EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia

Impact of current high order harmonic to core losses

of three-phase distribution transformer
Mihail Digalovski1, Krste Najdenkoski2, Goran Rafajlovski3
Faculty of Electrical Engineering and Information Technology
“Ss. Cyril and Methodius” University
Rugjer Boshkovic bb, 1000 Skopje, Republic of Macedonia
1
mihaild@feit.ukim.edu.mk
2
krste@feit.ukim.edu.mk
3
goran@feit.ukim.edu.mk

Abstract— Transformers are normally designed and built for life of transformer [3]. Harmonic voltage increase losses in its
use at rated frequency and sinusoidal load current. A non-linear magnetic core while harmonic currents increased losses in its
load on a transformer leads to harmonic power losses which winding and structure. In general, harmonics losses occur
cause increased operational costs and additional heating in from increased heat dissipation in the windings and skin effect
transformer parts. It leads to higher losses, early fatigue of
insulation, premature failure and reduction of the useful life of
both are a function of the square of the rms current, as well as
the transformer. To prevent these problems, the rated capacity from eddy currents and core losses. This extra heat can have a
of transformer which supplies harmonic loads must be reduced. significant impact in reducing the operating life of the
In this work a typical 50 KVA three phase distribution transformer insulation the increased of eddy current losses that
transformer with real practical parameters is taken under non- produced by a non-sinusoidal load current can cause abnormal
linear loads generated due to domestic loads. The core losses is temperature rise and hence excessive winding losses.
evaluated using the three dimensional model of the transformer Therefore the influence of the current harmonics is more
developed in Ansoft Maxwell based on valid model of important. From the above there is a need for detailed analysis
transformer under high harmonic conditions. And finally a of the impact of higher order harmonics on core losses (no-
relation associated with core losses and amplitude of high
load losses) in transformers [1].
harmonic order are reviewed & analyzed and then a comparison
is being carried out on the results obtained by different excitation
II. CORE LOSS
current in transformer windings.
Keywords: Core losses, Three-phase transformer, Harmonic, 3D
Model, Finite Element Method, Magnetic Flux Distribution
A. Hysteresis Loss
A significant contribution to no-load losses comes from
hysteresis losses. Hysteresis losses originate from the
I. INTRODUCTION molecular magnetic domains in the core laminations, resisting
In the past years, there has been an increased concern about being magnetized and demagnetized by the alternating
the effects of nonlinear loads on the power system. Nonlinear magnetic field. Each time the magnetising force produced by
loads are any loads which draw current which is not sinusoidal the primary of a transformer changes because of the applied ac
and include such equipment as fluorescent lamp, gas voltage, the domains realign them in the direction of the force.
discharge lighting, solid state motor drives, electrical energy The energy to accomplish this realignment of the magnetic
converters, static converters, rectifiers, arc furnaces, electronic domains comes from the input power and is not transferred to
phase control, cycloconvertors, switch mode power supplies, the secondary winding. It is therefore a loss. Because various
pulse width modulated drives and the increasingly common types of core materials have different magnetizing abilities,
electronic power supply causes generation of harmonics. the selection of core material is an important factor in
Harmonics are voltages and currents which appear on the reducing core losses. Hysteresis is a part of core loss. This
electrical system at frequencies that are integral multiples of depends upon the area of the magnetizing B-H loop and
the generated frequency. It results to a significant increase in frequency. Refer Fig. 1 for a typical BH Loop.
level of harmonics and distortion in power system. Energy input and retrieval while increasing and decreasing
Transformers are one of the component and usually the current. Loss per half cycle equals half of the area of
interface between the supply and most non-linear loads. They Hysteresis Loop. The B-H loop area depends upon the type of
are usually manufactured for operating at the linear load under core material and maximum flux density. It is thus dependent
rated frequency. Nowadays the presence of nonlinear load upon the maximum limits of flux excursions i.e. Bmax, the type
results in production harmonic current. Increasing in harmonic of material and frequency. Typically, this accounts for 50% of
currents causes extra loss in transformer winding and thus, the constant core losses for CRGO (Cold Rolled Grain
leads to increase in temperature, reduction in insulation life, Oriented) sheet steel with normal design practice. Hysteresis
Increase to higher losses and finally reduction of the useful losses are given with following equation:

