elk 1403 304 manuscript 1

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Windings temperature prediction in split-winding1

traction transformer2

Davood AZIZIAN*† 3

Department of Electrical Engineering, Abhar Branch, Islamic Azad University, Abhar,4

Iran5

*Corresponding author6

†Email: [email protected]

Phone: +98-912-24183538

9

Abstract:10

Incombustible feature of resin make multi-winding dry-type transformers suitable for11

using in traction systems. Nevertheless, due to resin’s heat transfer property and special12

structure of traction transformers, temperature distribution in traction transformer is13

undesirable and it is essential to study its thermal behavior. In this research paper,14

thermal behavior of traction transformers is modeled using finite difference approach.15

After validating the modeling results (using the experimental results), the temperature16

distribution in cast-resin traction transformer with split windings is calculated. The17

thermal behavior of split-winding traction transformer is compared to the normal two-18

winding cast-resin transformer. Traction transformer usually feeds the electronic19

converters; converter system as a nonlinear load causes the harmonics to appear in the20

windings currents. Thus the thermal behavior of traction transformer has been modeled21

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in presence of the harmonic currents and their effects on temperature distribution have1

been discussed.2

Keywords: Finite difference method (FDM), Split-winding, Thermal modeling,3

Transformer, Traction.4

1. Introduction5

In past years, traction networks and subways have been developed rapidly. The main6

and expensive equipment of a traction network is its transformer. The traction7

transformer that is the aim of this paper is manufactured as seen in the Figure 1 [1] and8

is usually called as split- winding transformer. Transformer in a traction network should9

be protected of explosion; thus it is essential to use transformers with non-flammable10

insulations. The most applicable kind of these transformers that is usually used in11

traction system is the dry-type (cast-resin) transformer [2]. In this transformer low12

voltage windings are impregnated and high voltage windings are casted by resins of13

class F [3].14

Figure 1

Traction transformer has special geometry and its thermal behavior is more important15

and serious in comparison with two-winding transformer that only has concentric16

windings [4-7]. Thus, studding the thermal behavior in dry-type traction transformers is17

essential.18

Some researchers used experimental temperatures to investigate the thermal behavior in19

dry-type transformer [8-11]. Previously, there are some mathematical models for20

analyzing the thermal behavior of the ventilated [12, 13] and the cast-resin [14, 15] dry-21

type transformers with two concentric windings. Also a study on dynamic thermal22

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behavior of the two-winding cast-resin transformer is presented in [16]. Unfortunately,1

no research about thermal modeling of the mentioned traction transformer is presented.2

Hence, using finite difference method (FDM), the thermal performance of this3

transformer is studied in this research. Thermal modeling results have been verified4

with the help of experimental data. Using the validated model, the temperature5

distribution in the split-winding traction transformer has been calculated and the results6

are compared to the normal two-winding transformer.7

In the practice, converters that are connected to the traction transformer’s low voltages8

cause the harmonics to influence the temperature distribution. The effect of voltage’s9

harmonics on the temperature is negligible, but harmonic currents strongly affect the10

windings temperature. Moreover, in this paper, the thermal modeling has been done in11

the presence of harmonic currents and their effects on the temperature have been12

studied.13

Consequently, reading this paper, one can meet new schemes as:14

- Traction transformer with four split windings (two pairs) that are manufactured15

on each other is studied in this paper. This transformer has special structure and16

its thermal behavior is more important.17

- Finite difference approach applied to temperature calculation of traction (split-18

winding) transformer19

- Temperature distribution analysis of traction (split-winding) transformer and20

comparing the temperatures with the normal two-winding transformer.21

- Analyzing the effects of harmonics on temperature distribution of traction (split-22

winding) transformer23

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2. Thermal modeling using finite difference method (FDM)1

Figure 2 shows geometry of the cast-resin dry-type traction transformer. Here, LV and2

