My Master of Science Thesis

LỜI CAM ĐOAN
Tôi xin cam đoan đây là công trình của tôi. Tất cả các ấn phẩm được
công bố chung với các cán bộ hướng dẫn khoa học và các đồng nghiệp đã
được sự đồng ý của các tác giả trước khi đưa vào luận án. Cáckết quả trong
luận án là trung thực, chưa từng được công bố và sử dụng để bảo vệ trong bất
cứ một luận án nào khác.
Tác giả luận án
Trần Duy Trinh
BỘ GIÁO DỤC VÀ ĐÀO TẠO
TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI
--------
HOÀNG THÀNH NAM
NGHIÊN CỨU PHƯƠNG PHÁP ĐIỀU KHIỂN DỰ BÁO
CHO CÁC BỘ NGHỊCH LƯU ĐA MỨC
RESEARCH ON MODEL PREDICTIVE CONTROL FOR
MULTILEVEL CONVERTERS
LUẬN VĂN THẠC SĨ KHOA HỌC
ĐIỂU KHIỂN VÀ TỰ ĐỘNG HÓA
HÀ NỘI-2018

LỜI CAM ĐOAN
Tôi xin cam đoan đây là công trình của tôi. Tất cả các ấn phẩm được
công bố chung với các cán bộ hướng dẫn khoa học và các đồng nghiệp đã
được sự đồng ý của các tác giả trước khi đưa vào luận án. Cáckết quả trong
luận án là trung thực, chưa từng được công bố và sử dụng để bảo vệ trong bất
cứ một luận án nào khác.
Tác giả luận án
Trần Duy Trinh
BỘ GIÁO DỤC VÀ ĐÀO TẠO
TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI
--------
HOÀNG THÀNH NAM
NGHIÊN CỨU PHƯƠNG PHÁP ĐIỀU KHIỂN DỰ BÁO
CHO CÁC BỘ NGHỊCH LƯU ĐA MỨC
RESEARCH ON MODEL PREDICTIVE CONTROL FOR
MULTILEVEL CONVERTERS
LUẬN VĂN THẠC SĨ KHOA HỌC
ĐIỂU KHIỂN VÀ TỰ ĐỘNG HÓA
NGƯỜI HƯỚNG DẪN KHOA HỌC
PGS. TS. TRẦN TRỌNG MINH
HÀ NỘI-2018

LỜI CAM ĐOAN
Tôi xin cam đoan bản luận này là công trình của riêng tôi, do tôi tự thiết kế dưới
sự hướng dẫn của thầy giáo PGS. TS. Trần Trọng Minh. Các số liệu và kết quả là
hoàn toàn trung thực.
Để hoàn thành luận văn này tôi chỉ sử dụng những tài liệu được ghi trong
danh mục tài liệu tham khảo và không sao chép hay sử dụng bất kỳ tài liệu nào
khác. Nếu phát hiện có sự sao chép tôi xin chịu hoàn toàn trách nhiệm.
Hà Nội, ngày 10 tháng 10 năm 2018
Tác giả luận văn

TỔNG QUAN VỀ ĐỀ TÀI
1 Lý do chọn đề tài
Điều khiển các bộ biến đổi đa mức như cầu H nối tầng đặt ra nhiều vấn đề do số
lượng các module tăng nên nhiều theo số mức. Bằng các cấu trúc điều khiển thông
thường thì các mạch vòng điều khiển sẽ rất phức tạp. Phương pháp điều khiển dự
báo FCS-MPC dựa trên tính toán tối ưu hàm mục tiêu (cost funcion) trong không
gian hữu hạn các trạng thái làm việc có thể cho phép xây dựng nên một hệ thống
điều khiển có cấu trúc đơn giản hơn, lược bỏ khâu điều chế PWM, có thể đưa đến
những ứng dụng thực tế.
2 Đối tượng nghiên cứu
Nghiên cứu phương pháp điều khiển dự báo dựa trên không gian hữu hạn các trạng
thái làm việc của sơ đồ nghịch lưu đa mức cấu trúc cầu H nối tầng. Sau đó áp dụng
thuật toán điều khiển này cho ứng dụng nghịch lưu nối lưới và điều khiển động cơ
không đồng bộ. Trong khuân khổ cuốn luận văn này, tính đúng đắn của thuật toán
điều khiển dự báo FCS-MPC sẽ được kiểm chứng thông qua mô hình mô phỏng
trên phần mềm Matlab-Simulink.
3 Đóng góp khoa học trong luận văn
Đưa ra thuật toán điều khiển dự báo FCS-MPC cho bộ biến đổi 7 mức cấu trúc cầu
H nối tầng với số bước tính là hai bước, giúp bù thời gian trễ trong quá trình tính
toán, đo lường, deadtime, v.v… khi triển khai thực nghiệm. Thuật toán lựa chọn
tập hợp các vector liền kề giúp giảm đáng kể khối lượng tính toán khi tối ưu hóa
hàm mục tiêu.

THESIS OVERVIEW
1 Problem statement
Control multilevel converters such as cascaded H-Bridge multilevel converters
pose many problems as the number of module increases. By the conventional
control strategies, the control loops will be very complex. The finite control set
model predictive control (FCS-MPC) control strategies is based on cost function
optimization in the finite number of switch states. This could allow the control
system to be simpler structure, the system does not need a modulator, can be led
to practical applications.
2 Object of the study
The FCS-MPC control strategy for three-phase CHB multilevel converter is
studied in this thesis. It is applied in grid-connected CHB as DC-AC converter for
isolated DC sources such as PV panels generating power to gird and an IM driver
application. Within the framework of the thesis, the correctness of the MPC
algorithm will be verified through Matlab-Simulink software.
3 My contributions
Proposal FCS-MPC control strategy for three-phase CHB seven level, predictive
horizon at two-steps compensate delay time. The subset of adjacent vector state
(SAVS) method is proposed to reduce computational when optimizing cost
function.

Acknowledgments
1
Acknowledgments
First of all, I would like to express sincere thanks to my supervisor: Assos. Prof.
Tran Trong Minh for his constant encouragement and guidance. He has walked me
through all the stages of the work of my Master of Science project. The work in
this thesis is based on research carried out at the Institute for Control Engineering
and Automation (ICEA), Hanoi University of Science and Technology (HUST).
I would like gratitude ICEA as well as the financial support provided by the
National project number: KC.05.03/16-20, “Nghiên cứu, thiết kế và chế tạo hệ
thống khắc phục nhanh sự cố tăng/giảm điện áp ngắn hạn cho phụ tải” and:
ĐTĐLCN.44/16, “Nghiên cứu thiết kế và chế tạo hệ truyền động servo xoay chiều
ba pha”.

