Optimal power flow for distribution networks with distributed generation

Abstract

This paper presents a genetic algorithm (GA) based approach for the solution of the optimal power flow (OPF) in distribution networks with distributed generation (DG) units, including fuel cells, micro turbines, diesel generators, photovoltaic systems and wind turbines. The OPF is formulated as a nonlinear multi-objective optimization problem with equality and inequality constraints. Due to the stochastic nature of energy produced from renewable sources, i.e. wind turbines and photovoltaic systems, as well as load uncertainties, a probabilisticalgorithm is introduced in the OPF analysis. The Weibull and normal distributions are employed to model the input random variables, namely the wind speed, solar irradiance and load power. The 2m+1 point estimate method and the Gram Charlier expansion theory are used to obtain the statistical moments and the probability density functions (PDFs) of the OPF results. The proposed approach is examined and tested on a modified IEEE 34 node test feeder with integrated five different DG units. The obtained results prove the efficiency of the proposed approach to solve both deterministic and probabilistic OPF problems for different forms of the multi-objective function. As such, it can serve as a useful decision-making supporting tool for distribution network operators.