Probabilistic Optimal Power Flow in Correlated Hybrid Wind–Photovoltaic Power Systems

As a matter of course, the unprecedented ascending penetration of distributed energy resources (DERs), mainly harvesting renewable energies (REs), is concomitant with environmentally friendly concerns. This type of energy resources are innately uncertain and bring about more uncertainties in the power system, consequently, necessitates probabilistic analyses of the system performance. Moreover, the uncertain parameters may have a considerable level of correlation to each other, in addition to their uncertainties. The two point estimation method (2PEM) is recognized as an appropriate probabilistic method in small scale or even medium scale problems. This paper develops a new methodology for probabilistic optimal power flow (P-OPF) studies for such problems by modifying the 2PEM. The original 2PEM cannot handle correlated uncertain variables but the proposed method has been equipped with this ability. In order to justify the impressiveness of the method, two case studies namely the Wood & Woollenberg 6-bus and the Mathpower 30-bus test systems are examined using the proposed method, then, the obtained results are compared against the Monte Carlo simulation (MCS) results. Comparison of the results justifies the effectiveness of the method in the respected area with regards to both accuracy and execution time criteria.