Stray Losses, Screening, and Local Excessive Heating...
Transcript of Stray Losses, Screening, and Local Excessive Heating...
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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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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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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 . 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
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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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
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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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)
JT 6Modern 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. 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
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
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
JT 8Modern 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
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)
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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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)
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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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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ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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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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
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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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
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.
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
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
ARWtr 2004 Lecture: STRAY LOSSES, SCREENING AND LOCAL EXCESSIVE HEATING HAZARD by Professor J. Turowski
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Fig. 3. Symmetric model RNM-3Dexehtt
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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
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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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
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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