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Showing papers in "IEEE Transactions on Power Systems in 2003"


Journal ArticleDOI
TL;DR: In this paper, a particle swarm optimization (PSO) method for solving the economic dispatch (ED) problem in power systems is proposed, and the experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
Abstract: This paper proposes a particle swarm optimization (PSO) method for solving the economic dispatch (ED) problem in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and nonsmooth cost functions are considered using the proposed method in practical generator operation. The feasibility of the proposed method is demonstrated for three different systems, and it is compared with the GA method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.

1,635 citations


Journal ArticleDOI
TL;DR: In this paper, the authors argue that increasing the short-run price elasticity of the demand for electrical energy would improve the operation of electricity markets, however, that enhancing this elasticity is not an easy task.
Abstract: This tutorial paper discusses some aspects of electricity markets from the perspective of the demand-side. It argues that increasing the short-run price elasticity of the demand for electrical energy would improve the operation of these markets. It shows, however, that enhancing this elasticity is not an easy task. The tools that consumers and retailers of electrical energy need to participate more actively and effectively in electricity markets are discussed. The paper also describes how consumers of electricity can take part in the provision of power system security.

807 citations


Journal ArticleDOI
TL;DR: In this paper, a dynamic model of doubly fed induction generator wind turbines and their associated control and protection circuits is derived, which can be used to simulate the DIF wind turbine using a single-cage and doublecage representation of the generator rotor.
Abstract: It is now recognized that many large wind farms will employ doubly fed induction generator (DFIG) variable speed wind turbines. A number of such wind farms are already in operation and more are planned or under construction. With the rising penetration of wind power into electricity networks, increasingly comprehensive studies are required to identify the interaction between the wind farm(s) and the power system. These require accurate models of doubly fed induction generator wind turbines and their associated control and protection circuits. A dynamic model has been derived, which can be used to simulate the DFIG wind turbine using a single-cage and double-cage representation of the generator rotor, as well as a representation of its control and protection circuits. The model is suitable for use in transient stability programs that can be used to investigate large power systems. The behavior of a wind farm and the network under various system disturbances was studied using this dynamic model. The influence of the DFIG control on the stability of the wind farm was also investigated by considering different control gains and by applying network voltage control through both stator side and rotor side converters.

735 citations


Journal ArticleDOI
TL;DR: The transmission planning state-of-the-art, which was obtained from the review of the most interesting models found in the international technical literature, is presented.
Abstract: In this paper, the transmission planning state-of-the-art, which was obtained from the review of the most interesting models found in the international technical literature, is presented. The classification of publications was made, keeping in mind the solution methods, the treatment of the planning horizon, and the consideration of the new competitive schemes in the power sector. A discussion about the available tools for development of transmission planning models is also included.

713 citations


Journal ArticleDOI
TL;DR: The results demonstrate the capabilities of the proposed approach to generate well-distributed Pareto-optimal solutions of the multiobjective EED problem in one single run and the comparison with the classical techniques demonstrates the superiority of the suggested approach and confirms its potential to solve the multi objective E ED problem.
Abstract: This paper presents a new multiobjective evolutionary algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem. A new strength Pareto evolutionary algorithm (SPEA) based approach is proposed to handle the EED as a true multiobjective optimization problem with competing and noncommensurable objectives. The proposed approach employs a diversity-preserving mechanism to overcome the premature convergence and search bias problems. A hierarchical clustering algorithm is also imposed to provide the decision maker with a representative and manageable Pareto-optimal set. Moreover, fuzzy set theory is employed to extract the best compromise nondominated solution. Several optimization runs of the proposed approach have been carried out on a standard test system. The results demonstrate the capabilities of the proposed approach to generate well-distributed Pareto-optimal solutions of the multiobjective EED problem in one single run. The comparison with the classical techniques demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EED problem. In addition, the extension of the proposed approach to include more objectives is a straightforward process.

