prasenjit short circuit doc

Revision 0 - Date 21/11/2011 - Written by PRASENJIT PAUL page 1 / 17

TECHNICAL COMMON SPECIFICATION SCHNEIDER ELECTRIC = S =

SHORT CIRCUIT WITHSTAND CAPACITY Dynamic Ability to withstand SC Forces by core-type transformers

1) Reference Standards and Books: • IEC 60076 -5 : Ability to withstand Short Circuit

• ANSI / IEEE C57.12.00 : General Requirements for Liquid-Immersed Distribution, Power and Regulating Transformers .

• Books : “ The Short-Circuit Strength of Power Transformers “ by M . Waters , “ Transformer Book” by J & P , “ Large Power Transformers “ by K. Karsai , D. Kerenyi , L. Kiss , “ Transformer Engineering “ by S. V. Kulkarni , S. A. Khaparde

“ Power Transformer Expertise “ by AREVA .

2) Scope / Applicable :

• This specification applies to all core type 3 phase transformers having both the windings with strip / CTC conductor . Both copper and Aluminium type .

• Foil Type , Shell type & special transformers can be applied with some modifications.

3) Definition of SC Current & Forces : • Transformer is part of a system . Due to system faults transformer experience over current .

Current in magnetic field produces force . The mechanical forces in transformer winding is proportional to square of the current . These forces are relatively small under rated current but can be very large under short circuit condition .

Fig 1 : Flux and current interact to give rise to mechanical Fig 2 : Current , Flux and Forces

Forces


• The electromagnetic forces due to this over current must be calculated and methods of determining the strength of the windings must be devised so that these forces must be successfully resisted .

• First we have to calculate the maximum fault current . There are two types of current . One

is Symmetrical Fault current and another is Asymmetrical Fault current . If the picks of the sine waves are symmetrical against zero axis is called symmetrical fault current . When it’s not symmetrical against zero axis , it’s called asymmetrical fault current . Asymmetrical fault current is a combination of symmetrical a.c. component and d.c. component .

Fig. 3 : Asymmetrical Fault Current

The decrement or rate of decay of the d.c. component is dependent on the X/R ratio of the Circuit . The oscillograms shows that short-circuit currents are nearly always asymmetrical during the few cycles after the short circuit occurs . The asymmetry is maximum at the instant of the short circuit occurs and the current gradually becomes symmetrical after a few cycles of the occurrence of the short circuit . Peak asymmetry can be calculated by multiplying the symmetrical peak ( √2 x Isc ) with a factor k .

Hence the peak asymmetry î = K x √2 x Isc

In IEC the value of asymmetry factor , K x √2 has been define as below .

If not otherwise specified , in the case X/R > 14 the factor k x √2 is assumed to be equal to

1.8 x √2 = 2.55 for all transformer upto 100 MVA 1.9 x √2 = 2.69 for all transformer above 100 MVA


Fig. 4 : Short-circuit current and Electromagnetic force as functions of time

• For calculation and design verification , reference must always be made to the maximum pick force value Fmax which takes place at the same time the first pick of prospective short circuit current attained in the winding .

• Symmetrical r.m.s. fault current of a 3-phase two winding transformer is defined as

Where , Zs is the short circuit impedance of the system ,

Here Us is the rated voltage of the system in kV and S is the apparent short circuit power of the system in MVA

Ur is the rated tapping voltage of winding under consideration in kV Zt is the short circuit impedance of the transformer referred to the winding & tapping under consideration , it is calculated as follows :

Where ,

If Zs < 0.05 x Zt we can neglect the value of Zs for Isc calculation .


4) Mechanical Forces

• Radial and Axial Electro magnetic forces in Core-Type Transformers : The magnetic leakage field in the core type transformer having two concentric windings whose m.m.f. are uniformly distributed and balanced is predominantly axial over the greatest part of the winding height . It diverges at the winding ends and there the flux density vector can be resolved into an axial component and a radial component as shown in the below fig-5 .

Fig.-5 : Magnetic leakage field lines with axial and radial flux density component at a specific location

The radial electro magnetic forces, which tend to reduce the diameter of the inner winding by radial compression and to increase that of the outer winding by radial expansion , are due to the action of the axial component of the flux density vector on the respective winding. For concentric winding the force per unit length of winding conductor is maximum in the conductors located in the proximity of the radial gap between the windings , where the axial flux density component attains its highest value ( see the below fig-6 )

Fig – 6 Notional m.m.f diagram for a two winding transformer and produced hoop stress & compressive stress generated

in the windings.

