Cumulant based stochastic optimal power flow (S-OPF) for variance optimization

This paper presents a cumulant method based solution for stochastic optimal power flow (S-OPF) including a variance minimization objective function. In this case, the objective of the problem is to minimize the variance of the active power generation at the slack bus by optimizing the decision variables given uncertainty in loading levels. Results using the proposed method are compared against Monte Carlo simulations to demonstrate accuracy of the results. Additionally, variances computed at the optimal point are compared against the variances computed at the minimum cost point to provide a measurement of the improvement by the optimization process. Two systems are tested consisting of 30 and 57 buses respectively. In general, variances computed using the proposed methodology are within 1% of those computed using 10,000 sample Monte Carlo simulations and the variances are between 3 and 11% narrower than those at the minimum cost solution.