Cuong Tran Hung, Minh Tran Trong, Nam Hoang Thanh, “Model Predictive Control Method for Modular Multilevel Converter Applications”, SEATUC-2016.

1. The 11th SEATUC Symposium
1
MODEL PREDICTIVE CONTROL METHOD FOR MODULAR
MULTILEVEL CONVERTER APPLICATION
Tran Hung Cuong(1), Tran Trong Minh(2), Hoang Thanh Nam(2)
(1)Hong Duc University, Viet Nam
(2)Ha Noi University of Science and Technology, Viet Nam
Email: tranhungcuong@hdu.edu.vn
ABSTRACT
This paper proposes a Model Predictive Control
(MPC) method for Modular-Multilevel-Converter
(MMC) applications for connect renewable energy
sources. Modular multilevel converter has some
advantages in comparison with conventional multilevel
converters such as: scalable to different power and
voltage levels; expandable to any number of voltage
steps with low total harmonic distortion; only one DC
bus voltage input is used; transformerless. To control the
MMC system properly, the ac current, circulating
current, and submodule (SM) capacitor voltage are taken
into consideration. However, the applications of control
methods to ensure the normal operation of the inverter
MMC is difficult, especially voltage balance over
capacitors. This paper deals with an application of
Model Predictive Control and an energy balancing
algorithm for a modular multilevel converter to solve the
voltage balance problem. The proposed method has
significantly reduced the switching frequency and
produced output voltage with very low total harmonic
distortion at the AC side of the converter.
KEYWORDS: Modular multilever converter, energy
balancing algorithm.
1. INTRODUCTION
Multilevel converters receive increasing attentions in
recent years due to the demands of high power and high
voltage applications for connect renewable energy
sources [1]. Among the existing multilevel converters,
diode-clamped and cascaded H-bridge (CHB) multilevel
converters are the most widely used [5]. For medium-
voltage (2.3, 3.3, and 4.16 kV) applications, three level
neutral-point-clamped (NPC) topology is a good solution
[7], but some problems exist while extending NPC
converter to higher voltage levels, such as mass clamping
diodes and the voltage imbalance of dc-link capacitors
[8]. For applications with voltage higher than 6 kV,
CHB multilevel inverters are commonly used [7], [9],
[10]. Recently, a new multilevel topology gains more and
more attentions in high-voltage applications: modular
multilevel converter [10]. It is regarded as one of the
next-generation high-voltage multilevel converters
without line-frequency transformers [12]. The MMC is
suitable for high-voltage power conversion due to its
modular structure, simple voltage scaling, and common
dc bus [11]. However, it also has some drawbacks, such
as voltage imbalance of floating capacitors and acute
voltage fluctuation at low frequency [12]. This paper
proposes a Model Predictive Control (MPC) method for
Modular-Multilevel-Converter (MMC). Model Predictive
Control or MPC was first introduced in 1960s . It has
more complex calculations compared to classical linear
controllers, while it provides faster controller with higher
accuracy and stability. From 1980s, the idea of MPC in
power electronics applications was introduced although
lack of the fast processors at that time, limited its
applications only to low switching frequencies. Due to
invention of fast and powerful processors such as DSP
and FPGA, the power electronics industry could take the
advantages of MPC strategy in practice. Many papers
have studied a finite MPC method to control the power
converter. In the MPC method, first, the future values are
predicted on the basis of the switch states, and then the
final switch state is decided in a way to minimize the cost
function. The cost function is designed according to the
control goal, cost function may include a control goal,
such as switching frequency reduction, improve total
harmonic distortion (THD)[2], common-mode voltage
reduction, and current ripple reduction in order to control
the power converter[3]. The proposed control method
applied the cost function to control the ac current,
circulating current, and SM capacitor voltage balancing.
This paper proposes an MPC method with a reduced
number of considered states for ac-side current control.
The details are described by the following parts. In
Section 2, the system structure and operating principles
of the MMC are introduced. Section 3 analyzes
mathematical model of a dc-ac MMC and derives
discrete mathematical models of variables for the MPC
strategy. Section 4 presents the design of control system.
in Section 5, simulations studies analyses are carried out
in the Matlab/Simulink software. Conclusions are
summarized in Section 6.

