FOC of SRM using More Efficient DC-DC Converter Topology

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 8, No. 2, June 2017, pp. 534~547
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v8i2.pp534-547  534
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
FOC of SRM using More Efficient DC-DC Converter Topology
Emad S. Abdel-Aliem
Departement of Electrical Engineering, Shoubra Faculty of Engineering, Benha University, Egypt
Article Info ABSTRACT
Article history:
Received Feb 16, 2017
Revised Apr 16, 2017
Accepted May 1, 2017
Numerous studies had been made to improve the switched reluctance motor
operation depend on the modification of the machine design, proposing the
converter designs and/or applying a suitable control method. This paper
introduces the field orientation control method for that motor using a simple
and very efficient DC-DC converter topology. This control method is
presented by two techniques; first technique is the advance of the turn-on
switching angle and the other technique is the retard/delay of the turn-off
switching angle. Instantaneous and average motor characteristics are
obtained using Matlab/Simulink software package. Comparison between the
simulation results presented using two converter types. A precise speed and
torque control are obtained. The average total torque per current is
maximized.
Keyword:
Advance turn-on
Angle control
FOC
Retard/Delay turn-off
SRM Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Emad S. Abdel-Aliem,
Department of Electrical Engineering,
Shoubra Faculty of Engineering,
Benha University, 108 Shoubra Street, Cairo, Postal code: 11241, Egypt.
Email: emad.sami@feng.bu.edu.eg
1. INTRODUCTION
The switched reluctance motor (SRM) is being used in various number of applications because of it
has many merits over the other motor types. The SRM has a simple and robust construction. However, it
basically generates large torque ripples compared with the other types of brushless DC motors. For that
reason, to improve its operation and reducing the torque ripples, a development in its converter construction
and/or a best control strategy is used [1]-[6], [37]-[38].
One of the main approaches of the research in SRM drives is the converter design. The operation
and the cost of SRM drive system is mainly affected by the performance of the motor converter [7,8]. Many
converter topologies have emerged through continued researches by reducing the number of switches in the
converter and also getting faster switch commutation time [3,9-10]. This leads to a simple drive system and
enables significant energy savings [11]-[14]. A high performance SRM drive is mainly characterized by
minimization of the torque ripples and maximization of the motor efficiency and the torque per current
[6],[15]. This criterion can be realized by optimizing the control parameters of the motor such as supply
voltage, current level, turn-on, turn-off and the dwell angle [16]-[20].
A closed loop control with a simple DC-DC converter construction [21] for a 3-phase 6/4 SRM with
Field Orientation Control (FOC) (known as some times; the switching angle control) method is introduced in
this research to get the most efficient operation over the entire range operation of the SRM.
The complete block control diagram for a 3-ph 6/4 SRM drive system using FOC is shown in
Figure 1. A standard DC source of 220V is used with the 3-ph DC-DC converter. The speed sensor is an
integral part of the SRM drive system, may be optical encoders, resolver or hall-effect sensor [22]-[24] is
mounted on the motor shaft to determine the actual rotor speed. A speed-angle converter can used to convert
the measured speed into actual measured angle (θm) for comparison with the turn-on (θon) angle and the turn-
off (θoff) angle to excite and commutate the phase windings. A digital controller named as a switching angle

