Total Harmonic Distortion Analysis of a Four Switch 3-Phase Inverter Fed Speed Sensorless Control of IM Drives

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 4, No. 1, March 2014 pp. 81~90
ISSN: 2088-8694  81
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Total Harmonic Distortion Analysis of a Four Switch 3-Phase
Inverter Fed Speed Sensorless Control of IM Drives
ZMS El-Barbary*, HZ Azazi, MK Metwally **
* Departement of Electrical Engineering, Kaferelsheikh University, Egypt
** Departement of Electrical Engineering, Menoufiya University, Egypt
Article Info ABSTRACT
Article history:
Received Nov 2, 2013
Revised Feb 4, 2014
Accepted Feb 21, 2014
This paper investigates the performance of a Model reference adaptive
system (MRAS) based cost-effective drive system of an induction motor
(IM) for low-cost applications - high performance industrial drive systems. In
this paper, the MRAS is used as a speed estimator and the motor is fed from
a four-switch three-phase (FSTP) inverter instead of a conventional six-
switch three-phase (SSTP) inverter. This configuration reduces the cost of
the inverter, the switching losses, and the complexity of the control
algorithms and interface circuits, the proposed control approach reduces the
computation for real-time implementation. The robustness of the proposed
MRAS-based FSTP inverter fed IM drive is verified by Experimental results
at different operating conditions using digital signal processor (DSP1103) for
a 1.1 Kw motor. A performance comparison of the proposed FSTP inverter
fed IM drive with a conventional SSTP inverter system is also made in terms
of speed response and total harmonic distortion (THD) of the stator current.
The proposed FSTP inverter fed IM drive is found quite acceptable
considering its performance, cost reduction and other advantages features.
Keyword:
Four switch inverter
Induction motor
Sensorless speed control
Six switch inverter
Total harmonic distortion
Digital signal processor
Copyright © 2014 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
ZMS El-Barbary
Departement of Electrical Engineering,
Kaferelsheikh University,
Kaferelsheikh, Egypt,
Email : z_elbarbary@yahoo.com
1. INTRODUCTION
The induction motors are called the workhorse of the motion industry because they are most widely
used motors for appliances, industrial control, and automation. They are robust, reliable, simple, cheap and
available in all power ratings. The squirrel cage types of induction motors are very popular in variable-speed
drives. When AC power is supplied to an induction motor at certain specifications, it runs at its rated speed.
However, many applications need variable speed operations. Due to the progress in the field of
semiconductor field i.e. power electronics and Integrated circuits enables the application of induction motors
for high-performance drives. These power electronics not only control the motor’s speed, but can improve
the motor’s dynamic and steady state characteristics. In addition, this improves the energy savings and
reduces noise generation of the motor. A standard three-phase voltage source inverter utilizes three legs (six-
switch three-phase voltage source inverter or SSTPI), with a pair of complementary power switches per
phase. A reduced switch voltage source inverter (four switch three-phase voltage source inverter or FSTPI)
uses only two legs, with four switches. The Several papers report on FSTPI structure, Most of the reported
works on 4-switch, 3-phase (FSTP) inverter for machine drives did not consider the closed loop vector
control scheme, which is essential for high performance drives. Induction motor drives have been thoroughly
studied in the past few decades and many vector control strategies have been proposed, ranging from low
cost to high performance applications. Traditionally, 6-switch, 3-phase (SSTP) inverters hive been widely

