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
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 c) to propose preliminary standards regarding voltage unbalance to be applied in low and medium voltage distribution systems in 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.
OBJECTIVES
The main objectives of this paper are as follows: a) to study the opportunity of using digital simulations for the analysis of voltage unbalance disturbances; b) to compare field measurements and results from simulations;
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 (DQV
2
) are equal and given by the following equation:
D QV
2
=
V
AN 2
V
AN 1
=
V
AB 2
V
AB 1
(1) where V
AN 1
, V
AN 2
are positive and negative sequence phase-to-ground voltages and V
AB 1
, 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:
DQV (%)
=
1
−
1
+
3
−
3
−
6
⋅ β
6
⋅ β
×
100 (2) where:
β = (
V
V
AB
AB
2
4
+
+
V
AB
V
AB
2
4
+
+
V
AB
V
AB
2
4
)
2
A variant of the above method is here named CIGRÉ-2 and is based on the relative deviations in phase-to-phase voltage magnitudes
δ
AB
,
δ
BC
and
δ
CA
, with respect the average value V
M
, given by:
DV Q
′ = 2
3
δ
(
AB
2 + δ
BC
2 + δ
CA
2
)
(3) where:
δ
AB
=
δ
CA
V
AB
−
V
M
=
V
M
V
CA
−
V
M
V
M
,
δ
BC
and V
M
=
V
BC
−
V
M
V
M
=
V
AB
,
+
V
BC
3
+
V
CA
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
Compatibility Level
(95% probability of not exceeding the amount)
Standards Normal condition
Majority of single and double phase loads
3 %
Sampling Period
EN50160 2 % 10 min 1 week
NRS-048 2 % 3 % 10 min 1 week(*)
(*) this standard considers the maximum daily voltage unbalance index
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.
vertical configuration triangle configuration
(A, B and C are phase conductors and N is the ground conductor)
Fig. 1 – Conductor configurations
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
(a)
Triangle configuration
(b)
L
(m)
Vab
(V)
Vbc
(V)
Vca
(V)
D% Vab
(V)
Vbc
(V)
Vca
(V)
D%
100 219.10 219.10 219.10 0.00 219.09 219.09 219.09
0.00
150 211.14 212.53 211.80 0.38 211.75 211.75 211.75
0.00
180 206.45 208.68 207.54 0.62 207.47 207.47 207.47
0.00
200 203.36 206.15 204.76 0.79 204.67 204.67 204.67
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).
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.
Table 3 – Characteristics of the selected low voltage
Case Netw. Transf.
L networks
CUSTOMERS
Number of customers
Monthly energy (kWh)
# Code (kVA) (m) R C I T R C I T
1 C0148 75,0 781 126 04 03 133 25314 2636 687 28637
2 C0950 45,0 401 55 0 0 55 12525 0 0 12525
3 C0994 45,0 399 71 02 03 76 12659 719 674 14052
4 C1317 75,0 518 106 03 00 109 16145 810 0 16955
5 C3807 45,0 487 97 04 0 101 16229 2179 0 18408
6 C4211 45,0 382 69 02 0 71 10532 2241 0 12773
7 C4835 75,0 694 99 01 03 103 20919 180 563 21662
8 C4974 75,0 642 118 02 0 120 20722 554 0 21276
9 C5174 45,0 394 26 0 03 29 9583 0 1369 10952
10 C6212 45,0 485 72 0 0 72 12466 0 0 12466
11 C9079 112,5 312 35 07 03 45 7038 3152 3238 13428
12 C4617 112,5 582 68 16 04 88 14502 18584 4298 37384
1
0.8
0.6
0.4
0.2
0
Consumo 200-400kWh hora {20,20:15,20:30,20:45} 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.
