Stability analysis of an observer-based nonlinear model predictive controller for resonant grounded power distribution systems

This article presents the stability analysis of a resonant grounded power distribution system (RGPDS) in which a nonlinear model predictive controller (NMPC) with a nonlinear extended state observer (NLESO) is used to achieve the desired fault current compensation through the residual current compensation (RCC) inverters. The detailed model of the system is developed to appropriately model nonlinearities so that these can be represented as an extended state and estimated using the ESO. The closed-loop model of the system is developed in the discrete-time to conduct the frequency-domain analysis using two different methods, for example, the describing function (DF) method and Tsypkin criterion. The main target of these analyses is to gain useful insights on different control parameters and get an idea about their effects on the overall stability of the RGPDS with an REFCL. The relationship between the Nyquist plot and the trajectory of the key control parameter is used to determine the boundary up to which the control parameter can be adjusted to maintain the stability of the system. Finally, it is identified that the Tsypkin criterion allows more flexibilities compared to the DF method for selecting the control parameter.