Contents
2
Contents
Acknowledgments ................................................................................................ 1
Contents................................................................................................................. 2
List of figures........................................................................................................ 4
List of tables.......................................................................................................... 5
List of abbreviations ............................................................................................ 6
1 Overview FCS-MPC for CHB multilevel converter .................................... 7
1.1 Three-phase CHB multilevel converter.................................................... 7
1.1.1 Structure of a three-phase CHB multilevel converter ....................... 7
1.1.2 Modulation techniques....................................................................... 9
1.2 Modeling of three-phase CHB multilevel converter .............................. 11
1.3 FCS-MPC control strategy ..................................................................... 14
2 FCS-MPC for gird-connected three-phase CHB ....................................... 17
2.1 FCS-MPC for grid-connected formulation............................................. 17
2.1.1 Discrete-time model predictive current control............................... 18
2.1.2 Cost funcion optimization and vector state selection ...................... 19
2.1.3 Subset of adjacent vector state......................................................... 20
2.2 Current reference generation .................................................................. 21
2.3 Simulation results ................................................................................... 22
2.4 Conclusion.............................................................................................. 24
3 FCS-MPC based current control of an IM................................................. 25
3.1 Mathematical model of an IM ................................................................ 25
3.2 FCS-MPC for IM formulation................................................................ 25
3.2.1 The required signal estimation......................................................... 27
3.2.2 Discrete-time model predictive current ........................................... 27
3.2.3 Cost funcion optimization and vector state selection ...................... 28
3.3 Simulation results ................................................................................... 28
3.4 Conclusion.............................................................................................. 31

Contents
3
4 Summary and future works ......................................................................... 32
References ........................................................................................................... 33
Appendix A Simulation FCS-MPC for a gird-connected details................. 35
A.1 Simulation model ................................................................................ 35
A.2 MPC algorithm function ..................................................................... 36
Appendix B Simulation FCS-MPC for an IM details................................... 37
B.1 Simulation model.................................................................................... 37
B.2 MPC algorithm function......................................................................... 38
Appendix C List of publications ..................................................................... 40

List of figures
4
List of figures
Figure 1.1 H-Bridge switch state ..................................................................... 7
Figure 1.2 Three-phase CHB seven level converter........................................ 8
Figure 1.3 SPWM multicarrier strategy........................................................... 9
Figure 1.4 Space vector for three-phase CHB three level ............................. 10
Figure 1.5 H-Bridge converter....................................................................... 11
Figure 1.6 Vector state in CHB seven level converter .................................. 13
Figure 1.7 Classification of MPC strategies applied to power converter...... 14
Figure 1.8 FCS-MPC block diagram ............................................................. 15
Figure 2.1 Block diagram of FCS-MPC gird-connected............................... 17
Figure 2.2 Vector state for CHB seven level three-phase ............................. 20
Figure 2.3 Simulation results of the proposed FCS-MPC ............................. 23
Figure 2.4 FFT analysis output current (phase A)......................................... 24
Figure 3.1 Block diagram of FCS-MPC for IM ............................................ 26
Figure 3.2 Simulation results of output current and voltage ......................... 29
Figure 3.3 Simulation results of the proposed FCS-MPC ............................. 30
Figure 3.4 FFT analysis output current (phase A)......................................... 31
Figure A.1 Simulation overview of FCS-MPC for a grid-connected............. 35
Figure A.2 FCS-MPC controller in subsystem............................................... 36
Figure B.1 Simulation overview of FCS-MPC for an IM.............................. 37
Figure B.2 FCS-MPC in subsystem ............................................................... 38

List of tables
5
List of tables
Table 1.1 Switch state H-Bridge converter...................................................... 11
Table 1.2 Level state CHB seven level converter............................................ 12
Table 2.1 Simulation FCS-MPC for grid connected parameters..................... 22
Table 3.1 Simulation FCS-MPC for IM parameters........................................ 28

List of abbreviations
6
List of abbreviations
NPC Neutral diode clamped multilevel converters
FC Flying capacitor multilevel converters
MMC Modular multilevel converters
CHB Cascaded H-Bridge multilevel conveters
IGBT Insulated Gate Bipolar Transistors
DC Direct Current
PS Phase-shift
PD Phase disposition
APOD Alternative phase opposite disposition
POD Phase opposite disposition
SVM Space vector modulation
MPC Model predictive control
FCS-MPC Finite control set model predictive control
CCS-MPC Continuous control set model predictive control
OSV-MPC Optimal switching vector model predictive control
OSS-MPC Optimal switching sequence model predictive control
IM Induction motor
SAVS Subset of adjacent vector state
RMS Root mean square
FFT Fast Fourier transform
THD Total harmonic distortion
FOC Field oriented control

Chapter 1. Overview FCS-MPC for CHB multilevel converter
7
Chapter 1
Overview FCS-MPC for CHB multilevel converter
Multilevel converters include: Neutral diode clamped (NPC), flying capacitor
(FC), modular multilevel converters (MMC) and cascaded H-Bridge (CHB).
However, technology of CHB is one of the well known, most advantageous and
basic method.
Control CHB multilevel converters will be complex when number of cells
increase. The FCS-MPC control strategy can be considered as a solution simply
handles this problem.
1.1 Three-phase CHB multilevel converter
1.1.1 Structure of a three-phase CHB multilevel converter
The Figure 1.1 shows three switch state of H-Bridge (as named is cell), each cell
make three level voltage: -1; 0 and 1.
STATE = 1
STATE = 0
STATE = -1
vac
vdc vdc vac
vdc vac
Figure 1.1 H-Bridge switch state

8
In CHB multilevel converter, number of cells are connected in series. Each
cell has separate DC source which is obtained from fuel cells, batteries, capacitors,
transformers,…
Activity of m cells in each phase will make 2m+1 voltage level. Figure 1.2
is example of CHB three-phase seven level. Three-phase CHB multilevel
converter is simply like three single-phase converter connected in wye
configuration.
Vdc1
S1
Vdc2
C1
vac2
vac1
C2
S2
S3
S4
ZA ZCZB
Z
A B C
Vdc3 vac3C3
N
Figure 1.2 Three-phase CHB seven level converter
Advantages:
 It doesn’t need capacitors or diodes for clamping.
 Entire IGBT switching in basic fundamental frequency (or near this
frequency), so that reduce power lose switch.
 The harmonics reduce because IGBT switching small frequency.

9
 The wave is quite sinusoidal in nature.
Disadvantages:
 CHB needs separate DC sources for each leg.
 Controller will be complex if number of cells increase.
Additional detail can be found in Appendix C [2], [3] and [4].
1.1.2 Modulation techniques
a. Sin-PWM (SPWM) multicarrier strategy
In the SPWM, each phase uses single sinusoidal reference. For m cells need 2m
triangular carriers. The carriers have the same frequency, the same peak to peak
amplitude. Sinusoidal reference is compared with each carrier to determine the
switching output voltages for the power converter.
-1
0
1
-Uc1 -Uc2Uc1 Uc2
a. PS carrier
-1
0
1
-Uc1
-Uc2
Uc1
Uc2
b. PD carrier
-1
0
1
-Uc1
-Uc2
Uc1
Uc2
c. APOD carrier
-1
0
1
-Uc1
-Uc2
Uc1
Uc2
d. POD carrier
Figure 1.3 SPWM multicarrier strategy
There are four strategies of multicarrier PWM. Figure 1.3 is showed
multicarrier PWM strategy for single-phase CHB five level. It requests four
triangle carriers and only one sinusoidal reference.