2. The 11th SEATUC Symposium
2
2. THE DC-AC MODULAR MULTILEVEL
CONVERTER
2.1 Structure Modular Multilevel Converter
Modular Multilevel Converter is an AC to DC
converter topology that was first introduced in 2003 [9].
It is very suitable for high power-high voltage, high -
power applications especially applications for connect
renewable energy sources. In this section, a brief
description of MMC topology and its operation
principles will be presented. MMC topology will be
explained as well as its advantages and disadvantages
comparing it with high power Voltage Source Converters
(VSC) shown in Fig. 1.
vupa
vlowa
l
r
l
r
iupa
ilowa
va
vb
vc
iz
0
SMn+1
SM2n
Idc
ia L R ea
LOAD
D1
D2
S1
S2
C
SM1
SMn
Fig 1. Topology of the (n+1) level MMC connected to a
typical load
A three-phase (n+1)-level MMC has three upper and
three lower arms that are all identical (Fig. 1). Each arm
has been made of a specific number (n) of units named
Sub-modules (SMs) and a small inductor (l) which is
called arm inductor. Each SM has been made of a series
connected of two IGBT/diode parallel combinations and
a precharged capacitor in parallel with them (Fig. 2).
D1
D2
S1
S2
C
i
VSM
Fig 2. Sub-module cỉcuit
The main purpose of using arm inductor is limiting
AC current when a short circuit occurs at the DC-line
[6]. Hence, high di/dt which is dangerous for equipment
can be controlled and minimized by this inductor.
Although it is very useful during fault, it does not
contribute to the normal operation of MMC because the
internal arm currents are flowing continuously. Voltage
sharing between switches is important for high voltage
converters. Sometimes especially during the switching
time, harmful high voltages may destroy the power
switches or at least shorten their life time. The SMs’
capacitors have solved this problem by maintaining the
voltage level across the switches to a certain value.
Moreover, MMC provides the advantage of scalability,
modularity and high power quality. Another remarkable
feature of using MMC in high power applications is that
there is no need of input transformer to adjust the voltage
in contrast with the conventional converters. As a result,
the elimination of the transformer itself and its cooling
equipment that are usually large in size and weight will
lead to saving money and space. Furthermore, the input
filter installations, which are necessary for classical
converters, are not needed when using MMC. When
using VSC, a DC-line capacitor is needed to keep the
voltage constant and the stored energy in this capacitor
may result in extremely high surge currents during short
circuit occurrence [8]. There is no need for this capacitor
in MMC installations.
MMC operates in lower switching frequency than
VSC. Therefore, switching power loss is less. This
feature makes MMC an appropriate converter for high
power applications. However, MMCs are more
expensive and complicated than VSCs and controlling
them is more difficult. A big challenge regarding MMC
controlling is how to keep the capacitor voltages around
the initial value that is equal to 𝑉𝑑𝑐/𝑛
2.2 Sub-Module operating principles
In order to create the desired output voltage at the
MMC terminals, the controller command the switches in
SMs to be turned on or off. Regarding SM circuit in Fig.
2, there are two complementary switching states: S1 is on
and S2 is off and S2 is on and S1 is off. It is not allowed
to turn on both switches simultaneously, because the
capacitor voltage will be totally discharged and afterward
it becomes useless. By considering the switching states,
four different working states can be made based on the
current direction:
S1
S2
S1
S2
S1
S2
S1
S2
ON
OFF
OFF
ON
ON
OFF
OFF
ON
1) 4)2) 3)
Fig 3. Sub-Module operating principles
1) S1 is OFF and S2 is ON: The current (i) will pass
through S2 , VSM will be zero (IGBT on-state voltage
drop is assumed to be zero) and the capacitor is
bypassed.

