄year Revenue certificates 131 kSEK⁄year Revenues reduced distribution cost 120 kSEK⁄year Revenue reduced power charge fee 164 kSEK⁄year Aggregated Total revenue 1600 kSEK⁄year Total O&M costs 700 kSEK⁄year Net operational benefit 900 kSEK⁄year Net electricity value, after fuel costs 0.34 SEK⁄kWh Profitability measures NPV 2.3 MSEK IRR 7.9% Payback period 9.9 years

Table 4.4 Financial analysis of a 500 kWel ORC.

The model is simulated for power ratings of 100 kWel to 2000 kWel, in steps of 100 kWel, and the net present values, internal rates of return and payback periods are determined. The results are presented in figures 4.21 4.22 4.23. For the default case, i.e. an electricity price of 0.45SEK/kW h, the maximum NPV is estimated to 2.3 MSEK, for a 400 kWel system. The maximum IRR and

73 minimum payback period is estimated for a 300 kWel system. Something worth noting, might be that the IRRs are greater than zero for power ratings below 1000 kWel and electricity prices greater than 0.35SEK/kW h.

Figure 4.21: Net present value of ORC´systems as a function of electric power rating and elec- tricity price.

74 Figure 4.22: Internal rate of return of ORC systems as a function of electric power rating and electricity price.

Figure 4.23: Payback period of ORC systems as a function of electric power rating and electricity price.

75 4.7 Sensitivity Analysis

The sensitivity of the valuation of the investment, with respect to certain input variables, is invest- igated for a 500 kWel system. The result is shown in table 4.5 and illustrated in figure 4.24. The sensitivity is calculated in both directions, i.e. by both increasing and decreasing the value of the input variable. It is calculated as

Percentage change in output variable Sensitivity = (4.6) Percentage change in input variable

The result shows that the NPV is most sensitive to changes in net electric efficiency and electricity price, and less so for changes in maintenance cost. However, some variables are more likely to substantially change than others, something which is not captured here due to their probability distributions being unknown. This may be true for e.g. the operational expenditure which could very well increase by 50% or 100% in an actual project.

The sensitivity of all other variables are approximately symmetrical in both directions, expect for the mass flow rate. The valuation is much more sensitive, more than twice, to a reduced DHS mass flow rate than to an increased mass flow rate.

Table 4.5 Sensitivity of the NPV with respect to certain variables.

Variable Sensitivity+ Sensitivity− Electricity price 6.3849 -6.384 Fuel price -2.9863 2.9872 CAPEX cost -3.8464 3.8464 Maintenance cost -0.79844 0.79931 Electric efficiency 5.5057 -5.504 Lifetime 2.7919 -2.9308 DHS mass flow rate 1.5283 -3.7952

76 Figure 4.24: NPV sensitivity plot.

77 4.8 Scenario Analysis

4.8.1 Scenario 1: Aggregating the boiler powers

The aggregated boiler power profile is shown in figure 4.25. It closely follows the DHS demand; the aggregated boiler power is low during the summer and high during the winter.

Figure 4.25: Aggregated boiler power profile.

The maximum NPV is 2.88 MSEK for a 400 kWel system, and the maximum IRR is 9.40% for a 300 kWel system, shown in figure 4.26. Thus, aggregating the boiler powers does not seem to increase the profitability much at all. The additional electricity generation is a modest 134 000 kW h/year, or an additional 5.8%. This is due to the limited mass flow (cooling flow) available to the ORC condenser; increasing the power rating of the system to e.g. 2000 kWel such that the machine can receive up to 2 MWth would result in a very high condensation temperature. Furthermore, for a smaller system the additional revenues will solely come from the available power production during the 30 day period in which FPC is shut-off, which is not much at at.

78 Figure 4.26: NPV and IRR for scenario 1: Aggregated boiler power.

79 4.8.2 Scenario 2: Lowering the DHS supply and return temperature

Scenario 2a: Slightly reduced DHS supply and return temperature

The supply and return temperatures in the case that they are reduced by 10°C is shown in figure 4.27. Anomalies in the data, i.e. the very few high and low values, are set to the mean.

Figure 4.27: DHS Return and Supply Temperature for scenario 2a: Slightly reduced DHS supply and return temperature.

The NPV and IRR as a function of power rating is shown in figure 4.30. A maximum NPV of 4.68

MSEK is found for a power rating of 600 kWel, whereas a maximum IRR of 10.97% and minimum payback period of 6.82 years is found for a power rating of 300 kWel.

80 Figure 4.28: NPV and IRR for scenario 2a: Slightly reduced DHS supply and return temperature.

81 Scenario 2b: 4th generation DHS supply and return temperature

The supply and return temperatures are set close to as low as possible [58][59], and for sake of simplicity set to be fixed throughout the year. The temperature profile distribution is shown in figure 4.29.

Figure 4.29: DHS Return and Supply Temperature for scenario 2b: 4th generation DHS supply and return temperature.

In the case of a very low supply- and return temperature the NPV and IRR is shown in figure 4.30. A maximum NPV of 12.60 MSEK and IRR of 13.49% are found for system power ratings of 1400 kWel and 1100 kWel, respectively. A minimum payback period of 6 years is found for a 1100 kWel system.

82 Figure 4.30: NPV and IRR for scenario 2b: 4th generation DHS supply and return temperature.

83 Chapter 5

Discussion

The results show that it can be profitable to implement an ORC in a boiler station. The find- ings are not in line with the research by Eriksson [8], Sundberg [6] and Svensson [7] which found similar investments to be unprofitable. The differences are most likely due to the fact that small differences, e.g. in available thermal power, plant layout, operation, power rating and economic parameters, greatly affect the results. Therefore, the profitability of these kinds of investments needs to be assessed on a case-by-case basis. Furthermore, ORC technology is quickly progressing and the capital costs have decreased recently, which may make previous, earlier, research obsolete and in need of an update. The differences may also arise due to the fact that some authors may not have included the additional revenues incurred from a reduction in distribution cost and power charge fee, which together make up for a substantial share of the total revenues.

To validate the results, the ORC manufacturers Againity and Svenska Rotor Maskiner (SRM) both provided estimations on the yearly power production for a certain power rating, shown in appendix A.5. The validation shows that the developed model in this thesis closely approximates the estim- ated power production by the commercial suppliers; the difference is 13% for Againity and 4% for SRM. The differences may be due to many different factors, however most likely due to differences in the TTD values of the heat exchangers and in the pump and expander isentropic efficiencies.

It is also very likely that the assumed part-load operation characteristic differs in an actual system. The pressure over the expander also depends on the rotational speed of the generator. If the gener- ator is operating at a fixed rotational speed, then the pressure over the expander is reduced at low part-load operation. This can be understood by looking at the opposite scenario; by reducing the rotational speed of the generation, the pressure over the expander can be understood to increase. If the rotational speed is reducing such that is approaches zero, then the pressure over the expander will approach infinity. Therefore, the type of generator also influences the performance of the sys-

84 tem, and especially during part load operation.

Furthermore, discussion with Againity [53] have revealed that their turbines strongly suffer from reduced performance whenever the condenser cooling flow outlet temperature exceeds 80°C. For this reason they have chosen to limit the condenser cooling flow outlet temperature to 80°C, by either choosing a smaller unit or limiting the thermal heat input to the machine. This is not captured by the developed model of the ORC since its efficiency is shown to be linearly dependent on the condensation temperature, for a fixed operating condition ψ, unlike the efficiency of Againity’s sys- tem. However, the implications of this are not that major, since the condenser cooling flow outlet temperature rarely exceeds 80°C, at least for smaller systems (<500 kW). Also, when the cooling flow outlet temperature exceeds 80% it does so during the summer period when the DHS cooling flow is at its lowest, and during that period the ORC does not produce that much power anyways.

In order to limit the scope of the study, the very interesting scenario of connecting an ORC to a hot oil boiler was not evaluated. If the boiler would have been using oil as the heat transfer fluid instead of water, it would be possible to achieve higher temperatures due to the higher satura- tion temperatures of some thermal oils compared to water. This is interesting since it would yield higher evaporation temperatures, turbine inlet pressure and net electric efficiency for an implemen- ted ORC. It would therefore be interesting to assess the profitability of implementing an ORC in a hot oil boiler. The results of such a study might make it interesting to replace old hot water boiler for hot oil boilers.

The result of the scenario analysis in which the DHS supply and return temperatures were lowered in interesting, and shows a greatly increased profitability. Reducing the supply and return temper- ature a such that the temperature difference between the supply and return is the same as before, should leave the mass flow rate and pump power consumption unaffected. However, it is difficult to control the return temperature; therefore, it might be appropriate to only reduce the supply temperature. This would increase the mass flow rate of the cooling flow available to the condenser, which would decrease the temperature difference from the condenser inlet to its outlet and thus also decrease the condensation temperature. This might be a more correct approach, however in that case, the additional power consumption of the pumps due to the increased mass flow rate needs to be considered.

