Evaluation Method for Equivalent Models of PMSG-Based Wind Farms Considering Randomness

Power-system sub-synchronous oscillation (SSO) caused by direct-driven permanent magnetic synchronous generator-based wind farms has attracted significant attention from researchers. An equivalent model (EM) is typically used to describe the wind farm dynamics; however, very few works investigated the suitability of EMs for SSO-based research studies. In this paper, a method for evaluating the applicability of EMs to SSO-based phenomena that takes into account wind-power (WP) randomness is proposed. First, EM parameter calculation is modeled as an optimization problem, in which the average Euclidean distance between the corresponding eigenvalues of the detailed and equivalent systems is considered an objective function. The nonlinear relationship between the average Euclidean distance and the injected WP is described by a quadratic function. Further, a Gaussian mixture model is introduced to obtain the distribution function. It is found that the EMs with smaller expectations and variances of the average Euclidean distance can better preserve the dynamics of the real wind farms at random WP fluctuations. The aggregated and output multiplication EMs are considered to illustrate the application scope of the proposed evaluation method. Finally, the feasibility of further equivalence of multiple wind farms in a WP collection region is discussed.