IJPEDS ISSN: 2088-8694 
FOC of SRM using More Efficient DC-DC Converter Topology (Emad S. Abdel-Aliem)
535
controller [25] is used to synchronize the switching angles with their respective positions. This angle
controller regulates the angles at which excitation of motor phases is achieved. So, it allows the rotor to
continuously rotate, producing torque in accordance with the load being applied. The gate drive circuit
(triggering circuit) contains integrated circuit components must be used between the angle controller and the
power converter. The control logic signals are too small to drive the power switches of the converter. So, the
gate drive circuit is used to amplify the control logic signals to the value of current levels required for
switching the power converter, and also acts as a good isolation circuit (because it contains opto-coupler)
between controller circuit and converter [26].
Figure 1. Main components of SRM drive system
This research is organized as follows. The operation of SRM and its mathematical model are
reviewed in Section 2. DC-DC converter topology is presented in Section 3. Simulation results using FOC
are illustrated in Section 4. The research conclusions are given in Section 5.
2. OPERATION AND MATHEMATICAL MODEL OF SRM
Due to the advances in power electronics, sensors and controllers in the recent years, the SRM has
gained a great of commercial and industrial interest [27]. It has a simple and robust construction due to the
magnetic circuitry of the motor neither requires permanent magnets nor windings in the rotor. The stator has
concentrated coils around the poles that are excited sequentially through DC voltage pulses. The motor has
salient poles on the stator and also on the rotor, so, it is named as a doubly salient pole machine [27,28]. The
term “switched reluctance” tends to that the reluctance of the machine is switched. The term magnetic
“reluctance” depends on the rotor position and the term “switched” refers to the electronic commutation of
the electrical phases by means of a power electronics converter [28].
(a) unaligned position (b) aligned position
Figure 2. Unaligned and aligned positions for phase-A of a 3-phase 6/4 SRM
The SRM torque production is based purely on the variation of the magnetic reluctance. The
magnetic circuits of the motor are symmetrical and have almost zero mutual flux linkages among stator

 ISSN: 2088-8694
IJPEDS Vol. 8, No. 2, June 2017 : 534 – 547
536
windings even under saturated conditions. The self inductance of the phase windings only is responsible for
production of torque [28]. Figure 2 shows a typical three-phase machine configuration, Nph = 3. The machine
has six stator poles Ns= 6 and four rotor poles NR = 4, this configuration is known as a 6/4 SRM. From a
magnetic perspective, each phase of the 6/4 machine has two magnetic poles per phase, i.e., one pole pair,
given that diametrically opposed coils are electrically connected in series or in parallel. For example, the
phase A is made up of concentrated coils on poles A and A’. The rotor position shown in Figure 2a is called
the unaligned position with respect to phase A–A’, this unaligned position for the phase A is the position of
the largest magnetic reluctnace between stator and rotor poles. If the phase A is excited, a magnetic flux path
is formed by the two stator pole A–A’, as in Figure 2b, which is the position of the smallest magnetic
reluctance [29]. The complete mathematical model of the SRM in [21] is a set of differential equations which
are obtained using standard electromagnetic theory. These differential equations are as follows:
 



d
i
d
R
i
U j
j
j
j
j
,

 (1)
Where Uj denotes the phase voltage, ij denotes the phase current, Rj denotes the phase resistance, j is the
active phase, and λj (ij,θ) is the flux linkage. Equation (1) can be rewritten as:
   
, ,
j j j j
j
j j j
i i
di d
U i R
i dt dt
    

 
  
 
(2)
The flux linkage in an active phase is given by the product of the self-inductance and the instantaneous phase
current as follows:
    j
j
j
j
j i
i
L
i 
 

 ,
, (3)
By substituting from Equation (3) into Equation (2) gives:
  










,
j
j
j
j
inc
j
j
j
j
i
L
i
dt
di
L
R
i
U (4)





 v
j
inc
j
j
j K
dt
di
L
R
i (5)
       
i
i
L
i
i
L
i
i
i
L
i
i
L j
j
j
j
j
j
j
j
j
j
inc
j
















 ,
,
,
, (6)
dt
d
  (7)
Where Ljinc is the phase incremental inductance, Kv is the current-dependent back-emf coefficient, and ω is
the rotor angular speed. Rearranging Equation (4) gives:
 














 


,
1 j
j
j
j
j
j
inc
j
j i
L
i
R
i
U
L
dt
di (8)
   





L
K
J
j
j T
B
i
T
dt
d
J
dt
d
J 


 
1
2
2
, (9)
Where J and B are the moment of inertia and the viscous friction coefficient, respectively; and TL is the load
torque. Equations (7), (8) and (9) represent the complete mathematical model of the SRM in the case of non-
linear modeling for operation of the motor in a real mode. With the non-linear operation; the shape of the
inductance is sinusoidal depends on the rotor position, the phase current, and the motor geometry.

