VOLTAGE UNBALANCE IN LOW VOLTAGE DISTRIBUTION NETWORKS
Paulo Vinícius Santos Valois – COPEL – Companhia Paranaense de Energia, Brazil
Carlos Márcio Vieira Tahan – University of São Paulo, Brazil
Nelson Kagan – University of São Paulo, Brazil
Hector Arango – EFEI – Federal School of Engineering at Itajuba, Brazil
SUMMARY
This paper presents a methodology for
measuring, monitoring and controlling
voltage unbalance in electrical power
distribution networks. The distribution of
single-phase and double-phase loads
along the network and their random
instant demand values can be considered
as the main causes to voltage unbalance
in three-phase distribution systems.
The work considers voltage unbalance
measurements carried out in a Brazilian
distribution company located in the State
of Paraná, namely COPEL – Companhia
Paranaense de Energia.
Since voltage unbalance gradually affects
equipment, this disturbance should be
dealt with by statistical analysis.
Regarding voltage regulation and voltage
unbalance, a world-wide tendency is to
consider their monitoring and measuring
on 10 minute intervals along a 1 week
period.
Thus, this paper aims at:
-
-
studying the opportunity of using
digital simulations for the analysis of
voltage unbalance disturbances;
comparing field measurements and
results from simulations;
proposing preliminary standards
regarding voltage unbalance to be
applied in low and medium voltage
distribution systems in Brazil.
VOLTAGE UNBALANCE IN LOW VOLTAGE DISTRIBUTION NETWORKS
Paulo Vinícius Santos Valois – COPEL – Companhia Paranaense de Energia, Brazil
Carlos Márcio Vieira Tahan – University of São Paulo, Brazil
Nelson Kagan – University of São Paulo, Brazil
Hector Arango – EFEI – Federal School of Engineering at Itajuba, Brazil
INTRODUCTION
There has been a growing concern to supply power to
customers mainly when their processes are based on
susceptible loads. In such scenario power quality
becomes extremely relevant. Reliability indices and
voltage levels, for instance, are parameters much more
regulated now. Other power quality phenomena are also
being taken care of in much more detail, such as voltage
sags, harmonic distortion, voltage and current unbalance
and so forth.
This paper presents a methodology for measuring,
monitoring and controlling voltage unbalance in
electrical power distribution networks. The distribution
of single-phase and double-phase loads along the
network and their random instant demand values can be
considered as the main causes to voltage unbalance in
three-phase distribution systems.
Contrary to some other disturbances in electrical power
systems, for which the performance is evident for the
ordinary customer, voltage unbalance belongs to those
disturbances in which their perceptible effects are
produced in the long run.
Voltage unbalance leads to a sharp decrease on the
efficiency of three-phase induction motors. In Brazil,
50% of the electric energy is absorbed by industrial
customers. Since induction motors represent the largest
portion of industrial loads, it is seen that the voltage
unbalance should be carefully studied and controlled.
This work considers voltage unbalance measurements
carried out in a Brazilian distribution company located
in the State of Paraná, namely COPEL – Companhia
Paranaense de Energia.
Since voltage unbalance gradually affects equipment,
this disturbance should be dealt with by statistical
analysis. Regarding voltage regulation and voltage
unbalance, a world-wide tendency is to consider their
monitoring and measuring on 10 minute intervals along
a 1 week period.
c)
to propose preliminary standards regarding voltage
unbalance to be applied in low and medium voltage
distribution systems in Brazil.
BASIC CONCEPTS
Voltage unbalance in three-phase distribution systems
regards the changing in phase angles and/or in the
magnitude of voltage phasors. The main causes leading
to voltage unbalance are the following ones.
a)
Unsymmetrical distribution systems, that is
equipment and phase conductors present different
impedance values.
b) Unsymmetrical loads, such as arc furnaces, single
and double phase loads;
c) Different voltage drops due to differences in mutual
impedances between phase conductors and between
phase conductors and ground. This depends on the
spatial configuration of conductors.
Low voltage distribution networks – the main focus of
this paper – introduce a small amount of voltage
unbalances due to their impedances. The main cause can
be considered as the current unbalance, due to the
distribution of single-phase and double-phase loads
along the network, such as public lighting and
residences.
COMPUTING THE VOLTAGE UNBALANCE
INDEX
The voltage unbalance index is generally related to the
negative symmetrical component system. This is due to
the large number of pieces of equipment that have their
efficiency and life affected, mainly the ones like
generators and motors (based on rotating magnetic
fields), where the major part of electrical energy is
transformed.
