Ha Thanh Vo, Nam Thanh Hoang, Phuong Hoang Vu, Minh Trong Tran, Dich Quang Nguyen, “FCS-Model Predictive Control of Induction Motors feed by MultilLevel Casaded H-Bridge Inverter”, RCEEE-2018.

1. 36
FCS-Model Predictive Control of Induction Motors
feed by MultilLevel Cascaded H-Bridge Inverter
Ha Thanh Vo
University of transport and
communications
Ha Noi, Viet Nam
vothanhha.ktd@utc.edu.vn
Minh Trong Tran
Ha Noi university of science and
technology
Ha Noi, Viet Nam
minh.trantrong@hust.edu.vn
Nam Thanh Hoang
Ha Noi university of science and
technology
Ha Noi. Viet Nam
thanhnambka@gmail.com
Dich Quang Nguyen
Ha Noi university of science and
technology
Ha Noi, Viet Nam
dich.nguyenquang@hust.edu.vn
Phuong Hoang Vu
Ha Noi university of science and
technology
Ha Noi, Viet Nam
phuong.vuhoang@hust.edu.vn
Abstract— This paper presents a finite control set – model
predictive control (FCS-MPC) of induction motor fed by a
multilevel cascaded H-bridge inverter. The control scheme has
been based on discretized model of the IM motor and also on
the discrete nature of power electronic converter. In each
predict time period the optimization procedure estimates cost
function under a finite control set which is among the most
effective switching voltage vectors of the multilevel converter.
To ease the future experimental prototype building, this work
has purposely developed a MPC algorithm for 2 step
prediction time and the IM fed by a 3-levels cascaded H-bridge
inverter. The simulation results show all good attractive
performance and potential implementation.
Keywords— model prediction control (MPC), three level-
inverter, Cascaded H-bridge, induction motor, FCS-MPC
I. INTRODUCTION (HEADING 1)
Nowadays, Field-Oriented-Control (FOC) and Direct
Torque Control (DTC) are the most popular control
strategies of the induction motor (IM). FOC is a technique
which provides a method of decoupling the air-gap flux and
the other producing the electromagnetic torque. Therefore, it
provides independent control of torque and flux, similar to a
separately excited DC machine. DTC is a control method
without a coordinate transformation [4], [5]. DTC offers an
excellent torque response using a less parameter sensitive
model than FOC. For the last decade as an alternative
control strategy come out is the model predictive control
(MPC).
The basic idea of MPC is to pre-calculate the optimum
values for the actuating variables based on a mathematical
model of the system, the history of past control actions and
an optimization of a cost function over a receding prediction
horizon [6]. MPC has many advantages: the basic concept is
easy to understand, the algorithm is simple to implement, it
can handle multi-variable systems and constraints can be
included. The main disadvantage of MPC is the big online
calculation effort, especially with long horizons [7].
Fortunately, the modern digital signal processing (DSP) and
the Field Programmable Gate Arrays (FPGAs) have made it
possible to use MPC in fast dynamic processes such as
power electronics and control of electrical drives [8], [9],
[10] and [11]. Therefore, different applications in voltage
source inverter with predictive control has been successfully
investigated in recent few years, such as a predictive current
control fed by voltage source inverter [12]; predictive torque
and flux control of IM fed by indirect matrix converter
(IMC) with unity power factor control at the input side [13];
multilevel inverter fed induction motor predictive control
[14]; predictive current control of a three-phase four-leg
inverter [15]; torque ripple reduction of IM with predictive
direct torque control method [16], and a weighting factor
optimization method in the predictive control algorithm for
reduction of torque ripple [17], [18].
Especially, the studies on multilevel cascaded H-bridge
inverters for induction motor are of great interest, because
multilevel inverter could increase number of voltage levels,
higher voltage can be generated using the devices of lower
rating, lower switching frequency while producing better
voltage waveform and reduced total harmonic distortion
(THD). The last characteristics are of vital importance for
the operations in high voltage, high power range. In this
work a FCS-MPC technique has been proposed to control
induction motor flux and torque accurately. The control
procedure is to minimize the cost functions for all possible
switching states and to select the optimal state vector for the
next sampling period.
This paper is organized in the following manner: the second
section describes the modeling of the induction motor, three-
level cascaded H- bridge inverter; the third the model
predictive control of induction motor with delay time
compensations, consideration of long prediction horizons for
determination of the predicted variables in the second next
(k+2) sampling time instant, an overall quality function of
the MPC method, and a comprehensive predictive control
scheme. In the fourth section, the simulation results are
discussed to prove the feasibility of the proposed method.
The last section is concluded with a comprehensive
conclusion.
II. SYTEM DESCRIPTION
A. Modeling of induction motor
The induction motor (IM) can be modeled with the
following. The  and  axes stator voltages of IM are
derived as the sum of the resistive voltage drop and the
derivative of the stator flux linkages in the stationary
reference frame as.
;0
;
s s s s s r r r r r
s s m r r r m s
p
s r
u R i L R i L jz
L i L i L i L i

