A frequency and duration analysis method for probabilistic optimal power flow with wind farms

Probabilistic optimal power flow (POPF) is an important tool in power system planning and operation. One limitation of conventional POPF is that only the probability information of random variables is obtained as a reference for related analyses. Frequency and duration information often plays an important role in power system assessment. In this study, a frequency and duration analysis method for POPF with wind farms (WFs) is proposed, which is based on Markov chains by improving the traditional probability-frequency distribution function (PFDF) method. The main advantage of the proposed method is that highly accurate solutions can be obtained with less computation. Random input variables, including intermittent loads and WF power outputs associated with both wind speed uncertainties and wind turbine (WT) failures, are modeled using the corresponding PFDFs. With the proposed method, not only probability information but also frequency and duration information of random POPF outputs are efficiently and analytically computed through the operations of PFDFs of random inputs. Moreover, an optimization method for determining the clustering number of random states is proposed to improve the credibility of stochastic process modeling of Markov-chain-based random variables. The test on the modified IEEE-RTS79 system with WFs demonstrates the rapidity and validity of the proposed method. (c) 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.