Determination of OD cooling system parameters based on thermal modeling of power transformer winding

8/12/2019 Determination of OD cooling system parameters based on thermal modeling of power transformer winding

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Determination of OD cooling system parameters based on thermalmodeling of power transformer winding

R. Hosseini a , M. Nourolahi a , G.B. Gharehpetian b, *

a Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iranb Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran

a r t i c l e i n f o

Article history:Received 8 November 2005Received in revised form 23 January 2008Accepted 25 February 2008Available online 10 March 2008

Keywords:Thermal modelingPower transformerOil directed cooling system

a b s t r a c t

Power transformers are the main and one of the most expensive parts of electrical net-works. Optimum design of power transformers and their cooling system requires the pre-cise calculation of losses, hot spot temperature and position. In this paper, thermalbehavior of winding in power transformers and its insulation system have been modeledand parameters affecting the transformer cooling have been determined. This study isbased on the thermal modeling of disk winding. Using software programs, several coolingschemes have been simulated and the results show the effect of different geometricalparameters on cooling of the transformer winding. The exact position of hot spot andthe heat loss of a model transformer has been obtained and compared with the results pro-vided by the manufacturer. It is shown that inclusion of eddy current losses improves theprediction of the hot spot position, while ignoring this loss could lead to inaccurate predic-tion of the hot spot position and temperature.

2008 Elsevier B.V. All rights reserved.

1. Introduction

The importance of power transformers in transmission and distribution systems deserves a specic attention, sinceincreasing the output power, reducing the size, optimum design and manufacturing with longer lifetime of transformerstranslates into higher availability and reliability of power systems with lesser expenses. It is known that transformers arethe main part of each substation. As a result, maintenance and optimum utilization of transformers should be correctlyand seriously observed from both technical and economical points of view. Overloading the power transformer increasesthe heat produced inside the transformer, while the lifetime of a power transformer is very much dependent upon the con-dition of its winding insulations and the quality of the transformer oil. The deterioration of the winding insulation and trans-formers oil are all directly related to theworking temperature of the transformer [1] . The transformer lossesare converted to

heat in the windings, core and tank. Even when the transformer does not have any load, no-load losses exist inside the core.Large power transformers with disk windings are generally cooled by pumping oil inside the oil channels. Oil is entered

from the bottom of the windings and exits from the upper part. The exact position and temperature of hot spot is an impor-tant parameter for the design, manufacturing and utilization processes. The effective lifetime of the winding insulation (andthe transformer) can be determined using hot spot temperature [2] . Different equipments and methods are used for mea-suring the temperature of transformers oil at different positions. With these measurements, it has been possible to approx-imately estimate the hot spot temperature.

Since transformers are electrical equipments, they are mostly being considered from electrical points of view. However,reports by mechanical engineers show the effect of heat transfer or other thermal uids on performance. In [3] , Godec and

1569-190X/$ - see front matter 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.simpat.2008.02.013

* Corresponding author. Tel.: +98 21 6646 6009; fax: +98 21 6640 6469.E-mail address: [email protected] (G.B. Gharehpetian).

Simulation Modelling Practice and Theory 16 (2008) 585596

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Simulation Modelling Practice and Theory

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Sarunac reported improvement of performance of a 40 MVA transformer by installation of a pump between shell and radi-ators bank of the cooling system. Transformers with ONAN (oil natural and air natural) cooling systemarea quiet system andhave more reliability, because they are not dependent on mechanical systems such as fans and pumps. On the other hand,transformers with ONAF (oil natural and air forced) cooling system have better efciency and performance, but they producenoise due to the use of fans for cooling of radiators. Radiators may be installed in a distance from transformers, but thiswould increase the pressure drop and consequently decrease the thermo-siphon effect. This in turn causes increase in thetemperature difference between the top and the bottom of the radiators. If a pump is added between the transformerand the radiators in ONAN/ONAF cooling systems, the power of the transformer would increase. When a pump is installedin an ONAF system, the cooling capacity of the radiators is determined by the differences between the oil temperature at thetop of the transformer and the ambient temperature. If the cooling capacity is determined by the temperature differencesbetween winding and ambient, it would not be possible to increase the power of the transformer by increasing the owvelocity inside the radiators; therefore the use of a pump would not be necessary. That is because with equal losses in atransformer under OFAF (oil forced and air forced) cooling systems, the average temperature difference between oil andambient temperature in radiators would remain constant, while the temperature difference between the oil at the top

