GENERATOR RESOURCES AND THE SCHEDULING

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1 GENERATOR RESOURCES AND THE SCHEDULING PROBLEM by MEADHBH ELLEN FLYNN A thesis presented to The National University of Ireland in fulfilment of the requirements of the degree of PHILOSOPHIAE DOCTOR in the Department of Electronic and Electrical Engineering Faculty of Engineering and Architecture University College Dublin April 999 Supervisor of research: Dr. M. J. O Malley Nominating Professor: An tollamh A. M. de Paor Head of Department: Professor J. O. Scanlan

2 Abstract The obective of a power system is to economically supply energy to match system demand with a required level of security. The temporal and stochastic variability of demand and supply and the inability to efficiently store electrical energy are characteristics of the electricity industry. The reliability of the power system is influenced by the reliability of the generators and, in the event of a contingency, their dynamic response. Reliability comes at a price and to operate the system economically a balance must be achieved between the reliability level and the acceptable cost. The system operator must therefore schedule units in advance taking into consideration energy costs, dynamic response and reliability. To facilitate the decision-making process, suitable optimisation techniques and models of individual units and of the overall system are required. A boiler model based on fundamental physical laws is proposed. It is suitable for analysing plant dynamics in the longer time-scales, i.e., beyond 0 seconds, following a maor system contingency such as loss of a large generator. It can predict the reserve capacity of the unit and also the variation of critical internal parameters that may cause disconnection of the unit from the system during a severe system transient. Identification and validation of control parameters was carried out using data from an actual plant. Generator characteristics and cost information are modelled in an algorithm developed to assist the system operator in scheduling units in an economic way. This scheduling algorithm is developed for a centrally optimised market where generators submit prices and response characteristics for energy and spinning reserve. These costs are all considered simultaneously by the scheduling algorithm which also considers unit forced outage probability estimates, submitted by the generators. The scheduling problem is formulated as an Augmented Lagrangian problem and solved using a new recurrent neural network. It addresses the scheduling of generator operating modes using the specific example of a thermal unit operating in constant pressure or sliding pressure mode. The solution technique may also applied to schedule units with piece-wise convex cost curves. A number of system reserve constraints are proposed and system marginal reserve cost information, combined with unit forced outage estimates, is used to balance reliability and cost. A novel technique to explicitly schedule units to provide reserve is introduced. ii

3 Acknowledgements I would like to express sincere thanks to the following people who have contributed to this thesis: Dr. Mark O Malley, my supervisor, for his dedicated work, adherence to consistent high standards and his enthusiasm, which kept me motivated through even the most tedious parts of this proect. Dr. David Timoney who first encouraged me to pursue a Ph.D. and who contributed to the initial stages of the proect. ESB International for an extended career break to allow completion of the Ph.D., especially Gerry Breen who initially granted me the leave of absence. ESB National Grid for guidance and financial support, in particular Andrew Cooke, John Kennedy and Adèle Sleator. Tom Canning, Alan Egan and Stephen Walsh from ESB Powergen for information for boiler modelling. Paul Sheridan and Dr. Michael Walsh for close collaboration on many key parts of this work and Dr. Jonathan O Sullivan and Jody Dillon for also sharing their expertise. Madeleine, Hugh, Garret and Michael for guaranteed light relief from academia. Any of the aforementioned who undertook the tedious task of proofreading the thesis and the papers. Dr. Richard Reilly, Dr. Stephen Dorgan, Liam Carroll and Brian Turner for their technical support and patience whenever the gremlins attacked my computer hardware and software. Ciara, Sarah, my adopted Sligo clann and the spinners for their friendship and countless favours. My parents and brothers for their faithful support and encouragement in all my ventures. This work is dedicated to my friend Fr. Eamon ( )- ar dheis Dé go raibh a anam. Oce nas, koi esi nebesima, sveti se ime tvoe! iii

4 Publications arising from this thesis The following ournal papers have been published: [] Flynn M.E. and O Malley M.J., 999, A drum boiler model for long term power system dynamic simulation, IEEE Transactions on Power Systems, ol. 4, no., pp (Appendix 5). [2] Flynn M.E. Walsh M.P., O Malley M.J., 999, Efficient use of generator resources in emerging electricity markets, IEEE Transactions on Power Systems, in press, Paper PE-373- PWRS-998 (Appendix 6). [3] Walsh M.P., Flynn M.E., O Malley M.J., 999, Augmented Hopfield Network for Mixed- Integer Programming, IEEE Transactions on Neural Networks, ol. 0, No. 2, pp (Appendix 7). The following ournal paper is in review: [] Flynn M.E., Sheridan W.P., Dillon J., O Malley M.J., 999, Reliability and reserve in competitive electricity market scheduling, IEEE Transactions on Power Systems, in review (Appendix 8). The following conference papers have been published: [] Flynn M.E. and O Malley M.J., 997, Modelling boiler response to co-ordinate reserve in isolated power systems, IFAC / CIGRE Symposium on Control of Power Systems and Power Plants, Beiing, China, pp [2] Flynn M.E. and O Malley M.J., 999, Balance between generating plant costs and system load following requirements, CIGRE Symposium on Working Plant and Systems Harder, to be presented in London, June. [3] O Sullivan J.W., Flynn M.E., O Malley M.J., Power M., 999, Modelling of Frequency Control in an Island System, Proceedings of IEEE PES Winter Meeting, New York, pp iv

