Optimal Power Dispatch under Load Uncertainty Using a Stochastic Approximation Method

This paper applies a known stochastic approximation method to solve a two-phase optimal power dispatch problem under load uncertainty using a novel realistic model for random loads. The stochastic power dispatch problem is solved with the Robbins-Monro method applied with the Kiefer-Wolfowitz procedure with random directions. The constraints of this optimization problem have been investigated and considered by truncated algorithms. Two numerical examples are presented for illustration of the significant improvement obtained with the proposed method. In the first example, the optimizable cost of the system can be reduced by 1.6% under 2.68% load variation. In the second example, the results show that the possibility of voltage violations is reduced from 49.5% to 0.01%. All the improvements are compared with deterministic optimal solutions validated with scenario-based Monte Carlo simulations. The method is 60 times faster than scenario-based Monte Carlo for similar accuracy for the IEEE 30-bus test system.