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1
Unbalance on Power Systems: A General
Review
Claudio A. Reineri, Juan C. Gomez Targarona, Senior Member, IEEE, Norberto G. Campetelli
Abstract-- A general revision of different aspects in relation to
the voltage unbalance in electric power systems is presented, that
should necessarily be deeply known by technical operators and
designers of facilities, installations, and electric equipment.
Dissimilar unbalance definitions, unbalance measurement
methods, their quantification and the interpretation of such
magnitudes are revised. The causes of the unbalances in electric
power systems were described and analyzed. The effects on
power systems are also studied, specially those that have
influence on: system operability, lost of efficiency of the threephase system and their impact in the definitions of traditional
power. Similarly is studied the unbalance effect on certain loads,
in particular: three-phase motors, power electronics and ASD’s.
Also methods to locate the origin of these problems, as well as the
different normative or standards, and possible methods to
mitigate their effects are deeply detailed. It is concluded in the
necessity to deepen the study of the power system unbalance,
because numerous non resolved aspects still exist whose solution
requires of a deep knowledge on the part of the involved
professionals.
Index Terms--Power Quality, Voltage Unbalance.
on applied or when its implications are analyzed.
This article presents a general revision of the unbalance
problem in electric power systems, including the following
topics approached in that order:
Definitions: the different definitions that exist to quantify
the unbalance are revised and it is made the consequence
analysis that these definitions have when such factors are
employees for circuit or components studies (for instance on
three-phase motors derating).
Causes and propagation: the origins of this type of
perturbation, the propagation ways and the analysis basic
tools are described to study an electric system operating under
unbalanced conditions.
Effects: the direct effects are analyzed on the most
susceptible loads to the voltage unbalance: three-phase motors
and rectifiers. Aspects related to the power measurement
under unbalanced conditions are also discussed.
Standards and mitigation: the possible mitigation methods
are exposed. The more prominent aspects of the international
normative are discussed.
I. INTRODUCTION
II. DEFINITIONS, IMPLICATIONS, APPLICATIONS AND USES
N a three-phase systems a voltage unbalance take place
when the magnitudes of line or phase voltages are different,
or the phase angle are different from the balanced conditions,
or any combined situation of the two previously mentioned.
The unbalance in three-phase electric systems is framed
inside the problems of Power Quality, for instance:
harmonics, flicker, over and undervoltage, etc. Of these
subjects the unbalance problem, seems to be one of the topics
more relegated by technicians and investigators that work on
Power Quality. However there are several problems that
unbalance presents in the operation of electric power systems.
The factor of more concern is its incidence on the efficiency
of the system: losses in the transmission and distribution
systems, losses in three-phase motors, etc. Non less alarming
turns out to be the effects on the normal operation of threephase electronic equipment or aspects related with power and
energy measurement.
An element that show its marginality in the Power Quality
context turns out to be the frequent ambiguity or the evident
imprecisions with which the phenomenon is defined and later
The National Equipment Manufacturer’s Association
(NEMA) defines Line Voltage Unbalance Rate (LVUR) as
[1]:
MVDALV .100
% LVUR = =
(1)
ALV
where:
MVDALV : Maximum Voltage Deviation from Average
Line Voltage,
ALV : Average Line Voltage.
NEMA standards assume that the average voltage is
always the rated value.
In [2] and [3], the unbalance is defined by IEEE as:
MVDAPV .100
(2)
% PVUR = =
APV
where,
MVDAPV : Maximum Voltage Deviation from Average
Phase Voltage,
APV : Average Phase Voltage,
Denominated as Phase Voltage Unbalance Rate (PVUR),
where the only difference with the previous definition is that
uses phase-voltages instead of line-voltages. This standard is
particularly indicated to motors and generators.
Standard [4] define the Unbalance Ratio as “the difference
I
The authors are with the Electric Power Systems Protection Institute
(IPSEP), National University of Río Cuarto, Argentine (email:creineri@ing.unrc.edu.ar)
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THE 8 LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009
between the highest and the lowest fundamental rms values
referred to the average of the three fundamental rms values”,
which expressed as an equation is:
DBH & LV
(3)
% LVURIEEE 936 =
ALV
where,
DBH&LV : Difference Between the Highest and the
Lowest Fundamental rms Values.
This is not the same as defined in [2] or [3], being also
discussed by [5].
IEEE standards in references [4] and [6] introduce, from
the voltages of each of the three phases, the Voltage
Unbalance Factor (VUF) as:
V
VUF = 2
(4)
V1
where,
V2 : Negative Sequence Voltage,
V1 : Positive Sequence Voltage.
This concept is also presented by the IEC Standard in [7].
In reference [8] %LVUR and VUF are jointly defined, and
also the possibility that the unbalance can be expressed as
zero sequence component to positive sequence component
ratio is mentioned.