5 Nomenclature Generator scheduling (Chapters 2, 5, and 6) Symbol Description Units α i slope of reserve characteristic for unit i MW/MW A service mode where reserve is a function of output power - a i quadratic energy cost co -efficient of unit i /MW 2 AS Ancillary services - β set of parameters for equality constraints /MW 2 B service mode where reserve is independent of output power - BASE lower range of unit that has flexible operating modes - b i linear energy costs co -efficient of unit i /MW c i idling cost of unit i CP constant pressure operating mode - CRR i bid price for ramping from unit i /MW 2 curt i unserved load due to failure of unit i at hour MW χ slope of the sigmoid function - δ λ step size for update of equality neuron input - δ γ, step size for update of inequality neuron input - δ c step size for update of continuous neuron input - d i linear reserve cost coefficient for unit i /MW E network energy function - e i constant reserve cost coefficient for unit i /hour f obective function - FOP ss i steady state forced outage probability of unit i at hour - FOP su i start -up forced outage probability of unit i at hour - FOP tot i total forced outage probability of unit i at hour - γ set of Lagrange multipliers for reserve inequality constraints /MW g c transfer function for continuous neuron - g d transfer function for discrete neuron - g rd transfer function for discrete reserve neuron - g sd transfer function for discrete status neuron - h set of equality constraints - h m m th equality constraint - v

6 k set of equality constraints - k q q th equality constraint - K c parameter associated with continuous reserve constraint neuron - K d parameter associated with discrete reserve constraint neuron - λ set of Lagrange multipliers for load balance equality constraints /MW L Lagrangian function - LCR load control ratio - L load at hour MW µ set of Lagrange multipliers for inequality constraints /MW P Augmented Lagrangian function - PEAK SP or CP operating mode - P i power output of unit i at hour MW P max i maximum power output capacity of unit i MW P min i minimum power output capacity of unit i MW P unit i power where discontinuity in SBF reserve occurs MW Rmax i R parameter associated with ramping constraint neuron - R system reserve constraint function - Res system reserve target at hour MW R i reserve output of unit i at hour MW RISK system risk index at hour MW R max i maximum reserve capacity of unit i MW RRd i decreasing ramp limit for unit i MW/hour RRu i increasing ramp limit for unit i MW/hour s i start -up cost of unit i SB straight back reserve characteristic - SBF straight back and flat reserve characteristic - SMCR i system marginal cost of reserve constraint associated with unit i at hour /MW SMEP system marginal price of energy /MW SP sliding pressure operating mode - SWITCH i heuristic cost for changing operating modes on unit i T d i minimum down time for unit i hours T up i minimum up time for unit i hours u set of discrete variables - U λ set of inputs of the Lagrange neurons for vi

7 U µ U γ U γ i U λ U µ equality constraints - set of inputs of the Lagrange neurons for inequality constraints - set of inputs of the Lagrange neurons for inequality constraints - input of the Lagrange neuron for inequality constraint associated with unit i at hour - input of the Lagrange neuron for equality constraint - input of the Lagrange neuron for inequality constraint at hour - U c set of inputs of the discrete neurons - U ci input of the continuous neuron for unit i at hour - U d set of inputs of the discrete neurons - U res ci U res di input of continuous reserve constraint neuron for unit i at hour - input of discrete reserve constraint neuron for unit i at hour - U rdi input of the discrete reserve neuron of unit i at hour - U input of the discrete status neuron for unit i at hour - U A_B di A_B di BASE_PEAK i res ci res di input of the discrete intermodal constraint neuron for unit i at hour - output of the discrete intermodal constraint neuron for unit i at hour - output of the discrete intermodal constraint neuron for unit i at hour - output of continuous reserve constraint neuron for unit i at hour - output discrete reserve constraint neuron for unit i at hour - output of the continuous neuron of unit i at hour - λ µ set of outputs for the Lagrange neurons for equality constraints - set of outputs for the Lagrange neurons for inequality constraints - vii

8 γ γ i λ µ set of outputs for the Lagrange neurons for inequality constraints - output of the Lagrange neuron for inequality constraint with unit associated i at hour - output of the Lagrange neuron for equality constraint at hour - output of the Lagrange neuron for inequality constraint at hour - c set of outputs of the continuous neurons - ci output of the continuous neuron of unit i at hour - d set of outputs of the discrete neurons - rdi output of the discrete reserve neuron for unit i at hour - output of the discrete status neuron of unit i at hour - OLL value of lost load /MW OLU reliability scaling factor at hour /MW x ri binary variable for reserve status of unit i at hour - x si binary variable for generating status of unit i at hour - y set of continuous variables - Superscripts A B BASE CP PEAK SP Description service mode A service mode B base operating mode constant pressure operating mode sliding pressure or constant pressure operating mode sliding pressure operating mode Boiler model (Chapters 3 and 4) Symbol Description Units a surface area m 2 α thermal diffusivity m 2 /s am volumetric quality m 3 /m 3 c specific heat capacity kj/kgk viii

