## 2 Practical Considerations on the Implementation of Matrix Converters  
Being an \"all silicon\" topology with bidirectional switches, matrix converters require dedicated commutation schemes that go beyond the simple use of \"dead-times\" or overlapping the semiconductors driving signals. Furthermore, unlike typical VSCs, in matrix converters there are no natural freewheeling paths for the output currents. Openingsuch currents when using inductive loads will result in high transient overvoltages that ultimately can damage the semiconductors or the load. The commutation strategy can be undertaken in either two steps or four steps and can either be based on the output load currents or the input phase to phase voltages [1]. On four-step based commutation methods, both devices in the current path of the conducting bidirectional switch are enabled during the normal conducting stage, while on two step-based method only the devices that match the direction of the load current are enabled. The advantage of two-step methods is that they require fewer commutations of semiconductors than the four-step methods. However, depending on the type of bidirectional switch used it might be beneficial to keep both semiconductors enabled. For example, when using MOSFET and junction field effect transistors (JFET) semiconductors that allow source to drain currents when the channel is active, a four-step method might result in lower conduction losses. Figure 3 represents the application of the current-based four-step commutation method when switching from the bidirectional switch \(S_{1}\) to the bidirectional switch \(S_{2}\) with a positive output current. Step 1, represented in Figure 3a, initiates the commutation process by opening the non-conducting semiconductor of the conducting switch (\(S_{1}\) in the depicted case). Step 2, represented in Figure 3b, closes the semiconductor that will conduct the output current of the future conducting switch (\(S_{2}\) in the depicted case), which semiconductor of the switch is closed in this step depends on the signal of the output current of that particular phase. Step 3, represented in Figure 3c, fully opens the previously conducting bidirectional switch. This can be done since a new path for the output current was created in Step 2. Finally Step 4, represented in Figure 3d, closes the non-conducting semiconductor of the new conducting bidirectional switch (\(S_{2}\)) finalizing the commutation process. The voltage-based techniques are very similar but instead of using the measurement of the output current to select the conducting and non-conducting switches they use the measurement of the input phase to phase voltage and select the sequence ensuring that no short circuits happen. The two step techniques as stated above use only Steps 2 and 3 of the four step commutation methods keeping only one semiconductor closed per switch. Typically, due to timing requirements for the commutation steps, FPGAs are used to handle these commutation schemes. Besides the implementation of each step and the selection of the appropriate timings, it is important to latch both the measurement signals input and the new conducting switches' signal input so that these signals do not change during the commutation period, which otherwise could lead to open circuits on the output, or input short circuits. Along with this work, a base implementation in VHDL of a current-based four step commutation method is provided so that it can facilitate the process of implement  
Figure 3: Representation of a current based four-step commutation method switching from bidirectional switch \(S_{1}\) to bidirectional switch \(S_{2}\). The different commutation steps are represented: (**a**) Step 1, (**b**) Step 2, (**c**) Step 3 and(**d**) Step 4.  
ing matrix converters, that can be found [[https://github.com/pccosta/MatrixConverter4](https://github.com/pccosta/MatrixConverter4) StepCommutation]([https://github.com/pccosta/MatrixConverter4](https://github.com/pccosta/MatrixConverter4) StepCommutation) (accessed on 18 May 2021).