Theoretical Investigation on the Connections Between Loop Impedance-Based Criterion and State-Space-Based Method

The loop impedance-based criterion (LIC) is a practical approach for studying the sub-synchronous oscillation (SSO) instability induced by converter-interfaced wind turbine generators (WTGs) via checking whether the resistance is positive or not. However, few existing works have discussed the background mathematical theory of such criterion. In this paper, a theoretical impedance solving method is raised based on a forced oscillation analysis method, which is efficient to obtain accurate impedance and can connects the state-space function, eigenvector and impedance inherently. Therefore, the applicability of LIC can be revealed in different stability regions from the viewpoint of the strict eigen-analysis based method (EBM). The general LIC stability criteria is then derived, and the conditions where LIC may cause misjudgment are discussed. Cases considering different operating scenarios are conducted to verify the proposed impedance calculation method and illustrate the connections and differences between LIC and EBM.