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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.

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.

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.

This paper addresses the congestion management problem avoiding offline transmission capacity limits related to stability. These limits on line power flows are replaced by optimal power flow-related constraints that ensure an appropriate level of security, mainly targeting voltage instabilities, which are the most common source of stability problems. Results from an illustrative case study based on the IEEE 24-bus Reliability Test System are analyzed. Conclusions are duly drawn. Index Terms--Congestion management, nonlinear programming, transmission capacity.

Considering the viewpoint of a retailer, this paper analyzes the problem of setting up contracts on both the supplier and end-user sides to maximize profits while maintaining an acceptable level of settlement risk. The proposed stochastic optimization model can assist retailers with these efforts and guide them in their contractual arrangements. A realistic example illustrates the capabilities of the methodology proposed. Index Terms--Contract design, electricity market, mixed-integer nonlinear programming, retailer viewpoint, stochastic optimization.

This paper proposes a novel technique for representing system security constraints that properly include voltage stability limits in the operation of competitive electricity markets. The market-clearing algorithm is modeled as a voltage stability constrained optimal power flow (OPF) problem, while the distance to the closest critical power flow solution is represented by means of a loading parameter and evaluated using a continuation power flow (CPF) technique. Sensitivities obtained at the OPF step are used to estimate power directions for the CPF method, while the CPF analysis provides the loading parameter to be used in the OPF problem based on an N-1 contingency criterion. The OPF and the CPF steps are repeated until the maximum loading parameter is found, thus providing optimal solutions considering both proper market conditions and security margins. Two benchmark systems with both supply and demand bidding are used to illustrate and test the proposed technique. Index Terms--Continuation power flow (CPF), electric energy markets, optimal power flow (OPF), security, sensitivity analysis, voltage stability.

This paper considers a profit-maximizing thermal producer that participates in a sequence of spot markets, namely, day-ahead, automatic generation control (AGC), and balancing markets. The producer behaves as a price-taker in both the day-ahead market and the AGC market but as a potential price-maker in the volatile balancing market. The paper provides a stochastic programming methodology to determine the optimal bidding strategies for the day-ahead market. Uncertainty sources include prices for the day-ahead and AGC markets and balancing market linear price variations with the production of the thermal producer. Results from a realistic case study are reported and analyzed. Conclusions are duly drawn. Index Terms--Electricity spot markets, market power, optimal bidding strategies, stochastic programming.

Within an optimal power flow market clearing framework, this paper provides expressions to compute the sensitivities of locational marginal prices with respect to power demands. Sensitivities with respect to other parameters can also be obtained. An example and a case study are used to illustrate the expressions derived. Index Terms--Locational marginal prices, optimal power flow, sensitivities.

This paper analyzes the market-clearing formulation with stochastic security developed in its companion paper through two case studies solved using mixed-integer linear programming techniques. The generation and reserve schedules as well as the nodal prices of energy and security are assessed under various conditions such as a) line flow limits, b) when nonspinning reserve is excluded from the formulation, c) demand-side valuation of energy not served, d) generator ramping limits, and e) the set of pre-selected contingencies. Index Terms--Computational complexity, electricity markets, expected load not served, marginal pricing, mixed-integer linear programming, reserve, security, stochastic unit commitment, value of lost load.

The first of this two-paper series formulates a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixed-integer linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed. Index Terms--Deterministic/probabilistic security criteria, electricity markets, expected load not served, failure rate, reserve, stochastic programming, transmission limits, unit commitment, value of lost load.

This paper deals with the problem of transmission cost allocation (TCA) in very large networks with multiple interconnected regions or countries. The basis of one scheme recently put forward is a single-area TCA algorithm from which inter-regional compensations are computed. One concern about this approach is that an international operator (IO) must have access to detailed information that autonomous regions or countries may not be willing or able to share. This led to the development of a new multiarea TCA scheme, called multiarea decoupled (MAD), in which each region carries out its own TCA, while the IO carries out a region-wise TCA on the network of tie lines. In MAD, the IO does not require detailed and possibly proprietary information about regional networks, relying only on the characteristics of the tie-line network and the extent to which each region uses such a network. This is a key issue, especially in North America, considering FERC's intention to provide Regional Transmission Organizations (RTOs) with exclusive autonomy to provide transmission service and to set and administer their own transmission-use tariffs. Numerical studies on the proposed scheme are described, including a four-area system based on the IEEE reliability test system (RTS) network. Index Terms--Equivalent bilateral exchange, flow based, multiarea networks, proportional sharing, tie lines, transmission cost allocation (TCA).

