Mathematical Modeling and Analysis of an Inverter-Based Resource

Abstract

The transition from traditional synchronous machines to inverter-based resources is evident due to their ability to integrate renewable energy sources. Problems of instability due to the dynamics of the inverter, which is a major component of an Inverter-Based Resource (IBR), need to be modeled accordingly to stabilize the system behavior. This paper includes the development of a linearized state space model for a three-phase standalone inverter equipped with an LCL filter and RL load comprising IBR. A detailed mathematical framework in MATLAB, which includes a system of differential equations, state matrices (A, B, and C), and eigenvalue analysis for stability assessment of the small-signal behavior of the inverter system, has been developed. The result includes the identification of critical modes and their participating states that provide insights into system nonlinearity and stability. All eight eigenvalues have real parts lying in negative real axis, with two of the modes having damping ratio 0.24% and 0.25% suggesting critically with frequency of oscillation of 3.69 kHz and 3.59 kHz, respectively. The model’s efficacy to capture electromagnetic dynamics depicting two of the electromagnetic modes with a high frequency of oscillation around the resonance frequency has been presented, alongside a solid foundation for future feedback controller design in enhancing IBRs stability in renewable integration.