Symmetries in Power Electronics and Lattice Converters

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 rise to cascaded-bridge and multi-parallleled converters, respectively. Nevertheless, power converters with both high-voltage and large-current capabilities are still obscure yet important. This article 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 the creation of new topologies. Based on wallpaper groups, this article proposes the lattice converters, which readily scale to manage high voltages and large currents. The proposed lattice converters benefit from 1) modularity and scalability, 2) boundless current and voltage ratings, 3) multiple input/output ports, 4) sensorless voltage balancing, 5) high power quality, and 6) flexible control. Simulation and experimental results demonstrate the effectiveness and superiority of the proposed theory and lattice converters.