International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 1, Issue 2, December 2011)
Analysis of Distribution Transformer Performance under
Non-linear Balanced Load Conditions and Its Remedial
Measures
Sanjay A. Deokar1, Laxman M. Waghmare2
1
Dnyanganga College of Engineering and Research, Pune University, Pune-411041
2
S.G.G.S., Institute of Engineering and Technology, Nanded- 431606
1
s_deokar2@rediffmail.com
2
lmwaghmare@yahoo.com
non-linear loads should be estimated after proper
evaluation of present load conditions[1].The increasing
usage of non-linear loads on electrical power systems is
causing greater concern for the possible loss of
transformer life. Manufacturers
of
distribution
transformers have developed a rating system called Kfactor, a design which is capable of withstanding the
effects of harmonic load currents. An application of this
rating system to specify a transformer for a particular
environment requires knowledge of the fundamental &
harmonic load currents predicted. In almost all the cases,
the field measurements are required to diagnose problems
at a specific location, by analyzing load currents.
Electrical insulation
used in
distribution
transformers gets degraded when it is subjected to the
thermal, electrical, environmental, mechanical and
combined stresses during its operation.
Electrical
stresses are caused by voltage gradient. The average life
expectancy of a transformer is decided by the average life
of insulating materials. The steady-state power quality
problem like harmonics and variation in frequency are
responsible for accelerated aging of its insulating
material. A transformer designed without considering all
these issues will result into premature failure. In [2], a
different method to calculate the impact of non-linear
loads has been discussed. It also gives an overview of
impact
of
nonlinear
load
on the distribution
transformer winding losses. The standard K-factor
transformer ratings and typical loads as well as its design
guidelines are given in [3]. In [4], measurement methods
for reactive power demand under non-linear loads have
been presented.
In [5], on line monitoring of all losses of both single
and three-phase transformers has been investigated under
a different percentage of load conditions.
Abstract— In recent years there has been very extensive use
of power electronic devices, which result in harmonic
proliferation in the power distribution system. In this paper,
as per IEEE C 57.110 standards, procedure to calculate total
loss in the distribution transformer under non-linear
distortion environment is proposed. The power factor
capacitor performance under non-linear load conditions is
also analyzed. The relation of total current harmonic
distortion in the distribution system with load power factor,
transformer losses, efficiency and maximum current
delivered is also analyzed. The mitigation methods are
proposed to minimize the non-linear load impact on the
distribution transformer performance. Instead of K-factor
transformer approach, a passive harmonic filter method is
developed based on higher savings in energy losses. The
simulation studies, are performed using Math works
MATLAB 7.0.1 for distribution system at 11/0.440 kV, 200
kVA distribution transformer under non-linear balanced
load conditions. It is observed that the power factor
capacitor bank acts as a source of harmonic under the nonlinear load conditions in the presence of passive filters.
Keywords— Harmonic Proliferation, k-Factor, Non-linear
Load, Power Factor, Mitigation.
I. INTRODUCTION
The transformers are designed and manufactured to be
used for non-linear load, at rated frequency and balanced
supply voltage. The present design trend in electrical load
devices is to increase energy efficiency with solid-state
electronics. One of the major drawbacks of this trend is
the injection of harmonics into the power systems. Almost
all the utilities have expressed
concern
about
overheating of oil immersed distribution transformers,
which supply the non-linear loads. A transformer thermal
response to sinusoidal loads is properly evaluated at the
transformer design stage, but it’s actual response to
152
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Website: www.ijetae.com (ISSN 2250-2459, Volume 1, Issue 2, December 2011)
