Research Journal of Applied Sciences, Engineering and Technology 3(10): 1209-1213, 2011
ISSN: 2040-7467
© Maxwell Scientific Organization, 2011
Submitted: July 19, 2011
Accepted: September 17, 2011
Published: October 20, 2011
Employing Finite Element Method to Analyze Performance of Three-Phase
Squirrel Cage Induction Motor under Voltage Harmonics
1
1
Ali Ebadi, 2Mohammad Mirzaie and 2Sayyed Asghar Gholamian
Young Researchers Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2
Department of Electrical and Computer Engineering, Babol University of Technology,
Babol, Iran
Abstract: Due to various techno-economic advantages associated with induction motors, they are widely used
in industrial, commercial and residential applications. also, most of them are connected to electric power
distribution system directly, thus they will be affected by voltage quality problems, drastically. One of the
important voltage quality problems in power systems is voltage harmonics. Therefore, it is very important to
study performance of the motors under nonsinusoidal voltages. This paper presents employing TwoDimensional Finite Element Method to analyze performance of a three-phase squirrel cage induction motor
under voltage harmonics.
Key words: FEM, induction motor, loss evaluation, torque, voltage harmonic
C
INTRODUCTION
Three-phase induction motor is one of the most
widely used equipments in industrial, commercial and
residential applications for energy conversion purposes.
Based on U.S. Department of energy documents,
industrial motors consume seventy percent of electricity,
and particularly induction motors consists eighty percent
of the loads in a typical industry (Souto et al., 2000).
These motors are designed and built to work under
balanced sinusoidal voltage supply, however, they are
exposed to no ideal voltage conditions in practical
applications. For example, most of them are connected to
electric power distribution system directly while for
various reasons there are harmonics in the power system
voltages in most cases. Harmonic Pollution in power
system is generally caused by non linear loads. The
sources of harmonics in power system can be broadly
classified as follows (Souto et al., 2000; Hegazy and
salama, 1994; Alcaraz et al., 2006; Duarte and Kagan,
2010):
C
C
Harmonic originated at high voltages by supply
authorities such as HVDC systems, Static Var
compensation system and, Wind and solar power
converters with interconnection.
Harmonics originated at medium voltages by large
industrial loads like traction equipment, variable
speed drives, thyristor controlled drives, induction
heaters, arc furnaces, arc welding, capacitor bank and
electronic energy controllers.
Harmonic originated at low voltages by consumer
end like single phase loadings, uninterrupted power
supplier, semiconducting devices, Solid state devices,
domestic appliances and accessories using electric
devices, electronic fluorescent chokes and electronic
fan regulator/light dimmers.
Presence of voltage harmonics has significant effects
on performance of three-phase induction motors. The
inXuence of voltage harmonics on the efficiency (Oraee
and Emanuel, 2000), temperature rise of machines as a
most effective parameter that decreases the age of
insulation (Oraee and Filizadeh, 2001) and life reduction
due to temperature rise (Brancato, 1992), are some
contributions in this area.
This article attempts to study performance of a threephase squirrel cage induction motor under balanced
nonsinusoidal voltages using finite element method
simulation. For this purpose a 2.2 kW, 380V induction
motor has been simulated in Maxwell 12.1 and effects of
numbers of the voltage harmonics (harmonics 5th, 7th and
11th) on the performance of the simulated machine have
been investigated.
Simulation of induction motor by using 2D fem: In this
section, procedure of induction motor simulation using
FEM has been introduced briefly.
Analysis model: Figure 1 and Table 1 show the meshed
quarter cross section of the analyzed motor and its brief
specifications (Ebadi et al., 2011).
Corresponding Author: Ali Ebadi, Young Researchers Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran. Tel.:
0098-9113535718
1209
Res. J. Appl. Sci. Eng. Technol., 3(10): 1209-1213, 2011
WR = I 2 R = σE 2 . ∆ s. L
(3)
r r
∆ × A= B
(4)
r
∇×E=
r
∂B
∂t
= −∇ ×
r
∂A
∂t
(5)
In which, B, E, F and )s.L are magnetic flux density,
Electric field intensity, the rotor bar conductivity and an
element volume in the conductor bars.
Calculation of core loss: According to traditional ac
machine theory, iron loss in watts per kilogram can be
calculated in each element by using Eq. (6) and therefore
total iron loss obtained from the summation of iron losses
in the all elements.
