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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 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 presents a new mixed-integer linear formulation for the unit commitment problem of thermal units. The formulation proposed requires fewer binary variables and constraints than previously reported models, yielding a significant computational saving. Furthermore, the modeling framework provided by the new formulation allows including a precise description of time-dependent startup costs and intertemporal constraints such as ramping limits and minimum up and down times. A commercially available mixed-integer linear programming algorithm has been applied to efficiently solve the unit commitment problem for practical large-scale cases. Simulation results back these conclusions. Index Terms--Mixed-integer linear programming (MILP), thermal generating units, unit commitment.

This paper presents a solution procedure for the mixed-integer bilevel programming model of the electric grid security under disruptive threat problem, here concisely denoted by (ST-MIBLP), that was recently reported. Using results from linear programming theory and some basic linearization of products of binary-binary or binary-continuous variables, we recast (ST-MIBLP) into a standard (one-level) mixed-integer linear program (ST-MILP) with no more binary variables than in the original (ST-MIBLP). This transformation provides a framework for globally solving (ST-MIBLP) using available mixed-integer linear programming solvers. Some numerical results obtained by the new method are compared with those recently published, based on IEEE Reliability Test Systems. Index Terms--Bilevel programming, linear duality, mathematical program with optimization in the constraints, mixed-integer linear programming, network security.

This paper analyzes some unresolved pricing issues in security-constrained electricity markets subject to transmission flow limits. Although the notion of separate reserve types as proposed by FERC can be precisely and unambiguously defined, when transmission constraints are active, the very existence of separate reserve prices and markets is open to question when the prices are based on marginal costs. Instead, we submit here that the only products whose marginal costs can be separately and uniquely defined and calculated are those of energy and security at each node. Thus, under marginal pricing, at any given network bus all scheduled reserve types should be priced not at separate rates but at a common rate equal to the marginal cost of security at that bus. Furthermore, we argue that nodal or area reserves cannot be prespecified but must be obtained as by-products of the market-clearing process. Simulations back up these conclusions. Index Terms--Contingency-constrained scheduling, demand-side reserve, electricity markets, security and energy pricing, transmission constraints, up and down-spinning reserve.

This paper generalizes the 'terrorist threat problem' first defined by Salmeron, Wood, and Baldick by formulating it as a bilevel programming problem. Specifically, the bilevel model allows one to define different objective functions for the terrorist and the system operator as well as permitting the imposition of constraints on the outer optimization that are functions of both the inner and outer variables. This degree of flexibility is not possible through existing max-min models. The bilevel formulation is investigated through a problem in which the goal of the destructive agent is to minimize the number of power system components that must be destroyed in order to cause a loss of load greater than or equal to a specified level. This goal is tempered by the logical assumption that, following a deliberate outage, the system operator will implement all feasible corrective actions to minimize the level of system load shed. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program by replacing the inner optimization by its Karush--Kuhn--Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. The equivalent formulation has been tested on two case studies, including the 24-bus IEEE Reliability Test System, through the use of commercially available software. Index Terms--Bilevel programming, deliberate outages, load shedding, mixed-integer linear programming (MILP), power system security and vulnerability, terrorist threat.

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.

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.

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.

This paper presents the numerical analysis of the bilevel programming approach for revenue- and network-constrained market clearing developed in its companion paper. The impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies. First, the results from an illustrative example including minimum revenue conditions are comprehensively analyzed. The second case study is based on the IEEE Reliability Test System and considers minimum declared profits. In the third case study, a modified version of the IEEE 118-bus system is tested while accounting for minimum revenue conditions. In addition, the computational behavior of the proposed approach is illustrated with several case studies including the IEEE 300-bus system. Numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the Iberian electricity market. Moreover, simulations reveal that, unlike previous works in the literature, generation revenue constraints can be precisely incorporated in day-ahead market clearing while explicitly considering the standard economic-dispatch-based marginal pricing scheme and without requiring price uplifts. [ABSTRACT FROM AUTHOR]

The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach. [ABSTRACT FROM AUTHOR]