Improved Generation Dispatch In Power Systems

Imperial College of Science, Technology and Medicine

t

A thesis submitted for the degree of Doctor of Philosophy of the University of London and for the diploma of Membership of Imperial College

-by-

Fergal McNamara

Electrical Energy Systems Section Department of Electrical Engineering Imperial College

August 1990

Page i Improved Generation Dispatch in Power Systems

To my Mother and Father

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ABSTRACT

The economic allocation of generation among individual generating sets performed in an En­ ergy Management Centre relies on simple models of power plant behaviour. The plant is re­ garded as a power source which can be varied at will, with some maximum rate of change. However, there are many other relevant power station attributes, which, although clearly re­ cognized, are not explicitly taken in consideration in the Energy Management Centre. Primary control of grid frequency, achieved by governor action, relies on the fact that some generators are operating above the minimum pressure necessary to achieve their dispatched load. The response of such a generator to a frequency deviation from nominal, termed the governor gain, is an automatic control action aimed at reducing supply and demand imbal­ ance and hence containing frequency within limits. The ability of a generating unit to provide active power reserve for frequency regulation is a function of its dispatched load and operating pressure. If this relationship and the associated costs are known then the required reserve can be scheduled in the most economic way over the entire power system by an enhanced dispatch algorithm which includes the operating pressure. The nature of these relationships is examined in this thesis using plant models and tests and a system simulation is presented to test the advantages of the proposals by comparison with the original system. A method of trading reserve provision on thermal plant with other means such as pumped storage, gas turbines and combined cycle plant is discussed. The modes of operation are discussed and it is seen that worthwhile gains in system economics and per­ formance are possible.

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ACKNOWLEDGEMENTS

I would like to thank my supervisor Dr. R.M. Dunnett for his helpful comments, friendly advice and approachability which gave me confidence and encouragement during my research. I would also like to sincerely thank my group head Dr. J.F. Macqueen for his help and support in steering the project. I would like to express my appreciation to my academic supervisor Dr. M.J. Short and to Mr. E.D. Farmer for their help and comments. I am also indebted to the convenor of WG04 Mr. F.L. Carvalho for his counsel and advice and particularly for making available the opportunity to obtain the plant test data presented throughout this thesis. In addition, I am grateful to all my colleagues on WG04 for the stimu­ lating and lively workshop sessions and the feedback and comment obtained from Dr. F.J McDyer of ESB, Dipl.-lng. H. Kurten of KWU, Si. A. DeMarco of ENEL and Mr. P. Bodach of Ontorio Hydro. Acknowledgements are due for the help of Mr. T. Canning of ESB in performing some of the plant tests reported in this thesis and to Mr. D. O'Connor and Mr. A. Egan for many interesting meetings. A special mention is made of Mr. J. Corr of the North Wall Power Station for his useful suggestions. Similarly, I would like to thank Dr. B. Fox of QUB for his advice and guidance. Finally, my gratitude is shown to all the station staff who helped in performing the tests, my colleagues in the Power Systems Group at NGRDC and in the Electric Energy Systems Section at Imperial College ( who are too numerous to mention individually ) for providing a pleasant working environment. In particular, I would like to thank Mrs. H.M. Chandler for her indispensible assistance. This work was carried out at the National Grid Research and Development Centre and is published by permission of the National Grid Company pic.

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Table of Contents

1.0 CHAPTER ONE - INTRODUCTION ...... 1 1.1 PREAMBLE ...... 1 1.2 PLANT AND SYSTEM INTERFACE ...... 2 1.2.1. POWER PLANT CONSTRAINTS ...... 2 1.2.1.1 MAXIMUM AND MINIMUM POWER ...... 2 1.2.1.2 RATE OF CHANGE LIMITATIONS ...... 2 1.3 PLANT REPRESENTATION IN DISPATCH SYSTEMS ...... 2 1.3.1 OBJECTIVE FUNCTION ...... 3 1.3.2 PLANT CONSTRAINTS ...... 4 1.3.2.1 COAL MILLS ...... 4 1.3.2.2 BOILER FEED PUMP ...... 4 1.4 CURRENT DISPATCH PRACTICES ...... 5 1.4.1 U.K. SUPPLY SYSTEM ...... 5 1.4.2 IRISH SUPPLY SYSTEM ...... 5 1.4.3 ITALIAN SUPPLY SYSTEM ...... 5 1.5 ACTIVE POWER RESERVE ...... 6 1.5.1 ISLAND SYSTEMS ...... 7 1.5.2 FREQUENCY REGULATION ...... 7 1.6 OVERVIEW OF THESIS ...... 8

2.0 CHAPTER TWO - FREQUENCY REGULATION FROM THERMAL PLANT...... 10 2.1 INTRODUCTION ...... 10 2.2 POWER PLANT MODELLING ...... 11 2.2.1 MODEL EQUATIONS ...... 11 2.2.1.1 EVAPORATOR ...... 11 2.2.1.2 SUPERHEATER ...... 13 2.2.1.3 REHEATER ...... 13 2.2.1.4 GENERATED POWER ...... 13 2.2.1.5 COMBUSTION SYSTEM ...... 13 2.2.1.6 GOVERNOR VALVE MODEL ...... 13 2.2.2 SIMPLIFYING ASSUMPTIONS ...... 15 2.2.3 PARAMETERS AND SCALING ...... 16 2.2.4 VARIABLE BOUNDS ...... 16 2.3 STATE VARIABLE REPRESENTATION ...... 17 2.4 STEADY STATES ...... 17 2.5 LINEARIZATION ...... 18 2.6 GOVERNOR GAIN ...... 20 2.7 STEP RESPONSE ...... 21 2.8 GAIN AND ENERGY CALCULATIONS ...... 22 2.9 CONCLUSIONS ...... 23

3.0 CHAPTER THREE - ACTIVE POWER RESERVE PROVISION COSTS ...... 27 3.1 INTRODUCTION ...... 27 3.2 MODERN POWER STATION PLANT ...... 27 3.2.1 TURBINE PLANT ...... 29 3.2.2 BOILER PLANT ...... 29 3.2.3 METHODS OF GOVERNING ...... 31 3.2.4 THE DESIGN POINT ...... 32 3.3 AERODYNAMICS AND THERMODYNAMICS ...... 32 3.3.1 MOLLIER CHART ...... 33

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3.3.2 TEMPERATURE ENTROPY DIAGRAM ...... 34 3.4 SINGLE CYLINDER TURBINE MODEL ...... 34 3.4.1 OFF-DESIGN OPERATION ...... 37 3.4.2 VARIATION IN TOTAL-TO-TOTAL EFFICIENCY ...... 37 3.4.3 HEAT RATE SENSITIVITY ...... 40 3.5 TURBINE MODEL INCORPORATING REHEAT ...... 42 3.6 EXPERIMENTAL VERIFICATION ...... 46 3.6.1 GRAIN POWER STATION ...... 46 3.6.2 POOLBEG POWER STATION ...... 51 3.7 DISCUSSION OF RESULTS ...... 51 3.7.1 ATTEMPERATORS ...... 52 3.7.2 CONDENSER MODEL ...... 52 3.7.3 BLED STEAM ...... 52 3.7.4 FINAL POINT WETNESS ...... 52 3.7.5 MANUFACTURERS HEAT-RATE CORRECTION CURVES ...... 52 3.7.6 MONEYPOINT POWER STATION ...... 54 3.8 CONCLUSIONS ...... 54

4.0 CHAPTER FOUR - PARAMETER ESTIMATION IN POWER PLANT MODELS ...... 56 4.1 INTRODUCTION ...... 56 4.1.1 TERMINOLOGY AND CLASSIFICATION OF MODELS ...... 56 4.1.2 PROCESS ERROR ...... 57 4.1.3 LEAST SQUARES ESTIMATION ...... 58 4.1.4 COMPUTATIONAL DIFFICULTIES ...... 59 4.1.5 MULTICOLLINEARITY ...... 59 4.1.6 STATISTICAL ANALYSIS ...... 60 4.2 EXPERIMENTAL DESIGN ...... 60 4.2.1 STATEMENT OF OBJECTIVES ...... 61 4.2.2 CHOICE OF INPUTS ...... 61 4.2.3 INSTRUMENTATION AND CALIBRATION ...... 62 4.2.4 PLANT AND SYSTEM PREPARATION ...... 62 4.3 DETERMINISTIC MODEL EQUATIONS ...... 62 4.4 POWER PLANT TESTS ...... 63 4.4.1 DRAX POWER STATION ...... 63 4.4.2 GRAIN POWER STATION ...... 65 4.4.3 MONEYPOINT POWER STATION ...... 66 4.4.4 FAWLEY POWER STATION ...... 67 4.5 ON-LINE PARAMETER ESTIMATION ...... 68 4.6 CONCLUSIONS ...... 69

5.0 CHAPTER FIVE- DISPATCH AND SIMULATION ...... 78 5.1 INTRODUCTION ...... 78 5.2 GENERATION DISPATCH ALGORITHM ...... 78 5.3 FEASIBLE REGION ...... 80 5.4 CASE STUDY ...... 80 5.5 SIMULATION ...... 82 5.5.1 SYSTEM FREQUENCY ...... 82 5.5.2 DEMAND FREQUENCY CHARACTERISTICS ...... 84 5.5.3 DISPATCHING INTERVALS ...... 85 5.5.4 NUMERICAL PROBLEMS ...... 85 5.6 LOSS OF GENERATION ...... 86 5.6.1 PRESSURE DISPATCH ...... 87 5.6.2 STEAM PRESSURE CONTROL ...... 88 5.6.2.1 BOILER FOLLOWS TURBINE ...... 88 5.6.2.2 TURBINE FOLLOWS BOILER ...... 88 5.6.3 OUTPUT POWER CONTROLLERS ...... 88 5.6.4 UNIT CO-ORDINATED MODE ...... 88 5.6.5 GENERALISED PREDICTIVE CONTROL ...... 88 5.7 OTHER RESERVE PROVISION OPTIONS ...... 90 5.7.1 PUMPED STORAGE ...... 90 5.7.1.1 SPINNING IN AIR ( GENERATING DIRECTION ) ...... 90 5.7.1.2 GENERATING ...... 90

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5.7.1.3 PUMPING ...... 90 5.7.1.4 SPINNING IN AIR ( PUMPING DIRECTION ) 90 5.7.2 GAS TURBINES ...... 91 5.7.3 STORED ENERGY RELEASE ON STEAM PLANT ...... 91 5.7.3.1 CONDENSATE STOP VALVE ...... 91 57.3.2 IP/LP THROTTLING ...... 91 57.3.3 STORED ENERGY RELEASE BY OTHER MEANS ...... 91 5.7.4 COMBINED CYCLE GAS TURBINE ...... 92 5.7.5 MISCELLANEOUS ...... 92 57.5.1 SYSTEM INERTIA ...... 92 5.7.6 STORAGE SCHEMES ...... 93 57.6.1 BATTERY STORAGE ...... 93 5.7.7 LOAD SHEDDING RELAYS ...... 93

6.0 CHAPTER SIX - CONCLUSIONS AND RECOMMENDATIONS ...... 95 6.1 CONCLUSIONS ...... 95 6.2 NOVEL IDEAS PRESENTED ...... 96 6.3 RECOMMENDATION FOR FURTHER RESEARCH ...... 96

REFERENCES ...... 97

TAXONOMY ...... 103

Appendix A. LINEARISATION OF PLANT MODEL EQUATIONS ...... 104 A.1.1 STATE MATRIX ...... 104 A.1.2 INPUT DISTRIBUTION MATRIX ...... 105 A.1.3 MEASUREMENT MATRIX ...... 105 A.1.4 FEED FORWARD MATRIX ...... 105 A.2 CONTROLLABILITY AND OBSERVABILITY ...... 106

Appendix B. LAPLACE TRANSFORMS ...... 107

Appendix C. LINEARISATION OF GOVERNOR GAIN EQUATIONS ...... 108 C.1.1 TERM 1 ...... 108 C.1.2 TERM 2 ...... 111 C.1.3 TERM 3 ...... 111 C.1.4 CHARACTERISTIC ...... 111 C. 1.5 TERM 5 ...... 112

Appendix D. NOVEL STORED ENERGY TECHNIQUES ...... 113 D.1 INTRODUCTION ...... 113 D.2 SIMULATED STORED ENERGY TESTS ...... 113 D. 2.1 SIMULATED STORED ENERGY TYPE 2 ...... 114 D.2.2 SIMULATED STORED ENERGY TEST TYPE 3 114 D.3 MONEYPOINT TEST SPECIFICATION AND RESULTS ...... 114 D.3.1 MEASURED STORED ENERGY TEST TYPE 1 114 D.3.2 MEASURED STORED ENERGY TEST TYPE 2 115 D.3.3 MEASURED STORED ENERGY TEST TYPE 3 115 D.3.4 DATA ROUTE ...... 115 D.4 DISCUSSION ...... 115 D.5 CONCLUSIONS ...... 116 D.6 RECOMMENDATIONS ...... 116

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List of Illustrations

Figure 1. Power Spectrum of System Frequency on 19-20 April 1978 ...... 9 Figure 2. Non-Linear Boiler-Turbine Model ...... 12 Figure 3. Governor Valve Characteristic ...... 14 Figure 4. Steady State Power Contours ...... 19 Figure 5. Model Response to a step change in Frequency ...... 20 Figure 6. Step Response of Linear andNon-Linear Model ...... 23 Figure 7. Governor Gain vs Power ...... 24 Figure 8 . Stored Energy vs Power ...... 24 Figure 9. Governor Gain vs Pressure ...... 25 Figure 10. Stored Energy vs Pressure ...... 25 Figure 11. Contours of Constant Gain ...... 26 Figure 12. Contours of Constant Stored Energy ...... 26 Figure 13. Typical Large Generating System Layout ...... 28 Figure 14. HP Rotor of a 270 MWe Alsthom Turbine ( Courtesy of ESB-IRL) ...... 30 Figure 15. LP Rotor of a 270 MWe Alsthom Turbine ( Courtesy of ESB-IRL) ...... 31 Figure 16. A Simple Turbine Stage/Cylinder ...... 33 Figure 17. Mollier Chart for turbine cylinder/stage ...... 34 Figure 18. Temperature Entropy Diagram ...... 35 Figure 19. Mollier Chart for a turbine loaded to design value ...... 38 Figure 20. Mollier Chart for a turbine loaded to 50% of design value ...... 39 Figure 21. Feed pump power requirement as a function of pressure at 50% Load ...... 39 Figure 22. Total-to-Total efficiency as a function of turbine load ...... 38 Figure 23. Points selected to conduct heat rate test on pressure-power plane ...... 41 Figure 24. Mollier Chart for a Generating Set with Reheat ...... 43 Figure 25. Mollier Chart for a Reheat Turbine Loaded to Design Value ...... 45 Figure 26. Mollier Chart for a Reheat Turbine at 50% of Design Load ...... 45 Figure 27. Grain Steady State Tests ...... 48 Figure 28. Standardised Estimates of ...... 53 Figure 29. Information flow for the process and the model ...... 58 Figure 30. Parameter fitting procedure ...... 61 Figure 31. Output Power for Drax Power Station ...... 70 Figure 32. Superheater Pressure for Drax Power Station ...... 70 Figure 33. Drum Pressure for Drax Power Station ...... 71 Figure 34. Reheater Pressure for Drax Power Station ...... 71 Figure 35. Output Power for Grain Power Station ...... 72 Figure 36. Superheater Pressure for Grain Power Station ...... 72 Figure 37. Drum Pressure for Grain Power Station ...... 73 Figure 38. Reheater Pressure for Grain Power Station ...... 73 Figure 39. Output Power for Moneypoint Power Station ...... 74 Figure 40. Superheater Pressure for Moneypoint Power Station ...... 74 Figure 41. Drum Pressure for Moneypoint Power Station ...... 75 Figure 42. Reheater Pressure for Moneypoint Power Station ...... 75 Figure 43. Output Power for Fawley Power Station ...... 76 Figure 44. Superheater Pressure for Fawley Power Station ...... 76 Figure 45. Drum Pressure for Fawley Power Station ...... 77 Figure 46. Feasible Region for Power and Pressure Dispatch ...... 80 Figure 47. The Merit Order Solution to the Dispatch Problem ...... 81 Figure 48. System Gain for Case Study ...... 83 Figure 49. Reserve Provision Costs for Case study System ...... 83 Figure 50. Generation Loss Incident of 660 MW with System Loading of 9 GW ...... 86

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Figure 51. Response of Units 14-17 in the case study Power System to Generation Loss 87 Figure 52. Maximum Initial Frequency Error and Time at Which itOccurred ...... 89 Figure 53. System Costs and Scheduled Gain ...... 89 Figure 54. View of the Battery Strings in the Chino Facility ...... 94 Figure 55. Stored Energy Tests, Power Output plotted against Time ...... 118 Figure 56. Stored Energy Tests, Drum Feed Flow ...... 119 Figure 57. Stored Energy Tests, Drum Exit Steam Flow plotted against Time ...... 119 Figure 58. Stored Energy Tests, Primary Attemperator Flow plotted against Time . 120 Figure 59. Stored Energy Tests, Secondary Attemperator Flow plotted against Time . . 120 Figure 60. Stored Energy Tests, Drum Level Plotted against Time ...... 121 Figure 61. Stored Energy Tests, Economiser Outlet Temp, plotted against Time . 121 Figure 62. Stored Energy Tests, Saturation Temperature plotted against Time ..... 122 Figure 63. Stored Energy Tests, Primary S/H Outlet Temperature plotted against Time 122 Figure 64. Stored Energy Tests, Secondary S/H Outlet Temperature plotted against Time 123 Figure 65. Stored Energy Tests, Final S/H Outlet Temperature plotted against Time . . . 123 Figure 66. Stored Energy Test Type 1 124 Figure 67. Stored Energy Test Type 2 ...... 125 Figure 68 . Stored Energy Test Type 3 ...... 126

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List of Tables

Table 1. Regression Parameters for fit to Governor Characteristic ...... 15 Table 2. Model Parameters and Variable Bases ...... 16 Table 3. Data and Design Values for Single Cylinder Turbine ...... 37 Table 4. Regression Analysis Results for Single Cylinder Turbine ...... 41 Table 5. Data and Design Values for Reheat Turbine ...... 44 Table 6. Regression Analysis Results Generating Set with Reheat ...... 44 Table 7. Regression Analysis Results Generating Set with Reheat without Feed Pump . 46 Table 8 . Plant Parameters Recorded by Orion Data Logger ...... 47 Table 9. Regression Analysis Results For Grain Data ...... 49 Table 10. Steady States identified by a t test on Grain Data ...... 50 Table 11. Regression Analysis Results from Poolbeg Data ...... 51 Table 12. Parameter Estimates and Associated Statistics for Drax Power Station ...... 64 Table 13. Per-unit bases selected for Parameter fitting process ...... 65 Table 14. Parameter Estimates and Associated Statistics for Grain Power Station ...... 66 Table 15. Parameter Estimates and Associated Statistics for Moneypoint Power Station 67 Table 16. Parameter Estimates and Associated Statistics for Fawley Power Station .... 68 Table 17. Power Plant used in Power and Pressure Dispatch Case Study ...... 81 Table 18. Coefficients of the linearised governor gain equations...... 112 Table 19. Subset of Plant Parameters Recorded by Quaestor ...... 117

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1.0 CHAPTER ONE - INTRODUCTION

1.1 PREAMBLE

The primary goal of power system operation is to supply consumer demand for electric power at a specified quality at minimum cost. This quality is defined in terms of voltage and fre­ quency standards which must be maintained within certain bounds dictated by statutory reg­ ulations. Since electric energy cannot be stored in any appreciable amount, consumer demand must by met by generation as and when it arises. Consequently, system operators must ensure that they have enough energy conversion plant available to meet this demand and likely future changes. This requires careful planning as some plant needs several hours advance warning before synchronisation is possible. The task can be divided into two phases; one of planning the required capacity and one of requesting generation levels. The first stage is known as unit commitment where the operators look forward, typically twenty four hours, and with a know­ ledge of plant availability, likely consumer demand, with a certain reserve margins and se­ curity of supply considerations give approximate synchronisation times and loading levels to the generators. In recent years this procedure has been performed by computer and in the U.K. supply system such an algorithm has been in use for several years ( Browning et al., 1985). The second main duty of power system operators is to request generation levels from the synchronised plant to meet the consumer demand. This procedure has a lead time from five minutes to two hours and is known as economic dispatch. The demand is allocated among the generating units so that total system costs are minimised subject to certain constraints. This calculation is performed by utilities typically every five minutes and instructions conveyed to the stations either manually, by telephone, or automatically. If the new set point in­ structions are automatically telemetered to the unit process control computer from the dis­ patch computer and thereby implemented then this is a form of Automatic Generation Control ( AGC ), Athy ( 1987 ). The practices of different utilities in respect of the above vary considerably due to many fac­ tors such as utility size, plant mix, proportions of thermal and hydro etc.. A recent survey of some forty one countries showed that thirty nine of them use unit commitment and thirty five use economic dispatch ( Rumpel, 1987 ). The survey also requested the extent to which these functions were performed by computer and twenty four counts resulted for unit commitment and twenty five for economic dispatch.

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1.2 PLANT AND SYSTEM INTERFACE

There is a clear difference in the priorities of power plant and power system operators. The power system operators would like to have controlled ideal voltage sources at their disposal which can be switched and whose power output can be varied continuously at will. The power station operators would like to run their plant for long periods at design power and at a con­ stant speed. In do doing they can get their machines into perfect mechanical and thermal equilibrium and thereby maximize efficiency. Clearly, some compromise, mutual under­ standing and appreciation is needed to match these two extreme requirements. Moreover, power station and power system operators form two distinct bodies and communication is usually on an as needed basis. The Energy Management Centre must therefore be conversant with plant constraints to make the optimal use of the power plant. These constraints will now be discussed and their relevance to power system operation indicated.

1.2.1 POWER PLANT CONSTRAINTS

Real power plant does not behave in the ideal way sought by the grid operators and some of the constraints on its operation will now be discussed. The dispatch algorithm must represent these constraints so that the target loadings will be less onerous for the plant thereby result­ ing in better station and system control.

1.2.1.1 MAXIMUM AND MINIMUM POWER

There are maximum and minimum power output levels which can be delivered by plant. The upper limit is set by the turbine designers and can be lowered by problems with plant auxil­ iaries for example coal mills in thermal plant or an extraordinary low water head in hydro plant. Minimum power is a feature of the boiler where a flame cannot be continuously controlled to zero - beyond a certain point it extinguishes. Typical minimum powers are in the region of 20-40% for oil and gas-fired and 40-50% for coal-fired plant ( Rumpel, 1988 ).

1.2.1.2 RA TE OF CHANGE LIMITA TIONS

Thermal processes in power plant have one major energy reservoir which is the heat content of the metal and steam volumes of the boiler. This energy may be depleted by opening the turbine governor valve in time scales of several seconds. However, refilling this reservoir is only achieved by a coordinated control action involving combustion and feedwater control and has a response time of several minutes. Loading rates depend on plant size and typical val­ ues are approximately 4-5% of Maximum Continuous Rating ( MCR ) per minute. Rates of change are also limited by thermal stress constraints mainly related to the turbine. These are supplied by the manufacturer following detailed study of the frequency of temper­ ature cycles, fatigue parameters of the metal, admissible temperature differences etc.. These constraints are not hard limits but repeated violation will result in decreased plant life and perhaps sudden failure.

1.3 PLANT REPRESENTATION IN DISPATCH SYSTEMS

Power plant is represented with various levels of complexity in the Energy Management Centres. Some of the differences can be accounted for by the size and special requirements of the power systems and the commissioning date of the respective control centres: newer ones tend to have more facilities. The aim of the generation dispatch algorithm is to allocate the consumer demand econom­ ically among the generators so that global costs are minimised subject to certain constraints. This optimisation requires some model of the power plant, its running costs and the operating constraints. Accurate representation of the complex processes involved in energy conversion

PhD Chapter 1 Page 2 Introduction Improved Generation Dispatch in Power Systems would require extensive models which would have inordinate execution times. Consequently, a reduced model is usually used accounting only for the main constraints of the plant. The optimal solution obtained using a simple power plant model will of course by subject to the assumptions made in its construction. Interpretation by the unit operators of dispatch in­ structions thereby obtained will, of course, be subject to immediate plant constraints with which she is more familiar. Moreover, natural equipment deteriorations over time will alter the constraints of the dispatch model and frequently they are not updated. Representation of power plant in dispatch system will now be considered and the assumptions made discussed. The inadequacies of these assumptions and the consequences of their vio­ lation on power system control and economics will be discussed.

1.3.1 OBJECTIVE FUNCTION

The efficiency with which a power plant converts chemical energy into electrical energy varies from station to station. The differences arise from fuel type, steam cycle conditions, materials, age and plant conditions. Other costs to be reckoned arise from proximity to fuel supplies, means of providing cooling water, emission regulations etc.. These costs must be determined and made known to the energy management centre for use within the dispatch procedure. The efficiency of the plant is usually measured by a team of specialists with carefully cali­ brated equipment. These tests are not conducted at regular intervals but usually on an ad hoc basis. The cost the dispatch algorithm uses in its optimisation procedure for a particular unit is therefore a snapshot of the efficiency at a point in time anything up to five years ago. This will not represent the power plant costs accurately as day to day plant problems and systematic deteriorations will alter the efficiency. Although the absolute costs are not re­ presented accurately the optimal generator loadings are determined by the relative costs be­ tween the sets. If one had an instantaneous snapshot of all the generators costs and assumed that the plant deteriorations were equal, and that day to day effects were random then on average the system costs would equal the dispatch costs. However, this is not the case as resources do not permit the simultaneous testing of all plant and different running times and maintenance schedules result in an uneven deterioration. The extent by which the costs must change to alter the solution may be determined by a sensitivity study on the converged solution of the dispatch process. This can then be com­ pared to the likely variations in the costs of the generators and the penalties incurred in making incorrect assumptions quantified. On this basis, a judgement can be made as to whether or not further resources should be applied to this problem. This is a utility specific calculation and is outside the scope of this thesis which examines principles common to all power systems. It suffices to say that there is a likely benefit available if current station costs were known to the dispatch algorithm. Towards this end, many utilities have been involved with on-line monitoring projects. Efficiency calculation on-line are conceptually simple where measure­ ment of power output and fuel input are made and the ratio taken. The main difficulty involves obtaining accurate measures of the fuel calorific values particularly in the case of coal which is the predominant fuel source in the World. There are many on-line monitoring schemes described in the literature ( Foley, 1985 ) and their objectives vary considerably. From a station point of view, knowledge of a deteriorated efficiency is useful only as a management tool if no hints as to the source of the deterioration is available. Other schemes simply monitor efficiency with a view to scheduling maintenance outages ( Cotton and Schofield, 1971 ). The reliability of efficiency calculations preformed on line in thwarted by instrumentation problems. Calibrations tend to drift and all instruments need frequent maintenance which is carried out at a priority determined at local level and often is neglected. Finally, there is a natural human reluctance in communicating deteriorated efficiencies to the energy management centre it may result in reduced running hours and, on a personal level, may be seen to reflect on the station staff competence. Altbach power station in Germany owned by Neckarwerke Elekrizitaetsversorgungs AG em­ ploys an on-line monitoring tool which is incorporated in the process control system ( Herbig et al, 1986 ). It provides an efficiency estimate after a period of steady running has been es­

PhD Chapter 1 Page 3 Introduction Improved Generation Dispatch in Power Systems tablished which is gauged to have occurred when the numerical derivatives of key plant vari­ ables are sufficiently small. However, the results are not communicated to the Energy Management Centre as the prevailing utility constraints and costs allow no margin for optimisation and this is used as a management tool only. A more sophisticated cycle analysis package, known as ANCYCLE ( Keller and Urban, 1989 ) is being developed by Siemens. It calculates the cycle efficiency and provides hints as to the source of a deteriorated heat rate. At Poolbeg Power Station in Dublin a prototype monitoring facility has recently been installed and further investigations are currently underway. At the present time ( 1990 ) there is no on-line monitoring facility known to the author which automatically updates the dispatch al­ gorithm costs. Moreover, the system would require quality assured absolute heat rate data which is more onerous than monitoring relative daily performance at station level.

