Symmetries in Power Electronics
The past 50 years witnessed the inventions of more than one thousand power electronic topologies. However, we still lack a common standard to compare and classify various topologies. Moreover, topologies are often created through intuition rather than systematic approaches. The intuition of voltage and current sharing, along with modularity and scalability, gives rises to cascaded-bridge and multi-paralleled converters, respectively. Nevertheless, power converters with both high-voltage and large-current capabilities are still obscure yet important. This paper first investigates the symmetries of circuit topologies through group theory. Notably, symmetries lie in twofold - individual modules and connections. Symmetries not only help to classify topologies but also play an important role in creation of new topologies. Based on wallpaper groups, this paper proposes the lattice converters that can theoretically undertake infinite voltages and currents. The proposed lattice converters will find applications in 1) high-voltage dc/ac transmissions; 2) renewable energy generation; 3) power quality conditioning equipment; 4) electric vehicles; 5) marine and aircraft propulsion; 6) medical applications such as noninvasive magnetic stimulators; 7) high-frequency high-power power supplies; 8) plasma applications; 9) future power grids. For validations, simulation results are presented, demonstrating that the lattice converter related to p4m operates well as high-power inverters.