 ISSN: 2088-8694
IJPEDS Vol. 4, No. 1, March 2014 : 81 – 90
82
utilized for variable speed IM drives. This involves the losses of the six switches as well as the complexity of
the control algorithms and interface circuits to generate six PWM logic signals [1].
In the past, researchers mainly concentrated on the development of the efficient control algorithms
for high performance variable speed IM drives However, the cost, simplicity and flexibility of the overall
drive system which become some of the most important factors did not get that much attention to the
researchers. That’s why, despite tremendous research in this area most of the developed control system failed
to attract the industry.
Usually, high performance motor drives used in robotics, rolling mills, machine tools, etc. require
fast and accurate response, quick recovery of speed from any disturbances and insensitivity to parameter
variations. The dynamic behavior of an AC motor can be significantly improved using vector control theory
where motor variables are transformed into an orthogonal set of d-q axes such that speed and torque can be
controlled separately. This gives the IM machine the highly desirable dynamic performance capabilities of a
separately excited DC machine, while retaining the general advantages of the ac over DC motors [2, 3].
In this paper, a cost effective FSTP inverter fed sensorless IM drive is developed. The four switches
makes the inverter less cost, less switching losses, less chances of destroying the switches due to lesser
interaction among switches, less complexity of control algorithms and interface circuits as compared to the
conventional SSTP inverter, the proposed control approach reduces the computation for real time
implementations. Furthermore, the use of speed sensorless for induction motor drives besides being reduce
bulky and increase the robustness, it reduce additional electronics, extra wiring, extra space. And reduce
extra cost to the drive system, Speed sensor, also, implies and careful mounting which detracts from the
inherent robustness of the drive.
The proposed sensorless control method verifies the validity of an MRAS-based FSTP inverter fed
IM drive system for cost reduction and other advantages such as reduced switching losses, reduced number
of interface circuits to supply logic signals for the switches, easier control algorithms to generate logic
signals. Thus, the main issue of this paper is to analysis a cost effective, simple and efficient high
performance IM drive.
The performance of a closed-loop vector control scheme of the proposed FSTP inverter fed IM
speed sensorless drive is implemented using digital signal processing DSP1103 interfaced with the
MATLAB/SIMULINK software. A comparison of the proposed FSTP inverter fed IM drive with a
conventional SSTP inverter system is also made experimentally in term of total harmonic distortion (THD) of
the stator current and speed response. The proposed inverter fed IM drive is found good considering its cost
reduction and other advantageous.
2. DRIVE SYSTEM
The control scheme of low cost induction motor drive consists of the modeling of the IM, inverter,
sensorless control and the controller, which are discussed in the following subsections:
A. Four Switch Three-Phase Inverter
This inverter is configured with four switches Q1, Q2, Q3 and Q4, respectively, as shown in figure 1.
Two output phases are taken from the inverter legs directly where the third output is taken from the midpoint
of the two capacitors. The inverter converts the DC-voltage to a balanced three-phase output with adjustable
voltage and frequency.

IJPEDS ISSN: 2088-8694 
Total Harmonic Distortion Analysis of a Four Switch 3-Phase Inverter Fed Speed … (ZMS El-Barbary)
83
Figure 1. Four switch three- phase inverter with IM
In the analysis, the inverter switches are considered as ideal power switches and it is assumed that
the conduction state of the power switches is associated with binary variables Q1 to Q4. Therefore, a binary
“1” will indicate a closed state, while “0” will indicate the open state. Pairs Q1 to Q3 and Q2 to Q4 are
complementary and as a sequence: (Q1 = 1-Q3, Q4 = 1-Q2). Two control possibilities exist to control the
four-switch bridge inverter, i.e., two- level current control to force the two controlled phases currents to
sinusoidal, or using PWM to control the voltages applied to the three-phase quasi- sinusoidally. The two-
level current control of the four-switch bridge inverter used to control the load current by forcing it to follow
a reference one. This is achieved by the switching action of the inverter to keep the current within the
hysteresis band. The load currents are sensed and compared with respective command currents using two
independent hysteresis comparators. The output signals of the comparators are used to activate the inverter
power switches.
This controller is simple and provides excellent dynamic performance. The modulated phases
voltages of four switch inverter are introduced as a function of switching logic NA, NA1, NB and NB1 of
power switches by the following relations [4].
1).2.NBNA
3
dc
E
.aV  4( (1)
1)..NBNA
3
dc
E
.
b
V  42( (2)
).2.NBNA
3
dc
E
.cV 22(  (3)
In matrix form,
4 2 1
2 4 1
3
2 2 2 1
     
            
           
a
dc
b
c
V NA
E
V NB
V
(4)
Where, NA1 and NB1 are complementary of NA and NB, Also, it will be assumed that a stiff voltage is
available across the two dc-link capacitors
B. Induction Motor Model
Squirrel-cage induction motor is represented in its d-q dynamic model. This model represented in
synchronous reference frame is expressed as follows;

 ISSN: 2088-8694
84
m m
s e e ee
r r qsqse
ee
m m dsdse
e s e e
r r qr
e
r m r e r m dr
r m e r m r
L L
R pL L p
L L IV
L L IV
L R pL p
L L0
RL 0 R pL ( )L0
0 RL ( )L R pL
 
 


 
                                    