10
 Phase-shift (PS) carrier PWM strategy. Each carrier is phase-shift by
360°/4=90° from it’s adjacent carrier.
 Phase disposition (PD), all carriers are in phase 0°.
 Alternative phase opposite disposition (APOD), all carriers are alternatively
in phase opposition.
 Phase opposite disposition (POD), all the carriers above the zero reference
are in phase among them.
For single-phase converter, SPWM is still a good choice, but for three-phase
converter different techniques have been developed to take the advantage of three-
phase systems in reducing harmonics. The most popular technique is space vector
modulation (SVM).
b. Space vector modulation (SVM)
SVM technique reduces the influence of common-mode voltages and this avoids
the use of any triangular carriers. SVM conveniently provides more flexibility such
as redundant switching sequences, adjustable duty cycles; and it is more suited to
digital implementations.
(1,-1,-1)
V7
(1,1,-1)
V9
(-1,1,-1)
V11
(-1,1,1)
V13
(-1,-1,1)
V15
(1,-1,1)
V17
(0,-1,-1)
(1,0,0)
V1
(1,1,0)
(0,0,-1)
V2
(-1,0,-1)
(0,1,0)
V3
(0,1,1)
(-1,0,0)
V4
(-1,-1,0)
(0,0,1)
V5
(1,0,1)
(0,-1,0)
V6
(1,0,-1)
V8
(0,1,-1)
V10
(-1,1,0)
V12
(-1,0,1)
V14
(0,-1,1)
V16
(1,-1,0)
V18
(0,0,0)
(1,1,1)
(-1,-1,-1)
V0
21
1
3
4
2
Figure 1.4 Space vector for three-phase CHB three level
These advantages of SVM can lead to a significantly improved performance
of multilevel converters, especially when the level number of the converter is large.

11
The space vector of a three-phase CHB three level shows in Figure 1.4.
However, SVM for higher level converter is difficult. There generally are 6(n-1)2
triangles in the space vector diagram of a three-phase n level converter, reference
vector can be located within any triangle. SVM selects suitable switch states of the
located triangle and apply them for corresponding need duty cycles in an switching
sequence.
1.2 Modeling of three-phase CHB multilevel converter
Each cell of converter is described in Figure 1.5.
vdc
S1
S2
S3
S4
C vac
Figure 1.5 H-Bridge converter
Sign IGBT switch state: “0” corresponding IGBT is off and “1”
corresponding IGBT is on. Table 1.1 shows switch state each cell. Output voltage
obtained are 0; Vdc and –Vdc corresponding switch state is 0; 1 and -1.
Table 1.1 Switch state H-Bridge converter
Gate state
vac Switch state
S1 S2 S3 S4
1 0 1 0 0 0
1 0 0 1 Vdc 1
0 1 1 0 -Vdc -1
0 1 0 1 0 0
Three-phase CHB seven level converter is showed in Figure 1.2, level state
shows in Table 1.2. Output voltage ANv , BNv , CNv ; load voltage: AZv , BZv , CZv and

12
common-mode voltage ZNv .
Table 1.2 Level state CHB seven level converter
Switch state acv Level state
(1,1,1) 3Vdc 3
(1,1,0) (1,0,1) (0,1,1) 2Vdc 2
(1,0,0) (0,1,0) (0,0,1) Vdc 1
(0,0,0) 0 0
(-1,0,0) (0,-1,0) (0,0,-1) -Vdc -1
(-1,-1,0) (-1,0,-1) (0,-1,-1) -2Vdc -2
(-1,-1,-1) -3Vdc -3
Assume, Vdc each cell is balance, Vdc,k = Vdc (k = 1,...n). Output voltage vAN,
vBN, vCN obtains {-3Vdc, -2Vdc, -1Vdc, 0, +1Vdc, +2Vdc, +3Vdc}, corresponding {3, 2,
1, 0, -1, -2, -3}*Vdc, this is called level state {3, 2, 1, 0, -1, -2, -3}.
Level state phase A, B and C are grand total 127 reasonable different vector
state v.
Output voltage each cell:
0 0
1
1
A
ac dc A
dc A
s
v V s
V s


  
  
(1.1)
And, output voltage CHB multilevel converters express:
.
.
.
AN A dc
BN B dc
CN C dc
v k V
v k V
v k V



 
(1.2)
where  , , 3, 2, 1,0,1,2,3A B Ck k k    
Assuming, load is balance, output voltage each phase can be showed:
AZ AN ZN
BZ BN ZN
CZ CN ZN
v v v
v v v
v v v
 

 
  
(1.3)

13
V1
V2V3
V4
V5 V6
V7
V8
V9V10V11
V12
V13
V14
V15 V16
V18
V19
V20
V21
V22V23V24V25
V26
V27
V28
V29
V30
V31 V32 V33
V17
V34
V35
V36
V37
V38
V39
V40
V41V42V43V44V45
V46
V47
V48
V50
V49
V51
V52
V53 V54 V55 V56 V57
V58
V59
V60
V0 V61
V62
V63
V64
V65
V66V67V68V69V70V71
V72
V73
V74
V75
V78
V79
V76
V77
V80
V81 V82 V83 V84 V85 V86
V87
V88
V89
V90
V91
V92
V93
V94
V95
V96
V97V98V99V100V101V102V103
V104
V105
V106
V107
V108
V109
V110
V111
V114
V115
V112
V113
V116 V117 V118 V119 V120 V121
V122
V123
V124
V125
V126
0 α
β
Figure 1.6 Vector state in CHB seven level converter
Because of 0AZ BZ CZv v v   , so common-mode ZNv as express:
 
1
3
ZN AN BN CNv v v v   (1.4)
The level state can be expressed by the vector as following:
 22
3
v A B Cv a v a v     (1.5)
where
2 4
23 3
;
j j
a e a e
 
 
The vector state v can be expressed in terms of complex coordinate by
using the Clarke transformation:
v v jv   (1.6)

14
where:
 
1
3
A
B C
v v
v v v





 

1.3 FCS-MPC control strategy
Model predictive control (MPC) is understood as a wide class of controller, the
main characteristic is the use of the model of the system for the prediction of the
future behavior of the controlled variables over a predictive horizon, n-steps. The
information is used by the MPC control strategy to provide the control action
sequence for the system by optimizing a user-defined cost function. It should be
noted that the algorithm is executed again every sampling period and only the first
value of the optimal sequence is applied to the system at instant k.
Model predictive control
(MPC)
Finite control set MPC
(FCS-MPC)
Optimal switching vector MPC
(OSV-MPC)
Optimal switching sequence MPC
(OSS-MPC)
Continuous control set MPC
(CCS-MPC)
Generalized predictive control
(GPC)
Explicit MPC
(EMPC)
Figure 1.7 Classification of MPC strategies applied to power converter
Classification of MPC strategy applied to power converter is showed in
Figure 1.7, [2]. MPC strategy can be divided into two types: continuous control
set MPC (CCS-MPC) and discrete of the power converters finite control set MPC
(FCS-MPC).
The CCS-MPC computes a continuous control signal and then uses a
modulator to generate output voltage in the power converter. The main advantage
of CCS-MPC when applied to power converter is that it produces a fixed switching
frequency. The main disadvantage of CCS-MPC is present a complex formulation

