Probabilistic Optimal Power Flow with Weibull Probability Distribution Function of System Loading Using Percentiles Estimation

Abstract

This article proposes a probabilistic optimal power flow for hour-ahead scheduling in a power system considering the statistical distribution function of system loading using the Weibull probability distribution function. In the proposed probabilistic optimal power flow, the deterministic optimal power flow problem is solved as the sub-problem in probabilistic optimal power flow and decomposed into a total operating cost minimization sub-objective, which is solved by successive quadratic programming and the real power loss minimization sub-objective, which is solved by successive linear programming. In the proposed method, the Weibull probability distribution function parameters of the optimal power flow variables are estimated from percentile values and evaluated by Akaike information criteria. The proposed probabilistic optimal power flow algorithm is tested on the IEEE 30-bus and IEEE 300-bus systems and compared to Monte Carlo simulation. The investigations show that the proposed probabilistic optimal power flow can successfully estimate the probability distribution function parameters of optimal power flow output variables considering the Weibull probability distribution function of system load with simple and minimal computational procedure. With the proposed estimation of the Weibull parameters method, the number of optimal power flow runs can be reduced substantially in the probabilistic optimal power flow process.