Temp Rise Dry Type Transformer

5/19/2018 Temp Rise Dry Type Transformer

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Dedicate to Aademician Toma Dordea on his 8t anniversa

CONSIDERATIONS OVER GEOMETRI MODELLING

OF AIR COOLED DRY ELECTRIL TRANSFORMER

CONSTANTN-VIOREL MARIN

Ky w: G llg l y f

In the transrmer desgn the knowledge of the teperature rise in windngs isnecessary to provde a reliable and ecient sulaton. he paper deals wth a methodr constructng reduced sze transrmer models r therma testng It presets thenecessary matheatcs ad llustrtes the method by exmple usng a 250 kVA dryautotransrmer s orgnal and a 20 kVA model

I. INTRODU,CTION

n the design of a transrmer mee any specifed loadng condtions the

knowledge of the theral rise is necessary to make the most econoic and

ecent use of material t is therere essential to know the temperature gradients

throughut the dry-type transrmer Some papers reporte the resuts of test

programs to obtain basic heat transr data in dr-tpe transrmers or eveope

mathematical modes to calculate the temperature rises

n [I] a number of thermal ects of dry-type transrmer geoetry are

eaated and data preseted showin their nterrelations Some representatve

ratis of hotspot temperature rises are given alowing a coser co-ordinationbetween a dryype transrmer ageing mode an its proote

Te paper [2] presents a meto r caculaton of temperature rise o drtype trasfrmers or esign purposes he paper es o wth te temperature

rse of te coils o dry-type transfrmers Only the stea state o the cois s

considered. Transient phenomena ke temperature rise ue to short circuits are notconsidered

The paper [3] develops a mahematical mode to predct hotest spot

emperatre rises n ventilated dry-type transrmers. A correatin r the localheat transr coecient in the cooing ducts as developed The model was used to

study the eect of various parameters on the ratio of hottest sot to average

winding temperature rise

Rev Roum Sci ecn Electrotechn et Energ 46 1, p 39- Bucarest, 200.


2/8

40 Constntin-Viorel Mrin 2

In order to obt in the necessary infrmation t 1s more practical to usereduced size trasforer model in theral studies because of its cost.

Te present paper develops a ethod fr te constrction of reduced sizeodel transforers or teral testing

2. BASIC RELATIONS

Taking nto consderation the connection betwee the losses in windings,cooing conditions and temperature rise, one of te relations wo ave to bedeterined as to connect the electric tress, windng densions and temperaturerise. In that purpose is used the relation wich expresses the surce density oflosses as nction of teperature rise cooling surface and coeficent of heat

transssion by convecton ac .

There was considered as constction type the cylindrical coils and iron coreith vertical legs transfrmer The cnstrction of the windings as concentriccylinder cois separated o the core by cooing air ducts perits an intense

colig due to the heated air crrentThe losses in the transformer winding e:

P=pJtD; + g)hob106, 1where

- P are the osses in te transrer ndgs in W;

ks is the coecient of supleentar oses

p s the coductor resistivty in .m D; is the inner diameter of winding i ;

g is the radial thickness of winding in m;

hbob is the lengt of winding in

- j is the current density in Am2 .he cooling surface in 2 is

(2)

Specific losses in W/mC fr urce unt a fr one degree ofteperature rise e are

p= P= k,g/ l06., xe 2 e

3

This rate has to be less than the coecient of eat trasmssion by

convection a . In case of an inner winding the radiation can be neglected.


3/8

3 Gomtric modllng of air oold dry rarmr 41

The temperature rise on te winding surce can be written down as llows:

k 8=10 (4)2 acWe may therefre express the cuent density j in ters f temperatue rie

8 ceicient o heat transmission by convectin and thicknessof the winding:

}= eac2x10 5k,g Pc

The equation 5 tat pesents te relationhip between load, geometricaldimensions f the inding temperature ise and cooling conditions is one o thebic eations to establish the proportnality between the orginal and the model

Further i necessay t nd the relatonip between geometrical dimensionsf the winding geoetrical dimeions of te magnetic core electric data eectricand magnetic stresses.