This last calculation requires working and operating with
phasors. It must be remembered that the decomposition of a
three-phase system of phase voltages ( Va ,Vb ,Vc ) in their
symmetrical components of sequences zero, positive and
negative, ( V0φ ,V1φ ,V2φ ) can be expressed as:
⎡V0φ ⎤
⎡1 1
⎢ ⎥ 1⎢
=
V
⎢ 1φ ⎥ 3 ⎢1 a
⎢V2φ ⎥
⎢⎣1 a 2
⎣ ⎦
1 ⎤ ⎡Va ⎤
⎢ ⎥
a 2 ⎥⎥ ⎢Vb ⎥
a ⎥⎦ ⎢⎣Vc ⎥⎦
(5)
where a = −0.5 + j 0.87 and a 2 = −0.5 − j 0.87 . The
unbalance factor in complex form is given by:
V2φ
jα
(6)
VUF φ = VUFφ e φ =
V1φ
If the same transformation is applied to the line-to-line
values, the previous expressions become:
⎡V0 ⎤
⎡1 1
⎢ ⎥ 1⎢
=
V
⎢ 1 ⎥ 3 ⎢1 a
⎢V2 ⎥
⎢⎣1 a 2
⎣ ⎦
1 ⎤ ⎡Vab ⎤
⎢ ⎥
a 2 ⎥⎥ ⎢Vbc ⎥
a ⎥⎦ ⎢⎣Vca ⎥⎦
The equation for VUF, now will be expressed as:
V
VUF = VUFe jα = 2
V1
(7)
(8)
The relationships between the phase and line-to-line
sequence components are:
V1 = 3V1φ e j (π 6 )
(9)
V2 = 3V2φ e − j (π 6 )
(10)
While the zero-sequence component is zero. Both
equations show that basic relationships between the balanced
three-phase line voltage and phase voltage (the
2
3 factor
and π / 6 phase difference) appear again after the
symmetrical transformation. The negative phase difference in
(1) reflects the reversed phase sequence of negative sequence
components. From (9) and (10):
VUF = VUF φ e − j (π 3)
(11)
Therefore, the VUF of line voltages is the same as that of
phase voltages in magnitude. This applies not only in threephase three-wire systems where line voltages rather than
phase voltages have physical significance but also in threephase four-wire systems as the definition of VUF is not
concerned with zero-sequence component.
However, the application of the definition of the VUF
becomes effective just as it is show by (4). It is the
relationship between the magnitudes of the component of
negative sequence regarding the component of positive
sequence, without considering in any moment their angle or
phase.
Another definition, of the same type that the VUF but that
includes the relationship between the phases of both sequence
components, (8), it has been considered in some cases to the
only objective of evaluating the unbalance definitions [9] and
in other cases as evaluation like parameter related to the
behavior of different loads when their supplies are unbalanced
[10]-[13]. It is the Complex Voltage Unbalance Factor
(CVUF) that in spite of having been its definition expressed
above, it is now defined as:
V
V ∠θ
(12)
CVUF = 2 = 2 2 = K v ∠θ v
V1 V1∠θ1
This definition is found at levels of technical articles and
not in any internationally known standard (IEC, IEEE, etc). It
is clear that not only the consideration of the relationship
between the magnitudes of the sequence components but also
the relationship between its phases “accuracy” characterizes
the unbalance. For the time being it do not appear opportune
to say “exactly” since, for example, when it is necessary to
quantify unbalance effects on components it can be necessary
that the magnitude of positive sequence is also referred to the
nominal value of the equipment or component under study.
Finally it is necessary to say that all these definitions can
be also applied on three phase currents.
A. Discussion
In order to be exact in the use of the word unbalance and
their quantification and fundamentally in the applications that
from it derive (for example in case of equipment derating) it is
necessary to mention some ambiguities that can be seen in the
specific references.
Reference [14] compares (1) with (4) arguing that NEMA
standard is the one that gives the curve of motor derating in
[1] and it could be entered to such a curve with (4). It is
shown that for low unbalance values (under of 5 %) when the
derating is applied, both forms give practically the same
result.
In reference [15] it is done the comparison taking the phase
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THE 8 LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009
values, the (4), with (2) and with (3). Somebody not alerted
could consider this last one as (2). In the reference, it is also
compared (4) with (1); always for small unbalance values,
resulting that equation (4) gives the same value that (1). But
among (4), (2) and (3) exist substantial differences, for
example for motor derating. The application of (4) or (3)
could imply to leave the machine without derating, if (4) is
used or a derating to 90% if (3) is applied.
The derating curve given by IEC [7] is the same than the
given by [1], and it is clear that the used definition is the one
given by (4).
III. CAUSES AND PROPAGATION
The power generation in the electric systems is essentially
balanced. The unbalances along the system, and basically in
the consumption points, it appears for some of the two
following circumstances or for a combination of them:
• The load currents are balanced but the impedances of the
system for those that such currents flow or the impedance
of some of their components are not. The flow of balanced
currents circulating for components where the impedances
characteristic of each phase and their respective couplings
are not the same, will produce unbalanced voltage drops
what determines that in the use points the voltages are
unbalanced.
• The impedances of the system are balanced, for example,
the 3 conductors of the three-phase line are identical
(physically) and they are in the corners of an equilateral
triangle, but the currents that circulate for them are
unbalanced; therefore unbalanced voltages in the use points
will appear.
As origin of the unbalance in currents or voltages, in spite
of having originally a balanced voltage system, it can be
mentioned:
• An unbalanced three-phase load, for instance a motor
with unbalance in their windings.
• Distribution systems having single-phase or two-phase
loads.
• The operation of a protection device on some load, on
some series component (line, transformer, etc.) or on a
shunt component (bank of capacitors).
• Line or substation voltage regulators improperly adjusted
(in this situation, for a regulation scheme of line voltage
drop, an unbalance of currents could also imply an
unbalanced operation of the regulator regulated voltages).
The unbalance problem has the tendency to be accentuated
at distribution levels, being industrial, commercial, or yet
more in domestic or rural distribution systems. Paradoxically,
these systems are the use points and it is there where the
unbalance takes place and where accentuates their negative
effects.