HV symbolize the low and high voltage windings respectively. According to the3

symmetry, heat transfer of the transformer has been taken into a two dimensional (2D)4

coordinates.5

Figure 2

Finite difference method (FDM) is a numerical approach based on mathematical6

discretization of partial differential equations. Using FDM, continuous problems are7

studied in a finite number of small time intervals. So in the small intervals, it is possible8

to approximate a problem by approximate expressions. As it has been shown in [14],9

FDM is an efficient, accurate and easy implemented method for thermal modeling of10

cast-resin dry-type transformer.11

As shown in Figure 3, in the FDM, windings are to separate into small units that each is12

represented through a node (each node is connected to the others through thermal13

resistances) [14]. Finite difference technique and extracting nodal equations are based14

on the rule of energy conversion: “heat generated in the unit is equivalent to heat15

transferred to other units". The heat flow among a pair of nodes might be explained as16

“temperature difference / thermal resistance among nodes”.17

Figure 3

By applying the energy conversion law to the node presented in Figure 3, (1) can be18

resulted:19

m,ntopn

m,nm,n

n-bottom

m,n-m,n

out m

,nmm,n

m-in

,nm-m,nQ

R

)T (T

R

)T (T

R

)T (T

R

)T (T

1111 (1)

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wherein Rm-in, Rm-out , Rn-bottom, and Rn-top are the thermal resistances connecting the node1

(m,n) and neighboring nodes and Qm,n is the generated heat or losses in the unit.2

Thermal resistances and losses are explained in the next subsections. In the units belong3

to the air (outer surface, the walls of axial and radial air channels and the bottom and top4

surfaces), temperature must replaced by the ambient temperature.5

By applying (1) to all nodes in the windings, matrix form of the nodal heat transfer6

equations can be derived. Heat transfer equations depend on temperature [14]; so an7

iterative process had been used to solve them and windings temperatures had been8

calculated.9

2.1. Heat transfer in solid parts (windings)10

According to the firm structure of windings, heat transfer method is the conduction [17,11

18]. Thermal resistance related to conduction between two nodes can be described as12

(2).13

c

wcw

L

A k R (2)

wherein, A is the heat transfer cross-section (2π×mean radius of the related nodes), LC is14

length of the heat flow path (distance between the related nodes) and k w is the winding’s15

thermal conductivity across the heat flow.16

17

2.2. Heat transfer in outer surfaces18

Outer surfaces of the split-winding cast-resin transformer might be assumed like vertical19

plates [14]. Heat transfer in these surfaces can be considered as natural convection and20

radiation:21

Natural Convection: In order to avoid difficulty of convection equations [17, 18], here22

some simple experimental equations are used. By assuming the outer surfaces as same23

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as infinite walls, the natural convection in these surfaces can be expressed as following1

[14]:2

)T A(T h(z)q air scoco (3)

Ah R

coco

1 (4)

Z

k Nu(z)h air z

co (5)

wherein, qco is the heat transferred by convection in the outer surface, hco is the3

convection coefficient in the outer surface, Rco is the thermal resistance due to the4

convection, Z is the vertical distance, and5

5

12

Pr 4536

Pr 4

*

z Gr

Nu (6)

2

4

νk

Z q g βGr

air

co* (7)

where, Gr * is the Grashoff number, Pr is the Prandtl number, Nu z is the Nusselt number,6

and g is acceleration of the gravity. k air , ν and β are the thermal conductivity, the7

kinematical viscosity and the volumetric expansion of the air and they depend on8

temperature [14].9

From the equations (4) and (5), it is seen that the thermal resistivity between the outer10

surfaces and the ambient temperature increases with an increase in height. This will11

cause a considerable increase in temperature of the top windings in comparison with the12

bottom windings.13

Radiation: Radiation in outer surfaces of the split-winding dry-type transformer can be14

expressed as following [17, 18]:15

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)T A(T h )T εσA(T (z)q air sroair sro 44 (8)

