Power System Security in Market Clearing and Dispatch Mechanisms

1 Power System Security in Market Clearing and Dispatch Mechanisms Claudio A. Cañizares, Senior Member, IEEE, Sameh K. M. Kodsi, Student Member, IEEE Abstract This paper presents and discusses some typical market clearing and dispatch mechanisms based on securityconstrained (SC) optimal power flow (OPF) techniques that are currently being utilized in various jurisdictions throughout the world, concentrating on how system security is accounted for in these auction systems and the effect that this has on the system dispatch schedules and energy prices. The Ontario market is used as an example to illustrate the practical application of these security-constrained clearing and dispatch mechanisms. The need for a better representation of system security in the existent auction systems is also discussed, based on the fact that unexpected dispatch solutions, resulting from diverse bidding patterns and the mechanisms used to clear and dispatch the market, may render ineffective the predetermined system security limits typically used in most auction models, leading to insecure operating conditions and/or unnecessary high prices associated with an unrealistic modeling of system congestion. The latter is illustrated using a simple 6 bus test system, comparing the dispatch levels and prices, as well as the general system operating conditions, obtained from a SC-OPF auction mechanism with respect to those obtained using a voltage-stability-constrained technique, which better represents system security. Index Terms Electricity markets, auction, market clearing, power dispatch, electricity pricing, system security, transmission congestion, security-constrained OPF. I. INTRODUCTION With the introduction of competitive electricity markets, system operation of power grids has changed significantly. In the new market environment, system operators in most jurisdictions are independent of all market participants, and in charge of clearing the market and dispatching generation and load based on the market participants bids, while guaranteeing certain minimum required stability margins to avoid system collapse even in the case of major contingencies, i.e. keeping the system secure (e.g. [1]). This is somewhat different from the operating procedures followed before the deregulation/privatization of electricity markets, when operators directly dispatched generators at minimum costs while maintaining grid security; however, the dominant concern was system reliability, while costs were somewhat secondary. In the current market environment, economic concerns are the primary driver of system operation, and while system reliability is still paramount, since an insecure grid may lead to system collapse, resulting in significant financial and societal losses (e.g. North American August 2003 blackout [2]), system The research work presented here was partially supported by the Natural Sciences and Engineering Research Council (NSERC), Canada. C. Cañizares is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. Email: ccanizar@uwaterloo.ca S. K. M. Kodsi is with AMEC, Oakville, Ontario, Canada. Email: sameh.kodsi@amec.com security has taken a secondary role, due to the fact that guaranteeing high levels of system reliability can be rather costly for all market participants. In this new environment, security is usually measured through system congestion levels, which have a direct effect on market transactions and energy prices. Thus, when the system is deemed congested, operators must take corrective actions (e.g. dispatch out-of-merit units, i.e. units that do not clear the market) to maintain certain mandated system security levels, which usually result in curtailment of power transactions and increased prices for most market participants. System congestion levels in competitive electricity markets are measured by means of power transfers on main transfer corridors (transmission lines), so that when these power transfers reach certain predetermined limits, the system is deemed congested; this is basically the same mechanism used before deregulation/privatization to determine system security levels. The problem with these limits is that they do not always represent the actual security levels directly associated with the current market and system conditions, since these limits are determined off-line, based on system conditions that do not necessarily correspond to the actual grid operating conditions, resulting in some cases in insecure operating conditions and/or inappropriate price signals [3]. This is particularly true if the bidding is such that the market clearing procedures yield dispatch conditions not considered during the off-line security studies, which is often the case. This security enforcement procedure was not a significant issue before deregulation/privatization, as the cost curves of the different generators were known by system operators ahead of time, and hence dispatch schedules could be adequately simulated for a variety of typical loading conditions in off-line system security studies. The present paper discusses some typical market clearing and dispatch mechanisms based on security-constrained (SC) optimal power flow (OPF) techniques typically used by system operators. The paper illustrates how system security is accounted for and managed in these auction systems, using Ontario s electricity market as a practical example, and discusses as well the effect that these mechanisms have on the system dispatch levels and energy prices using a simple 6-bus example, demonstrating the disadvantages of the mechanisms currently used to represent system security. The latter is illustrated with the help of a previously proposed voltagestability-constrained (VSC) OPF technique [4], which better models system security in a typical electricity auction. The paper is structured as follows: Section II presents some of the basic SC-OPF-based models that form the basis of various existing auction systems; how system security is