537
The static SRM characteristics can be represented basically via two methods. The first is to plot the
variation of phase inductance with respect to rotor position at different phase currents; this way is used in this
research. The second way is to plot the variation of phase flux linkage with rotor position and phase currents.
3. DC-DC CONVERTER TOPOLOGY
The SRM cannot run directly from AC or DC source; unlike induction motors or DC motors. So,
a power electronics DC-DC converter must be located between the motor and the source. The purpose of
the power converter circuit is to provide an increasing and decreasing the current supplied to the phase
winding in order to produce a continuous motion [28]. In the feedback path between the motor and the power
converter, a control circuit is used to monitor the current and the position feedback in order to produce the
correct switching signals for the power converter for matching the demands placed on the drive by the user.
Since the torque developed by the SRM not depends on the current polarity, the motor can operate
based on the principle of unipolar current. The current therefore can be supplied to the phase winding with
only one switch per phase connected in series with the winding, as shown in Figure 3 [21]. By turning on and
off this switch; the flow of the phases current can be regulated. The best feature for that converter is that each
phase contains only one switch. This converter topology can be used with a three phases SRM and can be
simply modified to suit another type of SRM has different number of phases. Since the mutual coupling
between phases is almost negligible, the stored magnetic field energy can create problem during
commutation of the phase. The stored magnetic field energy has to be provided a path during commutation
(as shown in Figure 3, a freewheeling diode is used in each phase): otherwise excessive voltage can develop
across the winding and may result in failure of the semiconductor switch that connected in series with the
phase winding [30]-[32].
Figure 3. Simple DC-DC converter for 3-phase, 6/4 SRM
As shown in Figure 3, the power switches can be protected using RC snubber circuit. This snubber
circuit protects the switch from a large di/dt during turn-on and large dv/dt during turn-off. Also the snubber
circuit provides an effective means of transferring the switching losses from the switch to the snubber
resistor, leading to a lower junction temperature rise and better thermal management for the switch and also
the no recover of energy to DC source not cause reduction of the overall efficiency of the drive drive
[33]-[34].
The diode Ds is used to safe the DC source from the recover energy of each motor phase. No
reduction of the overall efficiency of the motor drive because there is no recover of energy to the DC source.
The steady state of motor characteristics is reaches faster than using the traditional DC-DC converters
[35]-[36].
4. SIMULATION RESULTS USING FOC
The torque of SRM has a strong pulsations at the commutation intervals because the two adjacent
phases produce additive torques. Therefore, the FOC can be used to control the SRM drive. This control
strategy is based on controlling the values of the switching angles and the dwell angle. The machine
efficiency and the average total torque per current will maximize by using this control strategy. So, the FOC

 ISSN: 2088-8694
538
is used to control the dwell angle and the input source voltage instantaneously in order to obtain a precise
speed control.
In the real control system, control of the switching angles can be realized by a simple feedback
circuit using detecting position sensor on the motor shaft as shown in Figure 4. The switching angle
controller in that figure regulates the motor performance via integration of the motor speed to produce the
measured position of the rotor by comparing the measured rotor position with the switching angles θon and
θoff. In order to produce the gate signals of the converter switches. A gate drive circuit must be used between
the angle controller and the converter, it receives the logic signals that has a low level from the angle
controller and transmit these signals but with a high level to the converter. In other means; the gate drive
circuit is used to isolate the control circuit from the power circuit.
Figure 4. Complete block control diagram for 3-ph 6/4 SRM drive system using Field Orientation Control
The back-emf in the motor becomes significant as the motor speed increases. It is necessary to
retard the turn-off angle or advance the turn-on angle in order to reach the reference current before the poles
overlap. One reason of the torque ripple is that the negative torque due to the tail current (which will be
solved using the FOC method). Also, the decay of current in the demagnetizing case can be enhanced
through decaying it in fast time using FOC. In this part, the motor firing/switching angles change by the
means of a software to obtain the best values for these angles.
The block control diagram of Figure 4 can be simulated using Matlab/Simulink software package.
The data required for that motor drive system obtained from the APPENDIX. The simulation results obtained
for no-load, θon = 40o
, and θoff =70o
.
4.1. Instantaneous Characteristics with Advance Turn-On
The instantaneous phase current versus rotor position is shown in Figure 5. The principle of
increasing the advance of the turn-on angle θon (i.e., decreasing the value of the turn-on angle) is to increase
the average motor total torque. The phase current IA has θon = 40o
, θoff = 70o
and advance for θon by a step
of 2o
. The phase current IA has three cases for advance of θon. The case of the solid line (where, θon = 40o
)
there is no advance for the phase current. The case of the dashed line (where, θon = 38o
) an advance by 2o
is
obtained. The case of the dotted line (where, θon = 36o
), the phase current has an advance by 4o
. Then, when
we see deeply, the phases current increases as the turn-on angle is advanced, also, the motor total current or
the source current increases (but this is undesirable) to produce an increase in the average total torque as
shown in Figure 5 and Figure 6 respectively.