3. The 11th SEATUC Symposium
3
2) S1 is ON and S2 is OFF: In this case the current (i)
will pass through D1 and capacitor will be charged and
VSM = VC . The voltage of the arm, in which the SM is
placed, will increase one step.
3) S1 is ON and S2 is OFF: The controller will turn on
S1 in order to connect the capacitor to the circuit and
increase the arm voltage on step. In this state, the
capacitor is discharged and VSM=VC.
4) S1 is OFF and S2 is ON: In this state, D2 is turned on
and i will pass through it. The capacitor will be bypassed
and VSM = 0.
In this report, the term “turned on” SM means that
its capacitor is connected and the term “turned off” SM
means a bypassed capacitor. Charging and discharging of
capacitors depend on the currents direction.
2.3 Working principles of MMC
In normal operation of MMC, all of the capacitors are
charged up to its nominal value 𝑉𝑑𝑐/𝑛. In order to reach
this value, [9] has proposed to turn on one SM of a leg
and turn off the rest of SMs in that leg that are 2n-1 SMs.
When the capacitor is charged up, it should be turned off
by the controller command and the next SM should be
turned on. All of the capacitors will be energized
individually one after another. This process has been
shown in Fig. 3. However, it is not possible to charge
them by the main voltage source, because applying a
high step voltage to the capacitors will lead to extremely
high currents. As a consequence, an external voltage
source with lower DC voltage level is needed [12]. As a
better charging method, adding a resistor to the arms has
been proposed by [11]. By using this method, there will
be no need for any external voltage source and there is
no loss due to the resistors in the normal operation. The
controller should only provide the connection and
disconnection of the resistors when needed. When all of
the capacitors have been charged, the controller sends
turning on and off signals to SMs to create an AC
voltage from a DC source or vice versa. At each
sampling time, only half of the total number of SMs in
each phase is on (n SMs).Therefore, the total number of
the connected capacitors from upper arm and lower arm
together is equal to n at any instant. For example, if all of
the n upper SMs are on, all of the lower arm SMs should
be off. So, the AC-line voltage level will be minimum:
.
2 2
dc dc dc
ac
V V V
v n
n
 
     
 
(1)
And reversely, if all of the lower arm SMs are on,
the AC-line voltage level will be maximum:
0.
2 2
dc dc dc
ac
V V V
v
n
 
    
 
(2)
Therefore, AC-bus voltage can vary between -𝑉 𝑑𝑐/2
and +𝑉 𝑑𝑐 /2 with the steps of +𝑉𝑑𝑐/𝑛. Each arm of
MMC represents a controllable voltage source. AC-line
voltage increases by turning off upper arm SMs and
simultaneously turning on the same number of SMs in
the lower arm. However, it is better to increase and
decrease the voltage one step at each switching time to
have a smooth voltage waveform. Charging or
discharging of the capacitors depends on the current
direction as explained in section 2.1.
2.4. MMC control requirements
The following aspects from control point of view are
very important to transfer desired power with maximum
efficiency and minimum voltage and current harmonics:
1. Controlled variable reference tracking Depending on
the main controlled variable that can be output voltage or
current, the control scheme should be able to create the
turning on and turning off signals to make the required
output voltage and current with minimum error with their
reference signals.
2. Keeping the capacitor voltages balanced
As mentioned earlier, if SM is going to be turned on
or off, depending on the current direction, its capacitor
will be charged or discharged; so, it will be more or less
than 𝑉𝑑𝑐/n. The value of voltage variation obviously
depends on the capacitance value and the on-time
duration of SM. In high switching frequency, on-time
duration of Sub-𝑛. Modules is short; therefore, voltage
balancing is not critical. By the way, the control scheme
should consider it carefully to stabilize the voltage of
capacitors in its limitations especially in low switching
frequencies.
3. Circulating current minimization During the operation
of MMC, in addition to the AC side and DC side currents
there are three pure AC high frequency circulating
currents [13].The main reason behind these currents is
the voltage variation (ripple) of capacitors during
charging and discharging period [13]. These circulating
currents have no effect on the DC or AC side of MMC
and no power transfer occurs due to them. However, they
have a significant impact on the rating values of the
MMC components, SMs capacitor ripples and converter
loss [13]. Hence, the circulating current should be
minimized by the controller as much as possible.
In the next chapter, FSC-MPC will be applied to
MMC and it will be proved that it can handle all of the
above control challenges.
3. MATHEMATICAL MODEL OF MMC
The circuit model of a three-phase DC-AC MMC
has been demonstrated in Fig. 4. It is connected to the
utility grid or motor as a load. In this study, the loss in
Sub Modules and arm inductors has been modeled with a
small resistor (r) connected in series with them [3,13].
The resistivity of DC source and DC line has been
neglected. The load is three sets of series-connected
inductor (L), resistor (R) and voltage source (e) in star
shape. The voltage source has 50 Hz frequency. Each
arm of MMC represents a controllable voltage source
called 𝑣 𝑢𝑝𝑗 and 𝑣𝑙𝑜𝑤𝑗 [9], which are the sum of SMs
output voltages (VSM) of upper arm and lower arm in
phase j (a, b or c).

