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 Total Downloads : 1442
 Authors : J. Mahesh Yadav, Dr. A. Srinivasula Reddy, T.Sindhuja
 Paper ID : IJERTV2IS3355
 Volume & Issue : Volume 02, Issue 03 (March 2013)
 Published (First Online): 20032013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Determining Thermal Life Expectancy Of Power Transformer Under Non Linear Loads Using FEM By ANSYS And MATLAB
J. Mahesh Yadav [1], Dr.A.Srinivasula.Reddy [2], T.Sindhuja [3]
1 Research Scholar, JNT University, Hyderabad, India
2 Prof. & Principal, Samskruthi Engineering College, Hyderabad, India
3 Electrical Engineering Departments, GNITC, JNTU Hyderabad, India
Abstract
Power transformers have immense importance in power system and this should work very efficiently for good results. Hotspot temperature plays a vital role in transformers life expectancy. Temperature rise in a power transformer due to non linear load current is known to be most important factor in causing rapid degradation of its insulation. Core is one of the parts of transformer where hotspot temperature is effective. Therefore design of transformer should be considered. A non linear load in power systems has reduces transformers life due to additional losses, which is due to harmonics. In this paper, a design of transformer core and parameters of hotspot and top oil with and without harmonics and its life expectancy is discussed. In order to calculate accurate losses, initially flux density is calculated by Finite Element Method (FEM) in ANSYS software and next the hotspot and top oil temperature are calculated by a thermal model of transformer using MATLAB software. According to the ambient temperature and variation of daily load cycle, loss life, efficiency and core design is discussed. This model is applied on 400KVA, 20KV, ONAF transformer.
Keywords: transformer, design, flux density, losses, top oil and hotspot, Finite element method

Nomenclature
Tamb Ambient temperature. Ih Harmonic current
IR Rated current
Toil Top oil temperature. H Hot spot factor.
ILoad current. PNLNo load losses PLLLoad losses
PLLRRated load losses
PECEddy current losses.
PECRRated eddy current losses. POSL Stray losses.
PLLHlosses due to harmonics
ToilRatedtop oil temperature rise over ambient temperature.
Current density
Ths Ratedhot spot temperature rise over top oil temperature.
KFactor depends on type of transformer BmMagnetic flux density.
AiCross sectional area of the core
d Diameter of core.
KiFactor that shows steps of core. Q3phase KVA per phase
tchange in temperature KwWindow spacing vector. AwWindow area.
LHeight of window.
DCenter to center distance of the core. WOverall length of yoke.
BWidth of window.
FAA= Aging factor A = yIntercept
B = Slope
T= Hotspot temperature in degrees Kelvin

Introduction
Power transformers are the main components and plays crucial role in the power systems. The efficiency of transformer depends on its losses and the core dimensions. Increase in the transformer power losses and hence temperature rises are the primary concern of the impact of harmonics [1]. If this device is damaged it effects the network. Therefore transformer core should be designed in such a way that losses, weight and temperature should be maintained. Loss is the main factor in increasing the top oil temperature and hot spot temperature that leads to rapid thermal
degradation[2]. Ideally, the best method is to directly measure the winding hot spot temperature through a sensor [3]. However this may not be practical for existing transformers for some reasons. There are several models for predicting the hot spot temperature. In this paper at the first the calculation of core dimensions is given, then verifying the flux density using ANSYS software, with this accurate losses are obtained. Then by analyzing the total loss, the hot spot and top oil temperature at daily load and ambient temperature cycle will be predicted. Finally aging factor, efficiency, thermal life expectancy are mentioned with and without harmonics.

Impact of harmonics
Current harmonics have most significance in power systems. Additional losses will occur due to harmonic current components in the windings and other structural parts. Transformers losses(PT) are divided in to no load losses (PNL) and load losses (PLL). No load losses are due to the voltage excitation of the core and load losses will occur in winding of the transformer and it is expressed as:
proper way. Based upon the given specification, main dimension of the frame can be determined. In order to design of core, we should consider following phases.
Phase 1: calculation of e.m.f. per turn
The output in KVA of a transformer can be simply related to e.m.f. per turn as below
Et =K /
Phase 2: calculation of net cross sectional area
Ai=Et/4.44fBm
Any number of designs can satisfy the above equation. The flux is roughly a measure of the cross section of the iron core, and (NI) gives the cross section of the winding. The problem before a designer is to relate dimensions and the material in such a way so as to obtain the desired output and performance at the lowest cost.
Phase 3: calculation of core diameter d2=Ai/Ki
The value of Ki shows numbers of the steps of core. Phase 4: calculation of main cross section window Each limb wound with both primary and secondary windings of respective phases. i.e.; copper area in each window is :
PLL= I2R + PEC +POSL
AW=
Q3Ã˜ /
3.33 f Bm
KwAi
The total stray losses are determined by subtracting I2R from the load losses measured during the impedance test and there is no test method to distinguish the winding eddy losses from the stray losses that occur in structural parts[4]. Conventionally, the winding eddy current losses generated by the electromagnetic flux are assumed
Phase 5: calculation of overall length of the yoke Aw = L (D d)
bw = D d
W = 2 D + 0.9 d
The height of the window can be assumed varying from 2.0 to 4.0 times the width of the window as
L
to vary with the square of the rms current and the square of the frequency (harmonic order h) as
PEC=PECR= = p(Ih/IR) 2
2.0 m
This method is
Dd
used
4.0
to determine the core
=1
The flux magnitude is proportional to the voltage harmonic and inversely proportional to the harmonic order h. the harmonic distortion of the system voltage usually 5% in power systems[5][6]. Therefore neglecting the effect of voltage harmonics and considering PNL by fundamental components only.

