A Generalized Theory of Boundary Control for a Single-Phase Multilevel Inverter Using Second-Order Switching Surface

An extension of the use of the boundary control method using second-order switching functions for controlling single-phase multilevel inverters is presented in this paper. The time instant of switching the output voltage of the inverter bridge from one voltage level to another voltage level is governed by two second-order switching functions. The input variables of the switching functions are the input and output voltages of the inverter, reference output voltage, and output filter capacitor current. The switching functions are derived by first estimating the respective trajectories of the output voltage of the inverter with the two possible voltage levels from the inverter bridge supplying to the input of the output filter, and then formulating mathematical functions to approximate the two trajectories (one for each voltage level) that pass through the target operating point. The distinct feature of this method is that the output voltage of the inverter can reach the target operating point in two switching actions in the inverter bridge after the inverter is subjected to an external disturbance. Derivation of the switching functions and implementation of the controller will be given. Three single-phase inverter topologies, including cascaded five-level inverter, hybrid seven-level inverter, and three-level diode-clamped inverter, with the proposed control method have been built and tested. The steady-state and large-signal dynamic responses of the three inverters supplying to three different load types, including resistive, inductive, and nonlinear diode–capacitor circuits, will be discussed.