It would have been interesting to evaluate the greater societal impact, and potential, of the imple- menting these types of ORCs in boiler stations. If the heat energy is supplied using biomass, it may be seen as renewable and reduce greenhouse gas emissions. However, the electricity mix of Sweden is relatively low emitting, so it is questionable just how much an ORC of this application would reduce greenhouse gas emission. A further evaluation of that possible impact would therefore have been very interesting.

85 Chapter 6

Conclusion

The results show that it is both possible and profitable to implement an ORC in the boiler station. There are many possible ways to integrate the system into the station, however it is best to connect the evaporator of the ORC to the hot water circuit (HWC) of boiler C and its condenser to a point after the flue gas condenser belonging to boiler C.

The most profitable power rating is found to be 400kW, in terms of maximizing NPV, and 300 kW, in terms of maximising the internal rate of return, at the current electricity price. For higher electricity prices, or lower maintenance costs, slightly larger systems are found to be profitable.

In order to maximize the profitability of the investment, operate the plant in such a way to maximize the available thermal heat to the ORC as well as the cooling flow rate passing through the condenser of the ORC. To do this, shift as much of the heat production as possible from boiler A and boiler B to boiler C. Also, maximize the cooling flow rate to the ORC condenser by minimizing the mass flow rate to the heat exchanger of boiler A and B.

Furthermore, if the aim is to maximize the electricity production, the results show that the electricity production starts to decrease for power ratings exceeding 1000kW. This is due to the limited cooling flow rate to the condenser and the part-load operation characteristics of the ORC systems. Therefore, it is never wise, not in any sense, to purchase a machine larger than 1000kW.

86 References

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91 Appendices

92 A.1 Received plant data

Figure 1: FPC boiler power during 2018

Figure 2: FPB boiler power during 2018

93 Figure 3: FPA boiler power during 2018

Figure 4: Return and supply temperature during 2018

N.B: The supply temperature is an estimated temperature distribution, and not actual data.

94 A.2 Flowchart of the simulation algorithm

Figure 5: Flowchart of the computation algorithm

95 A.3 System output during the year with an ORC integrated

Figure 6: System output for a 800 kW ORC

A.4 Model verification

In this appendix the model of the boiler station with an ORC integrated is verified by manually computing the result and comparing it to the result of the iterative model. This is done for the 1st of january, a typical winter day, with inputs listed in table1. The results of the iterative model for the 1st of January is shown in table2. A convergent, satisfying solution is reached in 20 iterations. The results show that the desired supply temperature Te of

105°C is reached. The resulting supply temperature of Teres = 105.12°C is achieved by increasing the power in boiler AB by 537.8 kW, or 16.1%. Using some of the computed parameters, such as the mass flows, the model output of the 20th iteration can be validated without having to compute the previous 19 iterations, which would be very time-consuming. The parameters and values used for the manual computation is showed in table 3. First, given Tab the mass flowm ˙ ab is computed as

6 6 Q˙ F P AB + Q˙ F GC−F P AB 3.8786 · 10 + 1.1831 · 10 kg m˙ ab = = = 16.3249 (1) Cp(Tab − Ta) 4190(115 − 41) s

96 Table 1 Parameter inputs

Parameter Value Day 1 Ta 41 [°C] Te 105 [°C] kg mDHS 85.5424 [ /s] Q˙ FPC 14 [MWth] Q˙ F P AB 3.3408 [MWth] Power rating 1 MWe ˙ QORCRAT ED 10 [MWth] ˙ QORCIN 10 [MWth] Electric efficiency, net 0.95 ·(0.16738 − 0.0010936 · T4)

Table 2 Parameter outputs for the 20th iteration

Parameter Value Parameter Value

Total number of iterations 20 Q˙ FPC 14 [MWth] mDHS 85.5424 [kg/s] Q˙ F P AB 3.8786 [MWth] m 69.217 [kg/s] Q˙ HX−FPC 4 [MWth] mORC 69.217 [kg/s] Q˙ HX−F P AB 3.8786 [MWth] mab 16.325 [kg/s] Q˙ F GC−FPC 4.5858 [MWth] ˙ Ta 41 [°C] QF GC−F P AB 1.1831 [MWth] ˙ Tb 56.812 [°C] QORC−IN 10 [MWth] T4 88.993 [°C] ηel 6.6676 % Tc 88.993 [°C] Pel 0.66676 [MWe] ˙ Td 102.79 [°C] QORC−OUT 9.3332 [MWth] Tab 115 [°C] Total system power - IN 22.981 [MWth] Te 115.12 [°C] Total system power - OUT 22.981 [MWth]

This yields kg m˙ =m ˙ − m˙ = 69.217 (2) DHS ab s The temperature of the DHS mass flow after FGC-FPC is then calculated as

6 Q˙ F GC−FPC 4.5858 · 10 Tb = Ta + = = 41 + 15.812 = 56.812 °C (3) Cp · m 4190 · 69.217 In order to maximize the mass flow through the ORC condenser, let kg m˙ =m ˙ = 69.217 (4) orc s In order to compute the electric efficiency of the ORC, we need the temperature of mass flow exiting the condenser. In the iterative computation algorithm, the value of the previous iteration is used,

97 Table 3 Parameter used for the manual computation

Parameter Value Parameter Value

Total number of iterations 20 Q˙ FPC 14 [MWth] DHS 85.5424 [kg/s] Q˙ F P AB 3.8786 [MWth] To be computed Q˙ HX−FPC 4 [MWth] mORC To be computed Q˙ HX−F P AB 3.8786 [MWth] ab To be computed Q˙ F GC−FPC 4.5858 [MWth] ˙ Ta 41 [°C] QF GC−F P AB 1.1831 [MWth] Tb To be computed Q˙ ORC−IN 10 [MWth] T4 To be computed ηel To be computed Tc To be computed Pel To be computed Td To be computed Q˙ ORC−OUT To be computed Tab 115 [°C] Total system power - IN To be computed Te To be computed Total system power - OUT To be computed

which is T4 = 88.876°C. This yields

ηel = 0.95 · (0.16738 − 0.0010936 · T4) = 0.066676 or 6.667% (5)

The heat rejection and electric power is then

6 6 Q˙ ORC−OUT = Q˙ ORC−IN · (1 − ηel) = 10 · 10 · (1 − 0.066676) = 9.332 · 10 W (6)

6 6 Pel = Q˙ ORC−IN · ηel = 10 · 10 · 0.066676 = 0.66676 · 10 W (7) Now the temperature of the condenser outlet mass flow is calculated as

6 Q˙ ORC−OUT 9.332 · 10 T4 = Tb + = 56.812 + = 56.812 + 32.177 = 88.989 [°C] (8) Cp · m˙ orc 4190 · 69.217 After leaving the condenser, the mass flows to the heat exchanger of boiler C. The temperature of the mass flow after leaving the heat exchanger is calculated as

6 Q˙ FPC−HX 4 · 10 Td = Tc + = 88.989 + = 88.989 + 13.7922 = 102.7812 [°C] (9) Cp · m˙ 4190 · 62.217

In this case Tc = T4 sincem ˙ ORC =m ˙ .

The resulting supply temperature is then given as

m˙ · Td +m ˙ ab · Tab 62.217 · 102.7812 + 16.3249 · 115 Teres = = = 105.32 [°C] (10) m˙ +m ˙ ab 62.217 + 16.3249

98 The thermal output of the boiler station, i.e. the amount of thermal power that is fed to the DHS network is given as

6 POUT = Cp · m˙ DHS · (Ter es − Ta) = 4190 · 85.5424 · (115.32 − 41) = 23.05 · 10 W (11)

The combined thermal loading of the boilers and the flue gas condensers minus the electric power output of the ORC should equal the total thermal output. We have that

PIN = Q˙ aggregated − Pel

= Q˙ FPC + Q˙ F P AB + Q˙ F GC−FPC + Q˙ F GC−F P AB − Pel (12) = (14 + 3.8786 + 4.5858 + 1.1831 − 0.66676) · 106 = 22.98076 · 106 W

Comparing the the results of the manual computation with the iterative algorithm it can be seen that they are similar, with some deviations most likely due to rounding errors in the manual computation. Furthermore the total power input equals the power output. Thus, the principle of energy conservation is obeyed; this further reinforces the soundness of the computation algorithm.

99 A.5 Validation of Results

The results of the model are compared against the results of two ORC manufacturers. In order for the comparison to be accurate, the calculation has been performed using the same set of data. Fur- thermore, any economic analysis is performed using the same economic parameters. Therefore, the differences in the results are solely from differences in the model, and some assumptions regarding the model, and from the use of different sets of data or economic parameter values.

A.5.1 Svenska Rotor Maskiner Svenska Rotor Maskiner (SRM) estimated the power production for a 1000 kW unit [55]. The results of the estimation, compared to the results of the developed model, is shown in table4. It is found that the estimated production of the developed model differs by less than 4% compared to the estimation by SRM.