Selection of core design constants
Much of the transformer core design depends upon proper selection of design constants, flux density Bm, current density and window space vector Kw and determining factors Ai, Aw. Therefore, it is worthwhile to select the above parameters in a
dimensions. by using the proposed method The results of calculation are summarized in table I.
Ratio, m
L (cm)
b (cm)
w
W
(cm)
2.7
71.6
26.5
105.9
3.0
75.5
25.1
103.2
3.2
77.99
24.37
96.50
4.0
87.20
21.80
96.5
4.2
89.35
21.27
95.45
4.5
92.42
21.5
94.01
Tabel:1 dimensions of core design
Fig:1 3phase core transformer

Fem analysis in ANSYS software
Calculation of the magnetic flux density using core dimensions and current density as inputs by FEM (finite element method model) in ANSYS software
[9] The two dimensional FEM is used to estimate the transformer losses. Using the local flux density obtained from FEM the hysteresis losses and the eddy current losses due to the axial and radial magnetic flux density is calculated for each disc. The finite element method is to subdivide the region to be studied into small subregions calledfinite elements.
Fig: 3 transformer field solution

Top oil and hot spot temperature thermal model
Equations used for estimating the top oil temperature and hot spot temperature are given in below. Same equation can be used for case with and case without harmonics by varying PLLH in each case as follows.
Top oil temperature(k)
T t PLLH PNL
amb
P P .
P
LLR
NL
LLR
LLR
fl .t . Topoiltemperature(k 1)
PNL
PLLR
P t
NL
Hot spot temperature(k)
P P
Topoiltemperature (k)* t LLH NL
P P .
P
LL R
NL
fl .t LLR . Hotspottemperature(k 1)
PNL
PLLR
P t
NL
Formula for increased load losses without harmonic
Fig: 2 FEM model of transformer
= .
2
Fig:2 show the transformer fem model that is
Formula for increased load losses with harmonics
meshed using ansys software which divides the
= .
2
+ 2
2
+ 0.8
2
transformer's components. The flux density and losses in the windings and core surfaces are shown in below fig:3
Flux density
Flux density
Current core dimensions
Density
Loss factor
Loss factor
Daily load cycle & ambient temperature
then used in determining the transformers temperature and loading capability [11]. The ambient temperature seen by a transformer is the air in contact with its radiators or heat exchangers.
Top oil temperature
Hot spot temperature
Top oil temperature
Hot spot temperature
=
. 2
Aging factor
Aging factor
Fig:4 model for thermal life expectancy of transformer
The thermal equations are modeled using Simulink/Matlab the required input parameters for the models are as shown in Table 2. At each step the top oil temperature equation is solved by inputting the variable daily load data and the ambient temperature with the known parameters. The calculated top oil temperature is the input for the hot spot model as shown equation.
Top oil time constant 160
Top oil time constant 160
Hot spot factor 1.3
Hot spot time constant 6
I2R winding losses 123900
Other stray losses 11000
Other stray losses 11000
No load losses 111
Temperature base for losses 75
Top oil rise over ambient 50.6
Transformer KVA 400
Winding eddy current losses 11400
Cooling mode ONAF
Average oil to average winding 19.7
Rated pu PEC at hot spot location 0.52
Table: 2 transformer model input parameters

Ambient temperature and its influence on loading
Ambient temperature is an important factor in determining the load capability of a transformer since the temperature rises for any load must be added to determine operating temperature. Temperature ratings are based on a 24 hours ambient of 30oC. This is ambient used in guide. Whenever the actual ambient can be measured, such ambients should be averaged over 24h and
Fig:5 ambient temperatures

