Analysis of probabilistic optimal power flow taking account of the variation of load power

This paper presents a probabilistic optimal power flow (POPF) algorithm taking account of the variation of load power. In the algorithm, system load is taken as a random vector, which allows us to consider the uncertainties and correlations of load. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of POPF system are transformed equivalently into a set of nonsmooth nonlinear algebraic equations. Based on a first-order second-moment method (FOSMM), the POPF model which represents the probabilistic distributions of solution is determined. Using the subdifferential, the model which includes nonsmooth functions can be solved by an inexact Levenberg-Marquardt algorithm. The proposed algorithm is verified by three test systems. Results are compared with the two-point estimate method (2PEM) and Monte Carlo simulation (MCS). The proposed method requires less computational burden and shows good performance when no line current is at its limit.