4. The 11th SEATUC Symposium
4
As shown in Fig. 1, 𝑣𝑡𝑗 is the representation of pole
voltages with respect to 𝑉𝑑𝑐/𝑛 point O. By assuming
that each capacitor voltage is ideally equal to and
neglecting the voltage drop across arm inductor and
resistor, 𝑣𝑡𝑗 can be calculated by:
(3)
Where 𝑛 𝑢𝑝𝑗 and 𝑛𝑙𝑜𝑤𝑗 are the number of upper and
lower SMs that have been turned on. Total number of on
SMs in each phase of MMC is:
upj lowjn n n  (4)
According to [7, 11 and 13], the upper and lower
arm currents (𝑖 𝑢𝑝𝑗 and 𝑖𝑙𝑜𝑤𝑗) can be calculated by:
3 2
jdc
upj zj
iI
i i   (5)
3 2
jdc
lowj zj
iI
i i   (6)
Where 𝐼 𝑑𝑐 is the dc component of the dc line
current, 𝑖𝑗 is the output phase current and 𝑖 𝑧𝑗 is the
circulating current flowing through phase j. These
equations mean that the arm currents consist of three
main components with different frequencies: 1. zero
frequency current (Idc) that is its dc offset 2. 50 Hz
current (ij) that is transferring power to the load 3. 100
Hz circulating current (if capacitor voltages are balanced
and the circulating current is minimized very well).
According to Fig 1 and by applying Kirchhoff law, the
mathematical equations can be described as follows.
2
upj jdc
upj upj j j
di diV
v l ri Ri L e
dt dt
      (7)
2
lowj jdc
lowj lowj j j
di diV
v l ri Ri L e
dt dt
      (8)
Phase currents 𝑖𝑗 can be calculated by subtracting
Eq.6 from Eq.5 and the circulating currents 𝑖 𝑧𝑗 can be
found by adding Eq.5 and Eq.6.
j upj lowji i i  (9)
21
2 3
dc
zj upj lowj
I
i i i
 
   
 
(10)
By subtracting Eq.8 from Eq.7 and replacing Eq.9,
the main first order differential equation (Eq.12) that can
be used to predict the phase currents will appear:
 
  2 2 2 0
upj lowj j
upj lowj upj lowj j j
d i i di
v v l r i i Ri L e
dt dt

       
(11)
 
 
1
2 2
2
j
upj lowj j j
di
v v r R i e
dt l L
      
(12)
In order to predict the second controlled variable, i.e.
the circulating current, Eq.7 and Eq.8 should be added.
 
 .
upj lowj
dc upj lowj upj lowj
d i i
V v v l r i i
dt

     (13)
And Eq.10 should be replaced into the above
equation:
1 2
2
2 3
zj
dc upj lowj zj dc
di
V v v ri rI
dt l
 