9 cf friction coefficient - csa cross sectional area m 2 D controller derivative coefficient - d diameter m drt drum thickness m t timestep s ε emissivity - G power output MW γ convection heat transfer coefficient W/m 2 K h specific enthalpy J/kg HP high pressure - I controller integral coefficient - k thermal conductivity J/mK K valve constant coefficient - kqdc downcomer friction coefficient kg /2 /s l drum level m L length m LP low pressure - &m mass flow kg/s M mass kg Nu Nusselt number - O fractional valve opening % P pressure MPa Pr Prandtl number - Pro controller proportion coefficient - Q heat transfer W θ drum thermal time constant factor m - θ" fl dimensionless temperature of gas - ρ density kg/m 3 Re Reynolds number - RH reheater - s specific entropy J/K kg S entropy J/K SH superheater - σ Stefan Boltzmann constant W/K 4 m 2 ix

10 T temperature K t time s th metal thickness m volume m 3 ω perimeter m x spatial node position - xr steam mass quality kg/kg z vertical elevation m Subscripts a aft att cond d dc e f fuel furn fw g HP i in l liq LP m n o p rh ris s Description air adiabatic flame temperature attemperator condenser drum downcomer outer surface saturated liquid fuel furnace feedwater flue gas high pressure turbine inner surface inlet level liquid low pressure turbine metal spatial node number of heat exchanger outlet constant pressure reheater riser steam x

11 sat sh tot v vv saturated superheater total saturated vapour throttle valve For example T s vv is the steam temperature at the throttle valve Superscript t R Description time recorded during plant tests xi

12 Contents Introduction. Background.2 Boiler modelling 2.3 Optimal use of generator resources 3.4 Scope of work 4 2 Generator resources 6 2. Background Generator characteristics and costs Reliability Market structures Generator resources: costs, characteristics and system requirements Energy Ramping Reserve Operating modes Reliability Summary 27 3 Introduction to boiler and review of previous models Description of boiler Rankine cycle Feedwater Steam Gas Operating modes Constant pressure Sliding pressure Storage of energy Sources of spinning reserve Comparison of energy storage capacity and response times Boiler design Fuel Operating and control modes Modelling issues Distributed nature of models Decoupling of equations Heat transfer data Steam tables Tests and data collection 4 xii

13 3.3 Modelling approaches Black box Physical models High order models Low order models Review of previous component models Furnace Riser and downcomer Drum Superheater and reheater Summary 52 4 Development and validation of boiler model Plant description Data collection Model components Furnace Drum, riser and downcomer Superheater and reheater Throttle valve Turbine Controls Reheat steam temperature Drum level Superheat steam temperature Steam pressure Parameter identification Results of system identification and validation Discussion Summary 77 5 Scheduling of generator resources Augmented Lagrangian formulation New recurrent neural network Application to the generator scheduling problem Modifications to transfer functions Obective function Equality constraints Inequality constraints Constraint neurons Reserve constraint neurons Intermodal constraint neurons 90 xiii

14 5.4 Algorithm implementation Algorithm initialisation and convergence Example 93 6 Optimal scheduling of generator resources: results Set A Test system and algorithm details Results Energy and reserve costs Energy and ramping costs Unit operating modes Discussion Set B Test system and algorithm details Results Unit reliability term Energy and reserve costs- fixed reserve constraint Energy and reserve costs- unit-wise reserve constraint Discussion Discussion 25 7 Conclusion 28 References 32 Appendices Appendix Nelder Mead Simplex Search Method A. Appendix 2 Ziegler Nichols Tuning A.5 Appendix 3 Convergence proof for new recurrent neural network A.8 Appendix 4 Energy function for scheduling problem A.3 Appendix 5 IEEE Trans. on Power Systems, 999, ol. 4, no., pp A.22 Appendix 6 IEEE Trans. on Power Systems, 999, Paper no. PE-373-PWRS A.32 Appendix 7 IEEE Trans. on Neural Networks, 999, ol. 0, no. 2, pp A.42 Appendix 8 IEEE Trans. on Power Systems, 999, Paper in review A.46 xiv