15
of the MPC problem.
The FCS-MPC based on finite number of switching state to formulate the
MPC algorithm and does not need a modulator. FCS-MPC can be divided into two
types: optimal switching vector MPC (OSV-MPC) and optimal switching
sequence MPC (OSS-MPC). OSV-MPC is the most popular MPC control strategy
for power converter. It uses the output vector state of the power converter as the
control set. The main advantage of OSV-MPC: it only calculates prediction for this
control set, therefore it reduces the optimal problem to an enumerated search
algorithm. This makes the MPC strategy formulation very intuitive. The
disadvantage of OSV-MPC is that only one output optimal vector state is applied
during the complete sampling time period, lead to uncontrolled switching
frequency.
In FCS-MPC, the prediction model of the system needs to be discretized.
Therefore, the MPC algorithms are usually implemented in digital hardware like
as DSP or FPGA. The common of FCS-MPC regularly uses Euler approximation
to discretize a one-step or multiple-step.
Optimizaton
Predictive
model Conv.
Sopt
Load
Measurement
Estimation
FCS-MPC
xp
x
J
x*
Conv.
Figure 1.8 FCS-MPC block diagram
Figure 1.8 shows FCS-MPC block diagram. Assume, control variable x
follow the reference variable x*
, procedure design FCS-MPC following basic
steps:
 Measurement, estimation the control variable in the sampling time instant.
 For every switch states of the converters, predictive (using the mathematical
model) the behavior of variable x in the n-steps time.
 Evaluate the cost function for each prediction.

16
 Select the switch states that minimize the cost function, Sopt applied to the
converters.
In the experiment, driver, measurements and IGBT exist delay time. The
computational time is needed in the predictive control algorithm to predict the
variables, and processor delay deteriorates the performance of the predictive
control at the experimental investigation. To solve this problem, it can be
considered the predictive horizon at (k+n)th
sampling time to predict the variables
which are compared with the references, and determine the cost functions. The
optimum Sopt is selected corresponding to the minimum cost function, and applied
it in the power converter.

Chapter 2. FCS-MPC for gird-connected three-phase CHB
17
Chapter 2
FCS-MPC for gird-connected three-phase CHB
2.1 FCS-MPC for grid-connected formulation
The FCS-MPC control strategy predicts behavior of the load current for each
possible vector state v generated by the power converter. The prediction of the
current is based on discretized model of system.
HB 1 HB 2 HB 3 r L
N O
A, B, C
Filter
Current
reference
generation
Cost function
optimization
Prediction
(k+2)th
*
P
*
Q
Sopt
CHB
FCS-MPC
( )iabc k
, ( )vg abc k
*
( )iabc k
( )dcV k
( 2)iabc k 
Figure 2.1 Block diagram of FCS-MPC gird-connected
In abc coordinate, a block diagram of predictive current control is described
in Figure 2.1. The procedure designs FCS-MPC for grid-connected included
mainly three steps [5]:

18
 Computational current references ( )*
iabc k in the sampling time instant (k)
from references of active power P*
and reactive power Q*
.
 Prediction horizon at (k+2)th
sampling time to predictive current ( 2)iabc k 
the variables which are compared with the current references ( )*
iabc k .
 The optimum vector state is selected corresponding to the minimum cost
function and applied it to actuation.
2.1.1 Discrete-time model predictive current control
Grid-connected three-phase CHB converter, the following continuous time
dynamic equation for each phase current can be expressed:
,
( )
( ) . ( ) ( ) ( )
i
v i vabc
abc abc g abc NO
d t
t L r t t v t
dt
 
    
 
(2.1)
where r and L is the resistance and inductance of the output filter; vabc is phase
output voltage; ,vg abc is grid voltage. Therefore, from (2.1) can be inferred:
,
( ) 1
( ) ( ) ( ) ( )
i
i v vabc
abc abc NO g abc
d t r
t t v t t
dt L L

      (2.2)
For a three-phase n cell CHB converter, the phase output voltage in become:
,.v vabc dc l abcV (2.3)
where level state  , , 1,...,0,..., 1,vl abc n n n n     .
Additionally, common-mode voltage is given by:
 
1
( ) ( ) ( ) ( )
3
NO a b cv t v t v t v t   (2.4)
The first order forward Euler’s approximations:
( ) ( 1) ( )
s
dx t x k x k
dt T
 
 (2.5)
By applying (2.5) to (2.2) with sampling time sT , the discrete-time of current
as bellow:
,( 1) 1 ( ) ( ) ( ) ( )i i v vs s
abc abc abc NO g abc
rT T
k k k v k k
L L
 
         
 
(2.6)

19
The discrete-time dynamic model can be expressed [10]:
, ,( 1) ( ) ( ) ( )x Ax Bv Evl abc g abck k k k    (2.7)
where:
( )
( )
( )
x
a
b
i k
k
i k
 
  
 
,
, ,
,
( )
( ) ( )
( )
v
l a
l abc l b
l c
v k
k v k
v k
 
 
  
 
 
,
( )
( )
( )
v
ga
g abc
gb
v k
k
v k
 
  
  
1 0
0 1
A
s
s
rT
L
rT
L
 
 
  
 
  
2 1 1
1 2 13
B dc sV T
L
  
    
1 0
0 1
E sT
L
 
   
 
As applying the Forward Euler’s approximations, similarly (2.7), the
predictive horizon at two-steps sampling time k+2 as following [5][6]:
, ,( 2) ( 1) ( ) ( )x Ax Bv Evl abc g abck k k k     (2.8)
2.1.2 Cost function optimization and vector state selection
The last step is developing a cost function for the optimization. The cost function
is very flexible. It should be designed according to the specific control goals. The
cost function in the predictive control of grid-connected with delay compensation
can express [8][9]:
2 2
2 2
* *
2) 2) 1) 1)( ( ( (x x x xJ k k k k        (2.9)
where:    
2 2 2* * *
1 12
... p p
a a a a a a      and
*
*
*
( )
( )
( )
x a
b
i k
k
i k
 
  
 
is the reference current.
For sufficiently small sampling time, it can be assumed that
* * *
( 2) ( 1) ( )x x xk k k    . Therefore, cost function (2.9) can be rewritten as:
2 2
2 2
* *
) 2) ) 1)( ( ( (x x x xJ k k k k      (2.10)
The cost function (2.10) is evaluated for per possible three-phase level state,
and the one that minimizes it. And then, optimal level state is selected and applied
to the load. This mean that (2.7), (2.8) and (2.10) are calculated 73
=343 times for

