Three Levels Are Not Enough: Scaling Laws for Multilevel Converters in AC/DC Applications

Single-phase inverters and rectifiers in 230 Vrms applications, with a dc-side voltage of 400 V, achieve ultrahigh efficiency with a simple two-level topology. These single-phase designs typically utilize a line-frequency unfolder stage, which has very low losses and essentially doubles the peak-to-peak voltage that can be generated on the ac side for a given dc-link voltage. For certain applications, however, such as higher power grid-connected photovoltaic inverters, electric vehicle chargers, and machine drives, three-phase converters are needed. Because of the three-phase characteristic of the system, unfolders cannot be similarly used, leading to a higher minimum dc-link voltage of the three-phase line-to-line voltage amplitude, which is typically set to 800 V for 230 Vrms phase voltage systems. Previous demonstrations indicate that significantly more levels-and the associated higher cost and complexity-are required for ultrahigh-efficiency three-phase converters relative to their single-phase counterparts. In this article, we seek to determine the fundamental reason for the performance difference between three-phase 800 V dc-link converters and single phase 400 V converters. First, we build a 2.2 kW dc/ac hardware demonstrator to confirm the necessity of higher complexity converters, showing a simultaneous reduction in efficiency and power density between a two-level 400 V benchmark (99.2% peak efficiency at 18.0 kW/L) and a three-level 800 V inverter phase-leg (98.8%, 9.1 kW/L). With the motivation confirmed, we derive general scaling laws for bridge-leg losses across the number of levels and dc-link voltage, finding the efficiency-optimal chip area and the minimum semiconductor losses. With commercially available Si or GaN power semiconductors, the scaling laws indicate that six or more levels would be required for an 800 V three-phase ac/dc converter to meet or exceed the bridge-leg efficiency of a two-level 400 V GaN benchmark for a fixed output filter. With a complete Pareto optimization, we find that at least seven levels are necessary to recover the efficiency of the two-level 400 V benchmark, and we validate this theory with a seven-level 800 V 2.2 kW hardware prototype with a power density of 15.8 kW/L and a peak efficiency of 99.03%. Finally, two practical solutions that make use of the benefits of unfolder bridges familiar in single-phase systems are identified for three-phase systems.