Download Assessment to Study of Voltage Unbalance Effects about Efficiency

Effects of Voltage Unbalance on the Efficiency and Power
Factor of Induction Motors: A Statistical Approach
ENRIQUE QUISPE 1 , PERCY VIEGO 2 , JUAN COGOLLOS 2
1
Grupo de Investigación en Energías (GIEN), Departamento de Energética y Mecánica
Universidad Autónoma de Occidente
Km 2 Via a Jamundi, Cali, COLOMBIA
Tel (0572) 3188000 Ext 11856, Fax (0572) 5553911
2
Centro de Estudio de Energía y Medio Ambiente (CEEMA),
Universidad de Cienfuegos
Carr. Camajuaní Km. 4, Cuatro Caminos, Cienfuegos, Cuba
Tel 53-432 511963
Abstract: - When an unbalanced voltage system is applied to a three phase induction motor, several
characteristics are affected: efficiency, power factor, losses, insulation life, temperature rise, torque, etc.
Subsequently, it is important to develop mathematical models in order to evaluate these effects. In this paper
statistical models are developed in order to estimate the effect of unbalanced voltages on the efficiency and
power factor of induction motors. The equations relate the efficiency and the power factor with the positive
sequence voltage, the negative sequence voltage, the unbalance NEMA definition and the unbalance IEC
definition. The proposed equations permit to estimate the effect of voltage unbalance on the efficiency and
power factor with a satisfactory accuracy.
Key-Words: - voltage unbalance, efficiency, power factor, induction motors, NEMA and IEC definitions,
statistical models.
1 Introduction
The effects of unbalanced voltages on the
performance of a three-phase induction motor have
been studied widely. The influence of unbalanced on
the efficiency [1],[2],[3], power factor[2],[3],
derating in the machine [4],[5], temperature rise, and
life reduction [6], increase of losses, and negative
effects on the insulation [4],[6] y [7] are some
contributions in the area.
In recent papers, [1], [2] and [4], the authors have
concluded that the efficiency and power factor of the
motor depend on the positive sequence voltage, the
negative sequence voltage, the voltage magnitude and
the voltage angle. Likewise, these authors show that
the derating factor given by the NEMA standard is
insufficient to evaluate the effects of unbalance
voltage on the motor, because it is based only in
NEMA definition. However, these authors do not
give a mathematical relation that may be used to
evaluate the efficiency and power factor.
There are two widely accepted definitions for
voltage
unbalance,
the
IEC
(International
Electromechanical Commission) definitions [8] and
the NEMA (National Electrical Manufacturers
Association) definitions [9]. The IEC definition is
mathematically more rigorous compared to the
NEMA definitions.
In this work, using a statistical approach, the
authors developed several multiple regression models
to estimate the effect of unbalance voltage on the
efficiency and power factor of induction motors. The
equations relate the next variables: the positive
sequence voltage, the negative sequence voltage, the
NEMA definition and the IEC definition. These
mathematical models estimate the effect of unbalance
voltage on the efficiency and power factor of
induction motors with satisfactory accuracy. It is
important to mention that the equations were
developed for a particular group of induction motors;
therefore it is important to obtain a more general
equations in a future work.
2
Characterization of
Unbalance and their Effects
Voltage
Several authors [1], [2] and [4] had concluded that
the efficiency and power factor of the motor
depended on the positive sequence voltage, the
negative sequence voltage, the magnitude of voltage
and the angle of the voltage, likewise these authors
show that Line Voltage Unbalance Factor (LVUF)
given by NEMA standard is insufficient to evaluate
effects over the induction motor. However these
authors only give a qualitative explication and precise
numerical values and characteristics have not been
given.
max imum voltage deviation
LVUF 
from average voltage
average voltage
(2)
This definition avoids the use of complex algebra,
and is called Line Voltage Unbalance Factor (LVUF)
or NEMA definition.
2.1 Voltage Unbalance Definitions
The level of voltage unbalance that is present in a
system can be specified using two commonly used
definitions. The first definition is widely used in
European standards and is based on the Theory of
Symmetrical Components. The second definition is
used in USA and avoids the use of complex algebra.
2.1.1 IEC Definition
The definition of voltage unbalance used by academic
community is the ratio of negative sequence voltage
Vab2 to the positive sequence voltage Vab1 and is
called Negative Sequence Voltage Unbalanced Factor.
This definition is adopted by IEC 60034-26 [8] and is
also known as the Voltage Unbalance Factor (VUF)
or IEC definition.
