Analytical Examination of Oscillatory Stability of a Grid-Connected PMSG Wind Farm Based on the Block Diagram Model

This paper analytically derives oscillatory stability criteria of a grid-connected PMSG based on the block diagram model. The derivation reveals the general mechanism about how the condition of grid connection, loading and converter control parameters setting of the PMSG jointly affect the oscillatory stability of the PMSG. It logically explains why the condition of weak grid connection and heavy loading may cause destabilization. In addition, computationally simple and modal-computation free indices are proposed to identify the instability risk caused by the "improper parameters setting" of the control system of grid side converter (GSC) and the phase locked loop (PLL). Following analytical conclusions are obtained: (1) When the PLL is of high-frequency bandwidth, high-frequency oscillations are mainly caused by the PLL or the open-loop modal resonance between the PLL and current control of the GSC. In addition, the low-frequency oscillations may also occur as caused by the power control of the GSC. (2) When the PLL is of low-frequency bandwidth, low-frequency oscillations may be caused jointly by the power control of GSC and the PLL. An example grid-connected wind farm with eighteen similar PMSGs is presented to demonstrate and evaluate the stability criteria derived and analytical conclusions obtained in the paper.