  
 
    
   
(1)
Where s
i : stator current; r
i : rotor current; s
R : stator
resistance; r
R : rotor resistance;  : rotor angular

2. 37
frequency; pz : number of pole pair; ,s r
L L : self –
inductances; m
L : mutual inductance
The developed electrical torque in the IM can be represented
by stator current and stator flux as the following equation:
3
( )
2
e p s s
T z xi (2)
B. Multi-level voltage source inverter
The cascaded H-Bridge (CHB) multilevel inverter is
frequently studied for command improvement involving
synchronization strategy and output voltage power levels
enhancement. It has a modular structure that produces a stair
wave voltage output from a multitude of DC sources.
The number of voltage levels in a CHB inverter can be
found from:
m=(2H+1) (3)
Where: H is the number of H-bridge cell per phase leg.
The voltage level m is always an odd number for the CHB
inverter while in other multilevel topologies such as diode-
clamped inverter, it can be either an even or odd number.
The total number of active switches (IGBT) used in the
CHB inverter can be calculated by
Nsw= 6(m-1) (4).
In the article we present at a three level H-bridge multilevel
with three separated DC sources with unequal voltage
levels. The inverter is capable of creating three levels of
output voltage (Fig.1), to apply the proposed method.
ZA
ZB
ZC
A
B
C
Z
N
vZN
C
Vdc1
S2
vac
S4
S1 S3
+
-
C
Vdc2
S2
vac
S4
S1 S3
+
-
C
Vdc3
S2 S4
S1 S3
+
-
vac
ia
ib
ic
Fig. 1. Simplified circuit diagram of three-level cascaded H-Bridge
inverter
Fig.1 can express three types of switching states, by
considering all of the three-phase switching states, a total of
27 switching states can be combined. The operating status of
the switch and the pole voltage in the three-level inverter
can be represented by the switching states shown in Table I.
Table I in the symbol is “1” is ‘’ON’ switching state and “0”
is ‘’OFF’ switching state. State level as the following
equation (3):
0 0
1
1
A
ac dc A
dc A
s
v V s
V s

  
  





(3)
TABLE I. OPERATING STATUS OF THE SWITCH AND POLE VOLTAGE
State switch State level
S1 S2 S3 S4 Vac State level (SA)
1 1 0 1 0 0 0
2 1 0 0 1 VDC 1
3 0 1 1 0 -VDC -1
4 0 1 0 1 0 0
(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)
V0
21
1
3
4
2
Fig. 2. Vector diagram and sectors of the three-level inverter
Fig. 2 shows the vector diagram and sectors of three-level
inverter. Generally, the voltage vector of the three-level can
be largely divided into 6 sectors and each sector can be
divided into 6 segments. In the three-level, when expressing
the reference voltage vector, the sector and segment where
the reference voltage vector is located is designated, and, by
calculating the effective time of the three active vectors that
are most closely located to the reference voltage vector, the
reference voltage vector is generated through the switching
method. Note that there are 6 pairs of nonzero identical
voltage vectors which can be generated using two different
switch states and the zero vector can be made using 3
different switch states. Therefore,19 different voltage vectors
can be generated by the use of the 3-level inverter. The
effects of voltage vectors on the balance of capacitor
voltages are illustrated.
III. PREDITIVE CURRENT CONTROL
A. The required signal estimations
Based on the squired-cage induction machine model
presented in section II, the relationship among stator flux,
rotor flux can be expressed as [16]:
r
r m
m
m s
r
d
T L
dt
L
L L
L
 