2 2 represented in these models, as well as the advantages and disadvantages of each model are also discussed in some detail. In this section, the clearing and dispatch mechanisms currently used in the Ontario electricity market are described to illustrate the practical application of some of these SC-OPF models. In Section III, a previously proposed VSC-OPF technique is presented and applied to a 6-bus test system to show that a better representation of system security in the auction mechanism lead to better market and operating conditions, i.e. higher security and transaction levels and lower locational marginal prices. Finally, in Section IV the main results and contributions of this paper are summarized and highlighted. II. SECURITY-CONSTRAINED CLEARING AND DISPATCH TECHNIQUES There are several optimization-based techniques that have been proposed and are being used throughout, in various forms, by system operators for clearing energy markets and dispatching power. These auction models represent system security by means of simple power-flow constraints, and hence can be viewed as SC-OPF problems. The basic models and concepts behind some popular auction systems are described in some detail in this section, using Ontario s electricity auction model to illustrate the practical application of some of these techniques. A. Security-constrained dc-opf (SC-dc-OPF) A typical dc-opf-based auction is basically a linear programming problem, consisting of maximizing a social benefit linear objective function, subject to a set of linear equality and inequality constraints. The following optimization problem forms the basis of this clearing and dispatch mechanism [5]: Min. (1) s.t. #%$ & ('!( *),+.- "!!!( 0/!1 2! 2 *)3+.-46574-98 :5!( ;!(6<>=? +@-A465B4&-C8 :5 ) ; ; <D=E? where and are vectors of supply and demand bids in $/MW, respectively; and represent the supply and demand power levels in MW, with maximum bid limits <>=? and <>=? /, respectively; defines the bus voltage phasor angles;!( represents - 5 the -465F HG74JIKIJI4L transmission system -*8 M5 admittance between buses and (, ); and!( stands for the power flowing through the transmission system, which are used to represent system security by imposing limits on these power flows. The system losses are modeled with #%$ N using an approximate representation of losses in the transmission P lines; thus, #O$ N (' QP!(!(, where the value of!( is a piece-wise-linear function of!1 [6]. In this model, which is typically referred to as a securityconstrained dc-opf-based auction,!( limits are usually obtained by means of off-line loadability studies and, in some cases, stability studies. Thus, power-flow-based maximum loadability analyses, such as those based on continuation power flow tools and PV curves [7], are performed for a variety of dispatch and load scenarios, considering the worst system contingencies based on, at least, an N-1 contingency criterion, i.e. accounting for the worst single contingencies in the system (in some systems, certain significant double contingencies are also considered). In this security analysis procedure, the maximum loading conditions may correspond to thermal limits in the transmission system equipment, bus voltage limits, and/or voltage stability limits; the latter typically correspond to loading points at which power flow solutions disappear due to the Jacobian of the power flow equations becoming singular or certain voltage controls reaching their limits (e.g. generators reactive power limits) [7]. These power transfer limits do not necessarily represent the actual security limits of the solutions obtained from the auction, since these limits are determined using operating conditions that do not necessarily correspond to actual solutions of the SC-dc-OPF-based auction, especially if the bidding is such that the solutions correspond to dispatch conditions not considered during the off-line security studies. Hence, this model may lead in some cases to insecure operating conditions and/or inappropriate price signals, as discussed in detail in Section III. B. Security-Constrained OPF (SC-OPF) The auction model (1) does not properly represent a power system, since reactive power flows and bus voltages, which can have a significant effect on active power flows, especially in heavily loaded systems, are simply not represented, thus rendering the results of this auction inaccurate. Hence, the following OPF, which is typically referred to as a SC-OPF and includes the full ac power flow equations as part of the optimization problem constraints, has been developed to directly account for reactive power and voltage controls and their associated limits [3]: Min. s.t. " R 0 (2) SUT"V E2W4AXY4AZ[\4 4 ]) ) ; ; <D=E?!1 2^4AX ;!1 <>=? +@-A465B4&-98 _5 `!( E2W4AX ; `!( <D=E? Z[ <>b c ; Z[ ; Z[ <>=? X>dfe g ; X ; X>dfh&i +@-4a5B4&-98 _5 where SUT"V stands for the power flow equations of the system; X and 2 correspond to the bus voltage phasor components; Zj[ stands for the generator reactive powers; and `!( represents the current in the transmission line -k5, so that thermal limits can be directly modeled in the auction process. In this auction model, the limits in!1 are basically the same as the ones used in the SC-dc-OPF problem (1), and could be used to also represent thermal limits in the transmission system, in which case the limits in `!( may be removed from (2). Even though the limits in!( may be computed considering thermal

