The Application of Optimization Technology for Electricity Market Operation

THE APPLICATION OF OPTIMIZATION TECHNOLOGY FOR ELECTRICITY MARKET OPERATION David Sun, Xingwang Ma, Kwok Cheung AREVA T&D Inc. Bellevue, Washington Abstract – Mathematical optimization provides a formal framework that enables systematic and transparent decision making. Significant progress has been made in recent years in applications of formal optimization techniques for competitive market based resource commitment, scheduling, pricing and dispatch. This paper describes experiences with the application of optimization technology for electricity market operation. Experiences with and the status of the latest development in the security-constrained unit commitment and economic dispatch algorithms are described with references to actual market practices. key words – Electricity market operation, optimal power flow, security-constrained unit commitment and economic dispatch, locational marginal pricing, formal optimization. I. INTRODUCTION A fundamental attribute of successful electricity market is its ability to satisfy and balance diverse set of business requirements. Examples of business process requirements are maintaining secure and reliable operation of the physical system, providing correct economic signals to enable competitive market activities, etc.. Mathematical optimization provides a formal framework that enables systematic and transparent decision making. This paper describes experiences with and the status of the development of optimization-based applications for electricity market operation. The unified framework for competitive electricity market and grid reliability is founded on the duality theory that is concerned with the outcome in a competitive market and the mathematical solution to a constrained optimization problem. This duality result states that a competitive market solution consists of both the market clearing quantities and the associated market clearing prices that equate market demand to market supply in all interrelated parts of the market. Only when the market clearing quantities are priced at the logically associated prices is the overall solution incentive compatible. When prices are incentive compatible, participants will provide bids that reflect its actual cost or value, and produce or consume the efficient quantities. Participants’ production or consumption of the efficient quantities leads to grid reliability. The duality theory clearly suggests that formal optimization techniques be utilized for electricity market clearing so that market based dispatches, when executed in realtime grid operation, may lead to harmonious unification of market efficiency and grid reliability. This fundamental principle of the duality theory has been reflected in most existing market designs. Most market rules require that RTO • Provide a reliable grid and coordinate grid operation to minimize costs consistent with secure operation of the grid; • Schedule and dispatch generation to satisfy market demand for electricity at minimum price while taking into account the security of the grid; • Purchase for the benefit of grid reliability the ancillary services and resources that are necessary for economic and secure delivery of electricity; X. Ma, D. Sun and K. Cheung are with AREVA T&D Inc., 11120 NE 33rd Place, Bellevue, WA 98004. • Provide information to participants in an open, nondiscriminatory manner to help them make consumption and production decisions. These competitive market rules are also in line with the longheld industry principle about reliable and economic grid operation. Optimization based economic dispatch and unit commitment has been practiced for decades to coordinate grid’s economic and reliable operation. But traditional optimization methods for economic dispatch and unit commitment are less rigorous and the underlying grid models are over-simplified. The key to competitive market success lies in the dealings with modeling details. The constrained optimization problem behind electricity market dispatch and pricing must therefore model grid details in order to realize the market efficiency as promised in the theory of economics and mathematics. As a result, significant progress has been made in recent years in applications of formal optimization techniques for competitive market based resource commitment, scheduling, pricing and dispatch. Two important optimization based applications for market clearing, security constrained economic dispatch (SCED) and unit commitment (SCUC) are discussed in this paper. The paper is organized as follows. The SCED algorithm and its evolution are presented in Section II. The SCUC algorithm is discussed in Section III. Section IV concludes the paper. II. SCED FOR MARKET CLEARING The market clearing function determines the quantities that market participants produce or consume, and the prices that are used to settle the quantities of electricity services produced or