However , innermost conductors of the inner winding and the outermost conductors of the outer winding undergo the compression or expansion effects respectively , arising from the forces transferred to them by the adjacent conductors in their own winding . The calculation of electromagnetic forces generated by short-circuit currents has a prerequisite , i.e. the calculation of the magnetic leakage field . Lots of advance methods like 3D simulation , Image method , Analytical methods ( Roth or Rabins ) , Numerical methods etc. are used for leakage flux .


Frad , Total radial force either outward or inward is defined as

Or alternatively ,

Where ,

• Mean hoop stress calculation in outer winding

The mean hoop stress in the outer winding is calculated as for a cylindrical boiler shell as illustrate in the following fig.- 7 . The transverse force F on two opposite halves is equivalent to the pressure upon a diameter , whilst the total radial force , Frad is equivalent to the pressure on the winding circumference .

Fig-7 : Method for calculating mean hoop stress


Pressure P is equal to force / surface , i.e.

• The mean hoop stress on conductor is defined by

Alternatively

σt = ((30.9 x Wcu)/Hw)x(100/(zt + zs))2 [ MPa ] For Copper

σt = ((18.8 x Wcu)/Hw)x(100/(zt + zs))2 [ MPa ] For Aluminum

Where , Wcu = I

2Rdc loss in winding in kW at rated full load current and at 75 deg C

and Hw = Axial height of the winding in mm .

This value of mean hoop stress can assume to be applicable for an entire tightly would disc winding without much error . This is because of the fact that although the stress is higher for the inner conductors of the outer winding , these conductors can’t be elongated without stressing the outer conductors . This results in near uniform hoop stress distribution over the entire winding . In Layer/Helical windings having two or more layers , the layers do not firmly support each other and there is no transfer of load between them . Hence the hoop stress is highest for the innermost layer and it decrease towards the outer layers . For a double-layer winding , the average stress in the layer near the gap is 1.5 times higher than the average stress for the two layers considered together . Generalizing , if there are L number of Layers , the stress in kth layer from gap is defined as

[ 2 – ((2k-1)/L)] x σt [ for Layer & Helical outer winding ]

Since the inner winding can either fail by collapsing or due to bending between supports, the compressive stresses of the inner winding are not the simple equivalents of the hoop stresses of the outer winding . Thus , the inner winding considerations are quite different and will be clubbed with failure mode analysis.


• Stress due to radial bending on inner winding between support sticks On the assumption of the uniformly shared loads among winding conductors, and absolutely rigid support sticks in the radial direction , the conductors behave like a series of parallel beams with ends restrained at each location of the support sticks . The bending occurs between the axial spacers and if the axial ducts exist within the winding the stresses are largest in the portion of the winding between the outer diameter and the duct nearest to it. The maximum stress for radial bending on each conductor is :

Where ,

l is the edge-to-edge distance between consecutive support sticks.

b is the radial thickness of the strand . Jr is the current density corresponding to the rate current Ir Where the winding has one or more axial ducts , the whole set of conductors can no longer share the load . The calculation for this case is performed by considering the group of conductors located between the main duct and the nearest axial cooling duct . Alternate method when axial support sticks are more than 8 ( Ref. GECA -3.6.1 ) σbr= σt *(Dk/Dm)*(2 - kn )*( 1 – 2/T + ( 2 * Dk * α

2)/(T*b))

Where T = 2 + 0.133*(( Dk * α

2 )/b)2 + 4 δ α

δ = (Ec/Es)* (ts/w)*(2nb/Dk ) and α = π/z – w/ Dk where , Dk = Mean diameter of the portion of the winding considered in mm kn = Ratio of the number of conductors in the portion of the winding considered to the total number of conductors in the winding . α = The half angle subtended at the centre of the winding by the edges of adjacent segments , in radians . δ = Axial spacer stiffness coefficient , n = number of conductors radially in the portion of the winding under consideration . ts = Total thickness of the axial support , in mm w = Width of the axial spacer , in mm z = Number of axial spacers per circle of the winding considered . Ec = Young’s modulus for the conductor material , N/mm2 [ 110,000 N/mm2 for copper & 65,000 N/mm2 for Aluminium ]

Es = Young’s modulus for the material of the axial spacers , N/mm2 [ 250 N/mm2 for pressboard ] For a winding without axial ducts the whole winding must be considered ; i.e. kn = 1 and Dk = Dm


• Minimum Number of Axial Spacers per Circle Radial Failure Modes : Compressively stressed winding may collapse in one of two patterns “ Forced buckling “ and “ Free buckling “ as shown in the fig.-8 .

