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Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8321-8327 8321 
 

www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

T-Type Multi-Inverter Application for Traction Motor 

Control 
 

Vo Thanh Ha 

Faculty of Electrical and Electronic Engineering 

University of Transport and Communications 
Hanoi, Vietnam 

vothanhha.ktd@utc.edu.vn 

Pham Thi Giang 

Faculty of Electrical Engineering 
University of Economics-Technology for Industries 

Hanoi, Vietnam 

ptgiang@uneti.edu.vn 

Vu Hoang Phuong 

School of Electrical Engineering 

Hanoi University of Science and Technology 
Hanoi, Vietnam 

phuong.vuhoang@hust.edu.vn 
 

Received: 29 January 2022 | Revised: 10 February 2022 | Accepted: 13 February 2022 

 

Abstract-The structure and principle of the T-type 3-level reverse 

voltage source that will be fed to three-phase induction motors 

will be presented in this study. The implementation of Space 

Vector Pulse Width Modulation (SVPWM) and the math models 
of the induction motor, the stator currents, and the speed 

controller design of the electric traction drive system based on 

Field-Oriented Control (FOC) will be also shown. This three-level 

T-type inverter in the FOC structure decreases Total Harmonic 

Distortion (THD) more than the previous two-level inverters. By 

combining the FOC control structure with the T-type 3-level 

inverter, the speed and torque responses necessary for railway 
traction motor load were improved. Finally, Matlab/Simulink 

will be used to demonstrate the correctness of the T-Type multi-
level inverter theory. 

Keywords-multilevel inverter; t-type inverter; induction motor; 

field oriented control; railway traction motor 

I. INTRODUCTION  

Since the '90s, most asynchronous motors have been 
replaced, mainly by DC motors. The induction motor 
outperforms the DC motor in maintenance cost, mechanical 
stability, and energy efficiency, whereas it can also work in the 
flux-weakening mode [1-4]. Thus, the induction motor is 
widely used for railway traction motors. Nowadays, traction 
electric transportation systems are widely used in developed 
and developing nations to alleviate traffic congestion in major 
cities. Traction power systems typically employ big capacity 
(200kW-300kW), and traction motors are driven from high 
voltage (25kV, 50Hz) to low voltage (1500V-750V, 50Hz) [5]. 
Furthermore, since the traction drive system runs at high 
voltage, a voltage source inverter is required to power the 
traction motor and assure 100% harmonic distortion of the 
stator current and, low voltage, standard sine phase voltage, 
and appropriate controls (torque, speed) for traction electric 
motor and train operating characteristics. In the control 

structure of traction power transmission systems, 2-level 
voltage source inverters with power circuits including 6 
semiconductor valves and the PWM SVM technique are often 
used. However, compared to a multi-level inverter, this 2-level 
inverter has greater THD [6]. According to [7], the multi-level 
inverter comprises semiconductor valves and a DC voltage 
source, and the output voltage is in the form of wavelengths. 
Therefore, the output voltage of a multi-level inverter may be 
made sinusoidal with low THD by increasing the number of 
voltage levels. Currently, clamp diode (NPC), variable 
capacitor (FC), H-bridge stage (CHB), and T-type multi-level 
inverters are extensively used in industry and transportation 
(such as pumps, fans, wind energy, and traction motors for 
electric trains, electric vehicles, etc.). Based on the literature 
review [8], the NPC-type multi-level inverter offers benefits 
over the standard 2-level voltage inverter, such as reduced 
stator current harmonic distortion and lower TDH voltage. 
However, because of the NPC's construction, increasing the 
number of voltage levels will increase the number of diodes 
and IGBTs, making it impossible to raise further the number of 
voltage levels [9]. 

The FC variable-capacitor multi-level inverter has seen a 
lot of applications. This multi-level inverter has the same 
construction as the NPC multi-level inverter. Instead of diode 
transistor valves, a capacitor is used, resulting in different 
voltages. This benefit allows semiconductor valves to operate 
without requiring continuous switching. THD is lower than that 
of the NPC set, resulting in higher efficiency of the FC multi-
level inverter than in the NPC set. However, this multi-level 
inverter costs more than the NPC multi-level inverter [10, 11]. 
In addition, it has been shown [12, 13] that a multi-level 
inverter structure of H-bridge cascade (CHB) employs an 
IGBT semiconductor and a separate DC source (electrolytes). 
The voltage is provided via several output transformers or 

