Stray Losses, Screening, and Local Excessive Heating …arwtr04.webs.uvigo.es/Presentaciones_Lectures/Turowski.pdf · Stray Losses, Screening, and Local Excessive Heating Hazard in

Stray Losses, Screening, and Local Excessive

Heating Hazardin Large Power Transformers

Janusz TUROWSKIDept. of Intelligent Information Systems, WSHE - Lodz, and Institute of Mechatronics and Information Systems*)

Technical University of Lodz, Poland

Advanced Research Workshop on Modern transformers ARWtr 2004. October 28 - 30, 2004. Vigo, Spain

_______________________________________ *)Former Electrical Machines and Transformers

Modern TransformersARWtr 2004 28 -30 October. Vigo – Spain http://webs.uvigo.es/arwtr04

ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski

II. INTRODUCTION

In spite of long power transformers history many important stray field problems were not resolved

so far

• A simple approach based on deep theoretical and industrial research gives

such chance• Application of the proposed 3-D methods

enabled to do it easily and rapidly

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Fig. 1. Steel parts in 3-D field, at risk of excessive stray loss and heatinga) 1-bushing, 2-turret, 3-cover , 4-tank, 5-Fe screen, 6-Cu screens,

7-oil pockets, 8-tap changer, 9 - tank asymmetry, 10-Hot-Spot; b) 1-Acceptable region of 2D calculation [Kazmier.5], 2-bolt & Al/Cu screen,

3-Stray flux collectors, 4-flatwise fields enter, 5-yoke beam

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II . RAPID DESIGN AND MECHATRONIC IMPACT

Fig.2. Impact of Mechatronics upon: a) "Time to Market”, b) Sale of small catalogue machines in UK

Sale, mln. PiecesSale, $

PRODUCT MANUFACTURECriteria

MARKET

COMPETITIVENESS

INNOVATIVENESS

RAPID DESIGN !

1."Tailored" Machines2. Cheaper Know-How3. Company secrets

Year

MECHATRONICS

1950

2000

(a) (b)

Conclusion

RAPID DESIGN THEREFORE IS THE MAIN IMPERATIVE OF SUCH METHODS IF ONE WISH

TO MEET THE MARKET COMPETITION

JT 4Modern TransformersARWtr 2004 28 -30 October. Vigo – Spain http://webs.uvigo.es/arwtr04


Power loss density W/m2 in solid metal P1 ≈ ap

22

2mss H

γωµ (1)

The tangential component Hms(x, y, z) of magnetic field intensity on thesurface of metal body is therefor responsible both for power losses, and

overheating hazard.Main problem hence is estimation of field Hms(x,y) distribution

and materials selection. Nevertheless it causes many particular technical and methodologicalproblems. They are for instance:

1. Mechatronic impact and rapid design imperative of market 2. Reliability, safety and economy aspects (Capitalised cost of losses = 3000÷10 000 $/kW) 3. Approximation and linearisation theory for ferromagnetic and thermal material nonlinearity 4. Losses and local overheating hazard in covers and bushing turrets 5. Losses and local overheating hazard in tanks 6. Structural and dimensional optimisation of electromagnetic and magnetic (shunts) 7. Non-linear dependence of load losses on current and temperature 8. "Critical distance" of tank walls and its influence on forces and losses 9. Experimental separations of stray losses from basic I2R and total load losses10. Experimental measurement of per-unit loss distribution in structural parts11. Effectiveness of stray flux collectors over and under winding edges12. Possibility and scale of capitalised cost reduction thanks to proper screening



III. RELIABILITY, SAFETY AND ECONOMY ASPECTSGreat North-East Blackout N.Y. 1965, New York 1977, France 1978, USA Pacific Region 1996,

Canada 2003, Italy 2003,... Who next ?...

Unfortunately available professional computer programs like most popular FEM-3D, are very expensive and time consuming. After Coulson, Preston and Reece [9] FEM-3D is still "not useful for regular design use...".

In spite of serious increase since 1985 of computer capability, our recent experience shows still the same.

Accuracy of FEM-3D is not better than much simpler programs like for instance recommended RNM-3D.

