Multifrequency small-signal model of voltage source converters connected to a weak grid for stability analysis

To investigate the instability issues of three-phase voltage source converters (VSCs) connected to a weak grid, this paper develops a modeling method based on the harmonic-balance approach. The nonlinear coordinate transformation in the control system would generate two sideband components. If the grid is not strong while the bandwidth of phase-locked loop (PLL) is high enough, the sideband components would be coupled, and both of them have influence on system stability, neither of them could be neglected. Hence, there would be two feedback loops of grid-current representing two sideband frequencies. Taking this effect into account, the multifrequency small-signal model is proposed. It is further demonstrated that the sum of the two grid-current loop gains determines the stability and transient performance. Simulations and experimental results were conducted to validate the analysis.