consumed. Correctly determining spot electricity prices is critical not only to successful competitive market operation, but also to the reliability of the grid. The optimal power flow (OPF) based framework [1] has been proposed for spot electricity pricing in many academic publications [2,3]. Due to practical limitations of non-linear optimization methods and intrinsic properties of grid operations, the DC model SCED algorithm, which is a variant of the AC OPF with many market related extensions, has been commonly accepted as the market clearing method [4,5]. Below, traditional OPF methods are described first, followed with discussion of the SCED method for market clearing. A. OPF Evolution for Electricity Pricing OPF is aimed to find a power flow solution that leads to both economic and reliable grid operation. It is common practice that the control variable values determined in the OPF solution are used as guidance to achieve optimal grid operation. The dual solution, that defines the marginal prices of relevant quantities, has been largely ignored until the advent of competitive markets. According to the duality theory, the dual solution in the form of prices is equivalent to the primal solution in the form of quantities in achieving the optimal objective. The OPF problem is stated in mathematical terms as follows: min f (u P , uQ ) subject to (λ ) (µ ) g (u , x ) = 0 h(u, x) ≤ 0 u min ≤ u ≤ u max where u = [u p , uQ ]T : Control variables, such as generator real and reactive power output and transformer tap positions; f (u , x) : Objective function typically represented with total production cost; x = [ xθ , xV ]T : State variables, such as bus voltage angles and magnitudes; g (u , x) = [ g P (u , x ), g Q (u , x)]T : Bus real and reactive power balance equality constraints; h(u, x ) = [hP (u , x ), hQ (u, x )]T : Inequality constraints, such as transmission line and transformer thermal limits and bus voltage magnitude limit constraints; λ = [λ P , λQ ]T : Shadow prices of bus real and reactive power balance constraints; µ = [ µ P , µ Q ]T : Shadow prices of grid security constraints; u min = [u Pmin , uQmin ]T : Minimum limits for control variables; u max = [u Pmax , uQmax ]T : Maximum limits for Control variables. In the OPF formulation, each of the equality or inequality constraints has a corresponding shadow price at its optima. The shadow price, µ , of a binding grid security constraint defines the marginal cost of maintaining the specific grid security constraint. The shadow price, λ P of bus real power balance constraint can be used to define the short-run marginal prices of producing/consuming real power at a bus. The shadow price, λQ , of bus reactive power balance constraint may be interpreted as the marginal cost of producing/consuming reactive power at a bus. When generators or loads are allowed to respond to the spot price signals, the prices can induce generator responses to achieve economic and reliable grid operation as effectively as the MW dispatches. In order for price signals to be able to convey effective control information for economic and reliable grid operation, price signals must be unambiguous, transparent and explainable. While the OPF formulation provides the theoretical basis for calculating spot prices of electricity, finding a global optimal solution to a realistic non-linear optimization problem is still artful, and thus it has not been widely utilized in practice. However, real and reactive power problems are only loosely coupled. While the reactive power problem is highly non-linear, the real power problem is very linear. Therefore, real and reactive power problems can be solved in a decoupled fashion. The decoupled OPF formulation [6] for real power can be described as follows: min f (u P ) subject to (λ P ) g P (u P , xθ ) = 0 (µ P ) hP (u P , xθ ) ≤ 0 u Pmin ≤ u P ≤ u Pmax This formulation is very similar to the previous full AC OPF formulation, except that reactive power related control variables, voltage magnitude variables and voltage security constraints are reduced to parameters with pre-determined values. This is currently the most commonly used optimization framework in electricity market clearing and price calculation. B. SCED for Market Clearing The security constrained economic dispatch, which is essentially a reformulation of the decoupled OPF, is the commonly used algorithm for market clearing. The SCED algorithm has been successfully applied to solve market clearing problem with large scale grid models, such as 2000 bus ISO-NE market, 15,000 bus PJM market, and 30,000 bus MISO market in the US. The SCED algorithm provides several advantages over the traditional optimal power flow: • The SCED algorithm uses a detailed, linearized grid model, and is solved with state-of-the-art linear programming (LP) techniques. • With the use of standard LP methods, the SCED algorithm provides almost unlimited capability to handle as many linear constraints as