Harmonic Transfer-Function-Based Impedance Modeling of a Three-Phase VSC for Asymmetric AC Grid Stability Analysis

Impedance modeling and stability analysis of a grid-voltage source converters (VSC) system under symmetric ac grids have been extensively discussed in the literature, where the dq domain impedances are usually adopted. As for asymmetric ac grids, impedance modeling is no longer straightforward in the dq domain due to the presence of negative sequence components, where the linearization will result in a linear-time-periodically-varying system, making the frequency-domain analysis intractable. One way to address this issue would be the harmonic-transfer-function (HTF) approach. Although this method is conceptually clear, its application to the stability analysis of an unbalanced grid-VSC system is still challenging and an effective model is missing here, therefore this paper aims to bridge this gap. First, the sequence impedances of an unbalanced grid-VSC system is modeled in the HTF framework. Then the HTFs are truncated into four-by-four matrices by exploiting the property of frequency couplings. Based on this, the equivalent source and load model for Nyquist-based analysis are established, and they are thoroughly verified by impedance measurements as well as the accuracy on stability analysis. Finally, several stability concerns of the unbalanced grid-VSC system, as well as the feasibility of symmetric models for asymmetric ac grid stability analysis are discussed and clarified.