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 EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia

Wh=Kh·f·Bm1,6 (W/kg) Eddy current losses are given with following equation:
, where We=Ke·Bm2·f2·t2 (W/kg)
Kh - the hysteresis constant
, where
f - Frequency (Hz)
Ke - the eddy current constant
Bm - Maximum flux density (T)
f - Frequency (Hz)
Bm - Maximum flux density (T)
t - Thickness of lamination strips
For reducing eddy losses, higher resistivity core material
and thinner (Typical thickness of laminations is 0.35 mm)
lamination of core are employed. This loss decreases very
slightly with increase in temperature. This variation is very
small and is neglected for all practical purposes. Eddy losses
contribute to about 50% of the core losses [3].

C. Effect of Harmonics on Core Losses

Transformer manufacturers usually try to design
transformers in a way that their minimum losses occur in rated
voltage, rated frequency and sinusoidal current. However, by
increasing the number of non-linear loads in recent years, the
load current is no longer sinusoidal. This non-sinusoidal
current causes extra losses and temperature in transformer.
Transformer losses is divided into two major groups, no load
and load losses as shown as:
Fig. 1. B-H Loop
PTL=PNL +PLL
Where PNL is no-load loss (core loss), PLL is load loss, and
B. Eddy Current Losses in the Core PTL is total loss. A brief description of core losses and
harmonic effects on them is presented in following:
The alternating flux induces an EMF in the bulk of the core
No load loss or core loss appears because of time variable
proportional to flux density and frequency. The resulting
nature of electromagnetic flux passing through the core and its
circulating current depends inversely upon the resistivity of
arrangement is affected the amount of this loss. Since
the material and directly upon the thickness of the core. The
distribution transformers are always under service,
losses per unit mass of core material, thus vary with square of
considering the number of this type of transformer in network,
the flux density, frequency and thickness of the core
the amount of no load loss is high but constant this type of
laminations. By using a laminated core, (thin sheets of silicon
loss is caused by hysteresis phenomenon and eddy currents
steel instead of a solid core) the path of the eddy current is
into the core. These losses are proportional to frequency and
broken up without increasing the reluctance of the magnetic
maximum flux density of the core and are separated from load
circuit. Refer Fig. 2 below for a comparison of solid iron core
currents. No-load losses are given with following equation:
and a laminated iron core. Fig. 2b shows a solid core, which is
split up by laminations of thickness d1 and depth d2 as shown PNL=Wh+We=Kh·f·Bm1,6+Ke·Bm2·f2·t2=Kh·f·Bm+Ke’·Bm2·f2=
in 2c. This is shown pictorially in 2a. =Kh·Kf·fn·KB1,6·Bmn1,6+Ke’·Kf2·fn2·KB2·Bmn2=
= Kf·KB1,6· Whn+ Kf2·KB2·Wen
PNLn=Whn+Wen
PNL/PNLn=(Kf·KB1,6·Whn+Kf2·KB2·Wen)/(Whn+Wen)
W’·(Kf·KB1,6+ Kf2·KB2)/2·W’=(Kf·KB1,6+ Kf2·KB2)/2
PNL=K'·PNLn

K fi ⋅ K Bi + K fi ⋅ K Bi
n 1, 6 2 2
PNL = PNLn ⋅ ¦
i =1
2
= PNLn ⋅ K '

, where
i - high order harmonic
K’ - constant
Fig. 2. Core Lamination to Reduce Eddy Current Losses
Ke’=Ke·t2 - constant

