Stochastic optimal load flow using a combined quasi-Newton and conjugate gradient technique

Abstract

This paper treats the problem of optimal power flow in electric power systems using a method which includes the effects of uncertain variables in formulating the problem for an all thermal electric power system. The method assumes that the system power demand is random and is normally distributed with zero mean and unit variance. The equality constraints associated with the formulation are the power flow equations in polar form utilizing the nodal admittance matrix approach. The non-linear programming technique of Powell's penalty function is used to allow the incorporation of inequality constraints in the formulation. The resulting stochastic optimal power flow problem reduces to one of solving a set of non-linear equations. Here we use a technique that combines the quasi-Newton method and the conjugate gradient method in what is referred to as the CONMIN algorithm. Computational implementation results involving four IEEE standard test networks are given to demonstrate the validity of this method.