V
VUF  ab 2
Vab1
(1)
For a set of unbalanced voltages Vab ,Vbc ,Vca , the
positive and negative sequence voltages Vab1 and
Vab2 are given by
Vab  a Vbc  a 2 Vca
3
2
V  a Vbc  a Vca
 ab
3
Vab1 
Vab2
The VUF can also be expressed in a more userfriendly form than given by equation (1), which
requires only the three line-line voltage readings
Vab , Vbc ,Vca .
Where  
Vab  450 0,Vbc  363 .6  121 .44,Vca  405 130 
Then, using Symmetrical Components the
positive
sequence
voltage Vab1 is
404 .625 2.89 and the negative sequence
voltage Vab2 is 50.217   23.98 . So, using
the IEC definition, equation (1),
the
unbalance is :
VUF 
50.217
 0.124
404.625
But if we use the NEMA definition, equation (2), the
average voltage is 406.2 and the maximum voltage
deviation from average voltage is 450-406.2=43.8,
and the unbalance voltage is:
LVUF 
43.8
 0.108
406.2
Therefore, there is a difference results between the
two values.
An extensive analysis made by Pillay [4] revealed
that the differences are not significant when the
motor operates by unbalanced supplies in the 5%
range.
where a  0.5  j0.866 and a 2  0.5  j0.866
1  3  6
V
VUF  ab2 
Vab1
1  3  6
2.1.3 Comparative Example
Consider three unbalanced line to line
voltages:
En
Vab4  Vbc4  Vca4
(Vab2  Vbc2  Vca2 ) 2
En la
2.1.2 NEMA Definition
The NEMA Standard MG1.1993 [9] and the IEEE
community use the following definition:
2.2 Influence of Voltage Unbalance type
In a recently work, Lee [2] show a comparison
between different kinds of unbalance voltage and
their effects on the efficiency, power factor and losses
in a three phase induction motor of 3 HP. The Table
1 shows the partial results. The different types of
unbalance are considered: mono-phase, bi-phase and
three-phase,
unbalanced
with
undervoltage,
unbalanced with overvoltage and angles unbalances,
respectively. RLI is the rate of the loss increment
with respect to the balance condition.
Lee reaches the conclusion that both the positive
sequence voltage and the negative sequence voltage
must be considered in order to evaluate the effects of
the unbalance. Lee shows that when the valued of
the positive sequence component ( V1 ) is large then
the efficiency will be high and the power factor will
be low (see Table 1). Also, if V1 is constant and V2
increases, the efficiency will be reduced more than
the power factor.
L
V
U
F
0,00
V
U
F
Va
Vb
Vc
V1
V2

R
L
I
fp
0
83,80
1,0
83,1
115,8
4,6
80,53
1,3
85,3
3,99
4
117,7
4,7
81,38
1,2
84,7
3,94
4
122,1
4,9
81,51
1,2
83,9
3,96
4
126,8
5,1
82,25
1,1
83,0
3,41
4
126,8
5,1
83,04
1,1
82,9
4,04
4
132,3
5,3
83,23
1,0
81,6
3,64
4
137,1
5,5
83,40
1,0
81,2
3,55
4
139,0
5,6
83,58
1,0
80,8
6,00
6
111,8
6,7
79,67
1,3
85,4
6,00
6
113,5
6,8
80,20
1,3
85,2
5,91
6
119,8
7,2
80,85
1,2
84,8
5,91
6
126,5
7,6
81,48
1,2
83,4
5,33
6
126,6
7,6
81,86
1,2
82,9
6,10
6
127,0
120
125,0
120
127,0
120
127,0
120
127,0
116,0
127,0
113,1
127,0
120
127,0
120
129,0
120
125,0
120
127,0
120
127,0
120
127,0
113,9
127,0
109,7
127,0
120
127,0
120
129,0
120
0,0
4
127,0
240
112,7
240
114,3
240
127,0
240
127,0
231,9
127,0
240
127,0
240
138,3
240
139,7
240
107,2
240
108,6
240
127,0
240
127,0
227
127,0
240
127,0
240
144,7
240
146,2
240
127,0
3,96
127,0
0
110,0
0
111,8
0
112,4
0
127,0
0
127,0
0
142,9
0
145,9
0
148,2
0
103,2
0
105,0
0
105,4
0
127,0
0
127,0
0
151,3
0
156,5
0
159,0
0
135,1
8,1
82,17
1,1
81,8
5,35
6
6
3 The Statistical Models to Evaluate
the Efficiency and Power Factor
Using the experimental results give by Lee [2] and a
statistical approach, in this paper the authors
developed mathematical equations that relate the
next variables: the positive sequence voltage, the
negative sequence voltage, NEMA definition and
IEC definition, with the efficiency and power factor.