Figure 7: Estimated production for a 1000 kW system by SRM [55]

Table 4 Validation of results, SRM

Estimation performed by: SRM Developed model Power rating 1000 kW 1000 kW Power production, net 3 312 000 kWh⁄year 3 196 000 kWh⁄year

100 A.5.2 Againity Againity estimated the power production and payback period for a 385 kW system [53]. The results of the estimation is shown in figure8. The result is also compared to the results of the developed model, shown in table5. It is found that the estimated power productions differ by about 13%, resulting in a difference in payback period of about 7%. The reason why Againity estimates a lower power production may be due to the fact that they are assuming a lower evaporator inlet temperature resulting in a lower evaporation temperature.

Figure 8: Estimated production for a 385 kW system by Againity [53]

Table 5 Validation of results, Againity

Estimation performed by: Againity Developed model Power rating 385 kW 385 kW Economic life 20 years 20 years Total electricity Production, net 1 980 000 kWh⁄year 2 267 500 kWh⁄year Revenue electricity trade 1 128 600 SEK⁄year 1 292 485 SEK⁄year Revenue reduced network costs 215 105 SEK⁄year 218 509 SEK⁄year Revenue electricity certificates 92 093 SEK⁄year 90 699 SEK⁄year Yearly savings, net 940 798 SEK⁄year 1 025 300 SEK⁄year Payback period 7.3 years 6.7 years

101 A.6 Code: Constructing model input data clc; close all;

DATA=readtable(’DATA.xlsx’); global T_a T_a=table2array(DATA(:,7)); %(C) Return temperature global T_e T_e=table2array(DATA(:,8)); %(C) Supply temperature T_hwc=table2array(DATA(:,6)); %(C) FPC Hot Water Circuit Temperature T_hwc(isnan(T_hwc))=mean(T_hwc(T_hwc>1)); %Setting 0 values to the mean Q_agg=table2array(DATA(:,5))*10^6; %(W) FPC+FPB+FPA boiler power El_use=table2array(DATA(:,9)); %Electricity consumption

% Scenario 2a %T_a=T_a-10; %[M,I]=min(T_a); T_a(I)=mean(T_a); %[M,I]=max(T_a); T_a(I)=mean(T_a); %T_e=T_e-10;

% %Scenario 2b %T_a=20*ones(364,1); %T_e=T_e-40; %T_e(T_e<55)=50; days=1:364; Q_min=1e6;

%Contructing boiler FPC and FPAB power loads for d=days if Q_agg(d,1)>=14e6+Q_min Q_FPC(d,1)=14e6; Q_FPAB(d,1)=Q_agg(d,1)-Q_FPC(d,1); elseif Q_agg(d,1)>14e6 Q_FPC(d,1)=Q_agg(d,1)-Q_min; Q_FPAB(d,1)=Q_min; else Q_FPC(d,1)=Q_agg(d,1); Q_FPAB(d,1)=0; end end

%Adjusting for minimum boiler stop-time == 30 days for d=1:(364-30) Q(d)=sum(Q_FPC(d:d+30)); end [MIN,I]=min(Q); Q_FPAB(I:I+30)=Q_FPC(I:I+30); Q_FPC(I:I+30)=0;

%Adjust for boiler minimum run time == 1 week Q_min=1e6; for d=1+5:364-5 vec_a=Q_FPAB(d-4:d-1,1); vec_b=Q_FPAB(d+1:d+4,1); if Q_FPAB(d)==0 && max(vec_a)>0 && max(vec_b)>0 Q_FPC(d)=Q_FPC(d)-Q_min; Q_FPAB(d)=Q_min; elseif Q_FPAB(d)~=0 && max(vec_a)==0 && max(vec_b)==0 Q_FPC(d)=Q_FPC(d)+Q_FPAB(d); Q_FPAB(d)=0; end end

%Adjust s.t. max(Q_FPC)<=14e6

102 %Shifting excess load to previous day for d=1+1:364-1 if Q_FPC(d,1)>14e6 delta=Q_FPC(d,1)-14e6; Q_FPC(d)=Q_FPC(d,1)-delta; Q_FPC(d-1,1)=Q_FPC(d-1,1)+delta; end end

%Flue-gas condenser power for d=days Q_FGC_FPC(d,1)=FGC(Q_FPC(d),T_a(d)); Q_FGC_FPAB(d,1)=FGC(Q_FPAB(d),T_a(d)); end

%District heating load/demand Q_DHS for d=days Q_DHS(d,1)=Q_FPC(d)+Q_FPAB(d)+Q_FGC_FPC(d)+Q_FGC_FPAB(d); end

%DHS mass flow C_p=4190; m_DHS=Q_DHS./(C_p*(T_e-T_a)); %(kg/s)

A.7 Code: Flue gas condenser model function Q = RGK(Q,T_a)

%y_0 - 40 grader %y_1 - 43.5 grader %y_2 - 47 grader %y_3 - 51 grader %y_4 - 40 grader

x=Q/10^6; %x in MW ---> Q_RKG in kW

if T_a<=40 && Q>0 y_0=0.3659*x^3 - 5.9704*x^2 + 351.67*x - 92.29; k=-92.7164; y=y_0+k*(T_a-40); elseif T_a<43.5 && Q>0 y_0=0.3659*x^3 - 5.9704*x^2 + 351.67*x - 92.29; y_1=0.3512*x^3 - 5.7829*x^2 + 331.83*x - 87.78; k= (y_1-y_0)/(43.5-40); y= y_0 + k*(T_a-40); %kW elseif T_a<47 && Q>0 y_1=0.3512*x^3 - 5.7829*x^2 + 331.83*x - 87.78; y_2=0.3389*x^3 - 5.7126*x^2 + 309.98*x - 86.415; k= (y_2-y_1)/(47-43.5); y= y_1 + k*(T_a-43.5); %kW elseif T_a<51 && Q>0 y_2=0.3389*x^3 - 5.7126*x^2 + 309.98*x - 86.415; y_3=0.3188*x^3 - 5.5214*x^2 + 279.23*x - 81.979; k= (y_3-y_2)/(51-47); y= y_2 + k*(T_a-47); %kW elseif T_a<55 && Q>0 y_3=0.3188*x^3 - 5.5214*x^2 + 279.23*x - 81.979; y_4=0.294*x^3 - 5.2826*x^2 + 241.55*x - 76.463; k= (y_4-y_3)/(55-51); y= y_3 + k*(T_a-51); %kW elseif T_a>=55 && Q>0 y_4=0.294*x^3 - 5.2826*x^2 + 241.55*x - 76.463; k=-135.8126; y=y_4+k*(T_a-55); %kW else y=0; end

103 Q=max(0,1000*y); %W end

A.8 Code: ORC model import numpy as np import CoolProp.CoolProp as CP

# SIMPLE ORC NO SUPERHEAT NO PREHEAT def ORC(sysvals): fluid = sysvals[0] T_hot_in = sysvals[1] T_hot_out = sysvals[2] T_cold_in = sysvals[3] T_cold_out = sysvals[4] TTD_evap = sysvals[5] TTD_cond = sysvals[6] dT_crit = sysvals[7] eta_p = sysvals[8] eta_t = sysvals[9]

T_crit = CP.PropsSI(’TCRIT’, fluid)

# STATE 1: Just before evaporation #t1=min(T_hot_out-TTD_evap, T_crit-dT_crit) t1=(T_hot_out-TTD_evap) print(f"TTD_evap: {TTD_evap}") print(f"T hot out: {T_hot_out-273.15}") p1 = CP.PropsSI(’P’, ’T’, t1, ’Q’, 0, fluid) h1 = CP.PropsSI(’H’, ’P’, p1, ’Q’, 0, fluid) s1 = CP.PropsSI(’S’, ’P’, p1, ’Q’, 0, fluid)

state1 = np.array([p1, t1, h1, s1])

# STATE 2: just after evaporation p2 = p1 t2 = t1 h2 = CP.PropsSI(’H’, ’P’, p1, ’Q’, 1, fluid) s2 = CP.PropsSI(’S’, ’P’, p1, ’Q’, 1, fluid)

state2 = np.array([p2, t2, h2, s2])

# STATE 3: After Turbine and before Condenser p3 = CP.PropsSI(’P’, ’T’, T_cold_out + TTD_cond, ’Q’, 0, fluid) # Condenser pressure s3s = s2 h3s = CP.PropsSI(’H’, ’P’, p3,’S’,s3s,fluid) h3 = h2 - eta_t*(h2 - h3s) t3 = CP.PropsSI(’T’,’P’, p3,’H’,h3,fluid) s3 = CP.PropsSI(’S’,’P’, p3,’H’,h3,fluid)

state3 = np.array([p3, t3, h3, s3])

