Thd minimization of modular multilevel converter with unequal dc values

THD Minimization of Modular Multilevel Converter
With Unequal DC Values
Ghazal Falahi, Wensong Yu, Alex. Q. Huang
Department of Electrical and Computer Engineering
North Carolina State University
FREEDM Systems Center
Raleigh, NC, 27695, USA
Abstract—Different modulation techniques used to control
multilevel converters can be classified based on the selected
converter topology and optimization goals. Among all
proposed modulation methods low switching frequency
modulation techniques are very popular for multilevel
converters yet non-real time low switching frequency methods
cannot be applied to multilevel converters with unequal or
varying DC values because these modulation techniques rely
on look up tables and the size of look up tables will be huge in
this case. This paper proposes a new modular multilevel
converter (MMC) structure with unequal DC values. Some
well-known low switching frequency modulation techniques
and the commonly used PWM based methods are compared
and using the new low switching frequency modulation
technique called minimal total harmonic distortion (THD)
modulation for MMC with unequal DC values is proposed.
The PSCAD simulation results show that the new converter
topology with unequal DC values has much lower THD
compared to the typical MMC. Modulation algorithm is
implemented in digital signal processor (DSP) and controller
hardware in the loop (CHIL) implementation in RTDS verifies
the real-time performance of the algorithm.
I. INTRODUCTION
Recent advancements in voltage source converter (VSC)
topologies that increase their power rating by adopting
higher dc operating voltage, lower semiconductor losses and
elimination of ac side filters have made them more attractive
in many applications. Modular multilevel converter (MMC)
is an emerging multilevel converter topology introduced in
2001 and it is highly appealing for medium and high voltage
applications [1]. MMC modulation approaches have been
divided to three main categories: Pulse width modulation
(PWM), staircase modulation and Space vector modulation
(SVM) [1-3]. The most common modulation technique used
for MMC so far is phase shifted or carrier shifted PWM
(CS-PWM) method [4-7]. The main drawback of the typical
PWM based methods is the increased switching losses of
the converter switches, which is a big concern in systems
with high number of sub modules. The SVM based
techniques have also been used for MMC converters. SVM
based modulation generally provides good utilization of the
DC-link voltage, are simple to implement and can operate
with reduced switching frequencies. However, as the
number of voltage levels increases, the number of the
redundant states increases, which in turn increases the
complexity of the design in order to select the proper states
for optimized operation. There are also some non-
conventional modulation techniques such as SHE-PWM,
which rely on look up tables. Staircase modulation renders
low switching frequencies and a staircase waveform will be
generated, following a sinusoidal envelope [7]. In this paper
a new configuration is proposed for MMC, which uses
unequal DC values, and minimal THD modulation
technique, which is a staircase-based modulation, is used to
switch the proposed MMC. THD and harmonics are
compared with the typical MMC converter switched with
CS-PWM. The proposed configuration is a good candidate
for medium power applications such as PV inverters; drive
applications or any other application that requires high
voltage quality.
II. MMC SYSTEM STRUCTURE AND OPERATION
PRINCIPAL
The single-phase configuration of Modular Multilevel
Converter (MMC) topology is shown in Fig. 1. MMC
consists a series of half-bridge sub-modules, which are
cascaded in series to form the phase-legs of the converter.
Each phase-leg is made of an upper and a lower arm and
each arm includes some series connected sub-modules. The
arm inductor is necessary to limit the short circuit and
circulating currents through the phase-leg. Sub-modules are
2153U.S. Government work not protected by U.S. copyright

connected in series and arm current flows through each of
the sub-modules and affects the voltage of the capacitor.
The capacitors are charged when a positive current flows
through the arm of the converter, they discharge if arm
current is negative and their voltage remains constant in
case the sub-modules is not connected to the arm of the
converter. The phase-legs of the converter can be configured
either for single-phase or three-phase applications [8]. From
Fig. 1, the upper and lower arm equations can be derived for
the phase-leg of the converter. Each arm of the converter
can be considered as a controllable voltage source with a
value that depends on number of sub-modules in that arm
and their switching states. The two switches in each sub-
module are complementary and table I shows the sub-
module output voltage in different switching states [9-13].
Equations (1)-(6) describe the operation principal of MMC,
Ssm is the switching state of each SM and VC the voltage of
the SM. The output current (iout) is defined in (4) as the
difference between the upper and lower arm current and (5)
defines the circulating current within the arms of the
converter (icirc) as one-half of the sum of the upper and
lower arm currents. The output and the arm currents of the
converter depend on the switching states of the arm sub-
modules and the modulation method of the converter. The
modulation techniques and the derivation of the switching
states of the SMs for the MMC are analyzed in the
following section.
