No abstract

The electric power industry is going through deregulation. As a result, the load on the generating units of a utility is becoming increasingly unpredictable. Furthermore, electric utilities may need to buy power or sell their production to a power pool that serves as a spot market for electricity. These trading activities expose utilities to volatile electricity prices. In this paper, we present a stochastic model for the unit commitment that incorporates power trading into the picture. Our model also accounts for fuel constraints and prices that may vary with electricity prices and demand. The resulting model is a mixed-integer program that is solved using Lagrangian relaxation and Bender's decomposition. Using this solution approach, we solve problems with 729 demand scenarios on a single processor to within 0.1% of the optimal solution in less than 10 minutes. Our numerical results indicate that significant savings can be achieved when the spot market is entered into the problem and when stochastic policy is adopted instead of a deterministic one.

Ab.Wact-We develop a technique for refining the unit commitment solution obtained from solving the Lagrangian. Our model is an integer program with nonlinear constraints. It can be solved to optimality using branch-and-bound. Numerical results indicate a significant improvement in the quality of the yolution obtained.Indar Terms-Branch-and-hound, dynamic programming, Lagrangian relaxation, mixed-integer programming, unit commitment.

No abstract

Many production problems involve facility setups that lead to integer variables, production decisions that are continuous, and demands that are likely to be random. While these problems can be quite difficult to solve, we propose a model and an efficient solution technique for this basic class of stochastic mixed-integer programs. We use a set of scenarios to reflect uncertainty. The resulting mathematical model is solved using Lagrangian relaxation. We show that the duality gap of our relaxation is bounded above by a constant that depends on the cost function and the number of branching points in the scenario tree. We apply our technique to the problem of generating electric power. Numerical results indicate significant savings when the stochastic model is used instead of a deterministic one.