      
(14)
For simplification, the DC line current is assumed to
be constant (𝑑𝐼 𝑑𝑐/𝑑𝑡 = 0).
The third and last controlled variable is the capacitor
voltages that can be calculated by
cij mjdv i
dt C
 (15)
Where i = 1,2,..,2n is the SM number and 𝑖 𝑚𝑗 can be
zero if SM is off, or 𝑖 𝑢𝑝𝑗 if SM is located in the upper
arm or 𝑖𝑙𝑜𝑤𝑗 if SM is located in the lower arm.
4. PROPOSED MPC STRATEGY BASED ON THE
MATHEMATICAL MODEL OF THE MMC
4.1. Introduction of Model Predictive Control
The operating principle of MPC is based on the cost
function can contain different linear function and depend
on the characteristics of each system [8].
Converter LoadCost function
minimization
Controled
variables
prediction
Sxref(k+1)
x(k)
MPC controller
Fig 4. The control lock diagram of MMC
Where x(k) is the controlled variables. Based on the
discrete model of system (load and converter), the
current values of the controlled variables x(k) are used to
predict their future values x(k+1) for all N possible
switching states. All the predicted values of the
controlled variables x(k+1) are compared with their
reference values xref(k+1) in the cost function
minimization block. Finally, the switching state (S) that
minimizes the cost function will be selected as the next
switching state and it will be applied to the converter.
The procedure of switching state selection has been
shown in Fig 5; tk is presenting the current state, tk+1 and
tk+2 are the next time steps. The sampling time is Ts.
Assume that the MPC is applied to a converter with
three possible switching states (x1, x2 and x3) and the
reference is constant in a short period of time. The cost
function is defined as the distance between the controlled
variable and its reference value that should be minimized
in order to track the reference. The controlled variable at
the next step time is predicted for all the switching states,
but choosing x3 provides the least distance to the
2
lowj upj
tj dc
n n
v V
n



5. The 11th SEATUC Symposium
5
reference value xref ; as a result, it will be applied to the
converter at time tk+1. Subsequently, all the process will
be shifted one step forward. By repeating the procedure
once again for tk+2 will be selected due to its minimum
distance with xref . Thus, the whole procedure will be
repeated again.
Ts Ts
x
xref(k)
tk tk+1
tk+2
t
x1(k+1)
x3(k+1)
x2(k+1)
x2(k+2)
x1(k+2)
x3(k+2)
x(k)
Fig 5. MPC operating principle
Mô hình MPC áp dụng cho bộ biến đổi điện tử công
suất được bắt đầu bằng các biến rời rạc như dòng điện,
điện áp… hàm mục tiêu phải được xác định theo hành vi
mong muốn của BBĐ. Tại mỗi thời điểm lấy mẫu, hàm
mục tiêu sẽ tính tất cả các trạng thái chuyển mạch có thể
cho chu kỳ trích mẫu tiếp theo dựa trên các trạng thái
hiện tại. Sau đó, các trạng thái tối ưu sẽ được lựa chọn để
áp dụng cho bộ chuyển đổi. Để thiết kế bộ điều khiển
MPC cho bộ biến đổi điện tử công suất ta thực hiện ba
giai đoạn: Lấy mô hình rời rạc của hệ thống theo các dẫn
xuất biến điều khiển để có thể dự đoán trong tương lai;
Xác định tất cả các trạng thái chuyển mạch có thể cho
chuyển đổi và mối quan hệ của chúng với các biến khác;
Xác định hàm mục tiêu để tính các giá trị tối ưu đại diện
cho hành vi mong muốn của hệ thống.
4.2. MPC strategy of the MMC
This Section proposes a MPC strategy to control the
ac-side currents, regulate the SMs capacitor voltages, and
eliminate/minimize circulating currents. The proposed
MPC strategy is based on the following steps:
• Development of a discrete-time model of the system
for one-step forward prediction of an MMC variables.
• Definition of a cost function associated with control
objectives.
• Evaluation of the defined cost function for all
possible switching states of the converter and selection of
the best switching state that minimizes the cost function.
FCS-MPC can fulfill all the MMC control requirements
simultaneously and very well. By defining a proper cost
function, it can make the output currents to follow their
references, keep the capacitor voltages in a balanced
position around 𝑉𝑑𝑐/n and minimize the circulating
currents as much as possible. In a single-phase (n+1)-
level MMC, the total possible switching states are:
 2
2 !
! 2 !
n
n
n
n C
n n n
 

(16)
Consequently, for a three-phase one it will be equal
to 𝑁3
. For example, a 3-level MMC has totally 63
= 216
switching states. This number is important because the
controller speed depends directly to it. Cost function
calculation process repeats for all the switching states
and then, the one that minimizes the cost function will be
selected to be applied at the next switching instant.
As mentioned earlier, there are three controlled
variables regarding MMC; output AC currents, capacitor
voltages and circulating currents. In order to predict the
one-step ahead value of the controlled variables, Eq.11,
14 and 15 should be discretized by one of the Euler
methods. As the system model accuracy is very
important for the controller performance, midpoint Euler
method is selected. However, the system model based on
both backward and forward Euler methods will be
calculated and used for a single phase 3-level MMC.
AC-Side Current Control: The objective of current
control is to regulate the MMC ac-side currents at their
reference values, i.e., reference current tracking. Based
on Eq.11 and assuming a sampling period of Ts, the
discrete-time model of the MMC ac-side current, with an
Euler approximation of the current derivative, is deduced
as:
 
