Applied Mechanics and Materials
ISSN: 1662-7482, Vols. 313-314, pp 337-340
doi:10.4028/www.scientific.net/AMM.313-314.337
© 2013 Trans Tech Publications, Switzerland
Online: 2013-03-25
A Novel SHE Modulation Method for Modular Multilevel Converter (MMC)
with Reduced Switching Frequency
Ma Xiaoxiao1, a, Wang Ping2, b
1, 2
Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering,
Chinese Academy of Sciences Beijing, China
a
[email protected], [email protected]
Key words: MMC, selective harmonic elimination (SHE), switching frequency;
Abstract. Modular multilevel converter (MMC) is one of the most attractive converter topology
intended for high power conversion without transformer. In this paper, a new modulation method
for MMC is proposed and verified by simulated model. The main advantage of reduced switching
frequency is also proved in the simulation results.
Introduction
Many multilevel converters have been proposed to satisfy the need for medium and high voltage
applications. Recently, modular multilevel converter (MMC), which first presented in [1,2], is
gaining popularity in a wide range of applications because of its several substantial advantages such
as modular design, redundancy in operating mode, filterless and transformerless configuration, high
reliability, etc.
The most common modulation method for MMC proposed by [3, 4] is SPWM. It solves the
capacitors balancing problem by sorting the submodule capacitor voltages at each control cycle, and
charging the capacitors with low voltage while discharging the ones with high voltage. SPWM
method is very convenient mainly because its simplicity, and effectiveness in balancing the
submodule capacitor voltages. But there also exists a vital weakness of this method that is the high
switching frequency and the losses come from it.
There are also other modulation methods such as phase shift PWM [5], nearest level control
(NLC) [6], etc. The phase shift PWM can not assure that N submodule capacitors are connected
between the positive and negative DC-link in each phase all the time. Therefore the arm inductor
must endure the high voltage due to the fluctuation of DC-link voltage. And the NLC method does
not produce good harmonic characteristic.
This paper focuses on a new modulation method for MMC which is related to selective harmonic
elimination scheme. The new modulation method brings two main advantages, reduced switching
frequency and fewer losses.
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338
Machinery Electronics and Control Engineering II
Modular multilevel converter
The structure of MMC is shown in Fig. 1(a) and the submodule is illustrated in Fig. 1(b).
(a)
(b)
Fig.1 (a) Topology of MMC; (b) configuration of submodule of MMC;
Selective harmonic elimination
The voltage waveform of a single phase can be decomposed into Fourier series as following:
∞
∞
n =1
n =1
V (t ) = a0 + ∑ an cos(ωt ) + ∑ bn sin(ωt )
(1)
Assuming V (t ) to be an odd function, the cosine terms can be omitted. The Fourier coefficients
of odd harmonics are given by:
bn =
4VDC
nπ
N
∑p
k =1
k
cos nα k
(2)
Where n is the harmonic order. And if pk is given by:
 1 when k is odd
pk = 
−1 when k is even
(3)
Then the SHE method can be applied in the three level voltage source converter, shown in figure
2a, otherwise if pk is given by pk = 1 , then the SHE method can be shown in figure 1b, which is
the modulation method adopted by this paper.
The advantage of this modulation scheme is reducing the switching frequency significantly and
producing a stair-shaped voltage wave. Any harmonic can be eliminated by solving the
corresponding equation obtained from setting Eq. 2 to zero. And the fundamental wave should be
equal to the modulation index M. The equations can be expressed by:
b1 = M
n = 5,7,11......

 bn = 0
(4)
Applied Mechanics and Materials Vols. 313-314
339
SHE(stair wave)
SHE
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-1
0
0.002
0.004
0.006
0.008
0.01
t
0.012
0.014
0.016
0.018
0.02
(a)
(b)
Fig.2 (a) Wave of SHE modulation; (b) stair-shaped wave of SHE modulation adopted in this
paper;
Since the three or multiples of three harmonics can automatically eliminated in the line voltage,
it is not considered in the harmonic eliminating equations.
Usually, the Newton iteration method is used to solve such nonlinear equations. In this paper, the
switch angle groups are calculated off line. The correct solution must satisfy the constraint
α1 < α 2 < ... < α k，α i ∈ [0 , 90 ]
(5)
When applying the SHE modulation method to MMCs, each α k is corresponded to the state
changing (switching on or off) of a specific submodule. The submodule voltages of each arm are
sorted at each instant of α k in order to decide which submodule to switch on (or off), while the
others stay the same. The rule is that the submodule with the lowest voltage should be switched on
when the arm current is positive, and the one with the highest voltage be switched off when the arm
current is negative. In this way, only 2 k switches take place during one line voltage cycle in one
arm, and 1 switch per IGBT in one line voltage cycle, which is significantly less than the SPWM
modulation scheme.
When applying the SHE modulation method to MMC rectifier, the system contain two closed
loop control, thus the modulation index is not certain. So for this reason, every switch angle group
that corresponded to the specific modulation index should be decided in advance.
Simulation results
The validity of new modulation method is verified by simulation. Matlab/Simulink is adopted as the
simulation tool. Fig. 3 shows the waveforms for the new modulation method (right column)
compared to the common SPWM method (left column). Fig. 3(a) shows the waveforms working
under inverter mode, and Fig. 3(b) shows the ones under rectifier mode. The waveforms in first row
are AC phase voltages, in second row are AC currents, in third row are submodule capacitor
voltages in phase A.
It can be seen that the new modulation method can be used in both inverter and rectifier mode,
and the switching frequency is significantly less than that in SPWM method. The difference in
waves of submodule capacitor voltages is owing to that the new method changes state only at α k
instant while the SPWM method changes state at every control cycle.
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Machinery Electronics and Control Engineering II
2
4
x 10 Vabc(SPWM)
Va Vb Vc
0
-2
4
4
2
x 10 Vabc(SHE)
Va Vb Vc
1
0.02
0.04
-2
0
0.02
Iabc(SPWM)
50
Ic
Ia
0.04
50
0
Ib
Ic
Ia
-1
0.16
200
0.18
Iabc(SPWM)
Ia
Ib
0.2
Ic
0
0.02
0.04
-50
0
vc(SPWM)
1600
1500
1500
0
0.02
0.04
0.16
vc(SHE)
1600
1400
0.02
1400
0.04
0
0.02
0.04
Ia
Ib Ic
-200
0.18
vc(SPWM)
0.2
0.57 0.58 0.59
vc(SHE)
1800
1800
1600
1600
1400
1400
1200
0.16
0.57 0.58 0.59
Iabc(SHE)
0
-200
-50
-1
200
0
0
x 10 Vabc(SHE)
Va Vb Vc
0
Iabc(SHE)
Ib
1
0
0
0
4
x 10 Vabc(SPWM)
Va Vb Vc
0.18
0.2
1200
0.57 0.58 0.59
(a)
(b)
Fig. 3(a) MMC work as an inverter; (b) MMC work as a rectifier;
Summary
This paper proposed a new modulation method for MMC which brings many advantages such as
reduced switching frequency and fewer losses. And the new modulation method is demonstrated by
Simulink model. The simulated results also compare the difference between the new method and
the popular SPWM method.
References
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[3] S. Rohner, S. Bernet, M. Hiller, and R. Sommer, "Pulse width modulation scheme for the
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