Phase-to-phase and phase-to-ground voltage unbalance
indices (DQV2) are equal and given by the following
equation:
OBJECTIVES
V AN 2
DQV 2 =
a)
where V AN1 , V AN 2 are positive and negative sequence
to study the opportunity of using digital simulations
for the analysis of voltage unbalance disturbances;
b) to compare field measurements and results from
simulations;
V AN 1
=
V AB 2
The main objectives of this paper are as follows:
V AB1
(1)
phase-to-ground voltages and V AB1 , V AB 2 are positive
and negative sequence phase-to-phase voltages.
Equation (1) allows for the computation of voltage
unbalance in a system by using phase-to-phase voltages
only. Such computation is carried out by utilising
voltage magnitude only whereas methods based on
phase-to-ground voltages require the magnitude and
phase angles. However such method demands lots of
arithmetic operations. The CIGRÉ method was chosen
to be used, since it is derived from the CO-SENOS
method, that keeps the accuracy. The voltage unbalance
index can be readily determined by the following
equation:
1− 3 − 6 ⋅β
DQV (%) =
where: β =
×100
1+ 3 − 6 ⋅β
V AB
(V
4
2
AB
4
+ V AB
+ V AB
2
+ V AB
+ V AB
(2)
4
)
2 2
INFLUENCE OF NETWORK IMPEDANCES ON
VOLTAGE UNBALANCE
Networks can contribute on voltage unbalance due to
the unsymmetrical spatial configuration of conductors.
This leads to different phase voltage drops due to
different mutual impedances. In order to evaluate this
effect on the voltage unbalance, a number of
simulations were carried out on low voltage networks.
Voltage drops due to mutual inductances are
proportional to the flowing electric current and to the
conductor length. Thus, a typical distribution network
branch was assumed to have the current fixed by the
maximum allowed voltage drop. In order to ensure the
current balance, a three-phase balanced resistive load
was considered to be installed in the receiving bus. Two
different conductor configurations were considered in
the simulations, as shown in figure 1.
A variant of the above method is here named CIGRÉ-2
and is based on the relative deviations in phase-to-phase
voltage magnitudes δAB, δBC and δCA, with respect the
average value VM, given by:
DVQ ′ = 2
3
(δ
2
AB
+ δ BC 2 + δ CA 2
)
(3)
where:
δ AB =
δ CA =
V AB − V M
VM
VCA − V M
VM
, δ BC =
V BC − V M
and V M =
VM
,
vertical configuration
V AB + V BC + VCA
Fig. 1 – Conductor configurations
3
Equation 3 is a simpler calculation method as compared
to equation 2, though there is a slight loss in accuracy.
ALLOWED VOLTAGE UNBALANCE INDICES
Brazilian standards do not establish limits for voltage
unbalance indices as yet. There are some references to
those indices in norms that regulate equipment tests and
standards [7] [8]. Table 1 shows a comparative figure of
adopted limits in world-wide standards.
Table 1 – Voltage unbalance limits
Voltage Unbalance
Immunity Levels
triangle configuration
(A, B and C are phase conductors and N is the ground conductor)
Compatibility Level
(95% probability
of not exceeding the
amount)
Standards Normal Majority of
condition single and Sampling Period
double phase
loads
EN50160
2%
3%
10 min
1 week
NRS-048
2%
3%
10 min 1 week(*)
(*) this standard considers the maximum daily voltage unbalance index
Table 2 presents the computed voltage values and the
corresponding voltage unbalance indices (D%) along
the branch, for different distances (L) from the source.
Table 2 – Voltage unbalance due to different conductor
configurations
Vertical Configuration Triangle configuration
(a)
(b)
L
(m)
100
150
180
200
Vab
(V)
219.10
211.14
206.45
203.36
Vbc
(V)
219.10
212.53
208.68
206.15
Vca
(V)
219.10
211.80
207.54
204.76
D%
0.00
0.38
0.62
0.79
Vab
(V)
219.09
211.75
207.47
204.67
Vbc
(V)
219.09
211.75
207.47
204.67
Vca
(V)
219.09
211.75
207.47
204.67
D%
0.00
0.00
0.00
0.00
Results shown in Table 2 confirm the small influence
from conductor configuration on the voltage unbalance
indices.