The fundamental tool to analyze the unbalance behavior
and propagation is the electric load-flow. Historically, and
perhaps for a natural inheritance of their original application
to transmission systems, this was always applied considering
the system as a balanced system (working therefore only with
3
the positive sequence component). When the objective is to
analyze unbalance problems it will necessarily to carry out to
an analysis by phase or in its respective sequence
components. This requires a bigger effort in the modeling of
the system, in the development of the necessary algorithms
and in the computational effort. It could be said that the work
multiplies by three.
Reference [16] can be a first step to the interpretation of
this situation, there the different factors that will be
considered are enumerated, together with the outlines of the
elementary equations and with the comparison of results
obtained on typical distribution systems. Reference [17]
conceptually faces the same situation with the particular
considerations that it can require a rural distribution system.
In references [18] and [19] the modeling of transformers to
be applied in this type of conditions is deepened, showing the
importance of the transformer modeling under unbalance
conditions. In reference [20] it is also analyzed the
phenomenon of unbalance propagation, being observed the
way in which a transformer can attenuate (filter) or not the
unbalance. In reference [21] the problem is approached for
sub-transmission networks where have been measured and
simulated situations where the unbalance levels overcome 1%
in networks of 66kV.
In reference [22] an assessment of voltage unbalance
emission by installations connected to MV, HV and EHV
power Systems is given. This requires a quantitative measure
of propagation of voltage unbalance from upstream (higher
voltage) to downstream (lower voltage) systems in terms of
transfer coefficients. Reference [23] presented a study of such
transference coefficients as function of the load types.
Determined types of loads when feed by a three-phase
unbalanced voltage system can produce unbalanced currents
in a bigger level to that of the feeding voltages, for instance an
induction motor fed by a voltage system with 2,5% of
unbalance can take a load current with an unbalance of 20%
[24]. This value will be proportional to the relationship
between the positive sequence and negative sequence
impedances of the load (in this case a motor). These
situations, therefore, can cause magnification of the unbalance
effects.
It is not simple to identify the contributions of the different
components of the electric system to the unbalance. In
reference [25] a tool is presented that allows to identify the
levels of contribution of the asymmetric lines (or non
transposed lines) and of the loads to the unbalance, inclusive
distinguishing the contribution of both parts.
IV. EFFECTS
A. Three-phase Motors
This turns out to be a typical load of those more damaged
by the unbalanced feeding and also one of the problems more
studied in relation to the unbalance. In first place, a general
description of the problem is made and then some more
punctual aspects will be presented.
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As previously cited, due to induction motor operating
characteristics, small percentage voltage unbalance will result
in a much larger motor percentage current unbalance. The
mentioned magnification roots in the rotor dissimilar behavior
for applied positive or negative sequence voltage systems,
resulting that the negative sequence impedance at normal
running speed can be approximated to the positive sequence
impedance at standstill. In other words, the negative sequence
current (in p.u.) will be approximately equal to the product of
the negative sequence voltage and the ratio of the starting
current to the full load running current. For instance, when a
voltage having 0.05 per-unit negative sequence component is
applied to the motor, negative sequence currents of 0.30 per
unit will flow through the rotor winding. Thus, a 5% voltage
unbalance produces a rotor negative sequence current of 30%
of full-load current. In such conditions the motor may
experience a 40-50% increase in temperature rise [26].
However, the positive sequence current will continue being
proportional to the positive sequence voltage. A deeper study
regarding the behavior of the sequence component currents
and also their manifestation on the line currents under
unbalanced conditions can be seen in [27].
Rotor losses are also affected by rotor current frequency
that can be nearly twice the power system frequency,
producing an important Skin effect. The effective resistance
depends on rotor winding or bar depth inside the rotor slots,
having been measured ratios of 1.25 to 6 between 100 Hz (or
120 Hz) and d.c. resistances, effect frequently leave aside for
several researchers.
Thus the heating of one unit of negative sequence current
is for the motor greater than the heating effect of one unit of
positive sequence current. It has been shown (analytically
determined) that the rotor losses increases at a faster rate than
the stator losses as the unbalance voltage increases.
This phenomenon leads to a reduction of induction motor
life expectancy due to overheating.
Too, the reduction in the peak torque reduces the motor
reaction capability in front of sudden mechanical load
changes and decreases the motor ability to ride through
voltage sags, thus affecting the whole system stability.
In summary, the motor derating is necessary due to the
following reasons:
• The most important one, is due to the rotor current
increase causing overheating and life span shortening,
• Positive sequence torque under voltage unbalance is
lower than under balanced voltage (generally positive
sequence voltage is lower than supply voltage when the
voltage system is unbalanced),
• Negative sequence voltage torque must be subtracted
from the positive sequence torque,
• Rotor current increases due to unbalanced supply, thus
for the same shaft load the motor will operate at a higher
slip, and
• Skin effect on rotor bars increases their resistances due
to high frequency of induced voltages, nearly double than
power rated frequency.
In this sense, the IEC Standard in [27] suggests for
induction three-phase motors a derating that it is expressed in
the second column of the Table I and for which the unbalance
is quantified according to (4). The standard recommends not
to operate motors with unbalance higher than 5%. On the
other hand, NEMA [1] and IEEE [2]-[3], recommend a
practically identical derating to that of the IEC, third column
of Table I, but whose unbalance parameter is calculated with
(1).
