Combinatorics

Electrical engineering

Physics

Topology (electrical circuits)

Mathematics

Algorithm

Circulant matrix

Modulation (music)

Matrix (chemical analysis)

Engineering

Voltage

Artificial intelligence

Composite material

Acoustics

Control (management)

Materials science

Electronic engineering

Converters

Computer science

Control theory (sociology)

IEEE Transactions on Power Electronics

The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium voltage distribution systems. Inherent balance of submodule (SM) capacitor voltages is considered as an ideal property which avoids a complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This paper extends the inherent balance concept previously shown for square-wave modulation to a multilevel version for MMDCs. A switching duty matrix dU is introduced: it is a circulant matrix of preset multi-level switching patterns with multiple stages and multiple durations. Inherent voltage balance is ensured with a full-rank dU. Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A non-full rank dU causes clusters of SM voltage rather than a single common value, with the clusters indicated by the kernel of the matrix. A generalized co-prime criterion is developed into several deductions that serve as practical guidance for design of multilevel circulant modulation. The theoretical development is verified through full-scale simulations and down-scaled experiments. The effectiveness of the proposed circulant modulation in achieving SM voltage balance in an MMDC is demonstrated.

Inherent SM Voltage Balance for Multilevel Circulant Modulation in Modular Multilevel DC-DC Converters