)T T T T T σ εA(T Ah

R

air air sair s sro

ro

3223

11

(9)

where, qro is the radiation heat transferred in the outer surface, hro is the radiation1

coefficient in the outer surface, Rro is the thermal resistance due to radiation in the outer2

surface, ε is the emissivity coefficient, T s is the surface temperature, T air is the ambient3

temperature and σ is the coefficient of Stephen Bultzman.4

2.3. Heat transfer in air channels between windings5

Air channels in the split-winding dry-type transformer can be assumed as vertical6

channels [14]. Heat transfer in these surfaces might be considered as radiation,7

conduction and natural convection. It has been shown in [14] that the radiation in the air8

channels has negligible effect on heat transfer and so it has been neglected in this9

research. Conduction and natural convection in vertical ducts of the traction (split-10

winding) transformer are explained in the following.11

Conduction: Most of the conduction in the air channel may occur between the walls12

(radial direction) and conduction in axial direction may be neglected. Consequently,13

conduction’s thermal resistance in the air channel can be described as (10).14

(10)

b

A k R a

ca

where, k a is the thermal conductivity of the air.15

Natural Convection: Similarly, in order to avoid difficulty of the theoretical equations,16

some simple equations have been used for natural convection. The natural convection in17

air channels is similar to channels with infinite walls and its relations can be described18

as following [14]:19

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)T A(T hq air scd cd (11)

Ah

R

cd

cd 1

(12)

b

k Nu(z)h air z

cd (13)

601 3

1

6

1

1 Z Z Z ψ for ,ψ RC Nu (14)

602

1

70

9

1

2411

1

2

1

2

Z

Z

Z ψ , for Rψ RC Nu (15)

2

1

Pr

Pr

*

*

Z

Gr L

b

Gr Z

b

Φ (16)

2

4

k ν

bq g βGr * (17)

wherein, qcd is the convection heat transferred from the walls (inner or outer), Rcd is the1

thermal resistance due to the convection in the duct , q" is the average heat flux of the2

walls, R is the ratio of heat flux in other wall of duct / heat flux in considered wall, hcd is3

convection coefficient of the wall, b is width of the duct, L is the total height of the duct.4

In these equations C 1 and C 2 are constant coefficients that are related to the duct’s5

width.6

Similarly, thermal resistivity of the walls increases in proportion with the height that7

this causes a higher temperature to be appeared in the top windings.8

9

10

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2.4. Heat transfer in bottom and top surfaces1

Heat transfer in bottom and top surfaces is unknown and is a combination of radiation2

and natural convection. Total heat transfer in these surfaces can be described as (18) and3

(19).4

)T A(T hq air st,bt,b (18)

Ah R

t,bt,b

1 (19)

where, ht,b is the equivalent heat transfer coefficient, Rt,b is the equivalent thermal5

resistance, and qt,b is the heat transferred to the air from bottom and top surfaces.6

It had been shown that heat transfer from the bottom and top surfaces can be neglected7

without any considerable effect on thermal modeling [14].8

9

2.5. Heat transfer in distance between bottom and top windings10

Heat transfer in this part is a combination of conduction, radiation and convection; as11

same as bottom and top surfaces, its behavior is not known completely. Heat transfer12

from channel between bottom and top windings depends on many parameters and13

similar to the bottom and top surfaces it can be neglected.14

The only problem may be amount of air that enters the ducts from this distance and15

deforms the normal heat transfer mechanism in the air channels. Neglecting the air16

enters from this distance can cause the temperatures to be calculated slightly higher than17

the actual amounts. Additionally, the distance between the bottom and top windings18

usually designs very small and sometimes it may be removed because of mechanical19

reasons. 20

21

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2.6. Heat generation (losses) in the windings1

