PSO algorithm‐based scenario reduction method for stochastic unit commitment problem

Abstract

This paper proposes a particle swarm optimization (PSO) algorithm‐based scenario reduction method for stochastic unit commitment problems. In this method, the position of each particle is an index set of the preserved scenarios, that is, a possible solution to the optimal scenario reduction problem. The Kantorovich distance between the original scenarios and the preserved scenarios is used to calculate the fitness value of each particle. A repair procedure is carried out to ensure that there are non‐repeating index numbers in the newly generated position of each particle during the iterations. The performance of the PSO‐based method is tested on two scenario sets of electricity prices in a stochastic profit/price‐based unit commitment (SPBUC) problem, and is compared with backward reduction and forward selection. Test results show that the PSO‐based method performs very well with respect to the relative accuracy and running times when reducing large scenario set. Impacts of scenario reduction on the expected profits of the SPBUC problem are also investigated with different numbers of the preserved scenarios of electricity prices, which are obtained by these three different reduction methods from the same original scenario set. Simulation results show that optimal solutions of the SPBUC problem are related not only to the number of the preserved scenarios but also to the scenario reduction methods. The PSO‐based method can lead to less conservative solutions than the forward selection, while the backward reduction can result in nonconservative solutions.