1.3.2 PLANT CONSTRAINTS

Power plant operation in a commercial grid environment is never smooth and care free. The plant consists of many hundreds of motors, fans and pumps each with a local control loop and each susceptible to failure. This is recognised by the designers who enhance security pro­ viding duplicate items of plant as far as possible. In normal operation, if all the plant equip­ ment is functioning then the plant will follow its dispatch instructions with relative ease. However, if some items are out of service and standby equipment is being used, which is usually of lower rating and quality, then the plant's ability to follow its dispatch instructions may be curtailed. The power system integrity and security may be therefore reduced. Moreover, on a human level, if the station is receiving dispatch instructions which are unrea­ sonable in light of plant problems relations may be affected. If some of the plant constraints are not binding on the system and the effort made by the plant to provide them may be unnecessary. These considerations will now be treated more spe­ cifically in respect of coal-mills and boiler feed pumps.

1.3.2.1 COAL MILLS

Coal is pulverised in coal mills prior to being introduced to the furnace by an air stream. These mills require electric power to drive the motors and if the unit is de-loaded and unlikely to be needed to pick up power in the near future then any excess milling capacity could be removed. This would decrease the house load of the station and modify the power rate of change constraints. The dispatch algorithm should then be appraised of these changes. This led to the idea of mill dispatch involving a large number of integer decisions. The computing overheads would require an efficient efficient algorithm such as Benders Decomposition (Vlahos and Bunn, 1988 ). A similar theoretical study was made by Tamura et al ( 1988 ) for­ mulating the problem of scheduling the number of coal mills and oil burners in terms of gen­ erator output 'zones' determined by the number of mills and burners in service. However, the real life operation of milling plant complicates this simple picture. Running more mills than is strictly necessary may cause the coal to be ground more completely leading to better boiler efficiencies. Moreover, using a mill below capacity results in decreased wear and tear and thereby reduced maintenance. More often than not unit output is limited by the availability of mills and there is no choice regarding their running. On this basis the concept of mill dispatch was seen to unfavourable.

1.3.2.2 BOILER FEED PUMP

Water is introduced into the evaporator by the feed pump which operates over a substantial pressure differential leading to large power requirements. At low loads the reduced steam flows permit the removal of a feed pump thereby reducing house load and increasing effi­ ciency. The pick up capability of the plant is also reduced as the required water flow cannot be introduced to the evaporator with the remaining pumps. These changes should be also made known to the dispatch algorithm. The removal of a feed pump at lower loads will result in a step increase in efficiency resulting in a non-convex cost function. Special computational methods are needed to cater for this such as mixed integer and linear programming.

PhD Chapter 1 Page 4 Introduction Improved Generation Dispatch in Power Systems

1.4 CURRENT DISPATCH PRACTICES The dispatching practices of several utilities of various size will now be discussed.

1.4.1 U.K. SUPPLY SYSTEM

Prior to April 1990 the Central Electricity Generating Board ( CEGB ) was responsible for generating and transmitting electricity in England and Wales. It was subsequently privatised resulting in four successor companies; three involved with generation and one with trans­ mission. The power system supplies a peak load of 53 GW with 86 % fossil-fuelled plant, 9.6% Nuclear, 0.2% Hydro and 4% pumped storage. The Generation Dispatch Project trials were held in 1985 and were shown to make economic savings over the existing manual practice. The dispatch algorithm uses power plant models with up to three piecewise linear cost seg­ ments; maximum and minimum power levels and ramprate constraints ( Dunnett and Duckworth, 1986 ). Security is catered for approximately by group constraints which ensures that the output of particular groups of generators do not exceed certain limits which are up­ dated frequently by off-line studies. This optimisation is accomplished by formulating the problem in terms of a sparse dual re­ vised simplex method with the unconstrained merit order solution as the starting condition. This algorithm is described by Irving and Sterling ( 1983 ) and progresses towards optimality from the merit order solution. A method of constraint relaxation is provided whereby feasible solutions are generated from infeasible ones by relaxing soft constraints The algorithm is available in the Energy Management Centre and is used only as an advisory aid to the grid control engineer. The software is backed by extensive facilities such as State Estimation and Security Analysis ( Laing and Elder, 1986 ) , Demand Prediction ( Laing and Brewer ( 1986 ), Bunn and Farmer ( 1985 ), Laing and Smith ( 1987 ) ) and are described in general by Metcalfe and Murray ( 1987 ). In addition the treatment of pumped storage and its use to minimise system costs is reported by Broadbent et al ( 1987 ). The algorithm receives current loading information on all generators via the Supervisory Control and Data Acquisition ( SCADA ) system known as GI74. The incoming data which is asynchronous is validated, marshalled and passed to the dispatch computer up to one minute late. The algorithm is then executed in approximately two minutes and provides target tra­ jectories at six linked time points up to two hours in the future. This information is typically three minutes late and repeated every five minutes based on calculations made by Farmer (1980) on the consequences of the unpredicted load component will have on system frequency variation.

1.4.2 IRISH SUPPLY SYSTEM

The Electricity Supply Board ( ESB ) is responsible for generating, transmitting and distributing electricity in the Republic of Ireland. The peak system load of 2.4 GW is met by 10% hydro, and the remaining thermal and a substantial pumped storage capacity (10% ). The fuel types vary from indigenous gas and peat to imported coal and oil with no nuclear capacity. The National Control Centre was commissioned in 1986 and provides extensive facilities; state estimation, operator loadflow, economic dispatch and contingency analysis ( McDyer and Herger, 1987 ). The dispatch algorithm is run every three to five minutes limited only by the processing power of the CPU. A recent enhancement of this algorithm has been then inclu­ sion of primary and secondary spinning reserve constraints ( Brown, 1989 ) and the introduc­ tion of AGC is intended within the next five years.

1.4.3 ITALIAN SUPPLY SYSTEM

Ente Nazionale per L'Energia Elettrica ( ENEL ) are responsible for generating, in conjunction with other private generators, the bulk of the Itilian demand of 56 GW. This is comprised of 32% Hydro, 65% Thermal, 1.3% Nuclear and the remaining Geothermal.

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The dispatching problem is handled in three phases; day before dispatching, advance dis­ patching and instantaneous economic dispatch and is described by Marannino et al ( 1990 ). The advance dispatch employs a dynamic dispatch algorithm run every half hour and modifies the day-before schedule by supplying optimal trajectories for thermal units over very short periods. This procedure is open loop and provides security constrained participation factors for closed loop instantaneous economic dispatch. The dynamic dispatch algorithm is de­ scribed in a separate paper by Inorta et al ( 1988 ).

1.5 ACTIVE POWER RESERVE When the generators are loaded in the most economic manner as determined by the costs and constraints, generation should equal consumer demand plus system losses. In this situ­ ation the system frequency will be at the nominal value. Any imbalance between consumer demand and generation will be met by the stored energy of the generating sets. This stored energy is contained in the boilers of those sets which operate at pressures higher than nec­ essary to pass the required steam flow through the turbine. It is argued that this extra pres­ sure causes throttling losses at the turbine governor valves and thereby reduces the efficiency of the unit as a whole. Moreover, operating at high pressures will mean that the plant is continually tracking frequency and not operating in a steady state. There is a reluctance on the part of the generators to operate in this mode as it putatively increases their losses and decreases their profit. The stored energy is activated by opening the governor valves thereby decreasing the impedance resulting in an immediate increase in steam flow. The resulting increased steam flow appears as electrical power when it expands through the turbine. This incremental en­ ergy peaks within, typically, 30-45 seconds after the valves have opened and provides reserve to buffer the system until sustained responses are available through increases in boiler firing. Loss of generation is made up in the first instance by this stored energy release, followed by automatic startup of pumped storage and gas turbines and finally by increases in boiler firing. The generation is reallocated at the next dispatch interval in the most economic way. Some utilities employ Load Frequency Control ( LFC ) which attempts to reallocate generation with economic considerations prior to the next dispatch interval ( Birch et al 1990 ). Active power reserve has therefore three distinct timescales known as primary, secondary and tertiary. Primary reserve is that available within the first half minute from governor initiated output changes and is the main consideration of this thesis. This is assisted by natural de­ mand frequency characteristics and pumped storage units which are pumping or generating in merit. The presence of this reserve arrests the initial frequency fall and tides the system over until secondary reserve becomes available via increases in boiler firing. Tertiary reserve is then provided by the LFC or at the next Economic dispatch calculation with due regard to the system economics. The effects of spinning reserve are uncertain mainly because of the characteristics of the connected load. A relationship between the maximum infeed, spinning reserve, system load, plant inertia and the load frequency characteristic was developed by McDyer and Haren (1980). The load frequency characteristic was found to be a statistical variable with an ap­ proximate normal distribution and spinning reserve could be dispatched with a certain risk level according to this distribution. In Germany, the DVG ( Deutsche Verbundgesellschaft - Association of German Interconnected Utilities ) set requirements on all connected plant in respect of primary reserve following extensive studies ( Falgenhauer and Kiirten, 1985 ). This requirement is for a post-fault pickup of 2.5% in 5 seconds and 5% in 30 seconds if the German grid is disconnected from the European grid. The goal in the field of spinning reserve has always been to cover generation losses without disconnecting consumers and thereby provide a secure supply. Disconnecting consumers is a method of reducing the demand supply imbalance and it is suggested that there are many consumers who would not object or even observe brief ( five minute ) interruptions of supply. Indeed, consumers are frequently disconnected by distribution companies for maintenance purposes and by local faults. There are, of course, many other consumers who would not tolerate disconnections and busy metropolitan centres should be secure. Furthermore, total security may not be desirable to consumers on economic grounds when traded against the

PhD Chapter 1 Page 6 Introduction Improved Generation Dispatch in Power Systems inconvenience of a few five minute annual disconnections. However, from a grid point of view the demand relief available at certain busbars is difficult to quantify and rely upon as a source of reserve. The provision of primary reserve depends on the boiler operating pressure and the generator load. It is available only from those sets operating with governor valves throttling steam flow thereby increasing the operating costs. This primary goal of this thesis is to quantify the amount and cost of primary reserve and to dispatch it system wide in the most economic manner.

1.5.1 ISLAND SYSTEMS

Small electrically isolated power system known as island systems have particularly acute problems providing the necessary reserve to cover the loss of the largest set. In such systems the ratio of the largest infeed to the system demand is large and frequently such utilities must limit their maximum infeed thus negating the economy of scale considerations which initially lead to its commissioning. This has a tremendous impact on the economic dispatch problem as is discussed by Fox and McCartney ( 1988 ) in the case of the Northern Ireland System. Northern Ireland Electricity ( N te) acknowledge the fact that the loss of the largest infeed cannot be catered for and load shedding is inevitable. Consumer disconnections are rotated so that no one consumer is continually disconnected following a generation loss. Recent im­ provement by the use of flywheels are discussed in Chapter Five. Other systems where similar problems exist are in the Republic of Ireland ( ESB ), West Berlin ( BEWAG ) and Isarel ( IEC ). A recent paper by McDyer and Kiirten ( 1989 ) addresses the problem of providing reserve on Island systems yielding an optimal economic strategy of balancing reserve provision costs against the number of tolerable consumer disconnections per annum.

1.5.2 FREQUENCY REGULATION

The onus on power systems is to maintain the frequency within statutory limits but having accomplished this there are no further requirements. On interconnected power systems the inter-utility power flows must average at a negotiated value and tighter control of frequency makes this easier. Moreover, most utilities ensure that the average value of the frequency error is zero over a twenty four hour period so that electrical time is correct. The grid frequency error spectrum for the British grid shown in Figure 1 on page 9 shows a well pronounced peak at one cycle in 38 minutes. This is a function of manual control where the grid operator takes no remedial action until the frequency error has reached -0.1 Hz. Load is then re-dispatched and the frequency recovers. This would imply that the system has a time constant of approximately 19 minutes! However, the longest time constants in power systems are associated with the boiler and are of the order of 3-4 minutes. Investigations by Farmer ( 1982 ) suggest that the system time constant is larger by a factor of 4-5 times due to the interaction of sustained and un-sustained plant which would account for this apparent anom­ aly. The value of improved regulation in island power systems is a difficult concept to quantify. Frequency disturbances are wide-band effects as seen on the typical spectrum of grid fre­ quency variation shown in Figure 1 on page 9. Improved regulation will reduce the compo­ nents at various ( cycle ) frequencies but to what extent this would be visible and of interest to the users of the product is debatable. An experiment with a 'typical' cross-section of con­ sumers and 'typical' appliances being subject to supply with different spectra could be envis­ aged. The consumers would be asked to indicate when effects became noticeable and/or objectionable. Clearly, the results would have a very large subjective element and poor re­ peatability. The relation between regulation and generator output has quantified in terms of a regulation index by McDyer ( 1986 ). This is defined as the reduction ( or increase ) in the area under the grid frequency error spectrum at a base point. The area under the frequency spectrum is also dependent on the position in the network at which it is observed and the results are weighted

PhD Chapter 1 Page 7 Introduction Improved Generation Dispatch in Power Systems over the network space. This was then incorporated into a Linear Program to dispatch regu­ lation. A similar computational problem is evident with this constraint to the non-convex cost function resulting from switching out a feed pump. The benefits of tighter control of frequency were investigated by Ashmole et al { 1984 ) and attempts made to quantify the possible economic penalties incurred by the reduced outputs at lower frequencies of items of plant such as Forced and Induced Draft ( FD, ID ) Fans, Condenser Extraction Pumps and concluded that system costs of the order of £5M (1982 value) were possible.

Finally, poor regulation of grid frequency may be undesirable to many high-technology indus­ tries who require very tight tolerences on their manufacturing process. It has not been un­ known for such industries to reject plans to establish in a country where regulation is poor.

1.6 OVERVIEW OF THESIS

This thesis examines power plant representation in dispatch systems with a view to quantify­ ing its ability to supply primary regulating and emergency reserve. This ability will be quanti­ fied by use of a simple model of the major processes involved. The costs of providing this reserve is then deduced from suitable thermodynamic theory and plant tests. With a know­ ledge of both these components the required regulation is allocated to the individual units in the most economic way.

Chapter Two examines the ability of a generator to provide primary reserve in terms of its power and pressure set points. This is examined with the aid of a simple non-linear model with typical parameters. Chapter Three examines the costs involved in reserve provision us­ ing thermodynamic theory and plant tests. Chapter Four describes an algorithm by which the parameters of the non-linear model in Chapter Two are deduced from a series of plant tests worldwide. Chapter Five presents an enhanced dispatch algorithm which provides primary reserve and a simulation to investigate the benefits thereof. Conclusions are drawn in Chap­ ter Six and directions for future research identified.

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Figure 1. Power Spectrum of System Frequency on 19-20 April 1978: Diagram taken from Farmer ( 1982 ).

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2.0 CHAPTER TWO - FREQUENCY REGULATION FROM THERMAL PLANT

2.1 INTRODUCTION

When generation equals consumer demand plus system losses the grid frequency will not change from its set point. Any imbalance is met immediately by the generators where load angles change to supply additional electric power. This increase in power is transmitted along the shaft where it is initially met from the rotational energy of the turbine causing it to slow. The speed governors sense this change and open to admit more steam to the turbine producing extra power and reducing the imbalance. This is the process of primary frequency regulation and is assisted by natural frequency characteristics of the load as discussed in Chapter Five.

Implicit in the above is the assumption that the governor valves have the capability to be opened further. Steam flow through a turbine is, to first order, proportional to the load and if the governor valve is not fully open the impedance to steam flow is increased. Higher pres­ sures will then be needed to pass the required steam flow. The pressure that would pass the required steam flow with a fully open governor is known as the sliding pressure. Any increase in pressure above sliding results in the steam flow being throttled and the generator given the capability to regulate frequency.

It is argued that throttling steam flow reduces generator efficiency and increases costs. In addition, the unit will experience changes in its output power, steam pressure and temper­ atures and control actions due to the continual influence of grid frequency known as cycling. Consequently, there is a reluctance on the part of the station to operate in this mode.

Intuitively, one would expect that the ability of the generator to provide reserve would increase as the pressure is increased above sliding and decrease as the power increases. The inten­ tion in this Chapter is to quantify this ability as a function of the power and pressure set points. This is achieved by use of a simple model with typical parameters derived from plant tests.

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2.2 POWER PLANT MODELLING

The capability of power plant to provide active power reserve for frequency regulation can be examined by using a suitable mathematical model. There are two broad classes of power plant models in existence. The first class, known as reference models, use a modular ap­ proach to describe items of plant in great detail by ordinary and partial differential equations and are typified by those described by Kozlowski and Withmarsh-Everiss ( 1989 ), Sidders (1989) , Maffezzoni et al ( 1983 ) and Brereton ( 1983 ). These models are often used in the design stage to evaluate tenders or to consider the benefits of adding an extra superheater for example. The other class of model, known as the dispatcher's models, describe the salient portions of the plant relevant to a particular application and are typified by those described by Astrom and Bell ( 1988 ), Morris and Schweppe ( 1981 ), Farmer et al ( 1981 ) and Maples ( 1970 ). Models such as these have been used sucessfully for many years to design con­ ventional control systems ( Metcalfe , 1974 ) and more recently to apply Generalised Predictive Control techniques ( Rossiter et al, 1990 ). To examine the capability of power plant to provide primary regulating and emergency re­ serve a simple model incorporating the major thermal energy storage areas - the drum riser system and the reheater - is sufficient. Secondary regulating capability can be examined by incorporating combustion dynamics and control system strategies and tertiary regulation by coupling the models with the energy management system. The model should be kept as simple as possible so that execution time is minimised and to avoid confusing results with irrelevant detail.

2.2.1 MODEL EQUATIONS

The components of the plant to be modelled are depicted in Figure 2 on page 12. These in­ clude an evaporator where steam is generated, a superheater, governor valves, a High Pres­ sure ( HP ) turbine, a reheater and Intermediate and Low Pressure ( IP/LP ) turbines. These individual components will now be described in detail.

22.1.1 EVAPORATOR

A suitable representation of the drum/riser system can be deduced from the reference model described by Brereton ( 1983 ). The contents of the drum riser are assumed to be a homo­ geneous mixture at saturated conditions and the metal temperature closely follows that of the mixture. The mass balance of the fluid in the drum is given by dp = Mf -M s, dt where V is the volume of the drum and riser, p is the fluid density and MF and Ms are the feed water and saturated steam mass flow rates. The total energy balance may be written as

Mc l k + V ~di (pu) = hp - M s h s+ Of. where M is the mass of drum and riser metal, c is the specific heat capacity of the metal, T is the metal and saturated mixture temperature, u is the internal energy, QE is the rate of heat input and hF and hs are the total feed and saturated steam specific enthalpies respectively. This may be rewritten in terms of the empirical relationship d_ dPD (Mf -M s) (pu) = c' dt dt + V where c' is a constant and h0 is an enthalpy reference. The above equations may now be combined to yield,

PD = [

PhD Chapter 2 Page 11 Frequency Regulation from Thermal Plant Improved Generation Dispatch in Power Systems

Figure 2. Non-Linear Boiler-Turbine Model: Details of the model.

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2.2.1.2 SUPERHEATER

The pressure drop across the superheater can be represented by a simple impedance where the pressure drop is proportional to the square of the steam flow,

PD ~ p s = kSH^s - where Ps is the superheater exit pressure and kSH is the impedance. Steam flow through the HP turbine is proportional to the product of the superheater pressure and the governor valve effective aperture (A) as follows;

Ms = kTVPsA, where kTv is the valve constant.

2.2.1.3 REHEATER

The IP/LP steam flow ( MR ) is proportional to reheater pressure ( PR ),

Mr ~ ^ pr - where kR1 is a constant of the reheater and IP/LP turbines. The steam flow through the re­ heater is represented by a first order lag,

p r ~ ^R2(Ms ~ Mr ), where (tai/o ^)-1 is the reheater time constant.

2.2.1.4 GENERATED POWER

The generated power ( Wg ) is the sum of the power developed in the HP and IP/LP cylinders. This is given by the product of the total enthalpy drop across a cylinder and the steam flow through it as seen from the steady flow energy equation developed in Chapter Three, Wg = (h1- h 2)Ms-h(h3- h 4)MR, where h-, is the live steam enthalpy, h2 is the cold reheat enthalpy, h3 is the hot reheat enthalpy and /?4 is the exhaust enthalpy.

2.2.1.5 COMBUSTION SYSTEM

The combustion system is represented by a simple lag where changes in evaporator heat in­ put lag changes in firing ( F ),

QE — bgF — bgQE.

The value of the time constant 1 jbs depends on the type of plant. In an oil-fired plant it de­ pends the time taken for the additional oil to mix with the air and completely combust and would be of the order of ten seconds. In coal-fired plant extra fuel can only be introduced to the furnace after it has beenpulverised by the coal mills and the time constant will be larger, typically of the order of 130 seconds. This is a considerable simplification of the mill dynamics and a more detailed discussion is given in a paper by Corti et al ( 1986 ).

2.2.1.6 GOVERNOR VALVE MODEL

The steam flow through a governor valve is a non-linear function of the valve position. This non-linearity arises from two main sources: the valve profile and the aerodynamics of compressible fluid flow through orifices ( Kearton, 1966 ). For small openings the resultant steam flow is almost linearly related, but it saturates as the valve approaches the fully open position. An attempt is made to compensate for this non-linearity by including a cam whose charac­ teristic is the inverse, although the compensation is never perfect. These effects - valve pro-

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file, position and cam - are represented by a single function relating the actuator output to the effect this will have on the steam flow, termed the effective aperture and is depicted in Figure 3 on page 14 ( Nye and Sohal, 1970 ). This is representative of governor valves in general.

Figure 3. Governor Valve Characteristic: The function relating steam flow to valve aperture.

This curve was approximated by a hyperbolic tangent which was found, empirically, to give the best fit from a range of functions tried, A = a tanh(/?<£). The values of a and p were determined by a regression using the method of least squares and their values quoted in Table 1 on page 15. Frequency deviations affect the unit output by altering the governor valve position from its set point. A rise in frequency will close the valve further, reducing the effective aperture and decreasing the steam flow. Intuitively, one would expect a high sensitivity from a valve set point in the middle of the range, and reducing as the valve approaches the fully open position. Frequency errors are scaled by a factor known as the droop. This is usually taken to be 4%, meaning that the set's output changes by 100% of Maximum Continuous Rating ( MCR ) for a frequency change of 4% ( 2 Hz ). This is described by the following relation, MCR = Wg6t Df0l 100 where D is the percentage droop and f and f0 the actual and nominal frequencies. Alterna­ tively the actuator travels its full stroke for a D % change in frequency. Stroke <£ = 4>Set D/q/100

The maximum incremental power available from a unit, for frequency excursions in the neg­ ative sense, is obtained by choosing a droop which will open the valve completely and utilise all the available headroom.

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X Data Y Data Approx Difference m Y(i) Y(i) == a tanh(/?X(/)) e(i) 0.00 0.00 0.00 0.00 0.10 0.21 0.23 -0.02 0.20 0.43 0.44 -0.02 0.30 0.61 0.62 -0.01 0.40 0.75 0.75 0.00 0.50 0.87 0.84 0.03 0.60 0.93 0.91 0.02 0.70 0.95 0.95 0.00 0.80 0.97 0.98 - 0.01 0.90 0.99 1.00 -0.01 1.00 1.00 1.01 -0.01 a = 1.02946 /? = 2.30885 £e2(/) = 0.002

Table 1. Regression Parameters for fit to Governor Characteristic: Approximation minimizes the sum of squares of residuals. At present Energy Management Centres dispatch to every unit its active power output. Having received this instruction the station must provide this output in a way which minimizes its costs. It is commonly held that operating with anything other than maximum valve opening, or minimum pressure, incurs additional costs. As a result, unit operators tend to maximize their valve opening thereby providing little scope to regulate frequency. Regulating ability can be dispatched by imposing a particular valve position, or equivalently a particular operating pressure, in addition to the power set point. To achieve this the vari­ ation of active power reserve and costs with operating point must be quantified. This Chapter addresses the first of these and Chapter Three the second.

2.2.2 SIMPLIFYING ASSUMPTIONS

The model equations can be simplified by making the following assumptions, 1. Superheater - HP steam flow is independent of conditions at the HP cylinder outlet; 2. Superheater volume is negligible; 3. Feed flow and steam flow are equal ( MF = MS); 4. Feed and steam specific enthalpies remain constant ( hF, hss, h\, hz, h3< h4 are constant ). This will lead to the following equations

PD = b1 QE — b2PsA,

Pr — bgPsA — b4P R,

Qe ~ bgF — bQQE,

Ps = — -r [(l + 2V*2PD)1'2-l],

Wg = b7PsA + b ePR.

The constants will be given by,

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bi JL C ' (flss ~ hf) b0 = k TV

^3 — ^R2^TV< bA = ^R1^R2> ^6 = 2kSHkjV, b7 = /71 — h2, bs = h3 - h4.

2.2.3 PARAMETERS AND SCALING

The values of the parameters by,bz...b9 have been deduced elsewhere ( Metcalfe, 1974 ) by matching model and observed time constants of a plant transient on Unit 1 at Fawley Power Station in England. These parameters will be taken as representative of such units in general and the reserve provision capabilities of the model will be examined using these typical val­ ues. A series of operational plant tests designed to provide data to estimate these parameters in the least squares sense are described in Chapter Four. The model is scaled with the values reported in Table 2 as bases. The variable bases chosen are the design values.

Model Parameters Variable Bases by 0.00496 sec -1 Power ( Wg ) 500 MW bz 0.00553 sec -1 Drum Pressure ( PD ) 18.4 MPa bz 0.00253 sec -1 S/H Pressure ( Ps ) 18.4 MPa b< 0.1 sec -1 R/H Pressure ( PR ) 18.4 MPa bs 0.257 sec - 1 Heat Input ( Q£) 464 MJ b7 2.230 Firing Rate ( F ) Full Load Value b% 13.216 Valve Aperture ( A ) Fully-open Aperture bs 0.1 sec -1 Actuator ( ) Stroke of Actuator

Table 2. Model Parameters and Variable Bases: The parameters were deduced from plant tests at Fawley Power Station.

2.2.4 VARIABLE BOUNDS

The governor valve position is constrained to lie between the fully open and fully closed po­ sitions, 0 < A < 1.0 per unit. The fuel input is bounded in a similar way, 0 < F < 100 %. The boiler has an upper and lower pressure limits which it can tolerate, the upper being de­ termined by the safety valve settings and the lower by water carry over considerations to the turbine, PD< 104 % 73 % < Ps < 104 % .

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2.3 STATE VARIABLE REPRESENTATION

To quantify the active power reserve which can be obtained from the plant at a particular op­ erating point the system will be represented in state space form as follows:

* i = //(X 1, X2, ..., Xn, U1t U2.....Um), i = 1,2,..., n, Yj = gj (X1f X2.....X„, (71f U2, ..., Um), j = 1,2,..., €t where X = [%, X2,..., Xn]r are the state variables and n is the order of the system, U = [Lf1t l/2,..., UmJ represents the inputs which are m in number and Y = [Y1t Y2,..., Y,]7" represents the outputs which are t in number. This may be written as,

x =/(X, U), Y = g(X,U),

where / and g are vector functions of dimension n and £ respectively. The state variables are; drum pressure, P0, reheater pressure, PR and evaporator heat input, QE.