539
Figure 5. Instantaneous motor phases current versus rotor position for advance turn-on
As shown in Figure 5 the phase current increases with increasing the advance turn-on, because the
conduction period of the phase current increases as the advance increases. But, there is a limit of increasing
the phase current to be not greater than a maximum allowable range. This maximum allowable current occurs
when the source current has the value 1.25 of the rated source current. For that converter design; the average
steady state phase current at θon = 40o
, θoff = 70o
equals to 0.42A, but for the asymmetric bridge at the same
switching angles, the average steady state phase current equals 0.9A [35].
Figure 6. Instantaneous source current versus rotor position for advance turn-on
The instantaneous total torque versus rotor position is shown in Figure 7 the total torque increases as
the advance of the turn-on angle increases, also, if there is a negative torque found, the advance can eliminate
it. The average total torque at θon = 40o
and θoff = 70o
equals 4.279Nm but in the asymmetric bridge converter
equals 2.160Nm [35].
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Rotor Position,  (deg)
Instantaneous
Phase
Current,
I
ph
(A)
I
C
I
A I
B
0 100 200 300 400 500 600 700 800 900
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Instantaneous
Source
Current,
I
s
(A)
on
= 40o
on
= 38o
on
= 36o
on
= 34o
off
= 70o

 ISSN: 2088-8694
540
Figure 7. Instantaneous motor total torque versus rotor position for advance turn-on
4.2. Instantaneous Characteristics with Retard Turn-Off
On the other hand, the principle of retarding the turn-off angle (i.e., increasing the value of the
turn-off angle θoff) based on increasing the conduction period between the switching angles for increasing the
average motor total torque. The instantaneous phase’s current versus rotor position for retard the turn-off is
shown in Figure 8. The phase current IA has constant angles θon = 40o
, θoff = 70o
and retard for θoff by step
of 2o
. The phase current IA has three cases for retad/delay of θoff. The case of solid line there is no delay
(where, θoff = 70o
). The case of the dashed line a delay by 2o
(where θoff = 72o
) is obtained. The case of the
dotted line (where, θoff = 74o
) the phase current has a delay by 4o
. Then, when we see deeply, the phases
current decreases as the turn-off angle is delayed further, also, the motor total current decreases (this is
desirable); but the motor total torque decreases as the retarding/delaying of the turn-off angle increases, as
shown in Figure 9 and Figure 10 respectively.
Figure 8. Instantaneous motor phases current versus rotor position for retard turn-off
As shown in Figure 7 and Figure 10; the motor total torque at using the retarding of the turn-off
angle has a less negative vaule compared with using advancing of the turn-on angle. Also as shown in
Figure 5 and Figure 8; the average value of motor phase current increases as the advance turn-on increases
but decreases as the retard of the turn-off increases. Similarly, as presented in Figure 6 and Figure 9 the
0 100 200 300 400 500 600 700 800 900
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
Instantaneous
Motor
Total
Torque,
T
e
(Nm)
on
= 40o
on
= 38o
on
= 36o
on
= 34o
off
= 70o
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Instantaneous
Phase
Current,
I
ph
(A)
IB
IC IA