TABLE I
MOTOR DERATING FOR VOLTAGE UNBALANCE ACCORDING TO IEC AND
NEMA
Voltage unbalance
(%)
0 to 0.5
1
2
3
4
5
IEC derating
using (4)
0
0
≈0.955
0.9
≈0.835
≈0.755
NEMA derating
Using (1)
0
≈0.99
0.95
0.89
0.825
0.75
In reference [28] a per phase analytic study is done
analyzing the behavior of a motor fed by an unbalanced
voltage system, as unbalance parameter is used that given by
(1). Two types of unbalance are presented, which were
quantified in such a way, in both cases the average of the
three voltages stays constant. In one of the cases, one voltage
value stays constant while a second ascend and the third drop;
in the other case two voltage values ascend identically while
the third drop. Rotor and stator losses were observed for both
cases with different unbalance degrees. It is here observed
that the derating depends on the "way" in that the unbalance
takes place, being concluded that for the same unbalance
(5%), in a case the necessary derating is of 0.70 and in the
other of 0.77.
In an experimental work of similar characteristics to the
one observed in [28], Lee [29] demonstrates that for doing a
right derating, is not sufficient the simple quantification of the
unbalance by using (4). The root for such a statement is based
in that for the same VUF values, but reached varying in a
different way the voltages, different operation temperatures
are reached. It is also shown that the proposed derating
presupposes a positive sequence equals to the machine rated
value, if this magnitude is different from the rated one it also
introduces the necessity to reconsider the machine working
condition.
Wang, in [30], where a motor analytic model is presented,
suggests the necessity to quantify the unbalance by means of
the Complex Voltage Unbalance Factor (CVUF) in order to
analyze the unbalance effects on the motor. In reference [11],
Wang deepens its analysis in such direction, and takes as
analysis parameter the unbalance quantified in (12). It shows
that for the same value of Kv, what is equivalent to say that for
VUF kept constant, the maximum stator current, the slip and
the derating factor change with the θv value. There it is also
observed that the unbalance effects are more clearly expressed
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introducing the phase difference between the positive and
negative sequence voltages. In fact also it is observed that for
the same unbalance level quantified according to (4), different
derating values are necessary depending on the angle formed
between both vectors.
Pillay et al in [31] have considered on the derating curve
outlined by NEMA, the possibility that besides the unbalance
the machine is subjected to overvoltages or subvoltages. By
means of an electric and thermal model of the machine, curves
superimposed to the NEMA derating ones are determined as
function of the unbalance, where besides such an unbalance
the possible overvoltages or undervoltages are considered. In
reference [10] it is reinforced the necessity that the application
of the derating for unbalance should not leave aside the
magnitude of the operation voltage (in this case the average
voltage, since NEMA derating is applied). In reference [32] it
is settled down that although the CVUF clearly define the
machine behavior, the problem is not yet a closed one. The
problem is that Kv does not has a fix reference value, that
could be for instance to take as reference the positive
sequence voltage equals to the motor rated value, although it
seems that the problem persists.
Continuing with the apparent solution that would imply the
application of the CVUF, in [33] it is shown explicitly that the
same CVUF value can be obtained for different feeding
conditions. In such a case, so much for line-to-line voltages as
for phase voltages, it is observed that the same CVUF value is
obtained for circumstances in those that the machine rated
values are: 1) bigger, 2) smaller or, 3) the same that the
positive sequence voltages applied to the machine. At the
same time, in the case where the positive sequence voltage is
bigger than the rated voltage (case 1), two situations are
clearly distinguished: 1.a) the line-to-line or phase voltages
are all bigger than the rated voltage, or, 1.b) the line-to-line or
phase voltages can or not be bigger than the rated voltage.
When the positive sequence voltage is smaller than the rated
voltage (2), two situations can be distinguished: 2.a) the lineto-line or phase voltages are all smaller than the rated voltage,
or, 2.b) the line-to-line or phase voltages can or cannot be
bigger than the rated voltage. This defines the following
unbalance factor respectively: 1.a) overvoltage unbalance
(KOU); 1.b) mixed overvoltage unbalance (KMOU); 2.a)
undervoltage unbalance (KUU); 2.b) mixed undervoltage
unbalance (KMUU). The situation 3 is denominated unbalanced
equal voltage. Under these parameters the behavior of the
motor is observed: current unbalance, phase currents,
efficiency and power input. However their application
continues being restricted to circumstances where the
magnitude of the component of positive sequence voltage is
similar to the value of the rated voltage.
In reference [24] a three-phase wounded rotor motor is
subjected to different unbalance conditions using as study
parameter the CVUF value. Among the measured parameters
they are the currents of the three rotor windings. It can be
observed that a Kv of approximately 5%, and practically
independent of the value of θv, generate a rms magnitude that
5
results to be practically double of the value of such a current
under balanced conditions. If the thermal effect is added to the
classic derating method (NEMA and IEC), the derating is
greatly increased, for instance for a Kv or VUF of 5% the
derating value is increased to 50%.
B. Rectifiers
Power electronic converters serve as the interface for many
large electronic loads ranging from three-phase
uninterruptible power supplies (UPS’s) to motors operating at
variable speeds through the use of ASDs. Most the threephase converters contain diode rectifiers front-end. The
characteristic harmonics, for normal operation, in a six-pulse
converters are the non triplen odd harmonics, for example, the
5th, 7th, ll th, 13th, etc.:
(13)
h = kq ± 1
where:
k = any integer,
q = pulse number.
Under the conditions of voltage unbalance, the input
current harmonics are not restricted to the converter
characteristic harmonics, and non-characteristic triplen
harmonics can appear such as the 3rd and 9th harmonics [4].
The non-characteristic harmonics magnitudes are proportional
to the unbalance magnitude.
In reference [34] an analysis of unbalance magnification
effect for an ideal uncontrolled rectifier circuit without ac and
dc-side inductors is presented. The conditions of seven
distinct operating modes of the rectifier are established in
terms of the voltage unbalance factor (in this case the
parameter is the VUF). In each mode of operation, analytical
expressions of symmetrical components of fundamental line
currents and current unbalance factors were derived.