Nomenclature

Bm leakage maximum density (V s m 2)bc conductor wide (m)C P specic heat of oil (J/kg K)Dout diameter of outer winding (m)Din diameter of inside winding (m)dv thickness of vertical channel (m)ds height of horizontal channels (m)dc conductor height (m)dp insulator thickness paper (m) g acceleration (m/s 2)I current density (A)k oil thermal conductivity (W/m K)kc winding thermal Conductivity (W/m K)kp thermal conductivity of insulator paper (W/m K)L horizontal length channel (m)Ld length of conductor in direction of leakage density (m)l length of conductor in one disk (m)_m mass ow rate (kg/s)

n1

number of spacersn2 number of barsP pressure (Pa)Pr Prandtl numberQ c ohmic lossesQ e eddy current lossesq00 wall heat ux (W/m 2)R conductor electrical resistance ( X )R0 conductor electrical resistance at T 0 (X )Re Reynolds numberT temperature ( C)T air ambient temperature ( C)t 0 electrical resistance base temperature (=20 C)T ave average temperature rise for oil, oil to air ( C)

T max maximum temperature rise for oil, oil to air ( C)T ave average temperature rise for winding, winding to air ( C)T max maximum temperature rise for winding, winding to air ( C)W s width of spacers (m)W t width of bars (m) Z loss ratio (%)a thermal coefcient of electrical resistance (1/K)u conductor density (kg m 3)q density (kg m 3)l viscosity (kg/m s)c frequency (Hz)r electrical conductivity ( X 1 m 1)

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and the bottom of the radiators would decrease. If the temperature difference between oil at the bottom of the radiator andambient is higher, then average the temperature difference of winding and ambient would increase [4] .

If a transformer is designed for an ONAF system, then average temperature differences between winding and ambient isabout 10 C less than the allowed value in standards; installation of an oil pump would increase the capacity of the trans-former between 20% and 30%.

In [5] , Pivrnec et al. with hydrodynamic knowledge and experimental measurements of performance in power transform-ers, a method for obtaining the mass ow rate of oil in oil channels in an OD (oil directed) cooling systemhas been suggested.Calculation of ow velocity of oil inside the channels would facilitate the determination of heat transfer parameters in suchsystems. In oil cooling system, circulation of oil would be by thermo-siphon or pump. In both cases oil would enter the bot-tom of the transformer and ow inside the winding upward. In OD cooling systems, circulation speed would be ten timesfaster than the other methods. Flow velocity would also depend on hydraulic losses. Pivrnec et al. experiments have beendone on two kinds of disk type winding, one with and the other without oil directed pieces [5] . In [6] , Oliver has investigatedthe OD cooling system and suggested a mathematical model for this system with solving the simplied form of governingequations for a 250 MVA transformer. One important factor neglected by Oliver is the eddy current losses in windings. Eddycurrents exist both in radial and longitudinal axes of the winding and they are not constant along the length of the winding.However, in standard calculations their average quantities are counted. The results of [6] show that velocities of oil inside thehorizontal channels near the directed pieces are highest and inside the middle channels in each section are the lowest. More-over the temperatures of disks near the directedpieces are lower and increases for middle disks. According to Olivers results,the hot spot of the winding would be at the middle of the uppermost section.