20
a seven level in order to obtain the optimal solution. However, level state can be
defined from vector state. By that way, the calculation can be still reduced 127
times. The selection criterion is to select the voltage level states that minimize the
common voltage vector.
2.1.3 Subset of adjacent vector state
In the previous section, each sampling time cost function needs to be calculated
127 times. The vector state will fastly increase follow 12m2
+ 6m + 1 when the
number of cells m growth, it is very high. So that, subset of adjacent vector state
(SAVS) is proposed to reduce computational [7]. In this way, it is possible to
reduce the set of vector state to be evaluated to the vector state that are nearest to
the last applied vector, as shown in Figure 2.2.
Adjacent
vectors in time
[k]
β
α
1
2
3
4
5
6
7
Number of
redundancies for
each vector
Figure 2.2 Vector state for CHB seven level three-phase
For the calculation of the adjacent vectors to the last applied vector, the
distance between vectors can be calculated with the following function:
     
2 2
,x yv v x y x yd v v v v       (2.11)
If xv near yv , the distance should be equal or less than 2Vdc/3. The
calculation of distance is made offline, and it is stored in database. In this way, the

21
number of calculation is reduced to only seven predictions, irrespective of the
number of cells.
The predictive control algorithm present below:
Algorithm 1 The FCS-MPC predicts horizon at two-steps algorithm
1. Initialize the system and build a table: Subset of Adjacent vector state.
2. Measurements of ( )iabc k and , ( )vg abc k .
3. Determines of *
( )iabc k and vector state ( 1)v k  .
4. Predictions of ( 1)iabc k  and ( 2)iabc k  .
5. for i=1:7 do
2 2
2 2
) 2) ) 1)( ( ( (* *
s s s s
i i i iJ k k k k     
The minimum value of J and the corresponding vector state ( )v k are
kept.
end for.
6. ( )v k is injected into the converters.
2.2 Current reference generation
Cost function in (2.10) require references current *
is
. Based on references of three-
phase active power P*
, reactive power Q*
and grid voltage vsd,g, vsq,g and *
is
can be
calculated.
In the dq coordinate, three-phase active and reactive powers references can
be express:
 
 
* * *
, ,
* * *
, ,
3
. .
2
3
. .
2
sd g sd sq g sq
sq g sd sd g sq
P v i v i
Q v i v i

 

  

(2.12)
where , ,,sd g sq gv v and
* *
,sd sqi i are gird voltage and current references in dq coordinate.

22
Therefore,
* *
,sd sqi i can be express:
* *
, ,*
2 2
, ,
* *
, ,*
2 2
, ,
. .2
3
. .2
3
sd g sq g
sd
sd g sq g
sq g sd g
sq
sd g sq g
P v Q v
i
v v
P v Q v
i
v v
 




 
(2.13)
2.3 Simulation results
Simulation of FCS-MPC horizons at (k+2)th
sampling time for three-phase CHB
seven level converter is verified in Matlab-simulink software. The parameters used
in the simulation are given in Table 2.1.
Table 2.1 Simulation FCS-MPC for grid connected parameters
Parameter Description Value
P* Three-phase active power 1 MVA
Q* Three-phase reactive power 1 MVar
Cdc DC capacitor per H-Bridge 2500 F
Vdc DC capacitor voltage per H-Bridge 2300 V
L Filter inductor 10 mH
r Filter resistor 6 Ω
Ts Sampling time 100 µs
f Grid frequency 50 Hz
Vg Grid voltage (line-to-line RMS) 6.6 kV
The simulink model and cost function are showed in Appendix A, main
results are presented in Figure 2.3.
From Figure 2.3.b, immediately, real current closely follow reference
current, respond fastly. The common-mode voltage to a small value centered
around zero (see Figure 2.3.d). A symmetric output voltage is achieved seven
level, as show in Figure 2.3.c. The real active power and reactive power are
showed in Figure 2.3.e,f, it is around references. Output current phase A, B and C
are presented in Figure 2.3.a.

23
0.05 0.06 0.07 0.08 0.09 0.1
-200
-100
0
100
200
iabc(A)
a. Output current phase A, B and C
ia(A)
0 0.02 0.04 0.06 0.08 0.1
-200
-100
0
100
200
Ref.
Real
b. Gird, reference current phase A
0 0.02 0.04 0.06 0.08 0.1
-8000
-4000
0
4000
8000
vAN(V)
c. Output voltage phase A
0.08 0.085 0.09 0.095 0.1
-800
-400
0
400
800
vZN(V)
d. Common-mode voltage
0.05 0.06 0.07 0.08 0.09 0.1
0
5
10
15 105
P(W)
Ref.
Real
e. Three-phase active power
0.05 0.06 0.07 0.08 0.09 0.1
0
5
10
15 105
Q(VAr)
Ref.
Real
f. Three-phase reactive power
Figure 2.3 Simulation results of the proposed FCS-MPC

24
Fundamental (50Hz) = 176.8 , THD= 1.91%
0 2 4 6 8 10 12 14 16 18 20
Harmonic order
0
0.2
0.4
0.6
0.8
1
Mag(%ofFundamental)
Figure 2.4 FFT analysis output current (phase A)
Fast Fourier transform (FFT) analysis output current phase A, starting time
from 0.01s to 0.09s (four cycles) with fundamental frequency 50Hz and maximum
frequency 1000Hz. Result is showed in Figure 2.4, total harmonic distortion
(THD) is very small, result THD=1.91%.
2.4 Conclusion
The FCS-MPC horizons at two-steps sampling time k+2 for CHB seven level has
been presented. This presents very good reference tracking and reduced common-
mode voltage, with cost function calculation is reduced by SAVS method. The
selection among the adjacent vectors reduces dv/dt at the load side. FCS-MPC
control strategy can be easily applied to CHB multilevel converter when the
number of cell increases, also it can be applied to other multilevel converter
topologies.

Chapter 3. FCS-MPC based current control of an IM
25
Chapter 3
FCS-MPC based current control of an IM
3.1 Mathematical model of an IM
An induction motor can be described by complex equations [4]:
.s s sv i Ψs
d
R
dt
  (3.1)
0 . . .r r ri Ψ Ψr
d
R j
dt
   (3.2)
. .s s rΨ i is mL L  (3.3)
. .r r sΨ i ir mL L  (3.4)
 *3
. .Im .
2
s sΨ iTe p (3.5)
Equation (3.1) is the voltage equation of the phase winding: it describes the
relationship of the stator voltage, the stator current and the stator flux linkage of
the winding. In equation (3.2) the rotor voltage vector is equal to zero because a
squirrel-cage motor is considered. Hence the rotor winding is short circuited. The
winding and rotor flux can be calculated by using the stator current and the rotor
current in equation (3.3) and (3.4). The electromagnetic torque is (3.5).
m is a mechanical rotor speed and it is related to the electric rotor speed
 by the number of pole p:
. mp  (3.6)
3.2 FCS-MPC for IM formulation
In the field oriented control (FOC) control strategy of IM, it uses two loop include
external PI speed loop and internal PI current loop in dq coordinate. FOC describes