15 Chapter Introduction. Background The temporal and stochastic variability of demand and supply, the inability to efficiently store electrical energy and the dependence on a transmission system that is reliable and secure are all features of the electricity industry. The balance between system demand for energy and the supply available to meet it is constantly changing and when imbalance occurs, the voltage and frequency of supply is affected (Elgerd, 972). Such changes may be due to random deviations from a load forecast, predicted temporal changes or loss of a significant component of the system such as a transmission line or generator (IEEE, 972). Reduction of unpredictable factors is only possible to a limited extent, e.g., investment in maintenance to improve generator reliability. Generator resources, such as megawatt response and demand load control to restore the supply-demand balance and generator reliability can further improve system reliability. Megawatt (MW) response is the ability of generating units to change power output in response to system requirements and includes automatic generator control (AGC), ramping, and spinning reserve, governor response and ready reserve (IEEE, 972). An important characteristic of power systems is the ability to vary power output or demand to maintain load balance. AGC is used to respond to small changes in consumer demand and generator ramping can be used to meet larger predicted temporal changes in consumer demand (Herouard et al., 994). Following the loss of a generator, the resulting imbalance causes a drop in frequency, the rate of decrease being inversely related to the size of the power system. This imbalance must be reduced to arrest the frequency drop and restore the frequency to its nominal value by increasing generation or reducing customer demand, i.e. reserve (Herouard et al., 994, O Sullivan and O Malley, 996b). The increase in generation may come from on-line generators, known as spinningreserve. Other sources, such as disconnection of customers, are classified as non spinning reserve. A simple measure of system risk due to on-line generators is the product of the resources they are providing to the system, e.g. energy and spinning reserve, and the probability of failure of the unit, the forced outage probability. Reserve is provided to ensure continuity of supply in the event of such failures. The forced outage probability is a function of the unit reliability. Therefore, for a given system reliability level, improved reliability of individual generators may

16 require a reduced level of reserve. resource. Hence, generator reliability is an important generator Power system scheduling involves selecting the optimal combination of resources to meet load at minimum cost while maintaining security of supply (Merlin and Sandrin, 983). A system operator (SO) is a co-ordinator responsible for maintaining system reliability and security, coordinating generator resources and encouraging economic efficiency. The SO schedules the generators to supply the consumer demand over a given time period based on a load forecast. The customer demand may be price sensitive and this factor should also be considered by the SO. The decisions to be made are what units are on-line (discrete) and what is their output level (continuous). These have been traditionally known as the unit commitment and the economic dispatch problems. A study of the possible MW response requirements of a power system, and the capabilities of the available units to singly and collectively respond to these, requires an understanding of system response requirements, unit normal response capabilities and unit operating conditions which may limit normal response (IEEE, 972). To make economic decisions, knowledge of generator resources, in terms of both cost and performance, is required. This requires steady state information, such as unit capacity and operating constraints. Dynamic information is also needed, which covers the unit s ability to change load in different time scales, i.e. megawatt response, and its performance during a severe transient on the system such as loss of a large on-line generator in an island system (O Sullivan and O Malley, 996b). For the latter, boiler dynamics and power plant protections and controls become significant. These will vary depending on factors such as plant design, type of fuel used and plant operating practice. When integrated into a model of the entire system, suitable models of the generators will enable prediction of system performance in the event of contingencies. This will assist in decisions about the levels of reserve required to achieve a particular level of system security..2 Boiler modelling Because of their technical and economic importance in the power industry, the dynamics of the boiler and turbine processes have been the obect of considerable research effort since the late 950 s (Maffezzoni et al., 983). The range of models developed is very wide. Simplified models deduced by theoretical and experimental estimation have been developed as well as very detailed non-linear models. The more detailed models can be used for optimising construction as well as predicting behaviour during start-up or shutdown situations but contain excessive detail for system simulation. Much of the simpler modelling was done by the process control community who developed simple global boiler models suitable for control design. Several 2

17 models have been developed for the long-term simulation of power system transients. Many of these tools have tended to use simple low order models to represent the slow boiler dynamics, which become significant over the longer time frames. Schulz et al. (982), Herget and Park (976), Åstrom and Eklund (972), Anderson (974) and EPRI (985) used linear small perturbation models. Other low order models have been developed by Hemmaplardh et al. (985), Malachi et al. (990) and Cheres (990). Many of these models failed to address the issue of plant protection (Kundur et al., 989) which is critical during large changes in the power output of a unit. When a large generating unit is lost from the system, rapid control action is required from all the remaining units to restore the frequency to its nominal value. The initial response of any thermal unit depends on the governing system. However, in the longer term, the control and protection logic becomes important. If plant variables exceed safety limits, as is possible during severe system transients, the protection system may cause the unit to disconnect from the power system. This could play a vital role in whether or not the system integrity is maintained. It is necessary to estimate the impact of control actions on the plant lifetime and to consider operating constraints so that the plant is not overstrained when responding to system requirements (Bell and Åström, 996). Therefore, a fundamental approach based on physical laws is needed for modelling fossil fuel boilers for long term simulations. This will enable modelling the relevant internal variables that may cause a generator to trip from the system if they deviate outside safe operating limits (Flynn and O Malley, 999)..3 Optimal use of generator resources The worldwide trend towards restructuring the power industry is resulting in greater interest in efficient allocutilisation of generation resources. In vertically integrated power utilities electricity generation, transmission and local distribution are integrated within the one firm in which units are dispatched to minimise energy costs, subect only to system and unit constraints (Baldick, 995). Costs associated with services, such as frequency control, are less significant and are internal, so there is little motivation to unbundle these from the costs of producing a given power output. These costs, however, may be significant (Bakken, 997). There are also no common definitions in the industry for these resources. However, tto achieve minimum cost, all costs should be included in any cost optimisation algorithm that may be used to decide on resource allocation. In competitive markets, generators will have to become aware of the costs they incur when supplying resources, other than energy, to the system for their long-term economic survival. 3

