Modeling and control of the currents and capacitor voltages of a novel modular matrix converter

Modeling and control strategies are developed for a novel modular matrix converter for variable-speed wind power generation. The regulator is designed to control the input and output power factors, output currents and the capacitors voltages of the matrix converter as other parameters, such as wind speed, vary. Differential equations describing the system have been derived in terms of the input currents, output currents and the capacitor voltages of the matrix converter. The currents are transformed into the dq0 frame to obtain a nonlinear state space model of the matrix converter. The nonlinear model is then linearized to get a linear state space model for the matrix converter. The linear model represents the small variations in the matrix converter output states that need to be minimized. A regulator is designed for the linearized model using the pole placement method. The regulator is then tested with the nonlinear model of the matrix converter.; As the matrix converter parameters vary (input/output power factors, output current...etc.), the controller has to be modified in order to regulate the converter. In an attempt to find a relationship between the controller gain matrix elements and the matrix converter parameters, it is found that the controller designed via pole placement method is very sensitive to those variations and no clear relationship can be obtained. In practice, another method must be used.; Optimal control of the matrix converter produces better results than the pole placement method. Simulation results show that the matrix converter exhibits faster transient responses and less error when the optimal controller is implemented. Moreover, the elements of the optimal controller gain matrix are only dependent on the input line frequency and the output current amplitude. The relation is interpolated into a 3rd degree polynomial. The process of obtaining a pseudo-optimal controller by approximating the value of its elements, given the input line frequency and the output current amplitude, is faster than solving the optimal control problem every time there are variations in the matrix converter parameters. All nine capacitors were modeled in the simulation program to see their responses. Simulation results show that the capacitor voltages reach their nominal values when utilized with minimum transients and fast settling time.; Finally, the modeling and control schemes were tested on a laboratory prototype of the matrix converter. The converter was connected between the utility and a resistive load. It was found that some modes of the response were faster than the switching frequency and hence could not be controlled. Some components of the matrix converter (output filter inductors) had to be replaced with components that have bigger values so that all natural time constants were at least several switching periods. The resulting closed-loop converter system then operated as predicted by the simulation and model, with a stable response. The experimental results confirm the predictions of the simulation thereby proving the validity of the modeling scheme and optimal control strategy.