Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 285.
Brushless DC Motor Performance Improvement
through Switch-on and Switch-off Angles Control
Mohamed. A. Enany 1, Hamed. M. Elshewy 1, Fathy. E. Abdel-kader 2
1
2
Electrical Power & Machines Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt
Electrical Engineering Department, Faculty of Engineering, Menofeya University, Shebin El-Koum, Egypt
Abstract— This paper presents a method for improving the
performance of Brushless Direct Current (BLDC) motor
drive. This method depends on the varying of both switchon and switch-off angles of motor phase current. The phase
current, torque and efficiency for the proposed method are
discussed. The operation of BLDC motor drive at different
switch-on and switch-off angles for same speed is studied
and discussed. The results of this study give an analysis of
the motor characteristics of such method according to
torque, efficiency and torque ripples factor. Noticeable
improvement in the motor performance had been shown by
simulation results.
sequentially; any phase is connected to the supply after the
previous phase is disconnected with certain arrangement
according to excitation technique type to keep the rotor
rotation. A switching on point occur every 60 o and the
conduction period of any phase is equal to 120 o as illustrated in
Fig. 2(a).
The effects of advancing the switch-on and switch-off angles
(γ) of the current on motor characteristics are investigated. In
Fig. 2(a) normal motor operation is illustrated, but by
advancing the switch-on and switch-off angles (γ) of the
current; the motor operation will be changed as illustrated in
Fig. 2(b).
Index Terms— Brushless DC motor drive, Performance
improvement, Switch-on and Switch-off angle control
I. INTRODUCTION
HE brushless direct current (BLDC) motor is widely used
in computers, household and industrial products, more
over the application of these machines in electric vehicles
also. This is due to it has higher torque delivered to motor size
ratio. Although using an inverter and controller causes a higher
cost compared with the direct current (DC) motor [1], [2].
T
Fig. 1 A cross-sectional sketch of 3-phase BLDC motor and
corresponding winding connection.
The torque is produced without torque ripple in the ideal
BLDC motor with trapezoidal back-electromotive force
(EMF). Because the current made by the constant voltage
source instantly rises to steady state limited by a resistance
only. However, the current characteristic take a time to rise or
fall to the steady state in the actual BLDC motor. Because the
current of the actual BLDC motor is influenced by inductance
and resistance of the winding.
Ea conduction period
For the BLDC motor and the corresponding winding
connection shown in Fig. 1, Motor phases are supplied
β
0
conduction period
V
conduction period
Ec
Voltage (Volt)
Voltage (Volt)
Eb conduction period
90 120 150 180 210 240 270 300 330 360
Rotor Angle (Degree)
β
conduction period
α
conduction period
V
conduction period
α
α
β
0
conduction period
V
conduction period
Ec β
β
Eb
0
α
period
30 60
Ea
V
conduction period
Therefore, the ripples in current are due to the influence of the
motor phase inductance. The torque ripple is affected by
current ripple directly when the back-EMF has the trapezoidal
waveform [3], [4].
II. PROPOSED METHOD
α
conduction period
V
0
Smooth torque profile must be produced to get improved
operation. In this paper, the method to simply reduce the torque
ripples and improve motor operation is proposed by varying
the switching-on and the switching-off angles for motor phase
current.
V
β
α
conduction-
30 60 90 120 150 180 210 240 270 300 330 360
Rotor Angle (Degree)
(b) with advancing
(a) Without advancing
the both angles
the both angles
Fig. 2 Supply voltage and Back emf waveform of the BLDC
motor.
III. PROPOSED MODEL
A. Phase Current Waveform
The motor phases are supplied sequentially whenever the rotor
is rotated by an angle according to the type of excitation
technique as follow [4- 6].
In the proposed method, the currents IِA, IِB and IِC according to
the first sequence shown in Table 1(b) are determined as
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787
B
Fm : is the equivalent MMF of the magnets.
Pm : is the magnetic circuit permeance of the magnets.
i : is the stator winding current .