In reference [35] the behavior of the line currents for a 12
pulses rectifier is studied.
In reference [36] it has been explored, based on simulation
and experimental results, the effects of a dc bus choke
inductor on induction machine ASD performance during
voltage unbalance/sag conditions.
In reference [37] the behavior of the characteristic and not
characteristic harmonic of a AC-DC three-phase rectifier for
different unbalance degrees is studied. To describe the effect
of the three-phase current unbalance on the Total Harmonic
Distortion (THD), a new factor is defined, denominated
“Total Phase Harmonic Distortion Unbalance Factor"
(PTHDUF), that is proportional to the VUF.
In reference [38] the effects on the behavior of the
induction machine (as ASD load) are mainly analyzed.
In references [39] and [13] similar studies are presented on
an ASD under unbalanced supply conditions: the behavior of
the magnitudes of the phase currents, the THD, the derating
factor K for transformers, among others are analyzed, for
different unbalance levels. In [39] the unbalance is quantified
by means of (1), and in [13] by means of (12). Perhaps, for
the situation type that is analyzed, in theory would be
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THE 8 LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009
applicable (3), although in both cases studied in [39] and [13],
very similar situations are observed, thus the employment of
(12) will allow more clearly the identification of the most
unfavorable unbalance conditions. It can stand out the fact
that, for example, the selection of accessory components of an
ASD (transformers or cables) can be under-rated if the
selection or design conditions are the balanced one.
C. Operative: Power factor, apparent power, transmission
efficiency
The concept of power factor is a convenient figure of merit
representing the utilization of a supplying system and was
defined by the ratio of the average power or true power (W) to
the apparent power (VA). The notion of power factor is
understood as an important parameter in the engineering
economics of power systems.
However this concept, originally defined for single-phase
systems and then extended to three-phase balanced systems,
fails under certain unbalance conditions. This had given place
to new definitions of apparent power and power factor, but
the discussion is not yet closed. Examples of this situation in a
simple but clear presentation can be found in [40]. Another
example of the existing complexity can be seen in [41], where
a new definition of power factor based on symmetrical
components is presented, being also applied to a three-phase
rotational machine.
Also the IEEE in [42] takes this topic and shows the
difficulty and the contradictions that implies the application in
the classic sense, of the power and power factor definitions.
The subject is also studied in [43], including not only the
unbalance but also the non sinusoidal conditions. A physical
meaning is given of the apparent power and of the power
factor in its more elemental condition (single-phase circuit)
that then can be generalized to unbalanced and non sinusoidal
systems. However these concepts are verified only for certain
conditions and it is clear that non a single path exist that can
consider the power quality with a structure of economic
penalty (such as the power factor) and with which the
user/utility can design a compensation system.
Another aspect related to this topic, that deserves to be
shown explicitly, is the efficiency of the generation,
transmission and distribution of the electric power in a threephase unbalanced system. In such a sense, an exaggerated
example but clarifying of the situation, can be seen in [44],
where the same amount of power or load (kW) is fed in one
case by a three-phase system and in another case for a singlephase system. Such a situation implies, for the outlined
example, a 15% of lost of energy. In reference [45], the losses
are evaluated in a transmission line under unbalanced load
conditions, by using as parameter the CVUF, concluding that
for the case of an un-transposed transmission line the losses
are affected as much for Kv as for θv. Also there is shown in
the cited reference, that if the load unbalance is big it will also
increase considerably the line losses.
6
V. LOCALIZATION AND MITIGATION
A fundamental stage in the study of any problem of power
quality is the determination of the origin or the source of the
perturbation. Just as it was expressed to the beginning of this
article, the generation in the electric power systems is
essentially balanced; the unbalances appear in the system like
an interaction phenomenon among unbalanced loads
(unbalanced currents) and impedances. Therefore, and
similarly to the harmonics problem, their origin or source
have to be find on the “load side". Ferrero in [46] outlines as a
tool for the identification of pollution sources of harmonic or
unbalance, that only the active power at fundamental
frequency and of positive sequence will make “positive
direction” in a measure point. The sign that is obtained of the
difference between the recently defined one, and the total
active power will define the direction of the polluting power
and therefore of the polluting source (in this case it is not
distinguished the unbalance effect from the harmonics effect).
In a similar sense, in [47] it is proposed as variables to
evaluate the directions of the active power flows of negative
sequence, in order to declare the existence of a "source" or
“drain” of the unbalance. It is shown that this approach can
fail when it indicates a "drain" but not when it indicates a
"source" (this is basically due to the interaction among
unbalanced loads).
Efforts have been made to separate or to identify the
contributions to the unbalance from the different components
of the system; such identification constitutes a first mitigation
tool if it can be acted on it. In reference [47] it is reported the
work on the effects on the unbalance in a 66 kV network,
analyzing the effects of the load asymmetry, of the network
asymmetry (lines) and of their combined effect.
The growing capacity of power handling of the electronic
components allows the incorporation of equipment at
distribution networks or industrial plants levels, which are
very appropriate for an important part of the deficiencies of
power quality. In many circumstances, and as frequently
happens in the study of problems of power quality, an
equipment introduced in the network in order to improve an
aspect of power quality, ends being victim of some other
problem of quality (a following example is evidence of this).
