Stability Analysis Methods of a Grid-Connected Inverter in Time and Frequency Domains

A grid-connected inverter must be designed to assure stable operation. Stability analysis of the system is one of the most important design processes and it is calculated mainly by four types of analysis methods both in time and frequency domains. This paper investigates and compares these stability analysis methods. In frequency domain, according to the impedance method, frequency characteristics of an output impedance or admittance are calculated and investigated. Three frequency analysis methods, the analytical derivation method, the numerical frequency analysis method that is based on an automatic and numerical formulation and solution algorithm, and the simulator-based frequency scan method, are often used and useful. According to the impedance method, it is sufficient when the real part of the admittance of the inverter is positive and passive to ensure stability. Three types of passivity-based design examples are shown. In time domain, a unique analysis method which is based on the eigenvalue analysis of the Poincaré map or the sensitivity matrix of state-variables for perturbations along an operating trajectory, has been developed and it is also useful. These four methods are investigated for their features. Application example cases for grid-connected inverters are investigated and compared between the methods by simulation and experiment.