Fig. 1: Meshed model of the IM
Table 1: Technical data of three-phase induction motor
Item
Value Item
Rated voltage (V) 380
Stator outer diameter (cm)
Output power (W) 2200 Rotor outer diameter (cm)
Frequency (Hz)
50
Core length (cm)
Rated current (A) 5.3
Air gap (cm)
Pole number
4
Stator lamination type
Rated speed (rpm) 1410 Rotor lamination type
Connection
Y
Turns no. in stator coil
Value
15
9
9
0.03
M530-50A
M530-50A
44
Time-stepping 2D FEM: At this study, time-stepping
FEM is used for the analysis of the magnetic field. For the
time-stepping FEM, time step should be fixed and the
input voltage should be defined at each time step. The
governing equation for two-dimensional (2-D) FE
analysis is given by (Lee et al., 2004):
∂
∂x
( µ1 ∂∂Ax ) + ∂∂y
( µ1 ∂∂Ay )
=σ
dA
dt
− Jo
dI a
dt
+
dϕ a
dt
2
m
(6)
where, Ph and Pc are respectively, hysteresis loss
component and eddy current component, both in watts per
kilogram. Bm and f are the peak value of the flux density
and the frequency, respectively. Kh, Ke and " are constants
provided by the manufacture.
Simulation setting: In order to realize the variations of
the load, a torque with the following equation has been
considered as the load:
⎛ T
⎞
TLOAD = ⎜ FL 2 ⎟ × ω 2
⎝ ω rated ⎠
(1)
where, µ is the permeability, A is the component of
magnetic vector potential, F is the conductivity of the
materials, and J0 is the exciting current density of the
stator winding.
The voltage equation per each phase is:
Va = I a Ra + Le
Pc = Ph + Pe = Kh f B αm+ Ke f 2 B
(7)
In Eq. (7), TFL is full load torque, T, Trated are speed and
rated speed of the machine, respectively.
Transient solver with step time equal to 10G4s has
been used in simulations and quarter cross section of
motor is meshed with 9688 of triangles. Simulation of
each cycle (0.02 s) consumed 236.3 sec of time by using
3GHz core 2 Duo CPU and 2 Giga Byte of DDR2 Ram.
(2)
RESULTS AND DISCUSSION
where, Va, Ia, Ra, Ka and Le are the input voltage, the
current, the resistance, the flux linkage of each phase and
the end-coil inductance, respectively. It should be noted,
Le is calculated by using RMxprt toolbox in Maxwell
12.1.
Calculation of copper loss: The stator winding and the
conductor bar losses are calculated using FEM. The
conductor bar loss (WR) can be Calculated as follows
(Lee et al., 2004):
In this section, rated sinusoidal voltage and three
major harmonics namely, 5th, 7th and 11th harmonics with
THD equal to 10% are applied on the simulated machine
and its performance is analyzed under mentioned
conditions. Note that, According to the standards the
magnitude of the harmonics should be less than 3% of the
main frequency magnitude and in this study worse
condition is considered. As mentioned above, all
simulations are performed by Maxwell V. 12.1 and results
are processed in MATLAB/Simulink environment.
1210
Res. J. Appl. Sci. Eng. Technol., 3(10): 1209-1213, 2011
10.00
8.00
6.00
4.00
2.00
0.00
-2.00
-4.00
-6.00
-8.00
-10.00
500 510 520 530 540 550 560 470 580 590 600
Time (ms)
Stator Copper loss increment
Rotor Copper loss increment
4.0
i a (A)
3.0
(%)
2.5
1.5
0.5
0
5th
Harmonic
4
(%)
(A)
6
2
0
10
25
15
20
Harmonic order
30
35
7th
Harmonic
11th
Harmonic
Fig. 6: Copper losses under voltage harmonic conditions
8
5
2.0
1.0
Fig. 2: The phase a steady state current under 5th voltage
harmonic
0
Total Copper loss increment
3.5
40
Fig. 3: The phase a current in frequency domain under 5th
voltage harmonic
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0.85
0.80
Core loss increment
5th
Harmonic
7th
Harmonic
11th
Harmonic
Current THD
Fig. 7: Core loss under voltage harmonic conditions
12
10
(%)
8
6
(%)
4
2
0
5th
Harmonic
7th
Harmonic
11th
Harmonic
Sinusoidal
Fig. 4: Current THD in sinusoidal voltage and harmonic
condition
2192
Output power
2188
Watt
Efficiency
5th
Harmonic
7th
Harmonic
11th
Harmonic
Sinusoidal
Fig. 8: Efficiency under sinusoidal voltage and harmonic
condition
2190
2186
2184
2182
2180
5th
Harmonic
81.10
81.05
81.00
80.95
80.90
80.85
80.80
80.75
80.70
80.65
80.60
7th
Harmonic
11th
Harmonic
Sinusoidal
Fig. 5: Output power under sinusoidal voltage and harmonic
condition
Current: The stator currents in harmonic conditions are
distorted and involve harmonics. For example, Fig. 2
shows the steady state current of phase a under 5th
harmonic which is not sinusoidal significantly. this current
in frequency domain has been shown in Fig. 3. According
to this figure the current involves other harmonics addition
to main harmonic. Note that, 5th current harmonics is
resulted in the presence of 5th voltage harmonics and other
current harmonics are created due to nonlinear
characteristic of the machine and space harmonics. Current
THD in various conditions has been shown in Fig. 4. Based
1211
N.m
Res. J. Appl. Sci. Eng. Technol., 3(10): 1209-1213, 2011
15.10
15.08
15.06
15.04
15.02
15.00
14.98
14.96
14.94
14.92
14.9
CONCLUSION
Average produced torque
In this studuy, finite element method has been used to
analyze the performance of a three-phase squirrel cage
induction motor under voltage harmonics with same THD
equal to 10% and following results have been achieved:
C
5th
Harmonic
7th
Harmonic
11th
Harmonic
Sinusoidal
(%)
Fig. 9: Average torque under sinusoidal voltage and harmonic
condition
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
C
C
Produced torque ripple
C
C
The THD is not enough to estimate the induction
motor operating performance in the presence of
voltage harmonics, but the harmonic content must be
considered.