The inputs are firing rate, F and effective aperture, A,

“ - ( £ ) - ( 5 ) The outputs are superheater pressure, P, and the output power, Wg.

y=(9=ft) '=2-

The model equations in state space form are therefore:

2.4 STEADY STATES

The enhanced dispatch algorithm in the Energy Management Centre will firstly require the unit to generate a desired power output ( Wl9' ) and secondly, to operate at a desired pressure level ( Pfet )• In terms of this model, the outputs are specified and the inputs, or boundary values, must be determined. Once these are known the state variables can then be calcu­ lated.

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The steady state problem is therefore to find values of X and U such that Y takes the value Yset with X = 0, that is o =f(X,U), and ysel = g(X,U). The boundary conditions, U, are determined in a simulator by including an extra equation whose derivative is the difference between the actual outputs, derived from current estimates of the inputs, and the set point outputs in the following way:-

F = f ‘(Wg - W f ) d t + F0, Jo

A = - P f ) d t + A 0, with F0 and A0 initial guesses. In the steady state, since all derivatives are zero the power and pressure will take on the set point values. However, for every pair of desired power and pressure there may not be a valid steady state; it is not possible to operate at pressures below sliding. In the steady state, PR — 0 and hence 0 = b3PsA - b4PR. Consequently, the expression for output power then becomes b6b3 Wvvg = b7 4- PSA = BPSA, where ^qB3 B = b 7 + b4 Therefore, the sliding pressure is given by setting A = 1.0 Wset pSilde vvg B and the operating pressure must be greater or equal to the sliding pressure, pset pSlide r s — r S Steady states were determined for permissible power and pressure pairs and are presented in Figure 4 on page 19 as a contour diagram of the function h, where Wg = h(Ps, 4).

In the context of economic dispatch, a given power output can be attained by a multitude of (Ps, 4>) point pairs. The most economical solution is with the valve fully open, but no reserve is provided. Reserve may be provided by throttling the valve thereby increasing the operating pressure. The effects on cycle efficiency and therefore on production costs are examined in Chapter Three.

2.5 LINEARIZATION

Corresponding to a set of constant inputs, U0 = [Uqi,U0z, ..., l/om]r, the system can settle in the constant state, Xe= [X0i,X02,..., Xony , and hence X0 and U0 satisfy m , U0) = 0.

Perturbing the system from the above by letting

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n -----1------1----- 1------1------1----- 1------1------1----- 1------1 .00 .10 .20 .30 .40 .50 .60 .70 .80 .90 1.00 ACTUATOR OUTPUT ( p.u. )

Figure 4. Steady State Power Contours: Pressure plotted against Actuator Output for a constant Power.

X = X0 + x, and U = U0+u, where the deviations x and u are sufficiently small, the following may be defined A = Vx/ (X,U,t) n x n State Matrix, B = V y /(X,U,t) n x m Input Distribution Matrix,

C = Vxg(X,U,t) € x n Measurement Matrix,

D = Vt,g(X,l/,t) € x m Feed Forward Matrix, with all partial derivatives being evaluated at X 0 and U0. The linearization of the autonomous model equations is performed in Appendix A and found to be

It will be noted that the operating point depends on drum pressure ( X0i ) and the effective aperture ( U02). Those entries which depend on the operating point are highlighted. It is also seen that au, — h and — b9 are eigenvalues of the state matrix and the system is asymptotically stable if they are less than zero. The linearised system is also shown in Appendix A to be both controllable and observable.

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2.6 GOVERNOR GAIN

The governor gain of a generating unit is the response to frequency fluctuations. Shown in Figure 5 on page 20 is the response of the model to a negative frequency step for a set point power of 80% and pressure of 100%. After approximately 30 seconds the power peaks and then returns to the original set point with a time constant of approximately 3.5 minutes. This is expected as no increase in the firing rate was effected and since no extra fuel was burned, the power returns to the original set point. There will be a decrease, however, in the set's internal stored energy reflected by a decrease in the operating pressure and a measure of this loss is the area under the power transient. en On real power plant the magnitude and position of the peak dependsAthe rate at which the governor opens. This in turn depends on where in the governor mechanism a step is applied. The desired speed set value is provided by a combination of a fast acting speed controller and a slower load controller. This set value is the input to an admission controller which positions the governor .valves. If a step is applied to the admission controller the valve opens imme­ diately, whereas one to the load or speed controller incurrs additional delays. The stored energy extracted in all cases is however the same. The variation in the time and magnitude of the peak can be seen in simulated results presented by Kurten ( 1986 ). There are no control systems operating on this plant and the responses shown are the open loop responses. The frequency drop will be arrested in the first instance, by the release of extra energy reducing the supply and demand imbalance. However, this unit only provides short term frequency control as the power returns to its original level. Consequently, a unit without a control system can only contribute to primary frequency control. The peak incremental power, which occurs within the first 30 seconds following the disturb­ ance, due to boiler stored energy will be termed the immediate reserve. The maximum of this ephemeral increase divided by the frequency change will be termed the governor gain ( for primary frequency control ).

POWER SET POINT 8 0 X PRESSURE SET POINT 1 0 0 /

Figure 5. Model Response to a step change In Frequency: Incremental Power results from the increased steam flow when governor is opened.

PhD Chapter 2 Page 20 Frequency Regulation from Thermal Plant Improved Generation Dispatch in Power Systems

The dispatched values of power and pressure will determine the effective aperture and the actuator position Wsget and P f ' I - Ase' ^ set.

A frequency deviation from nominal will produce a change in the effective aperture causing the output power to change,

Af*-* A(f> AA, set AWg = Wga*'min -W, The governor gain is defined as the peak incremental power per unit frequency AW,__ g AA Governor Gain = MW/Hz. A f AA A(f> A f where A _ 1Q0 A f D x f0 ’ and the droop is expressed as the percentage change in frequency which will cause a 100% change in the set's output. By differentiating the approximation to the governor characteristic function,

- f ^ = «Psech2(M ).

To quantify the governor gain over all operating points the step response of output power to a step change in effective aperture is needed. This can be deduced from the linearised equations so far presented. The system gain is then simply the sum of the governor gains of all the units on the system.

2.7 STEP RESPONSE The step responses may be deduced from the Laplace transform of the linearised model equations. The transfer functions between the inputs and outputs are required, that is Y(s) = G(s)(/(«), where G(s) is £ x m matrix defined by G(s) = CO(s)x(0) + [C

PhD Chapter 2 Page 21 Frequency Regulation from Thermal Plant Improved Generation Dispatch in Power Systems

The inverse of this is given by, ^22 Wg(t) = [(^1 ld22 + y expfa^f) - (A^d22 - b4) exp( - b 4t) l a11 + £>4 which may be rewritten as wg{t) = A2 exp(a110 + A3 exp( - b 4t), where

^2 = ~ T~fT~ (^1/^22 + an)> a11 i d4 and

* 3 = = a, ,+<>„ (Ai l d 22- b t) .

This approximation is compared with the step response obtained using the full non-linear model in Figure 6 on page 23. The output power transient will have a maximum or minimum at time ^4^3 U = In seconds, a 11 + ^4 Si -j A2 provided that |b4| > lanl. The maximum of the step response is therefore

wg(^l) = ^2 exP(a11^l) + ^3 exp( - V i ) MW.

The governor gain will be given by

Gain = wg(t^ s e c h 2(P(j>) ~ ^f MW/Hz.

The change in stored energy is given by the area under the transient and can be calculated as follows:- J'oo poo ^ wg(t)dt = (A2 exp(a 1 >,0 + ^3 exP( - b 4t))dt = — . . 0 J0 “ a 11°4

And the stored energy per hertz is therefore —A* o inn S.E. = ---- apsech2((l) ~ ~ ~ MWs/Hz. a ^/34 D x iq

This approximation is not as accurate as the one for the gain ( Figure 6 on page 23 ) but the actual stored energy that would be obtained will be greater, and hence the error is an underestimate and on the safe side.

2.8 GAIN AND ENERGY CALCULATIONS

Governor gain and stored energy are required as functions of operating pressure and output power. The operating point variables, the effective aperture and drum pressure must then be calculated so that the linearization can be performed. These are calculated using the formu­ lae;

WrV¥9 A = BPs

Pd = Ps 1 where /q = kSnk}v.

PhD Chapter 2 Page 22 Frequency Regulation from Thermal Plant Improved Generation Dispatch in Power Systems

0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME ( SECONDS )

Figure 6. Step Response of Linear and Non-Linear Model: Linear Model accurately predicts the peak but not the area under the transient.

The governor gain and stored energy were calculated from 20 to 100% MCR and pressures from 70 to 1102of full pressure and the results are illustrated in Figure 7 on page 24, Figure 8 on page 24, Figure 9 on page 25 and Figure 10 on page 25. Gain and energy func­ tions show the same general dependence on output power and pressure; they decrease with increasing output power for given pressure and increase with pressure for given output power. The energy functions are however, less amenable to linear approximation.

These curves can be summarised in Figure 11 on page 26 and Figure 12 on page 26 where contours of constant gain and energy are plotted on the unit's state diagram, where the axes are output power and pressure and form the basis of the feasible region for the enhanced dispatch algorithm discussed in Chapter Five. A linearized relationship between gain, power and pressure is derived in Appendix C.

2.9 CONCLUSIONS

This chapter has examined the ability of a power plant to provide primary reserve as a func­ tion of its operating point. It was seen that more reserve was available at lower power outputs and with higher pressures. The intention in obtaining these relationships was to incorporate them into an enhanced dispatch algorithm which will allocate the required reserve econom­ ically. The costs associated with reserve provision must now be investigated thereby yielding an objective for minimisation and this is the subject of the next chapter.

PhD Chapter 2 Page 23 Frequency Regulation from Thermal Plant Improved Generation Dispatch in Power Systems

Figure 7. Governor Gain vs Power: Gain decreases with Power for given Pressure.

Figure 8. Stored Energy vs Power: Energy decreases with Power for given Pressure.

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Figure 9. Governor Gain vs Pressure: Gain increases with Pressure for given Power.

Figure 10. Stored Energy vs Pressure: Energy increases with Pressure for given Power.

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Figure 11. Contours of Constant Gain: Governor Gain plotted on the Unit State space

Figure 12. Contours of Constant Stored Energy: Stored Energy plotted on the Unit State space

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3.0 CHAPTER THREE - ACTIVE POWER RESERVE PROVISION COSTS

3.1 INTRODUCTION

The choice of operating pressure is of paramount importance to the regulation of grid fre­ quency. The regulating ability available from a generating set with given set points for active power and operating pressure was quantified using simple modelling in Chapter Two. It is envisaged that with a knowledge of such a relationship the dispatch algorithm could instruct the generating sets' operating pressure set points to ensure a certain primary frequency regulating ability. To allocate the required regulation economically among the generating units it is necessary to investigate and quantify the revenue costs associated with various operating points. The sensitivity of costs to active power is encapsulated in the well-known Willans line, ( Fenton, 1966 ), and is regularly determined by heat rate tests. However, the efficiency sensitivity with respect to operating pressure is not known and must be determined. This Chapter investigates, from first principles the efficiency sensitivity at various operating points using plant modelling and tests. A simple turbine model is presented where possible loss mechanisms can be examined and a series of tests carried out on operational power plant is described. With a knowledge of this sensitivity the costs of providing the required regulating reserve can be deduced and allocated in the most economic way.

3.2 MODERN POWER STATION PLANT

The production of electrical energy in modern power station plant is a very complex process and is depicted in Figure 13 on page 28. Chemical energy of fuel is released in a carefully controlled combustion within a furnace. The flame transfers its heat to the furnace walls which are composed of metal tubes containing water. This water evaporates to produce saturated steam to which further heat is added rendering it in a superheated condition. This steam is allowed to expand in a turbine to produce mechanical work by rotating a shaft loaded by an electric generator. The steam leaving the turbine is then condensed and returned to the boiler.

PhD Chapter 3 Page 27 Reserve Provision Costs Air Superheated □ ■ steam 1 Gas Cold Circulating 1 1 m m m □ m reheat steam - water Fuel oil delivery Condensate and Hot Coal and Fuel oil bulk storage tank L.P. feedwater □ reheat steam H pulverised fuel H.P. feedwater □ L.P. steam ■ Fuel oil FIG 13 Typical large generating system layout Improved Generation Dispatch in Power Systems

Modern power station plant can be divided into two major sections; the boiler which produces steam and the turbine which uses the steam to produce useful work.

3.2.1 TURBINE PLANT

The essential purpose of a turbine is to obtain useful work from a gas supply which drops in pressure and in temperature. In its simplest form a turbine consists of two rows of blades, a set of fixed blades ( nozzles ) and a set of moving blades ( buckets ). The fixed blades are attached to the stationary part called the stator or casing and the moving blades are attached to the rotating element or rotor. When the gas stream passes through the fixed blades it ex­ periences an increase in kinetic energy resulting from a drop in pressure. It then impinges on the moving blades where it suffers a change in direction and hence in momentum thus imparting a force on the moving blades. If the force on the moving blades is the result of the impact of the gas stream alone then the turbine is termed an Impulse Turbine. If, however, the gas is also allowed to expand while flowing through the moving blades the resultant force on the blades is that due to impulse and reaction. Turbines are classed with reference to the proportion of these two effects. A turbine in which half the tangential force on the moving blades arises from impulse and half from reaction is termed a 50% Impulse-Reaction Turbine. However, a turbine of this type is more commonly refered to as a Reaction Turbine or a Parsons Turbine after the inventor. If all the available energy from the gas supply were to be extracted by a single set of fixed and moving blades the rotor speed would be very high. For gas at high pressure and temperature these speeds can be unacceptably high and it becomes very difficult, mechanically, to support the shaft. In such cases, it is arranged that the available energy be extracted in several steps and so reducing the rotor speed. This process is known as compounding and involves ar­ ranging several sets of fixed and moving blades, called a stages, in series on the same shaft. A collection of fixed and moving blades is known as a turbine cylinder. Turbines used in electric power production invariably use steam at high pressure and tem­ perature as the working fluid which expands to the lowest possible pressure extracting the maximum amount of work. The steam is then condensed in a heat exchanger and returned to the boiler to complete the cycle. Steam flow in such turbines is parallel to the axis of ro­ tation and thus they are termed Axial flow Condensing Steam Turbines The superheated steam from the boiler, known as live steam, passes into the turbine through the steam chest. The steam chest houses the ( emergency ) stop valves and the control (governor) valves. These valves control the start up and shut down of the set and the steam flow. The available energy in the steam is usually extracted in several turbine cylinders. Live steam direct from the boiler is allowed to expand in a High Pressure ( HP ) Cylinder consisting of a purely impulsive stage and followed by several 50% Impulse-Reaction stages, as shown in Figure 14 on page 30 The resulting exhaust steam is returned to the boiler where it is re­ heated to the original temperature to expand further in the Intermediate Pressure ( IP ) Cyl­ inder and Low Pressure ( LP ) Cylinders. The steam leaving the HP cylinder is known as cold reheat steam and that returning to the IP cylinder hot reheat steam. Turbine cycle efficiency is broadly defined by the ratio of the electric energy output to the heat input. The inverse of efficiency is defined as Heat Rate and is a measure of how many units of energy are required to produce one unit of electrical energy.

3.2.2 BOILER PLANT

Steam is generated in the boiler at high pressure and temperature. The temperature of the incoming water is raised at constant pressure to saturation temperature in the economiser and evaporator. Steam and water are then separated and the steam undergoes further heating in the superheaters under constant pressure. The chemical energy in the fuel released during combustion is extracted in the various heat exchangers. The remaining flue gases, which carry away the waste products of combustion,

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IMPULSE STAGE REACTION STAGES

Figure 14. HP Rotor of a 270 MWe Alsthom Turbine ( Courtesy of ESB-IRL ): An Impulse stage followed by twelve 50% Impulse-Reaction Stages. leave the boiler through the stack and are allowed to rise to great height and disperse over a large area. These gases rise by virtue of their heat which is therefore lost to the process. The steam is allowed to expand to the lowest possible pressure, set by the cooling water temperature, to extract the maximum amount of work. The exhaust, or back pressure for an LP cylinder is determined by conditions in the condenser and the theoretical ideal is vacuum. The exhaust steam is condensed and the condensate is returned to the boiler which is oper­ ating at high pressures. This is accomplished by the use of a pump known as the feed pump. This pump is either driven electrically or by means of bled steam and its power con­ sumption is proportional to the pressure difference as shown in Figure 21 on page 39. The condensate undergoes several stages of heating - feed heating - prior to entering the economiser where it is called feed water. Feed heaters use steam bled from the turbine cyl­ inders to raise the temperature of the condensate and are of two types, surface heaters and direct contact heaters. The control of steam temperature is effected by several methods including attemperation, gas recirculation and damper vanes. Attemperation involves spraying cooler water into steam flow to reduce temperatures at discrete points, usually in the superheater. Gas recirculation involves reducing radiant heat transfer in the furnace by increasing the volume of gas carrying a given heat. Damper vanes bias the flow of the burning gases between superheat and reheat sections. The efficiency of the boiler is a measure of its effectiveness in extracting the chemical energy in the fuel. This has two aspects namely ensuring that (a) all the fuel is burnt, and (b) the maximum amount of energy in the burning gases is extracted. The first aspect is attained by careful control of the fuel and air proportions in the furnace. Boiler designers must tailor the boiler to suit the cycle by providing suitably sized superheaters, reheaters, evaporating sections, economisers and air heaters and the pressure and temperature of steam produced will have very little effect on the cycle efficiency. Generally a large boiler will be more efficient than a small one and the efficiency increase in recent years is not due to increase in steam conditions but due to increased physical size and improvements in the art of boiler making.

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3.2.3 METHODS OF GOVERNING

The annular space prior to the nozzles - the nozzle box - is supplied with live steam from the steam chest via ( usually ) four separate pipes. The arrangement of the nozzle box, nozzles and blades in the LP turbine is illustrated in Figure 15 on page 31. The steam flow through each pipe is controlled by a governor valve.

MOVING BLADES (BUCKETS) BLADE SHROUD

NOZZLE BOX NOZZLES (FIXED BLADES)

Figure 15. LP Rotor of a 270 MWe Alsthom Turbine ( Courtesy of ESB-IRL ): The arrangement of the nozzle box and fixed and moving blades is clearly shown.

Two methods of varying the steam flow present themselves. If all the governor valves move simultaneously then the full steam flow is throttled to a lower pressure. This is known as throttle control governing or full-circle steam admission and is favoured by U.K. Manufactur­ ers such as GEC and NEI Parsons. Since no heat is either added to or removed from the steam and no work crosses the boundary, the process is isenthalpic. However, pressure, and in the case of a real fluid, temperature are changed resulting in an entropy increase. If the valves are allowed to move independently it can be arranged that only part of the steam flow is throttled. This method of governing is known as nozzle control governing and is favoured by manufacturers such as Brown Boveri and Alsthom. In this method, each governor valve provides steam to a specific group of nozzles only. There is no communication between the nozzle groups and the nozzle box is partitioned. The second method is more efficient at part load as the entropy increase due to throttling is reduced. However, it is less efficient at full load due to partial admission loss which arises from the presence of eddy currents at the nozzle box partitions. However, improvements in manufacturing technology are continually reducing this difference.

3.2.4 THE DESIGN POINT

The design of modern power station plant is a compromise between technical feasibility and capital cost. The designers have at their disposal many parameters which are variable and the dimensions of all plant items are chosen to be optimum at one point - the design point.

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The plant is most efficient at the design point and is intended by the manufacturer to be op­ erated at this condition. In the U.K. the turbines are designed to be most efficient at Maximum Continuous Rating (MCR). The resulting linear cost curves lead in a merit order loading of plant where the cheapest units are fully loaded and the most expensive ones placed at minimum load. In the U.S.A. the plant is designed to be most efficient at part load and the resulting convex cost curves cause the majority of plant to be loaded at part-load design point. When a manufacturer installs a turbine, a joint test known as acceptance test ( BS 752 ), is performed by the utility and the manufacturer to test the turbine at design conditions. The result obtained is taken to be the maximum efficiency possible and all further tests will show a degrading of efficiency due to wear and tear. Subsequent efficiency tests should be con­ ducted at design conditions so that an authentic comparison can be made. However, due to system and plant constraints it is not always possible to conduct the efficiency test at design conditions. Consequently, the manufacturers provides correction factors, or curves, to be applied to the heat rate results obtained at off-design conditions. Among these corrections is one for changes in heat rate with changes in live steam pressure. Great care must be exercised in applying these corrections and interpreting the results ob­ tained. The corrections are valid only at a given valve position ( CEGB, Site Test code 2 ) and therefore there is a corresponding correction to output power due to change in live steam pressure. For this reason, the heat rate correction factors are not suitable for evaluating the heat rate sensitivity with respect to operating pressure at constant power.

3.3 AERODYNAMICS AND THERMODYNAMICS

The concept of a control volume is widely used in the study of compressible fluid flow. It is a surface which is fixed in space through which fluid may flow, for example a turbine cylinder. The steady flow energy equation for a system as it passes from state 1 to state 2 through a control volume is given by ( Rogers, 1980 );

q — E = w (h2 — hj) + + g(z2 - zfi where h is the specific enthalpy, c the fluid velocity, z the height above some datum, Q is the rate of heat addition, E is the shaft work and w is the fluid flow. The total ( specific ) enthalpy is defined by hQ = h + c2/2 + gz, and is also known as stagnation or reservoir specific enthalpy ( Liepmann, 1957 ). The total enthalpy is defined as the enthalpy the fluid would have if it were brought to rest at the datum level adiabatically. In a similar manner, total temperature of a fluid, T0, is defined as the temperature the fluid would have if it were brought to rest adiabatically at the datum and total pressure, p 0 is defined as the pressure the fluid would have if it were brought to rest reversibly and adiabatically at the datum. If the fluid flow through the control volume is adiabatic ( Q = 0 ) then the energy equation re­ duces to E = wA h0, and hence, the shaft work is the product of the fluid flow and the change in total specific enthalpy. In the flow of a compressible fluid the Mach number, M, is defined as the ratio of the local speed to the speed of sound. The total and static pressures are related by the mach number as follows { Shapiro, 1953 ); KI(K~ 1) Po k - 1 P 2

PhD Chapter 3 Page 32 Reserve Provision Costs Improved Generation Dispatch in Power Systems where k is the ratio of specific heats.

3.3.1 MOLLIER CHART

The performance of a turbine or compressor is most often depicted on a chart, with enthapy and entropy as the vertical and horizontal axis respectively, known as the Mollier Chart. The throttling process on throttle governed machines is represented by a horizontal line, as shown in Figure 17 on page 34 for the turbine shown in Figure 16.

P01'^01 P02'^02

Figure 16. A Simple Turbine Stage/Cylinder: Live steam at total pressure p 01 is throttled to nozzle box total pressure P 02 and expanded to condenser total pressure p0s.

It follows from the second law of thermodynamics that the maximum work output would be obtained if a turbine stage operated isentropically ( Horlock, 1966 ) and this is used as a cri­ terion for perfection for a real turbine stage. Such a turbine stage would be represented by a vertical line on the mollier chart of Figure 17 on page 34. The flow through a real turbine stage is adiabatic since the heat loss is small compared to the work output. The total-to-total efficiency is defined as the ratio of the real enthalpy drop to the isentropic enthalpy drop.

^02 ~ ^05

The value of the total-to-total efficiency for a very small increment of pressure is known as the polytropic efficiency or small stage efficiency. As was mentioned previously, the available pressure drop is utilised over several stages within a single cylinder. The properties of steam are such that the lines of constant pressure diverge with increasing entropy. Consequently, the overall cylinder total-to-total efficiency will be greater than the stage efficiency assuming the polytropic efficiency remains constant. This is known as the reheat factor. It follows that there are two motivations behind extracting the available energy from the steam in several stages; to reduce the rotor speed, and to extract the available enthalpy drop more efficiently.

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1 SPECIFIC ENTROPY(kJ/kg K)

Figure 17. Mollier Chart for turbine cylinder/stage: Isentropic expansion is represented by a vertical line; adiabatic expansion increases entropy.

3.3.2 TEMPERATURE ENTROPY DIAGRAM

In a similar way as a turbine's performance is best illustrated on a Mollier chart, a boiler's operating conditions are best illustrated on a chart with temperature and entropy as the ver­ tical and horizontal axis respectively. This diagram is shown in Figure 18 on page 35 where the line ABCD represents a contour of constant pressure corresponding to the boiler pressure. The area beneath AB is the sensible heat component, that below BC the latent heat addition and below CD the superheat addition, per unit flow rate. The area below EA represents the heat rejected in the condenser per unit flow rate. The thermal efficiency of the turbine plant is the ratio of the area ABCDEA to ABCDEFGA. The shape of this diagram is altered with pressure resulting in a change in the relative magnitudes of the areas.

3.4 SINGLE CYLINDER TURBINE MODEL

Live steam from the boiler at a total pressure p0i and total temperature T0i is throttled to first-stage nozzle box total pressure p 02 and total temperature T 02 isenthalpically by the gov­ ernor valves. It then expands in the nozzles with a resultant increase in velocity and impinges on the moving blades performing useful work. The cylinder exhausts to a total pressure p05 determined by the condenser. The relationship between the mass flow coefficient, defined by

where w is the steam flow, p 2 is the nozzle box static pressure and v2 is the specific volume, and the static pressure ratio, r, is given by;-

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CONTOUR OF CONSTANT

IDEAL ISENTROPIC EXPANSION

SPECIFIC ENTROPY (kJ/kgK)

Figure 18. Temperature Entropy Diagram: Heat added per unit flow rate is represented by the area under the curve.