Static Compensators (STATCOM), are typical equipment
to those that reference is made, and that arise as an alternative
for the unbalance mitigation. In reference [48] one of this
equipment is presented and analyzed, as an alternative to
compensate the voltage unbalances in a Point of Common
Coupling (PPC). This equipment can also be a victim of such
problems of quality. However, the control strategy that it is
used can not only make the equipment immune to these
deficiencies (inside certain margins) but can represent a
mitigation alternative to the deficiency. In reference [49]
another case is shown where the STATCOM is proposed as a
mitigation alternative. Another conception of these equipment
and closely related with them is the Parallel Active Filter.
Reference [50] presents the application of one of these
equipment as a compensator, that acts according to different
th
THE 8 LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009
control strategies in front of unbalance situations: unbalanced
load currents or unbalanced source voltages.
Distributed Generation can also be incorporated to
distribution networks acting as a compensator element of the
unbalances, characteristic of these type of networks [51].
Different countries or international institutions establish
Standards or guidelines; IEEE and ANSI suggest maximum
acceptable unbalances specifically for different applications.
Emission limits for individual equipment or a customer’s
installation are developed, based on the impact that these
emissions will have on the quality of the voltage.
Compatibility levels are reference values for coordinating the
emission and immunity of equipment or installations which
are part of, or supplied by, a supply system in order to ensure
the EMC in the whole system. Under this criterion, recently
the IEC established as indicative levels for MV, HV and
EHV, 1.8, 1.4 and 0.8 % respectively of unbalance. From this,
some countries try adjustments of such regulations that do not
turn out to be always simple [52]-[53].
VI. CONCLUSION
It is concluded with the following points which are
considered as the most prominent ones regarding the power
system unbalance problem:
• For the unbalance quantification it is necessary to specify
the unbalance definition that has been used, fundamentally
if such a quantity will be applied to evaluate its effects (for
example on motors derating).
• Although it is certain that the different unbalance
definitions require the application of dissimilar
methodologies and measure elements, it would be
appropriate that their quantification were made in just one
unique way.
• The modeling of the system components and the
simulation methodologies for the analysis of a three-phase
unbalanced system, should appropriately contemplate and
consider the unbalance sources, in general coming from the
loads, so much as the eventual inherent unbalances due to
the impedances of the system components.
• Three-phase motors and ASDs are the most sensitive
industrial loads to unbalance effects: 1) motor derating is an
extensively studied problem but the overheating effects on
the rotor conductors still need to be deepened; 2) it is
necessary to consider the operation of the ASD under
unbalanced conditions, due to its possible overstressing.
Besides, the ASD feeding elements can be overloaded
when operate unbalanced, for instance cables, transformers,
etc.
• The unbalanced operation of a system causes the lost of
efficiency in the transmission process. The application of
classic methodologies for power definitions and
measurement can lead to results that do not accurately
quantify a phenomenon in the classic sense.
• Particularly when their effect on loads is analyzed, it
should not be neglected an unbalance associated
phenomenon: the under-voltage and/or over-voltage. This
7
problem perhaps deserves a deep study that should be
related with the previously mentioned definitions of
unbalance.
VII. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
Motors and Generators, ANSI/NEMA Standard MG1-1993.
IEEE Standard Test Procedure for Polyphase Induction Motors and
Generators, IEEE Std 112-1991, Dec. 1991.
IEEE Standard Test Procedure for Polyphase Induction Motors and
Generators, IEEE Std 112-2004, May. 2004.
IEEE Guide for Self-Commutated Converters, IEEE Std 936-1987, Mar.
1987.
S. G. Jeong, “Representing Line Voltage Unbalance”, Industry
Applications Conference, 2002, 37th IAS Annual Meeting, vol. 3, pp.
1724-1732, Oct. 2002.
IEEE Recommended Practice for Electric Power Distribution for
Industrial Plants, IEEE Std 141-1993, Dec. 1993.
Effects of Unbalanced Voltages on the Performance of Three-Phase
Induction Motors, IEC-60034-26, 2002.
IEEE Recommended Practice for Monitoring Electric Power Quality,
IEEE Std 1159-1995, Jun. 1995.
P. G. Kini, R. C. Bansal and R. S. Aithal, “A Novel Approach Toward
Interpretation and Applications of Unbalance Voltage Factor”, IEEE
Trans. on Industrial Electronics, vol. 54, no. 4, pp. 2315-2322, Aug
2007.
J. Faiz, H. Ebrahimpour and P. Pillay, “Influence of Unbalanced
Voltage on the Steady-State Performance of a Three-Phase SquirrelCage Induction Motor”, IEEE Trans. on Energy Conversion, vol. 19, no.
4, pp. 657-662, Dec. 2004.
Y. J. Wang, “Analysis of Effects of Three-Phase on Induction Motors
with Emphasis on the Angle of Complex Voltage Unbalance Factor”,
IEEE Trans. on Energy Conversion, vol. 16, no. 3, pp. 270-275, Sep
2001.
C. A. Reineri, J. C. Gomez, E. F. Belenguer and M. Felici, “Revision of
Concepts and Approaches for Unbalance Problems in Distribution”,
IEEE/PES Transmission & Distribution Conference and Exposition:
Latin America, 2006, pp. 1-6, Aug. 2006.
C. A. Reineri, J. C. Gomez and N.G. Campetelli, “Adjustable Speed
Drives Supplied with Unbalanced Voltages: Study under Complex
Voltage Unbalance Factor Parameter”, Transmission and Distribution
Conference and Exposition: Latin America, 2008 IEEE/PES, Aug. 2008.
P. Pillay, M. Manyage, “Definitions of Voltage Unbalance”, IEEE
Power Engineering Review, pp. 50-51, May. 2001.
M. H. J. Bollen, “Definitions of Voltage Unbalance”, IEEE Power
Engineering Review, pp. 49-50, Nov. 2002.
