Quasi-Monte Carlo Based Probabilistic Optimal Power Flow Considering the Correlation of Wind Speeds Using Copula Function

Wind farms commonly cluster in regions rich in wind resources. Thus, correlation of wind speeds from different wind farms should not be ignored when modeling a power system with large wind energy penetration. This paper proposes a probabilistic optimal power flow (POPF) technique based on the quasi-Monte Carlo simulation (QMCS) considering the correlation of wind speeds using copula functions. In this paper, a copula function is used to model the dependent structure of random wind speeds and their forecast errors. QMCS is employed in the sampling procedure to reduce computation burden. The proposed method is applied in probabilistic power flow (PPF). Furthermore, the PPF is used in the POPF problem that aims at minimizing the expectation and downside risk of fuel cost simultaneously. Simulation studies are conducted on a modified IEEE 118-bus power system with wind farms integrated in two areas, and the results show that the accuracy and efficiency are improved by the proposed method.