= where r = p 5/p2, and k0)k2 are constants. This is known as the ellipse law and was first estab­ lished ( Stodola, 1927 ) early this century for an eight stage 50% Impulse-Reaction cylinder in a laboratory. The exponent, k2, was quoted as 2 giving an ellipse with semi-major axis of unity and semi-minor axis of kt>~ It is derived in Horlock { 1966 ) for an idealised multi-stage 50% Impulse-Reaction cylinder with the exponent f<2 = 2 - >7p(k - 1)/*. where t]p is the polytropic efficiency and k is the ratio of specific heats. Assuming superheated steam behaves as a perfect gas { obeying pv = RT ) and the Mach numbers at turbine inlet and exit are equal ( then the static pressure ratio equals the total pressure ratio ) the ellipse law may be written as :-

k \ 1/2 1 ~ (p osI p ) 2 \ w = ki p02 02 7 q2 ) ’ where k-i — /£/?_1/z. The difference in total enthalpy at two states is given by ( Kearton, 1966 ):

Afy)= z y P02 ~ r 3)’ where k3 = t]p(k — 1 )jk. If steam behaves as a perfect gas then this may be rewritten as

A/70 = k4 T02{ 1 — (P05/P02) 3)- The power output from the turbine, by the steady flow energy equation, is the product of steam flow and the change in total enthalpy, E = k5w Ah0,

PhD Chapter 3 Page 35 Reserve Provision Costs Improved Generation Dispatch in Power Systems where k5 is a scaling factor. The turbine cylinder is exhausting to a total pressure p 05 and condensing to water iso-thermally. The heat rejected to the condenser in this process is the difference between total steam enthalpy, h 05 , and condensate enthalpy, h0c, at total pressure

P 0 5,

fy)c = (P 05, x — 0 )> where x is the dryness fraction. The heat rejected is therefore; L = w (h05 - h0c). The turbine cycle efficiency, y\c, is then defined as Power Output Power Output 4- Heat Rejected E E + L The exported power is the generated power less that quantity needed to power the unit's auxiliaries. The boiler feed pump must pump water from the condenser pressure, typically 0.007 MPa ( 7.0 kPa ) to boiler pressure, typically 16 MPa. The feed pump power requirement is proportional to the pressure difference and if the pump is electrically driven the sent out power is less by this amount. Ideal pumping is isentropic and the pump power required to pump water from an inlet pres­ sure, poi, to an outlet pressure, p0o is obtained by

Epp = w {] h0o(p0o, Sqi ) — h§j (p0/, Sc>/)]/*7pUmp. The overall efficiency of the turbine cycle is therefore ( neglecting alternator efficiency ),

‘-soF

where E„ = E — EFp. The heat rate is the inverse of this quantity

The overall efficiency of the power plant is the product of the turbine cycle efficiency, r\Tt and the boiler efficiency, r\B , representing the combustion efficiency and the the stack losses. The boiler efficiency is assumed constant off-design and will not be considered in the following analysis. The steady state sensitivity of overall turbine cycle efficiency with the dispatcher's require­ ment for active power, E, and the unit operator's choice of pressure, p 01 is required. This sensitivity will be investigated by assuming 1. Condenser pressure remains constant over turbine load and steam flow. 2. Live steam temperature and pressure can be set by the operator. 3. Turbine power output can be set. For a given dispatched power output, the live steam pressure is bounded by the sliding pres­ sure for that load and the safety valves' settings. The above equations may be solved for Po2 and Toe given the values of E, p 01, 7 0i, p05, and the fact that throttling is isenthalpic ( /?oi = hm). Having determined the nozzle box total pressure and temperature the steam flow, enthalpy drop, cycle efficiency and heat rate may then be calculated.

3.4.1 OFF-DESIGN OPERATION

A decrease in turbine load may be effected by two methods. The live steam pressure can be maintained constant and the steam throttled, or the live steam pressure reduced while main­ taining a constant governor valve position. This section examines the heat rate variability as

PhD Chapter 3 Page 36 Reserve Provision Costs Improved Generation Dispatch In Power Systems predicted by the above model under the stated assumptions with data items quoted in Table 3 on page 37.

Data Items Symbol Value and Unit Ratio of Specific Heats for Steam k 1.3 Design Live Steam Total Temperature T01 814 K ( 541° C ) Design Live Steam Total Pressure P01 16.0 MPa Design Power Output EfACR 626 MW Maximum Boiler Total Pressure P Omax 18.0 MPa Design Condenser Total Pressure P05 7.0 kPa Feed Pump Efficiency ffpump 100 % Ellipse Law Constant Ai 1.052776x103 ms/T1/2 Enthalpy Equation Constant k< 1.55555 kJ/kJ K Output Power Conversion Factor k$ 1.00712x10-3

Table 3. Data and Design Values for Single Cylinder Turbine: The Design Output Power is that value which is generated when the governor valves are fully open with design stop valve conditions. The operation of the turbine for two load set points, design and 50% of design, will be com­ pared. In each case, the pressure set point will be varied from maximum, as determined by boiler safety valves, and the sliding pressure of the load. The Mollier chart for a turbine op­ erating at design load with maximum and design pressures is shown in Figure 19 on page 38, and that for 50% load with three pressure set points is shown in Figure 20 on page 39. At design load, it is seen that the turbine heat rate increases with increasing pressure. If the pressure is increased to the maximum the resulting throttling brings about a decrease in nozzle box total temperature and an increase in nozzle box total pressure. The net effect is to increase the steam flow bringing about an increase in heat rejected to the condenser as compared with the design point. The final point of the expansion contains steam at a lower quality { wetter) meaning the turbine has converted a higher proportion of the latent heat into work and the heat rejected to the condenser per unit flow rate is reduced. Nevertheless, the total heat rejected is increased due to the higher flow rate. At 50% of design load the sliding pressure option is again the most efficient. Any increase in pressure above sliding results in an increase in condenser losses brought about by an in­ crease in steam flow due to decreased nozzle box temperature. This increase in heat rate is exacerbated by the increased power consumption of the feed pump with pressure as shown in Figure 21 on page 39.

3.4.2 VARIATION IN TOTAL-TO-TOTAL EFFICIENCY

Implicit in the above model is the assumption that the polytropic efficiency, >/p, is constant. The ratio of the cylinder total enthalpy drop to the enthalpy drop that would be obtained in an isentropic expansion is the total-to-total cylinder efficiency. Shown in Figure 22 on page 38 is the variation in total-to-total efficiency with load when design pressure is maintained and is seen to be negligible.

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SPECIFIC ENTROPY!kJ/kgK)

Figure 19. Mollier Chart for a turbine loaded to design value: Two Pressure set points shown; maximum boiler pressure, design pressure ( sliding pressure is equal to design in this case ).

Figure 22. Total-to-Total efficiency as a function of turbine load: Live steam Pressure maintained at design. _____

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Figure 21. Feed pump power requirement as a function of pressure at 50% Load: This assumes constant pump efficiency off-design.

0 5

> Q_ -1 < I b- z iu O LL O UJ

< h o

SPECIFIC ENTROPY(kJ/kg K)

Figure 20. Mollier Chart for a turbine loaded to 50% of design value: Three Pressure set points shown are; maximum boiler pressure, design pressure and sliding pressure.

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3.4.3 HEAT RATE SENSITIVITY

The optimisation of frequency regulating ability over the power system requires a knowledge of the costs associated with various output power and operating pressure set points. More­ over, if the optimisation algorithm employs linear programming the relationship must be linearized. The above model may be use to derive the heat rate at a collection of power output and op­ erating pressure pairs and deduce the coefficients a, /?, and y in the relationship;

HR = a4- pE + yPoi> where a is the no-load cost, /? the conventional Table B cost and y a new cost hereafter refered to as the Table C cost. These costs may be estimated with minimum variance by linear re­ gression if heat rate results are obtained at the extremes of the practical range (Draper, 1981). For this reason a heat rate result was obtained at nine equally spaced load points from 100% to 20% MCR at the following pressures; (a) the sliding pressure (b) the maximum pressure (c) the design value, and (d) at intermediate pressures given by;

_ (Pomax ~ Ppslide) ' Pointer ~ Poslide + n ’ where / = 1,... ,n — 1. Figure 23 on page 41 shows the points that would be chosen for a value of n = 2 and equally spaced load points from 100% to 40% MCR. The results are scaled with design values as the base and reported in Table 4 on page 41. Linear regression uses the observations of the variable HR ( in this case 9 (n 4- 2) ) to minimize the the sum of squares of the residuals, i.e. to minimize

9(n+2)

s - £ (HR-Z-fe-yp01)2. /= 1 by choice of the variables a, /? and y. This sum of squares can be partitioned into two parts known as Model Sum of Squares and Total Sum of Squares as follows Total SS = Model SS + Residual SS

9(n+2) 9(n+2) 9(n+2)

(HR-HR)2= Yj (H R - H R )2 + Y j (H R -H R )2- i= 1 /'= 1 /=1 The Total SS is always the same for a given set of data but the partitioning into Model SS and and Residual SS depends on the model - the Residual SS of a perfect model would be zero. The mean square due to regression is the Model SS divided by the number of degrees of freedom associated with it ( in this case two as there are two independent variables ) defined as follows: Model SS MSreg ~ 2 The error mean square is the Residual SS divided by the number of degrees of freedom as­ sociated with it ( in this case 9(n + 2) - 2 - 1 ) defined as 2 _ Residual SS “ 9(n + 2) - 2 - 1 ' The ratio of these two sum of squares, MSreg F = s2 is an F statistic with (2,9(n + 2) - 2 - 1) degrees of freedom which can be used to test the significance of the overall regression. This is accomplished by testing the hypothesis that the parameters (/?, y) are zero by comparing the fit of the complete model to that using only the

PhD Chapter 3 Page 40 Reserve Provision Costs Improved Generation Dispatch in Power Systems

Figure 23. Points selected to conduct heat rate test on pressure-power plane: At the maximum, design, sliding and at an intermediate pressure. mean of the heat rate results. The null hypothesis - the one that will be accepted in absence of evidence to the contrary - is H0:p = y = 0, which will be tested against the alternative that at least one of the parameters is non-zero Hj .p 4- y =£ 0.

ANALYSIS OF VARIANCE Source Degrees of Sum of Mean Square F Value Significance Freedom Squares Model SS 2 2.44x10-1 /WS,eg = 1.22x10 1 1152.62 0.0001 Residual SS 105 1.11x10-2 s2= 1.06x10 4 Total SS 107 2.55x10-1 PARAMETER ESTIMATES Variable Estimate Standard t Significance 95% Standardised Error Confidence Estimates Interval a 1.13 4.19X10-3 270.662 0.0001 ± 8.30x10 3 0.0

P -2.05X10-3 4.56x10-5 -45.061 0.0001 ± 9.02x10-3 -1.090 y 5.70x10-“ 5.50x10-3 10.371 0.0001 ± 1.09x10-“ 0.251

Table 4. Regression Analysis Results for Single Cylinder Turbine: The Confidence Intervals are constructed by obtaining f0n9-sided(105,0.975) = 1.980 from tables. The observed value of F can be compared to tabulated values of F(2,9(n -f 2) — 2 — 1) to see if the null hypothesis can be rejected on the basis of the data. From Table 4 it can be seen

PhD Chapter 3 Page 41 Reserve Provision Costs Improved Generation Dispatch in Power Systems that the null hypothesis can be rejected at the 0.0001 significance level i.e. it is very un­ likely that there is no variation of heat rate attributable to changes in output power or oper­ ating pressure. The estimates of the parameters show that an improved ( lower ) heat rate results from an A increase in output power i.e. the heat rate decreases by /? if output power increases by one percentage point. Similarly, the heat rate disimproves by y if the live steam pressure is in­ creased by one percentage point ( Note all quantities are scaled with design values as the base ). The standard errors on the estimates of a, (1 and y are also quoted in Table 4 on page 41 which can be used to construct 100(1 - a) % confidence interval for the parameters as follows; Parameter + f(9(n + 2) — 2 — 1,1 — a/2)Standard Error, where t(9(n -f 2) — 2 — 1,1 — a/2) is the 100(1 — a/2) percentage point of a one sided t distrib­ ution with 9(n + 2) — 2 — 1 degrees of freedom. The null hypothesis that the true value of any parameter is zero may be tested against the alternative that it is non zero by comparing the fit obtained with a model containing the parameter and a reduced model without. This is ac­ complished by evaluating the t statistic j ____ Parameter ^/Standard Error which has 9(n 4- 2) — 2 — 1 degrees of freedom. In particular, the null hypothesis that there is no variation in heat rate due to a change pressure which is not due to a change in output power can be rejected with a 0.0001 significance. The standardised coefficients provide a comparison of the magnitude of the effects of the variables. Each coefficient indicates the number of standard deviation changes in the Heat rate associated with a standard deviation change in output power and pressure with the other one held constant. These coefficients show that heat rate has a higher sensitivity to output power than to operating pressure.

3.5 TURBINE MODEL INCORPORATING REHEAT

Modern power station plant usually employs reheat where the live steam is allowed to expand in the HP cylinder to some pressure intermediate between the boiler and the condenser. It is then returned to the boiler and reheated at constant pressure to the original temperature and allowed to expand further in IP and LP cylinders. The above model, although not repre­ sentative, is a very important first step in understanding the mechanisms by which losses may occur. The above model can easily be extended to include reheat. The HP cylinder expands live steam to a total pressure p03 and total temperature T03 which is returned to the boiler for re­ heating. The steam is reheated to a total temperature T04 which is, usually, equal to the live steam temperature. This hot reheat steam is then allowed to expand to condenser pressure in IP and LP turbine cylinders which will be lumped together for simplicity. The Mollier diagram for a reheat set is shown in Figure 24 on page 43 where reheating is accomplished at constant pressure. The steam flow through the HP turbine is obtained by the ellipse law: 1/2 1 ~ (.P03IPp2)^2HP whp — hp P02 Tq2

and that through the IP/LP turbines 1/2 1 ~ (Po5/Pp4)^2fP wlp ~ k/\ lp Po4! 7"o4

PhD Chapter 3 Page 42 Reserve Provision Costs Improved Generation Dispatch in Power Systems

which will be equal in the steady state. The corresponding enthalpy drops are given by

= ^4hp ^"02 0 ~ (P03/P02) 3HP)- and

AhoLP = ^4LP 7*04 0 ~ (P 05lP 04)k3LP)- The power output from the cylinders is product of the steam flow and the total enthalpy drop:

ehp = k5HpwHPAh oHP, and

^lp _ k5LpwLP&h0LP- The tola I power generated is the sum of the power developed in the HP, IP and LP cylinders;

E = ehp + e lp- The exported power is the generated power less the auxiliary power

Eso E EFP- A similar heat rate analysis was performed using this model with a value of n = 10 and using the data items quoted in Table 5 on page 44. The results, scaled on design value bases, are reported in Table 6 on page 44 where it is seen that an increase in output power reduces the heat rate and an increase in operating pressure increases it, as in the single cylinder case. The null hypothesis that there is no heat rate variation attributable to a change in pressure which is not accounted for by output power change can be rejected with a significance of 0.0001. The standardised estimates indicate that the sensitivity of heat rate with respect to output power and operating pressure has been reduced in comparison with the single cylinder mo­ del. This is due to the fact that the steam flow through the turbine changes very little with a

PhD Chapter 3 Page 43 Reserve Provision Costs Improved Generation Dispatch in Power Systems change in live steam pressure. This is a direct consequence of the fact that the hot reheat temperature is controlled to a constant value and the IP/LP pressure ratio is approximately zero. The ellipse law would predict a very small change in flow for a cylinder operating with these inlet conditions. Since the HP turbine flow is equal to the IP/LP turbine flow, in the steady state, it also changes very little. In order to maintain the HP steam flow near constant at live steam pressures above sliding the cold reheat pressure must increase thereby reduc­ ing the HP pressure ratio to offset the decrease in nozzle box temperature.

Data Items Symbol Value and Unit

Ratio of Specific Heats for Steam k 1.3

Design Live Steam Total Temperature T o i 814 K ( 541° C) Design Live Steam Total Pressure Pot 16.0 MPa

Design Power Output £ m c r 660 MW

Maximum Boiler Total Pressure P Omax 18.0 MPa

Design Condenser Total Pressure P05 7.0 kPa

Feed Pump Efficiency ^7pump 100 %

Ellipse Law Constant ( HP cylinder) k :H P 1.052776x103 ms/T1/z

Enthalpy Equation Constant ( HP Cylinder) k w p 1.55555 kJ/kJ K

Output Power Conversion Factor ( HP Cyl­ k$HP 1.00712X10-3 inder )

Ellipse Law Constant ( IP cylinder) k u p 3.817825X103 ms/T1'2

Enthalpy Equation Constant ( IP Cylinder) k iL P 1.76707 kJ/kJ K

Output Power Conversion Factor ( IP Cylin­ k$LP 7.52955x10-4 der )

Table 5. Data and Design Values for Reheat Turbine: The Design Output Power is that value which is generated when the governor valves are fully open with design stop valve conditions. This is illustrated in Figure 25 on page 45 where the live steam pressure is varied from design to maximum at design turbine load and Figure 26 on page 45 where the pressure is varied from sliding to design and maximum at 50% of design turbine load.

ANALYSIS OF VARIANCE Source Degrees of Sum of Mean Square F Value Significance Freedom Squares Model SS 2 1.60x103 MSreg = 8.01X102 701.162 0.0001 Residual SS 105 1.20x102 s2 = 1.14 Total SS 107 1.72x103 PARAMETER ESTIMATES Variable Estimate Standard t Significance 95% Standardised Error Confidence Estimates Interval a 1.12x102 4.36x10-1 255.843 0.0001 ± 8.63x10~1 0.0

P -1.62x10-1 4.73x10-3 -34.344 0.0001 ± 9.37x10-3 -1.051 y 3.42x10-2 5.72x10-3 5.974 0.0001 ± 1.13x10-2 0.182

Table 6. Regression Analysis Results Generating Set with Reheat: The Confidence Intervals are constructed by obtaining f 0ne-Sided(1 05,0.975) = 1.980 from tables.

The analysis above was repeated using the same model but excluding the effects of the feed pump. The results are reported in Table 7 on page 46 where it is seen from the standardised

PhD Chapter 3 Page 44 Reserve Provision Costs Improved Generation Dispatch in Power Systems

Figure 25. Mollier Chart for a Reheat Turbine Loaded to Design Value: Two Pressure set points are shown; maximum pressure and design.

Figure 26. Mollier Chart for a Reheat Turbine at 50% of Design Load: Three Pressure set points are shown; design, maximum and sliding.

PhD Chapter 3 Page 45 Reserve Provision Costs Improved Generation Dispatch in Power Systems estimate that the effect on heat rate of output power and operating pressure has been reduced but is still statistically significant.

ANALYSIS OF VARIANCE Source Degrees of Sum of Mean Square F Value Significance Freedom Squares Model SS 2 1.64x102 MSreg = 8.20x102 725.910 0.0001 Residual SS 105 1.19x102 s2 = 1.13 Total SS 107 1.76X103 PARAMETER ESTIMATES WITHOUT FEED PUMP Variable Estimate Standard t Significance 95% Standardised Error Confidence Estimates Interval a 1.12x102 4.34x10-1 259.371 0.0001 ± 9.59x10-1 0.0

P —1.62x10-1 4.71x10-3 -34.344 0.0001 + 9.32x10-2 -1.025 y 2.88x10~2 5.69x10-3 4.009 0.0001 ± 1.13X10-2 0.121

Table 7. Regression Analysis Results Generating Set with Reheat without Feed Pump: The Confidence Intervals are constructed by obtaining f one-sided(1 05,0.975) = 1.980 from tables.

3.6 EXPERIMENTAL VERIFICATION

A series of tests to confirm the above analysis were implemented at Grain Power Station on the Thames Estuary in England ( McNamara et al, 1989b ) and at Poolbeg Power Station in Dublin ( Canning, 1989 ). These tests were carried out under the auspices of CIGRE Study Committee 39 - Power System Operation and Control - Working Group 4 - Power Plant Control (SC39-04) whose interest was in quantifying the variability in key plant parameters to assess the feasibility of performing on-line monitoring.

3.6.1 GRAIN POWER STATION

Grain Power Station is a 660 MWe oil-fired station with a throttle governed reheat turbine. A Boiler follows Turbine control scheme is used where output power is controlled by a load controller which adjusts the governor valve position and operating pressure is controlled by adjusting the firing rate. Control of live steam temperature is effected by attemperation and reheat temperature by gas recirculation. The objectives of the test were to obtain periods of steady running at load points from 100% to 50% MCR at pressures corresponding to a value of n = 2, namely at sliding pressure, at maximum pressure and at a pressure mid-way between. The live steam temperature is to be held constant at design value. Having obtained the steady state, as indicated by near-constant values of output power and operating pressure, heat rate of the unit can be estimated, under the assumption of homogeneous fuel, simply by taking the ratio of heat input to output power. The plant parameters shown in Table 8 on page 47 were recorded using the normal plant in­ strumentation and no special measurement devices were made available. The pressures, temperatures and powers were recorded to indicate the steady state, the system frequency and governor valve positions to observe any system influences and the extent of throttling and the oil flow to determine the heat rate. The parameters were logged every 15 seconds and stored on magnetic tape by a Solarton Orion Data Logger. The test specification required the plant to achieve a steady state at six load set points with three different pressure set points at each load. Since testing time was limited to one shift (eight hours) each steady state would be limited to not more that twenty minutes duration to allow for manoeuvres between load points and time for the plant to reach a new steady state. This time will be minimized if data from one load set point is collected first. There was no

PhD Chapter 3 Page 46 Reserve Provision Costs Improved Generation Dispatch in Power Systems facility, on this plant, to impose a deadband on the governor and consequently variation in grid frequency entering the plant through the governor valve disturbing the steady state is una­ voidable at pressures above sliding.

Plant Parameter Units Economiser Outlet Gas Temperature Deg C Burner Rail Oil Pressure MPa Reheat Final Steam Temperature Deg C Generated Output MW System Frequency Hz TGV Position (RH) % Live Steam Pressure MPa Live Steam Temperature Deg C Drum Pressure MPa Generated Output MW Oil Flow to Burners Kg/s TGV Position %

Table 8. Plant Parameters Recorded by Orion Data Logger: The data were recorded every 15 seconds. All load manoeuvres required a close liaison with the Grid Control Centre and were only ac­ complished when prevailing system conditions were favourable, in particular, with respect to load following and frequency regulation. Moreover, the tests could be abandoned at any time at the discretion of the Grid Control Centre to assist with an emergency situation. This oc­ curred several times throughout the day due to adverse weather conditions resulting in light­ ning induced transmission line outages. Given the above constraints the tests were carried out on May 24 1989 and are summarised in Figure 27 on page 48. The relevant steady states can be identified visually in Figure 27 on page 48 by observing periods in which the variation of output power and superheater pressure is very small. Alternatively, the data can be broken up into five minute periods, i.e. the mini­ mum acceptable duration of steady state, and each window examined for a steady state. This can be accomplished by a statistical test where the window is divided in two equal parts and the means compared. If the means are not significantly different, as judged by some criterion, then the hypothesis that they are the same may be accepted and the fact that the system is in steady state can be tentatively entertained. A t statistic to test the equality of means x: and x2 from two independent samples with m and n2 observations is

(*1 ~ *2) A/s 2(1/n1 + 1 ln2) where s2 is a pooled variance given by

2 _ {(flj — 1)s2 + (n2 — 1)sf} S (ni + n2 - 2) where s? and s| are the sample variances. The value of |f| thus obtained can be compared to tabulated values of f(r?i + n2 - 2) to see if the means are significantly different. If the cal­ culated value of Ul is less than or equal to the tabulated value of f(/?i 4- n2 — 2) then the (null) hypothesis that the means are the same can be accepted at the tabulated significance level. In other words, the difference in the means of the samples is not unexpected by chance. If, however, the calculated value of \t\ is greater than the tabulated value of f(n, 4- n2 — 2) then the difference in the means is unlikely to have arisen by chance and the null hypothesis must be rejected.

PhD Chapter 3 Page 47 Reserve Provision Costs Improved Generation Dispatch in Power Systems

< ° d U ) ddnssddd wtG_LS anil 00 [v tD

to E-* CO © H © E-< ru 10 ro - v

Sh CC ■V CK Q o <

CO

• ' ■ ' r-i-r iii' - (Vi_ 1 ' © © © © © © © *• © © © © © © CO N to in ro ru cnuj) ddnod indino

Figure 27. Grain Steady State Tests: Overlaid Plots of Output Power and Operating Pressure.

PhD Chapter 3 Page 48 Reserve Provision Costs Improved Generation Dispatch in Power Systems

In the case of this data a five minute window contains 21 observations in which observations 1 to 11 consist the first sample and observations 11 to 21 consist the second sample. The number of degrees of freedom on which the t test is based is therefore 20. A two-sided test was applied to the data at the 2% significance level for 20 degrees of freedom and the steady states determined in terms of equality of means of both output power and operating pressure. Having identified a two consecutive periods in which the means are the same the window is extended to check if the steady state continues. The steady state windows identified for analysis by the above method should be carefully checked by eye on overlaid plots of output power and pressure to see if indeed a steady state does exist. The above statistical test should not be considered omnipotent but as a 'filter' used to extract a subset of data for further consideration. The windows identified by the sta­ tistical test are shown Table 10 on page 50 and those accepted and rejected also indicated. Having identified valid windows a linear regression analysis is performed to obtain the pa­ rameters of the model

= a -f PE 4- yp 4- ST, and the results are quoted together with 95% confidence intervals. The temperature term is included in the above equation since perfect temperature control was not attained. The re­ sults are reported in Table 9 where it is seen from the estimates of the parameters a and /? that heat rate decreases with increased output power and increases with increased operating pressure. An on-line monitoring strategy could be envisaged using data sampled every 15 seconds from the existing plant instrumentation and the steady states determined by the t test outlined above. However, steady state windows should be of not less than thirty minutes duration to ensure all transients have quiesced.

ANALYSIS OF VARIANCE Source Degrees of Sum of Mean Square F Value Significance Freedom Squares Model SS 3 3.037 MSreg= 1.012 405.591 0.0001 Residual SS 360 0.899 s2 = 2.50x10-3 Total SS 363 3.936 PARAMETER ESTIMATES Variable Estimate Standard t Significance 95% Standardised Error Confidence Estimates Interval a -9.23 1.475 -6.254 0.0001 ±2.89 0.0

P —1.51x10-3 4.65x10-5 -32.411 0.0001 ±9.11x10-* -0.957 Y 2.92X10"4 1.92x10-4 1.521 0.1291 ± 3.76x10-4 0.042 S 2.38x10"2 2.77x10~3 8.610 0.0001 ± 5.42x10-3 0.241

Table 9. Regression Analysis Results For Grain Data: The Confidence Intervals are constructed by obtaining fOne-sided(360,0.975) = 1.960 from tables.

PhD Chapter 3 Page 49 Reserve Provision Costs Improved Generation Dispatch In Power Systems

Steady State Accepted Start Finish 09:02:35 09:07:35 N 09:21:37 09:26:37 N 09:26:37 09:31:37 N 09:36:37 09:56:37 Y 09:56:37 10:01:37 Y 10:09:07 10:14:07 N 10:21:37 10:26:07 N 10:24:07 10:29:07 N 10:29:07 10:34:07 N 10:46:37 10:51:37 N 11:01:37 11:06:37 N 11:14:07 11:19:07 N 11:41:37 11:46:37 Y 11:46:37 11:51:37 Y 12:14:07 12:19:07 Y 12:26:37 12:31:37 Y 12:34:07 12:39:07 Y 12:41:37 12:46:37 Y 12:54:07 12:59:07 Y 14:09:07 14:16:37 Y 14:46:37 14:51:37 Y 14:56:37 15:01:37 N 15:04:07 15:09:07 N 15:11:37 15:16:37 N 15:29:49 15:34:49 N 15:58:51 16:03:51 Y 16:38:51 16:43:51 N 17:21:21 17:26:21 N 17:33:51 17:38:51 N 17:38:51 17:43:51 N 17:46:21 17:51:21 Y 17:51:21 17:56:21 Y 18:41:21 18:46:21 N 18:46:21 18:51:21 N 18:58:51 19:03:51 N 19:23:51 19:28:21 N

Table 10. Steady States Identified by a t test on Grain Data: The test was conducted at the 2% Significance level.

PhD Chapter 3 Page 50 Reserve Provision Costs Improved Generation Dispatch in Power Systems

3.6.2 POOLBEG POWER STATION

In the course of routine heat rate testing at Poolbeg Power Station in Dublin the Electricity Supply Board ( ESB ) agreed to perform additional tests at off-design live steam conditions in an attempt to quantify these effects. This unit is a 120 MWe natural gas-fired set with a nozzle governed reheat turbine. Steam pressure is controlled by adjusting the firing and live steam temperature by spraying. Reheat temperature is controlled by damper vanes in the burning gas path. The plant was specially instrumented with carefully calibrated equipment giving a heat rate result with an accuracy of ±0.6% ( Canning, 1981 ). Prior to the tests the governor valves were locked in position thereby removing system frequency effects. A further thirty minutes was then allowed for the plant to reach a steady state. The tests were then conducted for a period of half an hour and the plant parameters logged every 20 seconds. The as run heats rate were then evaluated using the procedure outlined in CEGB Site Test Code 2 and corrected for off-design values of all major plant parameters, except operating pressure, using the manufacturers heat rate correction curves. The results will then reflect the difference in the heat rate that would be obtained if all plant parameters except operating pressure were held at design value. A similar linear regression analysis was performed on these results and is summarised in Table 11. This shows that a lower heat rates result from increasing output power and decreasing operating pressure. These results show that the null hypothesis that there is no variation of heat rate attributable to changes in operating pressure which has not been explained by changes in output power only be rejected at the 53% significance level suggesting that the heat rate does not vary significantly with pressure. This is due to the fact that operating pressure did not vary signif­ icantly from design remaining within ± 0.01 MPa except on one occasion when it was dropped by 12% from design. The 95% confidence interval constructed from this data will conse­ quently be very large. The sensitivity of overall turbine cycle efficiency with respect to operating pressure will be increased due to increased feed pump power requirements.

