The Online Journal on Electronics and Electrical Engineering (OJEEE)
Vol. (2) – No. (1)
Impact Analysis of Unbalanced and Loading
Degree on Power Losses Weight
in a Distribution Network
I. Felea,
D. Popovici and
Albuţ-Dana Daniel
Department of Electrical Engineering, Faculty of Energy Engineering,
University of Oradea, Oradea, România
Boja Ionel
S.D.E.E., Oradea, România
Abstract: The paper is structured in four parts. In the
first part presents the analysis of the justification in the
context of existing concerns on the subject, identified in
the literature and from the entities of power distribution.
The second part presents electrical network which is the
subject of analysis and methodology applied for study.
Part three contains analysis on the weight loss of power
caused by the unbalanced state on power network and the
impact of the loading degree on the energy efficiency of
the network. The fourth part includes analysis
conclusions.
Keywords - electric network, unbalanced state, power
losses, level loading.
I. PRELIMINARY
Power system fulfills its duties if it satisfies simultaneous
the requested power to consumers throughout the
consumption time to certain quality standards.
Electronics and industrial processes involve the current
existence of a large number of receivers that distort the shape
of the voltage and current wave.
Due to appreciable harm arising from the operation of such
states are notes, currently a major interest from specialists in
the direction of identification, quantification and limit the
negative effects of distorting and unbalanced states.(RDN) [1].
In literature are evoked following general effects of the
deforming and unbalanced states [2, 6, 10]:
 power effects (additional loss of power to the reference
system, considered the rating state of operation);
 Ferro-resonances and over voltages effects;
 disturbances on the telecommunications and automation
circuits;
Over voltages caused by the unbalanced and distorting affect
insulations, which reduces the mean time before failure (MTBF)
and life time (V) of equipment (transformers, coils, condensers).
Additional losses of power (the energy losses) into the
deforming and unbalanced state (RDN), compared to the
reference state (RR), involve the operation at a bigger
temperature () than for the same payload in the two states.
The methodology, whose steps are summarized in [6],
aimed at assessing the impact of additional power losses in
Reference Number: W09-0036
the RDN on the energy performance of reliability and
economy (PEFE) of equipment, taking into account the fact
that - through their extensive and permanent - additional
losses of power can affect essential these performances.
II. THE OBJECT OF ANALYSIS AND HOW TO WORK
II.1. ELECTRIC NETWORK ANALYZED
The study was conducted as a result of the Power
Distribution Branch order in Oradea, Romania (SDEEO), an
entity that manages the power distribution network (RDEE) in
Romania.
The analysis was conducted with reference to a part of the
urban network of the city of Oradea. Client (SDEEO) aims to use
the findings of this study to define and implement efficiency
measures exploitation of electric networks. In accordance with
the objectives agreed with the client, the analysis was focused on
the low voltage network (JT), and aimed mainly the effects of
unbalanced state on energy losses (ΔW) in RDEE.
For a complete analysis was chosen a particular area of
RDEE supplied from PTAb 630 kVA Cuza Voda, Oradea.
This area has a pronounced unbalanced consumption and has
the advantage that the 552 of watt-hour meters are available.
Also the examined area network has the advantage of being
modernized, reflecting the perspective of RDEE Oradea. For
this network area, EL assessments were made in two ways:
 on the measurements basis: the energy registered in the
substation and energy recorded in each point of consumption;
 on the analytical basis, applying two mathematical models:
the classic model of currents load flow and model-based on
equivalent load [4, 8, 12].
To conclude, given the large difference between the results
obtained on the basis of measurements and calculations, in
addition to evaluations performed at constant current (mean),
has been evaluating demonstration for a part of analyzed
network at variable current.
Using measurements from the database of the client,
applying the model of evaluation presented in [6], will
determine the supplementary energy losses ΔW from RDEE
Oradea who are working in the unbalanced state.
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
Vol. (2) – No. (1)
Figure (1) Analyzed power distribution network
II.2. ENERGY AND POWER LOSSES EVALUATION ON
MEASUREMENTS BASES
The first assessment of power and energy losses is based on
the measurements. We made two reads to each consumer watthour meter and to the general watt-hour meter from substation,
Nr.
crt.
0
1
2
1
Cuza Voda nr. 38
Cuza Voda nr. 38
Meter
series
2
6325127
1410552
Atlas Telecom
General Meter
340247
1655043
Address
at intervals of a week, each substation departure being
disconnected. When we made the first reading on the substation
were mounted on each departure a Fluke network analyzer.
