Probabilistic optimal power flow incorporating wind power using point estimate methods

Global tendency toward environmental-friendly sources of energy with lower generation costs led to increased penetration of renewable energies in power systems, especially wind power. Stochastic nature of wind speed has introduced new challenges to the conventional power system studies including optimal power flow (OPF) analysis, unit commitment, etc. In this paper, a Weibull distribution for wind speed with actual data is assumed and system loads are considered as random variables (RV) with normal distributions. Point estimate methods (PEM) are used here in order to handle the probabilistic OPF problem for a 6-Bus test system. The PEMs are compared with respect to Monte Carlo simulation (MCS) results. It is shown that these methods give acceptable results with significant reduction in computation burden. However, under certain conditions (e.g. RVs with high values of skewness and high order of nonlinearity in the OPF problem), PEMs may give inaccurate results. This inefficiency has not been observed in previous studies and is demonstrated in the test case used here.