The copper and core losses and torque ripple increased
under voltage harmonics. This increment is lower at
higher order harmonics.
Output power and average torque is not affected
significantly by considered voltage harmonics.
The efficiency is better for higher order of voltage
harmonics. However, induction motor has maximum
efficiency under sinusoidal voltage.
Finite element method as a powerful tool can be used
to analyze performance of three-phase induction motor
under nonsinusoidal supply.
ACKNOWLEDGMENT
5th
Harmonic
7th
Harmonic
11th
Harmonic
Sinusoidal
Fig. 10: Torque ripple under sinusoidal voltage and harmonic
condition
upon this figure, current THD decreases with increasing
order of voltage harmonics. As expected, current THD in
sinusoidal condition is not equal to zero.
Power, losses and efficiency: According to Fig. 5, output
power is not affected significantly by considered voltage
harmonics. While, based on Fig. 6 and 7, the copper
losses (including copper loss of the stator and rotor) and
the core loss increase under voltage harmonic condition
and this increment is lower at higher order harmonics.
Note that, discussed figures show losses increment over
sinusoidal condition in percent. As expected, based on
Fig. 8, the efficiency decreases under harmonic condition
and this reduction is higher for lower order of voltage
harmonics.
Torque: Figure 9 and 10 show average and ripple values
of produced torque, respectively. Considering these
figures, torque average variations is negligible under
voltage harmonics with THD =10% while torque ripple
increases significantly and this increment is higher for
lower harmonic order. In practical point of view, torque
ripple increment means increase of vibration and noises
and this is not desirable.
The authors would like to thank Mr. Rahmani and Mr.
Setareh (R&D Management Office of Motogen
Corporation, Tabriz, Iran) for providing data of the studied
three-phase induction motor.
REFERENCES
Alcaraz, R., E.J. Bueno, S. Cobreces, F.J. Rodriguez,
F. Espinosa and S. Muyulema, 2006. Power system
voltage harmonic identification using kalman filter.
12th International Power Electronics and Motion
Control Conference. Aug. 30-Sept. 1, Portoroz, pp:
1283-1288.
Brancato, E.L., 1992. Estimating the lifetime expectancies
of motors. IEEE Electr. Mag., 8(3): 5-13.
Duarte, S.X. and N. Kagan, 2010. A power-quality index
to assess the impact of voltage harmonic distortions
and unbalance to three-phase induction motors. IEEE
T. Power Deliver., 25(3): 1846–1854.
Ebadi, A., M. Mirzaie and S.A. Gholamian, 2011. Torque
analysis of three-phase induction motor under voltage
unbalance using 2D fem. Int. J. Eng. Sci. Technol.,
3(2): 871- 876.
Hegazy, Y.G. and M.M.A. Salama, 1994. Identifying the
relationship between voltage harmonic distortion and
the load of harmonic producing devices in distribution
networks. Canadian Conference on Electrical and
Computer Engineering. Halifax, NS, Canada, Sep.
25-28, pp: 669-672.
1212
Res. J. Appl. Sci. Eng. Technol., 3(10): 1209-1213, 2011
Lee, J.J., Y.K. Kim, H. Nam, K.H. Ha, J.P. Hong and
D.H. Hwang, 2004. Loss distribution of three-phase
induction motor fed by pulsewidth-modulated
inverter. IEEE T. Magn., 40(2): 762-765.
Oraee, H. and A.E. Emanuel, 2000. Induction motor
useful life and power quality. IEEE Power
Engineering Review, 20(1): 47-47.
Oraee, H. and S. Filizadeh, 2001. The impact of harmonic
orders on insulation aging in electric motors. 36th
Universities Power Engineering Conference. Sep. 1214, University of Wales, UK, pp: 21-26.
Souto, O., J. Oliveira and L. Neto, 2000. Induction motors
thermal behavior and life expectancy under nonideal
supply conditions. Ninth International conference on
Harmonics and Quality of Power. Orlando, FL., Oct.
1-4, pp: 899-904.
1213