In this paper, a two-dimensional oil ow around the disk winding of a transformer has been modeled. Ohmic and eddycurrent losses and their dependencies on temperature have been determined and the velocity of the oil inside the oil chan-nels as well as the pressure drop and temperature gradients for oil and winding insulations have been calculated. Based onthis model and considering the above mentioned parameters, the position and temperature of the hot spot have been cal-culated. Furthermore, the effect of number of disks in each section of winding, thickness of horizontal and vertical channels,width of spacers on temperature distribution of winding and the position and temperature of the hot spot have also beenconsidered.

The temperature of each point on winding is proportional to the velocity of oil near that point. The ultimate situation onthe cooling point of view is to obtain a complete deviation of the ow through the horizontal channels. To create such a sit-uation, a step by step increase of the heat dissipation rate in the stream wise direction might apply [7] .

2. Generation of heat in disk winding

Every material shows some resistance when electrical current passes through it. Depending on the resistance and current

density heat is generated. This resistance is the main cause of the heat generated inside the transformers. Beside these lossesin winding conductors (known as copper or load losses), there are other losses including losses in the core, tank and otheriron parts. These losses are due to changes in the magnetic eld.

2.1. Load losses

The sum of ohmic and eddy current losses are called load losses. These losses are not uniform across different windingdisks. Difference of leakage uxes in winding length, oil temperature differences around each disk as well as the temperaturedifference of the conductors, are the main reasons of this phenomenon [2] . Heat transfer in the surface of the disks in contactwith spacers would be by conduction, which creates a small temperature gradient in winding.

2.1.1. Ohmic lossesElectric current in conductors ( I ) generate losses known as ohmic losses according to the following equation:

Q c XRI 2 1

It is well-known that the electrical resistance ( R) is a function of temperature in the form of

R R0 1 aT T 0 2

Also to include the variationof resistance due to temperature rise, i.e. ( T T 0), it is possible to use the following experimentalrelation [2] :

R 235 T 235 T 0

R0 3

2.1.2. Eddy current lossesEddy current losses created because of leakage uxes pass in the winding conductors. Since different amounts of leakage

ux exist at different parts of the winding, these losses are not the same in all parts of the winding. It must be noted that

R. Hosseini et al. / Simulation Modelling Practice and Theory 16 (2008) 585596 587


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these losses ( Q e) are inversely proportional to temperature and increase with a decrease in temperature and can be pre-sented as follows [2] :

Q e C rc 2 u 1 B2m L

2d 4

In this relation C is proportionality constant, r electrical conductivity, c frequency, u conductor density, Bm leakage maxi-mum density and Ld is the length of conductor in direction of the leakage density. The denition of parameters in this equa-tion is given in [2] in detail.

2.2. Oil temperature changes

Oil entering from bottom of the winding, absorbs heat from the winding and gets warmer and at the top would be muchwarmer than the temperature at entrance. Temperature gradients between oil and winding disks would be less and less withan increase in height and therefore less heat being removed at the top part. Consequently the temperature of disks in theupper part of winding increases. Increasing temperature causes higher electrical resistance of disks and the result increasesthe ohmic losses.

According to the above descriptions, total losses in disks can be written as

Q t Q c Q e 5

For calculation of Q t , we use the ohmic and eddy current relative losses as

Z Q e

Q c100 6

Combining Eqs. (5) and (6) one obtains

Q t Q c 1 Z 100 RI 2 1 Z 100 7

Regarding Eq. (3) for temperature dependency of electrical resistance and dening s 235 T 235 T 0 consequently

Q t RI 2 s R0 I 2

Z 100 s

8

3. Winding model

In large power transformers the cooling of the winding is based on the oil ow inside the oil channels. One of these cool-ing methods is called oil directed (OD) method with the following specications and advantages:

(i) Increasing the effective heat transfer area.(ii) Simplicity of winding production process and reduction of production time for both insulation and winding assembly.

(iii) Increase of mechanical stability against short circuit forces.(iv) Reducing temperature rise of winding.

