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1
Abstract— Multilevel converters have become very
attractive for high voltage-level power conversion in
renewable power generation applications. The converter
topology is an important issue in the studies of multilevel
converter. Many multilevel topologies have been developed,
but few of them are qualified with capacitor voltage
self-balancing capability. This paper proposes a novel
diode-clamped modular multilevel converter (DCMMC)
with simplified capacitor voltage balancing control. In this
topology, low power rating diodes are used to clamp the
capacitor voltages of the converter. Only the top
sub-module in each arm of the converter requires capacitor
voltage control. Consequently, very few voltage sensors are
needed for voltage control and the control computation
burden is reduced greatly when the quantity of the
sub-modules is high. A simple voltage balancing control
method with carrier phase-shifted (CPS) modulation
strategy is developed for this topology. Experiments based
on a laboratory prototype were carried out and the results
validated the capacitor balancing performance of the
proposed topology.
Index Terms— Multilevel converters, diode-clamped modular
multilevel converter, capacitor voltage balancing.
I. INTRODUCTION
IGH voltage-level power conversion and transmission
have become very popular for wind power and
photovoltaic power generation, since the power scale of a wind
farm or a photovoltaic power station is becoming larger and
larger, even over hundreds of MWs. And high-voltage AC/DC
or DC/AC converters are the basic elements in such
applications. With low total harmonic distortion (THD) and
low voltage stress on power switches the multilevel converter is
a good choice for these applications.
Since 1980, multilevel converters have been developed
extensively [1]-[6]. The most famous multilevel converter
topologies are the neutral-point clamped (NPC), the
flying-capacitor (FC) and the cascaded multilevel converters. It
is easy to achieve a three- or five-level converter using the NPC
or FC topology. However, numerous clamping diodes and
capacitors are required when the voltage levels are high.
Furthermore, the capacitor voltage balancing control is difficult
and complicated [7]-[10].
With superior modularity and the least component
requirement among various multilevel topologies, the cascaded
H-bridge (CHB) multilevel converter seems to be the most
Manuscript received ******, ******This work is supported by ******.
suitable for medium-voltage active power conversion [11]-[16].
The voltage of the cells is maintained by isolated dc voltage
source, which can be supplied by wind turbine generator,
photovoltaic-cell, or windings of a multiwinding transformer,
etc. However, the requirement of isolated dc voltage supplies
and energy storage systems is the shortcoming in some
applications. When the CHB converter is applied in reactive
power conversion, e.g., STATCOM [17]-[20], the floating
capacitor voltage balancing control becomes the most
challenging issue.
Over the last decade the modular multilevel converter
(MMC) topology as another kind of cascaded topology has
gained growing attentions and found itself very attractive for
medium/high-voltage applications [21]-[24]. Its modularity and
scalability enable it to meet any voltage level requirement
[25]-[27]. However, like the CHB topology, the capacitor
voltage imbalance distributed in sub-modules (SMs) still
remains. Many researchers concentrate on developing control
and modulation strategies to solve the problem [27]-[39]. The
most widely accepted voltage balancing strategy is based on a
sorting method [27]. Li proposed an improved modulation
method to balance the capacitor voltages [28]. The control
systems rely on voltage sensors installed in all the SMs. In
addition, extra switching actions [29] [30] or high execution
frequency of voltage sorting algorithms [31] [32] are usually
involved, and the situation will deteriorate when the number of
SMs is high [33].
In 2001, Peng proposed a generalized multilevel converter
[38], which can balance each capacitor voltage automatically
without any additional circuits when applied in active or
reactive power conversion. From this generalized multilevel
converter topology, several other multilevel topologies can be
derived including the diode-clamped, capacitor-clamped,
cascaded H-bridge, Marx and modular multilevel topologies
[39]. However, the quantity of components in the general
multilevel converter is too high, which limits its applications in
high voltage-level conversion. The Marx multilevel converter
was proposed by Rodriguez and Leeb in [40], which can also
realize voltage self-balancing at the price of extra active power
switches compared with the MMC.