3 and/or voltage limits, besides some stability limits, a more direct representation of thermal, voltage and stability limits in the auction mechanism would obviously yield better solutions, since the solution process would directly reflect these limits in the computation process and final solution. Hence, since these power transfer limits are computed off-line guessing the possible dispatch scenarios, this auction may also yield, as in the case of the SC-dc-OPF, insecure operating conditions and/or inappropriate price signals. C. Multi-period Auctions These types of auctions are typically SC-dc-OPF problems representing several intervals in a given time window, so that inter-temporal constraints, such as ramp-up and ramp-down constraints in generators, can be properly modeled in the auction. Most practical auction implementations are based on this model (e.g. [8]), which, in general, may be represented as follows: Min. a 0 (3) s.t. #%$ N '!1 *) +@-4 "! U "!!( /!( E2! 2 *),+.-4a5B4-C8 5B4!( ;!1 <>=? +.-4a5B4&-98 _5B4 ) ; ; <D=E? + ) ; ; <D=E? + ; + ; + GB4JIJIKI4 where stands for the time interval ( ), and and represent the ramp-down and ramp-up constraints of the generators, respectively. Once again, system security is represented through limits on the power flows in the transmission system computed off-line. Given the size of this optimization problem in real systems, especially if several time intervals are considered at a time, SC-dc-OPF-based models similar to (3) are preferred for multi-period auction systems in practice. Nevertheless, there are practical implementations recently reported in the literature of multi-period auction systems based on the SC-OPF model (2) [1], given that this model better represents system security, as reactive power and bus voltages are directly considered in the clearing and dispatch process. These models, however, still present the problem of relying on power flow limits to represent system congestion that do not correspond to the actual market and power dispatch conditions. D. Practical Applications: Ontario The auction system used in the Ontario electricity market is basically a variant of the multi-period SC-dc-OPF described above; energy and 3 types of reserve markets, i.e. 10 minute spinning and non-spinning reserves and 30 minute reserves, are jointly cleared and dispatched, and system congestion is represented and managed differently than in model (3) [8], [9], [10]. The basic market clearing and power dispatch procedures, including the handling of system congestion (security), are as follows (see Figure 1): 1) Every 5 minutes and for 5 time intervals ( ), a modified version of (3), which jointly maximizes the social benefit of energy and reserve bids, and considers all necessary constraints associated with these bids, is first solved without security constraints, i.e. without considering power flow equations nor limits (see [8] for more details on the optimization model). The solution of this unconstrained optimization problem defines the uniform energy and reserve market clearing prices (MCPs) for the Ontario market every 5 minutes. 2) The dispatch solutions of the multi-period auction are used to solve full power flows for all major system contingencies. If no power flow limits are violated, the process stops and the power and reserve dispatch schedules are published ; otherwise, the sensitivities of the power flows in the lines violating limits with respect to the suppliers powers (demand bids are treated as negative supply) are computed as follows:!(!1!1 (4) At this point, only power flow limit violations, associated with thermal and stability limits, are accounted for directly in the clearing and dispatch mechanisms; voltage and reactive power limit violations are handled manually by operators through ad-hoc reactive power dispatch. This security check and sensitivity computation procedures are at the core of the Network Security Analysis (NSA) module of ABB s auction tools used in the Ontario electricity market (similar software tools are used by the New England ISO) [10]. 3) If there are power flow limit violations, the multi-period optimization problem described in numeral 1 is solved again, but adding the following security constraints for the lines violating limits [8], [10]:!1A ;!( <>=?!( (5) where is the total number of supplier bids, and $ and!( are, respectively, the supply and power flows used to compute the sensitivities!( in the NSA module. Observe that no dc-power flow equations are used in this security-constrained multi-period auction, and only the lines violating limits in the security analysis phase are added to the optimization problem constraints; this allows to speed up the computation process, since all clearing and dispatch procedures, with security check, have to be repeated every 5 minutes for the full Ontario system, which comprises over 3,000 buses and about 300 market participants. The revised schedules obtained from this security-constrained multi-period optimization procedure are run through the NSA module to check for power flow violations, and the process, i.e. numerals 2 and 3, is repeated until no violations are encountered.