     
(5)
The electromechanical equation is also given by;
r
e L r
d
T T J B
dt

    (6)
Where, the electromagnetic torque is expressed as;
e e e em
e qs dr ds qr
r
3 p L
T . (I I )
2 2 L
    (7)
C. Spees Estimator Based on Mras
Model Reference Adaptive Systems (MRAS) techniques applied in order to estimate rotor speed.
This technique is based on the comparison between the outputs of two estimators. The outputs of two
estimators may be (the rotor flux, back emf, or motor reactive power). The estimator that does not involve the
quantity to be estimated (The rotor speed ωr) is considered as the induction motor voltage model. This model
considered to be the reference model (RM). The other model is the current model, derived from the rotor
equation, this model considered to be the adjustable model (AM). The error between the estimated quantities
by the two models is used to drive a suitable adaptation mechanism which generates the estimated rotor
speed [5].
In this paper, the observer depends on the MRAS technique. The speed observer is based on stator
current and rotor flux as state variables [9]. The speed estimating procedures from the stator current error are
as follows:
First, from the induction motor equation the stator current is represented as:
1
1
ds dr r r qr r dr
qs qr r r qr r qr
i T T p
Lm
i T T p
Lm
   
   
    
    
(8)
Using Equation (8), and estimated instead of measured speed, the stator current is estimated as
1
1
ds dr r r qr r dr
qs qr r r qr r qr
i T T p
Lm
i T T p
Lm
   
   
    
    
 
 
(9)
Form the relationship between the real stator current and the estimated stator current, the difference
in the stator current is obtained as
 
 
r
ds ds qr r r
r
qs qs dr r r
T
i i
Lm
T
i i
Lm
  
  
  
  
 
 
(10)
In Equation (10), the difference of stator current is sinusoidal value because it is the function of
rotor flux. Multiplying by the rotor flux and adding them together;

85
 
 
2
2
( )
( )
r
qrds ds qr r r
r
drqs qs dr r r
T
i i
Lm
T
i i
Lm
   
   
  
  
 
 
(11)
By summing the above two equations.
 
2 2
( ) ( ) ( )r
qr drds ds qr qs qs dr r r
T
i i i i
Lm
          
  
(12)
Hence, the error of the rotor speed is obtained as follows:
2 2
[( ) ( ) ]/
( )
r r ds ds qr qs qs dr
r
qr dr
i i i i K
T
Where K
Lm
   
 
    
 
 
(13)
The right hand term seems as the term of speed calculation from adaptive observer, so the speed can be
calculated from the following equation [8]:
1
[( ( ) ( ) )
( ( ) ( ) )]
r p ds ds qr qs qs dr
I ds ds qr qs qs dr
K i i i i
K
K i i i i
  
 
    
  
 
 
(14)
Figure 2 shows The MRAS system.
Figure 2. Block Diagram for the Speed Estimation Procedure
C. Overall System Contrller
As shown in Figure 3. It incorporates the speed controller which receives the error signal between
the preset speed and the actual observed speed of the motor shaft and then generates the torque command (
*
eT ) through a proportional integral (PI) speed controller. This torque command produces the quadrature
current command *e
Iqs
in the synchronous reference frame (SYRF). The direct current *e
I
ds
is sets by the
rotor flux level *e
dr
 . This flux level is calculated according to the method described in [6]. The two current
commands are then transformed to the stationary reference frame (STRF) with the aid of the calculated
command angle (
*
e ). This command angle is calculated in such away that aligns the direct-axis of SYRF
with the rotor flux axis. The two stator current commands, e
qsI * and e*
ds
I in the SYRF are then transformed to
STRF and then transformed to three phase references current iar,ibr and icr. Only, two currents reference ari
and bri required for the hysteresis current controller that generates the switching function for the pulse width
modulated voltage source inverter.