Varm = SsmV C
i=1
N
+ Larm
diarm
dt
+ Rarmiarm
(1)
VDC
2
−Vupper − Rarmiupper − Larm
diupper
dt
−Vmiddle = 0 (2)
−
VDC
2
+Vlower + Rarmilower + Larm
dilower
dt
−Vmiddle = 0 (3)
iout = iupper −ilower
(4)
icirc =
iupper +ilower
2
(5)
Vout =
Vupper −Vlower
2
(6)
III. MODULATION TECHNIQUE
The optimal modulation techniques are usually designed to
meet specific harmonic limitations with minimum switching
frequencies, additional filters or voltage levels. Elimination
of low order harmonics is usually an important goal and few
publications have focused on this issue in modular
multilevel converters. A multilevel selective harmonic
TABLE I. SWITCHING STATE OF SUB-MODULES
State S1 S2 Vsm
1 ON OFF Vc
2 OFF ON 0
3 OFF OFF 0
Figure 1: Modular multilevel converter, one phase
elimination (SHE) method has been recently proposed for
MMC, which offers tight control of low-order harmonics
and has the lowest switching frequency for power
semiconductors among all modulation techniques [14]. SHE
based methods have the crucial drawback of relying on look
up tables with pre-calculated angles, which results in some
problems in closed loop control of the system. A
comparison of some famous low switching frequency
modulation techniques is presented in table I.
No optimal modulation has been proposed for modular
multilevel converter that gives the limitation of voltage
THD. The minimal THD modulation presented here will
deal with this concern. In the minimal THD modulation, the
switching angles can be calculated in real-time and the
implementation does not rely on the look-up tables. Another
critical limitation of some optimal modulations is that they
are not suitable for the multilevel inverters with unequal or
variable voltage steps but minimal THD modulation does
not deal with this limitation. The minimal THD modulation
is designed for the staircase modulation and it has three
important advantages: minimization of voltage THD, real-
time calculation, and compatibility using the inverter with
unequal or variable voltage steps. The modulation block will
monitor DC voltages and the updated modulation magnitude
and calculates a set of switching angles based the minimal
THD criteria to achieve the minimum THD; the proof has
Cell 2
Cell n
Cell (n+1)
Cell (n+2)
Cell 1
Cell (2n)
Larm
Rarm
Rarm
Larm
Vdc/2
Vdc/2
iupper
ilower
S1
S2 VSM
Vc
Upper
arm
Lower
arm
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been presented in [15]. The calculations are rapid; therefore
the switching angles can be figured out in real-time and no
look-up tables are needed.
Assuming a basic staircase modulation as Fig. 4, there are s
positive, s negative and a zero voltage stage and there will
be a total of 2s+1 levels, which are defined as E1, E2,.., Es.
The voltage levels may vary or they might be constant, also
based on the value of DC voltages a switching pattern can
be defined to build the desired shape. The quantities 1, 2,..,
s are the switching angles that indicate the on or off instant
of switches of the sub-modules. These angles are calculated
based on the voltage steps and modulation at each instant.
The control system of MMC operates based on the defined
control targets and sends the modulation and timing
information to the minimal THD algorithm. The THD
minimization algorithm receives voltage step and signals
form the system controller and calculates the switching
angle such that THD is minimum.
TABLE II. COMPARISON OF SOME WELL-KNOWN LOW SWITCHING
FREQUENCY MODULATION TECHNIQUES
Modulation Optimization aim Real time
calculation
For
varying
steps
Staircase modulation
with elimination of
low order harmonics
Elimination of
lower order
harmonics
No No
Selective harmonic
elimination PWM
with equal voltage
steps
Elimination of low
order harmonics
No No
Selective harmonic
elimination PWM
with unequal voltage
steps
Elimination of low
order harmonics
No Yes
Minimal THD
modulation
Minimization of
voltage THD
Yes Yes
The algorithm comprises the following two steps and the
flowchart in Fig. 2 explains the calculations [15]:
Step 1. Calculation of the modulation
(7)
(8)
(9)
Step 2. Finding the switching angles by evaluating
k=1,2,..,s (10)
At each instant the algorithm compares the calculated
modulation with the modulation waveform from the
converter control system and if the difference was less than
a small pre-defined value ( ) it stops the iterations and
calculates the switching angles from equation 10.
Figure 2. Minimal THD algorithm flowchart
IV. PERFORMANCE OF THE PROPOSED MODULATION
TECHNIQUE
A modular multilevel converter with three sub-modules in
each arm is simulated using PSCAD-EMTDC and
modulated using the minimal THD modulation technique.
The control structure of the MMC outputs the modulation
waveform and phase ( t rad/s) of the system which are the
inputs to the angle calculator control block and the
switching angles are calculated in real time based on inputs
at each instant then the sub modules of MMC are switched
based on a staircase modulation to generate the target
waveform using a set of switching angles. Fig.3 shows the
overall layout of the proposed system. One of the main
advantages of the minimal THD modulation technique is
being applicable to multilevel converters with unequal DC
voltages. This paper proposes an alternative structure is for
MMC with unequal DC values for different sub-modules.
The sub-modules can also have different switching
frequencies to improve THD or in other words the sub-
module or sub-modules with lower DC values can have
higher switching frequencies to help the waveform shaping
function or the output quality [16]. The proposed structure
with unequal sub-module DC values also allows using
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different semiconductors for different sub-modules to
decrease the losses.