Harmonics and its impact on the power factor with
their relation have been investigated in [6]. It also
explains the important to the true power factor compared
with displacement power factor under non-linear load.
The transformer de-rating methods during non-linear load
supply conditions are given in [7].In [8], transformer
modeling under the non-linear load conditions is
investigated and tested under non-linear load conditions.
The measurement of the losses for estimation of the
transformer de-rating and harmonic loss factor
comparison has been discussed in [9]. The measurement
of eddy current loss coefficient and de-rating of single
phase transformers as well as comparison with K-factor
has been presented in [10]. The transformer design and
application considerations for non-sinusoidal load
currents has been discussed in [11].The impact of nonlinear loads on temperature rise of small oil filled
distribution transformers has been analyzed in [13]. A dry
type distribution transformer specifications and
calculations of winding temperatures in distribution
transformers under harmonic load conditions have been
elaborated in [14], [15].Considering all these issues it is
necessary to study and analyze the various effects of nonlinear load on distribution transformers. The power factor
during linear load condition is called displacement power
factor and during non-linear load condition, it is called
distorted power factor. If harmonic currents are
introduced in the system, true or total power factor is
always less than the displacement power factor. In this
paper, a case study of 200kVA, 11kV/440V, 3-phase
distribution transformer with balanced load nature is
simulated using Math works MATLAB-7.0.1 for
analyzing the impacts of non-linear loads. The relation
between current harmonics in the distribution system and
losses, efficiency, maximum current delivered, apparent
power capacity of the distribution transformer has been
analyzed and presented. The impact of ordinary power
factor capacitor bank on total current harmonic distortion
is also analyzed. A mitigation measures like K-rated
transformers and application of passive filters are
presented and results are compared with harmonic content
base case. From this comparison, instead of K-factor
transformer, passive filter method is recommended.
As per ANSI/IEEE C57.110-1986[7],[12], the
transformer losses are mainly no-load loss (excitation
loss); load loss (impedance loss); and total loss. This can
be written by using following expression,
(1)
PTOTAL  PCORE  PLOAD  L
Where,
PTOTAL  Total loss, PCORE  Core or No load loss and
PLOADL  Load loss
The total load loss can be given as,
PLOAD  L  I 2 RDC  PWEC L  POSL L
(2)
Where,
PWEC L is the winding eddy current loss and POSL L is
the other stray loss.
Total stray losses include winding eddy current losses and
structural part stray losses. These are given by the
following expressions [4],
PTotal  STR  P WEC L  POSL L  PLOAD  L  P
POSL L  PTotal  STR  PWEC L
(3)
(4)
The winding eddy current loss can be calculated using the
following expression,
(5)
PWEC L  0.33 P Total  STR
Losses during non- linear loading of a distribution
transformer
In modern power systems, the total harmonic voltage
distortion (THD v ) is normally below 5% and the
magnitudes of the voltage harmonic components are small
compared
to
fundamental
components(2%
to
3%).Therefore voltage harmonics effects are neglected.
The current harmonics are more significant. These
harmonic load current components cause additional losses
in the winding and other structural parts. Hence total load
losses under harmonics load condition can be given by the
following expression,
(6)
PLOAD  L  PCU  PWEC L  POSL L
The harmonic component of load current increases the
r.m.s. value of the load current and hence PCU  I 2 R
loss will be increased accordingly. PWEC L is the winding
eddy current loss due to the non-sinusoidal load current. It
can be given as follows,
II. LOSSES DURING NON-LINEAR LOADING OF
DISTRIBUTION TRANSFORMER
An easy way to comply with the conference paper
formatting requirements is to use this document as a
template and simply type your text into it.
PWEC L  PWEC R
153
I
h  h