necessary. • Both base and contingency grid security constraints can be effectively handled. • Ancillary services can be incorporated in the LP based optimization framework. • Participant bid data models can be accurately reflected in the formulation. This modeling flexibility makes it possible for an electricity market to offer as many participant choices as needed for them to manage risks. • The same framework can be applied for energy, ancillary service and transmission right market clearing. • Below we discuss the applications of the SCED algorithm to solve the joint optimization of energy and ancillary services. - Joint optimization of energy and ancillary services In many of the existing electricity markets, energy and ancillary services (AS) are both allowed for competitive bidding. The fact that the same resource and same capacity may be used to provide multiple products dictates that AS market operation should be closely coordinated with the energy market. This close coordination is best achieved through joint optimization of AS and energy markets, which minimizes the total market cost of meeting system demand and AS requirements while satisfying network security constraints. In the development of AS markets, different market designs have been attempted. The designs can be categorized as three approaches: independent merit-order stack approach, sequential market clearing, and joint optimization. • Independent Merit Order Dispatch: Independent merit order based market clearing ignores the capacity coupling between energy production and supply of ancillary services. Each product is cleared separately from other products based on a separate merit order stack. This approach is simple, but it easily leads to solutions that are physically infeasible. • Sequential Market Clearing: The sequential approach recognizes that energy and reserves compete for the same generating capacity. In essence, a priority order is defined for each product. Available capacity of a resource (e.g. generating unit) is progressively reduced as higher priority products are dispatched from that resource. The degree of sophistication of recognizing the coupling varies from market to market. While the sequential dispatch is an improvement over purely independent merit-order dispatch, it needs further improvements for handling inter-dependencies among the coupled products. Explicit evaluation of costs associated with lost opportunity, production cost impacts, etc. are mechanisms that are used to provide quantitative indices for analyzing tradeoff decisions. They also help reduce the arbitrariness in the dispatch sequence. • Joint Optimization: In the joint optimization approach, the objective is to minimize the total cost of providing ancillary services along with energy offers to meet forecast demands as well as AS requirements. The allocation of limited capacity among energy and ancillary services for a resource is determined in terms of its total cost of providing all the products relative to other resources. The effective cost for a resource to provide multiple products depends on its offer prices as well as the product substitution cost. Product substitution cost arises when a resource has to reduce its use of capacity for one product so that the capacity can be used for a different product (leading to an overall lower cost solution). The product substitution cost is determined internally as part of the joint optimization. This product substitution cost plus its bid price reflects the marginal value of a specific product on the market. The marginal value, which is typically the market clearing price, represents the price for an extra unit of the product that is consistent with the marginal pricing principle for the energy product. Market clearing prices for ancillary services reflecting product substitution costs create price equity among the multiple products. Price equity refers to the fact that a market participant can expect to receive equivalent amount of profits no matter which kind of service the participant is assigned to provide. Price equity incents participants to follow dispatch instructions. Without the price equity, participants would tend to provide those services that produce the most profits, which could deviate significantly from dispatch instructions. Significant deviations from dispatch instructions could seriously degrade dispatcher’s ability to maintain grid reliability. Therefore, joint optimization of energy and AS market has been accepted in many electricity markets, including PJM-RTO, New York-ISO, ISO-New England, New Zealand and Australian markets. - An SCED formulation example Assume that a joint market allows bidding for multiple products, generation energy offer, price-responsive demand bid, and two types of ancillary service - ten-minute reserve, and thirtyminute reserve. With unit commitment schedules given, an exemplar SCED formulation for this joint market may be described in mathematical terms