18 For economic allocation of generator resources to meet system demand in any market structure, a suitable decision making tool is needed. The allocation of generator resources, ideally, must be able to incorporate unit and system constraints and, also, reliability data. There has been much research carried out in the area of scheduling generator resources, because better coordination of resources can result in substantial savings for utilities (Walsh, 998). Several algorithms have been developed to solve the generic problem of minimising operational cost, subect to unit operation constraints and system constraints (Sheblé and Fahd, 994). Many methods focussed on the minimisation of fuel costs associated explicitly with energy provision only (Merlin and Sandrin, 983; Baldick, 995; Svoboda et al, 997). Allocation of resources, to meet reserve, must account for unit response capability and, also, the economic impact of its redispatch for reserve provision (Koessler et al., 999). More recently, there have been developments that aim to minimise energy and other resource costs. Rau (999a), Kaye et al. (998), Bakirtzis (998) and Ma et al. (999) developed algorithms to dispatch energy and reserve. The inclusion of unit flexibility in terms of operating modes has mainly been ignored in scheduling generator resources. Some authors including Cohen and Ostrowski (996), Walsh and O Malley (997b) and Flynn et al. (999a) have, however, considered it..4 Scope of work The scope of the work in this thesis includes: Development, identification and validation of a physically based boiler model to enable quantification of thermal plantsplant resources. This requires modelling the dynamic capabilities and limitations of a thermal generator in different operating and control modes in a period up to 5 minutes following a system transient. Certain critical parameters, that may cause action of the protection systems if they deviate outside safe limits, must also be modelled. Development of a scheduling algorithm to enable optimal use of generator resources in electricity markets using generator resource cost and capacity information. In a vertically integrated utility, these costs will be actual costs. In a competitive market, generators will bid in costs for resources that may or may not reflect true costs, depending on market design and strategy. To ensure a profit, submitted bids will exceed costs. Here,Only thermal generator resources are considered and the resources dealt with are limited to energy, megawatt response (spinning reserve and ramping) and reliability, where these resources are 4

19 defined in Chapter 2.. The flexibility of a unit to operate in different modes, each with distinct cost and performance characteristics, will also be considered. The solution technique to deal with operating modes is also applied to schedule units with piece-wise convex cost curves. A novel technique to schedule units to provide reserve is introduced. Different forms of reserve constraints are also implemented. Using cost information extracted from the developed scheduling algorithm, reserve constraints are set which balance the cost of provision with the cost of failing to meet the constraints. Chapter 2 introduces generator resources in more detail in terms of their costs, characteristics and the system requirements. Aspects of the scheduling problem are also presented. Chapter 3 reviews previous approaches to boiler modelling and Chapter 4 presents the development and validation of a boiler model. In Chapter 5, the generator scheduling problem is formulated using an Augmented Lagrangian formulation. This formulation is mapped to a new recurrent neural network to optimise the use of the generators resources in terms of their costs and operational characteristics. Scheduling results are given for small test systems in Chapter 6. In Chapter 7, conclusions are drawn and some possibilities for future work are outlined. 5

20 Chapter 2 Generator resources This chapter will begin with a general description of power systems including their obectives, their characteristics and the consequent need for generator resources to ensure reliable operation. Different approaches to scheduling generators to meet power system requirements for economic and reliable power supply will be discussed including market structures that have evolved worldwide. Details are presented of the costs, characteristic and system requirements for a number of generator resources, specifically energy, ramping, spinning reserve, operating modes and reliability. 2. Background The fundamental aim of a power system operator is to schedule generators to supply power to satisfy customer demand (Zhai et al., 994). To achieve this, the consumer load is allocated among the available generators, subect to various systems requirements and constraints as well as unit output limitations. The system constraints cover such aspects as transmission line physical capacities. System requirements may include restriction of sulphur dioxide emissions for environmental reasons or reserve levels to ensure system security. A primary obective is cost minimisation, which in any market structure requires accounting of all costs. In the past, the emphasis was on quantifying costs associated solely with energy production and costs related to other ancillary services necessary for secure power system operation, such as voltage control or frequency control, were neglected. With the advent of market restructuring and competition between generators, there now exists a motivation for unbundling individual generator resource costs and characteristics and transmission costs. The operation of a power system is a complex process with frequent changes in the operating state of the system. Every component failure, repair, planned or unplanned outage, or change in loading condition introduces a new operating state (CIGRE, 997). Power system reliability is described by adequacy and security. IEEE (978) and McGilis et al. (987) define these as follows: 6