541
instantenous source current increases as advance turn-on increases, but decreases as the retard turn-off
increases.
Figure 9. Instantaneous source current versus rotor position for retard turn-off
Figure 10. Instantaneous motor total torque versus rotor position for retard turn-off
4.3. Average Characteristics with Advance Turn-On
For easy comparison between motor characteristics at using the advance turn-on and the retard
turn-off; the motor average characteristics are introduced. The average source current versus rotor position at
using advance turn-on, is shown in Figure 11; at constant the turn-off angle (say θoff = 70o
), as the switching
turn-on angle decreases the average source current increases. Also; as shown in Figure 12; at constant turn-
off angle (say, θoff = 70o
) as the switching turn-on angle decreases, the average total torque increases. In other
words, for constant turn-off angle; the average source current or average total torque increases as the advance
of the turn-on angle increases.
From Figure 11 and Figure 12; more advancing of turn-on angle produces large increase in the
average source current and a small increase in the average total torque, so, this will lead to decrease in the
average total torque per current as presented in Figure 13. Also, as shown in Figure 14, increasing the
advance of turn-on angle leads to increases of motor speed.
0 100 200 300 400 500 600 700 800 900
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Instantaneous
Source
Current,
I
s
(A)

off
= 70
o

off
= 72o

off
= 74
o

off
= 76o

on
= 40o
0 100 200 300 400 500 600 700 800 900
0
2.5
5
7.5
10
12.5
15
17.5
20
Instantaneous
Motor
Total
Torque,
T
e
(Nm)

off
= 70
o

off
= 72o

off
= 74
o

off
= 76o

on
= 40o

 ISSN: 2088-8694
542
Figure 11. Average source current versus rotor position for advance turn-on
Figure 12. Average total torque versus rotor position for advance turn-on
Figure 13. Average total torque per current versus rotor position for advance turn-on
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
0.5
1
1.5
2
2.5
3
3.5
Average
Source
Current
(A)
A : on
=32o
B : on
=34o
C : on
=36o
D : on
=38o
E : on
=40o
F : on
=42o
advance
increases
off
= 70o
A
B
C
D
E
F
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
1
2
3
4
5
6
7
8
9
10
Average
Total
Torque
(Nm)
A : 
on
=32o
B : 
on
=34o
C : on
=36o
D : on
=38o
E : 
on
=40o
F : 
on
=42o
A
B
C
D
E
F
advance
increases

off
= 70o
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Average
Total
Torque
per
Current
(Nm/A)
A : on
=32o
B : on
=34o
C : on
=36o
D : on
=38o
E : on
=40o
F : on
=42o
A
B
C
D
F
E
advance
increases
off
= 70o

543
Figure 14. Motor speed versus rotor position for advance turn-on
4.4. Average Characteristics with Retard Turn-Off
After presentation of average characteristics with the change of the rotor position at using advance
turn-on angle; the average characteristics for the retard turn-off is presented in this subsection. As shown in
Figure 15 for a constant turn-on angle (say, θon = 40o
), as the value of the turn-off angle increases, the
average source current increases. This means that, the average source current increases as the retard of the
turn-off angle increases. Similarly, as shown in Figure 16, the average total torque increases as the retard of
the turn-off angle increases.
Figure 15. Average source current versus rotor position for retard turn-off
As shown in Figure 17 the average total torque per current versus rotor position is presented at using
a constant turn-on angle and applying variation for the turn-off angle. The torque per current increases from
θoff = 64o
until 68o
and decreases from θoff = 70o
until 74o
. But this is not standard case for variation of the
turn-off angle. Also, as shown in Figure 18 increase the retarding of the turn-off angle, this leads to an
increase in the motor speed.
In order to the motor phases respond to continuous drawing of a current from the source, there is
a maximum allowable range of θon and θoff for 3-ph 6/4 SRM. The motor average characteristics values for
this range will be stored in the following tables. These characteristics obtained at steady state speed by
applying a rated source voltage of 220V.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
400
800
1200
1600
2000
2400
Motor
Speed,
n
(rpm)
A : on
=32o
B : on
=34o
C : on
=36o
D : 
on
=38o
E : 
on
=40o
F : 
on
=42o
advance
increases
F
E
D
C
B
A
off
= 70o
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
Average
Source
Current
(A)
A : 
off
=64o
B : 
off
=66o
C : 
off
=68o
D : off
=70o
E : 
off
=72o
F : 
off
=74o
A B C D E F
on
= 40o
retard
increases