PROBABILISTIC COMPUTATIONAL MODEL
TO EVALUATE VOLTAGE UNBALANCE
A computational model was developed to evaluate
voltage unbalance indices in electrical power
distribution networks. The model considers a three-
phase representation of the network, taking into account
medium and low voltage network branches as well as
distribution transformers (three-phase transformers or
bank of single-phase transformers), capacitor banks, etc.
The load flow method is carried out as many times as
necessary following a Monte Carlo method that
randomly generates scenarios in a given instant along
the load daily curve.
Load modelling to support such simulations is the result
of an extended load demand measurement campaign
carried out in the 90´s to stratify all customers
connected to distribution networks in Brazil. This
method classifies residential customers according to
different ranges for monthly consumed energy and
commercial and industrial customers according to their
activities. Other load categories were also considered,
such as public lighting. Each customer is modelled by
its corresponding typical daily load curve. For every 15
minute intervals the probability distribution curve is
given to be used by the Monte Carlo simulation method.
Figure 2 illustrates a typical probability distribution for
the demand in residential customers during the peak
load period (from 8 to 9 pm).
1
0.6
0.4
0.2
10.71
2.142
1.5
1.125
0.75
0
0.375
Case Netw. Transf. L
#
Number of Monthly energy (kWh)
customers
Code (kVA) (m) R C I T R
C
I
T
1
2
3
4
5
6
7
8
9
10
11
12
C0148
C0950
C0994
C1317
C3807
C4211
C4835
C4974
C5174
C6212
C9079
C4617
75,0
45,0
45,0
75,0
45,0
45,0
75,0
75,0
45,0
45,0
112,5
112,5
781 126 04
401 55 0
399 71 02
518 106 03
487 97 04
382 69 02
694 99 01
642 118 02
394 26 0
485 72 0
312 35 07
582 68 16
03
0
03
00
0
0
03
0
03
0
03
04
Voltage Unbalance Index
(%)
Max. Value 95% Value
0.8
0
Table 3 – Characteristics of the selected low voltage
networks
CUSTOMERS
133
55
76
109
101
71
103
120
29
72
45
88
25314
12525
12659
16145
16229
10532
20919
20722
9583
12466
7038
14502
2636 687 28637
0
0
12525
719
674 14052
810
0
16955
2179
0
18408
2241
0
12773
180
563 21662
554
0
21276
0
1369 10952
0
0
12466
3152 3238 13428
18584 4298 37384
Table 4 – Results from field measurements
Consumo 200-400kWh
hora {20,20:15,20:30,20:45}
freqüência
Table 3 shows a compilation of the main network
characteristics taken from COPEL´s data base. The table
also presents the number and monthly energy of
residential (R), commercial (C) and industrial (I)
customers as well as total (T) figures. Table 4 shows the
most relevant voltage unbalance results obtained from
the measurements.
d(t)/dmed
Fig.2 Probability distribution (density and cumulative)
curves for residential customers, monthly energy
ranging from 200 to 400kWh
MEASUREMENT RESULTS
Since there are too many low voltage networks in the
distribution company, network selection criteria to carry
out measurements were adopted. A criterion was chosen
to select those networks more likely to have voltage
unbalance, such the ones having predominantly singlephase and double-phase loads, having higher
transformer loading, voltage drop and dispersion of
loads along the network. The selected networks were
submitted to simulations by using the developed
software and to measurement in the field during one
week and demand values stored on 15 second intervals.
A low cost electronic meter was used to monitor low
and medium voltage networks.
Probability of Voltage
Unbalance
≤ 2%
≤ 3%
Case Net
#
Code Inst. Average Inst. Average Inst. Average Inst. Average
1 C0148 3.7
2.6
1.7
1.4 97.64 99.21 99.82
2 C0950 5.5
3.4
2.2
2.0 92.85 95.84 99.05 99.70
3 C0994 2.9
1.9
1.3
0.9 99.07
4 C1317 4.5
3.5
2.5
2.4 83.26 85.87 98.74 99.50
5 C3807 3.5
2.1
1.5
1.1 98.98 99.88 99.96
6 C4211 4.1
3.0
1.8
1.7 97.62 98.91 99.87 100.00
7 C4835 3.9
2.8
1.7
1.5 98.08 99.70 99.94
8 C4974 4.3
2.8
1.8
1.5 96.62 98.58 99.55
9 C5174 3.0
2.2
1.4
1.3 99.38 99.80 100.0
10 C6212 3.9
2.5
1.4
1.1 99.28 99.80 99.95
Extreme (*) 5.50 3.50 2.50 2.40 83.26 85.87 98.74 99.50
(*): maximum voltage unbalance indices and minimum probabilities
Results obtained in table 4 lead to the following
preliminary conclusions:
a) All low voltage networks meet the criterion that
95% of the measured voltage unbalance indices are
less than or equal to 3%;
b) Only two low voltage networks do not meet the
criterion that 95% of the measured voltage
unbalance indices are less than or equal to 2%;
c) Maximum instantaneous voltage unbalance indices
are less than 5.5%;
d) Such results are a consequence of good network
management procedures.
