Three phase induction motors are widely used in industrial, commercial and residential systems, because of their ruggedness, simplicity and relatively low cost. Approximately 65% of the electricity consumed in industry is used to drive electrical motors. Therefore, the efficiency and reliability of induction motors operation is of major importance, in order to improve the energy efficiency in industry [1], and most of them are connected to electric power distribution system directly, thus they will be affected by voltage quality problems. An important voltage quality problem in power systems is voltage unbalance. Therefore, it is very important to study performance of these motors under unbalanced voltages. The paper tries to study the effect of voltage unbalance on the motor 3-phase negative sequence currents, toque and energy consumption. Further MATLAB/SIMULINK and environments have been used simultaneously for simulation purpose and uses from symmetrical components analyses.
Keywords : Induction motor, unbalanced voltage, Matlab, Energy
The operation of three-phase induction machines when supplied by unbalanced voltages has been of major interest [1], [2]. The National Electrical
Manufactures Association(NEMA) defines voltage unbalance as the maximum deviation from the average line voltage over the average line voltage. The
International Electrotechnical Commission (IEC) defines voltage unbalance as the ratio of the negative sequence voltage to the positive sequence voltage [3], [4]. In practice, induction machines experience unbalanced voltages and undervoltages, depending on the location of the motor and the length of the feeder used. During peak hours, some customers with three phase motors could experience minimum voltages guaranteed by the supply utility. Furthermore, the supply voltage is not always balanced. Therefore, the motor will experience a combination of under voltages with unbalanced voltages. In this paper for Inductionmotor analyse:
• To study the voltage unbalance we resolve the motor unbalance 3-phase voltages in to positive sequence voltages and negative sequence voltages by the method of symmetrical components.
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• We apply this positive sequence and negative sequence voltages to respective induction motor equivalent circuits.
• We arrive at positive sequence current and negative sequence current.
• Then we arrive at 3Φ currents and current unbalance factor.
• We study the effect of voltage unbalance on motor torque and energy consumption.
2.1 Unbalanced Voltages
In three-phase power systems the generated voltages are sinusoidal and equal in magnitude, with the individual phases 120 apart. However, the resulting power system voltages at the distribution end and the point of utilization can be unbalanced for several reasons. The nature of the unbalance includes unequal voltage magnitudes at the fundamental system frequency (under-voltages and overvoltages), fundamental phase angle deviation, and unequal levels of harmonic distortion between the phases. A major cause of voltage unbalance is the uneven distribution of single-phase loads, that can be continuously changing across a threephase power system. Example problem areas can be rural electric power systems with long distribution lines, as well as large urban power systems where heavy single-phase demands, such as lighting loads, are imposed by large commercial facilities [5], [6]. The voltage unbalance in percent is defined by the National
Electrical Manufacturers Association (NEMA) in Standards Publication no. MG 1-
1993 as [7]:
Unbalance (1)
Note that the line voltages are used in this NEMA standard asopposed to the phase voltages. When phase voltages are used, the phase angle unbalance is not reflected in the % Unbalanceand therefore phase voltages are seldom used to calculatevoltage unbalance. Another index used in European standards to indicate the degree of unbalance is the voltage unbalance factor (VUF) whichis the ratio of the negative sequence voltage to the positive sequence voltage represented as [8],
[9], [10]:
(2) and are V
1
and V
2
are the positive and negative sequence voltages, respectively, and can be obtained using symmetrical componentsas will be described in the next section.
2.2 Symmetrical Components
The basic premise of symmetrical components is that an unbalanced network of three related vectors can be resolved into three sets of vectors. Two of the sets have equal magnitude and are displaced 120 degrees apart while the third set has equal magnitude, but zero phase displacement. The three sets are known as the positive, negative, and zero sequence components of the electrical system. Figure 1
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enables us to see that we can exploit the symmetry of the systems to simplify the nomenclature [11].