h 1
 I RT
h  m ax
2




2
(7)
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 1, Issue 2, December 2011)
Where,
The distribution transformer must be de-rated under
non-sinusoidal load conditions [1].The transformers derating can be performed using following methods: a)
Direct loss measurement. b) Using K-Factor and c) Based
PWEC R is the rated eddy current loss under full load
conditions,
h is the harmonic order, I h is the r.m.s.
current at harmonic order h and I RT is the rated
on harmonic loss factor ( FHL ) .
fundamental current at full load conditions and rated
frequency. The increased winding eddy current losses
produced by a non-sinusoidal load current can cause
excessive winding losses and hence abnormal temperature
rise. POSL L are the stray losses in the structural parts due
A. Distribution Transformer De-rating Based on KFactor
The impact of nonlinear loads on distribution
transformers greatly depends on the nature and the
harmonic spectrum caused by the nonlinear load, which is
not considered by the manufacturers. The IEEE standard.
C57.110-1998[7] introduced a term called the K-factor for
rating a transformer as per their capability to handle load
currents with significant harmonic contents .It is an
alternate technique for transformer de-rating which
considers load characteristics. It is a rating optionally
applied to a transformer indicating its suitability for use
with loads that draw non-sinusoidal currents. It is an
index that determines the changes in conventional
transformers must undergo so that they can dissipate heat
due to additional iron and copper losses because of
harmonic currents at rated power. Hence the K-factor can
be written as,
to non-sinusoidal current. It can be calculated by the
following expression,
POSL L  POSL R
I
h  h