EVALUATION OF VOLTAGE DROPS BY
MEASUREMENT AND BY THE DISTRIBUTION
NETWORK MANAGEMENT SYSTEM
The existing distribution management system running at
COPEL does not determine voltage unbalance indices.
It only provides the distribution of total power flows in
each of the three phases of the transformer, estimated
from the billed customer energy values.
However, the system provides the minimum voltage
level in the distribution network, by considering the
nominal voltage (220V) in the low voltage transformer
bus. The voltage drops are evaluated at each branch, as
a function of load demands and cable characteristics,
what leads to the determination of the maximum
network voltage drop.
By analysing the maximum values of voltage unbalance
indices shown in table 6, one sees that the simulation
method is rather more conservative. However one
should not discard such simulations from a network
management system. The main causes for such
differences can be explained by the methodology
adopted, where 500 possible load unbalance scenarios
were analysed for each selected instant in the daily
curve. Such a high number of network conditions leads
to the evaluation of extreme cases and thus leading to
more conservative results. Also, while loads were
modelled by 15 minute measurements, simulations were
considered in 3 hour intervals
Table 6 – Maximum voltage unbalance indices
Case Network Simulation Instantaneous
#
Code
Measurement
1
C0148
5.87
3.7
2
C0950
6.43
5.5
3
C0994
7.65
2.9
4
C1317
5.27
4.5
5
C3807
8.10
3.5
6
C4211
4.83
4.1
7
C4835
9.05
3.9
8
C4974
7.87
4.3
9
C5174
5.63
3.0
10
C6212
8.58
3.9
Table 5 shows voltage drop values (∆V%) determined by
the distribution management system and obtained from
the field measurements. The latter are the voltage drop
values considering probability lower than 3%.
Table 5 – Voltage drop values (measurement and
distribution management system)
Field
Network Management
System
Measurement
V (volt)
V (volt)
Case Net
∆V%
#
1
2
3
4
5
6
7
8
9
10
Code
C0148
C0950
C0994
C1317
C3807
C4211
C4835
C4974
C5174
C6212
Ideal
6.69
6.16
3.32
3.93
4.70
2.20
6.24
6.91
5.31
3.81
Actual
10.05
8.81
7.74
10.64
8.50
6.13
8.41
9.87
8.42
10.47
Ideal
205.28
206.45
212.70
211.35
209.66
215.16
206.27
204.80
208.32
211.62
Actual
197.89
200.62
202.97
196.59
201.30
206.51
201.50
198.29
201.48
196.97
Vab
209.00
210.00
206.00
218.00
205.00
216.00
207.00
203.00
211.00
214.00
Vbc
209.00
209.00
207.00
212.00
205.00
212.00
205.00
201.00
209.00
215.00
Vca
208.00
206.00
207.00
212.00
205.00
212.00
205.00
200.00
209.00
213.00
It is seen that the network management system provides
more conservative results, mainly for the values with
probability lower than 3%.
Taking case #1, for instance, there was a 199V
instantaneous registered value, closer to the one
evaluated by the network management system. However
such value does not affect negatively customer
equipment due to its low probability (0.0025%). In such
location, a 206.5V voltage level corresponds to the 1%
probability whereas 208.5V corresponds to 3%
probability.
VOLTAGE UNBALANCE INDICES USING THE
MONTE CARLO SIMULATION METHOD
Table 6 compares the maximum voltage unbalance
indices obtained from simulation and from
measurement.
.
It is seen however that such discrepancies are
diminished when analysing probabilistic results. Figure
3 shows results for case #1.
Table 7 shows probabilities associated to voltage
unbalance indices lower than 2% and 3%, obtained from
measurements and simulations.
