Dual Lagrangian modeling and Lyapunov-based control of four-wire three-level three-phase NPC voltage-source rectifier

An ac neutral wire is connected to the midpoint of the dc bus of the three level/phase NPC rectifiers and then a new dual Lagrangian model of the rectifier is presented in this paper. At first, the load current can be obtained in two forms: 1. the load current involving the current of capacitor C1 2. The load current involving the current of capacitor C2 and then the new model is founded based on the superposition law, the load current and The Euler-Lagrange description of the rectifier. The new model is two nonlinear state space equations and as a result we define two positive definite Lyapunov function candidates based on two equations. Finally two Lyapunov-based controllers are designed to be gained desired output voltages, very low THD, unity power factor and Neutral Point Potential (NPP) 0 V. It is important to be known that One of the controllers is utilized to control the voltage of C1 and the other is used to control the voltage of C2 and also both controllers are used to keep NPP at 0 V. In addition to the above mentioned features of the controllers, The MATLAB/SIMULINK results showed that the rectifier can be stabilized globally for handling large-signal disturbances and Exhibits good transient response in the rectifying mode.