Mixed probabilistic and interval optimal power flow considering uncertain wind power and dispatchable load

Abstract

Considering uncertain wind power and dispatchable load, a mixed probabilistic and interval optimal power flow model is proposed, and Monte Carlo sampling and affine arithmetic method are used to solve it. First, an uncertain optimal power flow model with mixed probabilistic variables and interval variables is established by expressing the uncertain dispatchable load as the interval model and the uncertain wind speed and node load as the probabilistic model. Then Monte Carlo sampling is used to sample the probabilistic variables in the proposed model. By this way, the mixed probabilistic and interval optimal power flow can be transformed into interval optimal power flow with sampling points, and the interval optimal power flow of each sampling point can be solved by the affine arithmetic method. Finally, a maximum probability density function and a minimum probability density function are synthesized based on the interval extremum of unknown variables in optimal power flow for each sampling point. The numerical results obtained by the IEEE‐118 and IEEE‐300 bus systems show that the mixed probabilistic and interval optimal power flow model has the merits of handling the problem including both probabilistic variables and interval variables at the same time, obtaining the probabilistic interval of optimal power flow with any value and learning the maximum probability and minimum probability of the power system's possible operating status. The proposed algorithm has the advantage of high solution efficiency. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.