h 1
 IR
h  m ax
0.8



2
(8)
Where,
POSL R are the structural part stray losses under rated
conditions. The factor 0.8 is accepted by IEEE after
manufacturer’s verification. For oil filled transformers,
these stray losses increase the oil temperature and thus the
hot spot temperature. Total load losses in both oil cooled
and dry type transformer under non-sinusoidal load
condition with current harmonics are calculated by the
following expression,
PLOSD  L  PCU
 POSL R
h  max
h  max

h 1
2
h  max
I

  PWEC R   h
h 1  I R

I h
K
I
h 1
2
 2
 h

2
h
2
(10)
2
h
This K-factor is only an indicative value. The main
objective is to design and manufacture an oil filled
distribution transformer which can operate for a specific
K-factor value without loosing its expected life span.
Therefore, the maximum amount of R.M.S. harmonic
load current that the transformer can deliver is given by
the following expression,
2
 I h  0.8
 h
 R
  I
h 1
 Ih

 IR
hm ax
(9)
III. DE-RATING OF DISTRIBUTION TRANSFORMER
According to the IEEE dictionary, de-rating is defined
as "the intentional reduction of the stress/strength ratio
(e.g., real or apparent power) in the application of an item
(e.g., transformer), usually for the purpose of reducing the
occurrence of stress-related failure (e.g., reduction of
lifetime of transformer due to increased temperature
beyond the rated temperature)."Harmonic currents and
voltages result in harmonic losses increasing the
temperature rise. This rise beyond its rated value results in
a reduction of lifetime.
I max 
1  PECL  R
(I R )
1  kPEC  R
(11)
I R the fundamental rms current under is rated
load conditions, PECL  R is the eddy current loss to rated
Where
I 2 R loss in which I is the total rms current.
The reduction in apparent power is given by the
following expression,
PKVA Re duction  1  (
154
V Non linear  Rms p.u .
) I m ax
V Rated  Rms
(12)
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Where,
IV. MODELING AND SIMULATION OF DISTRIBUTION
TRANSFORMER
V Non linear  Rms the total rms is value of the secondary
A 200kVA three-phase distribution transformer is
modeled and simulated using Matlab-7.01 for different
load characteristics. All parameters when the transformer
is tested at balanced linear full load were taken from
Maharashtra State Electricity Distribution Company
Limited (MSEDCL) manual. All these parameters are
given in Table I.
voltage including harmonics and V Rated  Rms is the rated
R.M.S. value of the secondary winding without
harmonics.
B. Distribution Transformer De-rating Based on FHL
Factor
As per IEEE Std. C57.110/D7-1998[7], this represents
an alternative approach for assessing transformer
capability supplying non-linear loads. Hence FHL Factor
can be defined using following expression,
FHL
AT FULL LOAD
2
Ih  2

  h
h 1  I 1 

2
h m ax
Ih 

 
h 1  I 1 
h m ax
TABLE I
ALL PARAMETERS AND LOSSES OF 200KVA TRANSFORMER WORKING
Parameters
(13)
The stray loss harmonic factor can be given as,
FHL STRAY
2
 I h  0. 8

  h
h 1  I 1 

2
h m ax
 Ih 

 
h 1  I 1 
h m ax
Hence, the relation between K-factor and
as follows,
 h m ax 2
  Ih
K   h 1 2
 I
 R



F
 HL


(14)
FHL is given
(15)
Therefore, the maximum amount of R.M.S. harmonic
load current that the transformer can deliver is given as,
I max
PLOAD L
(16)

