Nonlinear Lyapunov Stability Analysis of Seven Models of a DC/AC Droop Controlled Inverter Connected to an Infinite Bus

The transient stability of inverter-based microgrids is important given the low inertia of microgrids especially in islanded mode. However, as a prerequisite to understanding transient stability of such microgrids, the transient stability of individual inverters requires further analysis. To address inverter stability, this paper presents the 13th-order nonlinear model of a dc/ac droop controlled inverter connected to an infinite bus. The singular perturbation method was used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd, and 1st-order models. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is investigated using two different tools, time domain simulations and Lyapunov functions for the estimation of the domain of attraction. The work aims to present the best model to use for time domain simulations and domain of attraction estimation. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those areas of study. This will enable future studies to save computational effort and produce the most accurate results according to the needs of the study being performed.