Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power System

Abstract

A bounding-based method is developed for estimating the expected operation cost of a multiarea electric power system in which transmission capacity limits interarea flows. Costs include the expense of power generation and losses suffered by consumers because of supply shortfalls, averaged over random generator outage states and varying demand levels. The calculation of this expectation, termed the distribution problem, is a large-scale stochastic programming problem. Rather than solving this problem directly, lower and upper bounds to the expected cost are created using two more easily solved models. The lower bound is from a deterministic model based on the expected value of the uncertain inputs. The upper bound results from a linear program with recourse whose structure permits relatively quick solution by Benders decomposition. The Benders subproblems use probabilistic production costing, which can be viewed as a stochastic greedy algorithm, to consider random outages and demands. These bounds are iteratively tightened by partitioning realizations of the random variables into subsets based on the status of larger generators and a cluster analysis of demands. Computational examples are described and application issues addressed.