Lyapunov-Krasovskii passivity based stability analysis of grid-tied inverters

Abstract

The non-linear dynamics of a grid-interfaced inverter (GII) in a distributed generation system results in dynamic instability and power quality issues. The conventional linear methods depend on parametric variations in controller parameters hence, tuning should be proper. Also, linearization of dynamical states around steady-state operating point works only if the controllers operate around a fixed operating point thus, only ensuring local stability. The feedback and feedforward damping methods can address some of the above challenges but requires additional sensors and also incapable of maintaining robustness against grid impedance variations and system parametric changes. To address aforementioned issues, this journal presents a non-linear Lyapunov Krasovskii Passivity (LK-PBC) based dynamic controller for Grid-interfaced Voltage Source Converters (VSCs). A generalized admittance model is derived which is used to calculate Non-passive regions of the VSC where the output admittance will have a negative real part. The damping provided by the proposed controller also eliminates the resonance instability issues in the concerned frequency scale regardless of the admittance seen at the inverter terminals. It also takes care of time delay and norm-bounded state uncertainties. The evaluation of the theoretical studies and efficacy of the proposed LK-PBC controller is confirmed by hardware in loop analysis on a laboratory experimental setup.