The proposed system is simulated for an MMC with three
cells in each arm when the DC voltages have VDC, 2VDC,
3VDC ratios, when the DC sources are unequal more
voltage levels can be generated which improves the
converters output voltage quality if the additional levels are
used effectively. The conventional modulation techniques
do not allow using the additional levels because the sub-
modules randomly turn on or off. Sometimes a capacitor
voltage balancing technique is incorporated and capacitors
are sorted based on their instantaneous voltages so the sub-
modules with lowest or highest capacitor voltage are
switched first based on the direction of the arm current. The
minimal THD modulation allows using the additional
generated voltage levels between the old voltage levels. At
each switching angle, 1, 2,.., 6 the sub-modules are
selected to turn on or off based on the new target waveform
which has more levels than the conventional one for the
same topology with the similar number of sub modules.
Figs 5-7 show the output voltage waveforms of a voltage
controlled MMC in volts; the output voltage generated using
typical MMC structure and minimal THD modulation is
shown in Fig. 5 .The same topology is switched using
carrier shifted modulation technique, which is a commonly
used modulation technique for MMC and is shown in Fig.6.
Fig. 7 shows the proposed solution, which has the lowest
THD amongst all three waveforms.
Comparing Figs 5-7, MMC converter with three sub-
modules in each arm which have unequal values of 1VDC,
2VDC, 3VDC ratio switched with minimal THD modulation
has the lowest THD which is 7.3% compared to the 15.45%
for the conventional MMC with carrier shifted PWM and
11.3% for the conventional MMC that uses minimal THD
modulation. Figs 8 and 9 show the harmonic spectrum of the
MMC output voltage using this two modulation techniques
and it can be seen that Fig. 9 has more harmonics and
smaller fundamental magnitude. The output of the proposed
structure has the highest fundamental magnitude and smaller
high order harmonics compared to the others. Fig. 11 shows
a visual comparison of the THD value for three mentioned
cases.
Table II. showed that one advantage of minimal THD
modulation compared to other common fundamental
frequency modulation techniques is online calculation of
switching angles. Controller hardware in the loop is
employed to verify the online performance of the algorithm.
Firing signals are generated using a DSP controller and sent
to RTDS using digital input ports. The power stage is
modeled in RSCAD, which includes an MMC inverter with
three half-bridge modules and an inductor in each arm.
Table III shows specifications of the modeled system in
RTDS. Fig.12 shows the digital input signals to RTDS,
which is the pulse pattern, generated in the DSP controller
and applied to the MMC switches in RTDS. The MMC
output voltage generated in RTDS is shown in Fig.13.
Figure 3. Overall structure of the converter and modulation technique
Figure 4. Multilevel inverter phase voltage with staircase modulation
TABLE III. SYSTEM SPECIFICATIONS
Rated active power 5KW
Rated line to line rms
voltage
208V
DC supply voltage 600V
Number of SM in
each arm
3
Rated frequency 60Hz
Figure 5. Output voltage, typical MMC structure, minimal THD
modulation
1 … s /2
Es
E1
E1
Es
......
2
t
Phase voltage
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
-400
-300
-200
-100
0
100
200
300
400
Outputvoltage(volts)
Vo
time (secs)
V
ol
ta
ge
(v
2156

Figure 6. Output voltage of typical MMC struct
Figure 7. Output voltage of MMC with unequal dc sou
THD modulation (proposed structur
Figure 8. Typical MMC with equal DC values, Vo h
minimal THD modulation
Figure 9. Typical MMC with equal DC values, Vo har
PWM
time (secs)
Vo
lta
ge
(v
olt
0.1 0.11 0.12 0.13 0.14 0.15
-400
-300
-200
-100
0
100
200
300
400
pg()
time (secs)
Vol
tag
e
(vo
lts)
0.1 0.11 0.12 0.13 0.14 0.15 0.16
400
300
200
100
0
100
200
300
400
ture, PS-PWM
urces using minimal
re)
harmonic spectrum,
rmonic spectrum CS-
Figure 10. MMC with unequal DC and m
harmonic spectrum
Figure 11. Comparison of the THD value in
Figure 12. Firing signal gene
Figure 13. Output voltage waveform of M
modeled in RTDS using controller
0.16 0.17 0.18
Vo
0.17 0.18
Vo
minimal THD modulation, Vo
three different cases
eration in RTDS
MMC with unequal DC values
r hardware in the loop
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V. CONCLUSION
THD and loss are important concerns in power converters.
This paper proposed an alternative structure for modular
multilevel converter with unequal DC values for different
sub-modules that uses minimal THD modulation technique
for switching. The proposed structure showed an
improvement in voltage quality comparing to the current
solutions. Moreover, it allows using different type of
semiconductors or different switching frequencies for
different sub-modules, which can further improve the output
quality and converter efficiency. The proposed system was
modeled in PSCAD and voltage waveforms and their
harmonic spectrums were shown and compared. Controller
hardware in the loop was also implemented using RTDS to
verify the online calculation of switching angles.
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