If one considers the criterion of 95% of monitored
values not exceeding 3%, measurement and simulations
for cases shown in table 7 lead to the same conclusions.
When adopting the 2% limit, more conservative results
where obtained when using the simulation method, what
is adequate for network management systems.
Table 7 – Probabilistic results – measurements and
simulations (probability of voltage unbalance)
Measurement
Simulations
Case
#
1
2
3
4
5
6
7
8
9
10
Net
Code
C0148
C0950
C0994
C1317
C3807
C4211
C4835
C4974
C5174
C6212
≤ 2%
≤ 3%
Inst. Average Inst. Average
97.64
99.21
99.82
92.85
95.84
99.05 99.70
99.07
83.26
85.87
98.74 99.50
98.98
99.88
99.96
97.62
98.91
99.87 100.00
98.08
99.70
99.94
96.62
98.58
99.55
99.38
99.80 100.00
99.28
99.80
99.95
-
≤ 2%
≤ 3%
96.00
97.00
95.00
96.00
95.00
94.90
94.00
94.00
98.00
89.50
98.00
99.00
98.00
97.00
97.00
97.00
97.00
99.50
95.80
Frequency (%)
Simulations
Instantaneous
Average
Voltage Unbalance Index (%)
Fig. 3 – Simulation and field measurement results
CONCLUSIONS
Voltage unbalance indices determined in field
measurements are considered to be low, possibly due
to network management procedures adopted in the
company. In such procedures, load current unbalance
are avoided by an appropriate distribution of singlephase and double-phase customers along the
distribution network. Simulation results were validated
mainly when considering that 95% of the time the
voltage unbalance index is inferior to 3%. The
probabilistic method should therefore be incorporated
into the company´s network management system. Low
cost measurement instruments were shown to be
effective enough for monitoring voltage unbalance
indices. Although results point out that simulation
should be included in the distribution management
system, when considering the 96 simulations (one
every 15 minute period) throughout a daily cycle (24h)
and the large number of low voltage distribution
networks (COPEL has approximately 250,000
distribution transformers), the computation time could
restrict the application of the method. A very
interesting approach would be to consider techniques
based on Artificial Neural Networks (ANN). In such
approach, the procedure is divided into two phases:
training and application. The training phase is based on
the data base for load curves and customers connected
to the system, on simulations and on measurement
campaigns. The voltage unbalance indices would be
stored for each type of distribution network, where the
type would be defined by given attributes such as load
balance amongst phases, network length, cable
characteristics, voltage drops, number of customers in
each category, monthly energy, etc.. In the following
phase, having known the network attributes and
corresponding loads, the software would be able to
estimate the resulting voltage unbalance index. A
similar procedure was successfully applied to a
distribution transformer loading management system
[9] [10].
REFERENCES
Brazilian legislation (DNAEE 46 and 47). 1978
CIGRÉ A new simple and effective approximate
formulation for the determination of three-phase
unbalances by the voltmeter method. Belgique,
CIGRÉ, 1986
[3] NEMA Standards Publication n. MG-1-1987
[4] BERNDT, M. M.; SCHMITZ, N. L. Derating of
Polyphase induction motors operated with unbalanced
line voltages.
[5] W. EDWARD REID, O. Power quality issues –
standards and guidelines. IEEE Transactions on
Industry Applications. V.32, n.3, p.625-632,
May/June. 1996.
[6] EUROPEAN STANDARD– EN50160. Voltage
characteristics of electricity supplied by public
distribution systems. Brussels, CENELEC, 1994.
SUPPLY
–
[7] NRS 048-1:1996 ELECTRICITY
QUALITY OF SUPPLY Overview of implementation
of standards and procedures. South Africa. 1996.
COMMITTEE
FOR
[8] EUROPEAN
ELECTROTECHNICAL STANDARDIZATION –
CENELEC Voltage caracteristics of Electricity
Supplied by Public Distribution systems.
[9] J. A JARDINI; H. P. SCHMIDT Seleção e
classificação de transformadores de distribuição
utilizando redes neurais. Internal Report – Department
of Electrical Engineering – University of São Paulo.
[10] J. A JARDINI; H. P. SCHMIDT S. U. AHN C. M. V.
TAHAN
C. C. B. OLIVEIRA “Distribution
Transformer Loss of Life Evaluation: A Novel
Approach Based on Daily Load Profiles” a ser
publicado no PES Transaction (paper 99WM 402 ).
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[2]