   
   
 
2
(
2 2 . 2
2
( )) (17)
2
lowj s upj s
j s
s j s
j s j
s
v t T v t T
i t T
T l L R i t T
l L
e t T i t
T
  
 
  

  
Predicted current, ij(t) is the measured ac-side
current, and esj(t + Ts) is the estimated grid voltage at the
low-voltage side of the transformer which is
approximated by the measured value of esj(t). vupa(t+Ts)
and vlowa(t+Ts) are the predicted arm voltages which can
be calculated based on adding up the one-step forward
predicted capacitor voltages, or directly the sampled
capacitor voltages of the predicted switched-on SMs in
upper and lower arms, respectively.
In the next step of designing FCS-MPC, a cost
function should be defined in order to force the output
AC currents to track their references, keep the capacitor
voltages balanced (i.e. around the nominal value 𝑉𝑑𝑐/𝑛)
and minimize the circulating currents. It should be
mentioned that the total switching states [  
3
2N n
nC ]
of a three-phase MMC are three identical sets. Therefore,
it is better and simpler to design three identical
controller’ codes to work in parallel instead of writing
one code for considering all of them; therefore, each
phase is controlled by their own cost function separately
and at the same time with the other two phases.
j jref s j sJ i t T i t T (18)
Where ijref is the reference current and ij(t+Ts)
obtained from Eq.17 is the next-step predicted current.
Ideally, the cost function Jj reaches its minimum value at
zero if the ac-side currents track their reference values.

6. The 11th SEATUC Symposium
6
This condition is used as a basis for the ac-side current
control. Within each sampling period, Jj is calculated and
evaluated for all possible switching states of the MMC.
The switching state which results in the minimum value
for Eq.18, is the best switching state for the next
switching cycle. For simplicity, 𝑖𝑗𝑟𝑒𝑓(t+Ts) is
approximated with 𝑖𝑗𝑟𝑒𝑓(t) in high sampling frequency.
Capacitor Voltages Balancing: Based on Eq.15, the
next step predicted value of the capacitor voltage,
Vcij(t+Ts), is calculated by :
   
 m
Cij s Cij s
i t
V t T V t T
C
   for an on-state SM (19a)
   Cij s CijV t T V t  for an off-state SM (19b)
Where im(t) = iupj(t) for the SMs in the upper arm
and im(t) = ilowj(t) for the SMs in the lower arm. To carry
out the voltage balancing task, the MPC strategy assigns
an additional cost to the capacitor voltage balancing task.
This is achieved by including an additional term,
associated with the voltage deviations of the SMs
capacitor voltages from their reference values, in the
original cost function. Consequently, the cost function Jj
is modified to:
 ' dc
j j C Cij s
i
V
J J V t T
n

 
    
 
 (20)
Where λC is a weighing factor and is tuned based on
the cost contribution assigned to the capacitor voltages
deviations. The procedure to determine λC is based on the
empirical method presented in [11].
Circulating Current Control: To reduce the SMs
Capacitor voltage ripples and converter losses and to
avoid the overrated design of the MMC components, the
circulating currents are required to be
eliminated/minimized. Based on Eq.14, the discrete-time
model of the circulating currents is deduced as:
        