Corresponding author: Vo Thanh Ha



Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8321-8327 8322 
 

www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

capacitors for industrial applications. This multi-level inverter's 
power circuit (staged semiconductor phases) is simple to build, 
replicate, and install in order to increase the number of voltage 
levels as required. Compared to NPC and FC, a CHB multi-
level inverter has this benefit. Furthermore, the CHB multi-
level inverter works with medium and high voltages. However, 
since this multi-level inverter structure requires DC balancing 
to assure output voltage quality, the control structure must 
propose a voltage balance management algorithm. Moreover, 
scientists have been researching the T-Type multi-level inverter 
because it has more benefits than the CHB structure, such as 
employing just one DC source and preventing DC voltage 
imbalance across phases [14, 15]. Besides, authors in [16] 
shown that the T-type multi-level inverter has the advantage of 
reducing the number of semiconductor valves and capacitors 
while increasing the voltage level.  

The current article's research, analysis, and assessment 
focus will be applied to the T-Type three-level inverter for 
traction motor control power supply in a high-capacity, high-
voltage traction power transmission system. In addition, the 
file-oriented control structure of a traction electric drive system 
using a T-type 3-level inverter combined with torque speed PI 
controllers is also provided. Again, this controller is designed 
so that the responses are accurate. 

II. SVM STRUCTURE AND MODULATION OF THE T-TYPE 3-
LEVEL INVERTER 

A. Control Structure 

The 3-phase 3-level T-type inverter structure is developed 
from the standard 3-phase 2-level voltage source structure. 
Each phase includes 8 semiconductor valves, such as 4 IGBT 
valves (SA1-SA4) and 4 diodes (D1-D4). The three-phase 
design of a three-level T-type converter is shown in Figure 1. 
The T-type 3-level inverter works on 2 DC capacitors to divide 
the input voltage into two voltage components Vdc/2 

and create 
a virtual neutral point. Properly adjusting and switching of the 
semiconductor valves will give a wire voltage of 5 levels: −Vdc, 
−Vdc/2, 0, Vdc/2, Vdc. Thus, the output phase voltage has the 
form of 3 levels: −Vdc/2, 0, Vdc/2. Based on the working 
principle of this 3-level T-type inverter, the switching status 
table is built as shown in Table I. 

 

 
Fig. 1.  3-phase T-type inverter structure power circuit. 

TABLE I.  T-TYPE 3-LEVEL INVERTER SWITCH ING STATUS 

Status ���� SA1 SA2 SA3 SA4 

P +Vdc/2 ON OFF ON OFF 

O 0 OFF OFF ON ON 

N −Vdc/2 OFF ON OFF ON 

B. Pulse Width Modulation SVM 

With a multi-level inverse scheme, the number of sub-
triangles on the vector plane increases rapidly as the number of 
levels (M) increases. The calculation becomes more 
straightforward if we use the system's symmetry in every sixth 
angle vector space shown on three-six quadrant vector plane 
coordinate systems (Z1x, Z1y), (Z2x, Z2y), (Z3x, Z3y), where: 

1
( )

3

A

B C

v v

v v v

α

β

=



= −


     (1) 

 

Z1x

Z1y Z2xZ2y

13

4
5

2

6

Z3x

Z3y

 
Fig. 2.  Coordinate systems (Z1x, Z1y), (Z2x,Z2y) and (Z3x,Z3y). 

The number of sub-triangles in the spatial vector diagram 
will increase as the degree increases. The calculation becomes 
much easier using the symmetry property of the space vector 
system in each arc. The coordinate systems (Z1x, Z1y), (Z2x, 
Z2y) and (Z3x, Z3y) are shown in Figure 2. First, we determine 
the projection of the desired voltage vector on the upper 
coordinate system (Z1x, Z1y), (Z2x, Z2y) and (Z3x, Z3y) Then 
we define three transformation matrices, M1, M2 and M3 
described as: 

1 2 3

1 1 2
1 1 0

3 3 3
; ;

2 1 1
0 1 1

3 3 3

M M M

     
−     

     = = =
     

− − −     
     

    (2) 

According to [6], PWM SVM is performed according to the 
following calculation steps: 

1) Step 1: Locating the Reference Vector 

The number of sectors S (S = I, II, ···, VI) is determined by 
Table II. 