Based on the Marx and modular multilevel converters, this
paper proposes a new type of multilevel topology in order to
achieve a simplified capacitor voltage balancing method with
modularity and good harmonic performance. In this topology, a
low current rating diode and an inductor are used to replace the
balancing switch installed in each cell of the Marx multilevel
topology. We refer this new topology as the diode-clamped
MMC (DCM2C). In this topology the number of voltage
A Novel Diode-Clamped Modular Multilevel
Converter with Simplified Capacitor Voltage
Balancing Control
H
2
sensors is greatly reduced, and a very simple balancing control
method is developed, avoiding high-frequency sorting
algorithm and extra switching actions.
The rest of this paper is organized as follows. Section II
introduces the DCM2C circuit topology and capacitor voltage
balancing control method. The voltage drop distribution in the
balancing circuit is then investigated in section III. The power
losses and device requirement comparison of MMC and
DCM2C are also discussed in this section. Experimental
validations of the proposed DCM2C are presented in Section
IV. A conclusion is made in section V.
II. OPERATION PRINCIPLES OF DCM2C
A. Topology of the proposed DCM2C
The generalized multilevel converter was proposed as a
primary multilevel topology and many other multilevel
topologies can be derived from it. Fig. 1 shows one phase leg of
a five-level generalized multilevel converter and its basic cell
circuit.
v
o
Basic cell
C
1
S
p
1
S
n
1
S
p
2
S
n
2
S
p
3
S
n
3
S
n
4
S
p
4
S
p
S
n
C
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
S
c
2
S
c
1
S
c
4
S
c
3
S
c
6
S
c
5
S
c
8
S
c
7
S
c
10
S
c
9
S
c
12
S
c
11
Fig. 1. Generalized multilevel converter (one phase leg, five-level).
The generalized multilevel topology maintains the five-level
voltage output by switches S
p1
-S
p4
and S
n1
-S
n4
. Meanwhile the
capacitor voltages are clamped by switches S
c1
-S
c12
. For
example, when S
c1
(S
c2
) switches on, capacitor C
1
and C
3
(C
2
)
are connected in parallel. If a voltage deviation exists between
the two capacitors, balancing current will arise and flow
through the clamping switch.
The generalized multilevel topology is redundant and not
suitable for practical applications. After removing the upper
components, the MMC and the Marx multilevel converter can
be obtained, as shown in Fig. 2 and Fig. 3. Compared with the
MMC, the Marx multilevel converter uses an extra switch in
each SM to realize the capacitor voltage balancing without the
requirement of voltage sensors and complicated control
methods [40]. Taking SM1 and SM2 as examples, according to
superposition theorem, the balancing circuit and its simplified
circuit are shown in Fig. 4. C
e
is the equivalent capacitance and
R
s
is the equivalent resistance of power switch. The direction of
the balancing current i
S1
depends on the two capacitor voltage
values. The state of switch S is determined by the states of
power switch S
c1
and S
n2
(logical AND).
v
o
U
dc
Basic cell (or SM)
Fig. 2. Deriving MMC from the generalized multilevel topology.
v
o
C
1
S
p
1
S
n
1
S
n
2
S
n
3
S
n
4
C
2
C
3
C
4
S
p
2
S
c
1
S
p
3
S
c
2
S
p
4
S
c
3
U
dc
S
p
S
n
C
S
c
Basic cell (or SM)
Fig. 3. Deriving Marx converter from the generalized multilevel topology.
In Fig. 4 the circuit parameters can be derived as follows,
12
21
1
21
11
22
2
&
e
e
e
S
s
nc
C C C
u u u
u
i
R
S S S
(1)
C
2
C
1
S
n
2
i
S1
u
2
u
1
S
c
1
C
e
S
u
e
i
S1
2R
s
(a) (b)
Fig. 4. Balancing diagrams of Marx multilevel converter. (a) Balancing circuit.
(b) Simplified circuit.
t
u
e
i
C1
0
u,i
U
0
Fig. 5. Voltage and current curves during the charging or discharging process
in the Marx multilevel converter.
Fig. 5 shows the voltage and current curves of the equivalent
capacitor in the charging or discharging process. The initial
value of u
e
is U
0
. Because R
s
is usually very small, the initial
amplitude of the balancing current can be large. If the voltage
deviation between the neighboring capacitors is big, the
balancing current will be very high. This is a common
disadvantage of the traditional self-balancing multilevel
converters.