Based on the two measurements we got energy consumption
for a week. A sample of these data is presented in Table 1.
Meter indication
Reading 1
Reading 2
3
4
11378.6
11412.5
5015.4
5018.8
W
[kWh]
5
33.9
3.8

552
553
TOTAL
ΔW [kWh]
14470.3
25239.9
14708.2
25329.9
237.9
27000
25463.6
1536.4
Table 1 - A sample of the data recorded in reading meters
Given the energy consumed for a week of each consumer,
based on the mathematical model [3] were calculated the load
Nr.
crt.
1
2
currents and the power and energy losses on each branch.
Illustrative results are presented in Table 2.
W
[kWh]
33.9
0
I
[A]
0.877329
0
L
[m]
25
25
R
[Ω]
0.075363
0.075363
ΔP
[W ]
0.058007488
0
ΔW
[Wh]
9.745258
0
237.9
27000
Total
6.156832
698.7578
30
0
0.090436
0
3.428110349
0
415.59
575.9225
0
69819.75

552
553
Table 2 - The values of the parameters and power and energy losses on branches
Reference Number: W09-0036
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
II.3. THE ASSESSMENT BY CALCULATING OF POWER
AND ENERGY LOSSES FOR THE DISTRIBUTION
NETWORK
A. APPLICATION OF MATHEMATICAL MODEL FOR
EACH PHASE AND NEUTRAL CONDUCTOR
Nr.
crt.
1
2
3
Rf
[Ω]
0.018066
0.018066
0.018066
Section
1
2
3
I-R
[A]
10.4089
22.66563
24.75932
Vol. (2) – No. (1)
We calculated, on the basis of mathematical model currents
on each network phase and the current on neutral conductor.
Results are presented in Table 3 (examples).
Power and energy losses are presented in Table 4 (example).
Departure I - Branch I.1
I-S
I-T
RN
[A]
[A]
[Ω]
1.400104 5.326087 0.025
7.888199 20.55901 0.025
8.928571 30.97308 0.025
Re[IN]
Im[IN]
7.045807
8.442029
4.808489
-3.4
-10.9732
-19.0911
IN
[A]
7.823261
13.84485
19.68736
Table 3 – Values sizes account foe evaluation of power and energy losses for departures from PT. Cuza Voda
Departure I – Branch I.1-Power and Energy Losses
Nr.
crt.
Section
ΔPR
[W]
ΔPS
[W]
ΔPT
[W]
ΔPN
[W]
ΔWR
[kWh]
ΔWS
[kWh]
ΔWT
[kWh]
ΔWN
[kWh]
1
2
3
1
2
3
1.957381
9.281135
11.07497
0.035415
1.124142
1.440222
0.512486
7.636066
17.33143
1.547993
4.848082
9.803209
0.32884
1.559231
1.860596
0.00595
0.188856
0.241957
0.086098
1.282859
2.91168
0.260063
0.814478
1.646939
605.2518
844.2557
Total
762.881
88.50764
128.164
101.6823
Total losses on sections+branches
141.835
14.86928
456.3703
kWh
Table 4 - The values of power and energy losses determined by calculating on phases and neutral conductor
B. APPLICATION OF MATHEMATICAL MODEL
BASED ON EQUIVALENT LOAD TO THE
DISTRIBUTION NERWORK
Nr.
crt.
1
2
3
4
5
6
Another method of calculating the power and energy losses
is a specific mathematical model for unbalanced state [5].
Results on the basis of this model are presented in Table 5
(example).
Departure I - Branch I.1-Power losses in unbalanced state
Tronson
β-R
β-S
β-T
ΔPcn
W
1
0.041636
0.0056
0.021304
15.91328
2
0.090663
0.031553
0.082236
141.5946
3
0.099037
0.035714
0.123892
226.6059
4
0.099037
0.035714
0.123892
231.8758
5
0.099037
0.035714
0.123892
231.8758
6
0.099037
0.035714
0.131874
246.4073
ΔPcN
W
0.01176927
0.7541345
1.99663965
2.04307313
2.04307313
2.3387799
Table 5 - The values of power losses caused in unbalanced state
Total energy losses by this method are:
W  PCN  t  10 3 [kWh]
3
W  560,508  168  10  94.165 [kWh]
II.4. ASSESSMENT IN THE VARIABLE LOAD
CONDITIONS (COMPUTING)
(1)
(2)
To check the values obtained by calculation, with reference
to the CPT has made an assessment for variable load
(computing) (Fig. 2). The calculations were made only to
section 1 of departure 1. Results are presented in Table 6.
