Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation

Abstract

This paper aims at establishing the cumulative distribution function (CDF) of the output variable of the probabilistic optimal power flow. In the context of the probability weighted moment (PWM), the uncertainties in the power system are modelled by a ninth-order polynomial normal transformation (NPNT) technique, whereby the dependencies among the inputs are conveniently handled. The quasi-Monte Carlo simulation (MCS) is employed to get the statistical information of the outputs. Based on the PWMs of the output variable, the CDF is reconstructed by NPNT technique. Testing on a modified 118-bus system, results from the proposed method are compared against those from MCS. The proposed method demonstrates a high level of accuracy for the mean, standard deviation and CDF, while significantly reducing the computational burden.