2
s
zj s dc lowj s upj s zj
T
i t T V v t T v t T i t
l
      
(21)
The MPC strategy aims at eliminating/minimizing
the circulating current by adding a third term, associated
with the circulating current, to the original cost function,
as follows:
 '' '
j j j Z Zj sJ J J i t T    (22)
Where λz is a weighing factor and is tuned based on
the design requirements or control objectives.
The MPC strategy evaluates the cost function J’’
for
all possible switching states of phase j and selects the
state which results in the minimum value for J’’
, as the
desired switching state. From the above analysis,
interpolation algorithm of the system control as follows:
Evaluate the cost function
based on (22)
No
Yes
Yes
No
Updete the switching state
Apply the selected switching state Sj
Measured
Calculate ij(t+Ts), Vcij(t+Ts), and izj(t+Ts)
based on (17),(19), and (21) for Sj(K)
Fig 6. Block fiagram of the per-phase MPC strategy for
the MMC
5. SIMULATION RESULTS
This section evaluates the performance of a five-level
gridconnected MMC system of Fig. 1 that operates based
on the proposed MPC strategy. The simulation studies
are conducted in the MATLAB/SIMMULINK
environment to demonstrate the performance of the
proposed MPC strategy in terms of capacitor voltages
balancing, circulating current elimination capabilities,
and power control which is based on current control. The
system parameters are given in Table 1.
Table 1. Parameters of the study system of Fig 1.
Vdc
f 50Hz
r
l
R 2
L 0.02
EXPERIMENT

7. The 11th SEATUC Symposium
7
REFERENCES
[1.1] Predictive Control in Power Electronics
Converters, Specialization Project, Razieh Nejati Fard,
January 2013.
[2.3] Predictive Control of Power Converters and
Electrical Drives, First Edition. Jose Rodriguez and
Patricio Cortes, 2012 John Wiley & Sons, Ltd.
[3.4] P. Cortes, M. P. Kazmierkowski, R. M. Kennel,
D. E. Quevedo, J. Rodriguez, “Predictive Control of in
Power Electronics and Drives”, IEEE Transactions on
Industrial Electronics, Vol. 55, No. 12, pp. 4312-4324,
December 2008.
[4.7] J. Rodriguez, J. Cortes, R. M. Kennel, M. P.
Kazmierkowski, “Model predictive control- a simple
and powerful method,” IEEE Power Electronics and
Motion Control Conference, Chile, 2009.
[5.8] P. Cortes , J. Rodriguez , R. Vargas and U.
Ammann "Cost function-based predictive control for
power converters", Proc. 32nd Annu. IEEE IECON,
pp.2268 -2273, 2006.
[6.9] P. Antoniewicz , M. P. Kazmierkowski , P.
Cortes, J. Rodriguez and A. Sikorski "Predictive direct
power control algorithm for three phase AC/DC
converter", Proc. IEEE EUROCON Conf., pp.1530 -
1534, 2007.
[7.10] P. Cortes , J. Rodriguez , D. E. Quevedo and C.
Silva "Predictive current control strategy with imposed
load current spectrum", IEEE Trans. Power Electron.,
vol. 23, no. 2, pp.612 -618, 2008.
[8.11] J. Rodriguez , J. Pontt , P. Correa , P. Lezana and
P. Cortes "Predictive power control of an AC/DC/AC
converter", Conf. Rec. 40th IEEE IAS Annu. Meeting,
vol. 2, pp.934 -939, 2005.
[9.13] Q. Jiangchao, M. Saeedifard, "Predictive Control
of a Modular Multilevel Converter for a Back- to-Back
HVDC System", IEEE Transactions on Power
Delivery, Vol. 27, No. 3, July 2012, pp. 1538- 1547.
[10.15] P. Cortes, S. Kouro , B. La Rocca , R. Vargas ,
J. Rodriguez, J. Leon , S. Vazquez and L. Franquelo
"Guidelines for weighting factors design in model
predictive control of power converters and drives",
Proc. IEEE Int. Conf. Ind. Technol., pp.1 -7, 2009.
[11.18] A. Lesnicar and R. Marquardt "An innovative
modular multilevel converter topology suitable for a
wide power range", Proc. IEEE Bologna PowerTech
Conf., pp.1 -6,2003.
[12.19] S. Allebrod, R. Hamerski, and R. Marquardt,
"New transformerless, scalable modular multilevel
converters for HVDC-transmission," in Conf. Rec. IEEE
PESC 2008, pp. 174-179.
[13.22] Rohner, S.; Bernet, S.; Hiller, M.; Sommer, R.;
Analysis and Simulation of a 6 kV, 6MVA Modular
Multilevel Converter. Industrial Electronics, 2009.
IECON '09. 35th Annual Conference of IEEE. 2009,
Page(s): 225-230..