Windings in split-winding dry-type transformer are usually constructed of foil2

conductors; it is convenient to consider the conductor’s cross section as Figure 4 (w'×h'3

and w×h are the dimensions of the conductor with and without insulation).4

Figure 4

For this unit, losses might be written as (20).5

dceddytotal ) P K ( P 1 (20)

where, K eddy and P dc are given in [19 and 20] and they vary with the temperature. K eddy 6

is calculated upon the magnetic field and its accuracy depends on the electromagnetic7

modeling method. In this research an analytic method [4] is used for magnetic field8

calculations. If a higher accuracy is needed, the semi-analytic calculation that had been9

introduced in [4] can be used for this purpose. Nodes are chosen in the insulations; thus10

each node contains

part of conductors (and conductors’ losses) adjacent to insulation11

(Figure 5).12

Figure 5

Note that the mentioned split-winding traction transformer can be considered as two13

pair of windings that are constructed on each other (axially). Each of these pair14

windings acts as a two-winding cast-resin transformer. Therefore it is helpful to analyze15

the temperature distribution of a normal two-winding cast-resin transformer (with16

concentric windings) and compare its results to a split-winding traction transformer.17

18

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3. Thermal analysis of two-winding dry-type transformer with1

concentric windings2

To verify the introduced model, a typical two-winding transformer (800kVA [14]) is3

chosen and the measured temperatures are compared to the modeling results on the4

outer surface of the HV winding (Figure 6). Note that the temperature rise test carried5

out in accordance with the simulated loading method as defined by the IEC 60076-116

standard [3 and 14] and the outer surface temperatures had been measured using the7

infrared gun [14].8

Figure 6

Table 1, shows the computed average and hottest spot temperatures and compares them9

with the experimental results. Similarly, the temperature rise test carried out in10

accordance with the simulated loading method as defined by the IEC 60076-11 and11

average temperature rises of the windings had been measured by gathering the hot and12

cold resistances of the windings [3 and 14]. The average temperature rises (AV) in this13

table are the average of the temperature rises in each winding and the hottest spot14

temperature rises (HS) are the maximum temperature rises occur in the windings. LV15

and HV in this table, denote the low and high voltage windings (Figure 1).16

Table 1

From Figure 6 and Table 1, it is seen that the FDM has good accuracy in predicting the17

temperature distribution of the cast-resin transformer (average temperature prediction18

error is lower than 3%). Additionally, the differences between modeling results and the19

experiments may be caused because of some experimental and modeling insufficiencies20

[14]. Consequently, the presented mathematical model (based on the FDM) can be21

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employed to analyze the thermal behavior of the cast-resin transformer with different1

structures (such as the mentioned split-winding traction transformer).2

Consequently, Figure 7 shows the temperature distribution of the windings in the3

mentioned two-winding dry-type transformer.4

Figure 7

4. Thermal analysis of dry-type (cast-resin) traction5

transformer with four split windings6

After reviewing the thermal behavior of the normal two-winding transformer, in this7

section temperature distribution of the split-winding dry-type traction transformer has8

been analyzed. The traction (split-winding) transformer is usually consists of two split9

transformers that are positioned on a same core leg. In fact, usually the bottom and top10

transformers are not the same. But to obtain a clear and obvious conclusion, the top and11

the bottom windings are assumed to be as same as 800kVA transformer in the section 312

(this will not cause a problem in studying the traction transformer’s behavior). Applying13

the nominal currents to the windings, temperature rises had been calculated and the14

results are given in table 2.15

Table 2

Consequently, temperature distribution in the bottom and the top windings are shown in16

Figure 8.17

Figure 8

It is clear that the top windings are considerably hotter than a similar two-winding18

transformer (section 3). Unlike this, the bottom windings are cooler than when they are19

used as a normal two-winding transformer. These behaviors must be taken into account20

by designers of traction transformers.21

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Someone may ask that why the bottom windings are cooler than when they are1

manufactured as a normal two-winding transformer? This can be correlated to2

characteristics of the air channels in (17) where the heat transfer is proportional to3

height of the air channel (L). It is obvious that when two windings are manufactured4

axially on each other, height of the ducts will be twice and thus heat transfer is5

increased in the bottom windings. In the top windings the local height of the nodes (Z)6

are increased more than the duct’s height (L) and so the heat transfer will be decreased.7