The authors thought that using this formulation it is
possible to evaluate the effects of unbalance voltage
on the efficiency and power factor of induction motor
in function of the voltage magnitude and unbalance
type.
Eficiencia vs V1
84
83.5
83
142,7
144,7
8,6
8,7
82,37
82,49
1,1
1,1
80,5
79,4
82.5
Eficiencia (%)
5,44
motor losses for a 0.05 of LVUF, depending on the
type of unbalance. So, if the average voltage is kept
fixed in 240 V, with Vbc constant, Vab increasing and
Vca decreasing, the total losses increase at 115%. By
other side, if the average voltage is maintained fixed
at 240 V , Vab and Vca increasing, and Vbc
decreasing, the total losses only increase at 105%. In
other words, there is 10% difference for the same
LVUF. By other side, the calculated derating factor
is 0.7 in the first case and 0.77 in the second case,
while the derating factor giving by NEMA is 0.75.
82
81.5
81
2
y = -0.0046x + 1.276x - 5.3088
2
R = 0.8288
80.5
80
79.5
Table 1. Different kinds of unbalanced and its effects on loss,
efficiency and power factor in a 3 HP three phase induction
motors.
79
100
105
110
115
120
125
130
135
140
145
150
V1 (V)
Figure 1. Efficiency vs. Positive Sequence Voltage
However, Lee gives only a qualitative description
and does not give a mathematical equation with
efficiency and power factor as function of V1 and
V2 .
On the other hand, Kersting and Phillips [5] show
that motor losses depend on voltage magnitude and
the type of unbalanced (magnitude and angle [2]).
Also, he shows that the derating factor give by
NEMA (based only in LVUF) in order to reduce of
horsepower of motor is very poor to express the
unbalance effects.
Kersting and Phillips calculations for a motor of 25
HP , 240 V show that there is a great difference in
3.1 Evaluating the effect of
unbalanced on the Efficiency
voltage
It is shown that there is a direct relation between the
efficiency and V1 , but the correlation between these
two variables is low. It is showed in the Figure 1, it
was obtain using the next quadratic model:
  0.0046  V12  1.276  V1  5.3088
The standard deviation for these model is 0.52 with a
R 2 = 0.83.
The model of figure 1 showed that in order to
improve the correlation between the efficiency and
voltage magnitude is necessary use a combination of
variables.
The next two models show a better correlation
between  and V2 when we add VUF factor. Then
the figure 2 showed the results of the next models:
For a VUF=0.04, the equation is
  2.3691 V22  27.272  V2  5.165
with a R 2 =0.9279
For a VUF=0.06, the equation is
  0.6867  V22  11.911 V2  30.779
3.2 Evaluating the effect of voltage
unbalanced on the Power Factor
In order to develop a equation to estimate the effect
of unbalance on the power factor, a similar way was
used.
So, the authors found a lineal relation between the
reduction of power factor and V1 . Figure 3 shows a
high correlation R 2 = 0.9775 and a low standard
deviation. The equation is:
fp  0.1812  V1  106.01
with a R 2 =0.9847
E ficiencia vs V 2
84
83.5
2
y = -2.3691x + 27.272x + 5.165
2
R = 0.9279
83
2
y = -0.6867x + 11.911x + 30.779
2
R = 0.9847
Eficiencia (%)
82.5
82
81.5
81
80.5
80
Figure 3. Power Factor vs. Positive Sequence Voltage
FD V = 4
FD V = 6
79
2
3
4
5
6
7
8
9
10
V 2 (V )
Figure 2. Efficiency vs. Negative Sequence Voltage
In order to increase the correlation is necessary to
include V2 and V1 . The model proposed is:
  23.94  0.81 V1  2.6  10 3 (V1  V2 )
(3)
 2.7  10 3  V12 (%)
The proposed model of equation (3) have a multiple
regression coefficient of 0.95 and a standard
deviation of 0.29.
By other side, through of multiple regression model
the influence of LVUF or NEMA definition on
efficiency was analyzed, :
  70.78  0.11 V1  1.04  10 2 (V1  V2 )
(4)
 4.03  10 3  ( LVUF  V1 ) (%)
This model of equation (4) has a multiple regression
coefficient of 0.95 and a standard deviation of 0.41.