ANALYSIS OF VARIANCE Source Degrees of Sum of Mean Square F Value Significance Freedom Squares Model SS 2 2.12x10-2 MSreg = 1.06x10 2 43.778 0.0001 Residual SS 11 2.66x10-3 2.42x10 4 Total SS 13 2.38x10-2 PARAMETER ESTIMATES Variable Estimate Standard t Significance 95% Standardised Error Confidence Estimates Interval a 2.37 1.43x10-1 16.642 0.0001 ± 3.14x10-1 0.0 P -1.81x10-3 2.06x10-4 -8.808 0.0001 ± 4.53x10 4 -9.22x10-1 y 7.27x10-3 1.12x10 2 0.651 0.5282 ± 2.45x10 2 6.82x10-2

Table 11. Regression Analysis Results from Poolbeg Data: The Confidence Intervals are constructed by obtaining f0n«-«id»d(11,0.975) = 2.201 from tables.

3.7 DISCUSSION OF RESULTS

Shown in Figure 28 on page 53 is a plot of the standardized estimates of the heat rate sensi­ tivity with respect to operating pressure, y, for the modelling with and without feed pump and the experimental results for Grain and Poolbeg. The Poolbeg results show consistency with the corresponding modelling i.e. with reheat. However, the Grain results and the corre­

PhD Chapter 3 Page 51 Reserve Provision Costs Improved Generation Dispatch In Power Systems sponding modelling do not overlap but show the same order of magnitude. The model used was very simple with far reaching simplifications and some of those which would bring the results into closer agreement will be considered.

3.7.1 ATTEMPERATORS

Control of live steam pressure is effected by spraying cooler water into the live steam flow thereby reducing the temperature of the mixture. Spraying has a detrimental effect on heat rate and is undesirable from a thermodynamic point of view. As the pressure increases the amount of spray water required is reduced thereby decreasing the heat rate in accordance with the heat rate formula in Site Test Code 2 ( CEGB, 1978 ) and can be easily seen on a T-S diagram. Moreover, spray water bypasses the economisers and HP feed heaters reducing the economiser heat pickup and increasing stack losses. The very simple model does not incor­ porate this effect which would decrease the coefficient y and bring the model and theory into closer agreement.

3.7.2 CONDENSER MODEL

The model assumes that the condenser pressure is constant over all loads and steam flows. In practice this is not true and depends on the cooling water inlet temperature, the heat transfer coefficient between the steam and the tubes and the heating load. As the turbine load is decreased the condenser vacuum usually improves. This would result in increased en­ thalpy drop and steam flow in the turbine cylinder ultimately leading to an increase in turbine load and lower heat rate. To maintain the turbine load at the desired value the sliding pres­ sure would be reduced moving the expansion further to the right on the Mollier chart. As was seen earlier, the heat rate is less sensitive when the expansion begins at higher entropies due to the decreased temperature drop due to throttling. Consequently, a more sophisticated condenser model would yield heat rate results less sen­ sitive to changes in pressure.

3.7.3 BLED STEAM

The feed pump at Grain Power Station uses steam bled from the turbine stages to drive the Boiler Feed Pump Turbine. This is more efficient than an electrical feed pump and makes the results agree better.

3.7.4 FINAL POINT WETNESS

The model uses the assumption that the polytropic efficiency is constant which leads to the fact that the total-to-total efficiency is almost constant. However, as the expanding steam passes through saturation the resulting wetness will degrade the total-to-total efficiency. Measurement of wetness at the back end of the turbine is a difficult task and has attempted by the CERL wetness probe { Walters, 1987 ). This would be useful in this analysis as a con­ firmatory tool since heat rate test infers the losses by measuring everything else

3.7.5 MANUFACTURERS HEAT-RATE CORRECTION CURVES

The turbine manufacturers quote heat rate correction curves ( Strotzki, 1950 ) which should be applied to heat rate results obtained at off-design conditions. The corrections are applied to the as-run heat rate and as-run output power to obtain corrected heat rate and power under fixed governing conditions. At design conditions of output power, ED, and live steam pressure, p0, the heat rate will be the guaranteed value ( HRg ), HRg = a + (3Ed + ypD.

PhD Chapter 3 Page 52 Reserve Provision Costs Improved Generation Dispatch in Power Systems

I X

c* £ X cn v ^ D ^ ^ CL (D _Q ~a3 ^ c ~o X ’o O o u- o L_- O o O Q_ K) -> z X

u E-i M

Q U C/)M Q

C\J o —

Figure 28. Standardised Estimates of y: The heat rate sensitivities with respect to operating pressure are compared.

PhD Chapter 3 Page 53 Reserve Provision Costs Improved Generation Dispatch in Power Systems

If live steam pressure increases above design from p D to p0 + Ap, Ap > 0 and the governor valve is fixed at a constant position then the power will increase from ED to E0 + AE, AE> 0 . The new heat rate will then be given by, HRar = a + /?(E + A E ) 4- y(p 4- Ap),

= HRg 4- /?AE 4- yAp. If live steam pressure and output power are proportional in steady state then,

A E = K A p . The change in heat rate is therefore given by A HR = HRg - HRgr = - (pK 4- y)Ap.

The correction factors quoted by the manufacturer enable A HR to be calculated. U.K. Man­ ufacturer give a factor c where A HR = (c - 1 )HRan and Continental manufacturers, such as Brown Boveri, give a factor p such that AMR = ( —p/100)HRar. And therefore, y = 1 — c — pK

= p/100 — /?K Typical values of care >1.0, typical values of pare<0 for Ap>0 and typical values of K are Ed/Pd ~ 7 MW/M Pa and consequently if /? < 0 then !/?K||>|1-c| and I p/1001 and con­ sequently y >0. In surmise, the manufacturers heat rate correction curves predict a higher heat rate will result from an increase in pressure.

3.7.6 MONEYPOINT POWER STATION

In the course of routine heat rate testing at Moneypoint Power Station in March 1990 ESB tested the plant at the power and pressure pairs shown in Figure 23 on page 41 with a view to quantifying the sensitivities. Unfortunately, due to plant and instrumentation problems the tests were declared null and void and repeats will be necessary.

3.8 CONCLUSIONS This Chapter examined the off-design operation of axial flow condensing steam turbines to quantify the associated efficiency penalties with a view to enhancing the generation dispatch algorithm to provide regulating reserve. This was accomplished using a very simple turbine model based on the ellipse law for a single cylinder turbine and broadened to consider the case of a turbine employing reheat. Having gained an appreciation of the magnitude and mechanism of the losses a series of tests were carried out at Grain Power Station using the existing plant instrumentation with a view to examining the feasibility of deducing the required costs and updating the generation dispatch algorithm on-line using a thermal performance auditing algorithm. In addition, an attempt to deduce these costs was made at Poolbeg Power Station using specially calibrated instrumentation. It was found that, in the case of the modelling, the turbine heat rate increased with decreasing output power and with increasing operating pressure. The losses arise from (a) increased steam flow at higher pressure due to decreased temperature resulting from throttling, and (b) increased house load due to increased feed pump power requirements. However, these ef­ fects were difficult to measure on in the plant tests. An optimisation algorithm should be developed to economically allocate regulating reserve on a system-wide basis. The costs to be used in the objective function can be taken simply as 1-2 % increase in heat rate ( Kiirten, 1986 ). This is corroborated by archived test records

PhD Chapter 3 Page 54 Reserve Provision Costs Improved Generation Dispatch in Power Systems on CEGB plant reported by Fenton ( 1976 ). A system simulation incorporating the above dispatch algorithm and simple non-linear models of generator and load dynamics should be developed to analyse the benefits of a power system operating with pressure dispatch.

PhD Chapter 3 Page 55 Reserve Provision Costs Improved Generation Dispatch in Power Systems

4.0 CHAPTER FOUR - PARAMETER ESTIMATION IN POWER PLANT MODELS

4.1 INTRODUCTION

The active power reserve available from generating plant can be examined by the use of simple plant models typified by those described in Chapter Two and by Astrom and Bell (1988) and EPRI (1980). The data items required by these models - time constants, flow impedances etc - can be determined from transients on real power plant. This has been accomplished on the NIE system ( N. Ireland ) where the user suggests parameters and improvements thereof to reduce the error between a measured and a predicted response observed with the aid of interactive graphics ( Fox and McCracken, 1987). Similar identification effort on the IEC sys­ tem ( Israel ) has been reported by Winokur and Pe'er ( 1986 ). This Chapter presents a method of identification based on least squares where parameters are chosen to minimize the sum of squares of the residuals subject to some constraints. The data used have been derived from plant tests carried out in England and Ireland under the auspices of CIGRE Study Committee 39.

4.1.1 TERMINOLOGY AND CLASSIFICATION OF MODELS

Process analysis refers to the application of scientific methods to the recognition and definition of problems and to the development of procedures for their solution. The process denotes an actual series of operations or treatments of materials, for example that which occurs within energy conversion plant. The model, on the other hand, is a mathematical description of the real process. Deterministic models or elements are those in which each variable and parameter can be assigned a definite fixed number, or series of fixed numbers, for any given set of conditions. In contrast, in stochastic or random models, uncertainty is introduced. The variables used to describe the input-output relationships of the process and the structure of the elements ( and the constraints ) are not precisely known. In a lumped parameter model spatial variations are ignored; the various properties and the states ( dependent variables ) of the system can be considered homogeneous throughout the entire system. A distributed parameter representation, on the other hand, takes into account

PhD Chapter 4 Page 56 Parameter Estimation in Power Plant Models Improved Generation Dispatch in Power Systems detailed variations in behaviour from point to point throughout the system. All real systems are, of course, distributed in that there are some variations throughout them. Power plant models usually assume that the reheater can be represented by a simple lag. In practice, reheaters are comprised of many sections arranged in various geometries and are modelled more accurately by distributed representations. Three very general types of models ( and their combinations ) can be written for a process; 1. Transport phenomena models. 2. Population balance models. 3. Empirical models. Transport phenomena models are typified by the phenomenological equations of change, that is, the continuum equations describing the conservation of mass, momentum and energy. A transport phenomena model is comprised of differential equations plus boundary and/or initial conditions. In an initial value model, for a set of differential equations, the initial con­ ditions must be given for each equation equal in number to the order of the highest derivative. On the other hand, in a boundary value model the proper number of values of the dependent variables or their derivatives must be given at various values of the independent variables. Some values may not be at the origin but at the end of the range for the independent variable. An nth order non-linear model may be expressed in terms of n simultaneous ordinary differ­ ential equations as follows,

x = f(x, u, p, t) x(0) = x0 where f(x, u, p, t) is a very general non-linear n vector of functions, x an n vector of dependent variables, u an m vector of inputs and p a p vector of parameters ( to be estimated ). Except in very rare instances, this equation does not have a analytical solution and must be solved by numerical methods.

4.1.2 PROCESS ERROR

In real life most measurements or experiments result in values of the measured variables which vary from one repetition of the experiment to another. These outcomes are termed random, stochastic, chance, statistical or probabilistic and the associated variables are termed random or stochastic. There are many reasons why observations obtained by experiment are random rather than deterministic. In some cases the randomness rests on the physical phenomena, such as the decay of a radioactive species or the emission of electrons from a thermonic cathode. In other cases there is insufficient information about the variables or lack of techniques to gather the required information, so only manifestations are observed. Often the observer is just negli­ gent or careless. Finally, uncertainty exists because the process models do not adequately represent the physical process. Other types of errors which are continuously introduced due to say, faulty calibration of an instrument or to a preconceived idea of the expected data are known as systematic errors. The 'true' value of a variable is that value which would be obtained on measurement if there were no stochastic features associated with the measurements. Stochastic effects add to the true value thereby producing error. Conceptually, the unobservable error s(t) is added to x{t) to give the observable dependent variable X(t) which can be written for discrete observa­ tions

If the estimated parameters p replace the model parameters the residual error is E(ti) = X(t,) —X(ti) as illustrated in Figure 29 on page 58.

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Figure 29. Information flow for the process and the model: x(f) is the deterministic model output; X(t) the experimental output; X(t) is the predicted output.

The objective in parameter estimation is to obtain the 'best' estimate of p based on the ob­ servations X(ti). To do this it is necessary to prescribe what u(t) is ( experimental design ) and to have some information about the nature of F.(t).

4.1.3 LEAST SQUARES ESTIMATION

Least squares parameter estimation does not require prior knowledge of the distribution of the A unobservable errors and yields unbiased estimates, that is £{X(f)} = x(t) where £ is the ex­ pectation operator, and is used extensively for transport phenomena models.

If the observations X are made at discrete instants of time t,. i = 1,2,... ,g from t = 0 \ o t = tf , then the parameters are chosen to minimize

i=9 * = y £ [ XW - X(*o. P. ',)]r[*((/) - *(*o.P.f/)] /=1 This equation may be differentiated with respect to p and Xo and equated to a null vector to minimize as follows;

i=9 A A dX{XQ, u, p, t,) ^ = °r=- £ [x^ - «. p. y ] r dp i= 1

•=9 d dX(XQ, u, p, t,) =oT= -^ w ff)-x(% u .p ,m T dXn dXn /= 1

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a A where [d X/dp] is an n x p matrix whose columns are the elements of the vector X(f,) differ­ entiated with respect to each element of p and [dX/dxo] is an n x n matrix whose columns are the elements of the vector X(t,) differentiated with respect to each initial condition in turn.

4.1.4 COMPUTATIONAL DIFFICULTIES

The choice of the disposable parameters p and x0 involves the solution of the above p + n non-linear simultaneous equations. There are often constraints to be satisfied in the choice of the parameters which can easily be incorporated in an optimisation algorithm. This will have the consequence of reducing the degrees of freedom by one for each equality constraint added.

The optimization algorithm will also be required to integrate the n non-linear simultaneous differential equations and consideration must be given as to the method to be used. In the case of power plant models, the time constants vary from seconds ( governor ) to minutes (boiler) resulting in a stiff system. Moreover, good initial guesses for the parameters and in­ itial conditions are needed to overcome the problems of local optima. This difficulty can be ameliorated if the starting conditions are taken so that the dominant time constants of the model are of the same order of magnitude as those of the measured responses ( Himmelblau, 1970 ) Because of the difficulties obtaining analytic or numeric solutions for the deterministic process model experiments are often arranged whereby the vector of derivatives dXjdt is measured rather than X itself. Indeed in some fields, e.g. optics and chemical engineering, instruments are available which measure the rate of change of the dependent variable thereby reducing the problem to one of optimisation only.

4.1.5 MULTICOLLINEARITY

The optimisation algorithm varies the parameters and initial conditions to minimize the sum of squares of the residuals. However, if there is a relationship existing between the inde­ pendent variables the optimisation algorithm may encounter numerical difficulties. When such relationships exist some of the parameters contribute little to the performance of the model and should be removed. A suitable means of detecting multicollinearity is afforded by a sin­ gular value decomposition ( Norton, 1986 ). The residual sum of squares for variable x,(f) is given by

Sf = ^ £ , 2(fy), y=i and the dependence of the residuals on each parameter may be calculated by computing the matrix

dpj ’ ...... ’ ' ....."

Multicollinearity among the parameters may then be examined by performing a singular value decomposition A = UDWT where U is an n x p matrix with orthogonal columns, D is a p x p diagonal matrix whose en­ tries are the singular values of A (i.e. the square roots of the eigenvalues of the matrix ArA) and W is a p x p orthogonal matrix. A zero singular value would indicate exact linear de­ pendence between columns of ATA reflecting a similar dependence between the regressors. Consequently, a drop tolerance for a parameter based on the singular values can be taken as (5 = Tol J2[df

PhD Chapter 4 Page 59 Parameter Estimation in Power Plant Models Improved Generation Dispatch in Power Systems where df is the number of degrees of freedom given by gn — p — c where c is the number of constraints and 2<£/c/f is an estimate of the variance per degree of freedom. Any singular va­ lues less than <5 are taken as not statistically significant and the associated parameters are removed from the optimization procedure. These parameters remain at the values the opti­ misation algorithm determined when the singular values became less than the tolerence.

4.1.6 STATISTICAL ANALYSIS

Approximate confidence intervals on the estimated parameters and initial conditions can be obtained by constructing the variance-covariance matrix 2 C = Cov(b ) = WD~2Wt ng-p-c ’ where b = [p1,Pi,... ,pp,xo1,x02, ... ,x0n] r

The diagonal elements of this matrix are estimates of the variances of the parameters and the initial conditions and can be used to construct confidence limits: Pi±t(df, 1 - a/2)Vc7, where a is the required significance level and t{df, 1 — nc/2) is the 100(1 — a) percentage point of a one-sided t distribution with df degrees of freedom. The following statistics can be calculated for each variable g Correlation Coefficient = CORR, = ^ 7=1 Vs7

v m Ev i - 1) Normalised Auto-Correlation Coefficient = AUCO, = l i S/

Auto-Correlation Index = AUCR, = ------

The correlation coefficient is a measure of whether the residuals for curve / are as likely to be positive as negative ( |CORR,|~1 ) or are one-sided ( I CORR, I > > 1 ). The second is the normalised auto-correlation index, which has a positive value considerably greater than the third if the residuals show some systematic behaviour, and comparable if they are random. The parameter fitting procedure may therefore be summarised by the following steps:- 1. Experimental Design ( discussed in the next section ). 2. Perform the experiment and obtain data. 3. From a given estimate of the parameters integrate the equations to obtain the predicted data ( integration ). 4. Iterate the process until the sum of squares of residuals is a minimum ( optimisation ).

4.2 EXPERIMENTAL DESIGN The design of an experiment is of paramount importance to the success of the model building procedure. No amount of analysis will overcome the handicap of poorly designed exper­ iments. Every experiment should have carefully defined objectives or criteria expressed in mathematical terms insofar as possible. It addresses issues such as choice of inputs, vari­ ables to be measured, instrumentation, data resolution and storage, plant and system prep-

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Figure 30. Parameter fitting procedure: Integration is performed by a suitable difference scheme and parameter updates by an optimisation algorithm. aration, integrity and safety, operator instructions, contingency plans, allowable costs and time schedule.

4.2.1 STATEMENT OF OBJECTIVES

The objective of the experiment is to obtain the parameters by , ..., b9 in the non-linear lumped parameter initial value transport phenomena model for drum-boiler power plant described in Chapter Two. This should be accomplished with the minimum of experimentation and at no time endanger the availability or integrity of the plant and system.

4.2.2 CHOICE OF INPUTS

The model is needed to examine the capability of the power plant to provide regulating and emergency reserve initiated by governor action. The experiment should therefore involve a step change to the governor valve position. Since the model does not employ any turbine or boiler controllers the experiment should be performed with the unit's controllers dis-engaged. Tests of this type are known as stored energy tests. The set points for output power and operating pressure should be chosen so that availability and integrity of the plant is not endangered and to enable the required test to be performed. The set point for output power should give the plant some manoeuvrability in the upward and downward directions and is chosen to be approximately 70-80% of Maximum Continuous Rating ( MCR ). The boiler pressure should be maintained at the full-load value thereby en­ suring the steam is throttled and giving the governor valve some headroom. The set point for pressure must be chosen with care if the safety valve settings are not to be exceeded. If the governor valve is closed the pressure builds up and may exceed the safety valve settings. Similar considerations apply when the governor is opened leading to a de­ crease in pressure. On some plant, e.g. Moneypoint ( ESB, IRL ), there is a safety mechanism

PhD Chapter 4 Page 61 Parameter Estimation in Power Plant Models Improved Generation Dispatch in Power Systems which senses the rate of change of pressure and the amount of depressurisation and takes action accordingly. Consequently, the general specification described above should be tailored to suit each indi­ vidual plant based on a knowledge of the plant, its auxiliaries, operational practices and in consultation with the unit operators and shift charge engineers at the locations.

4.2.3 INSTRUMENTATION AND CALIBRATION

The tests should be performed with as little as possible or no additional instrumentation. The data should be in stored on magnetic tape or disk and sampled at least every five seconds. A means of observing primary plant variables during the tests - generated power, steam pressures and temperatures and governor positions - should be available so a quick assess­ ment can be made as to the success or otherwise of the test. A comprehensive backup log of all plant variables should also be provided.

4.2.4 PLANT AND SYSTEM PREPARATION

Power plant dynamic testing requires special dispensation from the generation dispatchers in the National or Area Control Centers. The tests must be planned in advance and adequate emergency reserve provided against the loss of the unit. This required no special measures on the British grid as the loss of a unit at Fawley or Grain represented no more than 2% of the system demand. However, on the Irish grid the tests were more carefully supervised by the generation dispatchers as the loss of a 300 MW unit at Moneypoint represented 15% of system demand. Consequently, the tests were only given sanction for periods when adequate primary and secondary reserve was made available by the generation dispatch algorithm {Brown, 1989). Prior to test initiation, on either grid, sanction must be received from the generation dis­ patchers as minute to minute frequency conditions may not be favourable. Opening the gov­ ernor valve at times of high frequency is not desirable for example.

4.3 DETERMINISTIC MODEL EQUATIONS The model described in Chapter Two can be re-written in the following form:

C2( 1 + C 3A 2(0P D( 0 ) 1/2 c2 PD(t) = c,QE(t) + A(t) A(t) ' where C\ = b. c2 = ( -b 2/b6), and c3 = 2b6.

C4( 1 + C 3A 2(0 P D( 0 ) 1/2 c4 Pr(<) = A(t) A(t) + C5PR( 0. where c4 = (/?3/b6) and c5 = — b4. The test specification requires that the plant, initially in a steady state, is perturbed by a step change in the governor position. A(t) = a(J(t) -f- A(0~), where the constant a is chosen in consultation with the shift charge engineer to ensure that no safety limits are violated. The initial conditions for drum pressure and reheater pressure are therefore given by solving the above equations at the time origin.

PD(0) = ---- 1------[(1 - c:A(0~)QE(0)lc2f - 1] c3A2(0~)

Pr(0) = [ 1 “ 0 + c3^2(°")Pd(0))1'2]

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The model output equations can be differentiated to obtain two further differential equations,

. C^Qe C 2

Ps(0 (1 + c 3A2(t)PD(t))'12 + W) /A(()(1 + c3A2(t)PD(t))'12 '

_ b7c,A(t)QE( t ) ______b7c3 b8c4( l+ c 342(QPD(Q),;2 b8C4

9 (1 + c 3A'2(t)PD(t))V2 (1 + c3A2(0Pd(0 )'/2 A(l)

+ ^8 c5^r(0 with initial conditions

Ps(0+) = ----- § ~ r [(1 + c34 2(0+)Pd(0))1'2 —l], c 3 A 2 ( 0+) and Wg(0+) = b7Ps(0+)4(0+) + b„PR( 0). where A(0f) is needed in these initial conditions to overcome the simplifying assumption that superheater storage is negigible. The initial conditions have a dual purpose; they provide the starting conditions for the integration algorithm, and are constraints on the parameter choices. The estimation algorithm requires initial guesses for the parameters, and these are obtained by numerical differentiation of the measured variables and non-linear regression together with intuitive engineering skill and judgement; the value of the reheater time constant 1/b4 may be taken as approximately 10 seconds for example. The parameters of the model are chosen to minimize the sum of squares of the residuals, that is, to minimize the sum of the squares of the distance between the measured and predicted curves at the sample points i~9

..... c5,b7,b8) = £ (? ? ((,) - P^ i > f + (PR '((-> + K ( t , ) - Ps(.t,)f + (WgW - i= 1 which has ( n - 1 ) x g - p degrees of freedom. The parameter fitting procedure is illustrated in Figure 30 on page 61.

4.4 POWER PLANT TESTS

Working Group 4 of CIGRE Study Committee 39 ( SC39-04 ) has been involved in benchmarking the dynamic response characteristics of fossil-fuelled power plant of various size and type world wide ( Carvalho, 1990 ) and this was seen as an ideal opportunity to obtain the neces­ sary data. Among the plant tested by SC39-04 were Moneypoint ( 300 MW coal , ESB IRL ), Didcot ( 500 MW coal, NP UK ), Duvha ( 600 MW coal, ESCOM RSA ), Matla ( 600 MW coal, ESCOM RSA ), Fawley { 500 MW oil, NP UK ), Grain ( 660 MW oil, PG UK ) and Matimba ( 665 MW coal, ESCOM RSA ). The parameter estimation algorithm described above will be tested on data obtained from some of these stations. Those not used as test cases were either of the 'once through' variety or provided data with poor resolution and/or sampling frequency. On all plant, excepting the newest ones ( Matimba and Moneypoint ), additional instrumenta­ tion had to be provided to store the data on magnetic media.

4.4.1 DRAX POWER STATION

Data from a sophisticated computer simulation model of Drax Power station was used as an initial trial case for model fitting. The Drax model ( hereafter referred to as the plant ) uses eighty simultaneous differential equations to model the plant in some detail ( Sidders, 1989 ).

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This is an important first stage, as it provides a complete set of noise free data at any sam­ pling frequency. The per-unit bases for the variables were selected as full-load values and are quoted in Table 13 on page 65. The value of QE was taken to be proportional to fuel flow which is a reasonable assumption given that the total heat input to the plant is distributed between the evaporator, superheaters, reheater and stack losses. The plant was given a load set point of 500 MW and a boiler pressure of 16 MPa and allowed to run for a short time in steady state. The governor was then stepped open by 10 percentage points and the data captured every half second for a period of 2000 seconds. Data from the first 750 seconds of the test at 5 second intervals ( g = 151 ) were selected to determine the parameters. Shown in Figure 31 on page 70 to Figure 34 on page 71 are the measured and predicted re­ sponses with associated statistics reported in Table 12. There is some evidence of systematic error in the residuals as the normalized auto-correlation coefficient ( AUCO ) has a positive value considerably greater than the auto-correlation index ( AUCR ). This is not unexpected as the model is a very simple one making broad assumptions. The assumptions inherent in the model were detailed in Chapter Two. and only the implications will now be discussed. The saturated steam specific enthalpies were assumed constant but as the boiler de-pressu- reizes the enthalpy increases as was explained in Chapter Three. Moreover, the latent en­ thalpy also decreases, bringing about a decrease in saturated steam flow, resulting in generated power not returning to exactly the same initial condition. Neglect of factors such as these will result in simpler model equations but result in systematic errors.

Individual Differential Equation Statistics s, CORR AUCO AUCR Po 1.130x10 3 -9.2836 0.9912 0.0811 Pr 1.181X10-3 12.0868 0.9886 0.0811 Wg 6.041X10-4 -2.1702 0.5504 0.0811 Ps 2.712X10-3 10.7079 0.9486 0.0811 Parameters and Confidence Limits Parameter 5% Limit 95% Limit Ci 7.4125x10-3 7.1936X10-3 7.6380x10-3 c2 -5.9249X10-2 -5.7482x10 2 -6.1070x10-2 c4 1.8319x10-’ 1.6052x10-’ 2.0906x10-’ C5 -1.0224x10-’ -8.9583x10-2 -1.1669x10-’ b7 9.7715X10-2 5.5076x10 2 1.7336x10 ’ 3.8982x10° 3.6348x10° 4.1807x10° Initial Conditions Variable 0- O' Po 16.61 MPa 16.61 MPa Pr 3.11 MPa 3.11 MPa Ps 15.88 MPa 15.72 MPa W9 498.80 MW 504.47 MW Parameters Undetermined by the Data c3 2.295x10’

Table 12. Parameter Estimates and Associated Statistics for Drax Power Station: Data were de­ rived from the Simulation Model ANYDYM.