Figure 1 : (a) Positive, (b) Negative, and (c) Zero Sequence Components
Expressing the unbalanced currents as the sum of their components provides the
[ ] following transformation matrix.
[ ] [ ] a

1

120

(3)
3.1 Equation of Induction Motor Dynamic
The dynamicsof induction motor can be represented by the set of five equations as shown in 4 to 8.
(4)
(5)
(
(
(
)
)
)
(6)
(7)
(8)
Where,
Here, ,
: differential operator
, , represent the stator and rotor voltages, , , , represent the stator and rotor fluxes, , are stator and rotor resistances,
are stator and rotor currents, H is interia constant and
, , ,
, , are the rotor speed, base frequency and supply frequency respectively. is the electromegnatic torque and is the mechanical torque on the motor shaft. The implementation of this fifth-order model in stability study is not common because of the requirment for balancing of the degree of approximation with synchronous machines.
This paper, performance of a three-phase induction motor under unbalanced voltage imposed by power system grid is studied. The phase currents, the deliverable power to the motor, stator current and efficiency of the motor are propose. In fact, influence of power system and its unbalances on the motor itself are investigated. In order to analyze the performance of a three phase induction motor, symmetrical components analysis is normally used. In this method, positive and negative sequence equivalent circuits, as shown in Figure 2 and 3, are utilized to calculate different parameters of the machine under unbalanced voltage operation [12].
3

R
1
X
1
X'
2
V p
X m
R'
2
Figure 2 : Positive sequence of induction motor equivalent circuit
R
1
X
1
X'
2
V n
X m
R'
2
/(2-s)
Figure 3 : Negative sequence of induction motor equivalent circuit where
V p
: positive sequence voltage
V n
: negative sequence voltage
X
1
X
'
2
: stator reactance
: rotor reactance
R
1
: stator resistance
R'
2
: rotor resistance
S : slip
3.2 Model Developed to Include Saturation
During the development of dynamic models of induction motors, most of the researchers neglected the effect of magnetic saturation and assumed inductances to be constant. Whereas, in this paper, an attempt has been made to account the effect of magnetizing saturation in dynamic model of the motor [13]. Modeling results in to the following non-linear relation between magnetizing reactance,
X m
and magnetizing Current, i m
,
X m
= -0.0001 i m
+ 0.0084 i m
-0.6768 i m
+27.2815 Ω (9)
The magnetizing current, i m
is defined as:
√
(10)
.
(11)
(12)
Stator d-q axis currents and rotor d-q axis currents may be computed by solving the differential equation. Electromagnetic torque, mechanical sub-block and simulink model as proposed are used for Simulink.
Tabel 1 : Profile of induction motor used in the simulation
Nominal Power(Kw)
Nominal Voltage(V)
Nominal Frequency(Hz)
7.5
380
50
R` r
(ohm) , L` r
(H)
Inertia j(Kg.M
2
)
Pole pairs
0.7484 , 0.003045
0.0343
2
R s
(ohm) , L s
(H)
0.7384 ,
0.003045
Connection type
Delta
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If balanced 3-phase alternating current machines are fed from balanced three phase power systems, symmetrical phase voltages and currents are provided. In case of operating at unbalanced voltage system, in order to obtain the amplitude of any phase current, the effects of currents in the other phases to that phase should be known. For testing three phase induction motor model has been simulated in
MATLAB software and content have been used actual values of three phase induction motor is given in Table 1. Table 2 shows the three-phase voltages and currents in their Positive and negative sequence components in eight various unbalanced cases. Table 3 shows the comparison between parameters of threephase induction motor with voltage unbalance.