Method of calculation life expectancy
Assume that the data available for analysis is in the form of a typical daily load cycle showing load variation over a 24 hour period and harmonic distortion for 9 curves which is shown in below Fig. a curve showing the variation of ambient temperature for a period of 24 hours is shown in figure.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 5 10 15 20 25
Time in hours vs. load current (PU)
Fig.6 Daily load cycle with THD 22% .
The Matlab program proceeds through a series of calculations to convert the power transformer characteristics to constants which are used in determining the transformer winding hotspot temperatures For each of the input 2hours of intervals is given to the daily load cycle[12]. Throughout the loading cycle, and translation of the temperature data into corresponding aging data by means of experimentally determined aging curves applicable to the Insulation. These hotspot temperatures are then used by the program to calculate the percent loss of life.
—with harmonic Without harmonic
—with harmonic Without harmonic
Fig:7 top oil temperature
—with harmonic Without harmonic
—with harmonic Without harmonic
10. Transformer efficiency
A transformer loss is effective on Transformer efficiency. As core loss is the part of transformer losses, therefore core dimension can be effective on
the efficiency. The efficiency is obtained as[13]:
=1 + 100
Where S and cos are apparent power and power factor respectively. The below fig 10 shows transformer efficiency.
92.05
92
Efficiency (%)
Efficiency (%)
91.95
91.9
91.85
91.8
Fig:8 hot spot temperature
9. Aging factor
91.75
0 5 10 15 20 25
Time in hours
Fig: 10 transformer efficiency
Aging factors for the transformer were obtained from the curve shown in Fig.9 Aging factor is defined as the rate of aging at any given temperature, relative to the rate of aging at some reference temperature. The aging factor curve . can be described by the familiar Arrhenius
Equation:
11. Life estimation
The equations that relates the hot spot temperature and aging acceleration factors is given as [14].
15000 15000
FAA = 383 +273
0.035
0.03
0.025
Aging factor
Aging factor
0.02
0.015
0.01
0.005
0
log10 F=A+
To estimate insulation heating effect, the loss of life factor is integrated over a given period of time. Where FAA has a value greater than 1 for winding hottestspot temperatures greater than the reference temperature 110o C and less than 1 for temperatures below 110o C.
Since insulation aging is a cumulative effect ,the percent loss of life per day is the summation of the percent loss of life.
Percentage loss of life=
. %
Where . =
315 320 325 330 335 340 345 350 355
Hot spot temperature in deg K
Fig: 9 aging factor
,
=years per quarterhour
0.035
0.03
Percent loss of life
Percent loss of life
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 20 25
Time
fig: 11 loss of life
Conclusion
Non linear loads injects harmonic currents into power system. Transformers subject to this harmonic currents exhibits additional load losses. Using ANSYS software by finite element method 2D approach the accurate losses are estimated. The novel thermal model has been established to calculate the winding hot spot temperature. The top oil temperature calculated from the top oil equation becomes the ambient temperature for hot spot equation model. To correctly estimate a transformer loss of life the real load and ambient temperature variations should be considered. To evaluate life estimation the aging factor is integrated over a given period of time. Insulation aging is cumulative effect so using this percentage loss of life is predicted from MATLAB.
References

working group 1209,analytical determination of transformer windings hotspot factor Electra, no.161, Aug 1995, pp.2933.

IEEE std C571101998, recommended practice for Establishing Transformer Capability when supplying Non sinusoidal Load currents.

G. Swift, T .S .Molinski, Robert Menzies, IEEE trans.power delivery, vol.16, No.2, April 2001 A Fundamental Approach to transformer thermal modeling partII:field verification.

A.Elmoudi, M.Lehtonen, Hasse Nordman
,Conference Record of the 2006 IEEE International Symposium on Electrical Insulation.Effect of Harmonics on Transformer Loss of life.

M. T. Bishop, J. F. Baranowski, D. Heath, S. J. Benna, Evaluating HarmonicInduced Transformer Heating, IEEE Trans. on Power Delivery, vol. 11, no.1, Jan 1996, pp.305311.

A. Girgis, E. Makram, and J. Nims, "Evaluation of Temperature Rise of Distribution Transformers in the Presence of Harmonics and Distortion,"
Electrical Power Systems Research, vol. 20, no. 1, Jan. 1990, pp. 1522.

S.V.Kulkarni, S.A.Khaparde Transformer Engineering Design Practices.

Electromagnetic field analysis guide, ANSYS.

G. Swift, T. S. Moliniski, and W. Lehn, "A Fundamental Approach to Transformer Thermal ModelingPart I: Theory and Equivalent Circuit,"
IEEE Trans. Power Delivery, vol. 16, No.2, Apr. 2001, pp. 171175.

IEEE std C57.911995(R2004)IEEE Guide for loading mineral oilimmersed transformer.

Robert E.Rood A Method for estimating the Thermal Llife Expectancy of Distribution Transformer. approved by the AIEE presented at the IEEE Winter General Meeting.

Sh.Taheri, A.Vahedi, A.Gholami, H.Taheri Estimation of Hotspot Temparature in Distribution Transformer Considering Core design using FEM.

Kshira T.Muthanna, Abhinanda Sarkar, Kaushik Das, and Kurt Waldner, IEEE tans.power delivery,vol.21,NO.1,January 2006.Transformer Insulation Life Assessment.