Electrical Engineering

, Volume 100, Issue 2, pp 509–518

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

• Philippe Viarouge
Original Paper

## Abstract

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.

## Keywords

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

## List of symbols

$$C_\mathrm{sm}$$

Sub-module capacitor value

$$I_\mathrm{a}$$

AC line current (phase a)

$$I_\mathrm{circ}$$

Circulation current

$$I^\mathrm{hn}_\mathrm{cu,cl}$$

nth Harmonic of capacitor current

$$I_\mathrm{u,l}$$

Upper/lower arm current

L

Arm inductance value

M

Mutual inductance value

N

Number of sub-modules per arm

m

Number of parallel arms

R

Inductor resistance

$$S_\mathrm{m}$$

Modulation index

$$S_\mathrm{au,al}$$

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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