26
the way in which the control of torque and speed are directly based on the
electromagnetic state of the motor, similar to a DC motor. So that, internal PI
current loop can be replaced by FCS-MPC predictive current. The block diagram
of FCS-MPC for IM is showed in Figure 3.1.
This chapter will focus to design internal current loop using FCS-MPC
control strategy.
IM
Rotor flux estimation
PI
IE
dq
abc
HB 1 HB 2 HB 3
N
CHB
Cost function
optimization
Prediction
(k+2)th
Sopt
FCS-MPC
External loop
A, B, C
( )i k
( )iabc k
( )k
( )i k
( 2)i k 
*
( )i k
*
( )qi k
*
( )di k
*
( )k
( )k
( )k
, ( )Ψr k
Figure 3.1 Block diagram of FCS-MPC for IM
Based on FOC control strategy, external PI speed loop generates current
reference of FCS-MPC in the sampling time instant k. The FCS-MPC will predict
output current at two-steps sampling time k+2 and cost function calculations is
reduced by SAVS method. In αβ coordinate, the procedure designs FCS-MPC
included mainly three steps [5]:
 Estimation rotor flux; known speed, current reference in the sampling time
instant k.
 The prediction horizon at two-steps sampling time k+2to predictive current
( 2)i k  , the variables are compared with the current reference ( )*
i k .

27
 The optimum vector state is selected corresponding to the minimum cost
function and applied it to power converter.
3.2.1 The required signal estimation
Based on a induction motor model is presented in sector 3.1, the rotor flux can be
expressed [5][6]:
r
r s
Ψ
Ψ ir m
d
T L
dt
  (3.7)
where /r r r
T L R .
By applying the backward Euler’s approximations, rotor flux as following:
( ) . ( 1) ( )
. 1
r r sΨ Ψ imr
rr s r
s
LL
k k k
L T R
T

  
 
(3.8)
where s
T is a sampling time.
3.2.2 Discrete-time model predictive current
From the induction motor model, the current stator can be expressed as:
1 1
.
i
i vr r
t r
d
L k j
R d

  

 

  
      
  
(3.9)
Using the forward Euler’s approximations, the discrete equation (3.9) can
be obtained as follows:
1 1
( 1) 1 ( ) ( ) . ( ) ( )ri i Ψ vs s
r
r
T T
k k k j k k k
R
  
  

  
    
         
    
(3.10)
where . /sL R   .
Predictive stator current horizon at two-steps sampling time k+2 as follows
[5][6]:
1
( 2) 1 . ( 1) . . ( ) . ( 1) ( )
.
ri i Ψ vs s
r
r
T T
k k k j k k k
R
  
  

  
    
           
    
(3.11)

28
3.2.3 Cost function optimization and vector state selection
As can be seen in the previous chapter, the cost function can be expressed:
2 2
2 2
* *
) 2) ) 1)( ( ( (i i i iJ k k k k         (3.12)
Apply SAVS method, the cost function optimization calculate seven time
to choose Sopt and apply to the converters.
3.3 Simulation results
The simulation uses IM 2.2kW and CHB seven level because of the FCS-MPC
control strategy will be experimented in laboratory (C9-203 HUST). Simulated
parameters are showed in Table 3.1.
Table 3.1 Simulation FCS-MPC for IM parameters
Parameters Description Value
P Nominal power 2.2 kW
V IM voltage (line-to-line RMS) 400 V
In Rated phase current (RMS) 4.7 A
f IM frequency 50 Hz
p Number of pole pairs 1
Rs Stator resistance 1.99 Ω
Ls Stator inductance 0.043 H
Rr Rotor resistance 1.99 Ω
Lr Rotor inductance 0.043 H
Lm Mutual inductance 0.3452 H
wn Rate speed 2880 rpm
φ Power factor 0.86
Cdc DC capacitor per HB 2500 F
Vdc DC capacitor voltage per HB 150 V
Simulink model, cost function is presented in Appendix B. The simulation
follows scenario:
 At t = 0s, the magnetization process.
 At t = 0.2s, acceleration to the nominal value 300 rad/s.
 At t = 0.2s, connection of nominal load 10Nm.
 At t = 0.6 s, reversing process down to -300 rad/s

29
In the speed loop, proportional and integral is 0.8 and 60, rotor flux current
reference value 2.5 A. Sampling time internal loop Ts = 50us and external loop
value 10.Ts.
The simulation results are presented in Figure 3.2 and Figure 3.3.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-20
0
20
iabc(A)
a. Output current iabc
vAN(V)
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-500
0
500
b. Output voltage vAN
Figure 3.2 Simulation results of output current and voltage
Simulation results in Figure 3.3.a and Figure 3.3.b show that both the flux
forming and torque forming currents accurately follow the set point trajectories
(coming from the magnetic flux controller and the speed controller in the outer
loop) in all working mode. When the reference changed to negative direction, the
speed real is started to following the speed reference at exact time of 0.2s and 0.6s
at high and low speed, respectively, with the reverse high torque between 10 and -
10 Nm at 300 rad/s and -300 rad/s (see Figure 3.3.c and Figure 3.3.d). The three-
phase current is showed in Figure 3.2.a, waveforms sine. It proves that at the rated
condition, the controller IM with FCS-MPC method operates smooth. The output
voltage phase A is showed in Figure 3.2.b, when speed acceleration, state level
increase from three to five and seven level, value per level is 150V.

30
isd(A) Ref.
Real
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.5
1
1.5
2
2.5
3
3.5
a. Output current isd
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-15
-10
-5
0
5
10
15
isq(A)
Ref.
Real
b. Output current isq
w(rad/s)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-400
-200
0
200
400
Ref.
Real
c. Speed response
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-15
-10
-5
0
5
10
15
Torque(kg.m2
)
d. Torque response
Figure 3.3 Simulation results of the proposed FCS-MPC
The result of FFT analysis output current phase A is presented in Figure
3.4, starting analyze time from 0.5s to 0.58s (four cycles) with fundamental
frequency 50Hz and max frequency 1000Hz. The obtained result proves that the
distortion in the system is less. The current THD of the MPC is only 2.55%.

31
Fundamental (50Hz) = 8.465 , THD= 2.55%
0 2 4 6 8 10 12 14 16 18 20
Harmonic order
0
0.5
1
1.5
2
Mag(%ofFundamental)
Figure 3.4 FFT analysis output current (phase A)
3.4 Conclusion
The simulation results show that the FCS-MPC control strategy is a promising
control tool that is powerful to control the power converters and electrical drives.
Compensation delay time with the predictive horizon at two-steps sampling time
k+2. The delay time compensation has been taken in consideration in the
predictive control algorithm. Results in well tracking of the reference variables at
high speed, even at low speed regions of the IM. It is performance of IM will be
improved. However, the ripple of electromagnetic torque is significantly high.
Further implement needs to reduce the ripple.