as follows: min c( P) + cs( S ) + co(O) − cd ( D) subject to • System power balance constraint: (λ ) ∑ ( Pi − Di ) −FD − PL = 0 | Pi − Pi0 |≤ RRimax (φi ) where Greek labels are corresponding constraint shadow prices; c, cs, co, cd: Cost or benefit associated with unit production,tenminute reserve, thirty-minute reserve and demand bids; Pi , Di , S i , Oi : Decision variables for generation dispatch, load dispatch, spinning reserve dispatch and operating reserve dispatch of resource i; Pimin , Pimax : Min and max dispatch limit for generator i; Pi0 : Initial generation output for generator i; Dimax : Maximum dispatch limit for load i; FD , PL : Fixed demand and transmission losses; d i : Load distribution factor for fixed demand; S max , O max : Ten- and thirty-minute reserve requirement; : Grid security limit for constraint l; Lmax l al , i : Sensitivity of constraint l with respect to bus i. The optimal solution to this SCED problem determines the market clearing quantities and market clearing prices by location. The market clearing prices by location, called locational marginal prices, and AS market clearing prices are by-products of the optimization solution. Under the joint optimization based market for energy and multiple ancillary services, the market clearing prices for the multiple products have the following important characteristics: • Locational marginal prices for energy: ∂PL LMPi = λ − λ − ∑ al ,i µ l ∂Pi l These locational price results give precise representation of the cause-effect relationship that is consistent with grid reliability management. • Higher prices for higher quality of ancillary services o Market clearing pricing for ten-minute reserve: ρS = γ S + γ O o Market clearing pricing for thirty-minute operating reserves: ρO = γ O ≤ ρ S • Marginal equity between energy and reserve prices: ∂C ( P ) o LMPi − = ρ S , if S>0 ∂Pi i • Ten-minute reserve requirement constraint: (γ S ) • o max ∑ Si ≥ S i Thirty-minute operating reserve requirement constraint: (γ O ) max ∑ ( Si + Oi ) ≥ O i • Grid base-case and contingency constraint: (µl ) ∑ al ,i ( Pi − Di − d i × FD) ≤ Ll i • Generator minimum generation limit constraint: (τ imin ) • Generator joint maximum generation limit constraint: (τ imax ) • Pi + Si + Oi ≤ Pimax Price-responsive load dispatch range constraint: (η imax ) • Pi ≥ Pimin 0 ≤ Di ≤ Dimax Generator ramp-rate limit constraint: LMPi − ∂C ( P) = ρ O , if S=0 and O>0 ∂Pi • LMPs for energy are always higher than market clearing prices for ancillary services except that there exists ancillary service capacity shortage. This can be seen from the above equations. These price relationships are essential to encouraging rational participants’ responses to market signals. But these price relationships are true only under rigorous mathematical terms. Therefore, adopting a formal optimization technology in market clearing is central to market efficiency and grid reliability. III. OPTIMIZATION-BASED UNIT COMMITMENT A. Market Oriented Unit Commitment Problem Unit commitment determines unit startup and shutdown schedules that meet forecast demand at minimum startup cost and energy production cost. Traditional unit commitment problems in general did not explicitly take into account grid security constraints in the commitment process. Even with the simplified modeling assumption, finding an optimal solution to unit commitment has been a challenging task due to its nature of curse of dimensionality. Many existing electricity markets, such as PJM, ISO-New England, New York ISO, and Mid West ISO, allow three-part bids including startup cost, no load cost, and energy cost components. These markets also adopt a two-settlement market structure that consists of a day-ahead market and a real-time market. The dayahead market is a financial market that determines the minimum cost commitment schedules based on participants’ bid-in fixed demand, price-sensitive demands, virtual transactions, external interchange schedules and transmission security constraints. Because many trading activities of the day-ahead market are used as mechanism to hedge financial risks in the real-time market, participants’ bids for demands and virtual transactions can deviate significantly from the physical grid operation. To guarantee grid reliability, a reliability commitment is required after day-ahead market is cleared. In the reliability commitment, the units committed in day-ahead market remain committed. Additional units required to meet forecasted demand and reserve capacity requirements are committed in the form of reserve capacity by minimizing the startup and no load cost components of available units that are not commitment in the day-ahead market. The market oriented unit commitment problem becomes more complex compared to the traditional unit commitment problem. The unit commitment schedules are applied in the SCED based market clearing for determination of day-ahead settlement quantities and prices. From a market