Fig.-8 : Failure modes of compressive-stressed winding . The stress associated with this critical load , i.e. the critical stress is expressed as

( )2

2

12

1

⋅⋅⋅=

m

crD

bEz δσ (forced buckling failure mode)

and

( )2

4

1

⋅⋅=

m

crR

bE δσ (free buckling failure mode)

where:

crσ is the critical mean hoop compressive stress for buckling

z = number of supports on the circumference

( )δE = incremental modulus of elasticity of copper

b = conductor radial width

mD = mean diameter of winding

mR = mean radius of winding

Calculation using above formula for free buckling is pessimistic, as the windings are never fully unsupported. In addition, the friction between cables or between cables and spacers due to the axial clamping force improve the strength of the coil in regards to the buckling. Strength against buckling benefits by any increase in conductor thickness, or “equivalent thickness” if epoxy-bonding is involved, degree of hardness of the copper, and radial compactness of the winding.Resin-bonded CTCs made of work hardened copper or copper alloy constitute an excellent material for highly compressive stressed windings, especially if the number of individual strands in the conductor is higher than the minimum of 5 or 7 strands.


To avoid both the situation we have to select number of axial spacers as follows : ( GECA method ) z > ( π Dk √B )/300b for Copper z > ( π Dk √B )/230b for Aluminum Where , B = [σt *(Dk)*(2 - kn )] / Dm

• Axial Electromagnetic Forces :

The axial electromagnetic forces tend to compress the windings axially , if the windings are symmetrically arranged and m.m.f uniformly distributed . They are due to the radial component of the flux density vector . In a winding arrangement consisting of two windings symmetrically arranged and characterized by uniform m.m.f distribution , the axial force per unit length of conductor is a maximum in the conductors located at the winding ends , where the radial flux density component attains its highest value .

Windings having equal geometrical heights , uniform m.m.f. distribution , and being radially aligned undergo axial forces mainly directed from the winding ends towards the middle of the coils. By this arrangement , the inner winding located near to the core experience a higher axial forces , owing to the higher amount of flux that re-close radially into the core limb , compared with the outer winding .

A less rigorous formula than those used for the radial force calculation can be written for total axial force per limb , Fax in kN affecting a pair of windings of a power transformer at short circuit ( Refer fig.-9 )

Fig.-9 : Two-winding core-type transformer arrangement with geometrical data In which :


Hw is the geometrical average length of the windings [ m ] Dm is the mean diameter of the pail windings [ m ] d is the width of the main duct [ m ] a1,a2 are the radial widths of winding 1 and 2 respectively [ m ] K is the Rogowski factor , where , K = 1 – ( d+a1+a2 )/πHw [ Valid fro ( d+a1+a2 )/πHw <= 0.25 ] Fax is the sum of the compressions on both windings . Usually , about 2/3rd to 3/4th of this force acts on the inner winding with about 1/3rd to 1/4th on the outer , depending upon the proportions of the transformer . Where two windings of equal length and uniform m.m.f. distribution are displaced axially there is an axial thrust between the windings tending to increase the displacement . If the axial displacement is ν expressed as a fraction of the winding length Hw then the end

thrust Fs developed by each of them can be determined as follows :

922

2

2

10)2()(

6.1−⋅⋅⋅⋅⋅⋅⋅

⋅⋅= krDv

H

INF m

w

r

S π [ kN ]

The end thrust can also be expressed as a function of the total radial force for the complete

winding, radF by means of the approximate equation:

w

radSH

vFF ⋅⋅= 5.2 [kN]

• Axial compressive force for Asymmetric winding with tap in outer coil ( M. Waters /J & P )

The value of the total axial compression force for both the winding also can be calculated by ,

��

�� [ kN ]

Where , U is the rated kVA of per limb , Hw is the winding height in mm f is the frequency in Hz Zt is the per unit impedance Maximum compression in the inner winding is given by Fcw = 0.67xFc+ Fs Where Fs is the maximum end thrust calculated from Residual Ampere-turn method as described in Table-1 for different winding and tap arrangement .


