Quantitative Evaluation of Frequency Domain Approaches in Assessing Small-Signal Stability of Grid-Tied Converters

Frequency domain approaches have become essential tools for analyzing the stability of modern power systems with the high penetration of renewable energy. A widely used method is to simplify the multivariable interactions into single-input-single-output models using the Schur complement, enabling the formulation of approaches and the evaluation of stability margins through the well-known Nyquist criterion. However, there is still a lack of clear guidelines for applying the Schur complement to power systems, for instance, how to choose the input and output signals to obtain the closed-loop model and to derive their corresponding assessment criteria. As such, an inappropriate application of the method may lead to unreliable evaluations. To this end, a vector metric called loop gain sensitivity (LGS) is proposed in this article to evaluate the reliability of stability assessments. Moreover, two key principles are established: 1) the argument principle of loop gain sensitivity defines phase-angle requirements for valid stability margins, and 2) the magnitude principle of loop gain sensitivity shows that smaller LGS magnitudes improve accuracy under uncertainties. Finally, the effectiveness of the proposed method is validated by numerical case studies and experimental tests.