efficiency perspective, those units committed in the day-ahead market process should be able to collect sufficient financial proceeds from day-ahead market settlement to cover their production cost based on the day-ahead market clearing quantities and prices. With this result, uplift charges resulting from cost compensation for market committed units are reduced, cost socialization is minimized, and market efficiency is improved. More importantly, any units that would be able to make a profit in terms of the day-ahead market clearing prices, if they were committed, should not be left uncommitted in the day-ahead market solution. When a generator that could be profitable is not committed, a rational explanation must be presented to the generator. This is important for creating a fair and transparent market that encourages rational bidding behavior complying with grid reliability requirements. The key to fair and transparent market that involves day-ahead unit commitment is to include grid security constraints in the commitment solution. As such, security constrained unit commitment (SCUC) has become an integral part of many dayahead markets. Successful solution to the SCUC problem presents great technical challenges, due to its requirement on global optimality and the need to deal with large-scale commitment problems of 1000 to 3000 units over a 2 to 7 day time horizon with grid models of over 20,000 buses. In addition to the requirements of commitment optimality and the ability to deal with large scale problems, requirements on new functional capabilities increase. Hydro-thermal coordination needs to be handled more effectively and consistently. Combined-cycle units need to be modeled to reflect the coupling effect of gas turbines and steam components. In meeting the challenges, great efforts have been made and significant progress has been achieved in advancing unit commitment techniques. B. Advances in Unit Commitment Methods The Unit Commitment problem is a large-scale combinatorial scheduling problem. For N units over M time periods there are a maximum of (2N-1)M combinations to evaluate. For a small problem where N=5 and M=24, there are (s5-1)24 = 6.2x1035 possible combinations! Solving even this small problem by direct enumeration is clearly an intractable approach. Historically, unit commitment algorithms have focused on heuristic methods that intelligently reduce the number of combinations that need to be evaluated. A popular method is to assume that units are restricted to some fixed startup/shutdown order. This assumption reduces the number of possible combinations to 2N x M, or for our example above to 25 x 24 = 768 combinations. This new problem can be solved optimally using a dynamic programming algorithm. More recently, Lagrangian Relaxation (LR) algorithms have been utilized. The LR approach decomposes the problem by unit. Each single unit problem can be optimally solved using a small single unit dynamic programming (SUDP) algorithm. A coordination module is used to adjust parameters (Lagrange multipliers) sent to the SUDP to achieve feasibility of system constraints. This approach implicitly evaluates many more combinations than is possible using priority-based methods. The LR decomposition provides a duality gap, which is a measure of how far the current solution is from the estimated lower bound (the theoretical minimum). Early LR algorithms [7-9] had numerous convergence problems. Later a “sequential bidding” method was developed, which utilized many of the LR components, but avoided convergence issues. This method creates a priority order that is determined dynamically by the algorithm, rather than a priori. This worked well for non-market-based systems, and provided additional capabilities for fuel and emissions constraints. Early experiences with the market oriented unit commitment made it clear that priority-based methods were not appropriate for market clearing purposes. Temporal changes in both unit offers and availability effectively invalidate the assumption of using a fixed priority over all study periods. The requirements for optimal hydro-thermal coordination and explicit inclusion of many grid security constraints created nearly insurmountable difficulties for the traditional unit commitment algorithms, such as priority-based method and classic dynamic programming method. The LR method is the most commonly used algorithm today for market based unit commitment. In some practical market applications, LR algorithms provided significantly improved results that typically have duality gaps of less than 1%, indicating near-optimum schedules. It is interesting to note that the LR decomposition is analogous to an economic market simulation. The LR coordinator can be viewed as the market clearing function, and the SUDP as the participant bidding mechanism. Based on current estimates of system prices, the SUDP determines individual unit bids that maximize each unit’s profit. The LR