The difference between temperatures of the split-winding and the normal transformer8

(or difference between temperatures of the bottom and top windings in the split-winding9

transformer) is higher in the low voltage windings (especially in outer layers of the low10

voltage windings). Consequently, hottest spot (HS) temperature is more dangerous in11

top low voltage winding; in this winding HS/AV is about 1.36 where it is considerable12

in comparison with 1.26 in the normal two-winding transformer. A suitable and possible13

proposal is to decreasing the height of the split-winding transformer. It can be shown14

that decreasing the height of transformer can modify this phenomenon and will truly15

reduce the average (AV) and hottest spot (HS) temperatures of the top windings.16

5. Harmonics in the traction transformer and their effects on17

the temperature distribution18

Basically the transformer is designed to work with the 50 Hz frequency. However the19

loads in a traction system are usually nonlinear. Nonlinear loads cause high level of20

voltage and current harmonics. The most important effect of harmonics in the21

transformer is their influence on the temperature distribution of the windings. Voltage’s22

harmonics just influence the no-load losses that this easily can be neglected [21]. In this23

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section, only the effects of current harmonics on the temperature distribution of the1

windings have been analyzed.2

The traction (split-winding) transformer usually feeds a 12-pulse converter; this3

converter is a major source of harmonics. If we assume the current as I L=Ʃ I h cos(hωt ),4

harmonics ( I h) related to a traction transformer that feeds a 12-pulse rectifier can be5

calculated as (21) [22-24]. These harmonics are shown in Figure 9.6

2.11 5

1

hh I

I h

(21)

where,7

,...2,1,0and, pulse)(1212,12

k P k P

h (22)

8

Figure 9

Harmonic currents cause additional losses in windings; harmonics have major effects on9

the eddy losses. The harmonics may increase the ohmic losses because of increasing the10

current’s rms. Stray losses are negligible in dry-type transformers and here they are11

assumed to be zero. For a harmonic current, ohmic and eddy current losses can be12

expressed as (21) and (22) [22-24].13

2

1 00

n

h

hdcdc

I

I P P (23)

22

1 00 h

I

I P P

n

h

heddyeddy

(24)

wherein, P dc0 and P eddy0 are the ohmic and eddy current losses where there is no14

harmonic. Combining (23) and (24), total losses due to the harmonic currents can be15

expressed as (25).16

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n

heddy

hdctotal h K

I

I P P

1

22

00 1

(25)

Using (25) and applying it to the introduced thermal model, the windings temperatures1

of the traction transformer have been calculated as table 3 and Figure 10.2

Table 3

Figure 10

Rises in the temperatures due to the harmonic currents can’t be neglected in the traction3

transformer. In some cases temperature may reaches up to 127% of the temperature4

without harmonic consideration. The ratio of hottest spot to average temperatures5

(HS/AV) is invariant against linear and nonlinear loads and just depends on the6

transformer’s structure.7

6. Conclusion8

In this paper, cast-resin traction transformer with split windings was modeled in order to9

analyze the thermal behavior of windings. The model is validated using a typical10

800kVA cast-resin transformer. The validated thermal model has been used to calculate11

the temperature distribution of a normal transformer with two concentric windings.12

Afterwards, the thermal behavior of the traction transformer with four split windings13

was modeled and the temperatures were compared to a normal two-winding14

transformer.15

Reviewing the thermal behavior of the split-winding traction transformer, it has been16

seen that the top windings are considerably hotter than the bottom windings (and hotter17

than the same two-winding transformer). Unlike this, windings in the bottom are cooler18

than a same two-winding transformer. This problem is serious in outer layers of the low19

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voltage windings. Additionally, the hottest spot temperatures of the top low voltage1

windings are more dangerous than other parts. From the viewpoint of a designer, this2

phenomenon must be taken into account in temperature calculations of a split-winding3

traction transformer. A way for modifying this behavior in the traction transformer is to4

decreasing the height of windings in comparison with their radius.5

Finally, the effects of the current’s harmonics on the load losses and temperature6

distribution were discussed. An increase in the temperature due to the harmonics can’t7

be neglected in the design process of the traction transformer.8

References9

[1] Azizian D, Vakilian M, Faiz J, Bigdeli M. Calculating leakage inductances of

split-windings in dry-type traction transformers. ECTI Trans Elec Eng- Electr and

Com 2012; 10: 99 – 106.