TABLE :1

• Axial compressive stress on winding conductors

Winding conductors are subject to compression due to the axial force acting on the each physical winding . The axial compressive stress , σcwi, on the conductor’s material of winding i , is given by σcwi =( Fcwi/(π*Dmwi*Cc))*10-3 [ MPa ] Applicable for disc and helical winding . For layer-type windings , i. e. no radial spacers , σcwi =( Fcwi/(Cc z c))*10-3 [ MPa ] in the case of disc and helical windings with radial spacers, where : Fcw is the maximum compressive force on winding i , Cc is the quantity depending on winding conductors , as follows : Cc = pb for flat conductors Cc = g*((f-1)/2)*b for CTC conductor and p is the number of strands in winding radial width b is the thickness of the conductor strands [m] f is the number of strands in the CTC g is the number of CTCs in winding radial width Dmwi is the average diameter of winding i . [m] c is the radial spacer width [m]


z is the number of radial spacers on circumference

• Axial compressive stress on winding conductors ( GECA practice ) For either winding , assuming an asymmetry factor of 1.8 ;

σcwi = σt

( ��

�.�.�� ) loge[

�.��

� ] [N/mm2]

where , lr is the distance between edges of adjacent segment at Dm

Dmo is mean diameter of the outer winding Dmi is the mean diameter of the inner winding a is the radial dimension of the considered winding .

• Maximum total stress in conductors are given as

σmax = σcw +

�

� σbr for without tap section in winding

and

σmax = σcw +

�

� σbr for with tap section in main winding

• Stress due to axial bending of conductors between radial spacers

Due to the existence of a high radial component of magnetic flux density in the region of the winding ends, there the winding conductors are subject to an axial load, which tends to bend the conductors of disc and helical windings in the spans between consecutive radial spacers. Refere fig.10

Fig. 10 : Conductor axial bending between spacer rows

The calculation of the axial bending stress cannot be performed by using a simple formula based on the electrical and geometrical winding data. To be accurate, such calculation requires that the local radial component of the magnetic flux density is known, for example by running a leakage field calculation program.

The maximum axial bending stress on a conductor is:

2

2

2 hb

lFaulba

⋅⋅

⋅=σ

where:

aulF is the average axial force per unit length of conductor [ kN/m ]


l is the edge-to-edge distance between consecutive radial spacers [m]

b is the radial thickness of the strand [m]

h is the strand height if the conductor is a strand or twin conductor [m]

h is the height of the individual strand if the conductor is a non-bonded CTC [m]

h is twice the height of the individual strand if the conductor is epoxy-bonded CTC [m]

• Tilting Stress Tilting consists of the whole set of adjacent conductors within the radial width of the winding turning in the same direction, whilst the next axially-adjacent set of conductors turns in the opposite direction, building up a zig-zag pattern of conductors within the winding (refer Fig. 11). Thin conductors are more susceptible to tilting than thicker ones. Paper turn insulation may be damaged due to excessive compressive stress on the conductor/spacer interface or at the transpositions of strands in a multiple strand conductor due to excessive compression and shear stress on turn insulation.

Fig.11 : Conductor Tilting

Tilting stress can be calculated by GECA calculation formula :

⋅+=

wzD

h

hq

b

mw

ctt..3

54200.

.4522 π

σ [ MPa ]

Where , q = 1 for all conductors & q = 1.5 for CTC conductor

w = width of the spacers

Alternatively

In respect of tilting, general consensus appears to have been reached as regards the following formula of critical axial compressive force:

3

43

3

2

2

01

*

, 10−⋅⋅⋅

⋅⋅⋅⋅⋅⋅+

⋅⋅⋅⋅= KK

h

DbXnK

D

hbnEKF

mweq

mw

eq

crtax

γπ

where:

0E = modulus of elasticity of copper = 1.1*105 N/mm2

n = number of strands or twin conductors in winding radial width, in case of flat

conductors


= ( ) 21−fg in case of CTC, g being the number of CTC in the winding width

and f the number of CTC strands

eqb = radial width of the strand in case of flat conductors

= twice the radial width of a single conductor of resin bonded twin conductors = radial width of a single strand in case of non-bonded CTC

mwD = mean diameter of winding

mwD

zcX

⋅

⋅=

π = spacer coverage factor for disc/helical wdgs; for layer wdgs X = 1.0

c = radial spacer width (in circumferential direction)

z = number of radial spacers on circumference

h = strand height if the conductor is a flat conductor = twice the height of a single strand for two parallel strands in axial direction which are paper covered together = height of a single strand if the conductor is a CTC γ = constant for conductor shape

= 1.0 for standard strand corner radius = 0.85 for fully rounded strands or conductors

1K = coefficient for the twisting term = 0.5

2K = coefficient for the bedding term

= 45 for single and twin conductors = 22 for non-bonded CTC

3K = factor accounting for the copper work hardening degree (see Table 1)

4K = factor accounting for dynamic tilting (see Table 2)

Table 1: Values of K3

σ0.2 [N/mm2] K3

Annealed 1.0 150 1.1 180 1.2

230 1.3 >230 1.4

Table 2: Values of K4

Conductor type Winding type

disc-helical layer Strand or twin 1.4 1.0 Non-bonded CTC 2.0 1.2

• Allowable axial force (stress) to prevent conductor tilting The condition to prevent failure by conductor tilting is the following:

axcrtcw FF <


• Allowable axial bending stress between radial spacers of disc and helical windings The stress due to bending of conductors between radial spacers should not exceed the 0.2% proof stress, σ0.2 , of the conductor material.