1  [ FHL  PECL ]  [ FHL STRAY  POSL ]
Rating
KVA Rating
200 KVA
Voltage Range
11KV/440V
I1
10.5A
I2
266.7A
No load iron loss
500W
Full Load Cu Loss at
750C
3000W
R1
14.75Ω
R2
0.0062Ω
L1
0.003H
L2
0.067mH
Rc
728 kΩ
Lm
32105H
A transformer is tested
characteristics at full loads.
Under harmonic load condition, the new load loss can
be calculated by the following expression,
PLOAD  LNEW  I 2 [1  FHL  PECL  R  FHL STRAY  POSL ] (17)
The reduction in the apparent power rating is given by
the equation (12).
for
the
following
load
A. Base Case of 200kVA Distribution Transformer with
Linear Nature of Load at 0.8 P.F.
In this case 200kVA distribution, transformer is
loaded at its full capacity with non-linear load.
155
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The single-line diagram of the simulated power system
is shown in Fig.1 (a).Both primary and secondary full
load currents, current THD, and total losses are
calculated. It is matching with standard full load test data
of the 200kVA distribution transformers with 15%
tolerance given by distribution Company. Efficiency of
the transformer under this case is 98.12% at 0.8 lagging
power factor and current harmonics are below the IEEE
standard.
It is observed that the losses are reduced and hence
efficiency is also improved about 98.24%.For the same
load, current to be supplied by a transformer is reduced by
16%. This arrangement is simulated in matlab-7.01 as
shown in Fig.1 (b), and results are shown in Table I.
V. A CASE OF 200KVA DISTRIBUTION TRANSFORMER
FEEDING NON-LINEAR NATURE OF LOAD WITHOUT P.F.
IMPROVEMENT
In this case transformer, performance is checked
without power factor improvement for non-linear load
only in which load is adjusted at THDi=28.09% up to 35 th
harmonics level. From the simulation, it is observed that
the losses are increased drastically, which results in
efficiency at 96.60%. The transformer maximum current
delivery capacity is reduced by 15% as compared to
secondary full load current. The voltage profile is also
reduced due to increased voltage drop in distribution
lines. This arrangement is simulated and is shown in
Fig.1(c). The current spectrum and its harmonic current
level of a single phase are shown in Fig.2 (a) and (b)
respectively. The results are shown in Table 2.
Supply 11kV,
f rom power utility
11/0.433kV
200kVA
R1=14.75ohm L1=0.003H
R2=0.0062ohm L2=0.067H
Rm=728kohm Lm=32105H
X/R=2.5
BUS BAR
400
300
Linear Load
Full load 200kVA
p.f .=0.8lagging
S2
S3
Non-Linear
Capacitor
Load
bank
%THDi=28
67.41kVAR
S4
200
'a' phase current(A)
S1
Passiv e
Filters,5th,
30kVAR/Phase
7th and 15th
onwards20kVAR/
phase
100
0
-100
-200
-300
-400
0
0.01
0.02
0.03
0.04
0.05
Time (sec)
0.06
0.07
0.08
0.09
0.1
(a)
Fig.1. A distribution transformer feeding a linear/non-linear full
load; (a) The linear nature of load at 0.8 lagging p.f.; (b) The linear
nature of load with 0.95 p.f. improvement using capacitor bank; (c)
Non-linear nature of load without p.f. improvement with % THD
=28%.; (d) The Non-linear nature of load with p.f. improvement (e)
Non-linear nature of load with passive harmonic filters for p.f
improvement and %THD mitigation.
400
Amplitude of current (A)
350
B. Base Case of 200kVA Distribution Transformer
Feeding Linear Nature of Load with P.F. Improvement at
0.95
In this case, a transformer performance is checked
when a capacitor bank of 67 47kVAR. is installed at the
point of common coupling (PCC ) to improve power
factor of 0.95 lagging without changing load nature.
300
250
200
150
100
50
0
0
5
10
15
20
25
30
35
40
Harmonic order
(b)
Fig.2. (a) Harmonic current spectrum of phase A ; (b)Current
harmonic bar chart of phase A at non-linear full load without
power factor improvement.
156
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TABLE II
VI. A CASE OF 200KVA DISTRIBUTION TRANSFORMER
FEEDING NON-LINEAR LAD WITH P.F.IMPROVEMENT
SIMULATION RESULTS OF 200KVATRANSFORMER TESTED AT
DIFFERENT LOAD CHARACTERISTICS
In this case transformer, performance is checked with
power factor improvement capacitor and non-linear load
nature at full load. From the simulation results it is
observed that the THDi is increased to 35.42%.It is also
observed that the current harmonics are increased in each
level compared to previous case. The losses are increased
drastically results in efficiency reduction at 92.80%. For
the same load distribution, line is overloaded by 4.5% and
the load carrying capability of a transformer is reduced by
30% compared to previous case. The transformer
maximum current delivery capacity is reduced by 44% as
compared to secondary full load current. The voltage
profile is also disturbed due to increased voltage drop in