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 EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia

fi cross section area; for transformer core the exact magnetizing

K fi = - high order harmonic frequency ratio curve and specific core losses vs magnetic flux density curve
f1
are loaded. Also is taking in consideration lamination of the
Bm i transformer core and stacking factor of it. Boundary
K Bi = - high order harmonic magnetic flux density
B m1 conditions are defined on the surface of transformer tank and
ratio that limited part of space is domain of interest. They are of the
Dirichlet type (I order) and are set on the outer surfaces of the
Whn, Wen – nominal hysteresis and eddy current losses domain. Also that tangential component Ht of the magnetic
W’=Whn=Wen – approximation for equality of nominal field vector is a continuous function, while the normal
hysteresis and eddy current losses component Hn is zero. This means that magnetic field lines
will be parallel to the border area. On Fig. 5 and 6 is presented
B-H and P-B curves.
III. ANALYZED TRANSFORMER
The object of study is a three-phase (three-leg core type; oil
immersed) distribution transformer, from the production
program of “RADE KONCAR” transformer factory (Skopje,
Macedonia), type T 50-24, with winding configuration Yzn5.
The rated data of the transformer are: Sn=50 kVA;
U1/U2=20/0,4 kV; Si=24 kV; I1/I2=1,443/72,17 A; ukn=4 %;
fn=50 Hz; p=±2x2,5 %; Yzn5. Transformer is presented on
Fig. 3.

Fig. 4. 3D Simulation model of three-phase transformer

2.00

1.50
B (tes la)

1.00

0.50

Fig. 1. Analyzed transformer 0.00

0.00E+000 5.00E+004 1.00E+005 1.50E+005
H (A_per_meter)

Fig. 5. B-H curve

IV. TRANSIENT 3D MODEL FOR DETERMINATION OF CORE 3.00
LOSSES
2.50
The first step of the finite element modeling is to construct
a three dimensional model of the three-phase transformer. 2.00
Transformer model is drawn directly into the MAXWELL 3D
1.50
and is presented in Fig.4. Solution type in the model is
P

transient, because current loads are alternating sinusoidal 1.00

variables [6].
The model is made in accordance with the geometry of the 0.50

transformer. Transformer core is dark blue colored, low

0.00
voltage windings with red color and high voltage windings 0.00 0.25 0.50 0.75 1.00
B (Tesla)
1.25 1.50 1.75 2.00

with light blue. Three dimensional framework is

Fig.6. P-B curve
representation of transformer box in which electromagnetic
phenomena are considered. For all parts of the transformer in
In order to provide correct numerical computational results
the input database are listed relevant materials from which
for core losses, the mesh in the region of interest should be
they are made. Windings are defined with number of turns and

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 EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia

with high density. Meshed model of transformer is presented Current Curve

on Fig.7. 100
80
60
40
I-Harmonic

Percentage
20 III-Harmonic
0 V-Harmonic
-20 0 30 60 90 120 150 180 210 240 270 300 330 360 VII-Harmonic
Sumary Current
-40
-60
-80
-100
Degrees

`Fig. 8.c) Current curve (III case)

V. RESULTS AND COMPARISON OF RESULTS

After completion of preprocessor phase and transformer
discretisation with finite elements, the model is ready for
processing. At this phase Maxwell’s equation system to solve
Fig. 7. Meshed model of the three-phase transformer numerically and its solution is obtained magnetic field
In the transient model are defined the following three cases intensity H for each individual finite element. By association
of current load and are shown in Table 1. of all the values is obtained distribution of the magnetic field
in the domain. Through the magnetic field intensity H can be
TABLE I
expressed magnetic flux density B and its distribution (as a
Harmonic range of colors) is presented on Fig. 9. Obtained magnetic flux
Order KB1 KB3 KB5 KB7 density distribution is for rated load of the transformer (I case,
Case (%) (%) (%) (%) only with first harmonic). On Fig. 10 is given surface density
of core losses.
1 100 0 0 0
2 100 2,5 3 2,5
3 100 5 6 5

For those three cases of loadings, in program postprocessor

readings core losses and they are compared with the
approximate analytical values for the control. Hence, reflected
the impact and change core losses by changing of harmonic
components in excitation currents.
Forms of the currents for the three typical cases are given
on Fig. 8 a), b) and c).
Current Curve
100
80
60
40
Fig. 9. Distribution of magnetic flux density (I case)
Percentage