The secod euation is

u-= e = 444 x

fx x Sx 10

6whe- e is the volage per urn n - U s he edng voltage n V; w s the number of turns ofthe wndng;-f s te equency of edng voltage n z B s t agntc nducton in leg and yoke n T;- Ss the cross scon of leg and yok in m2This equaton presnts te relaionsp bwen elecrc and agnc

treses, equeny number of urns and gomrcal dnsons of teagnetc coe.

The trd equaon exprsses th llng coecn of wndo areaof ron core:

7whee

w and w

are the numbes f tus of the primay and seconday

inings;

- s1 an s2 are the cross sectins of the conductors of the primary anecary widings n ;

- i the ditance etween legs in m;

H is the ditance between tp and bottom yoes in m;

k is the lling coecient of wndow ea


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42 Constantin-Viorel Main

The equation (7) becomes r auotransfrer:2w = k1HFx0

6

4

This equation preent the relationsip eteen number of tus ndgeomericl dienions of boh magnetic core d inding.

The frth equation epre [4] the coeicen of ea transision ac r

inner ci o dry aturaly coe transfrmer

(9

here

- e is te temperature rie of the surfce in c; h,0b i the ength of inding in m;- !e the ept f cooig air col duct cm

The reao (9) is vali fr 05m"" 9m , 5 c:e:0 c ad05c25cm Coi ee parers are te [5 fr dry air-cooled

ranormer ithn 0kVA: Sn 400kVA rated poerI te hypothesi at er is propory bete rigia and e

md

Sm= Ps X,am=Xa

km,=pt Xkso'

U=Pu xUB"' =P xBo,

kf =p, xk '. m -

F =P x Fo

I=p1 x/0,8=p0X8

PXo

gm1g

Wm =Pw XW,

fm=P xfo

s - p 2 xs 1 - p xlm - I 0 ' cm- I co

(0)

Writing e equaions 5), () 8 (0) r org d m thertio etee the origial an model equaions, afr agrc picationbecoe:

Jo = 8 XaO XsmXmX

Jm soxXP em xam

Vo o X XBoxSo

Um wxmxBmSm

11)

(2


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5 Geometric modeling of air cooled dry rasrmer

WoXSo kJo XhbbOXFo

Wm m m xhbnbm xFm

43

(13)

(4)

Taking ito consideration relationships (0, the equations (11), (2) (3ad (4 become:

2_

k

x

xp

= Xpa

2wXr X BXt

= 1,u

2PkXPt

=l

X s

P =VP Pe

(15

6

(17)

(18)

It is more convenent to take into consderation oe smplfyg hpothesi:

- keepg unchanged the magnetic stresses and equency because of thenonlinear core characteritcs and the dculty to mode equency depedentparameters:

B=J f=}- coosing a standard tesion rate r the odel:

= ;- keepng uchaged the shape of the original r the odel:

k!= - the conductor material s the same:Pp =;

- the coecent of supplemeary losse n wnngs the same

k2 = .Usig those siplcations, the equatons ( 5)( 6) (17 and (18) become:

2Pt X

-=1 ' (19)x

=- t

(20)


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4 Constati-Vorel Mari

2

_P

i

=

l

Pw XsPa= PiPe

6

(2

(22)

The relationships 19, (20,21)

and (22) represet a system of furequatons wth six unnows.

Choosng the geoetrical proportioalty coecient Pi and puttng thecoditon that the model winding as to reac the sme temperature ise like theoriginal:

Pe= ,and the systemof equatons is deterned

3. ILLUSTRATVE MPLE

The ethod s llustrate by xaple [5] usig a 5 V A dry startng

autotransrmer as orignalChoosing fr the model the rato of reducing te geoetric desions

1i =1,

results the rato beteen tecurrent ensites

=

X

a

Fro euation (2an te citin Pe = 1 rsults

ad m equatons (2) an (25)

From uation (20 results

a= Pi '

p j =1.296.

P=4,

and naly te number of tus r the mode

wm= 4X4=64 tus ro eqaon (2) r sults

1P. ='

and the ratio between he cross-sectional areas of the conductors

Sm= s/16

(23

(4

(25)

(26)

27

(28)

(29)

30)

This ratio (0) prits the realisation of te odel wndng th oneconductor fr he urren path


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.