coordinator clears the market and commits additional units as necessary to meet system constraints. The solution iterates to achieve a minimum cost solution in much the same way as the market clearing process is repeated several times each day. As a result, the solutions from the LR tend to satisfy the participants, since their profits are maximized, while also producing secure and minimum cost system results. The LR method has been successfully applied in clearing large scale market of over 1000 units. But the LR method is frequently challenged due to its inability to prove that it has found a global solution. In search of a global optimal solution for the unit commitment problem, attempts were made decades ago to use mixed integer programming (MIP) method without success. In recent years there have been significant improvements in MIP algorithms. These MIPs utilize a “branch and bound” method that can implicitly evaluate all combinations, which enables MIP to ascertain global optimality. This claim of a globally optimal solution cannot be made for any of the other methods. Since its development in the early 1970’s, the branch-andbound method had suffered from poor and unpredictable performance when applied to practical sized mixed integer problems. However, the situation changed significantly during the last few years. A major contributor to MIP performance improvement is the drastic performance improvement of the LP, which is at the core of any MIP algorithm. In addition to improvements due to LP, there are a large number of schemes that have been developed over time for improving the intelligence of the branch and bound search logic. Although there was not a single monumental breakthrough in branch-and-bound, these different schemes collectively provide a tool-kit approach for tailoring to specific MIP problems. The use of MIP solvers is appealing in that they eliminate numerous heuristics utilized in other approaches, and theoretically allow for inclusion of complex constraints that are difficult to deal with using other methods. Intensive research on application of the MIP method is being conducted and initial success with MIP application to market based unit commitments with over 1000 units has been achieved [10]. C. An SCUC Example Problem: Reliability Commitment In this section, the reliability commitment problem in a multisettlement market system is used to demonstrate that successful market operation depends on not only the use of the right optimization methods, but the correct problem formulation and solution performance. - Solve the right problem While the Day-Ahead (DA) market produces financially binding schedules for the next operating day, these schedules may not provide an adequate resource plan for physical system operation. Reserve adequacy (RA) analysis must be performed to generate resource operating plans that ensure secure and reliable operation of the power system. Additional generation capacity may have to be committed for reliability purposes to bridge the gap between the capacities as seen from financially binding day-ahead schedules and the capacities needed to meet RTO’s forecast of the physical demand. Although the RA and DA market clearing processes share many common characteristics, such as the conventional UC problem definition, these are two fundamentally different business processes and have important differences in their respective problem definitions. The RA process not only needs to respect physical system requirements at least cost, but also must minimize any interference or distortion to the real-time economic price signals. The latter is particularly affected by the physical resource commitment schedules produced by the RA process. If the demand bids cleared in the day-ahead market should fall short of the forecast/actual demand, then real-time energy prices must be allowed to rise. The rise of real-time energy price would be the result of additional energy produced by units that were committed by RA. These are low cost providers of operating reserve but not necessarily energy. The decision criteria in RA commitment is based on start-up and cost of minimum generation, but not on incremental energy cost. The transition from 3-part energy bids in the DA market to the 2-part energy bid in the RA process is a relatively simple function from the application software and optimization method perspective. However, this fundamental transition in problem definition from DA to RA leads to additional important and related aspects of RA definition. The principal areas of continued RA problem definition centers on the issues of: (a) modeling and analysis of transmission security and incremental capacity commitment; and (b) RA input data preparation (interpretation and extrapolation). These are indicative of the challenge for the RA analysis; i.e. the transition between market operation and physical operation, which is essential for reliable operations. Thus, it is naturally