This paper proposes a novel technique to forecast day-ahead electricity prices based on the wavelet transform and ARIMA models. The historical and usually ill-behaved price series is decomposed using the wavelet transform in a set of better-behaved constitutive series. Then, the future values of these constitutive series are forecast using properly fitted ARIMA models. In turn, the ARIMA forecasts allow, through the inverse wavelet transform, reconstructing the future behavior of the price series and therefore to forecast prices. Results from the electricity market of mainland Spain in year 2002 are reported. Index Terms--ARIMA models, electricity market, price forecasting, wavelet transform.

This paper addresses generation maintenance scheduling in a competitive electric energy environment. In a centralized setting, the system operator derives a maintenance scheduling plan that attains the desired reliability while minimizing cost and imposes it to all producers. In a competitive environment, this is not possible because the operator is still in charge of maintaining an adequate level of reliability, but the target of each producer is to maximize its own profits, which conflicts in general with the reliability objective of the operator. This paper proposes a technically sound coordinating mechanism based on incentives/disincentives among producers and the operator, which allows producers to maximize their respective profits while the operator ensures an appropriate level of reliability. Index Terms--Coordination, electricity market, generation maintenance, restructured power system.

This paper addresses the self-scheduling problem of a price-taker power producer. It focuses on risk modeling, emphasizing the tradeoff existing between maximum profit and minimum risk. The paper analyzes a self-scheduling model that considers simultaneously profit and risk. This model is formulated as a mixed-integer quadratic programming problem, which is solved using commercially available software. Relevant results from a realistic case study are discussed. Index Terms--Pool-based electricity market, price-taker power producer, profit versus risk tradeoff, risk-constrained self-scheduling.

This paper presents a detailed formulation to model the power trajectories followed by a thermal unit during the start-up and shut-down processes, as well as the ramping limitations when increasing or decreasing power. This model is formulated using mixed-integer linear constraints, thereby overcoming some drawbacks of those approaches based on heuristics, dynamic programming or Lagrangian relaxation. The formulation presented can be used in different scheduling problems arising in centralized and deregulated frameworks. The self-scheduling problem faced by a thermal generator in a pool-based electric energy market is used to illustrate the proposed model. Finally, a realistic case study is analyzed to show the computational behavior of the proposed model. Index Terms--Ramping limits, start-up and shut-down power trajectories, thermal units.

Pool-based electricity markets can be simulated with various degrees of accuracy. When compared to actual markets, most of the simulators produce outcomes than cannot be extrapolated beyond the specific scenario analyzed. This is most critical for regulators and market participants which need tools to analyze market power and bidding strategies, respectively, for a broad range of scenarios. Both objectives can be tackled if the possible equilibria of a pool-based multiperiod market are determined. This paper presents a three-step methodology to find these equilibria. First, a detailed model of an electricity market is presented, considering multiperiod bidding, price elasticity, and network modeling. Second, an iterative simulation process is run to detect participants' bidding strategies implicit in the optimized production resulting from the simulation. Finally, output data from the simulator are analyzed to obtain Nash equilibria. Iterated deletion is used in the last step to remove strategies that are dominated by others that generate higher profits. A realistic case study illustrates the proposed technique. Index Terms--Electricity markets, market power, market simulation, Nash equilibrium.

This paper provides a procedure for the allocation of the cost of transmission losses that is based on deriving a radial network that is fully equivalent to the original one. This equivalence materializes in that voltage magnitudes and angles, and active and reactive power injections are identical for both networks. Once this radial equivalent network is available, the allocation of the cost of transmission losses to generators and demands can be performed in a straightforward manner. This equivalent network is derived solving a simple quadratic optimization problem whose solution can be obtained efficiently. A realistic case study including two load scenarios is analyzed. Results using the proposed technique are compared with those obtained using alternative allocation procedures. Index Terms--Allocation of the cost of losses, quadratic programming, radial equivalent networks, transmission losses.

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. Index Terms--Equivalent bilateral exchanges, transmission cost allocation.

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. Index Terms--Linearized power flow, mixed-integer linear programming, power loss modeling, transmission expansion planning.

Price forecasting is becoming increasingly relevant to producers and consumers in the new competitive electric power markets. Both for spot markets and long-term contracts, price forecasts are necessary to develop bidding strategies or negotiation skills in order to maximize benefit. This paper provides a method to predict next-day electricity prices based on the ARIMA methodology. ARIMA techniques are used to analyze time series and, in the past, have been mainly used for load forecasting, due to their accuracy and mathematical soundness. A detailed explanation of the aforementioned ARIMA models and results from mainland Spain and Californian markets are presented. Index Terms--ARIMA models, electricity markets, forecasting, market clearing price, time series analysis.

This paper presents a market clearing tool for the Market Operator of a pool-based electricity market for energy. This tool is transparent and fair for the market participants, and simple to implement and to interpret. It preserves the privacy of the corporate information of the participants and provides the right signals to achieve economic efficiency. Furthermore, it recognizes and properly models the technical (physical and inter-temporal) constraints of the participant thermal power generators. From a mathematical point of view, the proposed tool results in a mixed-integer linear programming problem that can be efficiently solved using currently available branch and cut software. To illustrate the adequate functioning of the proposed market clearing procedure different realistic case studies are analyzed in detail. Index Terms--Market clearing tool, maximum net social welfare, mixed-integer LP, pool-based electricity market.