683 citations


Journal ArticleDOI
TL;DR: The concept of cumulant and bispectrum are embedded into the ARMA model in order to facilitate Gaussian and non-Gaussian process considerations, and with embodiment of a Gaussianity verification procedure, the forecasted model is identified more appropriately.
Abstract: In this paper, the short-term load forecast by use of autoregressive moving average (ARMA) model including non-Gaussian process considerations is proposed. In the proposed method, the concept of cumulant and bispectrum are embedded into the ARMA model in order to facilitate Gaussian and non-Gaussian process. With embodiment of a Gaussianity verification procedure, the forecasted model is identified more appropriately. Therefore, the performance of ARMA model is better ensured, improving the load forecast accuracy significantly. The proposed method has been applied on a practical system and the results are compared with other published techniques.

597 citations


Journal ArticleDOI
TL;DR: In this article, two robust decentralized control design methodologies for load frequency control (LFC) are proposed, one is based on H/sub/spl infin// control design using linear matrix inequalities (LMI) technique in order to obtain robustness against uncertainties and the second controller has a simpler structure, which is more appealing from an implementation point of view.
Abstract: In this paper, two robust decentralized control design methodologies for load frequency control (LFC) are proposed. The first one is based on H/sub /spl infin// control design using linear matrix inequalities (LMI) technique in order to obtain robustness against uncertainties. The second controller has a simpler structure, which is more appealing from an implementation point of view, and it is tuned by a proposed novel robust control design algorithm to achieve the same robust performance as the first one. More specifically, genetic algorithms (GAs) optimization is used to tune the control parameters of the proportional-integral (PI) controller subject to the H/sub /spl infin// constraints in terms of LMI. Hence, the second control design is called GALMI. Both proposed controllers are tested on a three-area power system with three scenarios of load disturbances to demonstrate their robust performances.

458 citations


Journal ArticleDOI
TL;DR: In this paper, different control techniques for damping undesirable interarea oscillation in power systems by means of power system stabilizers, static VAr compensators, and shunt static synchronous compensators (STATCOMs) are compared.
Abstract: This paper discusses and compares different control techniques for damping undesirable interarea oscillation in power systems by means of power system stabilizers (PSS), static VAr compensators (SVCs), and shunt static synchronous compensators (STATCOMs). The oscillation problem is analyzed from the point of view of Hopf bifurcations, an "extended" eigenanalysis to study different controllers, their locations, and the use of various control signals for the effective damping of these oscillations. The comparisons are based on the results obtained for the IEEE 50-machine, 145-bus test system, which is a benchmark for stability analysis.

455 citations


Journal ArticleDOI
TL;DR: In this article, a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem is presented. But this approach is not suitable for large-scale systems, as the problem is large scale, mixed integer, nonlinear, and nonconvex.
Abstract: This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver's 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique.

454 citations


Journal ArticleDOI
TL;DR: In this paper, a new unit commitment problem, adapting extended priority list (EPL) method is introduced, which consists of two steps, in the first step, in order to get rapidly some initial unit commitment problems by priority list method, operational constraints are disregarded.
Abstract: This paper introduces a new unit commitment problem, adapting extended priority list (EPL) method. The EPL method consists of two steps, in the first step we get rapidly some initial unit commitment problem schedules by priority list (PL) method. At this step, operational constraints are disregarded. In the second step unit schedule is modified using the problem specific heuristics to fulfill operational constraints. To calculate efficiently, however, note that some heuristics applied only to solutions can expect improvement. Several numerical examples demonstrate the effectiveness of proposed method.

406 citations


Journal ArticleDOI
A.L. Ott1
TL;DR: In this article, the PJM day-ahead and real-time energy markets are discussed, where the latter is based on least-cost security constrained unit commitment and dispatch with several fundamental design features.
Abstract: This paper outlines the fundamental features of the PJM day-ahead energy market and real-time energy market. The Day-ahead market is based on a voluntary least-cost security constrained unit commitment and dispatch with several fundamental design features that ensure the market is robust and competitive. This market offers market participants the option to lock in energy and transportation charges at binding day-ahead prices. The flexibility of the day-ahead market rules provide all participants with equal access to the day-ahead market through consistent price signals and by providing all participants with the ability to submit virtual demand bids and virtual supply offers. These mechanisms promote liquidity in the markets. Economic incentives drive the convergence of the day-ahead and real-time market prices. The real-time energy market is based on security-constrained economic dispatch and is cleared based on the actual system operating conditions. The LMP-based markets support reliable grid operations through efficient price signals.

