## 8 Challenges and Research Needs of Matrix Converters
a comparable Ga\({}_{2}\)O\({}_{3}\) matrix converter could reach the MHz range with half the size of the SiC package. However, much research must be done to achieve fast multi-kilovolt-class power transistors. In particular, as Ga\({}_{2}\)O\({}_{3}\) may attain frequencies in the 10 GHz range [157], research on new magnetic and dielectric materials must be undertaken before the Ga\({}_{2}\)O\({}_{3}\) disruptive technology may be ready for commercial applications. Meanwhile, given the high voltage and high operating frequency, research on analysis and modelling of bidirectional JFETs, on mitigation of switching oscillations in JFET-based bidirectional switches, on integrated drivers with short circuit protection, on the commutation of bidirectional JFET in matrix converters, together with research on magnetic materials, electromagnetic shielding, and input and output filters should be carried on. In terms of topologies, the challenges of matrix converters concentrate on improving the efficiency of transmission by increasing modularity, power density and reducing power losses. For instance, modular topologies with fewer stages of conversion and lower switch count per module could be capable of replacing the state-of-the-art converters in new applications like those described in this work. On hybrid applications that need galvanic isolation in the interconnection of AC and DC microgrids, the development of topologies that provide soft switching capability when supplying high-frequency transformers will lead to more compact and efficient systems. Specifically, for the applications of SSTs, a novel topology in Figure 22 has the potential research and future application value where four bidirectional switches are replaced by three bidirectional switches at the primary side of the transformer and only one H-bridge with bidirectional switches is used at the secondary side, leading to a reduced switch count for the entire system compared to the structure in [29]. In the meantime, this topology also has the possibility of constructing a hybrid grid using less conversion stages compared to the conventional SST's topologies in [158] where a DC link is unavoidable when constructing a hybrid grid system. One of the challenges is the balancing of the capacitor voltages since capacitors in series are generally a preferred solution for the high voltage side of SSTs [159; 160]. Along with controllers, modulation methods are extremely important to ensure adequate balancing of the capacitor voltages. Figure 23 depicts the influence of modulation methods in the capacitor voltages where a triangular carrier for a half-Venturini modulator wave yields  
Figure 22: A novel topology proposed for the applications of SSTs. balanced capacitor voltages (Figure 23a), whereas a sawtooth carrier yields unbalanced capacitor voltages (Figure 23b). Such applications require novel control strategies to tackle these emerging topologies and functions. Currently, MPC algorithms in matrix converters allow a higher number of degrees of freedom by using an appropriate cost function capable of dealing with several goals at once, choosing the optimal available state that minimizes deviations from set-points. On the other hand, in specific applications such as electric drives, matrix converter topologies may contain enough semiconductors to lead to an unbearable number of possible switching states for the MPC. Research to use the redundant states for operation under faulty semiconductors is needed. New approaches need to be developed to account for the upcoming challenges on smart grids and sustainable transportation such as emulating inertia, multilayer control, improve power quality, managing energy storage systems, among others. Non-linear controllers such as Lyapunov-based methods and backstepping are promising techniques that can make use of high-frequency modulation techniques taking advantage of the allowable high switching frequency of wideband-gap devices.