Stability Analysis and advanced control strategies for Matrix Converter

Matrix Converter allows for m-phase to n-phase direct AC-AC conversion through an m x n array of bidirectional switches. It is a four-quadrant converter with controllable input power factor. Its main advantage lies on the absence of an intermediate DC stage, thereby obviating the necessity for heavy and bulky electrolytic capacitors. In fact, these components are prone to aging, compromising the overall system reliability. The focus of this dissertation is on three-phase to three-phase Matrix Converters, specifically on investigating the stability of three-phase applications employing this converter. The input side of the Matrix Converter can be considered as a controlled current source, requiring the connection of an LC filter to reduce the harmonic content of the input current and meet the EMC requirements. It is well know that this component connected to the input side of a power converter introduce instabilities, which depends on system topology and control strategy. This becomes more evident in presence of high bandwidth closed-loops. In the case of the Matrix Converter, this phenomenon is worsen by the absence of a DC stage, which, in traditional AC-AC converters, enhances stability. In particular, when analysing open-loop conditions, it is possible to demonstrate that instabilities depend primarily on the power exchanged between input and output. In the case of closed-loops the effect is worsen depending on control bandwidth. Stability studies on this converter are complicated by the fact that its average model equations are nonlinear making calculations more complex. Over the past few decades, the research on this field focus on solutions to enhance Matrix Converter applications stability. For example, the input filter can be properly designed to maximise the power transmission and the control bandwidth. However, this method is still intrinsically limited. Another approach adopted is to filter the input voltage signal necessary for the converter modulation. While this method allows to increase the transmittable power, it proves limited in case of high control bandwidth. In the literature there are also solutions that allow the transmitted power to be increased by modifying the voltage reference supplied to the modulator, however even in this case limitations are encountered in terms of control bandwidth. Model Predictive Control (MPC) strategies have been studied for this converter. Unfortunately, due to the high number of switches combinations, this approach requires a significant computational burden. In the preliminary phase of this dissertation, an analysis of existing stabilization methods is presented, focusing on their limits in terms of power and control bandwidth. Subsequently, a novel stabilization method employing full-state feedback is proposed. An H2-LMI inequality (LMI) algorithm is utilized to compute feedback gains that guarantee robust performance across a predefined bidirectional power operational range with high control bandwidth. The proposed system was found to be more stable than the methods present in the literature, thus increasing both transmissible power and control bandwidth while reducing the harmonic content of the input and output quantities, with a low computation burden. The effectiveness of the proposed algorithm has been tested firstly through simulations, using MATLAB Simulink, followed by subsequent experimental validation.