Complex phasor modeling and control of modular multilevel inverters

Modular multilevel power converters in a `bridge of bridge´ configuration have been introduced recently for realizing ac-dc, dc-ac and ac-ac power conversion functions with voltage step-up and step-down capability, bidirectional power flow and transformerless operation. While different modulation and control approaches have been introduced in an ad-hoc manner in the introductory literature, definitive models that may be used to characterize the steady state and dynamic performance are just beginning to be uncovered. It is the objective of this paper to introduce a canonical phasor or complex vector model to represent the ac variables along with the dc variables that are unique to this family of converters. The model is used to develop a suitable control approach using established techniques. The complex vector model is represented in the synchronously rotating dq reference frame, and illustrated using an application of a dc-ac step-up inverter for residential photovoltaic applications.