Inclusion of Current Limiter Nonlinearity in the Characteristic Analysis of Sustained Subsynchronous Oscillations in Grid-Connected PMSGs

Abstract

The interactions between permanent magnet synchronous generators (PMSGs) and weak grids may cause negatively damped or growing subsynchronous oscillation (SSO). The growing-SSO would evolve into a sustained-SSO when it is predominantly governed by the nonlinearities in the PMSG's converter control, such as current limiter. Most of the existing frequency-domain modeling and stability analysis methods are in the small-signal sense and thus unable to consider the impact of such nonlinearities. Besides, these methods can hardly give vital information to characterize the sustained-SSO, for instance, the magnitude. This paper presents a detailed characteristic analysis of the sustained-SSO while accounting for the effect of current limiter nonlinearity. First, a single-input-single-output (SISO) frequency-domain model of the PMSG is developed. This SISO model comprises the transfer functions of outer-/inner-loop controls and phase-locked loop (PLL). The nonlinear part, i.e., current limiter, is incorporated into the model using the describing function (DF) method. Then, the equivalent transformation on the system's closed-loop characteristic equation is used to separate the SISO model into independent linear and nonlinear parts. This separation enables the use of the DF-based Nyquist criterion for evaluating the system stability and determining oscillation attributes, such as the magnitude and frequency. Both the analytic results and time-domain simulations reveal that the current limiter has a significant impact on the characteristics of the sustained-SSO.