Based on the Marx multilevel converter, this paper proposes
an improved topology named as diode-clamped MMC
3
(DCM2C) to replace the extra switch with a low-current rating
diode and an inductor, which are called the balancing-branch
here. The inductor aims to suppress the peak current during the
discharging process. The clamping diodes transfer energy in
only one direction, and a simple control method is developed to
balance all the capacitor voltages in each arm. The three-phase
DCM2C topology is shown in Fig. 6. The balancing circuit and
its simplified circuit of SM1 and SM2 in the DCM2C are
derived in Fig. 7. The arm inductor L is used to limit the dc-side
short-circuit current, meanwhile as a filter for the arm current.
U
dc
S
p
1
S
n
1
C
1
S
p
(n-1)
S
n
(n-1)
C
n-1
S
p
n
S
n
n
C
n
S
p
1
S
n
1
C
1
S
p
(n-1)
S
n
(n-1)
C
n-1
S
p
n
S
n
n
C
n
v
a
v
b
v
c
SM1
SM(n-1)
SMn
SM1
SM(n-1)
SMn
A B C
Upper armLower arm
L L L
L L L
D
1
L
1
D
n-1
L
n-1
D
1
L
1
D
n-1
L
n-1
Fig. 6. The topology of three-phase DCM2C.
C
2
D
1
L
1
C
1
S
n
2
i
D1
u
2
u
1
C
e
D
1
L
1
S
n
2
i
D1
u
e
R
sum
(a) (b)
Fig. 7. Balancing diagrams of DCM2C. (a) Balancing circuit. (b) Simplified
circuit.
Equation (2) shows the parameters in the simplified circuit.
In this circuit only when u
2
> u
1
, the balancing current i
D1
can be
generated. This means that the initial capacitor voltage u
e
is
positive. R
sum
is the sum of the resistance, including R
s
of the
power switch, R
di
of the clamping diode and R
in
of the inductor.
1
21
1
1
2
e
e
sum s di in
e
D
e
CC
u u u
R R R R
u
i
R
(2)
It can be seen that this is a second-order circuit. The
differential equation and its roots, p
1
and p
2
, are expressed as (3)
and (4), respectively.
2
1
2
0
ee
e sum e e
d u du
L C R C u
dt dt
(3)
2
1
1 1 1
2
2
1 1 1
1
()
22
1
()
22
sum sum
e
sum sum
e
RR
p
L L LC
RR
p
L L LC
(4)
According to (4), there could be two cases about the relations
among the resistance, inductance and capacitance:
2
1
11
1
( ) 2
2
sum
sum
ee
R
L
R
L LC C
(5)
2
1
11
1
( ) 2
2
sum
sum
ee
R
L
R
L LC C
(6)
In the first case, p
1
and p
2
are negative real roots, and a
non-oscillatory discharging process will appear. The voltage u
e
and current i
D1
are shown in Fig. 8 (a).
In the second case, p
1
and p
2
are conjugate complex roots,
and a damped oscillation discharge process will appear. The
voltage u
e
and current i
C1
are shown in Fig. 8 (b). The balancing
current i
D1
is unidirectional due to the clamping diode. When it
drops to zero, the discharge process ends with a reversed
voltage deviation u
d
.
t
u
e
i
D1
U
0
0
u,i
t
u
e
i
D1
U
0
u
d
i
D1
=0
0
u,i
(a) (b)
Fig. 8. The voltage and current diagrams of the equivalent capacitor during the
discharge process. (a) Non-oscillatory discharge. (b) Damped oscillation
discharge.
Fig. 8 illustrates the discharge process with the power switch
S
n2
staying on all the time. Actually with S
n2
switching on and
off alternately, current pulses will be generated and the two
capacitor voltages will be balanced in several switching cycles.
Fig. 9 shows the capacitor voltage and current diagrams along
with the switching signals.
t
t
t
u
C
i
D1
u
C2
u
C1
S
n2
0
0
0
Fig. 9. The voltage and current diagram of the equivalent capacitor during the
discharging process.
