Impedance modeling and quantitative stability analysis of grid-connected voltage source converters under complex unbalanced conditions

The stability issues caused by voltage source converters (VSCs), which are commonly used in renewable energy systems, are investigated in this paper. Much literature has investigated the impedance models and quantitative stability analysis for converters under the weak and unbalanced grid. However, on the one hand, harmonic-transfer-function (HTF)-based modeling methods are complex, and the established infinite-order models may suffer from unreasonable truncation. On the other hand, these existing impedance models without considering all unbalance factors are inaccurate. Both of these may bring wrong stability analysis results. Therefore, this paper proposes a simple impedance extension method and considers all unbalance factors to derive the impedance model of the converter. However, due to the established higher-order impedance model, the traditional impedance-ratio based stability analysis method is not applicable to multi-input multi-output (MIMO) systems. The commonly used eigenvalue-based GNC and diagonalization-based methods applicable to MIMO systems are cumbersome and not suitable for quantitative analysis. Therefore, in this paper, a quantitative analysis tool of system stability based on the phase-frequency characteristics of determinants is developed. Then, stability regions in the multi-parameter space are obtained. Finally, the established impedance model and the quantitative analysis results are validated via both simulations and hardware experiments.