Journal ArticleDOI
TL;DR: In this paper, a modified price penalty factor is proposed to solve the combined economic emission dispatch (CEED) problem by considering both the economy and emission objectives, which is converted into a single objective function using a Price Penalty Factor approach.
Abstract: Economic load dispatch (ELD) and economic emission dispatch (EED) have been applied to obtain optimal fuel cost and optimal emission of generating units, respectively. Combined economic emission dispatch (CEED) problem is obtained by considering both the economy and emission objectives. This biobjective CEED problem is converted into a single objective function using a price penalty factor approach. A novel modified price penalty factor is proposed to solve the CEED problem. In this paper, evolutionary computation (EC) methods such as genetic algorithm (GA), micro GA (MGA), and evolutionary programming (EP) are applied to obtain ELD solutions for three-, six-, and 13-unit systems. Investigations showed that EP was better among EC methods in solving the ELD problem. EP-based CEED problem has been tested on IEEE 14-, 30-, and 118-bus systems with and without line flow constraints. A nonlinear scaling factor is also included in EP algorithm to improve the convergence performance for the 13 units and IEEE test systems. The solutions obtained are quite encouraging and useful in the economic emission environment.

Journal ArticleDOI
TL;DR: In this article, an optimal multiobjective design of robust multimachine power system stabilizers (PSSs) using genetic algorithms is presented, where stabilizers are tuned to simultaneously shift the lightly damped and undamped electromechanical modes of all plants to a prescribed zone in the s-plane.
Abstract: Optimal multiobjective design of robust multimachine power system stabilizers (PSSs) using genetic algorithms is presented in this paper. A conventional speed-based lead-lag PSS is used in this work. The multimachine power system operating at various loading conditions and system configurations is treated as a finite set of plants. The stabilizers are tuned to simultaneously shift the lightly damped and undamped electromechanical modes of all plants to a prescribed zone in the s-plane. A multiobjective problem is formulated to optimize a composite set of objective functions comprising the damping factor, and the damping ratio of the lightly damped electromechanical modes. The problem of robustly selecting the parameters of the power system stabilizers is converted to an optimization problem which is solved by a genetic algorithm with the eigenvalue-based multiobjective function. The effectiveness of the suggested technique in damping local and interarea modes of oscillations in multimachine power systems, over a wide range of loading conditions and system configurations, is confirmed through eigenvalue analysis and nonlinear simulation results.

Journal ArticleDOI
TL;DR: In this article, the authors mainly studied how to find proper splitting strategies of large-scale power systems using an ordered binary decision diagrams (OBDD)-based three-phase method and a time-based layered structure of the problem solving process was introduced to make this method more practical.
Abstract: System splitting problem (SS problem) is to determine proper splitting points (or called splitting strategies) to split the entire interconnected transmission network into islands ensuring generation/load balance and satisfaction of transmission capacity constraints when islanding operation of a system is unavoidable. For a large-scale power system, its SS problem is very complicated in general because a combinatorial explosion of strategy space happens. This paper mainly studies how to find proper splitting strategies of large-scale power systems using an ordered binary decision diagrams (OBDD)-based three-phase method. Then, a time-based layered structure of the problem solving process is introduced to make this method more practical. Simulation results on IEEE 30- and 118-bus networks show that by this method, proper splitting strategies can be given quickly. Further analyses indicate that this method is effective for larger-scale power systems.

Journal ArticleDOI
TL;DR: In this paper, the authors propose a decentralized solution of the DC optimal power flow (OPF) problem in large interconnected power systems by decomposing the overall OPF problem of a multiarea system into independent OPF subproblems, one for each area.
Abstract: This paper presents a new method for the decentralized solution of the DC optimal power flow (OPF) problem in large interconnected power systems. The method decomposes the overall OPF problem of a multiarea system into independent OPF subproblems, one for each area. The solutions of the OPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the global OPF solution. The prices used for the coordination of the subproblem solutions are the prices of electricity exchanges between adjacent areas. Test results from the application of the method to the three-area RTS-96 and the Balkan power system are reported.