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DRAX GRAIN FAWLEY MONEYPOINT Unit Size 660 MW 690 MW 500 MW 300 MW Fuel Type Coal Oil Oil Coal Drum Pressure 18.0 MPa 18.5 MPa 16.5 MPa 18.0 MPa Superheater 18.0 MPa 18.5 MPa 16.5 MPa 18.0 MPa Pressure Reheater Pres­ 18.0 MPa 18.5 MPa - 18.5 MPa sure Output Power 660 MW 690 MW 500 MW 300 MW Fuel Flow 75 kg/s 45 kg/s 32 kg/s 100 %

Table 13. Per-unit bases selected for Parameter fitting process.: The values were chosen from the steady state benchmarking tests.

4.4.2 GRAIN POWER STATION

Grain power station is a 660 MWe oil-fired set situated on the Thames Estuary in England and owned by the Power Generation Company pic. A stored energy test was carried out to the above specification in May 1989 after discussion with station operations staff and System Op­ erations Department ( McNamara et al, 1989b ). A series of steady state benchmarking tests were also performed with full load and governors open wide to obtain suitable per unit bases which are reported in Table 13. The variables were sampled by a Solarton Orion data logger every 15 seconds for the steady state tests and every 5 seconds for the dynamic tests. The logger was connected to the con­ trol room instrumentation via standard resistors and the data recorded on magnetic tape. Two six-channel multi-pen chart recorders were also provided so that visual output was available during the test, and a backup hard copy digital log of 15 variables was provided. The plant was given a load set point of 500 MW and a pressure set point of 16 MPa. Once the plant had quiesced the boiler and turbine controllers were disengaged and the governor valve stepped open 7 percentage points. The plant variables were recorded for 725 seconds ( g — 146) until a new steady state was reached. Figure 35 on page 72 to Figure 38 on page 73 shows the measured and predicted responses with the associated statistics reported in Table 14 on page 66 which shows some evidence of systematic behaviour.

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Individual Differential Equation Statistics Sy CORR AUCO AUCR Po 2.341x10"3 0.4054 0.9335 0.0825 Pr 3.834x10~3 -1.8293 0.8761 0.0825 Wg 2.884x10-3 -0.0763 0.9408 0.0825 Ps 1.912x10-3 -0.1143 0.9583 0.0825 Parameters and Confidence Limits Parameter 5% Limit 95% Limit Ci 6.4185x10-3 6.2277x10-3 6.6152x10 3 c2 — 1.3018x10~2 -1.2604x10 2 -1.3446x10-2 C3 2.0696x10° 2.0412x10° 2.0984x10° c4 1.2224x10-2 1.1559x10 2 1.2927x10-2 C5 -2.6655x10-2 -2.5220x10-2 -2.8172x10-2 by 1.3967x10° 1.3241x10° 1.4733x10° bi 1.4257x10° 1.2780x10° 1.5905x10° Initial Conditions Variable 0- 0+ Pd 17.5 MPa 17.5 MPa Pr 3.01 MPa 3.01 MPa P, 16.37 MPa 15.99 MPa Wg 490.79 MW 542.97 MW

Table 14. Parameter Estimates and Associated Statistics for Grain Power Station: Data were derived from Plant Tests in May 1989.

4.4.3 MONEYPOINT POWER STATION

Moneypoint power station is a 300 MWe set situated on the Shannon Estuary in Ireland and owned by the Electricity Supply Board. A stored energy test was carried out to the above specification in April 1990 after discussion with operations staff and with Operations Depart­ ment ( McNamara and Canning, 1990a ). A series of steady state benchmarking tests was also performed there in December 1988 with full load and governors open wide to obtain suitable per unit bases and is reported in Table 13 on page 65 ( McDyer et al, 1989 ). Special provisions for emergency reserve were necessary owing to the strategic importance of this plant in the Irish grid. The data were sampled 40 times per second and the first 500 seconds of data was used at 3 second ( g = 167 ) intervals to obtain the parameters. The data capture system at the station provides data with an eight bit resolution and it was necessary to smooth the data using a fifth order moving average. The measured and predicted re­ sponses are shown in Figure 39 on page 74 to Figure 42 on page 75 and the associated sta­ tistics are reported in Table 15 on page 67

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Individual Differential Equation Statistics S i CORR AUCO AUCR Po 2.961x10~3 -5.9718 0.9147 0.0772 w g 3.380x10-3 -0.3309 0.8823 0.0772 P, 4.242x10-3 9.4956 0.9385 0.0772 Pr 5.586x10-3 1.7020 0.9351 0.0772 Parameters and Confidence Limits Parameter 5% Limit 95% Limit

Ci 6.9319x10-3 6.5092x10 3 7.3820x10-3 c2 -1.3812x10-2 -1.4681x10 2 -1.2994x10 2

C3 1.6282x10° 1.6120x10° 1.6446x10° c4 3.6770X10-2 3.3619x10 2 4.0216x10-2

C5 -6.1941x10-2 -5.6660x10 2 -6.7715x10-2 b7 9.3563x10-2 2.0508x10 2 4.2687x10-1 bs 4.2681x10° 3.9838x10° 4.5727x10° Initial Conditions Variable o- O'

Pd 18.09 MPa 18.09 MPa

Pr 3.86 MPa 3.86 MPa w g 287.12 MW 288.27 MW Ps 16.64 MPa 16.37 MPa

Table 15. Parameter Estimates and Associated Statistics for Moneypoint Power Station: Data were derived from Plant Tests in April 1990.

4.4.4 FAWLEY POWER STATION

Fawley power station is a 500 MWe oil-fired set situated on Southampton Water in England and owned by the National Power Company pic. A stored energy test was carried out to the above specification in May 1989 after discussion with operations staff and with System Operations Department ( McNamara and Carvalho, 1989c ). A series of steady state benchmarking tests were also performed with full load and governors open wide to obtain suitable per unit bases which are reported in Table 13 on page 65. The variables were sampled by a Solarton Orion data logger every 15 seconds for the steady state tests and every 5 seconds for the dynamic tests. The logger was connected to the con­ trol room instrumentation by the use of standard resistors and the data recorded on magnetic tape. Two six-channel multi-pen chart recorders were also provided so that visual output was available during the test, and a backup hard copy digital log of 32 variables was provided. The plant was given a load set point of 430 MW and pressure set point of 13.8 MPa and allowed to reach a steady state when the governor valve was stepped open by 7 percentage points. The plant variables were recorded for 735 ( g = 148 ) seconds where a new steady state was reached. Figure 43 on page 76 to Figure 45 on page 77 show measured and predicted re­ sponses for this plant with associated statistics reported in Table 16 on page 68 which show some evidence of systematic errors. A notable absence from the data is reheater pressure owing to the failure of a transducer.

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Individual Differential Equation Statistics s, CORR AUCO AUCR Po 1.081x10~3 -0.7366 0.8858 0.0819 W9 1.289x10 3 0.0488 0.8604 0.0819 Ps 8.810X10-4 -0.8539 0.9389 0.0819 Parameters and Confidence Limits Parameter 5% Limit 95% Limit Ci 1.1410x10 2 1.1097x10 * 1.1732x10-* c2 —3.3148x10-* -3.2221x10 * -3.4101x10* C3 9.2428x10“1 9.1861x10 1 9.2999x10-’ C5 —5.8930x10-* -5.3674x10 * -6.4700x10 * b8 4.3675x10° 3.9786x10° 4.7945x10° Initial Conditions Variable o- 0h Po 15.47 MPa 15.47 MPa 426.70 MW 426.81 MW Ps 13.93 MPa 13.69 MPa Parameters Undetermined by the Data c4 3.8984x10 * b7 4.7151x10 3

Table 16. Parameter Estimates and Associated Statistics for Fawley Power Station: Data were derived from Plant Tests in May 1989.

4.5 ON-LINE PARAMETER ESTIMATION

The parameter estimation algorithm so far presented is specific to estimating the model pa­ rameters during a stored energy test. However, the algorithm can easily be modified to pro­ vide parameters for transients precipitated by other forcing functions for example a thermal inertia test where the heat input to the boiler is rapidly changed

QE(t) = qU(t) + 0 E(0"). The algorithm could be developed into a very general parameter estimation routine applicable to any test type if enhancements are made to incorporate boiler and turbine controllers. The development of an on-line non-linear recursive least squares parameter estimation algo­ rithm could then be envisaged. This would require the formulation of the above model to en­ compass all test types and telemetering the data to a central computer. The computational problems presented by this proposal would be onerous for a power system with many units. The NIE have modelled their plants with simple non-linear equations and the parameters are updated by data collected by special event recorders installed at major generating stations and triggered by generation loss incidents ( McCracken et al, 1986 ). The ESB have an on-going programme installing Micro-Vax 2000 computers at all stations to capture data following a generation loss incident and to telemeter this data to a central com­ puter for analysis. The ESB test their plant and recorders on the first Tuesday of every month by imposing a pumped storage induced frequency transient. When the system is finally commissioned these tests could also be used to determine parameters of simple models.

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4.6 CONCLUSIONS

This Chapter developed an algorithm to estimate the parameters of simple non-linear power plant models. This algorithm varies the disposable parameters so that the sum of squares of the residuals are minimized. The algorithm has been tested with data derived from experiments conducted on plant oper­ ating in a commercial grid environment. Subsequent simulated reconstructions were seen to faithfully reproduce the plant's generated power, live and reheat steam pressures. The r.m.s. modelling error was seen to as large as 6.4% of base value for generated power, 5.2% of base value for superheater pressure, 5.6% of base value for drum pressure and 6.4% of base value for reheater pressure. A power system simulation will be developed in the next Chapter using the parameters ob­ tained to investigate the feasibility of active power and pressure dispatch. The enhanced dispatch algorithm will be compared with the current dispatch algorithm against frequency control criteria.

PhD Chapter 4 Page 69 Parameter Estimation in Power Plant Models Improved Generation Dispatch in Power Systems

STORED ENERGY TESTS DRAX POWER STATION

Data From ANYDYM Hade 1 Figure 31. Output Power for Drax Power Station: Measured and Predicted Responses

STORED ENERGY TESTS DRAX POWER 5TATI0N

Data fram ANYDYH Idadel

Figure 32. Superheater Pressure for Drax Power Station: Measured and Predicted Responses

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STORED ENERGY TESTS DRAX POUER STATION

Data from ANYDYH Hadel

Figure 33. Drum Pressure for Drax Power Station: Measured and Predicted Responses

STORED ENERGY TESTS DRAX POUER STATION

Data from ANYDYH Hadel

Figure 34. Reheater Pressure for Drax Power Station: Measured and Predicted Responses

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STORED ENERGY TESTS GRAIN POUER STATION

Data from Plant Tests in Hag 1989

Figure 35. Output Power for Grain Power Station: Measured and Predicted Responses

STORED ENERGY TESTS GRAIN POUER STATION

Data from P lan t Tests in Nlaq 1989

Figure 36. Superheater Pressure for Grain Power Station: Measured and Predicted Responses

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STORED ENERGY TESTS GRAIN POUER STATION

Data from Plant Tests in Plan 1989

Figure 37. Drum Pressure for Grain Power Station: Measured and Predicted Responses

STORED ENERGY TESTS GRAIN POUER STATION

Data from P la n t Tests in flaq 1989

Figure 38. Reheater Pressure for Grain Power Station: Measured and Predicted Responses

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STORED ENERGY TESTS nONEYPOINT POUER STATION

T IN E (S ec.)

Data From Plant Tests in (April 1990

Figure 39. Output Power for Moneypoint Power Station: Measured and Predicted Responses

STORED ENERGY TESTS MOfiEYPO INT POUER STOTION

T IM E (S ec.)

Data from P la n t Tests in (April 1990 Figure 40. Superheater Pressure for Moneypoint Power Station: Measured and Predicted Re­ sponses

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STORED ENERGY TESTS rUDNEYPO IN T POUER STATIQN

Data fram Plant Tests in Apr i 1 1990

Figure 41. Drum Pressure for Moneypoint Power Station: Measured and Predicted Responses

STORED ENERGY TESTS MdNEYPOINT PQUER STATION

Data fram Plant Tests Ln April 1990

Figure 42. Reheater Pressure for Moneypoint Power Station: Measured and Predicted Re­ sponses

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STORED ENERGY TESTS F ftU LE Y P CIDER S T P T T D h

TINE (Sec . )

Data Cram P la n t Tests in Man 1989

Figure 43. Output Power for Fawley Power Station: Measured and Predicted Responses

STORED ENERGY TESTS FftDLEY POUER STftTrON

Data Cram Plant Tests in Flaq 1989

Figure 44. Superheater Pressure for Fawley Power Station: Measured and Predicted Responses

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STORED ENERGY TESTS FfiW LEY POWER S T R T IO N

Data Fram Plant Tests in Han 1933-

Figure 45. Drum Pressure for Fawley Power Station: Measured and Predicted Responses

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5.0 CHAPTER FIVE- DISPATCH AND SIMULATION

5.1 INTRODUCTION

Primary frequency regulating ability may now be economically allocated over the entire power system with a knowledge of the costs and constraints developed in previous Chapters. The algorithm which accomplishes this is presented in this Chapter together with a dynamic sim­ ulation to analyse the benefits.

5.2 GENERATION DISPATCH ALGORITHM

Conventional generation dispatch algorithms in Energy Management Centres allocate active power over scheduled units so that global costs are minimized. The costs are derived from heat rate tests conducted at individual generators. The objective is to minimize the cost function

/=1 where / is the cost function associated with the power output levels from the n committed generators ( Wg ). This is subject to the constraint that the sum of the power outputs equals consumer demand ( D ) and system losses ( L ) UTWg = D + L, where U is a unit vector of dimension rt. The power outputs from the generators are con­ strained to lie within the following limits < Wg < Wg™, where the maximum is determined by the turbine capability and the minimum by flame sta­ bility considerations. The above optimistion is also subject to a number of constraints which vary from utility to utility due to local requirements of the power system. Topology information is usually incor­

PhD Chapter 5 Page 78 Dispatch and Simulation Improved Generation Dispatch in Power Systems porated which often leads to deloaded units to avoid transmission plant overload and to en­ sure security. On predominately thermal power system the rate of change of output power is of great im­ portance. If short term demand prediction is available, then rate limits may be incorporated in a dynamic dispatch algorithm and suitable computational methods based on dynamic pro­ gramming are described by Ross and Kim ( 1980 ). In this method each generator receives a target load trajectory which it must follow in the future. Such an algorithm has the advan­ tage that it co-ordinates predicted load changes with the rate of response capability of gen­ eration units and, unlike a static dispatch, can foresee that the present loading can affect the future rate of response capability. Such an algorithm has been employed in the U.K. power system for several years and provides target trajectories at six linked time points up to two hours in the future ( Dunnett and Duckworth, 1986 ). In the ESB system, where the ratio of the largest unit or maximum infeed to system size is high, spinning reserve provision is a major concern. The dispatch algorithm used there loads the units such that the total primary and secondary spinning reserves available following a generation loss are 50% and 80% of maximum infeed. There is also a constraint that en­ courages indigenous natural gas usage up to the capacity of the supply pipes and within the permitted usage ( Brown, 1989 ). The enhanced dispatch algorithm proposes that operating pressure is incorporated in the optimisation where the objective function then becomes n £ = £/,< .P '), ;=1 where P, is an n vector of operating pressures. In addition to the above constraints the pressures should lie within the following limits pmin < P ,< P max where the maximum is determined by safety valve settings and the minimum by water carry over considerations. The pressure should never be less than the the sliding pressure for a particular load Wg>BP's, where B is the constant relating output power to superheater pressure in steady state as de­ fined in Chapter Two. The system gain should be greater than some requirement, n £ g, ( < p ')> Requirement, 1=1 where G is the n vector function relating system gain to generator powers and pressures. The system gain is simply the sum of the governor gains of the individual generators as discussed in Chapter Two. This optimisation is carried out with any other utility specific constraints. Optimisation techniques most often used in dispatch algorithms are based on linear pro­ gramming and consequently the above equations should be linearized. The objective function then becomes

£ = UT A 4- B TWg + CTPS, where A is an n vector of costs known as the no load costs, B is an n vector of costs known as the Table B costs and C is an new n vector of costs which we shall call the Table C costs. The system gain constraint becomes G = UTA + BTWg + r TP5, where A, B and and T are n vectors containing linearized governor gain coefficients the en­ tries of which are derived in Appendix C by linearizing the governor gain equations derived in Chapter Two.

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5.3 FEASIBLE REGION

The feasible region over which the optimisation is performed is depicted as ABODE in Figure 46 on page 80 for a single unit system. It is bounded by power and pressure upper and lower limits as already discussed. The constraint labelled 'Valve Limit' prohibits operat­ ing at pressures below sliding. Contours of governor gain are overlaid on this and increase with increasing pressure and decrease with increasing power. The loading on this unit can be varied from 40% to 100% of Maximum Continuous Rating (MCR) to meet to consumer demand and is represented by a vertical line. In the range 40% to 73% of MCR the most economic operation is at minimum pressure along the line segment AB. Some reserve is provided at these power and pressure pairs, as the valve must be throttling the steam flow to increase the pressure above sliding, and the gain may be in­ creased by increasing the pressure. When the dispatched power exceeds 73% the 'Valve Limit' constraint becomes binding and the most economic solution lies along this constraint. Once again more reserve may be provided by increasing the pressure above sliding. Con­ sequently, there is a certain level of reserve available from part loaded units at no additional cost to the power system. More reserve is made available by decreasing power and/or in­ creasing pressure.

5.4 CASE STUDY To examine the implications of the enhanced dispatch algorithm on power system operation a case study will be made. A power system was configured using the models deduced in Chapter Four for the various plants tested worldwide. The costs were chosen to reflect a merit order based on fuel types with coal as the cheapest and oil most expensive but apart from this do not reflect actual costs. The cost of providing the maximum power at minimum pressure is the base case to which all costs are refered. The Table C costs were taken as a fixed percentage of the Table B costs as concluded in Chapter Three.

Figure 46. Feasible Region for Power and Pressure Dispatch: Data deduced from tests at Faw- ley.

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Power Station Fuel Type Capacity Min. No. of Incremental Costs (MVA) Load Units (Arbitrary Units) (%) Drax Coal 660 50 6 80 Moneypoint Coal 300 50 3 90 Fawley Unit 2 Oil 500 40 4 100 Fawley Unit 1 Oil 500 40 4 110 Grain Unit 2 Oil 660 50 4 120 Totals 11500 21

Table 17. Power Plant used in Power and Pressure Dispatch Case Study: Table C costs were taken as 10% of the Table B costs. The solution to the optimisation problem with minimum system gain requirements and a sys­ tem load of 78% of committed generation is shown in Figure 47. The cheapest units - Drax and Moneypoint - are at their maximum output ( base loaded ). The most expensive oil units at Grain are loaded at minimum. The unit which makes up the balance of demand over supply is a mid-merit unit at Fawley and is referred to as the marginal generator. This is known as the unconstrained solution ( i.e. has no ramp rate, transmission, security or reserve con­ straints). The Table B cost of the marginal generator will be defined as the System Marginal Price ( SMP ).

UNIT NUMBER

Figure 47. The Merit Order Solution to the Dispatch Problem: System Load of 9 GW.

Within the merit order loading some system gain is available from those units whose pressure is above sliding due to its loading, for example units at minimum powers. There is also some gain available from the marginal generator before it operates in a pure sliding pressure mode. This gain will be termed the intrinsic gain and is available at no extra cost to the power sys­ tem. Additional gain may be provided, in the most economic way, by firstly increasing the

PhD Chapter 5 Page 81 Dispatch and Simulation Improved Generation Dispatch in Power Systems base load sets' pressure to maximum, followed by the marginal generator's pressure and fi­ nally by the minimum loaded generators' pressure. This will produce the maximum gain possible from the power system within the merit order and extra gain is then provided by de­ loading units which have high gain providing abilities. The cheapest solution is to minimize £ = e V g+ c Tps, subject to

UTWg = D. This will result in the merit order solution for power and the pressures will be at minimum, p _ p mln

The intrinsic gain ( G ^ ) will then be given by G1 = UTA + B Twg + r Tp f n, and the maximum gain available within this loading profile ( G2) is given by G2 = UT A + BrtVg + r rPjiaH. Finally, the maximum gain available ( G3) from the power system is obtained by maximising G' = BlVg, subject to the demand constraint and with Pf = Pr,x. The solution to this problem results in those units with the highest entries in the B vector base loaded and those with the smallest values at minimum load. These concepts are illustrated in Figure 48 on page 83 where the bottom line represents the intrinsic gain ( G, ) the middle line the maximum gain possible within the merit order solution ( G2 ) and the upper line the maximum gain available ( G3 ). The upper and middle lines converge at the installed capacity value where there is no margin for increase with either methodology as wg= tv g max and

p _ pmax r s ~ r s

Shown in Figure 49 on page 83 is the increase in incremental cost for two of the curves shown in Figure 48 on page 83. The bottom line is the percentage increase in total system incre­ mental costs to provide the gain G2 and the top one depicts the increase to provide G3. These are the costs of providing reserve.

5.5 SIMULATION

The benefits of pressure dispatch will be examined by coupling the above algorithm with the generator dynamics described by the models developed in Chapter Two. An additional dif­ ferential equation to define system frequency will also be incorporated.

5.5.1 SYSTEM FREQUENCY

The mechanical power developed by the turbine is transmitted along a shaft which is loaded by an electric generator. The generator rotor is energised by direct current from an exciter to create a rotating magnetic field. The frequency of the electrical power generated is a multiple fraction of the rotational speed of the shaft depending on the number of pole pairs. This spinning magnetic field induces currents in the stator or armature windings thereby pro-

PhD Chapter 5 Page 82 Dispatch and Simulation Improved Generation Dispatch in Power Systems

PhD Chapter 5 Page 83 Dispatch and Simulation Improved Generation Dispatch in Power Systems ducing a retarding torque on the rotor. Consequently, the shaft is loaded by two torques and the rotor motion is governed by Newton's second law, = Tm(t) ~ Te(t) = Ta{t), where J is the total moment of inertia of the rotating masses connected to the shaft, am the rotor angular acceleration, Tm the mechanical torque supplied by the turbine and Te the elec­ trical torque. This can be rewritten in terms of the mechanical ( Wg) and electrical ( Pe) powers and the angular velocity ( w ), Wg — Pe ~ Jaxb.

The moment of inertia is usually expressed in a per-unit form where

Stored Kenetic Energy at Synchronous Speed Joj0 H = Generator MVA Rating 2 S where a>0 is the synchronous speed and S the generator MVA rating. The rate of change of system frequency is therefore given by

f = 2HSf Pe)- The value of H has been the subject of an unresolved controversy for many years. The initial frequency transient following a generation loss is usually a factor of two different from that predicted by the above equation with a value of H obtained by summing the mechanical inertia of all the synchronised plant. This phenomenon has been observed on several power systems on the continent; Italian, French and Norwegian and are reviewed elsewhere ( Myerscough, 1974 ) and on the British grid system during the 'Cellarhead' tests ( Ashmole, 1974 ). There are several schools of thought to explain this 'missing inertia'; one claims that the in­ ertia of the plant auxiliaries and consumer rotating machinery is sufficient to account for it, another suggests that consumer demand relief due to voltage reduction should be considered and yet another more recent one claims phase sensitive load is responsible (Brereton, 1990). However, the above equation predicts the longer-term behaviour of the frequency with an in­ ertia value equal to the sum of the mechanical inertias. Moreover, the period of oscillation of phases in the network are also correctly reproduced. Simulations with and without the network effects are described by Ashmole ( 1975 ) and are seen to agree with each other and not reproduce the test results. Recent thoughts suggest that the frequency dependence of transmission plant should be incorporated in a simulation. The total system inertia is obtained by assuming the electrical coupling between generators is sufficiently tight that the whole system may be considered to rotate in synchronism. The total inertia is then simply the sum of the inertias of the committed plant. Typical values of the per-unit inertia of a 660 MW machine vary from 2.4-3.3 MWs/MVA with more recent machines having the lower values due to an enhancement in the turbine design. Of this inertia ap­ proximately 0.8 MWs/MVA is due to the generator. The average value of the system inertia at the time of the 'Cellarhead' tests was 5.2 MWs/MVA ( Myerscough, 1974 ) and since the simulation does not incorporate any transmission modelling this value will be used.

5.5.2 DEMAND FREQUENCY CHARACTERISTICS

The consumer load connected to the power system is composed of many items of plant whose power requirements are sensitive to the supply frequency. The power output from induction motors is proportional to the difference between the supply frequency and the rotational speed - the slip. If the supply frequency reduces then so also does the demand from this load. The demand from fluorescent lighting is also frequency sensitive. In recent years, the improve­ ments in motor speed control system has lead to decreased demand frequency sensitivity. In 1982, CIGRE Study Committee 38 ( Power System Analysis and Techniques ) Working Group 02 ( Power System Dynamic Performance and Analysis ) set up a task force on 'Load Model­ ling and Dynamics' and the ensuing report draws on the experience of many utilities ( McDyer et al, 1990 ). All load models have two inputs; voltage and frequency, and two outputs; real

PhD Chapter 5 Page 84 Dispatch and Simulation Improved Generation Dispatch in Power Systems and reactive power. The report's aims were to show that the selection of a load model can influence the results of an analysis, and to outline the main elements of a load model, the degree to which the level of detail of load representation is important in various situations and approaches that have been used to obtain load models. The task force propose a load model which reduces to the following in the case of the simu­ lation of active power only, Pe = Pe0(1+*A/), where Pe0 is the electrical load at nominal frequency and R is the load frequency sensitivity. Typical values of R range between 1.5-3.0 %/Hz depending on the time of day and season. The load changes seasonally due to the increased resistive heating load in winter. Indeed, Farmer et al ( 1972 ) examined load and plant models combined with system data obtained during special work-to-rule periods and concluded that the sensitivity factor was within the range 3-6 %/Hz. However, the report does not recommend the use of this higher figure in the absence of further tests which have subsequently not been available. This model is corroborated by an EPRI report on a similar topic which verifies it with some experimental data ( Price et al, 1988 ). A universal problem with load models is that once a suitable structure has been selected, obtaining the parameters is a difficult task. The voltage and frequency dependence of various types of loads is, in general, known or can be deter­ mined. However, the composition of the various classes of load at a busbar is unknown. A paper by Berg ( 1972 ) reporting tests on the Norwegian grid shows the responses for various types of load classed as rural domestic, urban domestic, commercial and industrial.

5.5.3 DISPATCHING INTERVALS

The dispatch algorithm loads the generators based on predicted demand and if the actual demand is different due to prediction errors or plant shortfalls then this difference is met by the stored energy in the sets. Clearly, the longer the interval between one dispatch and the next more onerous the regulating duty on the plant and the more severe the thermal stresses in the materials. On this basis the dispatching interval should be a short as possible. How­ ever, the limitations of the telemetry system in obtaining the data and the finite algorithmic computational time place a limit on this. Farmer ( 1980 ) used a simple model of tranches of generating sets to examine the quality of frequency control given a random walk load model with different proportions of sustained and un-sustained regulation. The conclusion drawn from this paper was that a dispatching interval of approximately five minutes is sufficient. The greatest benefits can be obtained if the dispatch algorithm provides signals to the units' control systems thereby implementing new set points as soon as they become available. However, there is an understandable ( and justifiable ) reluctance to trust an algorithm so completely until extensive experience has been gained with computer assisted manual oper­ ation.