In each switching cycle when S
n2
is on, D
1
and L
1
withstand a
4
voltage of u
C2
- u
C1
. If u
C2
> u
C1
, current i
D1
will arise and the
voltage deviation between the two capacitors will decrease. If
u
C1
≥ u
C2
, no current will arise in the balancing circuit. In the
topology of DCM2C the quantity of the cascaded SMs in an
arm is n. If u
Ci+1
is higher than u
Ci
, C
i
will be charged, absorbing
energy from C
i+1
. If u
Ci+1
is lower than u
Ci
, no energy transfer
happens. As a result, the capacitor voltages of the whole arm
will be
12C C Cn
u u u
. (7)
B. Capacitor voltage balancing control
In the DCM2C topology, only one voltage sensor is required
in each arm for the balancing control, which is installed in SM1.
Six current sensors are installed in the upper arms and the lower
arms respectively, and two voltage sensors are used to measure
the load line-voltages. The upper arm currents, lower arm
currents and load voltages are i
uj
, i
lj
, u
ab
and u
bc
respectively (j =
a, b, c).
According to the relations of the arm current direction and
the SM states, the capacitor states can be achieved as listed in
Table I.
TABLE I
STATES OF CAPACITORS
Arm current
direction
SM state
Capacitor state
Positive
On
Charged
Off
Bypassed
Negative
On
Discharged
Off
Bypassed
The control strategy for the proposed converter is shown in
Fig. 10. The current control is carried out in the d-q coordinate
system. u
*
d
and u
*
q
are the voltage references. The control
variables V
j
, j=a, b, c, are the modulation signals of the three
phase-legs.
According to (7), the capacitor voltages of each arm are
clamped in a descending order from SM
1
to SMn automatically.
Assume D
dc
is the dc component of the PWM duty cycles. The
relation between the capacitor voltages and the dc bus voltage
is
,,
11
nn
dc Ci u dc Ci l dc
ii
D u D u u
. (8)
u
Ci, u
and u
Ci,l
are the capacitor voltages in the upper arm and
lower arm respectively. When the unipolar modulation strategy
is employed as shown in Fig. 10(d), D
dc
is 0.5. Then
,,
11
2
nn
Ci u Ci l dc
ii
u u u
. (9)
Furthermore, due to the symmetry of the modulation signals
for the upper arm and the lower arm, the sum of the capacitor
voltages of each arm should be
,,
11
nn
Ci u Ci l dc
ii
u u u
. (10)
Combining equation (7) and (10), if the SM1 capacitor
voltage is kept to be u
dc
/n, then all the other capacitor voltages
in this arm will be balanced as follows,
,,
dc
Ci u Ci l
u
uu
n
. (11)
A closed-loop capacitor voltage control is carried out for
each SM1, as shown in Fig. 10(b). The polarity of PI controller
output depends on the direction of arm current, according to
Table I.
abc/dq
u
ab
u
*
d
= 0
u
*
q
dq/abc
V
j
3
PI
PI
wt
wt
u
bc
(a)
u
C1,u
1/n
i
uj
Upper arm
PI
sign
u
C1,l
1/n
i
lj
PI
sign
Lower arm
V
u1, j
V
l1, j
u
dc
3
3
3
3
3
3
(b)
-1
V
j
3
S
2~n, uj
S
2~n, lj
3(n-1)
V
u1, j
V
l1, j
PSC-PWM
S
1, uj
S
1, lj
Upper
arm
Lower
arm
3
3
3(n-1)
3
3
3(n-1)
3(n-1)
SM1
SM2~n
SM1
SM2~n
(c)
θ
Triangular
carriers
Upper arm
modulation signal
Lower arm
modulation signal
t
0.5
1.0
0
(d)
Fig. 10. Control block diagram of DCM2C as an inverter. (a) Load voltage
control. (b) Capacitor voltage balancing control. (c) Switching signal
generation. (d) PSC modulation.
The PSC-PWM is applied for switching signal generation, as
shown in Fig. 10 (c). n triangular carriers with the frequency of
f
s
are assigned to the n SMs respectively. The SMs share one
modulation signal except for SM1: 1) The control variables V
j
are the common modulation signals for SM2-SMn. 2) The
output of voltage controllers V
u1,j
plus V
j
are the modulation
signals for SM1. Fig. 10(d) shows the unipolar PSC-PWM
diagram. The phase-shift angle θ is 2π/n, and the upper arm
modulation signal is opposite to that of the lower arm. The
frequency of carriers is much higher than that of the modulation
signals.
III. SPECIFIC CONSIDERATIONS FOR DCM2C
A. Analysis of the balancing circuit
In practical operation, both the clamping diode and switch
