Small-Signal Stability Limit of a Grid-Connected PMSG Wind Farm Dominated by the Dynamics of PLLs

This paper presents a derivation of the small-signal stability limit of a grid-connected wind farm with M permanent magnet synchronous generators (PMSGs) as determined by the dynamics of phased locked loops (PLLs). The stability limit reveals the mechanism whereby the PLLs can destabilize the wind farm in the case of a weak grid connection. Computation of the derived stability limit is simple and obviates the need to establish a parametric model of the wind farm. The stability limit can approximately indicate the potential instability risk collectively posed by the PLLs in the wind farm. Case studies are presented to evaluate the analytical conclusions obtained and the derived small-signal stability limit. Application of the stability limit during the planning and operating stages of a grid-connected wind farm is also demonstrated. Various factors that can affect the stability of the wind farm, and that must be considered during planning and operation, are examined and useful conclusions are obtained. These factors include the length of the transmission line connecting the wind farm to the AC grid, the topology of the wind farm, the wind speed, and its distribution over the wind farm, as well as the parameters of the PLLs.