5.5.4 NUMERICAL PROBLEMS

The power system being simulated has n units each modelled by a system of third order non-linear differential equations resulting in (3n + 1)^ order system. The linearized versions of these equations have widely differing time constants as one intuitively expects from a fast responding turbine coupled with a slower boiler. This results in a stiff system with important implications when chosing the method used to integrate the equations. The ratio of the smallest to the largest eigenvalue of the linearized system is taken as a measure of the stiff­ ness and is typically of the order of 103 . To integrate equations such as these Hall and Watt { 1976 ) recommend a variable-order variable step backward differentiation scheme. Accuracy tests are made at each time step and are, in general, only reliable for each step individually. For most problems which are stable, that is those where no eigenvalues have positive real parts, there is no accumulation of error. This can be verified be using different tolerences and observing if the solution changes appreciably. Suitable tolerences were selected empirically as a compromise between absolute accuracy, relative accuracy and execution time.

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5,6 LOSS OF GENERATION

The frequency transient following a loss of generation will be examined by using this simula­ tor. The initial loading, for the purposes of this example, will be taken as 9 GW or 78% of committed capacity as was depicted in Figure 47 on page 81. A base load unit at Drax gen­ erating 660 MW or 7% of the initial load was lost. As can be seen from Figure 48 on page 83 a system gain of between 1.4 - 4.8 GW/Hz is available and the frequency containment will be examined with gains at these extremes.

MEAN 49 .92 Hz

TIME ( SECONDS )

Figure 50. Generation Loss Incident of 660 MW with System Loading of 9 GW: Loss occurred at time 50 seconds.

The frequency transient with the minimum gain loading profile ( case 'a' ) shows that the fre­ quency drops below the statutory limits whereas that with the maximum gain ( case 'b ') does not. The stored energy release in case 'a' from the base load Units ( 1-13 ) is very small and that due to the Units numbered 14 to 17 are shown in Figure 51 on page 87. The response from units 18-21 are simple unsustained stored energy releases. The frequency trace has turning points where mechanical and electrical powers temporarily equalise. The first turning point occurs at approximately five seconds after the loss and is the motivation behind the selection by the ESB of the primary reserve criterion { McDyer and Haren, 1980 ). Tests carried out on the South West section of the Norwegian grid showed that the frequency minimum occurred between 3.5 and 5.5 seconds depending on the magnitude of the generation loss ( Berg, 1972 ). Moreover, the frequencies at different portions of the network are not identical as the disturbance propagates from the source whose period is a function of the elasticity and impedance of the network ( Ashmole, 1975 ). This is discussed by Baker ( 1971 ) with reference to tests on the American grid carried out over a six year pe­ riod and a linear relationship relating initial peak frequency deviation and distance from the source was proposed. Thereafter the mechanical power exceeds electrical power leading to a partial frequency re­ covery. However, the stored energy soon becomes exhausted and another turning point is reached and the system once again slows. At the next dispatching interval the generation is

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Figure 51. Response of Units 14-17 in the case study Power System to Generation Loss: Unit 14, 15 and 16 were given new Power Set Points at time 300 seconds. redeployed in an optimal economic manner based on a target load at nominal frequency. The units' set points are altered and generation is then increased by changes in the firing. The previous marginal generator ( Unit 14 ) becomes a base load unit, and the next unit in the merit order ( Unit 15 ) becomes the marginal generator with a consequent increase in SMP. In this particular example Unit 16 was also part loaded due to influence of the pressure term in the objective function. The generation loss of 660 MW was completely made up by sus­ tained responses on these units. The frequency trace with the loading profile which yields the maximum system gain possible shows that much better control was achieved. The frequency in case 'b' has a mean value of 49.92 Hz and standard deviations of 0.02 Hz as contrasted with a mean of 49.51 Hz and a standard deviation of 0.64 Hz for case 'a'. The units' responses in this case are the free responses and will be modified by the influence of the plants' automatic control system. There are many combinations of control strategy employed on modern plant and possible effects of some of the most common will be discussed in following sections.

5.6.1 PRESSURE DISPATCH

The two cases depicted Figure 50 on page 86 corresponded to the maximum ( 4.8 GW/Hz ) and minimum ( 1.4 GW/Hz ) system gains possible given a demand of 9 GW. The pressure dispatch algorithm will now be used to provide a particular system gain and the performance and costs of the system considered. Shown in Figure 52 on page 89 is a plot of the minimum initial frequency - within the first 15 seconds - against the scheduled system gain. It is seen that the magnitude of this error de­ creases as the scheduled gain increases. The time at which this minimum occurred is also shown and becomes shorter as the gain increases. The time to the initial frequency minimum is crucial, as already discussed, and in the grid control room in Queensland Electricity Com­

PhD Chapter 5 Page 87 Dispatch and Simulation Improved Generation Dispatch in Power Systems mission there is an instrument which indicates the reserve necessary to contain the frequency within 6 seconds following the most onerous generation loss occurred ( Craven, 1989 ). The costs of providing this reserve are shown in Figure 53 on page 89 and are seen to in­ crease monotonically as the scheduled gain increases. The increase is gradual at first but when the gain reaches 4 GW/Hz - the maximum available within the merit order - the costs increases rapidly. The initial frequency error may be decreased at the expense of increased system costs and this must be traded against the reserve provision costs associated with other types of plant as are discussed in the following sections and the value attached to reg­ ulation as discussed in Chapter One. The spinning reserve policy may then be formulated at corporate level to provide the required level of security.

5.6.2 STEAM PRESSURE CONTROL

5.6.2.1 BOILER FOLLOWS TURBINE

In this scheme the fuel input is used to control the pressure and when the frequency drops the governor opens immediately and the initial response is unaltered. The pressure drop signals the need for extra power and this appears at the generator terminals after a time delay de­ termined by the boiler. The primary response is unaltered but there is additional secondary response due to increases in firing. The output power will increase to restore pressure to its set point. The maximum increase in output power can be read from Figure 4 on page 19 with the fully open valve { (f> = 1.0 ) and the set value for pressure. The steady state output for a sustained frequency drop will be that value of load which would result if the valve is opened fully at set point pressure. There is coupling between the frequency recovery and the power output. If the controller has a bias term in its set point to account for frequency deviations then the unit will ramp up to MCR. Examples of such responses may be viewed in the SC39-04 plant tests at Grain ( McNamara et al , 1989b ).

5.6.2.2 TURBINE FOLLOWS BOILER

If the steam pressure is controlled by the governor valve any movement thereof causing the pressure to change will be immediately annulled by this fast acting control loop. Examples of such responses can be viewed in the SC39-04 tests at Matimba ( Carvalho, 1990 ). The primary and secondary response of such units will be very small and they will only be rede­ ployed at the next dispatch interval.

5.6.3 OUTPUT POWER CONTROLLERS

Output power controllers are often incorporated in conjunction with the above boiler control strategies and will also annul any automatic action which results in a change of power output. However, if the controller has a frequency bias term the primary response should be unaf­ fected and the secondary response will be made available by increases in firing.

5.6.4 UNIT CO-ORDINATED MODE

There are several hybrids of the above control strategies which attempt to incorporate the advantages from both schemes. Power output and pressure set points are fed directly to the boiler and turbine simultaneously to obtain smoother co-ordination of boiler and turbine per­ formance.

5.6.5 GENERALISED PREDICTIVE CONTROL

The application of Generalised Predictive Control ( GPC ) to obtain a better response from the plant has been examined using the reference model described in Chapter Four by Rossiter et al ( 1990 ). This design of this scheme relies on advance knowledge of plant manoeuvres, provided by a dynamic dispatch algorithm, to optimise the plant response. The results of this

PhD Chapter 5 Page 88 Dispatch and Simulation Improved Generation Dispatch in Power Systems

SYSTEM COSTS CASE STUDY N U (P(D

SI □ £ f—f M- £ >- u uiz i ZI C3 Ul CL U. I-a

t-f£ h-

Sustem Load 9 GU

Figure 52. Maximum Initial Frequency Error and Time at Which it Occurred: The Minimum Fre­ quency occurs within the first 12 seconds.

SYSTEM COSTS CASE STUDY

System Load 9 GU

Figure 53. System Costs and Scheduled Gain: The Costs escalate when the gain exceeds 4.0 GW/Hz.

PhD Chapter 5 Page 89 Dispatch and Simulation Improved Generation Dispatch in Power Systems study showed that the response was somewhat better than PID control with advance know­ ledge and no worse without.

5.7 OTHER RESERVE PROVISION OPTIONS

There are many means of providing active power reserve on a power system each having different timescales and costs. Some of the most common will now be described and likely costs discussed.

5.7.1 PUMPED STORAGE

The potential energy of water stored in reservoir can be used to drive turbines and provide reserve. This is a limited resource and judicious planning of the operation must be made. The usual practice is to place water in the reservoir at times of low load when the SMP is small and to generate for peak lopping purposes. There is a cost benefit if the low toad SMP exceeds the peak load SMP by a sufficient margin to cover pumping losses. Savings are also made by avoiding the startup costs of a thermal generator for a short period. As a result of the presence of energy storage in this form, this type of plant is often used to provide reserve. However, because it has limited energy capacity special treatment is nec­ essary in a dispatch algorithm. If a single price were attached to this reserve, similar to the thermal generators, once it became committed it would be used until all the water was de­ pleted. This is overcome by providing a target reservoir level as a constraint in the optimi­ sation. This target in computed in advance so as to minimise system costs ( Broadbent et al, 1987 ). The operating modes of a pumped storage units will now be discussed with reference to the Dinorwig pumped storage station owned by the National Grid Company of England and Wales. A pumped storage station is designed for typically 10s mode changing operations in its life­ time. If frequency is badly controlled and the regulating duty of the units are increased then the station will not reach its design life.

5.7.1.1 SPINNING IN AIR ( GENERA TING DIRECTION )

The turbines consume approximately 4 MW from the grid and remain synchronous with it. A frequency transient will activate the set which temporarily consumes another approximately 20 MW before providing full output within ten to twelve seconds. This requires power from the grid in the initial period and does not therefore assist with primary spinning reserve and, in­ deed, exacerbates the problem. However, it is a very valuable source of secondary reserve.

5.7.12 GENERATING

Pumped storage generators, like any other generators, will have an output as requested by dispatch depending on the water price. It could be at maximum loading, minimum loading, or some intermediate output. If it is not at maximum output the water turbine has a very high droop of the order of 1%-as extra water may be provided almost instantaneously.

5.7.1.3 PUMPING

The water is replaced by reversing the turbines and pumping. The pumping load is 290 MW and may be switched out immediately if there is a grid emergency thereby providing reserve.

5.7.1.4 SPINNING IN AIR ( PUMPING DIRECTION )

This mode is a transitory mode before pumping is actually preformed and is of no interest to the load dispatchers. It requires approximately 4 MW from the grid and awaits favourable conditions to draw the remaining pumping load.

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5.7.2 GAS TURBINES

This plant has very high running costs but are often used for peak lopping purposes where they are cheaper overall than incurring the startup costs of a thermal generator. This plant is also often used to provide secondary reserve within three to five minutes and is started by automatic under-frequency relays or directly by the load dispatcher. This plant has low capital cost and is therefore economically sound with a low load factor.

5.7.3 STORED ENERGY RELEASE ON STEAM PLANT

The stored energy provided by throttling the HP steam flow is often refered to as throttle re­ serve and has been the main subject of this thesis. There are other means of providing re­ serve on steam plant, some requiring special measures and others available quite easily. These will now be discussed and the likely costs involved indicated.

5.7.3.1 CONDENSATE STOP VALVE

Steam is bled from the turbine to heat the feed water as discussed in Chapter Three. This reduces the turbine output as each unit of steam bled does not pass through all the turbine stages but is beneficial from a thermodynamic point of view ( Fenton, 1966 ). However, in an emergency situation, if some means were possible to overide this temporarily then the bleed steam would pass through all the turbine stages and increase the power output. This would have the effect of making the overall cycle less efficient in the short term and increase repair costs due to increased material stresses when the valve is opened and closed. Such a facility was developed by Siemens and was retrofitted in Rheinhafen power plant in Germany, owned by Badenwerk AG. This was designed to meet the DVG requirement for reserve placed on all plant in Germany discussed in Chapter One. The operating experience with this system described by Futterer et al ( 1989 ) and by Kinn and Kline { 1990 ).

5.7.32 IPfLP THROTTLING

The hot reheat steam may be throttled by interceptor valves prior to entering the IP/LP turbine trains as shown in Figure 13 on page 28. Although the temperature contours on the Mollier diagram show no dependence on entropy at reheat pressures, as seen in Chapter Three, the isenthalpic entropy increase deteriorates the cycle efficiency severely. However, primary re­ serve will be increased as the reheat time constant will be reduced.

5.7.3.3 STORED ENERGY RELEASE BY OTHER MEANS

The stored energy released when the throttle valves are opened is mainly due to the de­ creased metal temperatures in the steam generating circuits and superheat sections prior to attemperation. This is^consequence of depressurfysation and the associated drop in satu­ ration temperatures. The metal contained between the governor valve and the first stage at- temperators provides no stored energy as its temperature is controlled. This is a vast source of stored energy when the typical metal masses are considered. A novel method of extracting this stored energy was proposed by O'Connor and Egan by reducing the live steam temper­ ature set points in an attempt to raise steam by cooling this metal ( McNamara, 1989d ). A second method proposes that feed flow be reduced thereby decreasing the sensible heat requirements of feed water entering the drum. This sensible heat is then diverted to latent heat evaporating more water to produce additional power in the turbine. This has the added advantage of reducing feed pump power requirements and thereby contributing to primary spinning reserve. A limit is placed on this by the tolerable drop in drum level. A series of simulations performed on a reference model for Drax power station described in Chapter Four and operational tests carried out at Moneypoint power station in April 1990 and are discussed in Appendix D and reported by McNamara and Canning ( 1990a ).

PhD Chapter 5 Page 91 Dispatch and Simulation Improved Generation Dispatch in Power Systems

5.7.4 COMBINED CYCLE GAS TURBINE

This plant uses the exhaust gas from gas turbines to raise steam which is then expanded in steam turbines to produce useful work. This plant has a very quick return on capital and boasts operating efficiencies of greater than 50%. Such plant is becoming very popular and has been in use for many years in countries such as Turkey ( at Ambarli ) and Ireland. A very fast pickup is possible by increasing the exhaust gas temperature set point and thereby producing more load in the gas turbine. However, the boiler manufacturers strongly discour­ age this practice as the material stresses thereby induced are claimed to be onerous ( Joyce and Mayer, 1986 ). The ESB have been operating Combined Cycle plant since 1983 at the North Wall Power Sta­ tion in Dublin. The gas turbine ( GT ) generates 110 MW ( base ) and capable of 120 MW (peak). The usual mode of operation is that the GT generates 85 MW and the steam turbine ( ST ) generates 35 MW. A relay senses the rate of change of frequency and if it exceeds a threshold raises the GT gas exit temperature set point thereby ramping the set to 120 MW on the GT and 8-10 MW on the ST within six to eight seconds. This contributes 45 MW to primary and secondary spinning reserve. Downey ( 1988 ) discusses the operation of these sets and others at Marina in Cork Harbor and their role in system security. The operational efficiency of the gas turbine depends primarily on the firing temperature which decreases with load. Consequently, a gas turbine de-loaded as above will not be op­ erating at its optimal efficiency. Nevertheless, other factors such as metal creep, which is exponentially dependent on temperature and is the primary life limiting consideration, are reduced at the lower temperatures ( Davis and Jones, 1988 ). In surmise, the deloading for spinning reserve purposes has a beneficial effect by reducing the material creep and an ad­ verse efficiency effect. Since commissioning, the North Wall set's total time in a spinning reserve mode has been approximately 15,000 hours and it was desirable to examine the materials to quantify the re­ serve provision penalties. Investigations were carried out by the ESB during an extensive maintenance in Summer 1990 and suggests that there are no deleterious effect caused^n- voking this unit for spinning reserve purposes.

5.7.5 MISCELLANEOUS

5.7.5.1 SYSTEM INERTIA

The initial rate of change of frequency is proportional to the ratio of the power imbalance to the system inertia. In island power systems where the ratio of the largest generator to the system size is large the initial rate of change of frequency can be high and load shedding comes into operation before any remedial measures can be taken. This problem is exacer­ bated in a system where the generation is concentrated into a small number of very large units thereby resulting in a system with a small inertia. Such problems have been prevalent on the NIE system for many years and attempts have been made to increase the inertia by designing a flywheel. The design of the flywheel con­ sisting of a pony motor and induction generator is described by { McArdle et al, 1989 ). The induction generator provides energy to the grid when activated by an under-frequency relay. The original intention was that it would provide 20 MW of power for four minutes until standby gas turbines were started. This would require an inordinately large flywheel of three meters long and three meters in diameter suspended in a vacuum to reduce losses to 500 kW. For­ tunately, simulation studies indicated that the application of a large initial pulse of power would be sufficient to alleviate the short-term frequency and load variations leading to a much simpler design. The scheduling of the flywheel is reported by Thompson et al ( 1989 ) where it is represented as generator drawing power from the grid and is committed when the value of reserve ex­ ceeds the cost of the losses. The presence of the flywheel was seen to reduce system fuel costs by 0.21% with no reduction in system reliability.

PhD Chapter 5 Page 92 Dispatch and Simulation Improved Generation Dispatch in Power Systems

5.7.6 STORAGE SCHEMES

Electric energy can be stored in a variety of ways of which pumped storage and flywheels al­ ready mentioned are examples. Other storage schemes include compressed air storage, thermal storage by steam and oil, battery storage and Hydrogen storage. The following dis­ cusses battery storage.

5.7.6.1 BATTERY STORAGE

The use of batteries to store electric energy diminished with the advent of ac power system at the beginning of the century but has recently come back into favour due to increases in battery technology resulting in high reliability and energy efficiencies of the order of 87%.

In the West Berlin system ( BEWAG ) acute reserve provision problems lead to the installation of a 8.5 MW / 17 MWh Battery Storage Plant { BSP ) in 1986 { Voigt et al, 1989 ). The design of this plant was primarily driven by the reserve requirement to provide 8.5 MW for 30 minutes and is available instantly. In addition, the BSP plant assists with load levelling and load fre­ quency control. BSP also finds an application in the West Berlin public transport system where the transport peak occurs simultaneous with the electrical demand peak thereby exa­ cerbating the reserve problems.

BSP is also used in the United States at Chino, California where the Southern California Edi­ son Company installed a 10 MW / 40 MWh plant ( Rodriguez, 1989 ) and is shown in Figure 54 on page 94. The primary benefit is derived from the opportunity to purchase cheap energy from outside Edison's territory during off-peak hours. The battery system is designed to supply 10 MW for up to 4 hours with a lifetime of 2000 cycles or 8 years normal operation. A study was made of the economics and availability of off-peak energy in the United States by Huse et al ( 1975 ) resulting in a generalised relationship between the total off-peak energy, annual load factor, percent base load factor and energy storage conversion efficiency. A two year test phase was started in Summer 1988 to demonstrate the compatibility and reli­ ability of the system to effectively manage loads on a daily basis and to determine the actual operation and maintenance costs. The plant was intended for peak shaving but the current ( August 1990 ) operating mode is predominately load following.

5.7.7 LOAD SHEDDING RELAYS

Once the above means of reserve provision have been incorporated in the simulation the setting of the load shedding relays can be then be determined requiring a knowledge of the demand relief available at a particular relay. This could also be used to help form the cor­ porate spinning reserve policy if the number of consumers at a given relay were known.

Most relays disconnect consumers if the frequency drops below a treshold. However, if the relay did not operate the frequency would, in most cases, recover and rise above the treshold and the time at which the frequency was below the treshold was inconsequential. When the relay operate the effective spinning reserve due to demand relief results in a frequency re­ covery thereby causing a reduction in the utilisation of thermal reserve. Consequently, a sit­ uation arises where reserve has been provided with cost penalties but cannot be utilised. More recent load shedding relays have a facility to incorporate a time delay and load is only disconnected if a sustained frequency error occurs. This system gives the thermal reserve every opportunity to respond thereby affording maximum utilisation of the reserve. The sim­ ulator could also be used to determine this delay time.

PhD Chapter 5 Page 93 Dispatch and Simulation Improved Generation Dispatch in Power Systems

Kb!T' lT

Figure 54. View of the Battery Strings in the Chino Facility: Courtesy of Southern California Edison Company.

i

PhD Chapter 6 Page 94 Conclusions Improved Generation Dispatch in Power Systems

6.0 CHAPTER SIX - CONCLUSIONS AND RECOMMENDATIONS

6.1 CONCLUSIONS

This ha;T thesis examined current practices in Energy Management Centres regarding dis­ patch of active power and reserve. The representation of power plant models in dispatch systems was investigated and seen to be lacking in certain respects. The ability of the power plant to provide primary reserve was identified as being a function of both its loading level and its operating pressure. The idea then emerged that better accountability of the amount and cost of reserve could be made if the pressures of the generators were known. A certain amount of reserve could then be scheduled by a dispatch algorithm with a knowledge of these relationships. Towards this end suitable dynamic power plant models were investigated and the ability of the generators to provide reserve was examined. A series of plant tests were then conducted to deduce the disposable parameters of these models and to examine the variation in reserve provision abilities of various tranches of plant. The parameters of such models were esti­ mated by a least squares algorithm. The costs of operating at pressures above sliding were then investigated by considering the thermodynamics of the boiler and turbine using empirical relationships and the ellipse law. Having gained an appreciation of the mechanisms by which losses occurred a further series of plant tests were carried out to confirm the presence and magnitude of these effects. The conclusion was then drawn that pressures above sliding were detrimental to heat rate. An enhanced algorithm was presented which included both relationships and demonstrated that improved standards of frequency control could be traded against the cost of its provision following a generation loss incident. A method of trading this improved performance with other means of providing reserve were discussed and shown that corporate level decisions were needed to formulate the spinning reserve policy. The main conclusions are summarised as follows;- 1. The reserve provision ability of power plant decreases with output power and increases with operating pressure;

PhD Chapter 6 Page 95 Conclusions Improved Generation Dispatch in Power Systems

2. The power plant heat rate deteriorates with increased governor valve pressure drop for a given load; 3. The non-linear plant model proposed adequately represents the reserve provision abili­ ties of plant; 4. The enhanced dispatch algorithm attaches a cost to reserve and gives a utility the op­ portunity to decide how much it is prepared to pay for frequency control.

6.2 NOVEL IDEAS PRESENTED

This thesis investigated the feasibility of pressure dispatch in the context of power system operation to obtain the required standard of frequency control at minimum cost. The main ideas presented are summarised as follows;- The inclusion of a power plant's operating pressure in the generation dispatch algorithm as a means of providing reserve; Attaching a cost to operation at various pressures and thereby an objective for minimi­ sation; Deducing these costs on-line from the plants control room instrumentation when a period of steady running was established in terms of a statistical tests on comparison of the means. The algorithm for estimation of the the plant model parameters from test results; The methods of extracting stored energy presented in Appendix D from the superheater metal and the mass of water in the drum.

6.3 RECOMMENDATION FOR FURTHER RESEARCH

There are many directions for future research and they are summarised by the following;- Secondary Regulation The ability of the power plant to provide secondary reserve should be investigated by incorporating the control strategies of various units into the simulator. The parameters of such controllers can be deduced from the test-work carried out by Working Group 4 in a similar manner to the model parameters. Customisation The thesis addressed principles common to all utilities and broad de­ ductions were made on the feasibility and desirability of pressure dispatch. To establish the true value of the schemes proposed a simulation should be constructed incorporating all the plant on a particular system and all the reserve provision options mentioned in Chapter Five. The exact benefits of the proposals could then be evaluated. This would also assist in making corporate level decisions on spinning reserve policy and deciding the optimum load shedding relay set points. Model Performance Chapter Five compares the test and simulation results for the model at one particular operating point. The tests should be repeated and fits obtained at many different operating points and confidences established on the estimates. Sensitivity stu­ dies on the costs can be made and error bounds constructed. Adaptive Estimation Establishing plant model parameters on-line either continuously or following a generation loss incident should be investigated. Special instrumentation to log station parameters and telemeter them to the Energy Management Centre would be needed. The performance of the existing simulator and its 'current' parameters could also be gauged. Heat Rate A more detailed analysis of the heat rate of a unit should be made particularly in respect of the boiler where it was assumed constant. The heat pickup in the econom­ iser and stack losses should merit special attention.

PhD Chapter 6 Page 96 Conclusions Improved Generation Dispatch in Power Systems

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• Rossiter, J.A., Kouvaritakis, B. and Dunnett, R.M., 1990, 'Application of Generalised Pre­ dictive Control to a Boiler Turbine Unit for Electricity Generation', NGRDC Report NGRDC/L/TSP/0053/M90. • Rumpel, D., 1988, 'Towards an Improved Coordination of Power Plant and Power System Control', IFAC Symposium on Power Systems; Modelling and Control Applications, Brussels, Sept. 1988. • Rumpel, D., 1987, 'Power Plant Representaion in Dispatch Systems', CIGRE Study Com­ mittee 39 Meeting in Tokyo Japan, paper No. SC 87, Oct. 1987. • Shapiro, A.H., 1953, 'The Dynamics and Thermodynamics of Compressible Fluid Flow', Vol. 1 and 2, Ronald Press, New York. • Sidders, J.A., 1989 'ANYDYM A Fossil Fueled Fired Total Plant Mathematical Model', GDCD Report, PKR/SE/255. • Keller, H. and Urban, B., 1989, 'ANCYCLE - ein Diagnosesystem zur Thermodynamik von Dampfturbosatz und Wasser-Dampf-Kreisauf', Seimens Service Report, Kraftwerk, No. 11, pp. 18-22. • Silverstri, G.J. Aanstad, O.J. and Ballantyne, J.T., 1972, 'A review of Sliding Throttle Pressure for Fossil-Fueled Steam Turbine Generators', American Power Conference, 1972, Vol.34. • Skrotzki, B.G.A. and Vopat, 1950, 'Steam and Gas Turbines', McGraw Hill, New York. • Stodola, A., 1927, 'Steam and Gas Turbines', Vol. 1 and 2, translated into English by L.C. Loewenstein, McGraw Hill. • Tamura, Y., Yorino., N, Sasaki, H. and Hagiwara, S., 1988, 'A New Method of On-Line ELD for Thermal Power Plants', IFAC Symposium Power Systems, Modelling and Control Ap­ plications, Brussels, pp. 15.1.1-7, Sept. 1988. • Thompson, J.G., Fox, B., McArdle, J.M. and Tindall, C.E., 1989, 'Scheduling of Short-Term Flywheel Energy Storage Device in an Isolated Power System', 24 UPEC, Belfast 1989, pp. 623-626. • Vlahos, K. and Bunn, D., 1988, 'Benders' Decomposition for Mixed-Integer Programming - Application to Electricity Generation Capacity Planning', London Buisness School Dis­ cussion Paper, General Series GS-29-88, September 1988. • Voigt, B., Kunisch, H.J. and Kramer, K.G., 1989, 'On the Operation of Large Scale Battery Storage Systems', CIGRE Symposium Bangkok, Nov. 1989. • Walters, P.T., 1987, 'Wetness and Efficiency Measurements in L.P. Turbines with an Op­ tical Probe as an aid to Improving Perfomance', Journal of Enginneering for Gas Turbines and Power, Vol. 109/85, Jan. 1987. • Winokur, M. and Pe'er, A., 1986 'Unit Response Improvement to Enhance Security of Iso­ lated Power System', Second International Conference on PSMC, University of Durham 1986, pp. 102-106.