Mim : is the mutual inductance between a stator winding and the
one turn equivalent circuit of the magnets.
The EMF of a stator winding ei is related to the magnet flux by
(1)
(2)
2R
V − EB − EC (1 - e-( tbci / τbci) )
IC = −
2R
/τ )
-( t
-( t / τ )
_ V − E A − EC ( 1 - e caif cai ) × e cd cd (3)
2R
The currents IِA, IِB and IِC according to the second sequence
shown in Table 1(b) are determined as follows;
-( t / τ )
IA = IAo × e ad ad
(4)
-( tcd / τcd)
(5)
IC = ICo × e
t
/
τ
-(
)
−
V
E
b
b
B ( 1 - e
IB =
R
t /τ
t /τ
V − EB − EC
+
( 1 - e-( bc bc) × e-( bd bd)
(6)
2R
Where:
IAo : equal to IA given in equation (1)
ICo : equal to IC given in equation (3)
C. Motor Torque Ripples factor
The value of motor torque ripples at a certain speed TR is
determined by the following equation [9]:
TR =
tai,, tbi and tci: the time from the moment of phase connection.
taif,, tbif and tcif : the time at the moment of phase disconnection.
τai,,τbi and τci : the electrical time constant of phase during
connection.
tad, tbd and tcd : the time starting from the moment of phase
disconnection.
τad, τbd and τcd : the electrical time constant of phase during
disconnection
tabi,, tbci and tcai : the time starting from the moment of two
phase connection.
tabif,, tbcif and tcaif : the time at the moment of two phase
disconnection.
τabi,, τbci and τcai : the electrical time constant of two phase
during connection.
i =1
(11)
T av
The phase current and motor torque waveforms at different
values of advancing the both angles are shown in Fig. 3 and
Fig. 4 respectively
const
50
40
γ = 45
30
ο
γ = 30
ο
ο
γ = 15 γ = 0 ο
20
10
0
-10
-20
-30
Ia
Ic
-40
Ib
Kb = 0.1537 volt/(rad/sec),V= 240 V , N=2000 rpm
-50
0
30
60
90
120 150 180 210 240 270 300 330 360
Rotor Angle (Degree)
It can be noted that the self and mutual inductance coefficients
of the armature windings are dependent on the rotor angular
position θ. Thus, the electromagnetic torque can be expressed
as
z
( T i − T av ) / 360
Ti : instantaneous motor torque at i rotor angle
Tav : average motor torque at certain speed
(7)
T = ∑ F m ii
∑
i = 1
Where
B. Motor Torque Waveform
The electromagnetic torque can be expressed in terms of
co energy Wco variation as follows [7]:
i
(9)
Where:
φim, : is the magnetic flux produced by the magnets.
From (8) and (9) it follows:
z e i
(10)
i i + 1 F 2 d Pm
T = − ∑
m
ω
2
d
θ
i =1
m
The first term in (10) represents the permanent magnet torque
which is produced due to the amount of magnetic flux in the
permanent magnet [8], while the second term represents the
reluctance torque which is produced due to the saliency in
rotor.
i = 360
V : the voltage of the DC source.
EA , EB and EC: the back EMF of phase A ,B and C.
R : the resistance of phase winding.
∂W
T = CO
∂θ
d ϕ im
d M im (θ )
= − ω m Fm
dt
dθ
ei = −
Phase Current (A)
follows;
V − EA − EB ( 1 - e-( tcaif / τcai) ) × e-( tad / τad)
IA =
2R
V − EB − EC ( 1 - e-( tbc / τbc) )
I =
d Pm
d M im (θ )
1
+ Fm2
2
dθ
dθ
(8)
Where:
Z : is the number of phases.
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Fig. 3 Variation of phases current with rotor angle at different
values of both angles advance.