Journal ArticleDOI
TL;DR: In this paper, an optimal power-flow-based ATC enhancement model is formulated to achieve the maximum power transfer of the specified interface with FACTS control, and a power injection model of FACTS devices, which enables simulating the control of any FACTS device, is employed.
Abstract: From the viewpoint of operational planning, this paper focuses on the evaluation of the impact of FACTS control on available transfer capability (ATC) enhancement. Technical merits of FACTS technology on ATC boosting are analyzed. An optimal power-flow-based ATC enhancement model is formulated to achieve the maximum power transfer of the specified interface with FACTS control. For better studying the capability of FACTS control, a power injection model of FACTS devices, which enables simulating the control of any FACTS devices, is employed. Studies based on the IEEE 118-bus system with all categories of FACTS devices demonstrate the effectiveness of FACTS control on ATC enhancement.

Journal ArticleDOI
TL;DR: In this paper, a new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed using genetic algorithms (GAs), the model handles simultaneously the subproblems of shortterm Hydrothermal coordination, unit commitment, and economic load dispatch.
Abstract: A new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed. Using genetic algorithms (GAs), the model handles simultaneously the subproblems of short-term hydrothermal coordination, unit commitment, and economic load dispatch. Considering a scheduling horizon period of a week, hourly generation schedules are obtained for each of both hydro and thermal units. Future cost curves of hydro generation, obtained from long and mid-term models, have been used to optimize the amount of hydro energy to be used during the week. In the genetic algorithm (GA) implementation, a new technique to represent candidate solutions is introduced, and a set of expert operators has been incorporated to improve the behavior of the algorithm. Results for a real system are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, a general power flow algorithm for three-phase four-wire radial distribution networks, considering neutral grounding, based on backward-forward technique, is proposed, where both the neutral wire and ground are explicitly represented.
Abstract: The neutral wire in most power flow software is usually merged into phase wires using Kron's reduction. Since the neutral wire and the ground are not explicitly represented, neutral wire and ground currents and voltages remain unknown. In some applications, like power quality and safety analyses, loss analysis, etc., knowing the neutral wire and ground currents and voltages could be of special interest. In this paper, a general power flow algorithm for three-phase four-wire radial distribution networks, considering neutral grounding, based on backward-forward technique, is proposed. In this novel use of the technique, both the neutral wire and ground are explicitly represented. A problem of three-phase distribution system with earth return, as a special case of a four-wire network, is also elucidated. Results obtained from several case studies using medium- and low-voltage test feeders with unbalanced load, are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors provide a state-of-the-art summary of risk assessment in energy trading, including portfolio analysis and hedging instruments, and provide a comprehensive critical literature survey of what has been applied to date in the power markets.
Abstract: This paper provides a state-of-the-art summary of risk assessment in energy trading. Techniques from financial engineering are needed by electric energy companies to manage price risk. These tools are needed by suppliers, distributors, and traders in a competitive electric power marketplace. Tools that have been adapted to the specific environment of the electric power system include portfolio analysis and hedging instruments. This paper provides a comprehensive critical literature survey of what has been applied to date in the power markets and which areas continue to need additional research. One example market scenario is used throughout the paper to demonstrate the usefulness of the risk assessment methods.

Journal ArticleDOI
TL;DR: In this paper, a novel hierarchical control for both dynamic and steady state stability enhancement is proposed, and a complete analysis is presented of various locally measurable input signals that can be used for the controller.
Abstract: Different control aspects related to the use of TCSC for stability improvement of power systems are addressed in this paper. A novel hierarchical control designed for both dynamic and steady state stability enhancement is proposed, and a complete analysis is presented of various locally measurable input signals that can be used for the controller. Control strategies to mitigate adverse interactions among the TCSC hierarchical controls are also presented. A simplified model of the Argentinian high voltage interconnected system is used to illustrate the ideas presented in the paper.