Nevertheless even well-known transformer works still use 2-D models and semi-empirical formulae, like e.g. Mieczslaw Lazarz's (ASEA) formula in W:

PASEA= k2 (f Φmr)α; α=1,5÷1,9; Φms=(Hm,aver t laverage)n (2)


ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. TurowskiARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowsk

ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turow

Turowski 7

IV. BASIC THEORETICAL TOOLS. IV.1. MAIN METHODS

T a b l e 1 . T w o c o m p l e m e n t a r y s t r e a m s o f r a p i d d e s i g n o f e l e c t r o m e c h a n i c a l s y s t e m sF I E L D A P P R O A C H

D e s i g n o f m a c h i n e s a n d a p p a r a t u sC I R C U I T A P P R O A C H

D e s i g n o f d y n a m i c s y s t e m s m o t i o n a n d c o n t r o l

M o s t g e n e r a l d e s c r i p t i o n o f p h y s i c a l f i e l d s i n f o r m o fN a v i e r - S t o k e s e q u a t i o n s f o r e l a s t i c f i e l d s *

∂∂ ρ

ν νv ( v ) v v ( v ) Pt

+ = − + ∇ + +g r a d g r a d p g r a d d i vm

13

2

a n d K i r c h h o f f - F o u r i e r E q . f o r t h e r m a l f i e l d sa n d D u h a m e l - N e u m a n n E q . f o r t h e r m o - e l a s t i c i t y a r e

v e r y d i f f i c u l t f o r s i m u l t a n e o u s s o l u t i o nT h e r e f o r e , t h a n k s t o b i g d i f f e r e n c e s o f t i m e c o n s t a n t s T t

a n d m a t e r i a l s , t h e y a r e u s u a l l y m o d e l l e d a n di n v e s t i g a t e d a s i n d e p e n d e n t f i e l d s :

tBEcurl,JHcurl total ∂

∂−==

J t o t a l = σ E +t∂

∂ D+ σ ( v × B ) + ρ v ρ + c u r l ( D × v ) + J e x t e r n a l

D i f f e r e n t i a l e q u a t i o n s L u m p e d P a r a

M o s t g e n e r a l d e s c r i p t i o n o f s y s t e m s i n m o t i o nH a m i l t o n ' s P r i n c i p l e f o r c o u p l e d

e l e c t r o m e c h a n i c a l s y s t e m s a n d o t h e r s

I = ∫2

1

t

tL d t = m i n , L = T ' - V ( * )

S i m u l a t i o n o f a c t i o n o f c o u p l e d d y n a m i c s y s t e m se l e c t r o m e c h a n i c a l a n d e l e c t r o m a g n e t i c n e e d s s o l u t i o n o f

E u l e r - L a g r a n g e ' s p a r t i a l d i f f e r e n t i a l e q u a t i o n s o fm o t i o n ( d i s s i p a t i v e )

kkkk

GqF

qL

tqL

−=∂∂

−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂

&&dd

T h i s i s n e c e s s a r y c o n d i t i o n o f e x i s t e n c e o f m i n i m u m o fi n t e g r a l ( * ) o b t a i n e d a s v a r i a t i o n δ I = 0 . k = 1 , 2 , . . . n ;

L ( q k , kq& , t ) = T - V - L a g r a n g e ' s s t a t e f u n c t i o n ,T ', V - k i n e t i c ( c o ) e n e r g y a n d p o t e n t i a l e n e r g y r e s p e c t i v e l y ,

G ( t ) - f o r c e s o f c o n s t r a i n t s , F - R a l e i g h l o s s f u n c t i o n

F O R M A L I S E D D I A G R A M Sm e t e r s O F C R E A T I O N E Q U A T I O N S

O F M O T I O N

A P P R O X I M A T E C O M P U T E R M E T H O D S

AN

M

F E M - 3 DF i n i t e

E l e m e n t s

F D M - 3 DF i n i t e

D i f f e r e n c e s

B E M - 3 DB o u n d a r yE l e m e n t s

R N M - 3 DR e l u c t a n c e

N e t w o r k

T A B L E O F E N E R G Y E Q U A T I O N S + M A T L A BA l m o s t a s s i m p l e a n d r a p i d a s p r o g r a m R N M - 3 D