[2] Nunn T. A comparison of liquid-filled and dry-type transformer technologies. In:

2000 IEEE-IAS/PCA Cement Industry Technical Conference; 7-12 May 2000;

Salt Lake City, UT.

[3] IEC 60076-11. Dry Type Power Transformers. 1st ed. Geneva, Switzerland: IEC,

2004.

[4] Azizian D, Vakilian M, Faiz J. A new multi-winding traction transformer

equivalent circuit for short-circuit performance analysis. Int Trans Elec Energy

Sys 2014; 24: 186 – 202.

[5] Azizian D. Design Schemes in Traction Transformers (in Persian). Tehran, Iran:

Iran Transformer Research Institute, 2007.

[6] Chase DD, Grain AN. Split winding transformers. Trans American Inst Elec Eng

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1934; 53: 914-922.

[7] IEC 60310. Railway Applications –Traction Transformers and Inductors on

Board Rolling Stock. 3rd ed. Geneva, Switzerland: IEC, 2004.

[8] Dianchun Z, Jiaxiang Y, Zhenghua W. Thermal field and hottest spot of the

ventilated dry-type transformer. In: IEEE Proceedings of the 6th International

Conference on Properties and Applications of Dielectric Materials; 21-26 June

2000; Xi’an, China.

[9] Pierce LW. Thermal consideration in specifying dry-type transformers', IEEE

Trans Indus App 1994; 30: 1090-1098.

[10] Cho HG, Lee UY, Kim SS, Park YD. The temperature distribution and thermal

Stress analysis of pole cast resin transformer for power distribution. In: IEEE

Conference International Symposium on Electrical Insulation; 7-10 April 2002;

Boston USA.

[11] Pierce LW. An investigation of the temperature distribution in cast-resin

transformer windings. IEEE Trans Power Del 1992; 7: 920-926.

[12] Pierce LW. Predicting hottest spot temperatures in ventilated dry type transformer

windings. IEEE Tran Power Del 1994; 9: 1160-1172.

[13] Lee M, Abdullah HA, Jofriet JC, Patel D, Fahrioglu M. Air temperature effect on

thermal models for ventilated dry-type transformers. J Elec Power Sys Res 2011;

81: 783-789.

[14] Rahimpor E, Azizian D. Analysis of temperature distribution in cast-resin dry-

type transformers. J Elec Eng 2007; 89: 301-309.

[15] Eslamian M, Vahidi B, Eslamian A. Thermal analysis of cast-resin dry-type

transformers. J Energy Conv and Manag 2011; 52: 2479-2488.

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[16] Azizian D, Bigdeli M, Fotuhi-Firuzabad M. A dynamic thermal based reliability

model of cast-resin dry-type transformers. In: International Conference on Power

System Technology; 24-28 October 2010; Hangzhou, China

[17] Holman JP. Heat Transfer. 10th ed. New York, USA: McGraw-Hill Inc., 2009.

[18] Incropera FP, Dewitt DP. Introduction to Heat Transfer. 7th ed. New York, USA:

John Wiley & Sons, 2011.

[19] Dietrich W. Berechnung der wirbelstromverluste in den wicklungen von

mehrwicklungstransformatoren. J ETZ-Archiv 1998; 10: 309-317.

[20] Rahimpour E. Hochfrequente modellierung von trnsformatoren zur berechnung

der übertragungsfunktionen. PhD, University of Stuttgrat, Stuttgrat, Germany,

2003.