Chapter 4. Summary and future works
32
Chapter 4
Summary and future works
The FCS-MPC control strategy is a very attractive solution for controlling power
electronic applications. In the thesis presented the FCS-MPC for gird-connected
and IM application with a three-phase CHB seven level converter. The control
strategy has a simple algorithm structure, it is easy to implement with increased
number of cell, also it can be applied to other multilevel converter topologies.
FCS-MPC control strategy does not need a modulator stage. However, this
usually leads to spread harmonic of the output waveforms. Such critical challenges
as the accuracy of the model, high sampling rates, and high computational cost
function, etc… are disadvantages of FCS-MPC control strategy. But nowadays,
the continuous evolution of the microprocessor technology and the efforts of the
researchers, those problems will be overcome.
A future work is experimental the FCS-MPC control strategy. It can be
effectively evaluated of algorithm and delay time compensation at two-steps
sampling time k+2. And probably longer prediction time steps as 4, 6, etc…
Applying a multi-variable into cost function with the weighting factor. The
example is FCS-MPC for controlling the torque and flux in an IM [2][6].

References
33
References
[1] Sergio Vazquez, Jose I. Leon, Leopoldo G. Franquelo, Jose Rodriguez, Hector
A. Young, Abraham Marquez, and Pericle Zanchetta, "Model Predictive
Control: A Review of Its Applications in Power Electronics", IEEE Industrial
Electronics Magazine, March 2014.
[2] Sergio Vazquez, Jose Rodriguez, Marco Rivera, Leopoldo G. Franquelo,
Margarita Norambuena, “Model Predictive Control for Power Converters and
Drives: Advances and Trends”, IEEE Transactions on Industrial Electronics,
November 2016.
[3] Samir Kouro, Patricio Cortés, René Vargas, Ulrich Ammann and José
Rodríguez, “Model Predictive Control-A Simple and Powerful Method to
Control Power Converters”, IEEE Transactions on Industrial Electronics,
November 2008.
[4] J. Holtz, “The dynamic representation of AC drive systems by complex signal
flow graphs”, Industrial Electronics, 1994. Symposium Proceedings.
[5] Fengxiang Wang, “Model predictive torque control for electrical drive
systems with and without an encoder”, PhD Thesis, Technischen Universitat
Munchen, July 2014.
[6] Muslem Uddin, Saad Mekhilef, Mutsuo Nakaoka, Marco Rivera, “Model
predictive control of induction motor with delay time compensation: An
experimental assessment”, 2015 IEEE Applied Power Electronics Conference
and Exposition (APEC), May 2015.
[7] Patricio Cortes, Alan Wilson, Samir Kouro, Jose Rodriguez, Haitham Abu-
Rub, “Model Predictive Control of Multilevel Cascaded H-Bridge Inverters”,
IEEE Transactions on Industrial Electronics, February 2010.
[8] Ricardo P. Aguilera, Yifan Yu, Pablo Acuna, Georgios Konstantinou,
Christopher D. Townsend, Bin Wu, Vassilios G. Agelidis, “Predictive Control
algorithm to achieve power balance of Cascaded H-Bridge converters”, 2015

References
34
IEEE International Symposium on Predictive Control of Electrical Drives and
Power Electronics, February 2016.
[9] Ricardo P. Aguilera, Daniel E. Quevedo, “Predictive Control of Power
Converters: Designs With Guaranteed Performance”, IEEE Transactions on
Industrial Informatics, October 2014.
[10]Ricardo P. Aguilera, Yifan Yu, Pablo Acuna, Georgios Konstantinou,
Christopher D. Townsend, Bin Wu, Vassilios G. Agelidis, “Predictive Control
Algorithm to Achieve Power Balance of Cascaded H-Bridge Converters”,
2015 IEEE International Symposium on Predictive Control of Electrical
Drives and Power Electronics.
[11]Ricardo P. Aguilera, Pablo Acuna, Yifan Yu, Bin Wu, "Predictive Control of
Cascaded H-Bridge Converters Under Unbalanced Power Generation", IEEE
Transactions on Industrial Electronics (Volume: 64, Issue: 1, Jan. 2017).
[12]Roky Baidya, Ricardo P. Aguilera, Pablo Acuña, Sergio Vazquez, Hendrik du
Toit Mouton, "Multistep Model Predictive Control for Cascaded H-Bridge
Inverters Formulation and Analysis", IEEE Transactions on Power
Electronics (Volume: 33, Issue: 1, Jan. 2018).
[13]Luca Tarisciotti, Pericle Zanchetta, Alan Watson, Stefano Bifaretti, Jon C.
Clare, "Modulated Model Predictive Control for a Seven-Level Cascaded H-
Bridge Back-to-Back Converter", IEEE Transactions on Industrial
Electronics (Volume: 61, Issue: 10, Oct. 2014).
[14]Sumit Dutta, Samir Hazra, Subhashish Bhattacharya, "A Digital Predictive
Current Mode Controller for Single Phase High Frequency Transformer
Isolated Dual Active Bridge DC to DC Converter", IEEE Transactions on
Industrial Electronics (Volume: 63, Issue: 9, Sept. 2016).
[15]Jose Rodriguez, Marian P. Kazmierkowski, Jose R. Espinoza, Pericle
Zanchetta, Haitham Abu-Rub, "State of the Art of Finite Control Set Model
Predictive Control in Power Electronics", IEEE Transactions on Industrial
Informatics (Volume: 9, Issue: 2, May 2013).

Appendix A. Simulation FCS-MPC for a gird-connected details
35
Appendix A
Simulation FCS-MPC for a gird-connected details
A.1 Simulation model
Continuous
powergui
Vdc
i_ref
v_grid
iabc
Vector
MPC Controller
Iabc
A
B
C
a
b
c
Load Measure
N
A
B
C
Three-Phase Grid
6,6kV - 50Hz
Vabc
A
B
C
a
b
c
Grid Measure
a
b
c
A
B
C
RL Filter
6ohm, 10mH
P*
Q*
v_grid
i_abc
i_ref
i_ref Calculator
P*
Q*
Vector
Vdc
A
B
C
Three-Phase
Cascaded H-Bridges
i_abc
i_ref
v_grid
Figure A.1 Simulation overview of FCS-MPC for a grid-connected

Appendix A. Simulation FCS-MPC for a gird-connected details
36
Figure A.2 FCS-MPC controller in subsystem
A.2 MPC algorithm function
% Simulation file
% Master of Science Thesis
% Author: Eng. Hoang Thanh Nam
% Advisor: Assoc. Prof. Tran Trong Minh
% Version: V2.0
% Date: Aug/2018
% PELAB-HUST
function k = fcn(i_k, i_ref_k, v_g_k, Vdc, Ts, k_last)
% Parameters
L = 10e-3; % Inductance load (H)
r = 6; % Resistance load (Ohm)
u_k = zeros(3,1);
A = [(1-r*Ts/L), 0; 0, (1-r*Ts/L)];
B = ((Vdc*Ts)/(3*L))*[2 -1 -1; -1 2 -1];
E = (-Ts/L)*[1 0; 0 1];
temp = inf;
k = inf;
% MPC function
for i = 1:7
ss_temp = top(k_last+1,i) + 1;
u_k(1) = va(ss_temp); u_k(2) = vb(ss_temp); u_k(3) = vc(ss_temp);
x_load_k1 = A*i_k + B*u_k + E*v_g_k;
x_load_k2 = A*x_load_k1 + B*u_k + E*v_g_k;
J = (x_load_k1(1) - i_ref_k(1))^2 + (x_load_k1(2) - i_ref_k(2))^2
+ (x_load_k2(1) - i_ref_k(1))^2 + (x_load_k2(2) - i_ref_k(2))^2;
temp = min(temp, J);
if temp == J
k = ss_temp - 1;
end
end