 
 
 
 
r s
r s
s s
ψ
ψ i
ψ i
ψ i
(5)
Where /r r r
T L R
To discretize (5), the Euler backward approximation [18]:

3. 38
( ) ( 1)
s
dx x k x k
dt T
 
 (6)
( ) . ( 1) ( )
.
1
mr
rr s r
s
LL
k k k
L T R
T

  


r r s
Ψ Ψ i (7)
where sT :sampling time
Substituting (7) into (5), the discrete equation for the stator
flux can be obtained:
( ) ( ) ( )s r sk k L kk  r s
Ψ Ψ i (8)
Where:
2
/ ; 1 ( / )r m r m s r
k L L L L L  
B. Discrete-time model predictive current
From the induction machine model presented in section II,
the current stator can be expressed as:
1 1
( ( ) ) )s
s r r s
r
di
i L k j u
R dt T

      (9)
To discretize (9), the Euler backward, then, the discrete
equation for the current can be obtained as follows:
( 1) 1 ( )
1 1
( ) . ( ) ( )
s
s
r
r
T
k k
T
k j k k k
R

 


 
  
  
 
 
 
   
  
   
s s
r s
i i
Ψ v
(10)
Predictive stator current and torque in the next (k+2)th sampling
time instant become as follows: [16]
(1( 2) ) ( 1)
1
[ (( ) ( 1) ( )))
s
s r
r m r s
s r
u
T
k i k
T k
k j k k
T r
i

 

 
 
  
   

(11)
The predictive control scheme and algorithm for induction
motor control are presented in Fig.3 and Fig.4, respectively.
Known Speed, Ref. Current
Rotor flux
Prediction of Current and Rotor flux at (k+2)th
Sampling time
Cost function Calculation
For, i = 1:19
i > 19
Selection of Optimum Switching State
Yes
No
Fig. 3. Predictive control algorithm
In Fig.4. Firstly, the rotor speed and stator currents are
measured. Then the rotor flux vector is estimated. Its angle,
together with the torque and flux producing currents
components
*
d
i and
*
qi is used for stator current calculation
in stationary frame. After that, current predictions with
respect to all available voltage vectors will be made. These
predictions are substituted into the cost function, and the
prediction which minimizes the cost function is treated as
the optimal and its corresponding voltage vector used as the
applied vector for the electric drives in the next control
cycle.
The quality function in the predictive control of IM with
delay compensation is presented as below [17]
2 2
2 2
( ) ( 2) ( ) ( 1)J k k k k     
* *
s s s s
i i i i (12)
Where :    
2 2 2* * *
1 12
... p p
a a a a a a     
*
( )si k : reference current predictive variables at k time;
*
2( )si k  : reference current predictive variables at k+ 2