 ISSN: 2088-8694
544
Figure 16. Average total torque versus rotor position for retard turn-off
Figure 17. Average total torque per ampere versus rotor position for retard turn-off
Figure 18. Motor speed versus rotor position for retard turn-off
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
1
2
3
4
5
6
7
8
9
Average
Total
Torque
(Nm)
A : 
off
=64o
B : off
=66o
C : off
=68o
D : 
off
=70o
E : 
off
=72o
F : off
=74o
A B C D E F
retard
increases

on
= 40o
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Average
Total
Torque
per
Current
(Nm/A)
A : 
off
=64o
B : 
off
=66
o
C : 
off
=68o
D : off
=70o
E : off
=72
o
F : 
off
=74o
A B CD E,F
on
= 40o
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
250
500
750
1000
1250
1500
1750
2000
2250
Motor
Speed,
n
(rpm)
A : off
=64o
B : off
=66o
C : off
=68o
D : off
=70o
E : off
=72o
F : off
=74o
retard
increases

on
= 40o
A
B
C
D
E
F

545
The average source current is shown in Table 1 at different values of turn-on and turn-off angles to
obtain the optimum performance ch/s for the drive system at no-load; where the minimum allowable limit
and the maximum allowable limit of the switching angles are presented. From Table 1 adjustment of the
switching angles (turn-on angle of 60o
and turn-off angle of 64o
) is presented in order to get a minimum
average source current of 0.107A (at using the asymmetric bridge converter equals 0.152A) [36]. But in
Table 2 the maximum average total torque is 4.552Nm at turn-on angle of 36o
(at
using the asymmetric bridge converter equals 2.224Nm) [36]. But this value of the torque not present
optimum machine performance because the optimum performance depends on the maximum torque per
current is 6.016Nm/A at turn-on angle of 60o
(at using the asymmetric bridge
converter equals 2.224Nm) [36] as presented in Table 3. The motor speed at all switching angles is presented
in Table 4.
Table 1. The Average source current of proposed converter in (Ampere)
θoff
θon
64▫
66▫
68▫
70▫
72▫
74▫
76▫
78▫
80▫
82▫
84▫
86▫
88▫
90▫
36▫
1.090 1.120 1.156 1.199 1.247 1.301 1.361 1.428 1.501 1.582 1.672 1.773 1.885 2.013
38▫
0.970 1.002 1.039 1.081 1.128 1.181 1.238 1.302 1.373 1.451 1.537 1.633 1.742 1.865
40▫
0.857 0.891 0.929 0.971 1.017 1.067 1.124 1.187 1.255 1.330 1.413 1.507 1.613 1.733
42▫
0.753 0.787 0.826 0.868 0.914 0.964 1.019 1.080 1.146 1.220 1.301 1.393 1.496 1.615
44▫
0.656 0.692 0.730 0.773 0.818 0.868 0.922 0.981 1.046 1.118 1.198 1.288 1.390 1.508
46▫
0.566 0.603 0.643 0.684 0.730 0.779 0.832 0.890 0.954 1.025 1.104 1.193 1.294 1.411
48▫
0.485 0.522 0.562 0.603 0.648 0.696 0.748 0.806 0.869 0.939 1.016 1.105 1.205 1.322
50▫
0.409 0.448 0.487 0.529 0.573 0.620 0.672 0.729 0.790 0.859 0.936 1.023 1.123 1.240
52▫
0.339 0.379 0.419 0.460 0.504 0.550 0.600 0.656 0.717 0.785 0.861 0.948 1.048 1.165
54▫
0.276 0.316 0.356 0.397 0.440 0.485 0.535 0.589 0.650 0.716 0.791 0.877 0.977 1.095