4 Bus 3 Bus 2 (GENCO 3) (GENCO 2) Bus 1 (GENCO 1) Bus 6 (ESCO 3) $! " Bus 5 (ESCO 2) # Fig. 1. Market clearing and power dispatch procedures with security check in the Ontario Electricity Market. The price deviations between the first unconstrained optimization and the last security-constrained optimization solutions become part of the congestion management costs that, together with various other costs associated with the operation of the grid, define the market uplift costs, which are added to the MCP to determine the final uniform consumer prices. For more details on how electricity prices are obtained in the Ontario market see [11]. III. IMPROVING SYSTEM SECURITY CONSTRAINTS From the previous discussions, it is clear that system security representation in typical auction models is inadequate. Hence, this section discusses the application of a VSC-OPF to market clearing and dispatch to show, with the help of a simple 6-bus test system, that better market system and system operating conditions may be attained when system security is better accounted for in typical electric energy auction systems. A. Voltage-stability-constrained OPF (VSC-OPF) To improve the representation of system security constraints in the standard OPF, various techniques to better represent voltage stability limits in the OPF are proposed and discussed in [3], [4]. In [4], the minimum singular value of the power flow Jacobian, which may be used as an index to predict voltage instability in power systems as discussed in [7], is introduced as an additional constraint in the OPF to properly account for voltage stability limits in the dispatch problem. Thus, a VSC-OPF-based clearing and dispatch technique can Fig. 2. Bus 4 (ESCO 1) Six-bus test system. be defined as follows: Min. s.t. Y a Y 0 (6) S T"V 2^4AXY4AZ [ 4 4 )! T"V `!1 2^4AX ; `!( <D=E? +.-4a5B4-98 :5 Z [ <>b c ; Z [ ; Z [ <>=? X dfe g ; X ; X dfhi where T"V 2 X SUT"V $ ST"V $ is the power flow Jacobian of the system at a power flow solution point E2 $ 4X $ 4AZ $ 4 $ 4 $, and is a minimum limit for the voltage stability index, so that voltage stability problems can be avoided even in the case of the worst contingencies (N-1 or N-2 contingency criteria); such a value would have to be determined by means of off-line studies, as discussed in the example below. B. Example Figure 2 depicts a 6-bus test case extracted from [5], where three generation companies (GENCOs) and three energy supply companies (ESCOs) provide supply and demand bids, respectively. The complete system and bid data for this system are shown in Tables I and II, where U# and [ stand for the base system load and generation (non-dispatchable loads and generators). The results of applying the OPF formulation (2) to the test system are illustrated in Table III; the maximum loading (ML) value shown in this table was computed off-line using the generator voltages and load and generation power directions obtained from the OPF solution, with the help of a continuation power flow and enforcing all thermal, voltage and reactive power limits. Table IV, on the other hand, shows the solution ) I G obtained for the VSC-OPF (6) for a. This index minimum value was obtained from the off-line studies

5 TABLE I LINE DATA FOR THE 6-BUS TEST SYSTEM Line <>=? <D=E? - [p.u.] [p.u.] [p.u.] [MW] [A] 1-2 0.1 0.2 0.02 15.4 37 1-4 0.05 0.2 0.02 50.1 133 1-5 0.08 0.3 0.03 42.9 122 2-3 0.05 0.25 0.03 21.6 46 2-4 0.05 0.1 0.01 68.2 200 2-5 0.1 0.3 0.02 33.6 103 2-6 0.07 0.2 0.025 52.1 132 3-5 0.12 0.26 0.025 26.1 95 3-6 0.02 0.1 0.01 65.0 200 4-5 0.2 0.4 0.04 9.8 26 5-6 0.1 0.3 0.03 2.2 29 TABLE II GENCO AND ESCO BIDS AND BUS DATA FOR THE 6-BUS TEST SYSTEM Participant <D=E? b < [$/MWh] [MW] [MW] [MVar] [MVar] GENCO 1 9.7 20 90 0 150 GENCO 2 8.8 25 140 0 150 GENCO 3 7.0 20 60 0 150 ESCO 1 12.0 25 90 60 0 ESCO 2 10.5 10 100 70 0 ESCO 3 9.5 20 90 60 0 used to determine the transmission line power limits shown in Table I, and corresponds to a 95% maximum loading condition (e.g. WECC