Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and Gamma distributions

This paper introduces the cumulant method for the probabilistic optimal power flow (P-OPF) problem. By noting that the inverse of the Hessian used in the logarithmic barrier interior point can be used as a linear mapping, cumulants can be computed for unknown system variables. Results using the proposed cumulant method are compared against results from Monte Carlo simulations (MCSs) based on a small test system. The Numerical Results section is broken into two sections: The first uses Gaussian distributions to model system loading levels, and cumulant method results are compared against four MCSs. Three of the MCSs use 1500 samples, while the fourth uses 20 000 samples. The second section models the loads with a Gamma distribution. Results from the proposed technique are compared against a 1000-point MCS. The cumulant method agrees very closely with the MCS results when the mean value for variables is considered. In addition, the proposed method has significantly reduced computational expense while maintaining accuracy.