subjected to significant re-definition as the market continues to evolve. The early and principal focus of the RA process was to ensure that the RTO system would have sufficient incremental capacities committed, in the form of operating reserves, to meet forecast demand. In that model, the energy balance in the SCUC was maintained at the level of cleared DA demand bids and thus the resulting power flows on the transmission system does not reflect the level commensurate with the energy demand forecast. The growing need for further improvement over the earlier RA process clearly points in the direction of more accurate modeling and analysis of transmission security constraints. This direction implies potentially fundamental augmentation of the RA business requirements. More than system-wide incremental capacity commitment process, the RA commitment decision will need to better recognize the impacts of transmission security. This requires increased emphasis on energy scheduling, including possible redispatching MW from the reference DA schedules, which in turn requires modeling energy cost and energy demand. On the other hand, it is also fundamental that committing for reserves (based on 2-part bids of startup and min-generation cost but not energy cost) remains the primary business objective for RA. How to navigate through seemingly conflicting requirements to produce useful and consistent definition of the RA problem is important and challenging. Close co-operation with RTO customers is key to resolving the challenges confronting the market operators and security coordinators. - Solve the problem fast All markets have definitive time-lines for specific market events. For example, several day-ahead markets close at noon and publish their results by 4PM. To provide sufficient flexibility and margin, the market-clearing applications need to be completed in less than half of the total available time. This can be quite challenging given the size and complexity of the problem. The adopted system architecture for solving the SCUC-RA problem shall be able to withstand the challenges. Using the concept of Benders Decomposition [11], the problem is decomposed into a unit commitment module and a simultaneous feasibility test (SFT) module. Such a system design is shown in Figure 1. Some of the key system features include the following: • Increase speed by plugging additional processors – For the seven-day SCUC RA analysis, 168 SFT solutions must be conducted (one for each hour) and each SFT solution involves the analysis of thousands of power flows depending on the number of contingencies. Furthermore several iterations between SFT and SCUC may be needed to reach a secure commitment solution. The amount of SFT computation is tremendous. Since the MW dispatches for each of the 168 hours are available simultaneously from the SCUC solution, the hundreds of thousands of SFT power flow analyses may be performed in parallel to reduce the SCUC-RA problem solution time. As system size increases and requirements change, this system architecture would provide the capability to scale the system by plugging in more processors to meet performance requirements. • Improve performance through efficient data management – For the seven day SCUC RA analysis, the volume of data flowing between SFT and SCUC is huge when hundreds of security constraints may be detected. Generating the vast volume of topology and security constraint sensitivity data not only takes up computer disk resources and system support personnel’s burden to manage the data, it also decreases the performance of the analytical engines. To alleviate this problem, network topology for each of the hours is identified in advance so that hours with the same topology are grouped and one network topology is produced for each group of the same topology hours. This typically reduces the data volume dramatically. As many RTO markets may grow in size and expand in market products, performance, integration and manageability are the critical system issues for the continual growth in size and complexity of the markets. This SCUC-RA system architecture can better meet these challenges. With the integration of the transmission network security analysis in the RA unit commitment, the SCUC commitment and dispatch MW solutions from one iteration are fed to the SFT application for security analysis. Network security violations for each hour detected by SFT are formulated as sensitivity-based constraints to be enforced in the next pass SCUC commitment solution. This iteration continues until no new violation is found in a commitment solution for any of the study hours. The process guarantees a reliable and secure commitment solution with minimum heuristics and operator’s intervention. This SCUC schema can handle the circumstances where detailed SFT analysis for all 168 hours in the RA study is required and parallel SFT processing may become necessary. However, flexibility will be built into