The figure 4 shows another two equations that use a
combination of variables. So, the next two models
have a better correlation between fp and V2 when we
use VUF. Also the figure 4 shows the results of the
next models:
For a VUF=0.04, the equation is
fp  4.8119  V2  107.42
with a of R 2 =0.9881
For a VUF=0.06, the equation is
fp  2.935  V2  105.39
with a R 2 =0.9749
87
Factor de Potencia vs FDV
V2 = 4
FDV = 6
86
Factor de Potencia (%)
79.5
85
84
83
82
y = -4.8119 x + 107.42
R2 = 0.9881
81
y = -2.935 x + 105.39
R2 = 0.9749
80
79
The model giving by equations (3) and (4) showed
that in order to increase the accuracy of the model it
is necessary to use a several variables.
3
4
5
6
7
8
V2(V)
Figure 4. Power Factor vs. Negative Sequence Voltage
9
In order to improve the correlation, in the same way
that in the efficiency, is necessary include V2 , V1 and
VUF or LVUF . Then, the resulting equation is:
fp  115.892  2.0434  LVUF  0.1828  V1
(5)
 1.6685  V2  0.3388  LVUF  V2 (%)
This model of equation (5) has a multiple regression
coefficient of 0.98 and a standard deviation of 0.28.
3.3 Future Development
The equations showed were developed for a concrete
case. So for a future work this formulation will be
extended for a more general case that permit evaluate
the efficiency and power factor in function of
magnitude, kind of unbalance and parameters specific
in each machine (parameters that can be calculate by
no invasive methods).
4 Conclusion
To evaluate the efficiency the correlation using only
V1 is low. From this work we can conclude that the
correlation between the efficiency and voltage
magnitude is improved by adding more variables
such as V2 and VUF.
The correlation between the efficiency and the
voltage magnitude is higher when we include: V1 ,
V2 and VUF than we use only V1 . See the equations
(3) and (4).
To evaluate the power factor the correlation using
only V1 is high. But it is better if in the equations use
several variables: V1 , V2 and LVUF. See the equations
(5).
It is necessary to continue this work in order to
obtain a more general model considering the effect of
unbalance and the parameters of each motor.
References:
[1] J. Faiz, H. Ebrahimpour and P. Pillay, Influence
of Unbalanced Voltage on the Steady-State
Performance of a Three-Phase Squirrel-Cage
Induction Motor, IEEE Transaction on Energy
Conversion, Vol.19, No.4, 2004, pp.657-662.
[2] Ching-Yin Lee, Effects of Unbalanced Voltage
on Operation Performance of a Three-Phase
Induction Motor, IEEE Transaction on Energy
Conversion, Vol.14, No.2, 1999, pp. 202-208.
[3] P. Viego, E. Quispe and J. Cogollo, Operación de
los Motores Asincrónicos con Voltajes
Desbalanceados de Diferente Tipo y su Efecto
sobre la Eficiencia y el Factor de Potencia,
Memorias I Congreso Internacional sobre Uso
Racional y Eficiente de la Energía, CIUREE2004,
ISBN 9583371327, Colombia 2004, pp.151-154.
[4] P. Pillay, Derating of Induction Motors Operating
with a Combination of Unbalanced Voltages and
Over and Undervoltages, IEEE Transaction on
Energy Conversion, Vol.17, No.4, 2002, pp.485491.
[5] W.H. Kersting and W.H. Phillips, Phase Frame
Analysis Effects of Voltage Unbalance on
Induction Machines, IEEE Transaction on
Industry Applications, Vol.33, No.2, March/April
1977, pp. 415-420.
[6] B.N. Gafford, W.C. Duesterhoef and C.C.
Mosher, Heating of induction motors on
unbalanced voltages, AIEE Transaction on Power
Apparatus and Systems Pt.III-A, Vol.PAS-78, pp.
282-297, June 1959.
[7] E. Quispe, G. Gonzalez, J. Aguado, Influence of
Unbalance and Waveform Voltage on the
Performance Characteristics of three-phase
Induction Motors, Proceedings of International
Conference on Renewable Energy and Power
Quality
Applications,
ISBN
8460798870,
Barcelona, España 2004.
[8] IEC 60034-26, Effects on Unbalanced Voltages
on the Performance of Induction Motors,
Publishing by IEC, 2002.
[9] NEMA MG1-1993, Motors and Generators,
Publishing by NEMA, 1993.