56▫
0.216 0.257 0.297 0.338 0.380 0.424 0.474 0.527 0.586 0.652 0.726 0.811 0.911 1.030
58▫
0.160 0.201 0.243 0.283 0.323 0.368 0.416 0.469 0.526 0.591 0.664 0.748 0.848 0.968
60▫
0.107 0.149 0.191 0.231 0.272 0.315 0.362 0.413 0.469 0.534 0.605 0.689 0.789 0.910
Table 2. The Average total torque of proposed converter in (Newton.meter)
θoff
θon
64▫
66▫
68▫
70▫
72▫
74▫
76▫
78▫
80▫
82▫
84▫
86▫
88▫
90▫
36▫
3.608 3.845 4.042 4.202 4.328 4.424 4.492 4.534 4.552 4.545 4.517 4.465 4.392 4.297
38▫
3.457 3.693 3.889 4.049 4.177 4.275 4.344 4.387 4.406 4.401 4.373 4.323 4.250 4.155
40▫
3.283 3.518 3.716 3.878 4.008 4.109 4.181 4.226 4.247 4.244 4.218 4.169 4.098 4.003
42▫
3.084 3.321 3.521 3.687 3.821 3.925 4.000 4.049 4.073 4.073 4.049 4.003 3.933 3.841
44▫
2.862 3.101 3.305 3.476 3.615 3.724 3.804 3.857 3.885 3.888 3.868 3.824 3.757 3.667
46▫
2.617 2.860 3.070 3.247 3.392 3.506 3.592 3.651 3.684 3.692 3.676 3.635 3.571 3.483
48▫
2.355 2.603 2.819 3.003 3.156 3.277 3.369 3.434 3.473 3.485 3.473 3.437 3.376 3.289
50▫
2.080 2.333 2.555 2.748 2.908 3.037 3.138 3.209 3.253 3.272 3.265 3.231 3.174 3.090
52▫
1.792 2.050 2.284 2.484 2.652 2.791 2.899 2.978 3.029 3.053 3.051 3.024 2.969 2.888
54▫
1.500 1.763 2.002 2.212 2.393 2.540 2.657 2.744 2.803 2.834 2.838 2.814 2.764 2.687
56▫
1.204 1.475 1.720 1.940 2.127 2.287 2.413 2.509 2.576 2.613 2.624 2.606 2.560 2.486
58▫
0.909 1.182 1.435 1.661 1.862 2.031 2.168 2.273 2.350 2.395 2.412 2.400 2.359 2.289
60▫
0.613 0.889 1.151 1.385 1.596 1.775 1.923 2.039 2.124 2.177 2.202 2.198 2.162 2.094
Table 3. The Average total torque per mpere of proposed converter in (Newton.meter/Ampere)
θoff
θon
64▫
66▫
68▫
70▫
72▫
74▫
76▫
78▫
80▫
82▫
84▫
86▫
88▫
90▫
36▫
3.309 3.432 3.494 3.504 3.470 3.400 3.300 3.176 3.032 2.873 2.700 2.519 2.330 2.135
38▫
3.564 3.687 3.744 3.746 3.703 3.621 3.508 3.369 3.210 3.035 2.846 2.647 2.440 2.228
40▫
3.829 3.949 4.002 3.996 3.940 3.849 3.720 3.561 3.385 3.191 2.984 2.766 2.541 2.310
42▫
4.100 4.217 4.264 4.248 4.181 4.070 3.926 3.750 3.553 3.339 3.112 2.874 2.629 2.379
44▫
4.366 4.484 4.525 4.499 4.418 4.290 4.127 3.931 3.713 3.477 3.228 2.969 2.702 2.433
46▫
4.624 4.742 4.778 4.745 4.649 4.503 4.321 4.102 3.862 3.603 3.330 3.048 2.760 2.469
48▫
4.863 4.985 5.021 4.977 4.868 4.706 4.503 4.261 3.997 3.713 3.418 3.111 2.801 2.489
50▫
5.082 5.209 5.246 5.196 5.075 4.895 4.672 4.407 4.118 3.810 3.488 3.158 2.825 2.492
52▫
5.274 5.411 5.452 5.398 5.267 5.070 4.827 4.538 4.225 3.891 3.545 3.191 2.834 2.480
54▫
5.447 5.587 5.632 5.580 5.442 5.232 4.968 4.656 4.318 3.958 3.586 3.208 2.829 2.453
56▫
5.580 5.760 5.788 5.743 5.599 5.390 5.095 4.759 4.396 4.011 3.615 3.211 2.809 2.414
58▫
5.680 5.884 5.920 5.877 5.754 5.518 5.208 4.851 4.472 4.053 3.635 3.207 2.781 2.364
60▫
5.717 5.973 6.016 5.987 5.868 5.631 5.314 4.935 4.525 4.081 3.640 3.187 2.739 2.303