Reference Number: W09-0036
Figure (2) Characteristic of hypothetical load (computing)
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
Vol. (2) – No. (1)
II.6. EVALUATION BASED ON MEASUREMENTS OF
ENERGY LOSSES IN AN AREA OF URBAN RDEE
ORADEA
Staţia
Oradea Centru
Table 6 - Results for the variable load
For low voltage network supplied from PT Cristal, were
carried out measurements to determine energy losses. Figure
5 shows the single line diagram network and table 7 presents
the results obtained.
PT CRISTAL
2
250 kVA
II.5. RESULTS OBTAINED USING NETWORK
ANALYZERS
To make a more complete analysis, in addition to the above
methods we appeal to the recording of operational
characteristic quantities of RDEE electric networks using
networks analyzers. We used 5 Fluke 434 analyzers. Results
are presented by highlighting the following features: U = f (t),
I = f (t), P = f (t), S = f (t), Q = f (t) for a working day and a
Holiday. Examples are presented in Fig. 3 and 4.
Figure (5) Single line diagram for power supply from Cristal
substation
Nr.
crt.
Address
1
2
Avântului 12A
Avântului 12B
Meter
series
Meter indication
Reading1 Reading2
0852812
01731
1752,7
1064599 05590,3
05599
W[kWh]
21,7
8,7

18
19
Zalăului 9
0397302 17377,1
Grădiniţa
1333230
10920
Zalăului
Total consumption
General meter
W
17501,4
124,3
11208
288
1212,7
1153
- 59,7
Table 7 - Results on consumption for Zone II of Urban
Network Oradea
II.7. ESTIMATING THE ADDITIONAL POWER LOSSES
CAUSED BY THE UNBALANCED STATE AT RDEE
EXAMINED
Figure (3) Departure 2, S=f(t) for Holiday
Based on results obtained in the detailed evaluation of W
and the consumption retrieved from the client database, in
view of the unbalanced currents degree were calculated
additional power losses caused by the unbalanced state.
Evaluations conducted for the substations and network
related, to which there is a sensitive unbalanced, are presented
in Table 8.
Table 8 - Results of the evaluations performed for RDEE
Oradea
Figure (4) Departure 2, S=f(t) for a working day
Reference Number: W09-0036
The quantities meaning in table 8 are as follows:
 Sn - transformer rated power;
 (UMT, UJT) - rated phase-to-phase voltage (medium ad low
voltage)
 In - secondary rated current of the transformer;
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
 (IR, IS, IT) - load currents (JT) in transformer secondary
 Inul - current measured on neutral conductor departing from
transformer secondary
 PWn - rated power losses in transformer windings;
 (βR, βS, βT) – relative load in current of transformer;
 βe – equivalent relative load in current of transformer;
 (PT) – additional power losses caused by the unbalanced
state on the transformer;
 (WT) – additional energy losses caused by the
unbalanced state on the transformer;
 (WR) – additional energy losses caused by the
unbalanced state in the low voltage network;
 Imed – average load current (average values on the 3 phases);
 NI2 – unbalanced coefficient of the current;
 WT – energy consumed during the analysis.
For evaluating quantities mentioned above, have used the
following relationships:
2
2
2
1  I   I   I  
N 2I   R    S    T  
(3)
3  I med   I med   I med  


WR   kN 2I WT
(4)
R
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.98
1
1.02
1.04
1.06
1.08
1.1
Fig. 6ure (6) Changes in additional relative power losses,
depending on the unbalanced coefficient
The relationship for calculating the size (WR) was
achieved on the basis of the results of detailed analysis. After
evaluating quantities R = (WR) / WT and NI2 for each
departure and PT Cuza Voda, it was represented the R = f
(NI2) function (Fig. 6).
Given the rate of losses on RDEE, obtained from the
detailed analysis (5.69%), we obtained k = 31,46 X 10 -4.
Assessing energy consumption and energy losses was made
for a year.
III. CONCLUSIONS
1. Unbalanced state involve in the electrical networks of
further losses of power and energy to the operation on
balanced state.