21 Adequacy is the ability of the system to supply the aggregate electric power and energy requirements of the customers within the component ratings and voltage limits taking into account planned and unplanned outages. Security is the ability of the system to withstand specific sudden disturbances such as the unanticipated loss of system components. In system planning, reliability has been based on the concept of adequacy while in system operations, reliability is achieved if the system is secure at all times (CIGRE, 997). In addition to energy supply, the system requires other generator resources necessary for the security of the power system. Examples of these are reactive power for voltage control and ability to respond to changes in power demand, i.e., megawatt response, for frequency control (IEEE, 972; Herouard et al., 994). As electricity cannot be stored efficiently, the system requires units to be able to adust output to match temporal variations in demand in order to maintain the supply frequency and voltage within tolerable limits (IEEE, 990). These demand changes may be part of an hourly load forecast, random fluctuations in consumer demand or due to a contingency on the system such as the loss of generating unit. A contingency can be defined as the unplanned reduction of a grid system infeed (Whitmarsh Everiss, 99). The maor factors influencing system reliability are overall system strength, available megawatt response, which is a function of generator dynamics, unplanned generator or transmission line outages and load forecast uncertainty. During normal operation, the influence of an individual unit on system behaviour cannot be easily discriminated. However, during emergency conditions, e.g., loss of generation, the influence of the individual megawatt response of a unit can be significant (Läubli and Fenton, 97). In a small power system, the outage of a large unit may be very significant (O Sullivan and O Malley, 996b; 999; Gibescu and Liu, 998). There is a need to account for individual generator reliability when operating the system, as this will affect reserve levels required for system security (Gooi et al., 999). Zhai et al. (994) showed the effect of load forecast errors on risk and required reserve level. The economic impact of load forecasting errors was examined by Ranaweera et al., (997). In the event of a system contingency, which causes demand to exceed supply, frequency starts to drop. The additional generation or decrease in load is known as system reserve. Sufficient spinning reserve, i.e., reserve from on-line generators, must be scheduled to prevent large frequency deviations and loss of customers (Siddiqi and Baughman, 995; O Sullivan and O Malley 996a). Spinning reserve constraints to provide a given level of system reliability are a complex function of many factors including unit sizes, unit reliability, dynamic response of on- 7

22 line units, number of on-line units, system load forecast errors and lead time of additional generation (Chowdhury, 993). There are costs associated with such resources to improve system reliability and therefore economic choices must be made. To assess the risks of certain very large disturbances, it is necessary to develop more detailed and more global dynamic simulation models than those currently used in security assessment (CIGRE, 997; Flynn et al., 999a). Suitable models of both the system and the generators will assist the operator in efficient and economic decision making, particularly in the light of the emerging electricity markets, where competitive forces are encouraging the operation of systems closer to the edge (Zhai et al., 994). Environmental concerns are also exerting pressure to operate systems with lower security margins (CIGRE, 997). 2.. Generator characteristics and costs Knowledge of generator performance under various conditions is important from the generators perspective in bidding into markets for energy and other resources as well as for a system operator who needs to procure resources to match system requirements to guarantee secure load supply (Malachi et al., 990). Hemmaplardh et al. (986) summarise the uses of a long term (several minutes) dynamic simulation of a power system which include: (i) Being able to predict the effect of control alternatives on the ability of the units to react to a maor system disturbance. (ii) The allocation and distribution of spinning and non-spinning reserve. Suitable generator models are required for such a simulation. In order to evaluate system capability to meet frequency and voltage tolerances, research has been carried out on simulating power systems in various time scales. The focus of long term dynamic simulation of power systems is the analysis of the effects of large variations in voltage and frequency for extended periods on the bulk power system (Hemmaplardh et al., 986). Long term stability assumes that inter-machine oscillations have been damped out, resulting in uniform system frequency (Kundur, and Morison, 997). Fast dynamics are not significant in long term simulations (Ben-Abdennour and Lee, 996). The emphasis is on the slower and longer duration phenomena that accompany large-scale system upsets. Neglecting slower boiler dynamics, that may invoke protections associated with variables such as steam pressures, could have a tremendous impact on the simulation results. As a result, boiler dynamics and power plant protections and controls become significant (Sancha et al., 997). Malachi et al. (990) use long term simulation to reconstruct a system wide contingency on the Israeli power system (an island utility) for a period of 5 minutes using low order boiler models, i.e., a limited number of input, output and internal variables. 8