Journal ArticleDOI
TL;DR: In this paper, a method using trajectory sensitivity to reschedule power generation to ensure system stability for a set of credible contingencies while satisfying its economic goal is proposed, which can be used as a preventive control scheme for system operators in real time.
Abstract: In the deregulated environment of power systems, the transmission networks are often operated close to their maximum capacity to achieve transfer of power. Besides, the operators must operate the system to satisfy its dynamic stability constraints under credible contingencies. This paper provides a method using trajectory sensitivity to reschedule power generation to ensure system stability for a set of credible contingencies while satisfying its economic goal. System modeling issue is not a limiting concern in this method, and hence, the technique can be used as a preventive control scheme for system operators in real time.

Journal ArticleDOI
Dragan Jovcic1
TL;DR: In this paper, a new phase-locked loop (PLL) system that uses adaptation algorithms is developed with the aim of improving speed of responses, robustness to AC voltage depressions, and harmonic rejection.
Abstract: This research addresses the special requirements of phase locked loops (PLLs) for a typical application with FACTS elements. A new PLL system that uses adaptation algorithms is developed with the aim of improving speed of responses, robustness to AC voltage depressions, and harmonic rejection. The adaptive PLL consists of the three control units that individually control frequency, phase angle, and voltage magnitude. The voltage controller output is used to compensate for reduced gain caused by the AC voltage magnitude depressions. The output phase angle and its derivative, the frequency signal, are controlled in two independent control systems in order to enable elimination of frequency and phase error without compromising transient responses. The simulation results are compared with a PLL available with the PSB MATLAB block-set and noticeable improvements are demonstrated. In particular, settling time and overshooting are significantly lower with conditions of reduced AC voltage magnitude.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a market model that includes demand-side reserve offers and where energy and reserve are jointly dispatched, and the results suggest that not only do the consumers increase their profits but, in addition, the market power of the generators is reduced.
Abstract: We propose a market model that includes demand-side reserve offers and where energy and reserve are jointly dispatched. Generators and consumers can submit offers and bids on five distinct products-energy, upspinning reserve, downspinning reserve, and two kinds of standby reserve. The resources are scheduled and dispatched in a joint auction through a mixed-integer optimization program. The extra scheduling flexibility introduced by demand-side reserve offers can lead to significant gains in economic efficiency. Thus, the results suggest that not only do the consumers increase their profits but, in addition, the market power of the generators is reduced.

Journal ArticleDOI
TL;DR: In this article, a Monte Carlo-based method for the adequacy assessment of distributed generation systems is presented and implemented in a typical case study where several distributed generation units are running in parallel within a sample distribution system and the system margins and the average amount of unsupplied loads are estimated using Monte Carlo simulation.
Abstract: This paper presents a Monte Carlo-based method for the adequacy assessment of distributed generation systems. The state duration sampling approach is employed in this paper to model the operating histories of the installed distributed generators. A general procedure to assess the ability of the system power capacity to meet the total demand is presented and implemented in a typical case study where several distributed generation units are running in parallel within a sample distribution system and the system margins and the average amount of unsupplied loads are estimated using Monte Carlo simulation. The results obtained are presented and a new perspective to the power management of distribution systems is discussed.

Journal ArticleDOI
Qianchuan Zhao1, Kai Sun1, Da-Zhong Zheng1, Jin Ma1, Qiang Lu1 
TL;DR: A two-phase method to search for proper splitting strategies in real-time using highly efficient OBDD-based algorithm and power-flow analysis in the reduced strategy space in the second phase is proposed.
Abstract: System splitting problem, also known as controlled system separation problem, is to determine the proper splitting points for splitting the entire power network into islands when island operation of system is unavoidable. By "proper" we mean that the splitting strategies should guarantee both the power balance and satisfaction to capacity constraints of transmission lines and other facilities in each island. The system splitting problem is very hard because the strategy space is huge for even middle-scale power networks. This paper proposes a two-phase method to search for proper splitting strategies in real-time. The method narrows down the strategy space using highly efficient OBDD-based algorithm in the first phase, then finds proper splitting strategies using power-flow analysis in the reduced strategy space in the second phase. Simulation with symbolic model checking tool SMV indicates that this method is very promising.

