Corrected complex torque coefficient method for synchronization stability analysis of grid-connected VSC

Sub-synchronous oscillation of grid-connected voltage source converter (VSC) dominated by phase locked loop (PLL) is an important stability issue in nowadays power systems. The complex torque coefficient method has been used to investigate the issue because of its advantage of giving insights into source of damping and contributions of different components on damping. However, it is found that the classic complex torque coefficient method is not entirely applicable for stability analysis of VSC because of the proportional term in PLL. This paper proposes a corrected complex torque coefficient method and defines synchronous and damping coefficients. Based on the proposed method, a small-signal stability criterion is obtained, in which the system stability depends on the sign of corrected damping coefficient. The impacts of different elements on system damping can be quantitatively evaluated through the method. It is drawn that current control loop and line dynamics contribute negative damping, whereas power control loop contributes positive damping. Moreover, the impacts of operating conditions and controller parameters on damping of different elements are analysed. The eigenvalue analyses and electromagnetic transient simulations have verified the theoretical analysis. The paper proposes the corrected complex torque coefficient method for grid-connected VSC stability analysis. Based on the proposed method, a small-signal stability criterion of VSC considering the outer controller is obtained without complex eigenvalue calculation. Besides, impacts of different control elements and source of damping are quantitatively analysed.image