2. Evaluation losses of power and energy (W) in the
electrical network operating in unbalanced state can be
based on measurements or model;
3. Evaluation of energy losses based on measurements for the
Reference Number: W09-0036
Vol. (2) – No. (1)
area of urban RDEE Oradea - subject to detailed analysis,
supplied from PT Cuza Voda - made for the period of 7 days
led to the total amount ΔWR1 = 1536.4 kWh. The energy input
in the period, recorded at general watt-hour meter is WM =
27,000 kWh. Relative energy losses are 5.69%
4. Evaluation of energy losses by calculation was made on the
basis of the network parameters (sections and branches)
and the average current absorbed. The calculation based on
the mathematical model applied in each phase and neutral
conductor has led to the total amount of losses for the
period under review (7 days) ΔWR21 = 456.37 kWh. The
calculation based on the specific mathematical model for
unbalanced state (equivalent load) led to the following
amount of energy losses in the period under review (7
days): ΔWR22 = 318,537 kWh.
5. Assessment demonstration of energy losses to section 1 of
departure 1 PT Cuza Voda, for variable load lead to a
greater loss of energy in operation than to the average
current ( WRV  0.955 kWh  WRC  0,681 kWh ).
6. See a major deviation of the calculated energy losses value
from that determined by measurement. Admitting the
assumption that all meters recorded correctly, this
difference is explained as follows:
 calculation of energy losses has been made to the average
load, and to the variable load values are higher;
 evaluation based on model does not include additional
losses in the contact points;
 model based on the load flow on phase and the neutral
conductor, leads to results closer to reality, compared
to model based on equivalent load.
The substantial difference between losses measured and
calculated also suggests the need for verifying the existence
of commercial losses.
7. Registrations made using Fluke 434 network analyzers
allows the formulation of the following conclusions:
 the device allows the display and viewing of electrical
measurements spectrum (U, I, P, S, Q, W, cosφ) for the
three phases and neutral;
 to load sizes (I, P, Q) is found significant average
unbalancing and high momentary unbalancing;
 it notes large variations of the load curve (P, S);
 network analyzed and all supplied consumers acts as a
source of reactive power.
 the device is not playing the total consumption of
energy for the period under review and thus is not
useful for validating current energy measurements
recorded in electrical network.
8. Determination by measurements of energy losses for the
second area of urban low voltage electrical network (PT
Cristal) led to erroneous results (negative loss). This result
is explained as follows:
 measuring instruments used are of two types: classical
meters - to consumers and network analyzer- to
substation;
 current transformers for electric power station in
Oradea Centu operates at much under rated load,
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
which involves large registration errors. This is
confirmed by meter failing in Oradea Centru for
analyzed departure.
9. Based on the results, summarized in the previous [3  8],
we recommend that the CPT to be made through
measurements using the same type of measuring
instruments , checking that the normal field of current
measures.
10. A large number of transformers in the municipality of
Oradea (269) are unbalanced loaded. For 33 of this
unbalanced degree in current exceeds the normal limit.
11. Further losses of energy caused by the unbalanced state,
estimated for the period of analysis (a year), referring to
the 269 transformers identified by significant unbalanced
state, amounting to 1060 MWh, representing about 0.4%
of power consumption. Most of the additional W is
caused by the unbalanced state RDEE of the 15
transformers associated with a unbalanced degree above
normal.
12. Most of analyzed transformers are under load. Only 67 of
the 269 transformers have a loading degree close to the
optimum, 3 transformers (PT Adevarului, PT and PT
Leontin Salajan Ioşia 2) are loaded well above the
optimum, and the other 199 transformers are under load.
13. Further reduction of power losses caused by unbalanced
state can be made through the implementation of
measures to balance the load, starting with substations
identified with highly unbalanced degree. CPT to reduce
overall, it is recommended continuing the pace of
sustained good practices established within Oradea
SDEE:
 balancing the load on the phases;
 minimize electrical networks bounding
 replacement of old network with new installations,
which mean that an investment of this kind reduce the
loss from [8-10]% to [4-6]%. In the case examined in
detail these upgrades have resulted in savings of
approx. 1000 RON/month only on reducing energy
losses, notwithstanding the reduction in operating
costs;
 replacing induction meters with electronic meters;
Reference Number: W09-0036
Vol. (2) – No. (1)
 checks of meters with standard watt-hour meter;
 securing measuring circuits LV (CT sealing, measuring
boxes, circuits);
 sealed measuring points with identifiable unique seals;
 monitoring the important consumers;
 increasing the loading degree of transformers and
distribution network.
It is recommended to check carefully the consumer supplied
from PT Cuza Voda, without record consumption in the
analysis interval (Table 3).
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200