Probabilistic optimal power flow applications to electricity markets

This paper presents the comparison of two solution methods for Probabilistic Optimal Power Flow problems; namely, the Two-Point Estimate Method (2PEM) and the Cumulant Method (CM). The goal of the P-OPF problem is to determine the probability distributions for all random variables in the problem. In this paper, bus loading and generators' supply power bids are considered as uncertain or probabilistic parameters in a P-OPF problem. Due to their importance in the context of electricity markets, special attention is paid to the uncertainty in Locational Marginal Prices (LMPs) that results from uncertain behavior of market players. The proposed methods are tested on a modified version of the Matpower 30-bus system to demonstrate the capabilities of both approaches. Solution methodologies are compared in terms of accuracy and computational burden. Results are compared against those obtained from 10,000 sample Monte Carlo simulations (MCS). The proposed methods show high accuracy levels and are computationally significantly faster than an MCS approach.