Table 4 – Results from field measurements
Voltage Unbalance Index Probability of Voltage
Case Net Max. Value
(%)
95% Value
≤
2%
Unbalance
≤
3%
# Code Inst. Average Inst. Average Inst. Average Inst. Average
1 C0148 3.7
2 C0950 5.5
2.6
3.4
1.7
2.2
1.4
2.0
97.64 99.21 99.82
-
92.85 95.84 99.05 99.70
3 C0994 2.9
4 C1317 4.5
5 C3807 3.5
6 C4211 4.1
1.9
3.5
2.1
3.0
1.3
2.5
1.5
1.8
0.9
2.4
1.1
1.7
99.07
-
83.26 85.87 98.74 99.50
98.98 99.88 99.96
-
97.62 98.91 99.87 100.00
7 C4835 3.9
8 C4974 4.3
9 C5174 3.0
10 C6212 3.9
2.8
2.8
2.2
2.5
1.7
1.8
1.4
1.4
1.5
1.5
1.3
1.1
98.08 99.70 99.94
96.62 98.58 99.55
99.38 99.80 100.0
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.
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)
Network Management Field
System Measurement
Case
#
Net
Code
∆
V%
V (volt) V (volt)
Ideal Actual Ideal Actual Vab Vbc Vca
1 C0148 6.69
10.05
205.28 197.89 209.00 209.00 208.00
2 C0950 6.16
8.81
206.45 200.62 210.00 209.00 206.00
3 C0994 3.32
7.74
212.70 202.97 206.00 207.00 207.00
4 C1317 3.93
10.64
211.35 196.59 218.00 212.00 212.00
5 C3807 4.70
8.50
209.66 201.30 205.00 205.00 205.00
6 C4211 2.20
6.13
215.16 206.51 216.00 212.00 212.00
7 C4835 6.24
8.41
206.27 201.50 207.00 205.00 205.00
8 C4974 6.91
9.87
204.80 198.29 203.00 201.00 200.00
9 C5174 5.31
8.42
208.32 201.48 211.00 209.00 209.00
10 C6212 3.81
10.47
211.62 196.97 214.00 215.00 213.00
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.
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
2
3
4
5
6
Table 6 – Maximum voltage unbalance indices
Case
#
1
Network
Code
C0148
Simulation Instantaneous
5.87
Measurement
3.7
C0950
C0994
C1317
C3807
C4211
6.43
7.65
5.27
8.10
4.83
5.5
2.9
4.5
3.5
4.1
7
8
9
C4835
C4974
C5174
9.05
7.87
5.63
3.9
4.3
3.0
10 C6212 8.58
3.9
.
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
Case Net
≤
2%
≤
3%
# Code Inst.
Average Inst.
Average
1 C0148 97.64
2 C0950 92.85
3 C0994 99.07
4 C1317 83.26
5 C3807 98.98
6 C4211 97.62
7 C4835 98.08
8 C4974 96.62
9 C5174 99.38
10 C6212 99.28
(probability of voltage unbalance)
Measurement Simulations
≤
2%
≤
3%
99.21
99.82
96.00
98.00
95.84
99.05
99.70
97.00
99.00
95.00
-
85.87
98.74
99.50
96.00
98.00
99.88
99.96
95.00
97.00
98.91
99.87
100.00
94.90
97.00
99.70
99.94
98.58
99.55
99.80
100.00
99.80
99.95
-
-
-
-
94.00
94.00
98.00
89.50
97.00
97.00
99.50
95.80

Frequency (%)
Voltage Unbalance Index (%)
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
[1] Brazilian legislation (DNAEE 46 and 47). 1978
[2] CIGRÉ A new simple and effective approximate formulation for the determination of three-phase
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.
[7] NRS 048-1:1996 ELECTRICITY SUPPLY –
QUALITY OF SUPPLY Overview of implementation of standards and procedures. South Africa. 1996.
[8] EUROPEAN COMMITTEE FOR
ELECTROTECHNICAL STANDARDIZATION –
CENELEC Voltage caracteristics of Electricity
Supplied by Public Distribution systems.
[9] J. A JARDINI; H. P. SCHMIDT 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 ).