An Affine Arithmetic method to solve the stochastic power flow problem based on a mixed complementarity formulation

Abstract

An affine-based stochastic power flow problem is proposed in this paper. First, a novel optimization-based model of the power flow problem using complementarity conditions to properly represent generator bus voltage controls, including reactive power limits and voltage recovery is presented. This model is then used to solve the stochastic power flow problem to obtain operational intervals for power flow variables based on an Affine Arithmetic (AA) method to consider active and reactive power demand uncertainties. The proposed AA algorithm is tested on a 14-bus test system and the results are then compared with the Monte-Carlo Simulation (MCS) results. The AA method shows slightly more conservative bounds; however, it is faster and does not need any information regarding statistical distributions of random variables.