## 5 Matrix Converters Contribution towards the Innovation of Electrical Drives
### Direct Matrix Converter (DMC)-Based Works  
The higher number of phases or actively driving both ends of the machine windings increase the switch count but results in additional available switching states. From one perspective those extra switching states offer more control flexibility, but on the other hand the modulation complexity is increased. This might be the reason for the extensive research work on modulation techniques for such configurations.  
In [99] a space vector modulation (SVM) technique for OEW 3 \(\times\) 3 DMCs (3 input phases and 3 output phases) is proposed making only use of rotating space vectors, which are divided into a group rotating in the clockwise (CW) direction and other rotating in the counter-clockwise (CCW) direction. Using only one of these groups will not give the ability to control the input power factor, so the authors propose a technique where the usage of CW and CCW vectors is alternated allowing input power factor control at the expense of decreasing input/output voltage gain. For this modulation scheme the input-output voltage gain is set to 1.5 without controlling the input power factor. The usage of only rotating vectors in 3 \(\times\) 3 DMCs intrinsically eliminates CMV at load terminals. In [100; 101] detailed care is given to this topology, also using only rotating space vectors, and a comparison is made between each DMC having their own output vectors, and both DMCs being used together to synthetize one output vector. On the first case they are limited to a voltage gain of 1 while on the second they can achieve 1.5. Both CW and CCW situations are analyzed separately in those works.  
In single-ended multiphase DMCs, also called non-square DMCs, the vector-based techniques proposed do not take advantage of rotating space vectors since they are more complex to work with and in these non-square configurations the CMV would not be eliminated. In [102] a SVM technique is proposed for a 3 \(\times\) 5 DMC using 93 out of the 243 available vectors, where the output voltage magnitude is found to be limited to 78.8% of the input voltage magnitude for linear modulation regions. Later in [103] a SVM scheme was proposed for a 3 \(\times\) 7 DMC topology, using 129 different switching states out of the available 2187 states, achieving improved results in terms of output voltage and input current waveform quality. Efforts in scalar based PWM techniques for single-ended DMCs have also been published in the literature. In [104] a novel and simple carrier-based PWM scheme is proposed for a 3 \(\times\) 9 DMC that is able to achieve unity power factor operation and a voltage transfer ratio of 76.2%. Later, a generalized theory for m \(\times\) n scalar modulation techniques was presented in [105]. It was also shown that the Venturini method is only valid if the number of input phases is three and a simplified scalar-based modulation method for a general m \(\times\) n matrix converter is proposed. Experimental results are provided for a 3 \(\times\) 5 configuration.  
Multiphase single-ended DMCs are limited to relatively low voltage gains and are not capable of eliminating CMV. This led to the development of configurations that combine multiphase DMCs to OEW topologies. A generalized carrier-based PWM technique for OEW DMCs in 3\(\mathrm{n}\) configuration is presented in [106] that can achieve reduced CMV, unity power factor operation and a voltage gain of 1.5 on a laboratory prototype. On Vector based modulation techniques, strategies for 3 \(\times\) 5 in [107; 108; 109] and 3 \(\times\) 7 in [110] that eliminate CMV while achieving a 1.5 voltage transfer ratio at unity input power factor are proposed.