Oil entering frombottom of the winding absorbs heat during its pass through oil channels and exits fromthe winding top.Hot oil exited from the top of the winding then goes to a heat exchanger (radiator) to dissipate its heat to a cooling medium.Considering this well-known circulation, it is expected for the oil and the winding to be always warmer at the top but prac-tically this may not be true. This could be attributed to the non-uniformity of heat generated along the winding and the non-uniformity of oil ow everywhere. In order to arrive at a reliable and more precise result, a more exact model has been usedin this paper.

The position and the temperature of the hot spot are very important for transformer designers and utility engineers. Thedeterioration of the conductor insulation is dependent on temperature and the exact information about the hot spot tem-perature can aid in better estimation of transformer lifetime.

At present, the design method would determine the average temperature rise of winding. This temperature is added tothe top oil temperature and the obtained temperature in this manner is regarded as the winding temperature at the highestposition of winding. Adding about 10% of the average temperature rise of the winding is regarded as the hot spot temper-ature. This is an approximate method and widely used for estimation of the hot spot temperature [8] . It is worth mentioningthat the exact position of the hot spot cannot be obtained by this method. Instead, different equipments and instruments areused to measure the temperature of the transformer at different positions. Using these measurements, the approximate po-sition and temperature of hot spot are determined.

The model presented in this paper gives oil temperatures, velocity and pressure drops. The model is able to predict otherspecications of the uid, like velocity and pressure. As a case study, a disk winding with an OD cooling system has beenchosen. Each disk of HV winding consists of conductors with rectangular cross-sections. Each disk is separated from adjoindisk with spacers, creating a horizontal (radial) oil channel between disks. Fig. 1 shows the two-dimensional cutaway cross-section of a disk winding transformer where the winding is placed between two cylindrical pressboards.



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These pressboards separate the winding from the internal parts of the transformer and tank. Oil enters from the bottompart of the transformer and is directed to the winding. The system is designed so that the oil moves upwards but as shown inFig. 2 , in each section an oil directing washer change the horizontal direction of the ow. Each part of the winding positioned

between oil directing washers is known as a section and in any section oil moves in one direction (horizontally).In this study, a simple grid with square elements are generated and for different elements at a given ow rate of oil, thethermal behavior of the winding is investigated.

4. Governing equations

Flow of Newtonian uid in two-dimensional space including the temperature is normally presented by four equations

(i) Continuity equation (conservation of mass).(ii) and (iii) x and y momentum (conservation of momentum).(iv) Energy equation (conservation of energy).

In solving the related equations as will be described below, the commercial code, FLUENT 6.0 (2D, Segregated, Lam) has

been used and GAMBIT Software used to generate the mesh network. The model solved to nd out the results with segre-gated method and implicit formulation (because of incompressibility of transformer oil). After 254 numbers of iterations theresults are converged. The following interpolation schemes are used: standard for the pressure, SIMPLE for the pressure-velocity coupling and second order upwind for the momentum and energy.

4.1. Conservation of mass

For the ow under consideration, because of steady ow and non-variation of oil density with time and the two-dimen-sional ows, the continuity equation or conservation of mass equation can be simplied in the form of

CoreWinding

Oil washer

Cylindrical pressboard

Fig. 1. Two-dimensional cross-section of core and disk winding.

Fig. 2. Oil ow between oil directing washers.



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o quo x

o qv

o y 0 9

q ,u and v are density, x and y component of velocity, respectively.The density in the above mentioned equation depends on the temperature. Therefore it is not constant at different

places. The volumetric expansion coefcient of 6.8 10 4 (1/K) has been used for variation of density with temperature[9] .

4.2. Momentum equations (NavierStokes equations)

For the two-dimensional ow and the Newtonian uid, the NavierStokes equation at x direction can be written as

o quu o x

o quv

o y

o P o x

o

o x 2l

o uo x

k o u

o x

o vo y oo y l ouo y o vo x 10

And for y direction it is

o quvo x

o qvvo y

o P o y

o

o x l

o uo y

o vo x oo y 2l o vo y k o uo x o vo y 11

In these equations k is secondary viscosity dened as follows:

k

2

3l

12

The variation of viscosity with temperature as given by [9] has been considered in the following form:

l 6900

T 50 3 13

In this equation T is in C and viscosity in N s/m 2 .