M. E. Galey, “Benefits of Performing Unbalance Voltage Calculations”,
IEEE Trans. on Industry Applications, vol. 24, no. 1, pp. 15-24, Jan/Feb
1988.
W. H. Kersting and W. H. Phillips, “Modeling and Analysis of Rural
Electric Distribution Feeders”, IEEE Trans. on Industry Applications,
vol. 28, no. 4, pp. 767-773, Jul/Aug 1992.
W. H. Kersting and W. H. Phillips, “Modeling and analysis of
Unsymmetrical Transformer Bank Serving Unbalanced Loads”, IEEE
Trans. on Industry Applications, vol. 32, no. 3, pp. 720-725, May/Jun
1996.
T. H. Chen and Y. L. Chang, “Integrated Models of Distribution
Transformers and Their Loads for Three-Phase Power Flow Analyses”,
IEEE Trans. on Power Delivery, vol. 11, no. 1, pp. 507-513, Jan. 1996.
M. Chindris, A. Cziker, A. Miron, H. Balan, A. Iacob and A. Sudria,
“Propagation of Unbalance in Electric Power Systems”, 9th
International Conference on Electrical Power Quality and Utilization,
EPQU 2007, Oct. 2007.
P. Paranavithana, S. Perera and D. Sutanto, “Analysis of Network
Asymmetry of Interconnected 66kV Sub-transmission Systems in
relation to Voltage Unbalance”, Power Engineering Society Conference
and Exposition in Africa, 2007. Power Africa '07, IEEE, pp. 1–8, Jul
2007.
Electromagnetic Compatibility (EMC) - Limits - Assessment of Emission
Limits for the Connection of Unbalanced Installations to MV, HV and
EHV Power Systems, IEC Technical Report 61000-3-13, Ed. 1, 2008.
P. Paranavithana, S. Perera and R. Koch, “An Improved Methodology
for Determining MV to LV Voltage Unbalance Transfer Coefficient”
th
THE 8 LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
13th International Conference on Harmonics and Quality of Power,
2008. ICHQP 2008, Sep. 2008.
C. A. Reineri, J. C. Gomez, E. B. Balaguer and M. M. Morcos,
“Experimental Study of Induction Motor Performance with Unbalanced
Supply”, Electric Power Components and Systems, Vol. 34, no. 7, pp
817-829, Jul. 2006.
P. Paranavithana, S. Perera, D. Sutanto, and R. Koch, “A Systematic
Approach Towards Evaluating Voltage Unbalance Problem in
Interconnected Sub-Transmission Networks: Separation of Contribution
Lines, Loads and Mitigation”, 13th International Conference on
Harmonics and Quality of Power, 2008. ICHQP 2008, Sep. 2008.
IEEE Guide for ac Motor Protection, IEEE Standard C37.96-1988, Jun.
1989.
Effects of Unbalanced Voltages on the Performance of Three-Phase
Induction Motors, IEC-60034-26, 2002.
W. H. Kersting and W. H. Phillips, “Phase Frame Analysis of the
Effects of Voltage Unbalance on Induction Machines Effects of
Unbalance of Induction Machines”, IEEE Trans. on Industry
Applications, vol. 33, no. 2, pp. 415-420, Mar/Apr 1997.
C. Y. Lee, “Effects of Unbalanced Voltage on the Operation
Performance of a Three-phase Induction Motor”, IEEE Trans. on
Energy Conversion, Vol. 14, No. 2, pp. 202-208, Jun 1999.
Y. J. Wang, “An Analytical Study on Steady-State Performance of an
Induction Motor Connected to Unbalanced Three-Phase Voltage”, 2000
IEEE Power Engineering Society Winter Meeting, 2000, pp. 159-164.
P. Pillay, P.Hofmann and M. Manyage, “Derating of Induction Motors
Operating With a Combination of Unbalanced Voltages and Over or
Undervoltages”, IEEE Trans. on Energy Conversion, vol. 17, no. 4, pp.
485-491, Dec. 2002.
J. Faiz, and H. Ebrahimpour, “Precise Derating of Three-Phase
Induction Motors with Unbalanced Voltages”, Industry Applications
Conference, 2005, Fortieth IAS Annual Meeting. Conference, Vol. 1, pp.
485-491.
P. G. Kini, R. C. Bansal and R. S. Aithal, “A Novel Approach Toward
Interpretation and Applications of Unbalance Voltage Factor”, IEEE
Trans. on Industrial Electronics, vol. 54, no. 4, pp. 2315-2322, Aug
2007.
S.G. Jeong and J.Y. Choi, “Line Current Characteristics of Three-Phase
Uncontrolled Rectifiers Under Line Voltage Unbalance Condition”,
IEEE Trans. on Power Electronics, vol. 17, no. 6, pp. 935-945, Nov.
2002
A. D. Graham, “Line Harmonic Currents in 12 Pulse Rectifiers with
Unbalanced Supply Voltages”, 11th International Conference on
Harmonics and Quality of Power, 2004, pp. 368-373, Sep. 2004.
K. Lee, T. M. Jahns, D. W. Novotny, T. A. Lipo, W. E. Berkopec, and
V. Blasko, “Impact of Inductor Placement on the Performance of
Adjustable-Speed Drives Under Input Voltage Unbalance and Sag
Conditions”, IEEE Trans. on Industry Applications, vol. 42, no. 5, pp.
1230-1240, Sep/Oct 2006.
A. K. Singha, G. K. Singhb y R. Mitraa, “Impact of Source Voltage
Unbalance on AC-DC Rectifier Perfomance”, 2nd International
Conference on Power Electronics Systems and Applications, pp. 98-101,
Apr. 2006.