# Vapor quality s_f=CP.PropsSI(’S’, ’P’, p3,’Q’,0,fluid) s_g = CP.PropsSI(’S’, ’P’, p3, ’Q’, 1, fluid) x=(s3-s_f)/(s_g-s_f)

# STATE 4 / 4b

if x>=1: x=1 # State 4: At the start of the condensing process p4=p3 t4=T_cold_out + TTD_cond h4=CP.PropsSI(’H’,’P’,p4,’T|gas’,t4,fluid) s4=CP.PropsSI(’S’,’P’,p4,’T|gas’,t4,fluid)

104 state4 = np.array([p4, t4, h4, s4])

# State 4b: After Condenser and before Pump p4b=p4 t4b=t4 h4b=CP.PropsSI(’H’,’P’,p4b,’T|liquid’,t4b,fluid) s4b=CP.PropsSI(’S’,’P’,p4b,’T|liquid’,t4b,fluid)

state4b = np.array([p4b, t4b, h4b, s4b])

elif x<1: # State 4b: After Condenser and before Pump p4b=p3 s_f=CP.PropsSI(’S’, ’P’, p4b, ’Q’, 0, fluid) s_g=CP.PropsSI(’S’, ’P’, p4b, ’Q’, 0, fluid) s4b=s_f+x*(s_g-s_f) h4b=CP.PropsSI(’H’, ’P’, p4b, ’S’, s4b, fluid) t4b=CP.PropsSI(’T’, ’P’, p4b, ’S’, s4b, fluid)

state4b = np.array([p4b, t4b, h4b, s4b])

#STATE 5: After Pump and before Boiler p5=p1 s5s=s4b h5s=CP.PropsSI(’H’, ’P’, p5, ’S’, s5s, fluid) h5=h4b+(h5s-h4b)/eta_p s5 = CP.PropsSI(’S’,’P’,p5,’H’,h5,fluid) t5 = CP.PropsSI(’T’, ’H’, h5, ’S’, s5, fluid)

state5 = np.array([p5, t5, h5, s5])

if x>=1: state_vec=np.concatenate((state1,state2,state3,state4,state4b,state5)) state_vec = state_vec.reshape((6, 4)) elif x<1: state_vec=np.concatenate((state1,state2,state3,state4b,state5)) state_vec=state_vec.reshape((5, 4))

return [state_vec,x]

A.9 Code: Run ORC function from ORC import * from ph_plot import * from Ts_plot import * import numpy as np import CoolProp.CoolProp as CP

# INPUT PARAMETERS # fluid=’R1233ZD(E)’ T_hot_in=273.15+170 T_hot_out=273.15+145 T_cold_in=273.15+0 T_cold_out=273.15+10 TTD_evap=10 # Evaporator Terminal temperature difference TTD_cond=10 # Condenser Terminal temperature difference dT_crit=5 # dT_crit = T_crit - T_evap eta_p=0.8 eta_t=0.8 T_crit=CP.PropsSI(’TCRIT’,fluid) - 273.15 T_triple=CP.PropsSI(’TTRIPLE’,fluid) - 273.15

# Input vector sysvals=[fluid,T_hot_in,T_hot_out,T_cold_in,T_cold_out,TTD_evap,TTD_cond,dT_crit,eta_p,eta_t]

# Calling the function

105 [state_vec,x] = ORC(sysvals)

# state = [p,t,h,s] # State 1: Saturated liquid # State 2: Turbine inlet (saturated vapor) # State 3: Turbine outlet (vapor) # State 4: Start of condensing process (saturated vapor) # State 4b: End of condensing process (saturated liquid) # State 5: After pump

# Analysis if x==1: # If superheated vapor at turbine exit, then computing: W_t=state_vec[1,2]-state_vec[2,2] # Turbine work W_p=state_vec[5,2]-state_vec[4,2] # Pump work Q_in=state_vec[1,2]-state_vec[5,2] # Total Heat addition Q_out=state_vec[2,2]-state_vec[4,2] # Total Heat rejection elif x<1: # If two-phase mixture at turbine exit, then computing: W_t=state_vec[1,2]-state_vec[2,2] # Turbine work W_p=state_vec[4,2]-state_vec[3,2] # Pump work Q_in=state_vec[1,2]-state_vec[4,2] # Total Heat addition Q_out=state_vec[2,2]-state_vec[3,2] # Total Heat rejection

# For both cases, computing: P_evap = state_vec[0,0] /1e5 # Bar P_cond = state_vec[0,3] /1e5 # Bar BWR = W_p / W_t eta_th = (W_t - W_p) / Q_in eta_el = eta_th * 0.95 eta_C = 1 - (T_cold_in)/(T_hot_in) FoC = eta_th / eta_C

# rounding to n digits n=4 W_t=round(W_t,n)/1000 W_p=round(W_p,n)/1000 Q_in=round(Q_in,n)/1000 Q_out=round(Q_out,n)/1000 BWR=round(BWR*100,n) eta_th=round(eta_th*100,n+2) eta_el=round(eta_el*100,n+2) eta_C=round(eta_C*100,n+2) FoC=round(FoC*100,n+2) T_crit=round(T_crit,n+2) T_triple=round(T_triple,n+2) x=round(x*100,n+2) #P_evap=round(P_evap,n) #P_cond=round(P_cond,n) print(f"\033[4mConditions:\033[0m\nEvaporation temperature: {state_vec[0,1]-273.15}[C]\n\ Condensation temperature: {state_vec[3,1]-273.15}[C]\nWorking fluid: {fluid}\nCritical temperature: {T_crit}[C]\n\ Triple point temperature: {T_triple}[C]\n\033[4m\nOutput:\033[0m\nEvaporation pressure: {P_evap}\nCondensation pressure: {P_cond}\nTurbine work: {W_t}[J/kg]\nPump work: {W_p}[J/kg]\nBackwork ratio: {BWR}%\n\ Heat addition: {Q_in}[J/kg]\nHeat rejection: {Q_out}[J/kg]\nThermal efficiency: {eta_th}%\n\ Electric efficiency: {eta_el}%\nFraction of Carnot efficiency: {FoC}%\nVapor quality: {x}%")

# S,T,h and p vectors S_vec=state_vec[:,3] S_vec=np.append(S_vec,S_vec[0]) T_vec=state_vec[:,1] T_vec=np.append(T_vec,T_vec[0]) T_vec=T_vec-273.15 h_vec=state_vec[:,2] h_vec=np.append(h_vec,h_vec[0]) p_vec=state_vec[:,0] p_vec=np.append(p_vec,p_vec[0])

S_hot_source=np.linspace(state_vec[0,3],state_vec[1,3],2)

106 T_hot_source=np.linspace(T_hot_out-273.15,T_hot_in-273.15,2)

S_cold_source=np.linspace(state_vec[-3,3],state_vec[-2,3],2) T_cold_source=np.linspace(T_cold_out-273.15, T_cold_in - 273.15,2)

# Making plots TS_plot(fluid,state_vec,S_vec,T_vec,S_cold_source,T_cold_source,S_hot_source,T_hot_source) ph_plot(fluid,state_vec,h_vec,p_vec)

A.10 Code: T-s plot import matplotlib.pyplot as plt import numpy as np import CoolProp.CoolProp as CP import matplotlib def TS_plot(fluid,state_vec,S_x,T_y,S_cold_source,T_cold_source,S_hot_source,T_hot_source):

T_crit=CP.PropsSI(’TCRIT’, fluid) T_triple=CP.PropsSI(’TTRIPLE’, fluid)

s_vec1 = np.array([]) s_vec2 = np.array([])

T_range = np.linspace(T_triple, T_crit, 1000)

for T in T_range: s_L = CP.PropsSI(’S’, ’T’, T, ’Q’, 0, fluid) s_vec1 = np.append(s_vec1, s_L) s_V = CP.PropsSI(’S’, ’T’, T, ’Q’, 1, fluid) s_vec2 = np.append(s_vec2, s_V)

s_vec2 = np.flip(s_vec2) s_vec = np.append(s_vec1, s_vec2)

T_vec1 = T_range T_vec2 = np.flip(T_vec1) T_vec = np.append(T_vec1, T_vec2)

# Convert to Celcius T_vec = T_vec - 273.15

# Making plot L=2 # Linewidth fig, ax = plt.subplots() ax.plot(s_vec, T_vec, label="Saturation curve",linewidth=L) ax.plot(S_x, T_y, label="Power cycle",linewidth=L)

# Heat source ax.plot(S_hot_source, T_hot_source, label="Heating flow", linewidth=L,color=’red’) # Heating flow plt.text(S_hot_source[0] * 0.97, T_hot_source[0] * 0.97, ’Exit’) plt.text(S_hot_source[-1] * 1.01, T_hot_source[-1], ’Entry’) # Cold source ax.plot(S_cold_source, T_cold_source, label="Cooling flow",linewidth=L,color=’green’) # Cooling flow plt.text(S_cold_source[0]*1.01,T_cold_source[0],’Exit’) plt.text(S_cold_source[-1]*0.95,T_cold_source[-1],’Entry’)