4.3. Conservation of energy

Differential energy equation governing for two-dimensional ows in Cartesian space is in the form

o qEuo x

o qEvo y

P o u

o x o vo y

div k

o T o x

o T o y

l 2

ouo x

2

o v

o y

2

" #

o uo Y

o vo X

2

( )23

l o u

o x o vo y

2

14

In this equation E is the total energy of the uid which is the sum of the internal energy (thermal), kinetic energy u22 v2

2 and potential (gravitational) energy that isE h

P q

u2

2

v2

2 15 Some other works have been done by Mufuta based on numerical calculations and solved by nite difference technique[10] or nite volume method [11] and comprised with experimental data from model transformer. This paper presentsthe study of continuity, momentum and energy equations solved by nite volume method and numerical algorithmusing computational method. The model is solved to nd out the results with segregated method and implicitformulation.

4.4. Assumption and conditions

In solving the above mentioned equations the following assumptions have been made

(i) Temperature gradient in the radial direction and tangent of the winding cylindrical pressboards is negligible. As aresult, only the temperature gradient along the length of the winding (from bottom to the top) has been considered.Two-dimensional models would therefore be justied.

(ii) The ow of oil is laminar. Reynolds number at highest velocity (7.8 cm/s) and density (870 kg/m 3 ), smallest hydraulicdiameter (7 mm) and viscosity (0.0069 N s/m 2 ) would not exceed 69.

(iii) Prandtl number for oil used in transformer is about 74 ( Pr 1). Therefore the ow is considered to be fully developedhydrodynamically.

(iv) Conduction heat transfer at the walls of cylindrical pressboards has been neglected.(v) Temperature of each disk has been assumed uniform and constant.

(vi) Radial variation of eddy current losses are small in comparison with longitudinal, so only longitudinal variations hasbeen brought to calculations.



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5. Modeled transformer and its parameters

An HV disk winding of 200 MVA power transformers, which consists of 104 disks, has been studied in this paper. Ohmiclosses of each disk at a temperature of 20 C are equal to 788.5 W while (as shown in Fig. 3 ) the Z value at the length of thewinding is constant and has considerable variations only at the beginning and at the end [9] . Geometrical specications of this winding are given in Table 1 and the parameters are shown in Fig. 4 .

The physical properties of oil and thermal conductivity of insulation are shown in Table 2 . Variationof viscosity with tem-

perature is considered according to Eq. (13) .Oil directing washers separate the HV winding to three different parts: the rst part includes two disks of the rst section;the middle part includes sections 29. Each section of this part consists of twelve disks. The topmost part, which includesonly the last (or tenth) section, consists of six disks.

5.1. Flow rate and temperature boundaries

The temperature rise test for the transformer under consideration with oil ow of 2.4 kg/s showed that the oil temper-ature at the outlet of radiator is measured to be 65 C [6] . This ow rate and temperature have been taken as boundary con-ditions in this study.

0

10

20

30

40

50

60

70

80

90

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104

Disk No.

Z %

Fig. 3. Variation of Z along the winding.

Table 1

Geometrical specications of HV winding

Winding width ( L) 115 mmHeight of horizontal channels ( ds) 5.5 mmWidth of vertical channels ( dv) 7 mmInsulation thickness ( dp) 0.9 mmHeight of conductor with insulator ( dc + dp) 15 mmInternal diameter of winding 1356 mmNumber of spacers between each disc 32Width of spacers 35 mmNumber of bars 32

Width of bars 16 mm

Fig. 4. Geometrical parameters.



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The height of the oil in the transformer is about 2 m, which includes the oil in the transformer tank and oil inside theexpansion tank, exerting a pressure which applies as boundary conditions for pressure at the wall of the external cylindricalpressboard of the winding.

