Mathematical Framework for Stability Analysis of Grid-Connected Inverters in Renewable Energy Systems
Keywords:
Grid-connected inverters, renewable energy systems, stability analysis, small-signal modeling, state-space representation, eigenvalue analysis, Phase margin, gain margin, weak grid, short-circuit ratio, stability boundary, controller design.Abstract
With the rising share of renewables in the grid, the use of grid-tied inverters brings a lot of stability issues when operating on weak grid conditions, which have a low short circuit ratio (SCR), where standard fixed gain controls lack damping and are prone to instability. This paper presents a mathematical framework for stability analysis of grid-connected inverters, which includes small-signal state-space modeling and eigenvalue and frequency-domain (Bode) analysis of the system to characterize the stability of the system for different grid strengths. A stability boundary map of controller gain and critical SCR is developed to facilitate the design of a robust controller. These have all been successfully shown by simulation, whose results are impressive: phase margin rose from 23.9° to 48.8°; gain margin from 6.8 dB to 13.8 dB; damping ratio was increased from 0.08 to 0.25, and settling time dropped from 180 ms to 95 ms; critical SCR has been decreased from 2.0 to 1.2, meaning that operation is now more stable under much poorer grid conditions. It provides a model-based framework for the design of stability-aware inverter control strategy for renewable dominated power networks in electrical power systems with scalability.