TABLE II.  LO CATING THE HEX AGONS 

z1x.z1y < 0 z1x.z1y ≥ 0 
z2x.z2y < 0 z2x.z2y ≥≥≥≥ 0 

z1x<0 z1x≥≥≥≥0 
z3x<0 z3x≥0 z2x<0 z2x≥0 
Sec III Sec VI Sec V Sec II Sec IV Sec I 

 

2) Step 2: Determining the Duty Cycle 

In this step the three nearest vectors are determined based 
on the three vertices of the modulation triangle, the duty cycle 
of the three most similar defined vectors is calculated, and the 
switching states of the semiconductor valves are chosen. With 
the assumption shown in Figure 3, the sum of the output 
voltage vector is as follows: 

The vector is represented by the vectors in (3): 



Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8321-8327 8323 
 

www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

( ) ( )

( )
1 1 2 1 3 1

1 2 3

V p p p p p

1 p p p

g h

g h g h

m m

m m m m

= + − + −

= − − + +

r r r r r r

r r r     (3) 

( )( ) ( )( )
( ) ( ) ( )

2 4 3 4 2 4

4 3 2

1 1

1 1 1

g h

g gh h

V p m p p m p p

m m p m p m p

= + − − + − −

= + − + − + −

r r r r r r

r r r
   (4) 

The coefficients mg and mh are determined as follows: 

1 1 1

1 1 1

g x x x g

h y y y h

m z z z k

m z z z k

 = −   = − 


 = − = −  

    (5) 

with 
g 1x h 1y

k z , k z =   =   
. 

 

0

m
g

m
h

Z1y

Z1x
2
p(kg+1,kh)
rrrr

1
V
rrrr 2
V
rrrr

4
p(kg+1,kh+1)
rrrr3

p(kg,kh+1)
rrrr

1
p(kg,kh)
rrrr

 
Fig. 3.  Synthesizing the output voltage vector from the 3 vertex vectors of 

the sub-triangle. 

3) Step 3: Determining the Switching State 

If kA = k, the coefficient k must satisfy this condition: 
M 1 M 1

k
2 2

− −
− ≤ ≤ . The coordinates of the state vector in the  

(a, b, c) coordinate system are given by (6): 

1

1

1

1 1

AN

x

BN x

y

CN x y

k k
k

k k k
k

k k k k

  
    ≈ = −    
     − −   

    (6) 

Equation (6) shows the relationship between [k1x, k1y] 
coordinates (i = 1,2,3) and (a, b, c) coordinates. 

4) Step 4: Balancing the Voltage on the Two DC Capacitors 

Using SVM Modulation 

For multi-level inverters, voltage balancing for DC 
capacitors is always a challenge. Although just one DC source 
is utilized in the T-type inverter construction, voltage 
imbalance on the two capacitors in series is conceivable for a 
variety of reasons, including:  

• The DC capacitor's value is inaccurate in this case.  

• Due to inefficient circuit switching, the discharge and 
charge times of two capacitors differ.  

As a result, DC voltage will deteriorate the harmonic 
quality of the inverter output voltage, which is impossible. 

Thus, multi-level inverters in general, and T-type inverters in 
particular, must address this issue. The steps for balancing the 
capacitor voltage are: 

• Step 1: Measure the voltage on the capacitors Vdc1, Vdc2. 

• Step 2: Compare the two voltages.  

• Step 3: Discharge voltage on capacitor C1 and charge 
capacitor C2 if Vdc1 > Vdc2.  

• Step 4: Discharge voltage on the capacitor C2 and charge 
C1 if Vdc2 > Vdc1. 

TABLE III.  ORDER OF THE VECTOR SWITCHES 

Sector 
Triangle 

shape 
Switching order 

Case of 

unbalance 

1 

1 
(0 0 0) - (1 0 0) - (1 1 0) – (1 0 0) Vc1>Vc2 

( -1 -1 -1) – (0 -1 -1) – (0 0 -1) – (0 -1 -1) Vc2>Vc1 

2 
(1 0 0) – (1 0 -1) – (1 -1 -1) – (1 0 -1) Vc1>Vc2 

(0 -1 -1) - (1 -1 -1) - (1 0 -1) - (1 -1 -1) Vc2>Vc1 

3 
(1 0 0) - (1 1 0) -(1 0 -1) - (1 1 0) Vc1>Vc2 

(0 -1 -1) - (0 0 -1) - (1 0 -1) - (0 0 -1) Vc2>Vc1 

4 
(1 1 0) - (1 1 -1) - (1 0 -1) - (1 1 -1) Vc1>Vc2 

(0 0 -1) - (1 0 -1) - (1 1 -1) - (1 0 -1) Vc2>Vc1 

 

Table III shows the changing of the switching order in 
sector one to balance the voltage on the capacitor. We follow 
the same procedure in the remaining sectors. The voltage 
imbalance between the two capacitors C1 and C2 may be 
determined using the state table, and control can be used to 
balance the voltage on the two capacitors. 