distribution lines results in reduction in apparent power
capacity. Here under non-sinusoidal load condition,
power factor improvement is impossible with simple
capacitor banks only. An ordinary capacitor bank also
acts as a source of harmonics as current THD is increased.
This arrangement is simulated and is shown in Fig.1(d).
The current spectrum and harmonics level is shown in
Fig.3(a)&(b) respectively.The results are shown in Table2
Base
case
Load
Characteris
tics
(Total
Linear
nature
of
Load)
Base
Case+
Capacitor
Banks for
P.F.
improvem
ents
Total NonLinear
NonLoad
linear
without
Load+
....P.F……
P.F.
…....
Capacit
improveme
or.
nt
I1
10.3Am
p
8.67Amp
10.3Amp
9.38
Amp
I2
266.6A
mp
218.4Amp
261.5Amp
273.5
Amp
Total Load
Losses
3714.9
Watts
2852.9
Watts
5622.5
Watts
12347
Watts
THDi
<5%
<5%
28.09%
35.52%
Imax
Rated
Capacit
y
Rated
Capacity
221.78
Amp
155.13
Amp
K-rating
No Derating
No Derating
7.057
19.7
%
Efficiency
97.73%
98.24%
96.60%
92.80%
Total
Power
Factor
0.8
lagging
0.95
lagging
0.77
lagging
0.942
lagging
0.0%
17.1%
41.87%
600
'a' phase current(A)
400
200
0
-200
-400
-600
0
0.02
0.04
0.06
Time (sec)
0.08
0.1
(a)
400
350
Amplitude of current (A)
300
250
200
% kVA
Capacity
reduction
150
100
50
0
0
5
10
15
20
25
30
35
40
Harmonic order
(b)
Fig.3. (a) Harmonic current spectrum of phase A when distribution
transformer is feeding non-linear full load with capacitor bank for
p.f. improvement up to 0.95 lagging. (b) Current harmonic level bar
chart of phase A when base case feeding non-linear full load with
capacitor bank.
157
0.0%
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VII. POWER FACTOR UNDER NON-LINEAR LOAD
ENVIRONMENT
Since displacement power factor is always less than
unity, hence true power factor is always less than the
distorted power factor. The true power factor variation
under different non-linear load conditions is depicted
Table II and Table III respectively. It is seen that the
harmonic loads, especially current harmonic content has a
significant impact on the true power factor and the
transformer efficiency. The true or total power factor
variations with current total harmonic distortions are
plotted in Fig.6.
Under the harmonic load conditions, total harmonic
distortion or distortion factor is used for its level
measurement. It is the ratio of the rms value of the
harmonics (voltage or current) above fundamental to the
rms value of the fundamental. It can be given by the
following expression,
hmax
THDV 
V
h2
VIII. MITIGATION MEASURES
2
h
A. Harmonic filter design-A shunt passive filters
It can be seen that the shunt capacitor acts as a source
of harmonics when load nature is non-linear. With
incorporation of the power factor capacitor, total current
harmonic distortion level is increased from 28.09% to
35.52%. It is important to note that just by adding a shunt
capacitor poor distortion power factor can’t be
compensated. The displacement power factor can be
improved with shunt capacitors. Here existing power
factor capacitor is removed, and it is converted into
harmonic passive filter. A single tuned band pass passive
filter for 5th and 7th harmonic level and high-pass filter
from 15th harmonic onwards are designed and simulated
for 28.09 % of current THD. Harmonic filters are
designed to be capacitive at fundamental frequency, so
that they are also used for producing reactive power
required by non-linear loads and for power factor
correction. High-pass filters, which are used to filter highorder harmonics and cover a wide range of frequencies. A
shunt filter is said to be tuned to the frequency which
makes its inductive and capacitive reactance’s equal.
Three-phase harmonic filter are shunt elements that are
used in power systems for decreasing both current and
voltage distortion as well as for power factor correction.
The high-pass filter is a single-tuned filter where the L
and R elements are connected in parallel instead of series.
This connection results in a wide-band filter having
impedance at high frequencies limited by the resistance R.
The quality factor is adjusted according to the harmonic
order which determines the sharpness of tuning. It is
observed that the harmonic filters reduce the THD of the
current injected in the system from 28.09% to 4.8% which
is bellow IEEE standard [9]. The total 70 KVAR is
adjusted as per the following configuration: 30 KVAR
low-pass filter tuned to the 5th harmonic with quality
factor of 2 and 20 KVAR low-pass filter tuned to the 7th
harmonic with quality factor of 20 as well as 20 KVAR
 100
V1
OR
(18)
hmax
THDI 
I
h2
I1
2
h
 100
Hence, correct form of true power factor under linear
and non-linear load environments is given by the
following expression,
TRUEPF 

