Impedance Analysis of Voltage Source Converter Based on Voltage Modulated Matrix

The phase-locked loop (PLL) is essential for accurate power control of grid following voltage source converter (VSC). However, the adoption of PLL will introduce a negative resistance in the VSC, which might jeopardize the stability when it is connected to a weak grid. Thus, the voltage modulated matrix is proposed to avoid using PLL. Nevertheless, the effect of voltage modulated matrix on the impedance of VSC is ignored. In this paper, the mathematical derivation of voltage modulated matrix is presented and it is first revealed that the essence of voltage modulated matrix is equal to an open-loop arctan-PLL. Then, the small-signal model of the arctan-PLL is established, which can be considered as a conventional PLL with infinite bandwidth. Hence, the frequency coupling phenomenon is more serious by using a voltage modulated matrix, which is verified by the frequency scan in Matlab/Simulink. Furthermore, the stability of VSC under a weak grid has even deteriorated by using the voltage modulation matrix since it has no filtering ability, which has also been validated by the Generalized Nyquist Criterion and simulation results.