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This paper proposes a methodology to determine the required level of spinning and nonspinning reserves in a power system with a high penetration of wind power. The computation of the required reserve levels and their costs is achieved through a stochastic programming market-clearing model spanning a daily time horizon. This model considers the network constraints and takes into account the cost of both the load shedding and the wind spillage. The methodology proposed is illustrated using an example and a realistic case study. Some conclusions are finally drawn. Index Terms--Economic appraisal, reserves, stochastic programming, wind power.

To make informed decisions in futures markets of electric energy, stochastic programming models are commonly used. Such models treat stochastic processes via a set of scenarios, which are plausible realizations throughout the decision-making horizon of the stochastic processes. The number of scenarios needed to accurately represent the uncertainty involved is generally large, which may render the associated stochastic programming problem intractable. Hence, scenario reduction techniques are needed to trim down the number of scenarios while keeping most of the stochastic information embedded in such scenarios. This paper proposes a novel scenario reduction procedure that advantageously compares with existing ones for electricity-market problems tackled via two-stage stochastic programming. Index Terms--Decision making, electricity markets, scenario reduction, stochastic programming.

This paper presents a comprehensive and detailed study of an optimization-based approach to identify and analyze saddle-node bifurcations (SNBs) and limit-induced bifurcations (LIBs) of a power system model, which are known to be directly associated with voltage stability problems in these systems. Theoretical studies are presented, formally demonstrating that solution points obtained from an optimization model, which is based on complementarity constraints used to properly represent generators' voltage controls, correspond to either SNB or LIB points of this model. These studies are accomplished by proving that optimality conditions of these solution points yield the transversality conditions of the corresponding bifurcation points. A simple but realistic test system is used to numerically illustrate the theoretical discussions. Index Terms--Limit-induced bifurcations (LIBs), maximum loadability, optimization methods, saddle-node bifurcations (SNBs), transversality conditions, voltage stability (VS).

A generating unit can sell its production in the pool facing the financial risk inherent to volatile pool prices. Alternatively, it can sell its production through the futures market at comparatively stable but smaller average prices. Unlike the pool, forward contracts involve an obligation to sell during a specified time period, and, if the unit fails, it should buy energy from the pool to meet its futures market commitments. Hence, taking into account its forced outage rate, the unit should determine the appropriate mix of pool and futures-market involvement so that its expected profit is maximized for a prespecified risk level on profit variability. Within this context, this paper analyzes the impact of the degree of unavailability of the generating unit on its forward contracting decisions. A detailed case study illustrates the analysis performed. Index Terms--Forced outage rate (FOR), futures market, pool, power producer, risk, stochastic programming.

This paper addresses the optimal involvement in a futures electricity market of a power producer to hedge against the risk of pool price volatility. The considered trading horizon spans one whole year. Recognizing the highly uncertain nature of future pool prices, a stochastic programming framework with recourse is used to model this decision-making problem. The resulting problem is a large scale mixed-integer linear programming problem. Scenario reduction techniques are used to make this problem tractable. Risk is properly modeled using the CVaR methodology. Results from a realistic case study are provided and analyzed. Some conclusions are finally drawn. Index Terms--Conditional value at risk (CVaR) methodology, futures market, power producer, risk, stochastic programming.

In an electricity market cleared by a merit-order economic dispatch we first identify the necessary conditions for the market outcomes supported by pure strategy Nash equilibria (NE) to exist when generating companies (Gencos) game through their incremental cost offers or supply functions. A Genco may own any number of units, each offering to generate power through an incremental cost curve or supply function consisting of multiple blocks. Then, we develop a mixed-integer linear programming (MILP) scheme to find the NE without approximations or iterations. In Part II of this paper, we show how to use these NE to derive a dominant offer strategy in terms of gaming or not gaming that best meet the risk/benefit expectations of the participating Gencos. The MILP scheme is tested on several systems of up to 30 generating units, each with four incremental cost blocks. Finally, based on these results, we carry out a number of numerical analyses of how market power is influenced by the number and size of the competing Gencos. Index Terms--Electricity markets, gaming, market outcomes, market power, merit order, mixed-integer linear programming, pure strategy Nash equilibria, strategic offers, supply function equilibrium.

This paper provides a technique to determine the minimum required measurement set to ensure observability in state estimation even if any h meters fail. The technique relies on solving a nonlinear integer programming problem. The proposed procedure is illustrated through a simple example and three case studies based on the IEEE Test Systems. Conclusions are finally drawn. Index Terms--Binary variables, linear algebra, observability analysis, power system state estimation.

This paper presents a mixed-integer linear programming (LP) formulation for the long-term transmission expansion planning problem in a competitive pool-based electricity market. To achieve optimal expansion planning while modeling market functioning, we define a number of scenarios based on the future demand in the system and we simulate the maximization of the aggregate social welfare. Investment and operating costs, transmission losses and generator offers, and demand bids are considered. We propose to use a set of metrics to rate the effect of the expansion on the generators, demands, and the system as a whole. The proposed model is applied to the Garver six-bus system and to the IEEE 24-bus Reliability Test System. Simulation results can be interpreted in economic terms based on the values of the metrics obtained for different scenarios, parameters, and topologies. Index Terms--Electricity market, mixed-integer linear programming, social welfare, transmission expansion planning.