20 Sinusoidal Current
0
-20 0 30 60 90 120 150 180 210 240 270 300 330 360

-40
-60
-80
-100
Degrees

Fig. 8.a) Current curve (I case)

Current Curve
100
80
60
I-Harmonic
40
Percentage

III-Harmonic
20 V-Harmonic
0 VII-Harmonic
x
-20 0 30 60 90 120 150 180 210 240 270 300 330 360 Sumary Current
-40
-60
-80
-100 Fig. 10. Surface density of core losses (I case)
Degrees

Fig. 8.b) Current curve (II case) On Fig. 11 and 12 is presented magnetic flux density
distribution and core losses surface density.

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 EuroCon 2013 • 1-4 July 2013 • Zagreb, Croatia

transformer core and they are shown in Table 2, together with

the analytical calculated losses.
TABLE III

Method
Increasing
Relative
of core
Simulation Analytical Measured Deviation
Core losses
(%)
Losses (%)
Pcore1
170,7 / 168,2 1,49 /
(W)
Pcore2
174,4 176,6 / -1,25 2,17
Fig. 11. Distribution of magnetic flux density (II case) (W)
Pcore3
197,2 200,2 / -1,48 15,52
(W)

VI. CONCLUSION
The wide spread utilization of electronic devices has
significantly increased the numbers of harmonic generating
apparatus in the power systems. This harmonics cause
distortions of voltage and current waveforms that have
negative effects on transformers as increased total losses.
This paper has described distribution transformer no-load
Fig. 12. Surface density of core losses (II case)
losses, as well as the harmonic impact on no-load losses, and
has introduced a methodology based on FEM model, to
On Fig. 13 and 14 is presented magnetic flux density predict satisfactorily the harmonic impact on core distribution
distribution and core losses surface density. transformer. The methodology introduced in this paper, if
implemented at the design stage of distribution transformers,
may provide great services in reducing the no-load losses.

REFERENCES
[1] Amit Gupta, Ranjana Singh, "Computation of Transformer Losses
Under the Effects of Non-Sinusoidal Currents", Advanced Computing:
An International Journal (ACIJ), Vol.2, No.6, pp. 91 – 104, November
2011.
[2] Ahmed M.A. Haidar, S. Taib, I Daut, S. Uthman, "Evaluation of
Transformer Magnetizing Core Loss", Journal of Applied Sciences,
ISSN1812-5654, No. 6, pp. 2579-2585, 2006.
[3] Bureau of Energy Efficiency & Indian Renewable Energy
Development Agency, "Transformer – Best Practice Manual", New
Fig. 13. Distribution of magnetic flux density (III case) Delhi, India, 2006.
[4] S.B. Sadati, H. Yousefi, B. Darvishi, A. Tahani, "Comparision of
Distribution Transformer Losses and Capacity Under Linear and
Harmonic Loads", 2nd IEEE International Conference on Power and
Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia, No.
6, pp. 2579-2585, 2006.
[5] Sonja Tidblad Lundmark, Yuriy Serdyuk, Stanislav Gubanski,
"Computer Model of Electromagnetic Phenomena in Hexaformer",
Chalmers University of Technology, Goteborg, 2007.
[6] Mihail Digalovski, Lidija Petkovska, Krste Najdenkoski,
"Determination of Three-Phase Transformer Reactances With 3D
Finite Element Method", International Journal on Information
Technologies and Security, No. 2/2012, ISSN 1313-8251, pp. 65-72.
Sofia, Bulgaria.
[7] ANSOFT MAXWELL, User Manual, November 2010.

Fig. 14. Surface density of core losses (III case)

After receiving the distributions of magnetic flux density

and surface density of core losses for all three cases, in
MAXWELL postprocessor are reading summary losses in the

978-1-4673-2232-4/13/$31.00 ©2013 IEEE 1535