This paper addresses the self-scheduling of a hydro generating company in a pool-based electricity market. This company comprises several cascaded plants along a river basin. The objective is to maximize the profit of the company from selling energy in the day-ahead market. This paper proposes a 0/1 mixed-integer linear programming model to account, in every plant, for the nonlinear and nonconcave three-dimensional (3-D) relationship between the power produced, the water discharged, and the head of the associated reservoir. Additionally, start-up costs due mainly to the wear and tear are considered. Finally, different realistic case studies are analyzed in detail. Index Terms--Hydroelectric producer, mixed-integer LP, pool-based electricity market.

This paper addresses the unit commitment problem of thermal units. This optimization problem is large-scale, combinatorial, mixed-integer, and nonlinear. Exact solution techniques to solve it are not currently available. This paper proposes a novel repair genetic algorithm conducted through heuristics to achieve a near optimal solution to this problem. This optimization technique is directly parallelizable. Three different parallel approaches have been developed. The modeling framework provided by genetic algorithms is less restrictive than the frameworks provided by other approaches such as dynamic programming or Lagrangian relaxation. A state-of-the-art Lagrangian relaxation algorithm is used to appraise the behavior of the proposed parallel genetic algorithm. The computing time requirement to solve problems of realistic size is moderate. The developed genetic algorithm has been successfully applied to realistic case studies. Index Terms--Nonlinear mixed-integer optimization, parallel computation, repair genetic algorithm, unit commitment.

This paper provides a framework to obtain the optimal bidding strategy of a price-taker producer. An appropriate forecasting tool is used to estimate the probability density functions of next-day hourly market-clearing prices. This probabilistic information is used to formulate a self-scheduling profit maximization problem that is solved taking advantage of its particular structure. The solution of this problem allows deriving a simple yet informed bidding rule. Results from a realistic case study are discussed in detail. Index Terms--Bidding strategy, forecasting, MILP, pool-based electricity market, price-taker producer, self-scheduling.

This paper addresses the self-scheduling problem faced by a price-maker to achieve maximum profit in a pool-based electricity market. An exact and computationally efficient mixed-integer linear programming (MILP) formulation of this problem is presented. This formulation models precisely the price-maker capability of altering market-clearing prices to its own benefits, through price quota curves. No assumptions are made on the characteristics of the pool and its agents. A realistic case study is presented and the results obtained are analyzed in detail. Index Terms--Electricity pool market, market power, mixed-integer linear programming (MILP), price maker.

We present a single time period decentralized electricity market clearing model that includes reactive power and demand responsiveness in addition to the more common framework of generation-side competition for the real power commodity. The approach allows self-interested agents, namely producers and consumers, independently to maximize their individual surpluses subject to prices. This is consistent with the very notion of a competitive market as defined in equilibrium theory. An auctioneer computes equilibrium prices that achieve power balance at every network node as required by Kirchhoff's laws. The overall scheme is justified by duality theory for which there is a rich theoretical support, and convergence is achieved using a Newton price-updating algorithm. Index Terms--Auction, market coordination, market equilibrium, mathematical programming, optimization methods, power generation dispatch, power generation economics, power generation scheduling, power system economics.

This paper presents a multiperiod electricity auction market tool that explicitly takes into account transmission congestion and losses as well as intertemporal operating constraints such as start-up costs, ramp rates, and minimum up and down times that may be included in any generating unit's composite bid. This approach, which requires only existing mixed-integer linear solvers, provides the market operator with a valuable tool for scheduling participants in a competitive market where transparency, fairness, and confidentiality of participants' data are of paramount concern. Indeed, under this framework, only network data are of public domain; producers are not required to reveal corporate data, and they have more flexibility in specifying the structure of their composite bid. This paper demonstrates and illustrates, through numerical studies using test systems, that an efficient and fair competitive electricity market can be implemented, taking into account network constraints and losses. Index Terms--Congestion management, mixed-integer linear programming, nodal pricing, pool-based electricity market, social welfare maximization.

The electric power industry all over the world is undertaking major regulatory and operational changes. The understanding of power supply as a public service is being replaced by the notion that competitive markets constitute a more appropriate framework to supply reliable and cheap electric energy to consumers. As mandated by FERC orders 888 and 889, this paper considers simultaneously energy, AGC, and reserve markets in a pool framework. It provides a tool to enable a power generator to determine optimally its degree of involvement in each one of these markets. A real-world case study is analyzed and results are presented. Index Terms--AGC market, energy market, mixed-integer optimization, pool-based electricity markets, reserve market.