Small-Signal Stability of a Single Grid-Connected PMSG System

Weak grid connection, high loading condition, and improper setting of converter control systems of a grid-connected wind turbine generator (WTG) may bring about the risk of sub/super-synchronous oscillation. This chapter analytically examines those three key factors to explain why and how they may unfavorably affect the damping of sub/super-synchronous oscillation in a single grid-connected PMSG system. The examination is carried out by deriving the necessary and sufficient stability conditions of the single grid-connected PMSG system to reveal the connection of those three key factors and their impact on the system stability. First, the full-order state-space model of a PMSG is introduced. Second, a simplified reduced-order model of a single grid-connected PMSG system, which is dominated by dynamics of the phase locked loop (PLL), is established. Based on the established model, the stability limit of the single grid-connected PMSG system dominated by dynamics of the phase locked loop (PLL) is derived. Thirdly simplified reduced-order models of the single grid-connected PMSG system in the fast current timescale and the slow DC voltage timescale are derived, respectively. Based on the derived models, the necessary and sufficient stability conditions of the single grid-connected PMSG system are obtained. Finally in the chapter, examples of single grid-connected PMSG system are presented.