A comparison of probabilistic perturbation and deterministic based optimal power flow solutions

A method that reformulates the optimal power flow dispatch problem including power demand uncertainty is presented. It is assumed that the perturbations in system power demand are random and normally distributed with zero mean and some variance. The equality constraints associated with the formulation are the power flow equations in polar form utilizing the nodal admittance matrix approach. The reformulated model is applied to a 23-bus all-thermal power system, using Newton´s method and Powell´s penalty function approach, and computational results are obtained. The probabilistic perturbation based optimal dispatch results are compared with a probabilistic solution based on using four different deterministic optimal dispatches as input as well as a dispatch based on the mean loading condition. The reformulated model appears to have more realistic results than the alternative method when compared on the basis of system fuel cost, losses, and the standard deviation for the active power generations, the system fuel cost, and for the system losses