To procure the electric energy to be sold to its clients, a retailer has to face two major difficulties. While buying electric energy, it must cope with uncertain pool prices or sign forward contracts at higher average prices. While selling electricity, it should handle the uncertainty of the end-user demand and the fact that customers might choose a different retailer if the selling price is not competitive enough. We propose a risk-constrained stochastic programming framework to decide which forward contracts the retailer should sign and at which price it must sell electricity so that its expected profit is maximized at a given risk level. The developed model takes into account the elastic behavior of end users with respect to the selling price offered by the retailer. A realistic case study illustrates the methodology proposed. Index Terms--Electricity pool, forward contract, power retailer, risk, stochastic programming.

This paper addresses the optimal placement of static var compensators (SVCs) in a transmission network in such a manner that its loading margin is maximized. A multiscenario framework that includes contingencies is considered. This problem is formulated as a nonlinear programming problem that includes binary decisions, i.e., variables to decide the actual placement of the SVCs. Given the mixed-integer nonconvex nature of this problem, a Benders decomposition technique within a restart framework is used. Detailed numerical simulations on realistic electric energy systems demonstrate the appropriate behavior of the proposed technique. Conclusions are duly drawn. Index Terms--Benders decomposition, maximum loading margin, static var compensator (SVC) placement, voltage stability.

Within energy management systems, state estimation is a key function for building a network real-time model, which is a quasi-static mathematical representation of the current conditions in an interconnected network. The obtained model is dependent on the assumptions, and sensitivity analysis can be used to show how measurement schemes, transmission line modeling, and other parameters affect the quality of the state estimation solution. This paper provides expressions to compute all these sensitivities, and an example and a case study are used to illustrate them. Index Terms--Energy management system, least square estimation, power system state estimation, sensitivity analysis.

This paper provides a technique based on stochastic programming to optimally solve the electricity procurement problem faced by a large consumer. Supply sources include bilateral contracts, a limited amount of self-production and the pool. Risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study are provided and analyzed. Index Terms--Conditional value-at-risk (CVaR), electricity procurement, large consumer, stochastic programming.

This paper addresses the problem of allocating the cost of the transmission network to generators and demands. A physically-based network usage procedure is proposed. This procedure exhibits desirable apportioning properties and is easy to implement and understand. A case study based on the IEEE 24-bus system is used to illustrate the working of the proposed technique. Some relevant conclusions are finally drawn. Index Terms--Network usage, transmission cost allocation, [Z.sub.bus]

This paper proposes a simple multiarea decentralized state estimation procedure. This procedure allows estimating the state of a multiarea electric energy system while preserving the independence of each area. Information interchange among area operators reduces to just border information. The proposed algorithm is both simple and robust. The procedure developed is illustrated through several case studies carried out using the IEEE Reliability Test System. Conclusions are duly drawn. Index Terms--Decomposition, large-scale optimization, multiarea power system, state estimation.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.03.037 Byline: Raquel Garci'a-Bertrand (a), Antonio J. Conejo (a), Steven Gabriel (b) Keywords: Quadratic programming; Market equilibrium; Pool-based electric energy market; Linear complementary problem; Minimum profit conditions Abstract: This paper provides a tool to determine the near-equilibrium of an electric energy market. This market works under locational marginal pricing, i.e., generating units and demand loads are paid and pay, respectively, the locational marginal prices corresponding to the nodes they are connected to. The near-equilibrium is defined as the energy transaction levels for which generating companies maximize their respective profits and consumption companies maximize their respective utilities. An independent system operator clears the market maximizing the social welfare. Conditions that ensure minimum profit for generating units can be included. However, these conditions may render a generating unit uncompetitive and expel it from the market. Demands are taken to be non-constant and values are determined as part of the solution. The near-equilibrium is obtained through the solution of a mixed-integer quadratic problem equivalent to a mixed linear complementarity problem that includes the minimum profit conditions. It is important to note that the near-equilibrium concept presented in this paper does not solve a market equilibrium when indivisibilities such as start up costs or the like are present. Lastly, we validate the proposed model on a case study using data from the IEEE Reliability Test System. Author Affiliation: (a) Department of Electrical Engineering, Universidad de Castilla -- La Mancha, Ciudad Real, 13071 Spain (b) Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA Article History: Received 14 October 2003; Accepted 21 March 2005

A dynamic tool for calculating near-equilibrium in electricity markets under minimum profit conditions and marginal pricing is presented.

This paper provides a unified approach to observability checking, critical measurements identification, determination of observable islands, identification of irrelevant boundary injections, and pseudo-measurements selection to restore observability. A robust yet efficient algebraic technique is proposed. Several simple examples are used to illustrate the capabilities of the proposed procedure. Results from large case studies are presented to demonstrate the appropriate computational behavior of the proposed algorithms. Finally, conclusions are duly drawn. Index Terms--Linear algebra, null space, observability analysis, orthogonal transformation, power system state estimation.