Probabilistic power flow considering variable bandwidth kernel density estimation for traction substation loads of high-speed railways

A probabilistic power flow method considering variable bandwidth kernel density estimation (VKDE) for traction substation loads of high-speed railways is proposed. A variable bandwidth kernel density estimator, which varies the bandwidths to minimize mean squared errors at different estimation points, is adopted to model traction substation loads of high-speed railways. The traction substation loads are sampled by acceptance-rejection method for Monte Carlo probabilistic power flow calculation so that the effects of traction substation loads on power system operation can be effectively analyzed. The effectiveness of the proposed method is illustrated by simulations of practical traction substation loads and the modified IEEE 14-bus system.