Analytic Quantification of Controllers Interaction of Weak Grid Tied VSC in Current Control Timescale

The dynamic interaction between the controllers challenges the stability of weak grid tied VSC with phase-locked-loop. In this article, the impact of controllers' interaction on the stability in current control timescale is quantified in purely analytical way. First, a novel form of transfer function is developed to reveal that the main root cause of the instability of VSC in weak grid is the controllers' interaction. Second, by analyzing the closed-loop transfer function, the modes of grid tied VSC are divided into two parts of stable modes and possibly unstable modes, and then an equivalent reduced order transfer function is constructed to analytically study how the controllers' interaction affects the stability. Further, with the reduced order model, an analytical expression is derived to link the change of VSC parameters and the shift of system modes. Analytically studies are conducted for the impact of controllers' interaction on the stability in the case of stiff grid and weak grid. Finally, the method to eliminate the undesired interaction is presented. Both eigenvalue analysis and time-domain simulations are conducted to verify the proposed methods.