criterion); this off-line maximum loading studies are based on continuation power flows with load and generator dispatch patterns associated with the bids maximum powers shown in Table II, and neglecting contingencies to relax power transfer limits, so that a wider range of possible transactions are feasible to allow for better comparisons, without loss of generality. For both solutions, generator voltages are at their maximum limits, as expected, since this condition generally permits higher transactions levels. However, in comparison with the SC-OPF approach based on power flow limits, the solution of the VSC-OPF provides better LMPs, a higher total!! ) and a higher ML value, which transaction level ( demonstrates that off-line power flow limits are not adequate constraints for representing the actual system congestion. The improved LMPs result also in a lower total price paid to the ISO (Pay ISO ), i.e. the network congestion prices are lower, even though the system losses are higher (which is to be expected, as is higher). TABLE III SC-OPF RESULTS FOR 6-BUS TEST SYSTEM Participant " # $ %& Pay [p.u.] [$/MWh] [MW] [MW] [$/h] GENCO 1 1.100 9.70 14.4 90-1013 GENCO 2 1.100 8.80 2.4 140-1253 GENCO 3 1.084 8.28 20.0 60-663 ESCO 1 1.028 11.64 15.6 90 1229 ESCO 2 1.013 10.83 0.0 100 1083 ESCO 3 1.023 9.13 20.0 90 1005 TOTALS ' = 315.6 MW Losses = 11.2 MW Pay ISO = 388 $/h ML = 520 MW TABLE IV VSC-OPF RESULTS FOR 6-BUS TEST SYSTEM Participant " # Pay [p.u.] [$/MWh] [MW] [MW] [$/h] GENCO 1 1.100 8.95 0.0 90-805 GENCO 2 1.100 8.91 25.0 140-1469 GENCO 3 1.100 9.07 20.0 60-726 ESCO 1 1.021 9.49 25.0 90 1091 ESCO 2 1.013 9.58 10.0 100 1053 ESCO 3 1.039 9.35 8.0 90 917 TOTALS ' = 323 MW Losses = 11.9 MW IV. CONCLUSIONS Pay ISO = 61.2 $/h ML = 539 MW Three different types of popular security-constrained- OPF-based auction systems, namely, SC-dc-OPF, SC-OPF and multi-period SC-dc-OPF, were discussed in detail, highlighting the advantages and disadvantages of each one of them. The Ontario electricity market was used as an example to demonstrate the practical application of a modified version of the multi-period optimization problem. In all these auction models, system security was represented by means of limits on power flows in the transmission system that are computed offline. This representation of system security was shown here, with the help of a 6-bus test system, to yield poor market and system operating conditions when compared to a VSC- OPF-based auction model, which better models grid security limits. REFERENCES [1] E. Lobato, L. Rouco, T. Gomez, F. M. Echavarren, M. I. Navarrete, R. Casanova, and G. Lopez, A Practical Approach to Solve Power System Constraints With Application to the Spanish Electricity Market, IEEE Trans. Power Systems, vol. 19, no. 4, pp. 2029 2037, Nov. 2004. [2] Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations, Tech. 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6 Claudio A. Cañizares (S 86, M 91, SM 00) received in April 1984 the Electrical Engineer degree from the Escuela Politécnica Nacional (EPN), Quito-Ecuador, where he held different teaching and administrative positions from 1983 to 1993. His MS (1988) and PhD (1991) degrees in Electrical Engineering are from the University of Wisconsin-Madison. Dr. Cañizares has held various academic and administrative positions at the E&CE Department of the University of Waterloo since 1993 and is currently a full Professor. His research activities concentrate in the study of stability, modeling, simulation, control and computational issues in power systems in the context of electricity markets. Sameh K. M. Kodsi received the B.SC. degree from Ain Shams University, Cairo, Egypt (1994), and the M. Sc. in Electrical Engineering from Ain Shams University, Cairo, Egypt (2000). He finished his Ph.D. studies in Electrical and Computer Engineering at the University of Waterloo in December 2005, and is currently a Management Consultant at AMEC, Oakville, Ontario, Canada.