D i f f e r e n t i a l I n t e g r a l D i f f e r e n t i a l

* T h i s i s t h e e q u a t i o n o f h e a t e x c h a n g e b e t w e e n f l u i d a n d s u r f a c e o f s o l i d b o d y a n d f l u i d ( p l a s m a ) s p e e d v , w h e r e ρ m = ρ m ( x , t ) - f l u i d d e n s i t y , p = p ( x , t ) - h y d r o d y n a m i c p r e s s u r e , υ - c o e f f i c i e n t o f k i n e t i c

v i s c o s i t y o f i m c o m p r e s s i v e l i q u i d , υ ∆ v - d e n s i t y o f f o r c e o f i n t e r n a l f r i c t i o n , P - f o r c e a c t i n g o n m a s s u n i t , e . g . L o r e n t z ' s f o r c e d e n s i t y f L = J × B , g r a v i t a t i o n a l f i e l d , e t c

E L E C T R . - M A G N E T . - E L E C - M A G . T E M P E R . - M E C H A N . D = ε E B = µ H T t < < T t > > T t γ ≈ 0 ∂ / ∂ t = 0 T h e r m o - N e w t o n ' s M a x w e l l ' s e q u a t i o n s k i n e t i c s l a w s



I = I ejωt, I=I, curl Hm = γEm , curl Em = - jωµ Hm (3)

IV. 2. STRAY FIELDS, LOSSES AND FORCES

From Helmholtz Equation = α2 Hm we have solution

Hm=Hmse-αz , Em =Hmse-αz , Jm = γEm = αHmse-αz (4)

2

2

zHm

∂∂

α = = (1+j)k , k = = , λ =2πδ (5)ωµγj2

ωµγ

δ1

P1 = Emz Hmy* =ap = = (6)2

122

2mss H

γωµ

22

21m

spaΦ

µωγω

122 mmsH Φ⋅ω



From equation (6) it follows the basic author's [2]formula for total power losses in solid and screened

steel walls, in W:

∆P = ⎥⎦

⎤⎢⎣

⎡µ++ ∫∫∫∫∫∫γ

µωSt

xms

StArspm

mAmsme

eAmse dAHadAHpdAHp 222

20

21 =I2(a+bI)

(7)

where pe<<1, pm<<1 are screening coefficients, ,considering (8);Ae, Am, ASt - surfaces covered with corresponding (e, m) screens ornot screened (St), Hms - magnetic field strength on a metal surface.

The value of x varies for different transformers, but is typicallybetween 1,1 and 1,14 ([10], p. 169)



Fig.4. Non-linear steel permeability: a) Discrepancy of magnetisation curves of the samples of St3s steel used for

transformers tanks, b) author's analytical approximations.

(a) (b)



IV.3. MAGNETIC NON-LINEARITY INWARDS (Z axis) OF SOLID IRON

It was considered with average linearisation coefficients.

At Hms > 5 A/cm, they are:

ap =1,3...1,5 ≈ 1,4 for active poweraq= 0,8...0,9 ≈ 0,85 for reactive power.

At a lower fields Hms≤ 5 A/cm or at µs = const we can adopt ap = aq = 1.

E.g. equivalent depth of penetration δµ(H) = δµ=const ,

active reluctance Rµ(H) = 0,37Rµ=const,and reactive reluctance Rµ(H)r = 0,61Rµ=const , etc

pa1

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IV.4. MAGNETIC NON-LINEARITY ALONG THE STEEL SURFACE (X,Y)

It was considered with the help ofanalytical approximations

(Fig. 4a, Slide 10)

H2 = c1H+c2H2, , (8a,b,c,d)

( )n ≈ H , ≈ cHb

and corresponding exponent coefficient x in (7).

sµ Hµ+=µ 211 AA

Hrµ2Hrµ

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DEPENDENCE OF STRAY LOSS ON CURRENTAND TEM PERATURE !

Since Hms = C ( Hms)n = C (9)

IN STEEL ELEMENTS OF TRANSFORMERS STRAY LOSSESCAN GROW LOCALLY FASTER THAN WITH I2

One can conclude that 1) When Hms =cI , like in transformer coverplate

P1 ∼ I1,6 f0,5 γ-05 (9a)2) When Φm1 =cI , like interwinding stray flux entering the steel

P1 ∼ I2,8 f1,9 γ0,9 (9b)

THIS IS WHY SHORT CIRCUIT TEST SHOULD NOT BE CARRIED OUT AT TOO SMALL CURRENTS

rµ ( ) n102 mΦµ

γω

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IV.5. ELECTROMAGNETIC FORCES