7 Geometc modeling of air coled dry rsrmers 45

The number of tus (28) is very convenient because it aes possible tokeep unchanged r the odel the strctre of winding, and that was one of thereasons o choosing the value of the coecient of geometric reduction.

Thus the winding of the original 50 V A autotransrmer consists of conductors in paralle r 41 trns, so t contains n cross section 64 insulatedconductors the same as the odel winding

The tus of the mode winding are dvded into two coils with two layersech hus keepng unchanged he winding strctre

The coecient p1 ( 0) can be expressed as nction of pj and s, and

reslts:3)

For the sae standard tension rae r model ad original u = 1 the ratio

etween the rated powers is equal wth the current coecient 31) and results thecalclated rated power r he model:

Snm =008250=2025 kVA

As rated powerr the mode is cosen the nearest standard vale

Sn,=20kVA . (32)

The odel is designed usig the data deterined above.The ain atures of the model are:

- rated power: 20 A;

interittent periodic working power: 85 kV A;

- priary rated voltage: 380 V

secondary rated voltage 92 V;

priay ated crren f connous servce: 304 A;

- prmay interitte periodic orkng current: 29 A;

secondary nteriten periodc working curent: 25 A;

nmbe of phase: 3;

qency: 50 Hz;- orking service: three stars of 0 seconds ie, with 0 seconds pause

between two consecutive sarts

- class of insulation: F;

- coolig type: N (air natural)

4 REULT AD COCLUIO

Within the rocess o starting o an indction motor I o PN = 600 kW

rated powe sng the autotransrer AT) r reducig at half te voltage eding

in prpose o sartng crrent limitation he prmary AT crren s 5 imes


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46 Constantin-Viorel Marn 8

bigger than the rated I current The primary interittent periodi workgcurrent of 1612.5 A value is 4.243 times bigger than te prmary rated curret ofA r ontnuous service.

The eatig test fr AT of 250 kVA fr nterittent periodic servce wascarried out with a primry current of 1625 A and short circuitig the secondaryterminals, r the specied working service: three loads of 10 seconds time with

10 seconds pause betwee two consecutive loads The temperature rise measuredusig the eistance varation method was 27 C

The heating test r AT of kVA r intermttent periodc service wasaried out wih a primry current 29 A (being 4.243 times bigger than theprimary rated current of AT r contiuous srice) an short ciruting thesecondary terinals fr the specied working service three load o econdstime with 0 secods puse between two consecutive loads The temperature risemeasured using the resistance variation method was 28 C.

The thermal testing caried out oer the original and the mode prove thatbetween the rises of temratre is a dierence of (3 7 % a oupe o percentagesconrmng thus the justice o the equations empoye ad th acurcy of thegeoetric modellng mehod presented in the papr

he testig carried ot over the reduced scae md led to the moreaccurate nowledge of the herma stresses o ectric nsution of AT in ierentload and coig onditins

he frmation bsis gthere b xem coud be used fr the correcad economi design of seres of stng atotransfmers

h procedure of getri mg s dquate to generate model whiccan gie aurate nfrtn pre o speal transrmers design to meetay oa oing dtns th the most ecet use of materias

Received August I 5 00 "Poliehnica Uniers of Bucharest

REFERENCES

. LC. Whitman, Co-ordnation of DType Tnsformer Models with Transformer Geomet,AIEE Trans., ol. 75 Part III 328-332, June I 956

2 A.A. Halacsy, Temperature Rise of DT)e Tnsfoers AIEE Tan. l. 77, Pa III 4562

Augus 19583 W.. Linden, Predicting hottest spot temperaures in entilated d e tnsformer windings

EEE Trans on Power Delivey Vl. 9 No 2, pil 9944 C.. arn, D. Marin ontribufii la determinarea coecentului de transmisie a cldurii prin

conducie :i convecie la ransormaoarele electrice uscate, E.E.A. Electotehnica,lecronica utoca n 1999

5 C.. Marin, Porea prn autotnfomator a motorulu asincron Eit. rintech Ando TipoBucure 999 ISB 9797597 6

Temp Rise Dry Type Transformer

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