Electrical Engineering

, Volume 100, Issue 2, pp 509–518 | Cite as

Global optimization of high-power modular multilevel active-front-end converter using analytical model

  • Amin Zabihinejad
  • Philippe Viarouge
Original Paper


Modular multilevel converters (MMCs) have emerged in response to increasing the demands of converter in high-power applications. Because of the modularity, MMC structures are ideal in order to use in high voltage and current applications. Increasing the number of semiconductors and passive components made it so bulky and expensive. On the other hand, high number of variables and the circular interaction between the components values and electrical quantities of the MMCs make it difficult to analyze and design. In this paper, an accurate steady-state analytical model of modular multilevel active front end has been presented and developed. The proposed steady-state model provides more precise analytical expressions for capacitor voltage ripple and circulating current based on the input and output specifications. Then, a novel optimization approach has been proposed and integrated to determine the passive component values in order to maximize the performance and minimize the total volume using analytical model with respect to the technical and mechanical constraints. The optimization procedure uses a nonlinear numerical solver to calculate the optimal values of sub-module capacitor and arm inductance in order to minimize the total energy stored in the converter which is directly related to the total converter mass.


Modular multilevel converter Analytical model Steady state Global optimization Active front end 

List of symbols


Sub-module capacitor value


AC line current (phase a)


Circulation current


nth Harmonic of capacitor current


Upper/lower arm current


Arm inductance value


Mutual inductance value


Number of sub-modules per arm


Number of parallel arms


Inductor resistance


Modulation index


Upper/lower switching function

\(\theta _{1}\)

Phase of AC current

\(\theta _{2}\)

Phase of second-order current

\(\omega _{1}\)

Main angular frequency


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.LEEPCI LaboratoryUniversite LavalQuebecCanada

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