5.2. Constant heat ux boundary condition

Spacers predicted for creating horizontal channels and bars for creating vertical channels in HV winding constitute 3040% of the heat transfer area. Heat generated in the disks is conducted to spacers and bars by conduction mechanism and 6070% of the heat through insulation papers is by convection. Considering the material of the insulations and their low thermalconductivity, it is possible to ignore the heat transfer through them [2] . Therefore the heat transfer inside the winding can beconsidered to be by convection through oil. The heat transfer area for the disks, regarding Fig. 4 , can be written in the formof

A 2 p

4 Dout 2 dv 2 Din 2 dv 2h in1 L W sn o p dc dp Din 2 dv Dout 2 dv 2 n2 dc dp W t

16

Heat ux passing each disk is equal to the total heat loss divided by the total area

q00 Q t A

17

For each disk, from Eq. (8) , Q t and from Eq. (16) , A, can be calculated.

6. Winding temperature and oil velocity distribution

Disk numbering starts from bottom to top of the winding and the last number (disk no. 104) corresponds to the top most

disk of the winding. Fig. 5 shows the temperature distribution at the topmost section of the winding (consisting of 6 disks),which is considered to be the critical section. Hot spot is at disk 104 (topmost disk). This transformer has been consideredwithout modeling the eddy current losses. Considering these losses the hot spot would be at disk No. 92 (positioned at themiddle of section 9).

Fig. 6 shows the distribution of velocity at the same section. It can be seen that the velocity at the beginning and at theend is high and at the middle part reaches to its minimum. Hot spot temperature is obtained as 126.85 C and its position isat the end of the lower edge of the uppermost disk. In Table 3 a summary of the results are given.

Table 2

Thermal parameters of oil, insulation and ambient

Oil density at 20 C 870 kg/m 3

Oil thermal expansion coefcient 0.000831/KOil specic heat ( C p) 2080 J/(kg K)Oil thermal conductivity 0.1272 W/(m K)Insulator thermal conductivity ( kp ) 0.13 W/(m K)Prandtl number 74Ambient temperature 4 C

Fig. 5. Temperature distribution at the topmost section of winding (K).



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Fig. 6. Distribution of velocity at the uppermost section of winding (cm/s)

Table 3

Results for HV windingHot-spot temperature ( C) 126.9Hottest disc number 104Mass ow rate (kg/s) 2.23T ave (oil to air) ( C) 38.2T max (oil to air) ( C) 67.6T ave (winding to air) ( C) 53.8T max (winding to air) ( C) 86.9

Fig. 7. Position of hot spot (K).



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Fig. 7 shows the position of the hot spot. The importance of knowing the exact position of this point is due to the fact thatthe corrosion and chemical reactions of the insulation start from this point. This chemical reaction causes the reaction be-tween cellulose paper and oil, which in turn create gasses and humidity that decrease the dielectric properties of the oil.According to the standard, the hot spot temperature and its location should be determined by experimental or calculationand not exceeded to a certain threshold value [12,13] . The insulation of a transformer with standard hot spot temperaturewill deteriorate at the normal rate.

In Fig. 8 , temperature distribution and in Fig. 9 velocity distribution of oil at section 9 of the winding is shown. These tem-perature and velocity distributions are similar for the entire middle part (including sections 29).

Fig. 8 shows that the temperatures of the conductor, close to the oil directing washers, are minimum and by moving awayfrom them, the temperature inclines. This can be well understood by looking at the velocity prole inside the channels, i.e.Fig. 9 : whenever the oil has maximum velocity, because of better heat transfer, the temperature of disks declined and viseversa. In the middle channels in which the oil has minimum velocity, heat will not be transferred adequately to oil and there-fore the temperature of disks reaches its maximum.

To study the accuracy of the results obtained from computational model, values available from experimental results arelisted in Table 4 . Some discrepancies between computational and experimental results are expecteddue to inhomogeneity of

Fig. 8. Temperature distribution of oil at section 9 (K).

Fig. 9. Velocity distribution of oil at section 9 (cm/s).