23 When a large generating unit is lost from the system, rapid control action is required from all the remaining units to restore the frequency to its nominal value. The reserve, which a unit can supply, is dependent on a number of factors including boiler design, type of fuel, control mode and operating level. The energy stored within the steam cycle must be activated by the unit s primary control to counter sudden power drops inside the grid (Welfonder and Wendelberger, 995). The initial response of any thermal unit depends on the governing system. However, in the longer term, the control and protection logic becomes important (Kundur et al., 989). If plant controls are not properly co-ordinated it is possible for the system frequency to become unstable and units may be tripped leading to a system blackout. If plant variables exceed safety limits, the protection system may cause the unit to disconnect from the power system. This could play a vital role in whether or not the system collapses. During the course of the 973 Gulf Coast, USA, incident (Schulz et al., 982) a series of events occurred. A boiler tripped due to high pressure in the riser, thereby causing the turbine to trip. Another unit tripped due to failure of the drum level control system and a gas turbine tripped on under-frequency. A power system may recover temporarily after an initial disturbance, but it may be vulnerable to further disturbances if units trip due to protection leading to further outages (Frowd et al., 982). Even though a unit may have sufficient stored energy to provide a given reserve level within a few seconds, other factors may not allow unrestricted response (Concordia et al., 966; IEEE, 972; Kirchmayer and Schulz, 977; Frowd et al., 982; Maffezzoni, 986; Kundur et al., 989; Bell and Åström, 996). Examples of these factors include: (i) Pressure regulators that prevent an excessive pressure drop that would lead to carryover of water from the boiler to the turbine. (ii) Feedwater controls that may not be able to hold the drum level within safe limits. (iii) Limited allowable loading of auxiliaries such as mills and pumps. (iv) Temperature controls to prevent unacceptable thermal stresses that would affect the plant life. (v) Drum protection systems to prevent excessive changes in water level in the drum. Initial large output changes can be made rapidly, but only by sacrificing pressure which causes deep reversal in output after the first few seconds. This load reversal depends on how rapidly the fuel can be admitted to the furnace (Workman, 97). During rapid load change, large temperature deviations are possible which can take a few minutes to return to the set-point. This requires more firing to correct the load reversal problem. Conradie and Kürten (992) reported 9

24 that the power response characteristic of a unit is very important in the context of replacement of exhausted stored energy (seconds range reserve) by increased fuel input (minutes range reserve). In general, the turbine manufacturer specifies ramp limits for changes in power output and control of generated power must conform to these (Delfino et al., 986). Maffezzoni (986) discussed the possibility of equipping the plant controllers with dynamic models to estimate and predict thermal stresses and available energy storage within the boiler, as well as steam temperature and pressure variations as a function of loading rates. Turbine loading would then be limited when actual pressure deviations exceed model predictions. Long term models of thermal systems will enable the investigation of permissible ramp rates that will not cause deviations outside safety limits. While combustion turbines and hydro units are more tolerant of power system transients and can be represented satisfactorily by simple models for long term simulations, a more fundamental approach based on physical laws is needed for fossil fuel boilers (Armor et al., 982). This requires full models of different power plants including boiler and combustion chamber, heat transfer/ steam system and turbines (Bakken, 997). All generator resources such as energy, megawatt response and reliability have associated costs, whether it be fuel, lost revenue, maintenance, increased wear or larger capital costs (Bakken, 997; Flynn et al., 999a). System costs related to frequency control are not well known but are estimated to be in the range of 4% to 8% of total annual operational costs (Canning et al., 992; Bakken 997). This is due to operating the units less efficiently in order to provide reserve capacity and relocating generation to more expensive units. The throttling method (c.f. Chapter 3) is an expensive form of providing reserve. The heat rate (fuel required per MW power output) increases by up to.5%, depending on operating pressure and degree of throttling. Condensate stoppage (c.f. Chapter 3) is a significantly cheaper form of providing reserve (Bakken, 997). A unit may be dispatched at a lower operating point than would be the case if it were not needed for reserve capacity and, therefore, there may be opportunity costs for the generator associated with reserve provision (Singh and Papalexopoulos, 999). Larger capital costs are required for generators with bigger and faster reserve capabilities (Herouard et al., 994) Reliability Utilities must meet the conflicting demands of customers who require a higher quality of service and those who seek lower rates. Different customers may require different level of reliability and may be prepared to pay accordingly. The balance between the cost of improving service 0

25 reliability and security and the economic benefits that such improvements bring to consumers is a dominant factor in electricity markets. Probabilistic type reserve constraints are more realistic than deterministic techniques in setting reserve constraints (O Sullivan and O Malley, 999). In practice, system operators optimise the system such that the total cost is minimised while operating within the security region. It would be possible to operate the system probabilistically using cost-benefit analysis but probabilistic procedures for operating the system are not yet mature and are therefore risky (CIGRE, 997). At the planning level, value based reliability planning takes account of the value of reliability and power quality to customers in assessing the cost effectiveness of proposed investment alternatives (Sullivan et al., 995). In the system operations time frame, many algorithms, which have been developed for scheduling units to meet system demand, have omitted the stochastic nature of the problem (Chowdhury, 993). Billinton and Allen (996) define two values of risk: unit commitment risk is associated with the assessment of which units to have on-line at a given time while response risk is associated with the dispatch of these units. It may be beneficial to calculate risk factors even if it is not optimised on a cost- benefit basis (CIGRE, 997). A risk-based index would enable a consistent comparison between different strategies in terms of economics and reliability. The acceptable risk level must remain a management decision based on economic and social requirements (Anstine et al., 963). The PJM method (Anstine et al., 963) was proposed to evaluate the spinning reserve requirements of the Pennsylvania-New Jersey-Maryland (USA) interconnected system. This method evaluates the probability of the committed generation ust satisfying the expected demand during the time which generation cannot be replaced (lead-time). A capacity outage table is constructed using available units in merit order and from this, for a specified load, the risk level and required reserve is obtained. The original PJM method considers units in two states- inservice or failed. The method has been modified to deal with other conditions, unit fails to start and unit available but not in service, load forecast uncertainty and postponable outages (Billinton and Allen, 996). Merlin and Sandrin (983) proposed a probabilistic method of setting spinning reserve constraints. They defined the marginal utility for spinning reserve as the expected gain due to the marginal kw spinning reserve. This was calculated as the product of the cost of failure of production and the probability of spinning reserve marginal kw actually being called upon to generate, i.e., the probability that the loss in production, due to loss of a transmission line or generator or an unexpected increase in demand, reaches the marginal kw considered. Instead of

