Numerical estimation of the lock-in domain of a DC/AC inverter

TL;DR

This paper presents a numerical method to estimate the lock-in domain of a DC/AC inverter's control system, combining Lyapunov functions for stability analysis of the cascade system.

Contribution

It introduces a novel numerical approach to construct a vector Lyapunov function for the combined linear and nonlinear system in inverter control.

Findings

Successfully estimates the lock-in domain using numerical Lyapunov functions.

Proves convergence to the origin via LaSalle's invariance principle.

Provides a systematic method for stability analysis of inverter control systems.

Abstract

We estimate the lock-in domain of the origin of a current control system which is used in common DC/AC inverter designs. The system is a cascade connection of a 4-dimensional linear system (current controller, CC) followed by a two-dimensional nonlinear system (phase-locked loop, PLL). For the PLL, we construct a Lyapunov function via numerical approximation of its level curves. In combination with the quadratic Lyapunov function of the CC, it forms a vector Lyapunov function (VLF) for the overall system. A forward-invariant set of the VLF is found via numerical application of the comparison principle. By LaSalle's invariance principle, convergence to the origin is established.