Stability (learning theory)

Combinatorics

Electrical engineering

Physics

Nonlinear system

Topology (electrical circuits)

Mathematics

Circle criterion

Parametric statistics

Statistics

Diagonal

Impedance parameters

Machine learning

Engineering

Voltage

Artificial intelligence

Eigenvalues and eigenvectors

Exponential stability

Electrical impedance

Control (management)

Grid

Geometry

Converters

Stability criterion

Computer science

Quantum mechanics

Applied mathematics

Control theory (sociology)

Discrete time and continuous time

Nyquist stability criterion

IEEE Transactions on Power Delivery

In recent years, impedance-based methods have been widely used to analyze the stability of grid-connected converters. However, the impedance models in three-phase AC systems are 2 × 2 matrices and a strict stability analysis is based on the generalized Nyquist criterion, which involves eigenvalue computation. Hence many methods only study the diagonal elements of the impedance matrices, but the neglect of the non-diagonal elements may bring hidden dangers to the stability of the system. This letter proposes a stability criterion for grid-connected converters based on impedance models and Gershgorin's theorem. The effect of the non-diagonal elements is considered and the criterion is a strictly sufficient condition of stability, which is conservative but can guarantee the stability of the system.

A Strictly Sufficient Stability Criterion for Grid-Connected Converters Based on Impedance Models and Gershgorin's Theorem