the SCUC-RA system that allows the operator to perform the RA commitment task as practically needed: • • • Predefine security constraints for preemptive enforcement; Perform SFT analysis for selected hours; Control the iteration process between SFT and SCUC. MIP SCUC SFT SFT SFT SFT SFT SFT SFT SFT SFT Hour 1 Hour 2 Hour n Figure 1 - Parallel processing based SCUC architecture IV. CONCLUSIONS The unified framework for competitive electricity market and grid reliability is founded on the duality theory that is concerned with the outcome in a competitive market and the mathematical solution to a constrained optimization problem. Experiences with the implementation of several electricity markets suggest adoption of formal optimization technology as one of the key factors for a successful market. Significant progress has been made in recent years in applications of formal optimization techniques for competitive market based resource commitment, scheduling, pricing and dispatch. The SCUC and SCED algorithms are key components of a successful electricity market operation system. Traditional methods for the SCUC, such as the dynamic programming and the more recent Lagrangian Relaxation methods are being frequently challenged from ever-growing market demands for systematic and transparent decision-makings in market operations. The recent success in the application of formal optimization method, such as the MIP, is significant in improving market efficiency and enhancing grid reliability. The SCED algorithm is presently built on the LP based optimization method. It provides the capability to incorporate as many grid security constraints of linear format as needed and guarantees the consistency between market clearing quantities and prices. While the current SCED algorithm for View publication stats electricity market operation is mostly based on the DC grid model, there is a clear trend that the voltage/var impacts on market clearing quantities (in the form of MW-Mvar coupling) and prices be appropriately considered. Extension of the existing optimization-based SCED framework will be required. V. REFERENCES [1] D.I. Sun, B. Ashley, B. Brewer, B.A. Hughes, and W.F. Tinney, "Optimal Power Flow by Newton Approach", IEEE Transactions Vol. PAS-103, pp. 2864-2880, Oct. 1984. [2] F.C. Schweppe, M.C. Caramanis, R.D. Tabors and R.E. Bohn, Spot Pricing of Electricity, Kluwer Academic Publishers, 1988. [3] M.L. Baughman and S.N. Siddiqi, “Real-Time Pricing of Reactive Power: Theory and Case Study Results,” IEEE Trans. on Power Syst., vol. 6, no. 1, pp.23-29, Feb. 1991. [4] Check http://www.pjm.com for PJM market. [5] Check http://www.iso-ne.com for ISO-NE market. [6] A.A. El-Keib and X. Ma, “Calculating Short-Run Marginal Costs of Active and Reactive Power Production,” IEEE Trans. on Power Syst., vol. 12, no. 2, pp. 559-565, May 1997. [7] F. Zhuang, F. Galiana, “Towards a More Rigorous and Practical Unit Commitment by Lagrangian Relaxation”, IEEE Transactions on Power Syst., vol. 3, no. 2, pp. 763-773, May 1988. [8] S. Wang, S. Shahidepour, D. Kirschen, S. Mokhtari, “ShortTerm Generation Scheduling with Transmission and Environmental Constraints using Augmented Lagrangian Relaxation”, IEEE Transactions on Power Syst., vol. 10, no. 3, pp. 1294-1301, Aug. 1995. [9] F. Lee, “A Fuel-Constrained Unit Commitment Method”, IEEE Trans. on Power Syst., vol. 4, no. 3, pp. 1208-1218, Aug. 1989. [10] D. Streiffert, R. Philbrick, Andrew Ott “Mixed Integer Programming Solution for Market Clearing and Reliability Analysis”, to be presented at IEEE PES General Meeting, June 12-16, 2005. [11] H. Ma, S. Shahidehpour, “Unit Commitment with Transmission Security and Voltage Constraints” IEEE Trans. on Power Syst., vol. 14, no. 2, pp. 757-764, May 1999. VI. BIOGRAPHIES David I. Sun joined AREVA T&D Inc. in June 1980. He received his B.S. and M.S. from Rensselaer Polytechnic Institute, and his Ph.D. from University of Texas at Arlington, in 1974, 1976, and 1980 respectively, all in Electrical Engineering. His current focus is on the planning and development of deregulation applications. Xingwang Ma received his B.S. from Hefei University of Technology, China and his M.S. from the Graduate School, EPRI, Beijing, China in 1983 and 1985 respectively. He also received a M.S. in Electrical Engineering from The University of Alabama in 1995. He has been associated with EPRI(China) and ABB Systems Control. He joined AREVA T&D Inc. in 1996. He has been involved in the design and implementation of several electricity market systems. Kwok W. Cheung received the BS degree from National Cheng Kung University, Taiwan, in 1986, the MS degree from University of Texas at Arlington, in 1988, and the Ph.D. degree from Rensselaer Polytechnic Institute, Troy, NY in 1991. He joined AREVA T&D Inc. in 1991. His current focus is on the development of deregulation applications and market systems. Formatted: English (U.S.) Formatted: English (U.S.) Formatted: English (U.S.)