 ISSN: 2088-8694
546
Table 4. The Average motor speed of proposed converter in (revolution per minute)
5. CONCLUSIONS
At steady state; for a constant value of θoff; if the advancing of θon increases (i.e, decreasing the
value of θon), then: the average source current, average total torque and motor speed are directly proportional
to advance of the θon. The average total torque per current is inversely proportional to advance of the θon.
At steady state; for a constant value of θon; if the retarding/delaying of θoff increases (i.e, increasing value of
θoff), then: the average source current, average total torque and motor speed are directly proportional to retard
of θoff. The average total torque per current is inversely proportional to retard of θoff. At steady state, for a
constant switching angles: the average source current is inversely proportional to increase of source voltage.
The average total torque, average total torque per current and the motor speed are directly proportional to
increase of source voltage.
APPENDIX
DC voltage rating
Stator phase resistance
Aligned inductance
Unaligned inductance
Viscous friction coefficient
Rated speed
Rated phase current
Rated torque
Inertia constant
: U
: R
: Lal
: Lul
: B
: nr
: Ir
: Te
: J
= 220 V
= 17 Ω
= 0.605 H
= 0.155 H
= 0.0183 N.m.Sec2
= 1000 rpm
= 3 A
= 1 Nm
= 0.0013 Kg.m2
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θoff
θon
64▫
66▫
68▫
70▫
72▫
74▫
76▫
78▫
80▫
82▫
84▫
86▫
88▫
90▫
36▫
1883 2006 2109 2192 2259 2309 2344 2366 2375 2372 2357 2330 2292 2242
38▫
1804 1927 2029 2113 2180 2231 2267 2289 2299 2297 2282 2256 2218 2168
40▫
1713 1836 1939 2024 2091 2144 2181 2205 2216 2215 2201 2175 2138 2089
42▫
1609 1733 1837 1924 1994 2048 2087 2113 2125 2125 2113 2089 2053 2004
44▫
1493 1618 1725 1814 1886 1943 1985 2013 2027 2029 2018 1996 1961 1914
46▫
1366 1492 1602 1694 1770 1830 1875 1905 1922 1927 1918 1897 1863 1817
48▫
1229 1358 1471 1567 1647 1710 1758 1792 1812 1819 1812 1793 1761 1716
50▫
1085 1217 1334 1434 1518 1585 1637 1675 1698 1707 1703 1686 1656 1613
52▫
936 1070 1191 1296 1384 1456 1513 1554 1581 1593 1592 1578 1549 1507
54▫
783 921 1045 1155 1248 1325 1386 1432 1462 1479 1481 1468 1442 1402
56▫
629 769 897 1012 1110 1193 1259 1309 1344 1364 1369 1360 1336 1297
58▫
474 617 748 867 972 1060 1131 1186 1226 1250 1259 1253 1231 1194
60▫
320 465 600 723 832 926 1003 1064 1108 1137 1149 1147 1128 1093

547
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