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20.0
9
Total Motor Torque (N.m)
8
γ = 45
7
6
ο
γ = 30
5
ο
4
3
γ = 15
2
1
γ=0
0
17.5
Average Phase Current (A)
Kb = 0.1537 volt/(rad/sec),V= 240 V , N=2000 rpm
ο
ο
15.0
12.5
10.0
7.5
γ=0
5.0
2.5
o
γ = 15
o
γ = 30
o
o
γ = 45
Kb=0.1537 volt/(rad/sec), V=240 Volt
0.0
-1
0
30
60
0
90 120 150 180 210 240 270 300 330 360 390 420
500
1000 1500 2000 2500 3000 3500 4000 4500 5000
Speed (rpm)
Rotor Angle (Degree)
Fig. 5 Variation of phase current with speed at different values
of the both angles advance.
Fig. 4 Variation of motor torque with rotor angle at different
values of both angles advance.
IV. SIMULATION RESULTS
12
Average Motor Torque (N.m)
11
A. Motor Performance at Different Switch-on and Switch-off
Angles
9
γ=0
8
7
6
o
γ = 15
o
γ = 30
o
o
γ = 45
5
4
3
2
1
0
-1
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000
Speed (rpm)
Fig. 6 Variation of average motor torque with speed at different
values of the both angles.
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0.8
0.7
Average Efficiency (%)
In this section, the effect of advancing the both angles (γ) of
the current on the motor performance is studied. The
simulation program is developed to give the average phase
current, total motor torque, efficiency and torque ripples with
the variation of motor speed at different values of advancing
the both angles and fixing back EMF constant.
Fig. 5 shows the variation of the average phase current with
speed variation at different values of both angles advance. It is
clear that the phase current is reduced with the increase in
speed. And also the average value of the phase current slightly
increases with the increase in the both angles advance at any
speed.
The BLDC motor torque variation with speed is similar to that
of the series motor as shown in Fig. 6. It is noticed that, when
the motor applied voltage equals 240 V and advancing the both
angles equals zero, the motor torque reduces with the increase
in speed. And this torque reaches zero at speed approximately
equals 3250 rpm.
The Increase in advancing the both angles at the same voltage
leads to an increase in motor torque. Therefore, the motor
availability to rotate with load by a speed higher than 3250 rpm
will be achieved by increasing advancing the both angles as
shown.
Fig. 7 shows the variation of efficiency with speed variation. It
is clear that the efficiency curve increases with the increase in
advancing the both angles through all speeds. The motor
efficiency has high values at low speeds, and it is decreased
with increasing the speed.
Fig. 8 shows the variation of motor torque ripples with speed
variation. It is clear that torque ripples decreases with the
increase in advancing the both angles through all speeds. The
motor torque ripples is high during high speed.
Kb=0.1537 volt/(rad/sec), V=240 Volt
10
γ=0
0.6
Kb=0.1537 volt/(rad/sec), V=240 Volt
o
γ = 15
o
γ = 30
o
o
0.5
γ = 45
0.4
0.3
0.2
0.1
0.0
-0.1
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000
Speed (rpm)
Fig. 7 Variation of average efficiency with speed at different
values of the both angles advance.
789
9
3.5
Torque Ripple Factor (%)
2.5
γ = 15
o
γ = 30
o
o
γ = 45
2.0
1.5
1.0
0.5
0.0
Kb=0.1537 volt/(rad/sec), V=240 Volt
-0.5
0
500
N=1000 rpm
N=2000 rpm
N=3000 rpm
N=4000 rpm
N=5000 rpm
8
o
Average Motor Torque (N.m)
γ=0
3.0
7
6
Kb=0.1537 volt/(rad/sec), V=240 Volt
5
4
3
2
1
0
-1
1000 1500 2000 2500 3000 3500 4000 4500 5000
0
10
20
30
40
50
60
70
80
90
Advance Angle (Degree)
Speed (rpm)
Fig. 8 Variation of torque ripples factor with speed at
different values of the both angles advance.
Fig. 9 Variation of average motor torque with the both angles
advance at different speeds.
