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

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.

This paper presents a bilevel programming approach to solve the medium-term decision-making problem faced by a power retailer. A retailer decides its level of involvement in the futures market and in the pool as well as the selling price offered to its potential clients with the goal of maximizing the expected profit at a given risk level. Uncertainty on future pool prices, client demands, and rival-retailer prices is accounted for via stochastic programming. Unlike in previous approaches, client response to retail price and competition among rival retailers are both explicitly considered in the proposed bilevel model. The resulting nonlinear bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear programming problem by replacing the lower-level optimization by its Karush-Kuhn-Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. A realistic case study is solved to illustrate the efficient performance of the proposed methodology.

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.

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

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.