Journal ArticleDOI
TL;DR: In this paper, an interior point method is used to solve the optimal power flow problem with a multiobjective function for maximizing both social benefit and the distance to maximum loading conditions.
Abstract: This paper proposes a novel technique for representing system security in the operations of decentralized electricity markets, with special emphasis on voltage stability. An interior point method is used to solve the optimal power flow problem with a multiobjective function for maximizing both social benefit and the distance to maximum loading conditions. A six-bus system with both supply and demand-side bidding is used to illustrate the proposed technique for both elastic and inelastic demand, and a 129-bus test system that models the Italian HV transmission network is used for testing the practical applicability of the proposed method. The results obtained show that the proposed technique is able to improve system security while yielding better market conditions through increased transaction levels and improved locational marginal prices throughout the system.

Journal ArticleDOI
TL;DR: In this paper, a formulation of the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem is presented and a method to solve it is proposed.
Abstract: This paper presents a formulation of the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem and proposes a method to solve it. In the MC-TSCOPF formulation, this paper introduces a modified formulation for integrating transient stability model into conventional OPF, which reduces the calculation load considerably. In our MC-TSCOPF solution, the primal-dual Newton interior point method (IPM) for nonlinear programming (NLP) is adopted. Computation results on the IEEJ WEST10 model system demonstrate the effectiveness of the presented MC-TSCOPF formulation and the efficiency of the proposed solution approach. Moreover, based on quite convincing simulation results, some phenomena occurred when considering multicontingency are elaborated.

Journal ArticleDOI
TL;DR: In this paper, the market risks encountered by energy asset operators can be categorized as short term/operational, intermediate term/trading, and long term/valuation in nature, and how to optimize these portfolios for risk-return relationships.
Abstract: The market risks encountered by energy asset operators can be categorized as short term/operational, intermediate term/trading, and long term/valuation in nature. This paper describes how the market risks in operations can be measured and managed using real option models and stochastic optimization techniques. It then links these results to intermediate term value at risk and related risk metrics such as cash flow, earnings, and credit risk which can be used to measure trading risks over weeks to months; and how to optimize these portfolios for risk-return relationships. Finally, it then explores the risks in longer term energy portfolio management and how these can be simulated, measured, and optimized.

Journal ArticleDOI
TL;DR: In this paper, the authors present a methodology for allocating the cost of a transmission network to its users based on the principle of equivalent bilateral exchanges, which states that after all physical laws governing the flow of power have been met, each demand is assigned a fraction of each generation and each generator is assigned an equivalent proportion of each demand in a uniform manner.
Abstract: This paper presents a novel methodology for allocating the cost of a transmission network to its users based on the principle of equivalent bilateral exchanges, which states that after all physical laws governing the flow of power have been met, each demand is assigned a fraction of each generation and each generator is assigned a fraction of each demand in a uniform manner. Transmission cost allocation based on this principle presents several advantages, namely, independence from the choice of the slack bus, recognition of counter-flows, and transmission use charges that are stable and always positive.

Journal ArticleDOI
TL;DR: In this article, a unified framework for the mathematical representation of the market dispatch and redispatch problems that the IGO must solve in congestion management (CM) in these various jurisdictions is presented.
Abstract: The restructuring of the electricity industry has spawned the introduction of new independent grid operators (IGOs), typically called transmission system operators (TSOs); independent system operator (ISOs); or regional transmission organizations (RTOs), in various parts of the world. An important task of an IGO is congestion management (CM) and pricing. This activity has significant economic implications on every market participant in the IGO's region. The paper briefly reviews the CM schemes and the associated pricing mechanism used by the IGOs in five representative schemes. These were selected to illustrate the various CM approaches in use: England and Wales, Norway, Sweden, PJM, and California. The authors develop a unified framework for the mathematical representation of the market dispatch and redispatch problems that the IGO must solve in CM in these various jurisdictions. They use this unified framework to develop meaningful metrics to compare the various CM approaches so as to assess their efficiency and the effectiveness of the market signals provided to the market participants. They compare, using a small test system, side by side, the performance of these schemes.