Optimal control of linear periodically time-varying system with application to cascaded H-bridge reactive power generator

This article presents a finite-horizon optimal control based on a linear periodically time-varying (LTPV) state- space model for single-phase cascaded H -bridge (CHB) converter with low-capacitance. This LPTV model, characterized by periodic time-varying state matrices, integrates the branch current and capacitor voltages as state variables, modulation signals as control inputs. This article aims to design a full state feedback control for the periodic currents and capacitor voltages tracking, without decoupling control bandwidth for current and capacitor voltage as in conventional studies. This is indeed particularly important for low-capacitance CHB, because the capacitor voltage ripple and current are interacted with each other. After deriving the LPTV model from a bilinear time-varying model, an optimal problem with a performance index over a finite-time interval as the objective function is formulated. In order to solve this optimal problem, the dynamic programming is used so as to obtain an optimal control matrix. Simulations on a 45-level CHB converter and experiments on a 5-level low-capacitance single-phase CHB prototype verify the proposed control strategy, corroborating its excellent performance at transient- and steady -state.