IEEE Power Electronics Magazine - June 2018 - 57

optimum phase angle, the cell capa citor voltage ripple
can be reduced (while the dc and ac side waveforms stay
unaffected). The injection of optimum low-frequency harmonics (second or second + fourth) within the circulating current has widely been studied by researchers [4], [5].
This article is based on [6], where a special effort has
been made to minimize the size of passive elements within
the structure of the MMC in the AFE rectifier mode of operation. By taking advantage of a hidden optimum design
point in the converter structure, the size of the arm inductors and cell capacitors are reduced while no additional
complexity is introduced to the system. The proposed
method does not need any additional controllers and is
capable of achieving a similar reduction in the size of the
cell capacitors in low-frequency circulating current injection methods. Moreover, using the proposed design guidelines results in a roughly 90% reduction in the arm inductors in the MMC AFE converter and an approximately 65%
reduction of the total installed inductors in the converter
structure. The achieved reduction of the passive elements
(i.e., arm inductors and cell capacitors) will result in the
reduction of converter volume and the initial investment
needed for it, thereby increasing the popularity of the
MMC converter in the AFE application.

Circuit Configuration and Principles of Operation
Figure 1 shows the general circuit configuration of the gridconnected MMC AFE. There are a total of six arms in a
three-phase MMC converter, where each arm is formed by a
series connection of N identical cells together with an arm
inductor L. The cells used within the converter can be in a
half-bridge or full-bridge configuration. Also, in some cases,
the filter inductors are added between the MMC AFE and
the grid to improve the power quality and increase the short
circuit protection level of the converter. In Figure 1,
i vj ( j = a, b, or c) is the input current of the AFE in phase j,
I dc is the dc current delivered to the dc side (load), and i pj
and i nj are the upper and lower arm currents in phase j,
respectively. The input phase current is equally divided
between the upper and lower arms, thus (1) and (2) can be
written for the arm currents as
i vj
i pj = i circ, j + 2

(1)

i vj
i nj = i circ, j - 2 ,

(2)

where i circ, j is the circulating current in phase j.
The circulating current comprises a dc component
(which is one-third of I dc) plus even-order harmonics. The

Idc
C1
upa
Lfilter

CN
ipa
Udc

icirc,a

ina

uvb
uva

iva

uvc

L
CN+1
una
C2N

Fig 1 The MMC in the grid-connected rectifier mode operation.

even-order harmonics of the circulating current are generated due to the interaction between the fundamental
frequency current in the arms as well as the fundamental
frequency switching of the cells [7]. Theoretically, there is
no limit for the order of the even-order harmonics in the circulating current. However, it is shown in [8] that the major
even-order harmonics of the circuating current are the
second and fourth. Considering the second and fourth harmonics in the circulating current, (3) can be derived. It has
been shown in the literature that the even-order harmonics
of the circulating current do not considerably contribute to
the input and output waveforms of the MMC converter:
I
i circ, j = 3dc + I 2 sin ^2~t + i h + I 4 sin ^4~t + z h,

(3)

where I 2 and I 4 are the magnitudes of second- and fourthorder current harmonics, and i and z are their corresponding phase angles.

Proposed Optimum Design Guideline
for Minimization of Arm Inductors
An important step in designing the MMC converter is to size
the arm inductors and the cell capacitors within its structure. The cell capacitor value is usually selected to restrict
the voltage ripple to a specific amount. In this article, we
June 2018

z IEEE POwEr ElECtrOnICs MAGAzInE

Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - June 2018