Small-signal stability analysis of VSC-interfaced wind generators in weak AC grids

Abstract

Small signal stability issues for wind generators attached to weak AC grids are of great concern in the field. Prior to this research, it is found that such instability phenomena are mainly governed by the dynamics covering the converter outer power flow controls; while most of the current studies, such as the eigenvalue analysis and dq frame impedance analysis, are limited to numerical sensitivity analysis, the causes of instability are not fully understood. This research presents further analytical interpretations for understanding the origin of such instabilities, two different viewpoints are provided for stability explanation. The first viewpoint is in terms of the potential non-minimum phase behaviors considering the dynamics of converter outer power flow controls. In this research, this property is first identified in a grid-tied doubly-fed induction generator (DFIG) system. To study the impact of active/reactive power flow control interactions, a multivariable transfer matrix model for DFIG is proposed. Then, based on the loop decomposition based analysis, it finds out that a right-half-plane zero (RHPZ) will be induced in the open-loop active power control plant at particular high power angle operating conditions. It is also demonstrated that instability is closely related to the occurrence of this RHPZ due to its introduced sever phase lag. Such results are then extended to synchronous generator and voltage source converter (VSC) systems considering the similar power flow control structures. The conditions for the appearance of the RHPZs in these systems are analytically derived, and a unified explanation regarding the generation of these RHPZs is also provided. The second viewpoint is from the perspective of modal resonance. For a VSC system, this research analytically derived that the modal resonance between the phase-locked loop mode and DC-link voltage control mode will induce a so-called eigenvalue repulsion phenomenon, which results in damping degradation of one mode. Moreover, it finds out that higher power angle operating condition will amplify such eigenvalue repulsion effect, thus will drive system unstable. Meanwhile, it is also derived that the maximum power transfer limit for a vector-controlled VSC is 0.786 p.u. at SCR = 1.0 when disregarding the AC voltage control (AVC). In addition, we also proved that, without AVC, instability is presented in the form of monotonic divergence; while with the addition of AVC, instability must be oscillations. Except for the stability study in a single VSC system, this research also proposes an alternative net damping criterion for the stability analysis of multiple VSCs concerning the power flow control timescale dynamics. The proposed criterion is strictly mapped from Nyquist stability criterion with the gain margin concept, which preserves the advantage of the classical positive net damping criterion–allowing for decomposition analysis of component contribution to system damping in a single-input single-output (SISO) framework, but overcomes its deficiency of possibly erroneous prediction of system dynamic behaviors.