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3. EXPERMENTAL RESULTS
To verify the validity of the proposed system, an induction motor vector control system was
constructed. Figure 4 shows a block diagram of the experimental system, which was composed of a DSP
board DSP 1103 [10], Two phases currents and voltages Ia , Ib and Va,Vb are sensed by Hall-effect current
and voltage sensors. These signals are fed to the DSP through the signal conditioning circuit. Also the speed
of the rotor is sensed by 2048 PPR incremental encoder for detecting the motor speed and fed to the encoder
interface on the DSP board. The control algorithm is executed by ‘simulink’ [11], and downloaded to the
board through host computer. The outputs of the board are logic signals, which are fed to the three-phase
inverter through driver and isolation circuits. The performance of the conventional six switch inverter based
sensorless IM drive system and proposed system is compared at different operating conditions with the
proposed MRAS-based FSTP inverter fed IM experimentally. The response due to a step change in the speed
command is used to evaluate the performance in terms of steady state errors and stability both at no load and
full load conditions. Figure 5.a shows the estimate and measured speed response with a command speed of
90 rad/sec at no load at t=0.9 second, the speed reference has been changed to 120 rad/sec. It can be seen that
the rotor speed is accelerated smoothly to follow its reference value with nearly zero steady state error.
Figure 5.b shows the motor phase current and its reference whereas Figure 5.c shows the motor three phase
current . The motor current increase with increasing speed and return back to its normal value. These results
show a good correlation between the estimated speed signal and its corresponding measured as well as
reference speed signals. The total harmonic distortion (THD) of ia is found 27.0386% as shown in Figure 5(d)
MRAS Speed
Estimator
Figure 3. Block diagram for a vector-controlled induction motor based on speed estimation
Figure 4. Experimental-setup
Motor current

87
(a)
(b)
(c)
(d)
Figure 5. Experimental results of FSTP Drive at no load (a) Motor Speed; (b) Phase current and its reference
(c) Three-phase current (d) THD of ia
(a) (b)
(c)
(d)
Figure 6. Experimental results of SSTP Drive at no load (a) Motor Speed; (b) Phase current (c) Three-phase
current (d) THD of ia
Estimated speed
Measured speed
Reference speed
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
MagnitudeinAmp
Harmonic Number
Reference speed Estimated speed
Measured speed
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
MagnitudeinAmp
Harmonic Number

 ISSN: 2088-8694
88
(a)
(b)
(c)
(d)
Figure 7. Experimental results of FSTP Drive at full load (a) Speed; (b) Phase current and its reference (c)
Three-phase current (d) THD of ia
In order to provide a fair comparison, the speed responses of the conventional SSTP inverter fed IM drive at
identical conditions are shown in Figure 6. It is seen in Figures 6.a that the estimated and measured speed
follows the reference speed. Figure 6.b shows the motor phase current whereas figure 6c shows motor three
phase current for the step change in speed command. The total harmonic distortion (THD) of ia is found
24.44% as shown in Figure (6d)
(a)
(b)
(c)
(d)
Figure (8) Experimental results of SSTP Drive at full load (a) Speed; (b) Phase current and its reference (c)
Three-phase current (d) THD of ia
Estimated speed
Measured speed
Reference speed
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MagnitudeinAmp
Harmonic Number
Reference speed
Estimated speed
Measured speed
Reference speed
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MagnitudeinAmp
Harmonic Number

