Energy storage sizing by copula modelling joint distribution for wind farm to be black‐start source

To achieve fast power system restoration with high penetration of wind power, using wind farm (WF) as black-start (BS) source is a promising choice. An energy storage system (ESS) sizing method with the minimum investment cost is proposed to enable WF to be a reliable BS source. The proposed method covers three aspects: (i) providing WF self-starting power, (ii) dealing with frequency deviation when starting up ancillary machines and (iii) smoothing WF output power while starting up generator unit. During BS progress, ESS power sizing and capacity sizing are both considered as random variables and their marginal distributions are estimated by kernel density estimation to avoid the distribution model mismatch. The correlation between these two random variables is discussed, which shows that these two variables are not independent. To model the dependence structure between ESS power sizing and capacity sizing, copula theory is applied to build the joint probability distribution. A tail dependence analysis and goodness-of-fit test included copula selection procedure is conducted to choose the most suitable copula function. A case study with real WF data demonstrates that a better-fitted copula has lower ESS sizing cost.