# State numbers/labels plt.text(state_vec[0, 3], state_vec[0, 1] - 273.15+2, ’1’) plt.text(state_vec[1, 3], state_vec[1, 1] - 273.15 + 2, ’2’) plt.text(state_vec[2, 3] + 5, state_vec[2, 1] - 273.15, ’3’) if len(state_vec)==6: plt.text(state_vec[3, 3], state_vec[3, 1] - 273.15 - 4, ’4’) plt.text(state_vec[4, 3], state_vec[4, 1] - 273.15 - 6, ’4b’) elif len(state_vec)==5: plt.text(state_vec[4, 3], state_vec[4, 1] - 273.15 - 6, ’4b’)

107 plt.text(state_vec[-1, 3], state_vec[-1, 1] - 273.15 + 4, ’5’)

ax.set(xlabel=’Entropy [J/(kg K)]’, ylabel=’Temperature [C]’, title=fluid,) legend = ax.legend(loc=’upper left’, shadow=True, fontsize=’large’) ax.grid() fig.savefig("Ts_plot.png") plt.show()

A.11 Code: p-h plot import matplotlib.pyplot as plt import numpy as np import CoolProp.CoolProp as CP def ph_plot(fluid,state_vec,h_x,p_y):

P_crit = CP.PropsSI(’PCRIT’, fluid) P_triple=CP.PropsSI(’PTRIPLE’,fluid)

h_vec1 = np.array([]) h_vec2 = np.array([])

P_range=np.linspace(P_triple,P_crit,1000)

for p in P_range: h_L = CP.PropsSI(’H’, ’P’, p, ’Q’, 0, fluid) h_vec1 = np.append(h_vec1, h_L) h_V = CP.PropsSI(’H’, ’P’, p, ’Q’, 1, fluid) h_vec2 = np.append(h_vec2, h_V)

h_vec2 = np.flip(h_vec2) h_vec = np.append(h_vec1, h_vec2)

p_vec1 = P_range p_vec2 = np.flip(p_vec1) p_vec = np.append(p_vec1, p_vec2)

# Converting Pa to Bar p_vec = p_vec/1e5 p_y=p_y/1e5

# Making plot fig, ax = plt.subplots() ax.semilogy(h_vec, p_vec,label=’Saturation curve’) # Log plot #ax.plot(h_vec, p_vec,label=’Saturation curve’) ax.plot(h_x,p_y,label=’Power cycle’) ax.plot() ax.set(xlabel=’Enthalpy [J/kg]’, ylabel=’Pressure [Bar]’, title=fluid) legend = ax.legend(loc=’upper left’, shadow=True, fontsize=’large’)

d=0.5 # State numbers/labels plt.text(state_vec[0, 2],p_y[0]+d,’1’) plt.text(state_vec[1, 2],p_y[1]+d,’2’) plt.text(state_vec[2, 2]*1.01,p_y[2]-2.5*d,’3’) if len(state_vec) == 6: plt.text(state_vec[3, 2],p_y[3]-2.5*d,’4’) plt.text(state_vec[4, 2],p_y[4]-2.5*d,’4b’) elif len(state_vec) == 5: plt.text(state_vec[4, 2],p_y[3]-2.5*d,’4b’) plt.text(state_vec[-1, 2],p_y[-1]+d, ’5’) print(state_vec[-1, 2])

ax.grid() fig.savefig("ph_plot.png") plt.show()

108 A.12 Code: Boiler station model with an ORC integrated % MODEL DESCRIPTION % ORC condenser is connected in series with DHS return supply AFTER RKG-FPC

% MODEL OUTPUT %output_it: The result of each iteration. %output_it_Table: A table with output_it

% MAIN: Computes steady state temperatures and heat flows function [output_it,output_it_Table]=MAIN(in) %in=[T_a(d) T_e(d) m_DHS(d) T_hwc(d) Q_DHS(d) Q_FPC(d) Q_FPAB(d) Q_ORC_IN P_RATED Q_orc_rated];

%INPUTS: % FIXED/GIVEN/DEDUCED INPUT PARAMETERS C_p=4190; % Inputs T_a=in(1); %(C) T_e=in(2); %(C) m_DHS=in(3); % (kg/s) T_hwc=in(4); % (C) Boiler HWC temperature Q_DHS=in(5); % (W) Q_FPC=in(6); % (W) Q_FPAB=in(7);% (W) Q_ORC_IN=in(8); %(W) P_RATED=in(9); %(W) Q_ORC_RATED=in(10); %(W)

%controlls if Q_ORC_IN>Q_ORC_RATED Q_ORC_IN=Q_ORC_RATED; elseif Q_ORC_IN>Q_FPC Q_ORC_IN=Q_FPC; end

%Restraint Temp VVX-FPAB<=115 C. ---> Yields minimum m_ab T_ab=115;

Q_FGC_FPAB=FGC(Q_FPAB,T_a); if Q_FPC~=0 m_ab=(Q_FPAB+Q_FGC_FPAB)/((T_ab-T_a)*C_p); %P_RATED m=m_DHS-m_ab; %Mass flow through FGC-FPC m_orc=m; else m_ab=m_DHS; m=0; m_orc=0; end

%Initial guess T_4=60; T_d=T_e;

% ITERATIVE LOOP to find convergent steady-steady solution it=1;

%Defining vectors to hold output variables when iterating in while-loop T_a_vec=[]; %does not change T_b_vec=[]; %does not change T_4_vec=[]; T_c_vec=[]; %Before VVX-FPC) T_d_vec=[]; %After VVX-FPC T_ab_vec=[]; %After boiler FPC heat exchanger T_e_res_vec=[]; %After FPB and FPA m_vec=[]; m_orc_vec=[]; m_ab_vec=[];

109 eta_el_vec=[]; C_vec=[]; P_el_vec=[]; Q_FPAB_vec=[]; Q_FPC_vec=[]; Q_FGC_FPC_vec=[]; Q_FGC_FPAB_vec=[]; Q_FPC_VVX_vec=[]; Q_ORC_OUT_vec=[]; Q_ORC_IN_vec=[]; psi_vec=[];

C=1; while C>1e-4

Q_FGC_FPC=FGC(Q_FPC,T_a); T_b=T_a+Q_FGC_FPC/(m*C_p); T_3=T_b; psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p);

% ---- series-connection ---- % %Compute T_c if m_orc~=m T_c=(m_orc*T_d+(m-m_orc)*T_b)/m; else T_c=T_4; end Q_FPC_VVX=Q_FPC-Q_ORC_IN; T_d_it=T_c+Q_FPC_VVX/(m*C_p); C=abs(T_d-T_d_it); T_d=T_d_it; T_e_res=(m*T_d+m_ab*T_ab)/(m+m_ab);

%Power and heat flows P_el=min(Q_ORC_IN*eta_el,P_RATED); eta_el=P_el/Q_ORC_IN;

%Iteration count it=it+1; if it>100 break end

if m_ab==0 T_ab=0; end

%Saving values in vector T_a_vec=[T_a_vec,T_a]; T_b_vec=[T_b_vec,T_b]; T_4_vec=[T_4_vec,T_4]; T_c_vec=[T_c_vec,T_c]; T_d_vec=[T_d_vec,T_d]; T_e_res_vec=[T_e_res_vec,T_e_res]; T_ab_vec=[T_ab_vec,T_ab]; m_vec=[m_vec,m]; m_ab_vec=[m_ab_vec,m_ab]; m_orc_vec=[m_orc_vec,m_orc]; C_vec=[C_vec,C]; eta_el_vec=[eta_el_vec,eta_el]; P_el_vec=[P_el_vec,P_el]; Q_FPAB_vec=[Q_FPAB_vec,Q_FPAB]; Q_FPC_vec=[Q_FPC_vec,Q_FPC]; Q_FGC_FPC_vec=[Q_FGC_FPC_vec,Q_FGC_FPC]; Q_FGC_FPAB_vec=[Q_FGC_FPAB_vec,Q_FGC_FPAB]; Q_FPC_VVX_vec=[Q_FPC_VVX_vec,Q_FPC_VVX];

110 Q_ORC_OUT_vec=[Q_ORC_OUT_vec,Q_ORC_OUT]; Q_ORC_IN_vec=[Q_ORC_IN_vec,Q_ORC_IN]; psi_vec=[psi_vec,psi]; end

X_vec=[]; Y_vec=[];

% Desired T_e reached by increasing the boiler power of FPC, and then by increasing boiler power of FPAB % If Q_FPC >=14e6 and Q_FPAB==0 T_e is not reached, and iteration is stopped.