Appendix B. Simulation FCS-MPC for an IM details
37
Appendix B
Simulation FCS-MPC for an IM details
B.1 Simulation model
Continuous
powergui
Vdc
w
w*
is
Vector
MPC Controller
m
A
B
C
Tm
Asynchronous Machine
SI Units
p
Load torque
Vector
Vdc
A
B
C
Three-Phase
Cascaded H-Bridges
w*
Scope1
Ramp
Scope2
id
iq
Speed
Torque
isq
isd
Figure B.1 Simulation overview of FCS-MPC for an IM

38
Figure B.2 FCS-MPC in subsystem
B.2 MPC algorithm function
% Simulation file
% Master of Science Thesis
% Author: Eng. Hoang Thanh Nam
% Advisor: Assoc. Prof. Tran Trong Minh
% Version: V2.0
% Date: Aug/2018
% PELAB-HUST
function k = fcn(i_s_k_ref, flux_r_k, i_s_k, Vdc_k, Ts, w_k, k_last)
% Input
flux_r_a_k = flux_r_k(1);
flux_r_b_k = flux_r_k(2);
i_s_a_k = i_s_k(1);
i_s_b_k = i_s_k(2);
i_s_a_k_ref = i_s_k_ref(1);
i_s_b_k_ref = i_s_k_ref(2);
% IM parameters
J = 0.0018; %Momen quan tinh (kg.m2)
Rs = 1.99; %Dien tro stato
Rr = 1.99; %Dien tro rotor
Ls_sigma = 0.043; %Dien cam ro stato (H)
Lr_sigma = 0.043; %Dien cam ro rotor (H)
Lm = 0.3642; %Dien cam tu hoa (H)
p = 1; %So doi cuc
Ls = Ls_sigma + Lm; %Dien cam stato
Lr = Lr_sigma + Lm; %Dien cam rotor
% Const
kr = Lm/Lr;
R_sigma = Rs + kr*kr*Rr;
sigma = 1 - (Lm*Lm)/(Ls*Lr);

39
L_sigma = sigma*Ls;
to_sigma = sigma*Ls/R_sigma;
to_r = Lr/Rr;
gab_temp = inf;
k = inf;
va_k = (2/3)*Vdc_k*(2*vg+vh)/2;
vb_k = (2/3)*Vdc_k*(sqrt(3)/2)*vh;
for i = 1:7
j = top(k_last+1,i) + 1;
%----------Predictive current stator alapha, beta(k+1)----------
i_s_a_k1 = (1-Ts/to_sigma)*i_s_a_k +
(Ts/(to_sigma*R_sigma))*(kr*(1/to_r-0*w_k)*flux_r_a_k+va_k(j));
i_s_b_k1 = (1-Ts/to_sigma)*i_s_b_k +
(Ts/(to_sigma*R_sigma))*(kr*(1/to_r-w_k)*flux_r_b_k+vb_k(j));
%----------Predictive flux rotor alapha, beta(k+1)----------
flux_r_a_k1 = (Lr/(Lr+Ts*Rr))*flux_r_a_k +
(Lm/(to_r/Ts+1))*i_s_a_k1;
flux_r_b_k1 = (Lr/(Lr+Ts*Rr))*flux_r_b_k +
(Lm/(to_r/Ts+1))*i_s_b_k1;
%----------Predictive current stator alapha, beta(k+2)----------
i_s_a_k2 = (1-Ts/to_sigma)*i_s_a_k1 +
(Ts/(to_sigma*R_sigma))*(kr*(1/to_r-0*w_k)*flux_r_a_k1+va_k(j));
i_s_b_k2 = (1-Ts/to_sigma)*i_s_b_k1 +
(Ts/(to_sigma*R_sigma))*(kr*(1/to_r-w_k)*flux_r_b_k1+vb_k(j));
%----------MPC----------
% Cost function
% Quadratic cost function
% gab = (i_s_a_k_ref-i_s_a_k1)^2 + (i_s_b_k_ref-i_s_b_k1)^2;
gab = (i_s_a_k_ref-i_s_a_k1)^2 + (i_s_b_k_ref-i_s_b_k1)^2 +
(i_s_a_k_ref-i_s_a_k2)^2 + (i_s_b_k_ref-i_s_b_k2)^2;
gab_temp = min(gab,gab_temp);
if gab_temp == gab
k = j-1;
end
end

Appendix C. List of publications
40
Appendix C
List of publications
[1] Hoàng Thành Nam, Trần Hùng Cường, Trần Trọng Minh, Phạm Việt
Phương, “Điều khiển dự báo cho nghịch lưu bảy mức cấu trúc cầu H nối tầng”,
CASD 2017
[2] Hoàng Thành Nam, Trần Hùng Cường, Phạm Việt Phương, Trần Trọng
Minh, Vũ Hoàng Phương, “Giảm số lượt tính toán hàm mục tiêu của phương
pháp điều khiển dự báo cho bộ biến đổi đa mức cầu H nối tầng để giảm tần số
đóng cắt van”, VCCA-2017
[3] Trần Hùng Cường, Hoàng Thành Nam, Trần Trọng Minh, Phạm Việt
Phương, Vũ Hoàng Phương, “Điều khiển dự báo hữu hạn các trạng thái đóng
cắt các van cho bộ biến đổi đa mức có cấu trúc MMC”, VCCA-2017
[4] Hoàng Thành Nam, Nguyễn Đình Ngọc, Nguyễn Văn Tiệp, Vũ Hoàng
Phương, Trần Trọng Minh, “Mô phỏng bộ khôi phục điện áp động trong hệ
thống điều áp liên tục AVC”, VCCA-2017
[5] Vũ Hoàng Phương, Hoàng Thành Nam, Trần Trọng Minh, Nguyễn Huy
Phương, “Điều khiển bộ chỉnh lưu tích cực sử dụng mạch lọc LCL trong điều
kiện lưới điện không cân bằng”, Chuyên san Đo lường, Điều khiển và Tự động
hóa, số 20, 12/2017
[6] Ha Thanh Vo, Nam Thanh Hoang, Phuong Hoang Vu, Minh Trong Tran,
“FCS-Model Predictive Control of Induction Motors feed by MultilLevel
Casaded H-Bridge Inverter”, RCEEE 2018

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