Equivalence between State-Space Stability Analysis and Generalized Nyquist Criterion with Frequency Dynamics Included

TL;DR

This paper demonstrates the theoretical equivalence between impedance-based stability analysis with frequency dynamics and eigenvalue analysis, validated through real-time simulations of power electronic converters in power grids.

Contribution

It provides analytical expressions linking impedance criterion with frequency dynamics to eigenvalue analysis, establishing their equivalence under certain conditions.

Findings

Impedance and eigenvalue methods are theoretically equivalent when frequency dynamics are included.

Real-time OPAL-RT simulations validate the analytical equivalence.

The study enhances understanding of stability analysis methods for power electronic systems.

Abstract

Stability of power electronic converters connected to power grids is commonly assessed by using the impedance criterion. On the contrary, stability of power grids is typically analysed by using network state-space representation and system eigenvalues. It has been already reported in the literature that the impedance criterion may lead to erroneous results if the dynamics of the grid frequency is not taken into consideration. Meanwhile, the eigenvalue analysis is still considered as a reliable method for finding instabilities. However, the equivalence between these two methods (impedance criterion with frequency dynamics included and eigenvalue analysis) has not been thoroughly studied before. In this paper, the impedance method with frequency dynamics included is compared with the conventional eigenvalue analysis for a system fully based on electronic interfaces. Analytical expressions that link both methods are provided, showing that they are identical under certain conditions. Then, both methods are applied to a system based on a grid-forming and a grid-following converter. The results obtained from real-time simulations performed in OPAL-RT are used to validate the theoretical developments and main contributions of this work.