%Target T_ab=115;

X=1; Y=1;

it=1;

while X>1e-2 && it<100

if Q_FPC<14e6 Q_FPC=Q_FPC*1.01; elseif Q_FPC>=14e6 && Q_FPAB ~= 0 Q_FPAB=Q_FPAB*1.01; end

Q_FGC_FPAB=FGC(Q_FPAB,T_a); m_ab=(Q_FPAB+Q_FGC_FPAB)/(C_p*(T_ab-T_a)); m=m_DHS-m_ab; m_orc=m; %Using values of last iteration Q_FGC_FPC=FGC(Q_FPC,T_a); T_b=T_a+Q_FGC_FPC/(m*C_p); T_3=T_b; psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p);

while Y>1e-2 %Iterate psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el_it=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p); Y=abs(eta_el_it-eta_el); eta_el=eta_el_it; end

if m_orc~=m T_c=(m_orc*T_d+(m-m_orc)*T_b)/m; else T_c=T_4; end Q_FPC_VVX=Q_FPC-Q_ORC_IN; T_d=T_c+Q_FPC_VVX/(m*C_p); T_e_res=(m*T_d+m_ab*T_ab)/(m+m_ab);

%Computing error in supply temperature X=abs(T_e_res-T_e);

P_el=min(Q_ORC_IN*eta_el,P_RATED); eta_el=P_el/Q_ORC_IN;

if m_ab==0 T_ab=0; end

111 %Saving values in vector T_a_vec=[T_a_vec,T_a]; T_b_vec=[T_b_vec,T_b]; T_4_vec=[T_4_vec,T_4]; T_c_vec=[T_c_vec,T_c]; T_d_vec=[T_d_vec,T_d]; T_e_res_vec=[T_e_res_vec,T_e_res]; T_ab_vec=[T_ab_vec,T_ab]; m_vec=[m_vec,m]; m_ab_vec=[m_ab_vec,m_ab]; m_orc_vec=[m_orc_vec,m_orc]; C_vec=[C_vec,C]; eta_el_vec=[eta_el_vec,eta_el]; P_el_vec=[P_el_vec,P_el]; Q_FPAB_vec=[Q_FPAB_vec,Q_FPAB]; Q_FPC_vec=[Q_FPC_vec,Q_FPC]; Q_FGC_FPC_vec=[Q_FGC_FPC_vec,Q_FGC_FPC]; Q_FGC_FPAB_vec=[Q_FGC_FPAB_vec,Q_FGC_FPAB]; Q_ORC_OUT_vec=[Q_ORC_OUT_vec,Q_ORC_OUT]; Q_ORC_IN_vec=[Q_ORC_IN_vec,Q_ORC_IN]; X_vec=[X_vec,X]; Y_vec=[Y_vec,Y]; %psi_vec=[psi_vec,psi]

%Iteration count it=it+1;

%break-if if T_e_res>T_e break elseif abs(T_e_res-T_e_res_vec(end-1))<1e-2 break elseif it>100 break end end

Z_vec=[]; Z=1; while (T_e-T_e_res)>5

Q_ORC_IN=Q_ORC_IN*0.99;

while Z>1e-4

Q_FGC_FPC=FGC(Q_FPC,T_a); T_b=T_a+Q_FGC_FPC/(m*C_p); T_3=T_b; psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p);

% ---- series-connection ---- % %Compute T_c if m_orc~=m T_c=(m_orc*T_d+(m-m_orc)*T_b)/m; else T_c=T_4; end Q_FPC_VVX=Q_FPC-Q_ORC_IN; T_d_it=T_c+Q_FPC_VVX/(m*C_p); Z=abs(T_d-T_d_it); T_d=T_d_it; T_e_res=(m*T_d+m_ab*T_ab)/(m+m_ab);

112 %Power and heat flows P_el=min(Q_ORC_IN*eta_el,P_RATED); eta_el=P_el/Q_ORC_IN;

%Saving values in vector T_a_vec=[T_a_vec,T_a]; T_b_vec=[T_b_vec,T_b]; T_4_vec=[T_4_vec,T_4]; T_c_vec=[T_c_vec,T_c]; T_d_vec=[T_d_vec,T_d]; T_e_res_vec=[T_e_res_vec,T_e_res]; T_ab_vec=[T_ab_vec,T_ab]; m_vec=[m_vec,m]; m_ab_vec=[m_ab_vec,m_ab]; m_orc_vec=[m_orc_vec,m_orc]; C_vec=[C_vec,C]; eta_el_vec=[eta_el_vec,eta_el]; P_el_vec=[P_el_vec,P_el]; Q_FPAB_vec=[Q_FPAB_vec,Q_FPAB]; Q_FPC_vec=[Q_FPC_vec,Q_FPC]; Q_FGC_FPC_vec=[Q_FGC_FPC_vec,Q_FGC_FPC]; Q_FGC_FPAB_vec=[Q_FGC_FPAB_vec,Q_FGC_FPAB]; Q_ORC_OUT_vec=[Q_ORC_OUT_vec,Q_ORC_OUT]; Q_ORC_IN_vec=[Q_ORC_IN_vec,Q_ORC_IN]; X_vec=[X_vec,X]; Y_vec=[Y_vec,Y]; Z_vec=[Z_vec,Z]; psi_vec=[psi_vec,psi];

%Iteration count it=it+1; if it>100 break end

if m_ab==0 T_ab=0; end

end

end

%Power balance P_out=[m_DHS*C_p*(T_e_res_vec-T_a_vec)]; P_in=[(Q_FPC_vec+Q_FPAB_vec+Q_FGC_FPC_vec+Q_FGC_FPAB_vec-P_el_vec)]; if length(Q_FPC_VVX_vec)~=length(Q_FGC_FPC_vec) Q_FPC_VVX_vec=Q_FPC_VVX_vec(1)*ones(1,length(Q_FGC_FPC_vec)); end

it_vec=1:length(T_a_vec); output_it=[it_vec’,m_vec’,m_ab_vec’,T_a_vec’,T_b_vec’,T_4_vec’,T_c_vec’,T_d_vec’,T_ab_vec’,T_e_res_vec’,Q_FPC_vec’,Q_FPAB_vec’,... Q_FGC_FPC_vec’,Q_FGC_FPAB_vec’,Q_FPC_VVX_vec’,Q_ORC_IN_vec’,Q_ORC_OUT_vec’,P_in’,P_out’,eta_el_vec’,P_el_vec’]; output_it_Table=table(it_vec’,m_vec’,m_ab_vec’,T_a_vec’,T_b_vec’,T_4_vec’,T_c_vec’,T_d_vec’,T_ab_vec’,T_e_res_vec’,Q_FPC_vec’,... Q_FPAB_vec’,Q_FGC_FPC_vec’,Q_FGC_FPAB_vec’,Q_FPC_VVX_vec’,Q_ORC_IN_vec’,Q_ORC_OUT_vec’,P_in’,P_out’,eta_el_vec’,P_el_vec’); output_it_Table.Properties.VariableNames = {’Iteration’ ’m’ ’m_ab’ ’T_a’ ’T_b’ ’T_4’ ’T_c’ ’T_d’ ’T_ab’ ’T_e_res’ ’Q_FPC’ ’Q_FPAB’... ’Q_FGC_FPC’ ’Q_FGC_FPAB’ ’Q_FPC_VVX’ ’Q_ORC_IN’ ’Q_ORC_OUT’ ’P_in’ ’P_out’ ’eta_el_vec’ ’P_el_vec’}; end

113 A.13 Code: Boiler station model with an ORC integrated – for Scenario 1 % MODEL DESCRIPTION % SCENARIO 1: AGGREGATED BOIELR POWER IS MADE AVAILABLE TO THE ORC % ORC condenser is connected into DHS return supply AFTER RKG-FPC

% MODEL OUTPUT %output_it: The result of each iteration. %output_it_Table: A table with output_it

% MAIN: Computes steady state temperatures and heat flows function [output_it,output_it_Table]=MAIN_scenario1(in) %in=[T_a(d) T_e(d) m_DHS(d) T_hwc(d) Q_DHS(d) Q_FPC(d) Q_FPAB(d) Q_ORC_IN P_RATED Q_ORC_RATED];

%INPUTS: % FIXED/GIVEN/DEDUCED INPUT PARAMETERS C_p=4190; % Inputs T_a=in(1); %(C) T_e=in(2); %(C) m_DHS=in(3); % (kg/s) T_hwc=in(4); % (C) Boiler HWC temperature Q_DHS=in(5); % (W) Q_FPC=in(6); % (W) Q_FPAB=in(7);% (W) Q_ORC_IN=in(8); %(W) P_RATED=in(9); %(W) Q_ORC_RATED=in(10); %(W) Q_AGG=Q_FPC+Q_FPAB; %(W)