4. 39
Cost function
optimization
*
*
di
IM
rψ
Speed
controller
( 2)ksi
dq
( )k*
si
*
qi
si
+
-
+
-
+
-
IE
Cost function
optimization
Vdc3 Vdc2 Vdc1
S2 S1
S4 S3
Vac
iaib
A
B
ic
C
S2 S1
S4 S3
S2 S1
S4 S3
VacVac
N
C C C
; ;a cbS S S
Current
prediction for
(k+2)th sampling
time
Flux estimation
sαi
sβi
Fig. 4. Block diagram of the induction based on MPC using three-level cascaded H-Bridge inverter
IV. SIMULATION RESULTS
TABLE II. DESIGN SPECIFICATION OF INDUCTION MOTOR
Rated power dmP 2.2kW
Rated Torque dmM 7.3Nm
Rated phase current dmI 4.7A
Rated phase voltage dmU 400V
Rated frequency dmf 50Hz
Number of pole pairs p 1
Stator resistance sR 1.99
Rotor resistance rR 1.84
Mutual inductance mL 0.37
Rated speed dmn 2880 rpm
Torque of inertia J 2
.Kg m
Some of the typical working modes of the IMSR are
investigated through the following simulation scenario:
At t = 0s, the magnetization process.
At t = 0.5s, acceleration to the nominal value 150 rad/s.
At t = 0.5s, connection of nominal load (full load).
At t = 1 s, reversing process down to -150 rad/s
The Figs. 5 and 6 represent the results of IM control applied
with model predictive control (MPC) method at high speed
and low speed regions, respectively. Simulation results
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 modes (Fig 5 and Fig 6).
Fig. 5. Current response
*
sd sdi i

5. 40
0 0.5 1 1.5 2 2.5 3
Time [s]
-10
-5
0
5
10
(A)
i*sq: reference current
isq: measured current
Fig. 6. Current response
*
sq sqi i
When the reference speeds have been changed to negative
direction, the measured speeds are started to follow the
reference speeds at exact time of 0.5s and 1s at high and low
speed, respectively, with reverse high torque between +10
and -10.0 Nm at 150 rad and -150 rad/s in both the analysis.
The torque can be generated quickly and the speed in a short
time brought exactly to the set point (0.18s for the run-up
and 0.2s for reversing) Fig 7 and Fig 8.
0 0.5 1 1.5 2 2.5 3
Time [s]
-200
-100
0
100
200
(rad/s)
w*: reference speed
w: measured speed
Fig. 7. Speed response w*- w
0 0.5 1 1.5 2 2.5 3
Time[s]
-20
-10
0
10
20
(N/M)
Te*: reference torque
Te:measured torque
10 N/m load
Fig. 8. Toquer response Te*- Te
Fig.9 observes the three phase stator currents at steady state
with rated speed and torque. The stator current waveforms
are sine. It proves that at the rated condition, the controlled
AC motor with MPC method operates smoothly with a set
of balance three phase currents. And the stator flux
magnitude is kept at a constant.
0 0.5 1 1.5 2 2.5 3
Time [s]
-10
-5
0
5
10
(A)
ia
ib
ic
Fig. 9. Three phase stator current response
By subdividing the voltage vectors of the selected area, the
function is calculated for each voltage vector, and the
minimum value is selected in order to make the final
decision of the reference voltage vector. Finally, the selected
reference voltage vector is used for the control of the three-
level switch through FCS-MPC method (Fig.10).
0 0.5 1 1.5 2 2.5 3
Time [s]
-1000
-500
0
500
1000
(V)
Van: voltage
Fig. 10. Van phase voltage response
The harmonic spectrum of stator current at 150 rad/s with
load is shown Fig.11. The total harmonic distortion (THD)
values measured after the development of the system is
tabulated to analyze the efficiency or result obtained. The
THD is mainly concentrated on the stator phase output
current. The harmonics present in the three phases are so
found form the simulation done. The result obtained proves
that the distortion in the system is less. The current THD of
the MPC is only 1.25%.
Fig. 11. FFT of A phase stator current

6. 41
V. CONCLUSION
In this paper, FCS-MPC controller is proposed and
applied in an induction machine control system with high
power and voltage fed by multilevel-cascaded H-bridge
inverter. The proposed delay time compensated model
predictive control method utilizes the discrete with the
second next (k+2)th predictive variables are predicted. The
delay time has no effect on control performance when delay
time compensation has been taken in consideration in the
predictive control algorithm which results in well tracking of
the reference variables at high speed, even at low speed
regions of the induction motor. It is performance of electric
drive will be improved.
ACKNOWLEDGMENT
The authors are thankful to AUN/SEED-Net for financial
support
This paper is granted by the ĐTĐLCN.44/16 project.
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