Therefore:

2.0

σσ ≤ba

• Calculation of Stresses on Insulation and Clamping Structure Radial forces induce mechanical stresses on insulation components located both at the inside of the hoop compressive stressed windings and at the outside of the tensile stressed windings.The insulation parts subject to compressive stress, e.g. the axial sticks and dowels, are made of hard pressboard or other suitable material capable of taking high compression loads. As a general rule, they do not require any checks from stress point of view. Assumptions for insulation components and clamping structures

All electromagnetic forces are oscillatory at twice the power frequency and act on a complex elastic system immersed in oil and consisting of a variety of materials, in particular conductors, non-metallic materials provided for insulation and mechanical support purposes, and a clamping structure made of steel, all of which have quite different mechanical characteristics. The overall mechanical behaviour of such a composite structure is very complex and highly influenced by the mechanical processes to which the various parts have been subjected during the manufacturing stage and during their assembly and final clamping. The electromagnetic forces acting on the winding conductors are dynamically transmitted to the various parts. The result is that the actual forces applied to the various parts may be quite different, both in magnitude and wave shape, from the internally generated electromagnetic forces, depending on factors like internal friction, elastic hysteresis of the materials, internal solid and viscous damping, and hydrodynamic effects of oil motion. etc., as well as on the relationship between the excitation frequency and the resonance frequency of the system. In general, if proper manufacture, assembly and clamping procedures are adopted, mechanical resonance frequencies of the structures result in excess of twice the power frequency. As a consequence, in most of the cases a static approach is sufficient for calculation purposes.

Additionally:

upwi

n

iu FEFS −

=Σ=

1 = resultant force of all windings towards the upper yoke

downwi

n

id FEFS −

=Σ=

1 = resultant force of all windings towards the lower yoke


• Stresses on insulation of layer / radial spacers of disc and helical windings Axial forces cause compressive stresses on the turn insulation of layer windings and on both turn insulation and radial spacers of disc and helical windings. The compressive stress is equal to the axial compressive stress for the respective winding conductors calculated using formula

310

−⋅⋅⋅

=cmwi

cwicwi

CD

F

πσ for Layer windings, i.e. no radial spacers

310

−⋅⋅⋅

=czC

F

c

cwicwiσ for disc and helical windings .

• Stresses on insulation and common structural components The insulation and structural non-metallic components of the winding assembly are designed and built in order to perform the functions of providing an adequate clamping force on the limb winding assembly, and firmly withstanding the dynamic forces. As far as the latter issue is concerned, the components mentioned above are subject to basically two types of forces, namely the end forces (axial thrusts) exerted by the windings and the bounce-back effect produced by the windings, twice per cycle, when they are released from compression. A good stabilisation process and an adequate pre-stress force applied on the coil through the clamping structure reduce the bounce-back effect to a negligible value.

The maximum force on common structural components is :

{ }susdpp FFF ,max=

where:

ppF = force on common spacer rings, clamping plates, etc.

sdF = resultant force of all windings towards the lower yoke

suF = resultant force of all windings towards the upper yoke

The stresses in the structures are calculated on the basis of both the design force as per above condition and pre-load compression force to be applied for the purpose of final clamping.

• Stresses on core frame structure

The electromagnetic forces generated in the winding conductors are dynamically transmitted to the end stack insulation, common spacer rings, press plates (press rings) and core clamps

in that order. The design force of the core clamps ccF is:

χ⋅= ppcc FF


Where

ppF is the force on common structural components calculated before

χ is a corrective factor between 0.6 and 0.8, to take into account the dynamic

behavior of short-circuit forces in regard to the static approach used for the calculation

• Allowable stresses on insulation components

Manufacturers tend to adopt limiting compressive stresses on pressboard and laminated densified wood insulation depending upon their individual experiences. A limit of 80 N/mm2 would appear to be a reasonable . For paper, however, the maximum permissible compressive stress is somewhat lower at 40 N/mm2.

prasenjit short circuit doc

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