26 a fixed reserve constraint, a constraint that the system marginal cost of reserve at a given hour should equal the marginal utility for spinning reserve at that hour was used. Radi and Fox (99) developed a scheduling algorithm to address the balance between reserve and reliability costs, in terms of costs of load not met. They did not deal with a market where generators submit prices for reserve and no account was taken of the hourly variation in system marginal costs of reserve. Siddiqi and Baughman (995) used reliability differentiated pricing to derive an optimal level and price for spinning reserve from a societal welfare perspective. Instead of specifying a reserve constraint, the customers outage costs were included in the overall obective function. The obective function minimised included the costs of producing real and reactive power, the outage costs as a function of unserved real and reactive customer demand and the cost of use of real and reactive power reserve. Details of the cost functions used were not provided and the interdependence of reserve and energy from a generator was not explicitly given as a unit constraint. Using this formulation, the optimal reserve price is made up of the marginal increase in energy and reserve price plus the marginal reduction in outage costs due to an incremental change in reserve purchased. Siddiqi and Baughman (995) reported that the dominant component of the spinning reserve purchase price is the marginal change in the outage cost. Takriti et al. (996) solved the scheduling problem with a progressive hedging method, a type of Lagrangian relaxation technique. The uncertainty in load is modelled by choosing different scenarios, such as loss of a generator, each weighted by its likelihood of occurrence. Results showed possible savings for systems that account for stochastic aspects of the problem. Sheblé (996) suggested that penalties for generators / customers who aggravate and rewards for those who improve the dynamic behaviour of the system will be a feature of deregulated energy markets. This will motivate units towards more reliable operation and, consequently, may result in lower system reserve requirements and lower costs (Bakken, 997). Gooi et al. (999) integrated a Lagrangian Relaxation unit commitment algorithm with a probabilistic reserve assessment. A level of reserve was specified for each hour and a commitment schedule obtained. If at any hour the risk index was unacceptable, then the reserve for this hour was increased. A possible weakness in this method was the failure to consider the reliability of each generator during the commitment stage, i.e. no preference was given to reliable units. For example, there may be a large unit with a low energy cost but its high failure rate may 2

27 be pushing up the reserve requirement, and hence the overall system cost, to achieve a given level of system reliability. O Sullivan and O Malley (999) proposed a new economic dispatch methodology which enabled the cost of providing sufficient reserves to ust avoid load shedding, following the loss of any given unit, to be calculated and assessed against the risk and cost of load shedding Market structures In many countries, the electricity utility was, and in some cases still is, state-owned and operated. Examples include the Irish power system and the old UK system. Electricity supply was considered to be a service and units were scheduled to meet energy demand with the aim of minimising energy costs. Ancillary services, needed for proper system behaviour were constraints applied to the problem and had no specific cost associated with them (Rau, 999a). When a utility operated as a monopoly, the system operator, exercising the authority to dictate generator output, could execute frequency control (Kaye et al. 995). Generators received payment based on energy supplied. All generator resource costs were bundled with energy costs. No explicit financial compensation was received for resources such as reserve, which have cost implications for the generators (Bakken, 997). The main drawback with such a system is lack of cost transparency and efficiency. Electricity supply industries in many countries have been restructured to introduce competition to the industry, in an effort to reduce electricity consumer costs, and different markets have evolved (Kaye et al., 998; Singh and Papalexopoulos, 999). This restructuring must create incentives in the market place for the generators to support system frequency and voltage control (Kumar and Sheblé, 996). Competitive markets for energy require competitive markets for these ancillary services (Singh and Papalexopoulos, 999). The changing power industry is resulting in greater interest in efficient utilisation of generation resources. Both the system and the generator should be able to exploit the full capabilities of the unit, e.g., flexibility of operating modes (Polonyi, 99; Cohen and Ostrowski, 996; Walsh and O Malley, 997b; Flynn et al., 999a). In many market structures, an independent system operator (ISO) neutrally administers the processes of scheduling plants to meet load, subect to protocols for system security (Hunt and Shuttleworth, 996; Ma et al., 999; Ancona, 997). The ISO must ensure that there is 3

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