Power converters can be found in a wide range of applications, such as wind turbines, industrial machine drives, electric and hybrid vehicles, ships and submarines, etc. Power converters are used in energy conversion systems, and their objective is to transform the electric energy in a controlled manner. From the different power converter topologies available, the Matrix Converter (MC) can be highlighted because of the features it presents.

The MC performs direct AC/AC power conversion, and it has no significant reactive elements. Moreover, it can operate in all four quadrants, and currents and voltages with low harmonic distortion can be obtained at the inputs and outputs of the converter. In addition, unity power factor can be achieved at the converter input for any type of load. Finally, it can be said that the MC is very efficient. Taking into account the aforementioned features, MC technology could be very useful for a great number of applications. However, this power converter is not widely used yet, mainly because there is an absence of natural bidirectional switches, the architecture and the control of this converter is very complex, and its robustness is low.

At the beginning of this thesis, the fundamentals of the MC will be presented. After that, the wide range of modulation algorithms that can be found in the literature will be taken into account, and three remarkable modulation techniques will be explained: the Alesina and Venturini technique, the Space Vector Modulation (SVM) technique and the Generalized Scalar Pulse Width Modulation technique.

On the other hand, perturbations that can occur at the input side of the converter will be considered. In that sense, the state of the art of the most relevant solutions to compensate the effects of the aforementioned perturbations will be presented. Taking into account the synchronization needs of the aforementioned compensation techniques, the more convenient solutions to synchronize the MC with the power grid will be determined.

Later on, novel solutions to improve the design process of the MC will be proposed. On the one hand, it must be borne in mind that the simulation of models containing a MC is complex, and the simulation times required in order to perform the simulation of such models is extremely high. In that sense, a novel simulation method called SSMA (Switching State Matrix Averaging) that solves these problems will be presented and validated in this thesis. Moreover, real time simulation of a MC will be performed in a PC cluster, using the proposed SSMA simulation method. In that way, it will be possible to simulate very long transients in a reasonable time frame. Besides, a Rapid Control Prototyping (RCP) platform useful to accelerate the design process of the converter and to debbug its control algorithms will be presented.

Finally, the low robustness of the MC will be also considered in this thesis. The protection strategies of the MC are not capable of protecting the converter in 100 % of the cases. Therefore, in some situations, failures can occur in the elements that constitute the MC. If a failure occurs, it is necessary to use a fault tolerant strategy when the continuous operation of the system must be guaranteed. In that sense, the state of the art of the fault tolerant strategies for MCs will be presented, and the behaviour of a MC when open switch faults occur in its switches will be studied. After that, an strategy capable of identifying faulty MCs switches in open circuit will be presented, and new fault tolerant modulation strategies that improve the fault tolerance of the MC in the presence of open switch faults will be proposed. These techniques will be validated by simulation and by experimental results.