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Going out from general Hamilton's Principle and Euler-Lagrange's partialdifferential equations for coupled electromechanical systems (Table 1), wehave general expression [17] for electromagnetic force

fe (xk) = kj kj2

1x

ii k ∂∂

∑∑ ⋅ Mjk (xk) (10)

where Mjk (xk) inductance between the particular parts of winding (Fig. 5), tobe calculated with the help of Maxwell's theory; xk = x, y, z, t or r, θ, ϕ, t -co-ordinates in space and time. Then resultant axial force distribution aroundone leg in that case is

Fx (ϕ) = ∫L

fe (x, ϕ) dx (11)

Fig. 5. Axialforce Fx (ϕ)

Our study gives evidence that the destructive forces occurring in thecylindrical windings of high power transformers can be investigated atreasonable cost and time, thanks to the RNM-3D.



IV. 6. CHOOSING OF CALCULATION METHODS

3-D RELUCTANCE NETWORK METHOD RNM-3D _

Low, secondary school levelRegular PC

Simple Ohm's and Kirchhoff's lawsSmall, smoothed by integratiom

Low price

Half an hour

LESS THAN 1 SECOND

CRITERIA

⇐ User qualification ⇒⇐ Hardware ⇒⇐ Theory ⇒

⇐ Errors generation ⇒⇐ Software ⇒

Time of⇐ model formation ⇒

CPU timeof computation of one⇐ design variant ⇒

3-D FINITE ELEMENT METHOD FEM-3D _

High university levelHigh qualityVariation calculusLarge due to differential methodExpensive and sophisticated

5 to 12 months

30 TO 300 HOURS

Fig. 6. Dependence of effectiveness of modelling and simulation on the method selected.

STRAY FIELDS AND LOSSES IN LARGE POWER TRANSFORMERS

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Fig. 4. Stray loss in ABB-Elta transformers with magnetic screens (shunts). Turowski J., Kraj I., Kulasek K,: Industrial Verification of Rapid Design Methods in Power Transformers.

International Conference TRANSFORMER'01, 5-6.09.2001, Bydgoszcz, Poland

0

50

100

150

90 90 90 100 150 160 187 270 270 270 270 270 300 330

Rated power of transformer in MVA

Loss

es in

tank

[kW

]

Measured RNM-3Dexe Semiempirical formula

Fig. 2. Stray losses in ABB-Elta transformers with no screens

0102030405060

25 25 25 25

31,5

31,5 50 63 63 69 75 76 80

Rated power of transformer in MVA

Loss

in ta

nk [k

W]

Measured RNM 3D Semiempircal formula


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Fig. 3. Symmetric model RNM-3Dexehtt

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IV. 7. ELECTROMAGNETIC SCREENING

Fig. 7. Internal interference of electromagnetic wave in penetrable metal wall:a, b) Wave incident from both sides,

c) Coefficients of active χ , cos ϕ and reactive ξ power, d) Coefficients of active ζ , cos ϕ and reactive ψ power at symmetric both sided incident

c) d)

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IV. 7. ELECTROMAGNETIC SCREENING.

Since Zdiel ==377 Ω >> | ZSteel | >> |ZCu |,

we have simple wave reflection (Slide 16) coefficients

≈ ±1 (13)

Active P1 in W/m2 and reactive Q1 in var/m2 powers consumed by metal wall

P1 = pe and Q1 = r (14a, b)where pe = κ, ζ (Fig. 7c,d) and re = ξ , ψ respectively.

κ= ≤1, ζ = ≤ 1 (15)

Screening coefficient in its simplest form is pe ≈ kH (16) One have to remember however that ELECTROMAGNETIC SCREENS,

DUE TO THE SKIN EFFECT, CAN GENERATE FIELD CONCENTRATION AND HOT SPOTS ON THEIR EDGE

incref

increfr

incm

reflm

incm

reflmrefrin ZZ

ZZEE

HH

Mr +−==−=−

22

212 msH

γµω

22

212 msH

γµω

dddsd

k2cosk2chk2ink2sh

−+

dddsd

kcoskchkinksh

+−

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Stray Losses, Screening, and Local Excessive Heating …arwtr04.webs.uvigo.es/Presentaciones_Lectures/Turowski.pdf · Stray Losses, Screening, and Local Excessive Heating Hazard in