Probabilistic Load Flow With Wind Farms Using a Frequency and Duration Method

Probabilistic load flow (PLF) is an important tool in power system planning and operation. One limitation of conventional PLF 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 paper, a frequency and duration method for PLF with wind farms (WFs) is proposed based on Markov chains by using an improved probability-frequency distribution function (PFDF) method. Random input variables, including intermittent loads, conventional generator (CG) power outputs associated with CG failures, and WF power outputs associated with both wind speed uncertainties and wind turbine failures, are modeled using corresponding PFDFs. With the proposed method, not only probability information but also frequency and duration information of random PLF outputs are efficiently and analytically computed through the operations of PFDFs of random inputs. Moreover, an optimal decision-making model 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 performance of the proposed method is verified and compared with that of a sequential Monte Carlo simulation technique using two modified IEEE test systems.