A Nested Benders Decomposition Approach to Locating Distributed Generation in a Multiarea Power System

Abstract

A nested Generalized Benders decomposition scheme is used to solve a mixed-integer stochastic programming model. The model evaluates central station and distributed power generation, storage, and demand management assets on a linearized electric power transmission network. It considers temporal and spatial variations in the marginal cost of power, which are captured in the Benders cuts in the solution scheme. These variations are caused not only by differences in generating unit operating expenses and capacity expansion costs, but also by physical transmission constraints that can alter minimum cost dispatch and siting of these units. The transmission constraints addressed include limits on MW power flows and both of Kirchhoff's laws via a linearized DC load flow representation. The model consists of three modules: a stochastic linear production costing model for operating central system generation, a nonlinear program for planning central system generation and transmission, and a mixed-integer program for evaluation of local area distributed resources. Generalized Benders decomposition is applied twice to coordinate these modules. The production costing model is a subproblem to the central system planning model, which is in turn a subproblem to the distributed resource model. The coordination scheme is described in detail, including the calculation of marginal costs. An application shows the effects of marginal cost variations on capacity expansion decisions.