PAvg
V fun I fun

1
1  (THDV 100) 2 (19)
1
1  (THDI 100) 2
Normally in most of harmonic load cases, average
power variations are negligible and voltage total harmonic
distortion is also less than 5%, hence it is also
neglected[1],[6].By considering these assumptions the
approximate equation for true power factor is given as,
TRUE PF 
Pfun
V fun I fun

1
1  (THD I 100 ) 2
(20)
 Displaceme nt PF  Distortion PF
Where,
Pfun, Vfun and Ifun are the fundamental power, voltage
and currents.
158
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high-pass filter tuned to 15th harmonics onward. The total
load losses are reduced by 44% compared to 28.09% of
THDi case and 74.5% compared to 35.52% of THDi case.
The corresponding simulation results are shown in Table
3. From the table, it observed that the transformer
maximum current delivery capacity is close to be rated
current capacity and efficiency at full load is 98.37%. The
current spectrum and current harmonic bar chart of phase
A is shown in Fig. 4 (a) and (b) respectively.
400
350
Amplitude of Current (Amp)
300
250
200
150
100
50
0
0
5
10
15
20
25
30
35
40
Harmonic order
TABLE III
(b)
SIMULATION RESULTS OF 200KVA TRANSFORMER TESTEDWHEN
PASSIVE FILTERS ARE TESTED
Load Characteristics
Fig.4. (a) Harmonic current spectrum of phase A; (b) Current
harmonic level bar chart of phase A at non-linear full load with
passive filters.
Non-linear Loads+
Passive Filters
B. Transformer De-rating using K-Factor and FHL
Total Load losses
3143 Watts
THDi
1.1432%
Imax
264.00 Amp
K-rating
1.1432
Factor
If the filters are not installed then transformer derating using K-factor and FHL factor can be implemented.
Some of the changes in the design of K-rated transformers
are given below:
1) Optimum increase in the delta connected primary
winding conductor size which can tolerate the circulating
triplen harmonics.
% Efficiency
98.37%
Total Power Factor
0.95 lagging
2) Core design flux density should be minimum to
protect against voltage distortion.
Reduction in kVA capacity
0.97%
3) Multiple and transposed secondary winding
conductor to reduce resistance to avoid heating due to
skin effect from high frequency currents. These design
factors can improve the thermal dissipation to minimize
the additional losses.
400
300
a phase Current (Amp)
200
4) Heavier conductors and transposition of winding
conductor to reduce magnetic losses.
100
0
-100
5) Electrostatic shielding between primary and
secondary winding to reduce eddy current losses and
heating.
-200
-300
-400
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (sec)
60 Double sized neutral conductor to protect against
triplen harmonics.
As per reference [2], the standard K-factor transformer
ratings for specific loads are given in Table IV.
(a)
159
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TABLE IV
1
TRANASFORMER K-RATINGS
Type of Loads
K-factor
Incandescent lighting Electric resistance heating,
Motors, Control transformers without solid state
controllers.
K-1
0.9
Total pf
0.8
0.7
0.6
Electric discharge lighting UPS, Induction heating
equipment, Welders, PLC’s.
K-4
Telecommunication Equipments, UPS without
filtering, General health care and classrooms of
schools, Various testing equipments.
K-13
Mainframe computer loads, Moters with VFD’s,
Health care equipments in critical care areas and
operating rooms of hospitals.
K-20
Multi-wire receptacle circuits in industrial
,medical, educational laboratories etc.
K-30
Loads producing high order harmonics
K-40
0.5
0
Fig.6. Relation between total power factor and THDi.
The maximum current delivered by the transformer is
inversely proportional to the total current harmonic
distortion. Transformer KVA capacity also reduced with
current harmonic level. When total current harmonic
distortion level is 28.09%, K-13 rating and for
THDi=35.52%, K-20 rating transformer is recommended.
When passive filters are used, the K-factor is reduced to
K-1.Other mitigation measures suggested are given
below:
1) If the filters are not installed then transformer derating using K-factor and FHL factor can be implemented.
2) Use energy efficient transformers to control
temperature rise and losses. It will extend the life of
transformer.
3) Design of proper sizing of distribution transformer
neutral conductor.
4) Use of Star-delta connected transformer to block
triplen harmonics.
The calculations shown in Table I and Table II, it can
be observed that the K-factor rating increases with total
current harmonic distortion. The relation between Kfactor and THDi is shown in Fig.5, as given below.
50
%THDi
20 40 60 80 100 120 140 160180
%THDi
40
IX. CONCLUSIONS
30
A three -phase distribution transformer was simulated
for critical analysis under balanced non-linear load. It was
shown that the THDi has a significant impact on the
transformer efficiency as compared with linear nature of
the load. It is observed that power factor, KVA capacity
and transformer efficiency decreases with non-linear load.
It is also shown that the power factor capacitors act as a
source of harmonics during non-linear loading. The Kfactor de-rating of the distribution transformer increases
with an increase in % THDi. If the load THDi is increased
in such a way that the load K-factor greater than the rated
K-factor, then the transformer can’t be operated at its full
KVA capacity, and hence it would require de-rating.
20
10
1
4
13
20
K-FACTOR
40
Fig.5. Relation between K-Factor and THDi.
Power factor capacitor contributes for increase in total
current harmonic distortion level with non-linear load. It
alone doesn’t helpful for improving total power factor but
can improve displacement power factor. This relation is
plotted in Fig 6.
160
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[12] “IEEE Recommended Practices & Requirements for Harmonic
From this analysis, it is concluded that as compared to
K-factor transformer, a passive filter technique is
effective for harmonic mitigation and power factor
improvement. When ever the passive filter is used the
transformer apparent power capacity and distribution line
loading capability can be improved for the same nature of
load. With the implementation of passive filters, there is
significant reduction in the energy losses. In case of
unbalanced non-linear load, an active filter can be used to
improve the power system performance.
Control in Electrical Power Systems,” IEEE Std 519-1992.
[13] A.W Galli, M.D Cox, “Temperature rise of small oil filled
distribution transformers supplying non-sinusoidal load currents,”
IEEE transactions on Power Delivery, vol.11, no.1,PP 283-291,
January 1996.
[14] Isadoro Kerzenbaum , Alexander Mazur, Mahendra Mistry, Jerome
Frank “Specifying Dry type Distribution Transformers for SolidState Applications,” IEEE Transactions on Industry Application,
vol.27, no.1, pp. 173-178, January/ February 1991.
[15] M.D.Hwang,, W.M.Grady , H.W.Sanders Jr., “Calculation of
winding temperatures in distribution transformers subjected to
harmonic currents,” IEEE Transactions on Power Delivery,vol.3,
no.3, pp. 1074-1079, July 1988.
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