89
Another case to study the drive response. The drive is subjected to step change in the speed reference at full
load. Figure 7 shows the drive response when motor fed from FSTP inverter. The motor is running at 90
rad/sec, At t=0.9 second, the speed reference has been changed to 120 rad/sec. it shows that perfect speed
tracking with zero steady state error. The response indicates how well the controller succeeds in forcingthe
actual rotor speed to follow the desired reference trajectory. With nearly zero steady-state error. Figure 7.b
shows motor phase current, whereas figure 7c shows the motor three phase current, it increases with step up
of speed reference. The total harmonic distortion (THD) of ia is found 23.5169% as shown in figure 7d. Also,
Figures 8 shows the drive response when the motor is fed from SSTP conventional inverter at identical
conditions. Figure 8a shows that the estimated and measured speed follows the reference speed with nearly
zero steady state error. Figure 8.b shows the motor phase current, whereas figure 8c shows the motor three
phase currents for the step change in speed command. The total harmonic distortion (THD) of ia is found
20.2548%. However, after considering all the results, it is seen that the proposed inverter based drive phase
currents suffers from slight unbalance in the which cause relatively higher speed vibrations as compared to
the conventional 6S3P inverter fed drive. Also, the high switching of motor current makes the estimated
speed signal is very noisy in the proposed FSTP drive. The total harmonic distortion of the proposed inverter
is slightly increased as compared to conventional inverter. It is found that the performance of the proposed
inverter based drive is much closer to that of the conventional inverter and can successfully perform
sensorless control.
4. CONCLUSION
A cost-effective FSTP inverter fed IM drive using an MRAS has been implemented. The proposed
MRAS-based FSTP inverter fed IM drive system reduces the cost of the inverter, the switching losses and the
complexity of the control algorithms as compared with the conventional SSTP inverter based drive. The
vector control scheme has been incorporated in the integrated drive system to achieve high performance. The
MRAS as a speed estimator verified the robustness of the proposed approach. The performances of the
proposed MRAS-based FSTP inverter fed IM drive has been investigated. A comparison of performances for
the proposed FSTP inverter fed IM drive with a conventional SSTP inverter fed IM drive has also been made
in terms of the speed and total harmonic distortion under identical operating conditions. The proposed FSTP
inverter fed IM drive has been found robust and acceptable for low-cost applications such as automotive and
home appliance.
REFERENCES
[1] Jin-Su Jang, Byoung-Gun Park, Tae-Sung Kim, Dong Myung Lee, Dong-Seok Hyun. "Sensorless Control of Four-
Switch Three-Phase PMSM Drive Using Extended Kalman Filter". IEEE. 2008: 1368-1372.
[2] MN Uddin, TS Radwana, and MA Rahman. “Performance analysis of a 4-switch, 3-phase inverter based cost
effective IM motor drives”. Electrical and Computer Engineering, Canadian Conference. 2004: 85–88.
[3] Nasir Uddin, TS Radwan, and MA Rahman. “Performance Analysis of a Cost Effective 4-Switch 3-Phase Inverter
Fed IM Drive”. Iranian Journal of Electrical and Computer Engineering. Summer-Fall. 2006; 5(2).
[4] CB Jacobina, ERC da Silva, AMN Lima, and RLA Ribeiro. “Vector and scalar control of a four switch three phase
inverter”. in Conf. Rec., IEEE-IAS Annu. Meeting. 1995: 2422–2429.
[5] J Holtz. “Sensorerless Control of Induction Motor Drives”. Proceedings of IEEE. 2002; 90(8): 1359-1394.
[6] CB Jacobina, MB de Rossiter Correa, ERC da Silva, and AMN Lima. “A General PWM Strategy for Four-Switch
Three-Phase Inverters”. IEEE Trans. Energy Conversion. 2006; 21(4): 832-838.
[7] J Klima. “Analytical Investigation of an Induction Motor Fed from Four-Switch VSI with a New Space Vector
Modulation Strategy”. IEEE Trans. Power Electron. 2006; 21(6): 1618-1617.
[8] Nalin Kant Mohanty, Ranganath Muthu, Microcontroller M.” Based PWM Controlled Four Switch Three Phase
Inverter Fed Induction Motor Drive”. Serbian Journal of Electrical Engineering. 2010; 7(2): 195-204.
[9] Chul-Woo Park, Woo-Hyen Kwon. “Simple and robust speed sensorless vector control of induction motor using
stator current based MRAC”. Electric Power Systems Research. 2004; 71: 257–266.
[10] dSPdCE. "Digital Signal Proccssingmd Control Engineering”. Manual Guide. GmhH. Paderhom~ Germany, 2011.
[11] Matlab/Simulink Toolbox User’s Guide. The Mathworks Inc., Natick, MA, USA. 1998.

 ISSN: 2088-8694
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APPENDIX
Machine parameters of the applied induction machine
Rated power 1.1 kw
Rated load torque 7.5 N.m.
No. of poles 4
Stator resistance 7.4826 ohm
Rotor resistance 3.6840 ohm
Rotor leakage inductance 0.0221 H
Stator leakage inductance 0.0221 H
Mutual inductance 0.4114 H
Supply frequency 50 Hz
Motor speed 1500 r.p.m.
Supply voltage 380 volts
Inertia 0.02 kg.m2
List of Symbols;
2L mL L s L r
 
, r
r
r
L
T
R
 ,
2
m
s r
L
1-
L L
 
Vqse,Vdse qe-de –axis stator voltage
Iqse , Idse qe-de –axis stator current
qse , dse qe-de –axis stator flux linkage
Rs , Rr stator and rotor resistances
J, B moment of inertia and viscous friction coefficients
Ls, Lr, Lm stator, rotor and mutual inductances

Total Harmonic Distortion Analysis of a Four Switch 3-Phase Inverter Fed Speed Sensorless Control of IM Drives

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