Determining Thermal Life Expectancy Of Power Transformer Under Non Linear Loads Using FEM By ANSYS And MATLAB

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

1. Nomenclature

   Tamb Ambient temperature. Ih- Harmonic current

   IR- Rated current

   Toil -Top oil temperature. H -Hot spot factor.

   I-Load current. PNL-No load losses PLL-Load losses

   PLL-R-Rated load losses

   PEC-Eddy current losses.

   PEC-R-Rated eddy current losses. POSL- Stray losses.

   PLL-H-losses due to harmonics

   Toil-Rated-top oil temperature rise over ambient temperature.

   -Current density

   Ths- Rated-hot spot temperature rise over top oil temperature.

   K-Factor depends on type of transformer Bm-Magnetic flux density.

   Ai-Cross sectional area of the core

   d -Diameter of core.

   Ki-Factor that shows steps of core. Q3-phase -KVA per phase

   t-change in temperature Kw-Window spacing vector. Aw-Window area.

   L-Height of window.

   D-Center to center distance of the core. W-Overall length of yoke.

   B-Width of window.

   FAA= Aging factor A = y-Intercept

   B = Slope

   T= Hot-spot temperature in degrees Kelvin

2. 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.

3. 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=

   Q3Ø /

   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=PEC-R= = p(Ih/IR) 2

   2.0 m

   This method is

   D-d

   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.

4. 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 3-phase core transformer

5. 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 sub-regions called

   finite elements.

   Fig: 3 transformer field solution

6. 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 PLL-H in each case as follows.

   Top oil temperature(k)

   T t PLL-H PNL

   amb

   P P .

   P

   LL-R

   NL

   LL-R

   LL-R

   fl .t . Topoiltemperature(k -1)

   PNL

   PLL-R

   P t

   NL

   Hot spot temperature(k)

   P P

   Topoiltemperature (k)* t LL-H NL

   P P .

   P

   LL -R

   NL

   fl .t LL-R . Hotspottemperature(k -1)

   PNL

   PLL-R

   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

7. 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

8. 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 hot-spot temperatures For each of the input 2-hours 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 hot-spot temperatures are then used by the program to calculate the per-cent 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 hottest-spot 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 quarter-hour

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

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