K. Lee, T. M. Jahns, W.E. Berkopec, and T. A. Lipo, “Closed-Form
Analysis of Adjustable-Speed Drive Performance Under Input-Voltage
Unbalance and Sag Conditions”, IEEE Trans. on Industry Applications,
vol. 42, no. 3, pp. 733-741, May/Jun 2006.
K. Lee, G. Venkataramanan and T. M. Jahns, “Modeling Effects of
Voltage Unbalances in Industrial Distribution Systems with Adjustable
Speed Drives”, Industry Applications Conference, 2004, 39th IAS
Annual Meeting, vol. 4, pp. 2579-2586, Oct. 2004.
A. E. Emanuel, “On the Definition of Power Factor and Apparent Power
in Unbalanced Polyphase Circuits With Sinusoidal Voltage and
Currents”, IEEE Trans. on Power Delivery, vol. 8, no. 3, pp. 841-852,
Jul. 1993.
L. Eren and M. J. Devaney, “Power Factor Measurement For Rotating
Machines Under System Unbalance”, Proceedings of the 16th
Instrumentation and Measurement Technology Conference, 1999,
IMTC/99, IEEE, vol 2, pp. 1138-1141, May 1999.
IEEE Trial-Use Standard Definitions for the Measurement of Electric
Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or
Unbalanced Conditions, IEEE Std 1459-2000, Jan.2000.
8
[43] J. L. Willems and J. A. Ghijselen, “Apparent Power and Power Factor
Concepts in Unbalanced and Nonsinusoidal Situations”, Power Tech
Conference Proceedings, 2003 IEEE, vol. 3, Jun. 2003.
[44] L. S. Czarnecki, “Comments on Active Power Flow and Energy
Accounts in Electrical Systems with Nonsinusoidal Waveforms and
Asymmetry”, IEEE Trans. on Power Delivery, vol. 11, no. 3, pp. 12441250, Jul. 1996.
[45] T. H. Chen, “Evaluation of Line Loss Under Load Unbalance Using the
Complex Unbalance Factor”, IEE Proc. Generation, Transmission and
Distribution, vol. 142, no. 2, pp.173-178, Mar. 1995
[46] A. M. Ferrero, “Unbalancing and Distorting Loads: Can They Be
Detected and Their Detrimental Effect Be Measured?”, 8th International
Conference on Harmonics and Quality of Power, 1998, vol. 2, pp. 809813, Oct. 1998.
[47] P. Paranavithana, S. Perera, D. Sutanto, and R. Koch, “A Systematic
Approach Towards Evaluating Voltage Unbalance Problem in
Interconnected Sub-Transmission Networks: Separation of Contribution
Lines, Loads and Mitigation”, 13th International Conference on
Harmonics and Quality of Power, 2008. ICHQP 2008, Sep. 2008.
[48] K. Li, J. Liu, Z. Wang, and B. Wei, “Strategies and Operating Point
Optimization of STATCOM Control for Voltage Unbalance Mitigation
in Three-Phase Three-Wire Systems”, IEEE Trans. on Power Delivery,
vol. 22, no. 1, pp. 413-422, Jan. 2007.
[49] S.-J.S Tsai and Y. Chang, “Dynamic and Unbalance Voltage
Compensation Using STATCOM”, Power and Energy Society General
Meeting - Conversion and Delivery of Electrical Energy in the 21st
Century, 2008 IEEE, Jul 2008.
[50] Y. Xu, L. M. Tolbert and J.D. Kueck, “Voltage and Current Unbalance
Compensation Using a Parallel Active Filter”, Power Electronics
Specialists Conference, 2007. PESC 2007. IEEE, Jun 2007.
[51] A. Cziker, M. Chindris and A. Miron, “Voltage Unbalance Mitigation
Using a Distributed Generator”, 11th International Conference on
Optimization of Electrical and Electronic Equipment, OPTIM 2008, pp.
221-226, May 2008.
[52] R. Koch, A. Baitch, S. Perera and P. Paranavithana, “Voltage Unbalance
Emission Limits for Installations – General Guidelines and System
Specific Considerations”, 13th International Conference on Harmonics
and Quality of Power, 2008. ICHQP 2008, Sep. 2008.
[53] N. Browne, D. Spoor and J. Byrnes, “Voltage Unbalance in an Urban
Distribution Networks – A Case Study” 13th International Conference
on Harmonics and Quality of Power, 2008. ICHQP 2008, Sep. 2008.
VIII. BIOGRAPHIES
Claudio A. Reineri received the Ph.D. degree in Industrial Engineering from
Valencia Polytechnic University, Spain, in 2000. He is member of the Electric
Power System Protection Institute, Río Cuarto National University (RCNU),
Argentina since 1992. Dr. Reineri is also Associated Professor of Electrical
Engineering at RCNU. His research interests are power quality and
distribution protection.
Juan C. Gómez Targarona was born in Mendoza, Argentina, by May 3,
1952. He received the Electromechanical Engineer diploma in 1974 from
Cuyo National University and the Ph.D. degree in 1994, from Sheffield
Hallam University, United Kingdom. He is a Full Professor at the National
University of Río Cuarto and at the National Technical University at Córdoba,
both in Argentine. His main areas of research interest are Electric Power
System Protection, Power Quality, and Distributed Generation.
Norberto. G. Campetelli is member of the Electric Power System Protection
Institute, Río Cuarto National University (RCNU), Argentina since 1992.
Eng. Campetelli is also Auxiliary Professor of Electrical Engineering at
RCNU. His research interests are electric installations and distribution system
protection.