%controlls if Q_ORC_IN>Q_ORC_RATED Q_ORC_IN=Q_ORC_RATED; end

if Q_ORC_IN>Q_AGG Q_ORC_IN=Q_AGG; end

if Q_ORC_IN<=Q_FPC Q_FPC_VVX=Q_FPC-Q_ORC_IN; Q_FPAB_VVX=Q_FPAB; elseif Q_ORC_IN>Q_FPC if Q_FPC==0 && Q_FPAB~=0 Q_FPC_VVX=0; Q_FPAB_VVX=Q_FPAB-Q_ORC_IN; elseif Q_FPC~=0 && Q_FPAB~=0 Q_FPC_VVX=0; dQ=Q_ORC_IN-Q_FPC; Q_FPAB_VVX=Q_FPAB-dQ; elseif Q_FPC==0 && Q_FPAB==0 Q_FPC_VVX=0; Q_FPAB_VVX=0; end end

%Restraint Temp VVX-FPAB<=115 C. ---> Yields minimum m_ab T_ab=115;

Q_FGC_FPC=FGC(Q_FPC,T_a); Q_FGC_FPAB=FGC(Q_FPAB,T_a);

if Q_FPC~=0 && Q_FPAB~=0 m_ab=(Q_FPAB_VVX+Q_FGC_FPAB)/((T_ab-T_a)*C_p); m=m_DHS-m_ab; m_orc=m;

114 elseif Q_FPC==0 && Q_FPAB~=0 m_ab=(Q_FPAB_VVX+Q_FGC_FPAB)/((T_ab-T_a)*C_p); m=m_DHS-m_ab; m_orc=m; elseif Q_FPC~=0 && Q_FPAB==0 m_ab=0; m=m_DHS-m_ab; m_orc=m; end

%Initial guess T_4=60; T_d=T_e;

%ITERATIVE LOOP to find convergent steady-steady solution it=1;

%Defining vectors to hold output variables when iterating in while-loop T_a_vec=[]; %does not change T_b_vec=[]; %does not change T_4_vec=[]; T_c_vec=[]; %Before VVX-FPC) T_d_vec=[]; %After VVX-FPC T_ab_vec=[]; %After boiler FPC heat exchanger T_e_res_vec=[]; %After FPB and FPA m_vec=[]; m_orc_vec=[]; m_ab_vec=[]; eta_el_vec=[]; C_vec=[]; P_el_vec=[]; Q_FPAB_vec=[]; Q_FPC_vec=[]; Q_FGC_FPC_vec=[]; Q_FGC_FPAB_vec=[]; Q_FPAB_VVX_vec=[]; Q_FPC_VVX_vec=[]; Q_ORC_OUT_vec=[]; Q_ORC_IN_vec=[];

C=1; while C>1e-4

Q_FGC_FPC=FGC(Q_FPC,T_a); T_b=T_a+Q_FGC_FPC/(m*C_p); T_3=T_b; psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p);

%Compute T_c if m_orc~=m T_c=(m_orc*T_d+(m-m_orc)*T_b)/m; else T_c=T_4; end

% ---- Scenario 2b ---- if Q_ORC_IN<=Q_FPC Q_FPC_VVX=Q_FPC-Q_ORC_IN; Q_FPAB_VVX=Q_FPAB; elseif Q_ORC_IN>Q_FPC if Q_FPC==0 && Q_FPAB~=0 Q_FPC_VVX=0; Q_FPAB_VVX=Q_FPAB-Q_ORC_IN; elseif Q_FPC~=0 && Q_FPAB~=0 Q_FPC_VVX=0; dQ=Q_ORC_IN-Q_FPC;

115 Q_FPAB_VVX=Q_FPAB-dQ; elseif Q_FPC==0 && Q_FPAB==0 Q_FPC_VVX=0; Q_FPAB_VVX=0; end end

T_d_it=T_c+Q_FPC_VVX/(m*C_p); C=abs(T_d-T_d_it); T_d=T_d_it; %T_d value is updated for use in next iteration T_e_res=(m*T_d+m_ab*T_ab)/(m+m_ab);

%Power and heat flows P_el=min(Q_ORC_IN*eta_el,P_RATED); eta_el=P_el/Q_ORC_IN;

%Iteration count it=it+1; if it>100 break end

if m_ab==0 T_ab=0; end

%Saving values in vector T_a_vec=[T_a_vec,T_a]; T_b_vec=[T_b_vec,T_b]; T_4_vec=[T_4_vec,T_4]; T_c_vec=[T_c_vec,T_c]; T_d_vec=[T_d_vec,T_d]; T_e_res_vec=[T_e_res_vec,T_e_res]; T_ab_vec=[T_ab_vec,T_ab]; m_vec=[m_vec,m]; m_ab_vec=[m_ab_vec,m_ab]; m_orc_vec=[m_orc_vec,m_orc]; C_vec=[C_vec,C]; eta_el_vec=[eta_el_vec,eta_el]; P_el_vec=[P_el_vec,P_el]; Q_FPAB_vec=[Q_FPAB_vec,Q_FPAB]; Q_FPC_vec=[Q_FPC_vec,Q_FPC]; Q_FGC_FPC_vec=[Q_FGC_FPC_vec,Q_FGC_FPC]; Q_FGC_FPAB_vec=[Q_FGC_FPAB_vec,Q_FGC_FPAB]; Q_FPC_VVX_vec=[Q_FPC_VVX_vec,Q_FPC_VVX]; Q_FPAB_VVX_vec=[Q_FPAB_VVX_vec,Q_FPAB_VVX]; Q_ORC_OUT_vec=[Q_ORC_OUT_vec,Q_ORC_OUT]; Q_ORC_IN_vec=[Q_ORC_IN_vec,Q_ORC_IN]; end

Z_vec=[]; X_vec=[];

% Desired T_e reached by increasing the boiler power of FPC, and then by increasing boiler power of FPAB % If Q_FPC >=14e6 and Q_FPAB==0 T_e is not reached, and iteration is stopped.

%Target T_ab=115;

Z=1; X=1; it=1;

while Z>1e-2 && it<100

if 0

116 Q_FPC=Q_FPC*1.01; elseif Q_FPC>=14e6 && Q_FPAB ~= 0 Q_FPAB=Q_FPAB*1.01; elseif Q_FPC==0 Q_FPAB=Q_FPAB*1.01; end if Q_ORC_IN<=Q_FPC Q_FPC_VVX=Q_FPC-Q_ORC_IN; Q_FPAB_VVX=Q_FPAB; elseif Q_ORC_IN>Q_FPC if Q_FPC==0 && Q_FPAB~=0 Q_FPC_VVX=0; Q_FPAB_VVX=Q_FPAB-Q_ORC_IN; elseif Q_FPC~=0 && Q_FPAB~=0 Q_FPC_VVX=0; dQ=Q_ORC_IN-Q_FPC; Q_FPAB_VVX=Q_FPAB-dQ; elseif Q_FPC==0 && Q_FPAB==0 Q_FPC_VVX=0; Q_FPAB_VVX=0; end end

Q_FGC_FPAB=FGC(Q_FPAB,T_a); m_ab=(Q_FPAB_VVX+Q_FGC_FPAB)/((T_ab-T_a)*C_p); m=m_DHS-m_ab; m_orc=m;

%Using values of last iteration Q_FGC_FPC=FGC(Q_FPC,T_a); T_b=T_a+Q_FGC_FPC/(m*C_p); T_3=T_b; psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p);

while X>1e-2 psi=part_load(Q_ORC_IN,Q_ORC_RATED); % Working condition eta_el_it=psi*efficiency(T_4); Q_ORC_OUT=Q_ORC_IN*(1-eta_el); T_4=T_3+Q_ORC_OUT/(m_orc*C_p); X=abs(eta_el_it-eta_el); eta_el=eta_el_it; end

if m_orc~=m T_c=(m_orc*T_d+(m-m_orc)*T_b)/m; else T_c=T_4; end

T_d=T_c+Q_FPC_VVX/(m*C_p); T_e_res=(m*T_d+m_ab*T_ab)/(m+m_ab);

%Computing error in supply temperature Z=abs(T_e_res-T_e);

P_el=min(Q_ORC_IN*eta_el,P_RATED); eta_el=P_el/Q_ORC_IN;

if m_ab==0 T_ab=0; end

%Saving values in vector T_a_vec=[T_a_vec,T_a]; T_b_vec=[T_b_vec,T_b];

117 T_4_vec=[T_4_vec,T_4]; T_c_vec=[T_c_vec,T_c]; T_d_vec=[T_d_vec,T_d]; T_e_res_vec=[T_e_res_vec,T_e_res]; T_ab_vec=[T_ab_vec,T_ab]; m_vec=[m_vec,m]; m_ab_vec=[m_ab_vec,m_ab]; m_orc_vec=[m_orc_vec,m_orc]; C_vec=[C_vec,C]; eta_el_vec=[eta_el_vec,eta_el]; P_el_vec=[P_el_vec,P_el]; Q_FPAB_vec=[Q_FPAB_vec,Q_FPAB]; Q_FPC_vec=[Q_FPC_vec,Q_FPC]; Q_FGC_FPC_vec=[Q_FGC_FPC_vec,Q_FGC_FPC]; Q_FGC_FPAB_vec=[Q_FGC_FPAB_vec,Q_FGC_FPAB]; Q_FPC_VVX_vec=[Q_FPC_VVX_vec,Q_FPC_VVX]; Q_FPAB_VVX_vec=[Q_FPAB_VVX_vec,Q_FPAB_VVX]; Q_ORC_OUT_vec=[Q_ORC_OUT_vec,Q_ORC_OUT]; Q_ORC_IN_vec=[Q_ORC_IN_vec,Q_ORC_IN]; Z_vec=[Z_vec,Z]; X_vec=[X_vec,X];