Tabel 2 : Terminal voltage and current of three phase induction motor with voltage unbalance
A
B
C
D
E
F
G
H
A
B
C
D
E
F
G
H
V
I an
220
215
210
205
215
205
205
215 a
(v)
(A)
12.97
12.03
11.56
11.13
12.34
11.19
11.29
V
I bn
220
220
220
220
210
215
210
210 b
(v)
(A)
12.07
13.51
14.23
15.13
12.81
14.63
14.15
V
I cn
220
220
220
220
220
220 c
(v)
220
202
(A)
12.96
13.03
13.05
13.23
13.76
14.03
14.85
V
 a
(v)
0
V
 a
(v)
220
V a
0
(v)
0
1.667
218.333
1.667
3.333
216.667
3.333
5
2.886
215
215
5
2.886
4.409
213.333
4.409
4.409
211.667
4.409
2.886
210 2.886
I 0 a
(A)
I
 a
(A)
I
 a
(A)
0.088
12.876
0.088
0.351
12.946
0.351
0.745
12.976
0.745
1.155
13.1633
1.155
0.417
12.97
0.417
1.06
13.283
1.06
1.088
13.43
1.088
Figure 4 depict the active and reactive power simulation results in this case for 4 modes (a, d, g and h). Figure 4 shows the active and recative power of the simulated induction motor in time domain when supply voltage is unbalanced. Ripple in power waveform in time domain are mainly due to unbalanced voltage.
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( a ) ( b )
( c ) ( d )
Figure 4 : Active and recative power for a, d, g and h mode
Tabel 3 : comparison between parameters of three phase induction motor with voltage unbalance
Q in
(VAR)
P out
(W)
T
(Nm)
% η n r
(RPM)
P
+
(w) P
-
(w)
A 4258 7490 50.11
90 1430 7635.25
7.833
× 10
3
-
T
+
(Nm)
50.98
T
-
(Nm)
5.23
× 10
-3
B 3824 7484 50 86.5
1428 7381.37
1.27 49.36
8.49
× 10
-1
C 3389 7478 52.67
83.1
1426 7256.65
5.722
48.59
3.83
D 2957 7471 53.9
79.9
1423 7159.39
13.73 48.04
9.21
E 3951 7478 53 84.3
1428 7408.76
17.85 49.54
11.19
F 3092 7464 55.45
80.4
1423 7290.52
11.56 48.92
7.75
G 3420 7456 56.99
76.6
1423 7452.78
12.17 50.01
8.166
H 4713 7450 46.07
87.3
1424 7872.7
5.639 52.79
3.77
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6.1 unbalanced voltage and motor temperature
In this article, the specific equivalent circuits of an induction machine are obtained by resolving the mentioned quantities into symmetrical components. In these equivalent circuits, the opposite rotating torque occurs due to the reverse components of currents. Therefore the motor needs drawing more current from the supply to maintain the demanded mechanical power. As a result, the copper losses and the heat in the machine increase. This result has been also seen by loading the machine at 50 Nm torque in simulation. In addition, the harmonics generated during unbalanced operation are observed as electromagnetic noise in the machine. This noise appears as pulsations in motor bearings as well. This event may cause bearing faults for-long term operations from unbalanced supply. The following table illustrates voltage unbalance effects on a typical electric motor rated 5 hp, 3 phase,
220V, 50 Hz, 1725 rpm, and 1.0 service factor.
Tabel 4 : unbalanced voltage effects on motor temperature characteristic
Average voltage
Percent unbalanced voltage
Percent unbalanced current
230 performance
0.3
0.4
230
2.3
17.7
Increased temperature rise ° c 0 30
A most damaging effect is that winding insulation life is approximately halved for every 10°C increase in winding temperature. The 5.4% unbalance shown in the third column would result in an expected life of only 1/16 of normal due to the additional
40°C rise, a substantial and unacceptable reduction. A motor with a service factor of
1.15 could typically withstand an unbalance of about 4.5% provided it is not operated above its nameplate rated horsepower. In this case the 5.4% unbalance is excessive even for a 1.15 service factor motor. The following chart illustrates the typical percentage increases in motor losses and heating for various levels of voltage unbalance.