• McCracken, H.. Ferguson, M.A. and Flanagan, S.G. (1986), 'Generating Plant Transient Recording Equipment'. IEE PSMC Conference, pp. 378-383, Durham 1986.

Page 102 References Improved Generation Dispatch in Power Systems

TAXONOMY

AG Aktiengesellschaft ( Shareholder Company ) AGC Automatic Generation Control BSP Battery Storage Plant BEWAG Berliner Elektrizitatswerk AG CEGB Central Electricity Generating Board CIGRE Conference Internationale de Grand Reseaux Electriques International Conference Large High Voltage Electric Systems CPU Central Processing Unit DVG Deutsche Verbundgesellschaft ENEL Ente Nazionale per L'Energia Elettrica, Italy ESB Electricity Supply Board, Republic of Ireland ESCOM Electricity Supply Commission of South Africa FD Forced Draft ( Fan ) GI74 Analogue and Digital Telemetering ( General Indiacation 1974 Version ) GPC Generalised Predictive Control GT Gas Turbine HP High Pressure ID Induced Draft ( Fan ) IP Intermediate Pressure IEC Israel Electric Corporation LFC Load Frequency Control LP Low Pressure MCR Maximum Continuous Rating NIE Northern Ireland Electricity NP National Power Company pic, England and Wales PG Power Generation Company pic, England and Wales PID Proportional, Inegral and Derivative ( Control) SCADA Supervisory Control and Data Acquisition SC39 CIGRE Study Committee 39 entitled Power System Operation and Control SC38 CIGRE Study Committee 39 entitled Power System Analysis and Techniques SMP System Marginal Price ST Steam Turbine RMS Root Mean Square RSA Republic of South Africa WG04 Working Group 4 of Study Committee 39 entitled Power Plant Control

Page 103 Taxonomy Improved Generation Dispatch in Power Systems

Appendix A. LINEARISATION OF PLANT MODEL EQUATIONS

The model equations in state space form are:-

X '= b' x* ~ l t + - 11

*2 = ^ U2~’[(1 + 2b6°fxi)1/2 - 1] - b4X2,

X3 = b9U, - b 9X3,

V1 = ^ U2"2[(1 + 2b6u2x i)1'2 - 1]'

Y2 = Uj"1[(1 + 2b6u fx ,)1/2 - 1] +b8X2.

It is required to linearise these about an operating point X0 and l/0, that is for small perturba­ tions of X and U

X = X q + x, U = U0 + u.

A.1.1 STATE MATRIX

The n x n state matrix ( 3 x 3 in this case ) will be given by;- _ Jtyj______~ b2U02 ®11 “ a x , + 2(, 6u 022x 01)1'2

312 = 0 , a13 = b1t

PhD Appendix A Page 104 Lineraisation of Plant Model Equations Improved Generation Dispatch in Power Systems

b3U02

a 21 ~ (1 + 2b6U^X01)112 '

a 22 = ~ b 4 ’

a 23 = °- a31 = 0-

a 32 = 0-

J33 ~bQ.

A.1.2 INPUT DISTRIBUTION MATRIX

The n x m input distribution matrix ( 3 x 2 in this case ) will be given by;-

b-n = - ^ - = 0, 11 dU,

2A01 '>i 2 = - 5V [(1+ 2 ^ o22Xc )1,2- 1 ] - 2b,X' bGUQ2 (1 + 2 b6u*2x0, y 12

/?21 = 0,

3a 01 ft22 = — ^ - [( + 2b6u022x0i) 1,2- i ] + 2b’ Xl bcUr' 6U02 (1 + 2 fi6U022X01)1'2

^31 — ^9’ b32 = 0.

A.1.3 MEASUREMENT MATRIX

The / xn measurement matrix ( 2 x 3 in this case ) will be given by;- 001 1 C11 — 5*1 (l+ 2 b 6U022X01),/2 '

C12 — 0,

c 13 “ 0 ’ b7U02 c2^ ~ (l+ 2 b 6U022X01)1/2 '

c22 = ^8> C23 = 0.

A.1.4 FEED FORWARD MATRIX

The t x m feed forward matrix ( 2 x 2 in this case ) will be given by;-

PhD Appendix A Page 105 Lineraisation of Plant Model Equations Improved Generation Dispatch in Power Systems

■2[(1 + 2bsU^Xmy '2 -1 ] 2X(01 di2 - + bKU,6^02 U02(1 + 2{,6U022X01)1/2 — 0,

-b 2/?7X0i d22 = ----- [(1 + 2i>6l4,X01)1/2 - 1] + b6U02 (1 + 2b6U022X01)1/2

A.2 CONTROLLABILITY AND OBSERVABILITY

Kalman's criteria for controllability and observability are formulated in terms of the n x nrn matrix r and the /n x n matrix 0 where, r = [B,AB...... An- ' B \ (an — b9)bib3i a^b12 12 bibc 0 0 ai0b12^12 a12^1^31 — bgb^ 0 a 12^ 12(a 11 a 22 ) ^ 22a 22 bib9^31 0 and

0 = n—1 CA

'11 0 0 ’21 c 22 0 ’21 a 1 1 0 c 11b 1 *21a 11 + c 22a 12 c 22a 22 C21 f?1 0 ;11a ?i 2 c 1 1 ^ 1 (a 11 2 Cggb c 2 1 ^ l( a 11 ■21a 11 + a21C22(a 11 + a22) For complete controllability rank T = n and this system is completely controllable as rank T is 3. For complete observability rank 0= n, and this system is completely observable as rank 0= 3.

PhD Appendix A Page 106 Lineraisation of Plant Model Equations Improved Generation Dispatch in Power Systems

Appendix B. LAPLACE TRANSFORMS

From Appendix A the linearized system was found to be

0 *>1 ' bi2 _d_ x 1 \ / a 11 0 dt x 2 = a 21 a 22 2 U S b22 0 © ■ X3/ \ 0 a 3 3 '31 0

II C 11 0 c 2 2 C21 S)() so © The Laplace transform of the outputs with respect to the inputs is defined by Y(s) = Cd>(s)x(0) 4- [C(s)B 4- D](7(s).

Preforming the required multiplication yields

c^^'11 ^11^1

(s — a^) 0 (s — a11)(s 4- bg) O CM O CO y2(S)_ C21 c22a 21 '22 c22a 21 + C21 + (s ~ an) ( s - a 11)(s -a 22) (s-a^) (s - a^Xs - a22) [• (s + bg)

C11^31^1 ^12a "F {b^2*'^^ — ^12a1l)

/ (S ~ a1l)(S + bg) (S ail) ^ 1 (s)\ + U 2(s )J ' \ c2'\b3^a^3s ~F (c22^3i a 2i ai 3 bgC2-|b31a13) d22s 4- A>)S 4- Const

\ (s — aa11)(s n ) ( s —— a22)(sd u ) ( s— —a33) (s ~ anXs — a22) where Const 7 d22a11a22 — ^2l^i2a22 — b22c22a-j-j 4*c22b^2a 2-1 = 0, which can be shown by substitution, and Ai = c21b12 4" b22c22 — d22(a22 4*a-)'))-

PhD Appendix B Page 107 Laplace Transforms Improved Generation Dispatch in Power Systems

Appendix C. LINEARISATION OF GOVERNOR GAIN EQUATIONS

The expression for governor gain deduced in Chapter Two is given by,

G(W° Ps°) = w9((1)a^ech2(W 0), where and P? are the linearisation points and where

4>o —

and wg(fi) = A2 exp(a11f1) 4- A3 exp(a22f1),

where Az and A3 are dependent on the operating point and an and a22 are entries in the A matrix. It is required to obtain linearized relationships for the expression for the governor gain in terms of the operating point variables and P£. This problem will be linearized term by term and then combined.

C.1.1 TERM 1

The first term Y1 = exp(a11f1), can be rewritten in the following way for ease of differentiation, a22 — ^22a1l) In ln|yi|= 7^s!(a22/an) an(P — d22a22) where

P = C21fe12 ^22^22’ Differentiating this with respect to and P? gives

PhD Appendix C Page 108 Linearisation of Governor Gain Equations Improved Generation Dispatch in Power Systems

a22(P ~ ^22a1l) 1 a22(P ^22a1l) I + In Y1 dWg aw2 V 1 - (a22/an) a^(P — (^22^22) 1 — (a22/a1l) 5IC a11(p d22a22) I and similarly for P?. The first term is given by ( noting that a22 is a constant),

d ( 111 -«-( ____ 1 ^ \ — a22 ^a'1 3tv2 V ^ _ (a22/a11) / (an — a22)2 dl/Vp and similarly for Pf. The second term will is given by

a1l(P — d22a22) 0 a22(^* — ^22a1l) — a22(^ ~ ^22a1l) 0 a1l(^ d22a22) a22 (P — ^22a1l) aWg awjj In a11 (P ^22a22) aw.’9 a121a22(P — c/22a22)3(^ — ^22a1l) where

8P dd 22 5a 11 0 a22(P — ^22a1l) ~ a22 — a - a22^22 dW, dW% " < aw; and a ap ^ai 1 dd, 22 5"ail(P — <^22a22) = a11 ~ 5" + (P d— 22a 22) 5" ~ a 11a 22 ~ 5” > dWg dWg dWg 8\Ng and similarly for Ps°. The variables au, a2t, c1h c21, b12, b22, d12, d22 are dependent on the operating point and their sensitivities must be determined and a13, a22l b13, a33 and c22 are constants as was seen in Ap­ pendix A.

da a 0 = ~ b2 0 dW, dW, ’

da. 21 ap 0 = b* 0 ’ dW, aw

dc 11 6R BP” PSPS aw” aw° w° w.

ac2i dR = b aw° 7 aw° and similarly for PJ, where w; R = (B2(P°)2 + 2b6(W°)2P° + 2 b6«,(W”)4)0 \4 \1 /2 - and similarly for P?, where

kA = B2

dR [ B 2( P s f + 2d6(W ° )2P ° + 2b6/fi (W g)4]2b6(Wg)2(Ps + + 2/Ci(W °)2)

aw. (b 2(Ps0)2 4- 2b6(Wg)2P? + 2b6/Ci(W°)4)3/2 and

PhD Appendix C Page 109 Linearisation of Governor Gain Equations Improved Generation Dispatch in Power Systems

-W °(B2P° + b6(W°)2)

(B \P °)2 + 2b6(W°)2P° + 2b6A1(W°)4)3'2 '

Defining B(PS0)2 + k,BP°s(W °f S = (B2(P °f + 2be(W°)2P° + 2b6*1(W°)4)1'2 ' simplifies the following,

db12 b2 - BP dR BP* 2 B2(P°s)2 dS + 4- 2b dW°g bG WgR2 dW\ (W°p)2R ( < ) 3 2 dW°g

db -12 b2 BP dR 2 S2P° + e + 2b as dP° bQ WgR2 dP\ (W°)2 2

db -b . BP 2 e2(P°)2 22 ~ eps a* + -2 b as aw. WgR2 dWr (W0g)2R w 3 < K

db 22

dcl^ 2 aw£

ad, dP

dd. 22

ad22 dP 0~

The sensitivity of S will be given by

j S __ (b V s)2 + 2b6(W°)2P° + 2b6k1(W°)4)(2BP? + ^ (W g )2) + BPS°(PS° + ^ Wg)(fl2P° + b6(Wg)2)

ap? (b 2(Ps0)2 + 2 be(W °fp° + 2 b ^ i W ^ f 12 and

ds 2/c1BP > °(b 2(Ps0)2 + 2b6(W°)2P° + 2b6/c,(W°)4) + BP°(P° + ^(W°)2)2b6iyg(Ps° + 2k,(W °f)

dW; (B2(P°)2 + 2be(W0g)2P0s + 2b6*1(W#4)3/a

PhD Appendix C Page 110 Linearisation of Governor Gain Equations Improved Generation Dispatch in Power Systems

C.1.2 TERM 2

The second term is given by, V2 = A2, where P — ^22a22 (aH ~ ^ 22) dP dd22 dd 22 da -1 (a11 ~ a22) — a — (P — d22a22) dY2 dwl 22 Swg dW° (a11 ~ a22)* and similarly for P£.

C.1.3 TERM 3

The third term is given by, Y3 = ^3, where A _ a11^22 ~ p 3 (a11 “ a22)

5^22 , 5a11 dP da* 4 (a11 “ a22) + d22 0 “ (d22a11 5Yo 11 awg° aw, aw, ______^11 a22)2 and similarly for PP.

C.1.4 CHARACTERISTIC

V4 = sech2z, where W z = — tanh' *BP

The sensitivities are therefore given by av4 = — 2sech2z tanh z aw. aw,0 ’ where dz 0 ’ dW° 1 -(w°laBP°f aBP. s and

dz -W, dP® 1 - (W°/<*BPS°)2 aBP,0 ’

PhD Appendix C Page 111 Linearisation of Governor Gain Equations Improved Generation Dispatch in Power Systems

C.1.5 TERM 5

The fifth term is given by, y 5 = exp(a22f1). 0Y5 — exp(a22f-,) da^ dWg a 22(an /a22 1) dWg

G = Y2Y,Y4 + Y3Y5Ya. This may be linearised by an Taylor expansion where G = G° -f- AG, where

ag = y£[vy., + vy4]Ax + y 1°[vy 4 + vy2]Ax + y j[v y 1 + vy2]Ax + yj[v y 3 + vy5]Ax +

y 50 [vy 3 + vy4]Ax + y 3°[vy 5 + vy 4 ]Ax, where dYj dY® vy,= dW°g ' dP°s and

Ax = "a w °" Lap?J'

The entries in the A, B and T matrices given by the above equations are quoted in Table 18 and were verified by linear regression.

Unit a P y Fawley Unit 2 0.0350 -1.4438 1.2330 Fawley Unit 1 0.0222 -1.1932 1.2120 Drax 0.0328 -1.4909 1.3685 Grain 0.0299 -1.0642 2.2149

Table 18. Coefficients of the linearised governor gain equations: Plants correspond to those in case study of Chapter 5.

PhD Appendix C Page 112 Linearisation of Governor Gain Equations Improved Generation Dispatch in Power Systems

Appendix D. NOVEL STORED ENERGY TECHNIQUES

D.1 INTRODUCTION

The release of stored energy initiated by governor action to provide active power reserve has been the primary subject of this thesis. The energy liberated is due to metal cooling of the steam generating circuits and superheat sections prior to attemperation. The energy associ­ ated with the remaining superheat sections, the reheater and the mass of water in the drum is not released. This Appendix reports simulated and operational tests to investigate these sources of energy. The operational tests were carried out at Moneypoint Power Station over the two day period 5-6 April 1990 during routine heat rate tests. Moreover, these tests provided the data from which the power plant model parameters of Chapter Four were deduced.

D.2 SIMULATED STORED ENERGY TESTS

The release of stored energy following a generation loss is initiated by opening the governor valves and reducing the impedance to steam flow. This reduction in impedance results in an immediate increase in steam flow and subsequent depressurisation of the boiler. A decrease in the saturation temperature of the steam accompanies this drop in pressure and a conse­ quent decrease in the metal temperatures in the steam raising circuits and superheat sections prior to attemperation. The energy liberated is transferred to the steam and produces extra power when it expands in the turbine. A stored energy test of this type will be known hereafter as a Type 1 test. Typically, in the evaporator of a drum boiler one third of the heat input is used to raise the feed water temperature to saturation ( sensible heat) and two thirds are used for evaporation (la­ tent heat). In an emergency situation, if some means of diverting sensible heat to latent heat could be found then the steam generation would increase resulting in increased electrical power. This could be accomplished by reducing the flow of feedwater into the evaporator, allowing drum level to drop and thereby reducing its sensible heat requirements. The deficit is then diverted to latent heat resulting in increased steam generation. The practical imple­ mentation of this would be via the feed pump whose power requirements would also be re­

PhD Appendix D Page 113 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems duced thereby providing further valuable primary spinning reserve. Some power increase will also be due to reduced bleed steam requirements of the feed heaters. A stored energy test of this type will hereafter be known as a Type 2 test. The metal comprising the superheaters, after the first stage attemperators, and reheater does not contribute to this stored energy as their temperature is controlled. In the case of the su­ perheaters, if the metal temperatures could be lowered then the energy liberated to the steam would also be converted into electrical power. This could be accomplished in practice by in­ creasing the spray water flows. The turbine flow will increase due to the increase in pressure brought about by the presence of the additional mass of steam in the superheaters. A stored energy test using this scheme will hereafter be called a Type 3 test. A series of simulation runs on a reference model for Drax Power Station ( Sidders, 1989 ) were performed to test these strategies individually and combined and are depicted in Figure 55 on page 118 to Figure 65 on page 123. The unit was given a set point power of 93% of Maxi­ mum Continuous Rating ( 660 MW ) with full boiler pressure ( 16.5 MPa ) and the boiler and turbine masters were disengaged. This is similar to the operating mode at Moneypoint during the tests.

D.2.1 SIMULATED STORED ENERGY TYPE 2

The policy of the CEGB was to design its boilers with very small drums and some difficulty was encountered in performing this test type. The unit normally operates with a half-full drum corresponding to a level of 915.5 mm. For the purposes of this test the level was increased to 1100 mm and the drum level controller given a set point ramp decrease to 500 mm over 60 seconds. The water flow entering the drum decreases and the diversion of sensible heat re­ sults in an increase in drum pressure and consequent increase in steam flow leaving the drum. This ultimately leads to an increase in the power when the steam expands through the turbine cylinders. The boiler temperatures exhibit some transient behaviour but remain within tolerable bounds. The contribution of this strategy to primary reserve, defined as the incremental power at five seconds, would appear to be negligible from Figure 55 on page 118 but the reduction in house load due to reduced feed pump power requirements is not shown and would be of the order of 8 MW. The secondary reserve defined as the incremental generation available within 45 seconds is approximately 0.5 MW. The tertiary reserve defined as the incremental generation available within 150 seconds is approximately 17 MW.

D.2.2 SIMULATED STORED ENERGY TEST TYPE 3

This test was implemented on the model by imposing a step decrease of 20° C. to the set point of the final steam temperature controller. Once again the temperatures are seen to remain within tolerable bounds and the power developed does not contribute to primary spinning re­ serve, contributes 5 MW to secondary and 10 MW to tertiary spinning reserves.

D.3 MONEYPOINT TEST SPECIFICATION AND RESULTS

As a Moneypoint unit represents at least 15% of system demand, any testing which affects unit output must by carefully planned with the National Control Centre. Test types 1 and 3 were not considered by station staff to endanger the availability of the unit and were con­ ducted at a load set points of 280 MW. However, test type 2 involving a step to the boiler drum level was of more concern and was performed at 230 MW when adequate primary and sec­ ondary reserve was available as shown by the generation dispatch algorithm (Brown, 1989).

D.3.1 MEASURED STORED ENERGY TEST TYPE 1

Test type 1 required the plant to have reached a steady state at 90% of MCR with full boiler pressure. This ensured that the governor valves were throttling the steam flow and had some

PhD Appendix D Page 114 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems headroom available. The boiler and turbine masters were disengaged thereby ensuring the fuel input was constant and the turbine valve set point was given a step increase resulting in the governor valves being opened rapidly and remaining open. The generated power in­ creased at first, peaked and returned to near its original set point as shown in Figure 66 on page 124. The data from this test were used to extract the parameters of a simple non-linear plant model as described in Chapter Four.

D.3.2 MEASURED STORED ENERGY TEST TYPE 2

Once the turbine load was steady at 240 MW the boiler, feedwater, live and reheat steam temperature controllers were disengaged and turbine following control mode was selected. The drum level was then raised to 550 mm by manual action on the feedwater control valve and allowed to steady. The feedwater flow was then decreased by 30 kg/sec by the feedwater control valve and the load was then seen to increase by 10 MW over 200 seconds and then fell due to the drum water level reaching it lowest permissible value illustrated in Figure 67 on page 125. The primary reserve is approximately 2 MW due to the reduced feed pump requirements and the secondary reserve is approximately 4 MW. The usual primary spinning reserve available on a Moneypoint unit loaded at 300 MW is of the order of 5 MW and therefore this increase is valuable. Moreover, the reduction in feed flow was a moderate one and greater reductions could be envisaged.

D.3.3 MEASURED STORED ENERGY TEST TYPE 3

This test required that the boiler, live and reheat steam temperature controllers were disen­ gaged, the turbine in turbine follow mode and the feedwater control engaged. The generated power was set at 280 MW and the flow to the first stage attemperators increased by 5 kg/sec thereby lowering the metal temperatures. The load was seen to increase by 5 MW within 45 seconds and thereafter to reduce as saturation temperature was approached. This is the contribution to secondary spinning reserve.

D.3.4 DATA ROUTE

The plant parameters shown in Table 19 on page 117 were recorded 40 times per second by the station logging system Quaestor and stored on disk. The digital resolution of the samples obtained was 8 bits accounting for the quantization effects observed in Figure 66 on page 124 and Figure 67 on page 125 where a fifth order moving average and spline interpolation rou­ tines were used to generate these curves. These recordings were backed up a slower ( every 15 seconds ) more accurate ( 16 bit ) and comprehensive logging system used by Test and Efficiency Section of ESB for heat rate analysis. Due to a failure with the Quaestor logging system the only data available for the type 3 test was that on the accurate but slow backup logging system.

DA DISCUSSION

The incremental generation available from simulated types 2 and 3 stored energy tests does not contribute substantially to the primary and secondary spinning reserves. However, the results obtained do not fully reflect that which may be achieved in practice. The plant tests yield proportionally greater reserve values which can be mainly attributed to the proportion­ ately smaller drum at Drax and due to the fact that the decrease in house load is not included. Moreover, the simulation model does not model the feed heating system and this may result in higher reserve values. A step decrease in reheat temperature would augment these effects diverting heat to the superheaters and liberating energy as the metal cools. The greatest benefits from these strategies are in the longer timescales delivering peak re­ serves approximately 150 seconds after the initiating event. This helps to restore the system

PhD Appendix D Page 115 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems to 'normal' and is available faster than increases in firing which is determined by mill con­ straints and amount by which the set is deloaded; a typical boiler thermal inertia time constant for Moneypoint would be of the order of 180 to 240 seconds ( Carvalho, 1990 ). Simulation tests of the units response to a large frequency disturbance were not performed due to the inade­ quacies in the representation of the governing system. Similar conclusions were reached by Rabindran ( 1990 ) in a theoretical study of the applica­ tion of multi-variable control system design techniques to conventional power plant. The analysis revealed that a better dynamic response could be obtained if a mismatch between steam and feed flow was transiently allowed by preventing the initial influx of water into the drum. The thermal reserves of the boiler may be activated automatically by minor enhancements to the plants control schemes. It could be arranged that the rate of change of grid frequency would signal a reduction in boiler feed pump power and live and reheat temperature set points. However, more plant testing would be required with better data resolution to quantify exactly the gains available. If the response of the plant could be improved then other more expensive plant could be re­ lieved of spinning reserve duties and operated in a sliding pressure mode resulting in im­ proved overall system economics.

D. 5 CONCLUSIONS

This Appendix reported simulation and operational tests to quantify the stored energy avail­ able from the boiler. The results demonstrated that the primary spinning reserve was avail­ able due to reduced house load in the Type 2 test and virtually none from the Type 3 test. The secondary spinning reserve increased in both cases but was greater for a Type 3 test. The strategies make use of the boiler stored energy to provide tertiary spinning reserve in a timescale of 150 seconds and are therefore faster than increases in combustion which are constrained by mill dynamics and available power output headroom.

D.6 RECOMMENDATIONS

Further operational tests should be carried out to quantify these reserves and compare to thermal inertia tests. More severe transients could be performed in light of the experience gained from these tests and simulations results. The data should be captured using instru­ mentation with at least 12 bit resolution and sampled at a rate of not less than twice per sec­ ond.

PhD Appendix D Page 116 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

Plant Parameter Units Throttle Pressure Left MPa Throttle Pressure Right MPa Live Steam Pressure MPa Ctrl. Valve Right Top ( 3rd Valve ) % Main Steam Flow kg/sec Power Output MW Feedwater Flow % Ctrl. Valve Right Bottom { 2nd Valve ) % Final Steam Temperature Deg C Drum-Pressure MPa Reheat Pressure MPa Total Coal Flow 0-100% Reheat Steam Temperature Deg C Spray Attemperator 1 (LHS) kg/sec Drum Level mm ID Fan A Outlet Temperature Deg C ID Fan B Outlet Temperature Deg C Spray Attemperator 1 (RHS) kg/sec Spray Attemperator 2 (LHS) kg/sec Spray Attemperator 2 (RHS) kg/sec

Table 19. Subset of Plant Parameters Recorded by Quaestor: The data recorded is now stored in protected data sets.

PhD Appendix D Page 117 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS MU POWER STATION

TIME C seconds)

Figure 55. Stored Energy Tests, Power Output plotted against Time: Tests initiated at time 50 seconds.

PhD Appendix D Page 118 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS i m POUER STATION in

TIME (seconds)

Figure 56. Stored Energy Tests, Drum Feed Flow: Tests initiated at time 50 seconds.

SIMULATION RESULTS BRA): POWER STATION in

TIME (seconds)

Figure 57. Stored Energy Tests, Drum Exit Steam Flow plotted against Time: Tests initiated at time 50 seconds.

PhD Appendix D Page 119 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS M A X POUER STATION in \ u\

3 O _1 LL

> < & CL CO

CL Cl

TIME (seconds)

Figure 58. Stored Energy Tests, Primary Attemperator Flow plotted against Time: Tests initiated at time 50 seconds.

SIMULATION RESULTS M A X POUER STATION in \ □

3 O _l LL

> < CL Cl CO

O LLJ CO

TIME (seconds)

Figure 59. Stored Energy Tests, Secondary Attemperator Flow plotted against Time: Tests initi­ ated at time 50 seconds.

PhD Appendix D Page 120 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS i m power s t a t i o n

TIME (seconds)

Figure 60. Stored Energy Tests, Drum Level Plotted against Time: Tests initiated at time 50 seconds.

SIMULATION RESULTS m i POWER STATION

TIME (seconds)

Figure 61. Stored Energy Tests, Economiser Outlet Temp, plotted against Time: Tests initiated at time 50 seconds.

PhD Appendix D Page 121 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS i m PflUER STATION

TIME (seconds)

Figure 62. Stored Energy Tests, Saturation Temperature plotted against Time: Tests initiated at time 50 seconds.

SIMULATION RESULTS D M X PQUER STATION

TIME (seconds)

Figure 63. Stored Energy Tests, Primary S/H Outlet Temperature plotted against Time: Tests initiated at time 50 seconds.

PhD Appendix D Page 122 Novel Stored Energy Techniques Improved Generation Dispatch in Power Systems

SIMULATION RESULTS i m Pi]UER STATION

Figure 64. Stored Energy Tests, Secondary S/H Outlet Temperature plotted against Time: Tests initiated at time 50 seconds.

SIMULATION RESULTS m i PQUER STATION O 575

ETA Cl ' E m 565 -— r --- BOTH ...... !.... i- \ .. TYPE 3 — TYPE 2 E 550 - < LU i_ 555 - 07 U, 554 - > mM 545sus ------;------i------i------i------o 100 200 300 400 500

TIME (seconds)

Figure 65. Stored Energy Tests, Final S/H Outlet Temperature plotted against Time: Tests initi­ ated at time 50 seconds.

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