%Iteration count it=it+1;

%break-if if T_e_res>T_e break elseif abs(T_e_res-T_e_res_vec(end-1))<1e-2 break elseif it>100 break end

end

%Power balance P_out=[m_DHS*C_p*(T_e_res_vec-T_a_vec)]; P_in=[(Q_FPC_vec+Q_FPAB_vec+Q_FGC_FPC_vec+Q_FGC_FPAB_vec-P_el_vec)]; if length(Q_FPC_VVX_vec)~=length(Q_FGC_FPC_vec) Q_FPC_VVX_vec=Q_FPC_VVX_vec(1)*ones(1,length(Q_FGC_FPC_vec)); end

it_vec=1:length(T_a_vec); output_it=[it_vec’,m_vec’,m_ab_vec’,T_a_vec’,T_b_vec’,T_4_vec’,T_c_vec’,T_d_vec’,T_ab_vec’,T_e_res_vec’,Q_FPC_vec’,Q_FPAB_vec’,... Q_FGC_FPC_vec’,Q_FGC_FPAB_vec’,Q_FPC_VVX_vec’,Q_FPAB_VVX_vec’,Q_ORC_IN_vec’,Q_ORC_OUT_vec’,P_in’,P_out’,eta_el_vec’,P_el_vec’]; output_it_Table=table(it_vec’,m_vec’,m_ab_vec’,T_a_vec’,T_b_vec’,T_4_vec’,T_c_vec’,T_d_vec’,T_ab_vec’,T_e_res_vec’,Q_FPC_vec’,Q_FPAB_vec’,... Q_FGC_FPC_vec’,Q_FGC_FPAB_vec’,Q_FPC_VVX_vec’,Q_FPAB_VVX_vec’,Q_ORC_IN_vec’,Q_ORC_OUT_vec’,P_in’,P_out’,eta_el_vec’,P_el_vec’); output_it_Table.Properties.VariableNames = {’Iteration’ ’m’ ’m_ab’ ’T_a’ ’T_b’ ’T_4’ ’T_c’ ’T_d’ ’T_ab’ ’T_e_res’ ’Q_FPC’ ’Q_FPAB’... ’Q_FGC_FPC’ ’Q_FGC_FPAB’ ’Q_FPC_VVX’ ’Q_FPAB_VVX’ ’Q_ORC_IN’ ’Q_ORC_OUT’ ’P_in’ ’P_out’ ’eta_el_vec’ ’P_el_vec’}; end

118 A.14 Code: Financial investment valuation model function [NPV,IRR,Payback,FIN_DATA,CF_vec] = FIN(P_rated,sys_output)

Load_DATA

days=1:364;

%From sys output P_vec=sys_output(:,end); P_vec(isnan(P_vec))=0;

%Data El_use_day=table2array(DATA(:,9)); %(kWh/day) El_use_year=sum(El_use_day); %(kWh/year)

%Electricity production El_prod_day=P_vec*(24/1000); %(kWh/day) El_prod_year=sum(El_prod_day); %(kWh/year) El_saved_day=[]; for d=days if El_prod_day(d,1)=El_use_day(d,1) El_saved_day(d,1)=El_use_day(d); end end

El_saved_year=sum(El_saved_day); El_sold_day=El_prod_day-El_saved_day; El_sold_year=sum(El_sold_day);

% Network subscription cost reduction high_load_P=[P_vec(1:90);P_vec(300:end)]; %High load P [W] mean_high_load_P=mean(high_load_P)/1000; %Mean of high load P [kW]

eta_elgen=0.95; %Generator efficiency Q_fuel_day=(P_vec)*(24/1000)/eta_elgen; %(kWh/day) Q_fuel_year=sum(Q_fuel_day); %(kWh/day)

%Contants r=0.05; %Discount rate lifetime=20; %Economic lifetime

%Variables Price_el=0.45; %(SEK/kWh) Cost_dist=0.05; % (SEK/kWh) Price_cert=0.05; % Elcertifikat (SEK/kWh) Price_fuel=0.20; %(SEK/kWh)

%REVENUES Revenue_el_ext=Price_el*El_sold_year; %(SEK/YEAR) Revenue_cert=Price_cert*El_prod_year; %(SEK/YEAR) Revenue_dist=Cost_dist*El_saved_year; %(SEK/YEAR) Revenue_el_int=Price_el*El_saved_year; %(SEK/YEAR) Revenue_power_charge=mean_high_load_P*(172+256); %(SEK/year) Revenue_total=Revenue_el_int+Revenue_el_ext+Revenue_cert+Revenue_dist+Revenue_power_charge; %(SEK/year)

%COSTS %CAPEX Unit_cost=12e6*(P_rated/1000e3)^0.7; %SEK Specific_cost=Unit_cost/P_rated; %(SEK/kW) Installation_cost=0.20*Unit_cost; %(SEK) CAPEX=Unit_cost+Installation_cost; %(SEK)

%OPEX Fuel_cost=Price_fuel*Q_fuel_year; %(SEK/YEAR) O_M_cost=0.02*Unit_cost; %(SEK/YEAR) OPEX=Fuel_cost+O_M_cost; %(SEK/YEAR)

119 %CASH FLOWS CF_net=(Revenue_total-OPEX); % OPEX = Fuel + Maintenance. #(SEK/YEAR) CF_vec(1)=-CAPEX; CF_vec(2:lifetime+1)=(CF_net); CF_vec(end)=CF_vec(end)

%Outputs NPV=pvvar(CF_vec,r); IRR=irr(CF_vec); Payback=CAPEX/(Revenue_total-OPEX);

FIN_DATA=table([r;lifetime;Unit_cost;Specific_cost;Installation_cost;CAPEX;O_M_cost;Fuel_cost;OPEX;El_use_year;Q_fuel_year;El_prod_year;El_saved_year;El_sold_year;... Revenue_el_ext;Revenue_el_int;Revenue_cert;Revenue_dist;Revenue_power_charge;CF_net;NPV;IRR;Payback],’VariableNames’,... {’Financial_Data’},’RowNames’,{’Discount rate’,’Lifetime (years)’,’Unit cost (SEK)’,’Specific cost (SEK/kW)’,... ’Installation cost (SEK)’,’CAPEX (SEK)’,’O&M cost (SEK/year)’,’Fuel cost (SEK/year)’,’OPEX (SEK/year)’,’Electricity use (kWh/year)’,’Fuel use (kWh/year)’,... ’Electricity production (kWh/year)’,’Electricity saved (kWh/year)’,’Electricity sold (kWh/year)’,... ’Revenue electricity sold (Excl. certificates) (SEK/year) ’,’Revenue electricity saved (Excl. certificates) (SEK/year)’,... ’Revenue certificates (SEK/year)’,’Revenue reduced distribution cost (SEK)’ ’Revenue reduced power charge fee (SEK/year)’,’Net Revenue (SEK/year)’,’Net Present Value (SEK)’,... ’Return’,’Payback Period (years)’}); end

A.15 Code: Find max P % RUNS MAIN FUNCTION NUM_RAND TIMES FOR ONE (1) DAY AND FINDS MAX P function [output_day]=optimize_day(n,P_RATED,T_a,T_e,T_hwc,Q_DHS,Q_FPC,Q_FPAB,m_DHS)

C_p=4190; Q_ORC_RATED=P_RATED/0.10;

%Generating random inputs if Q_ORC_RATED<=Q_FPC Q_ORC_IN_RANGE=linspace(0,Q_ORC_RATED,n)’; else Q_ORC_IN_RANGE=linspace(0,Q_FPC,n)’; end

%Generating random inputs for Scenario 1: Aggregated boiler power %if Q_ORC_RATED<=Q_FPC % Q_ORC_IN_RANGE=linspace(0,Q_ORC_RATED,n)’; %else % Q_ORC_IN_RANGE=linspace(0,Q_FPC+Q_FPAB,n)’; %end

system_output=[]; %Running function n times to find maximum P_el for n=1:n output=MAIN([T_a T_e m_DHS T_hwc Q_DHS Q_FPC Q_FPAB Q_ORC_IN_RANGE(n) P_RATED Q_ORC_RATED]); system_output=[system_output;output(end,:)]; end

[M,I]=max(system_output(:,end));

output_day=system_output(I,:); %Output for daily maxiumum P end

120