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winding and insulation during manufacturing [14] . An accuracy class of VT and CT of 0.2 has been given in the test report bymanufacture [15] .

7. Discussion

7.1. Effect of washer arrangements

Effect of different arrangement of washers in the temperature distribution of disks is listed in Table 5 . As it can be seen inthis table, hot spot and oil average temperature are different for different arrangements. Hot spot will be low in arrangementof 26 sections with 4 disks at each section, while the oil average temperature is not much higher than other arrangements. Itis obvious that by increasing the oil directing washers and decreasing the number of disks in each section, the hot spot de-creases. Conversely if more oil washers are used the following disadvantages are observed:

(i) Accumulation of oil mold in places where oil is moving slower and decreasing the heat transfer with time.(ii) Increase in pressure drop.

(iii) Increase of winding assembly time.

Therefore a compromise in combination of number of sections would be necessary in order to fulll the standard require-ments and prevention of the above mentioned disadvantages.

7.2. Effect of horizontal and vertical channels height

Effect of the height of the horizontal (radial) and vertical channels on hot spot temperature can be seen in Tables 6 and 7 .Table 6 indicates that increasing the height of the horizontal channels will cause increase in the hot spot temperature. Thisincrease in temperature is due to increase of hydraulic diameter of the radial channels and reduces the heat transferred byconvection. Table 7 shows that increasing the width of the vertical channels increases the hot spot temperature, which couldalso be attributed to an increase of hydraulic diameter of the oil passage and virtually decreasing the heat transfer. Number

Table 4

Experimental and modeling results

Computational results Experimental data

Hot-spot temperature ( C) 126.9 Hottest disc number 104 T ave (oil to air) ( C) 38.2 34.1T ave (winding to air) ( C) 53.8 51.6

Table 5

Effect of different arrangement of washers

Arrangement Hot-spot temperature ( C) T ave (winding to air) ( C)

4 Sections with 26 disks in each section 165.4 38.58 Sections with 13 disks in each section 128.8 38.713 Sections with 8 disks in each section 118.3 39.126 Sections with 4 disks in each section 112.8 39.3

Table 6Horizontal channel height effect

Height (mm) Hot-spot temperature ( C)

ds = 4 124.3ds = 5.5 126.9ds = 7 129.6

Table 7

Vertical channel width effect

Width (mm) Hot-spot temperature ( C)

dv = 6 125.9dv = 7 126.9dv = 8 127.1



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of the spacers and bars also directly affects the disk and the hot spot temperatures. Increasing the number of spacers andbars causes the reduction of effective heat transfer area between winding and oil and the result would be an increase in tem-perature rise of disks.

8. Conclusion

With consideration of the above results and discussion, for design and manufacturing of the transformers the following

points should be considered:

(i) Given the ability of nding the position of hot spot, it is possible to predict the necessary arrangement to prevent thewinding insulation damage.

(ii) Eddy current losses have a considerable effect in temperature distribution in the winding as well as the position andtemperature of the hot spot.

(iii) Temperature distribution and maximum temperature of the hot spot, beside dependency on heat loss, are dependentof oil washer arrangements.

(iv) Increasing the number of oil directing washers increases the pressure drop and decreases the temperature rise.(v) Decreasing the height of horizontal cooling channels causes increase of pressure drop in winding and decrease in tem-

perature rise.(vi) Width of the vertical channels has minor effect on temperature rise of winding and increasing the width would

decrease the pressure drop along the winding.

(vii) Increase in the number of spacers and strips increases the temperature rise of the winding.(viii) Inclusion of eddy current losses improves the prediction of the hot spot position.(ix) Numerical study of the transformer cooling systems gives very close results to the experimental one.(x) Closer study would provide the optimum and efcient cooling system for power transformers.

Acknowledgement

First author would like to acknowledge the use of computer facilities (software and hardware) of University of Ottawa(Mechanical Engineering Department and School of Information Technology and Engineering) during his sabbatical leavein 20052006.

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Determination of OD cooling system parameters based on thermal modeling of power transformer winding