B. Motor Performance at Optimum Switch-on and Switchoff Angle
1.0
Kb=0.1537 volt/(rad/sec), V=240 Volt
0.9
Fig. 10 shows the variation of the efficiency with the both
angles advance at different speeds. It is clear that the efficiency
increases at any speed by the increase in the both angles
advance until it reaches its maximum value, and then it begins
reducing. It is noticed also that the value of advancing the both
angles; which gives the maximum efficiency increases by the
increase in the motor speed. Therefore, its value depends on
the motor speed. And also the maximum efficiency is increased
by speed increasing.
Fig. 11 shows the variation of motor torque ripples with the
both angles advance at different speeds. It is clear that torque
ripples decreases with the increase in the both angles advance
through all speeds. The motor torque ripples is high during
high speed.
N=1000 rpm
N=2000 rpm
N=3000 rpm
N=4000 rpm
N=5000 rpm
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
60
70
80
90
Advance Angle (Degree)
Fig. 10 Variation of average efficiency with the both angles
advance at different speeds.
2.00
N=1000 rpm
N=2000 rpm
N=3000 rpm
N=4000 rpm
N=5000 rpm
1.75
Torque Ripple factor (%)
The simulation program is developed to give the total motor
torque, efficiency and torque ripples with the variation of
advancing the both angles and fixing speed and back EMF
constant. Variation of motor torque is illustrated in Fig. 9
Increasing the both angles advance always increases the motor
torque at any speed. If the load torque is constant with speed
variation, the both angles advance must be increased to
increase the load speed although the supply voltage is constant.
So, it can be found that the control of motor speed is efficient
when the advancing the both angles is controlled.
0.8
Average Efficiency (%)
In this section, fixing the motor speed with any value, the
advance angle (γ) can be controlled to give the motor
characteristics to be suitable for the load case and give
improved operation.
1.50
1.25
1.00
Kb=0.1537 volt/(rad/sec), V=240 Volt
0.75
0.50
0.25
0.00
-0.25
0
10
20
30
40
50
60
70
80
90
Advance Angle (Degree)
Fig. 11 Variation of motor torque ripples with the both angles
advance at different speeds.
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790
From the previous results, the variation of the optimum switchon and switch-off angles advance; maximum motor torque,
maximum efficiency, and minimum torque ripples at different
speeds with the speed variation can be deduced as shown in
Fig. 12. Which presents the optimum value of switch-on and
switch-off angles to get the improved motor operation?
90
Maximum Efficiency
Maximum Torque
Minimum Torque ripple
Advance Angle (Degree)
80
70
50
40
30
20
Kb=0.1537 volt/(rad/sec), V=240 Volt
0
0
500
The parameters of BLDC motor used in simulation are:
DC supply voltage (V) = 240 V
Phase resistance (R) = 5 Ω
Stator phase inductance at aligned position (Ld) = 0.012 H
Stator phase inductance at unaligned position (Lq) = 0.007 H
Number of poles (P) = 2 pole
Back EMF constant (Kb) = 0.1537 volt.s/rad
VIII. REFERENCES
60
10
VII. APPENDIX
1000 1500 2000 2500 3000 3500 4000 4500 5000
Speed (rpm)
Fig.12 Variation of optimum switch-on and switch-off angles
advance with speed.
V. COMPARISON WITH EXPERIMENTAL RESULTS
Figure 13 shows different phase current waveforms of BLDC
motor using the same two phase excitation technique applied in
our simulation. From this figure there is a great acceptance of
our prediction model which in accordance with these
experimental results.
(a)
(b)
Fig. 14 Comparison with experimental results; (a) given by
[10], and (b) given by [11].
VI. CONCLUSION
Advancing of switch-on and switch-off angles had been
proposed here. From simulation results, the differences
between operation with and without both angles advance are
noticed, and it can be easily deduced that Increasing the
advance angle (γ) leads to lower phase current, higher motor
torque, lower torque ripples, higher no load speed and higher
efficiency comparing with normal operation. The Advance
angle (γ) can be controlled to make the motor characteristics
suitable for the load case and give improved operation.
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