III. MATHEMATICAL MODELS 

A. Mathematical Model of Induction Motor 

The FOC approach is used to regulate the induction motor, 
hence, the induction motor's mathematical model (based on [4]) 
is:  

1 1 1 1

1 1 1 1

1

sd
sd s sq sd

s r r s

sq

s sd sq m sq

s r s

rd m
rd sd

r r

p

rd sq L

di
i i u

dt T T T L

di
i i i u

dt T T L

d L
i

dt T T

zd
k i m

dt J
ω

σ σ
ω

σ σ σ σ

σ σ
ω ω

σ σ σ σ

ψ
ψ

ω
ψ

   − −   =− + + + +       − −   =− − + − +    
 =− + = −

    (7) 

with 

2 2
3

;
2

sq p mm
s r

r rd r

i z LL
k

T L J
ωω ω ω ω

ψ
= + = + = . 

The equation represents the IM's mechanical equation: 

M T

Jd
m m

dt

ω
= +     (8) 

B. Mathematical Model of the Traction Motor Load 

Traction motor load includes load torque and drag forces. 
The drag force of the electric traction motor is a characteristic 



Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8321-8327 8324 
 

www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

quantity for the train's movement, including two main 
components, essential and auxiliary resistance. 

1) Basic Drag 

The main factors that cause drag are friction and impact 
between the wheel and the rails, between the locomotive and 
the air, and between the locomotive parts. The essential parts of 
frictional resistance between the bearing and the wheel hub are: 
rolling resistance, sliding, shock and shock, and air. From the 
above factors, it can be seen that the factors affecting the 
essential unit resistance are very complex and, in practice, it is 
challenging to use theoretical formulas to calculate. Therefore, 
empirical formulas are often used, related to the square of train 
speed. The general form of the procedure for calculating 
essential train resistance is: 

2

0
W A BV CV= + +   (kN)    (9) 

The primary resistance of the locomotive when operating 
traction and when running momentum is not equal, so for all 
types of locomotives, it is necessary to find a formula for 
calculating separately the two primary resistances, which are 

the unit essential resistance 
'
0ω  and the elemental resistance 

when running momentum 
'
0cdω . The general formula for 

calculating the unit resistance of the locomotive is: 

2

'

0

127.5
6.37 0.98.

0.1. 10 0.1. . 10

V CA V

q i q
ω

 
= + + +  

 
    (10) 

The basic formula for calculating resistance when running 
momentum (generally used for locomotives) is: 

' 2

0
2.4 0.1. 0.00035.

cd
V Vω = + +     (11) 

2) Secondary Drag 

Slope resistance is the principal source of secondary drag. 
Auxiliary resistance differs from elemental resistance: It is less 
impacted by the locomotive or wagon type. Because route 
circumstances determine it, the additional damper does not 
differentiate between locomotives and wagons but is computed 
per train. The unit ramp resistance is calculated as: 

( )
1000.sin

.

i
i

W

P Q g
ω θ= =

+
    (12) 

IV. SIMULATION RESULTS 

A control structure for traction motors driven by a 3-level 
T-type inverter is depicted in Figure 4, based on the above 
findings. The simulation results for electric traction motors 
using the 3-level T-type inverter and induction motor 
specifications are shown in Table IV. 

TABLE IV.  PARAMETER TABLE  

Parameters Symbol Value 

DC voltage dcU
 

1000 

Frequency of modulation fs 2000Hz 

Power dmP
 

270 kW 

Rated speed dmn
 

2880 rpm 

Rated voltage 
dm

U
 

400V 

Pole pair P 1 

Power factor cosφ 0.9 

Stator resistance Rs 0.0138Ω 

Rotor resistance Rr 0.00773Ω 

Rotor inductance Lr 0.0078H 

Mutual inductance Lm 0.0077H 

Voltage  750 VDC 

Maximum speed for the train  80km/h 
 

 

IM

A

B

C

Train 

resistances

Traction motor and load

sje
ϑ

3

2

tu tv tw

usαusd

usq

isα isu

SVM

isq

isd

sje
ϑ−

usβ

isv
isw

s
ϑ

Speed measurement

isβ

*ω

(-)

*

sq
i

*
sd
i

Rω

3-level T-type

W
h
e
e
l

Gear

I
R

MHTT

(-)

 

 

R
ψ

K

AC -

DC

E
L
E

C
T

R
I
C

 

G
R

I
D

Electric traction substation

+

-

Resistance brake DC link

RD

TMω

rd
ψ

*

dc
u

rd
ψ

*

rd
ψ

 
Fig. 4.  Control structure of traction motor fed by T-type 3-level inverter.



Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8321-8327 8325 
 

www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

To evaluate the effectiveness of the 3-level T-type inverter, 
the stator current controller will be selected as PI in the control 
structure, with the adjustment parameters chosen as:

0 .3 85; 0 .0 52
p i

K T= = . In addition, the speed controller is a PI 

controller with parameters 4 .1; 0.8 2
p i

K T= = . 

A. Case 1: Simulation and Εvaluation of the 3-Level T-Τype 
Ιnverter with Τwo Classic Levels at 50Hz with No Load 

The phase voltage response and THD are displayed in 
Figure 5. Figure 6 depicts the DC voltage response on the two 
capacitors of a T-type 3-levels inverter. Through the simulation 
results (Figure 5), it was found that the output voltage of the 3-
level T-type inverter has a wavelength with the three required 
voltage levels. In addition, the current is sinusoidal with lower 
THD (7.53%) than a two-voltage level inverter (THD = 
11.39%). In addition, the difference in DC voltage between the 
two capacitors is not significant, with the most notable change 
being Vcmax = 3V (0.6%), demonstrating that the balancing 
procedure is successful. Furthermore, owing to the voltage 

balancing technique on capacitors, SVM modulation 
considerably reduces the voltage imbalance on the two DC 
capacitors. Consequently, the SVM modulation produces 
acceptable voltage and current quality with a THD of 7.53%. 

B. Case 2: Simulation and Evaluation of Traction Drive 
System Using the 3-Level T-Type Inverter 

Traction electric motor will operate according to the 
following simulation scenario: 

• From t = 0.5s to t=2.3s, the IM is operating at pull process 
with: t0.5s =0 (km/h), t1s=50 (km/h), and t2.3s=73 (km/h). 

• From t = 2.3s to t = 4.5s, the IM is operating at coasting 
process with: t2.3s =73 (km/h), t4.5s =73 (km/h). 

• From t = 4.5s to t = 8s, the IM is operating at braking 
process with: t7s =13 (km/h) and t8s=0 (km/h). 

The simulation results are shown in Figure 7.

 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

 
(f) 

Fig. 5.  Line voltage and THD of the T-type multi-level inverter and the classic 2-level inverter. (a), (b) T-type 3-level voltage inverter, (c), (d) inverter 2 

voltage levels, (e) 3-phase current response using the 3-level T-type, (f) classic 2-level inverter current response. 



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www.etasr.com Ha et al.: T-Type Multi-Inverter Application for Traction Motor Control 

 

 
Fig. 6.  The DC voltage response on two capacitors of a T-type 3-level inverter. 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

Fig. 7.  (a) Speed response, (b) torque response, (c) single phase voltage, (d) TDH when Rr is constant. 

Figure 7 shows that the output voltage of the 3-level T-type 
inverter has a wavelength with the required 3 voltage levels. 
Furthermore, the current is sinusoidal, resulting in decreased 
THD. In addition, the torque and speed controllers have been 
effective. Thus, the actual speed response closely reflects the 
reference speed response with a rapid reset time. On the other 
hand, the torque controller provided the required torque at each 
operating moment of the railway traction drive. As a result, 
boosting the voltage level and applying a nonlinear control 
approach to the controllers is a challenge that has to be handled 
in the future to assure minimal THD and minor torque 
pulsation.  

V. CONCLUSION 

The design and assessment of the control structure of a 
traction motor FOC driven by a 3-level T-type inverter were 
effectively suggested in this study. According to the simulation 
results, the harmonic distortion diminishes as the voltage level 
rises, resulting in increased inverter performance. The design 
and computation of this multi-level inverter, on the other hand, 

is complicated, mainly when the number of voltage vectors 
grows fast with voltage level. Furthermore, since the torque 
response still exhibits strong torque pulsation, a more 
straightforward voltage modulation method is required when 
the power level rises and the torque pulsation reduces. This is a 
promising area for future research, as methods to enhance the 
control quality of traction powertrains are developed. 

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