Figure 5 : Increase in Motor Heating and Losses vs. Voltage Unbalance
A motor often continues to operate with unbalanced voltages; however, its efficiency is reduced. This reduction of efficiency is caused by both increased current (I) and increased resistance (R) due to heating. The increase in resistance and current
"stack up" to contribute to an exponential increase in motor heating. Essentially, this means that as the resulting losses increase, the heating intensifies rapidly. This may lead to a condition of uncontrollable heat rise, called "thermal runaway", which
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results in a rapid deterioration of the winding insulation concluding with failure of the winding.
6.2 Importance of motor running cost
– Life Cycle Costs
The classic challenge for energy users is to determine whether it is appropriate to spend more money now in order to save money in the long term. However, just because something saves money in the long term does not necessarily mean that it saves an amount sufficient to justify the required additional investment. The law of diminishing returns suggests that even a good thing can be overdone. Properly applied, life-cycle cost analysis
(LCCA) is a decision support tools that will lead to appropriate energy project choices.
In many applications it is worthwhile replacing motors even when considerable working life remains. Motors can run without problems for 20 years or more with good protection and routine maintenance. [15]
Table 5 : Importance of Running Cost of Motor Driven Equipment
Motor rating (kW)
Efficiency, p.u
Power input (kW)
Running hours/year
Energy input (kWh/year)
7.5
0.86
8.72
6000
52320
Running cost @ US $ /kwh. 209.280
Running cost for 10 years ($) 2092.80
First cost ($ 284.65
7.5
0.88
8.52
6000
51120
204.480
2044.80
341.58
37
0.92
40.22
6000
241320
965.280
9652.80
1518.12
37
0.93
39.78
6000
238680
954.720
9547.20
1821.74
First cost as % of running cost for
10 years
0.136 0.161 0.157 0.1908
However, if they are running inefficiently, it is worthwhile replacing them as running costs are much more than first costs. Motors can be considered as consumable items and not capital items, considering the current energy prices. The importance of running cost can be seen from and Table 5. The following points may be noted:
1. The first cost is only around 1% of the running coast for 10 years. Hence running costs are predominant in life cycle costing.
2. Even a small difference in efficiency can make a significant difference in running cost.
3. When economically justified, motors may be replaced, even if these have been recently installed.
Induction motor is an important type of electric machines which is widely used and acceptable in industrial, commercial and domestic applications. These machines are meant to operate under balanced and rated supply system. But it is found that absence of voltage unbalance on a distribution system is almost impossible due to randomness of the connections and disconnection of single phase loads, uneven distributions of single-phase loads on the three phases and inherent asymmetry of power system. Sometimes this results in to the compulsion to operate such machines under unbalanced supply system.
Effects of negative sequence component on performance of induction motor:
• The motor will take longer time to run up .
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• Increases the thermal stress in the motor which lead to loss in life.
• The net torque is reduced and if full load is still demanded, then the motor will be forced to operate at a higher slip, thus increasing the rotor losses and heat dissipation.
• The reduction in the peak torque reduces the ability of motor to ride through dips and sags, thus affecting the stability of the entire system.
• Even a small voltage unbalance will result in large current unbalance during the running of motor.
• Negative phase sequence components will lead to heating of motor
• Negative phase sequence currents leads to reduction in motor output torque.
• Motor is forced to run at higher slip leading to increased rotor loss and reduced efficiency.
When these costs, excluding motor related energy costs, are combined, curves can be developed as shown in Figure. 5, that indicate the annual incremental cost to the customer for various percent voltage unbalance limits. The optimal range of voltage unbalance occurs when the cost to the customer is minimized, which is implied in
ANSI C84.1 to be at approximately 3% voltage unbalance as shown in Figure. 7.
[16], [17]
Figure 6: Annual incremental cost to the customer for various percent voltage unbalance limits, showing minimum costs at approximately 3% voltage unbalance
.
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