Influence of phase-locked loop aggregation on the dynamic aggregation of wind farm strings with heterogeneous parameters

Offshore wind farms are cornerstone solutions for enabling large-scale integration of renewable energy. Due to the large number of wind turbines in a wind farm, each with their individual complex control structure, a detailed time-domain model for analysis of wind farms is impractical from a computational burden perspective. Accordingly, aggregated models have been presented to reduce the computation time. Despite the high activity in aggregated modelling of wind farms, dynamic aggregation considering heterogeneous converter controllers and filter parameters, including different phase-locked loop (PLL) parameters have not been discussed previously. To remedy this issue, this study proposes an aggregated structure-preserving model of a wind farm string where all converters have heterogeneous parameters. The proposed model is verified by simulations against a detailed numerical model of the wind farm string, showing its accuracy in preserving the wind farm string dynamics under a severe grid fault with different short-circuit ratios and PLL parameters. Through a comparison of four different PLL aggregation methods under the considered case studies, it is found that the PLL aggregation has a negligible influence on the aggregated response and, hence, the particular aggregation method employed is not of great importance.