[21] Elmoudi AA. Evaluation of power system harmonic effects on transformers.

PhD, Helsinki University, Helsinki, Finland, 2006.

[22] Elmoudi AA. Evaluation of power system harmonic effects on transformers: hot

spot calculation and loss of life estimation. In: 5th International Multi-

Conference on Systems, Signals and Devices, IEEE - SSD; 20-22 July 2008;

Amman, Jordan.

[23] Zeraatparvar A, Sami T, Raheli FA. Evaluation of performance of distribution

transformers supplying non linear loads currents: Effect of oversizing. In:

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EEIC; 8-11 May 2011; Rome, Italy.

[24] IEC Std. 61378-1. Converter Transformers - Part 1: Transformers for Industrial

Applications. 2nd ed. Geneva, Switzerland: IEC, 2011.

1

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Figures1

Hf

C o r e

EsBs

L V 1

( 1 )

L V 2 ( 3 )

H V

H V 2 ( 4 )

H V 1 ( 2 )

LV 1: Bottom low voltage winding (winding 1)

LV 2: Top low voltage winding (winding 3)

HV 1: Bottom High voltage winding (winding 2)

HV 2: Top high voltage winding (winding 4)

H f : Height of the core leg

E s: Length of the core yoke

B s: Diameter of the core leg / yoke

Figure 1: Schematic view of split windings in a traction transformer

2

(a) (b)

Figure 2: Split-winding cast-resin transformer, a) three-phase, and b) single-phase view

3

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Δz

Δr

out-mR

R n-bottom

top-nR

m+1,n

,n+1m

m,n-1

m,n

m-1,nin-mR

Figure 3: A unit of FDM and its related node [13]

Figure 4: Foil conductor’s cross-section

1

Figure 5: Node losses (includes the adjacent conductors)

2

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º

200 400 600 80060

70

80

90

100

110

120

Vertical Distances (mm)

T e m p e r a t

u r e ( C )

Measured

Calculated

Figure 6: Temperature of the outer surface in a typical 800kVA transformer

1

Figure 7: The windings temperature distribution in 800kVA transformer

2

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Figure 8: Temperature distribution of the bottom and top windings in a typical 1600kVA split-

winding transformer

1

Figure 9: Magnitude of current harmonics proportional to fundamental component in a the

traction transformer

23456

7

0%

20%

40%

60%

80%

100%

I1 I5 I7 I11 I13 I17 I19 I23 I25

Harmonic's magnitude 100% 23% 12% 7.50 5.50 4% 3% 2% 2%

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(a)

(b) Figure 10: Temperature distribution in the outer surface of a) the low voltage and b) the high

voltage windings

1

2

3

4

5

7/23/2019 ELK 1403 304 Manuscript 1

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Tables1

Table 1: Temperature rises in the typical 800kVA transformer

HS/AV

HS: Hottest spot

temperature rise (ºC)

AV: Average

temperature rise (ºC)

HVLVHVLVHVLV

1.291.26118.1109.3695.886.88Modeling

Not Applicable Not Applicable9385Experience

2

Table 2: Average and hottest spot temperature rises in a typical 1600kVA split-winding traction

transformer

HS/AVHS (ºC)AV (ºC)

HVLVHVLVHVLV

1.291.23114.795.9288.7377.83Bottom windings

1.181.36122.37150.91103.46110.57Top windings

1.29

1.26118.01109.3691.886.88

Two-winding transformer (table 1)

3

Table 3: Temperature rises of the split-winding traction transformer due to the harmonics

HS/AVHS (ºC)AV (ºC)

HVLVHVLVHVLV

1.291.23114.795.9288.7377.83Bottom windings

Without harmonics

1.181.36122.37150.91103.46110.57Top windings

1.291.23123.710795.687Bottom windings

With harmonics

1.181.36135.5190115140Top windings

4

elk 1403 304 manuscript 1

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