Calculation of Eddy Current Loss and Short-circuit Force in SSZ11-50000/110 Power Transformer

doi:10.4236/epe.2013.54B211

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Energy and Power Engineering, 2013, 5, 1105-1108

doi:10.4236/epe.2013.54B211 Published Online July 2013 (http://www.scirp.org/journal/epe)

Calculation of Eddy Current Loss and Short-circuit

Force in SSZ11-50000/110 Power Transformer

Yan Li1, Bo Zhang1, Longnv Li1, Tongxun Yang2, Ning Wang2

1Power Transmission Technology Research Institution, Shenyang University of Technology, Shenyang

2TBEA Shenyang Transformer Group Co., Ltd. Shenyang

Email: [email protected]

Received April, 2013

ABSTRACT

The method is used in this paper to calculate the leakage magnetic field of SSZ11-50000/110 Power trans-

former, and by which the structures’ influences to the main leakage flux are analyzed. Through the combination of the

product and TEAM Problem 21B, the surface impedance method shows its great advantage in the calculation of eddy

current loss.

T

Keywords: Power Transformer; Finite Element; Short-circuit Force; Eddy Current Loss; Surface Impedance Method

1. Introduction

With the rising of voltage level and transformer capacity ,

the leakage flux of transformer increased, therefore, the

problem of structural part stray loss and short-circuit

strength has became one of urgent key technical issues

both in transformer companies and operation department.

To solve this type of problem, intra-industry corre-

sponding standards are already existed, and it changes

with the products upgrade.

The traditional analytical method cannot analysis the

local overheating, short circuit mechanical force withstand

capability and three-dimensional spatial distribution of

leakage flux which the new standards request. Based on

three-dimensional finite element numerical method, the

paper introduced transformer design criterion to discuss

the leakage flux distribution, short circuit strength, and

eddy current loss of transformer, and the fitted engineer-

ing design loss calculation numerical method is also pr-

oposed [1,2].

2. Mathematical Model

The method which uses scalar magnetic potential

and electric vector potential can reduce unknown number

and save computer memory when high precision is re-

quired.

T

The governing equations in eddy zone is



σε TμT0

t(Ω)









 













(1)

penalty function is introduced,

σε T









 







, then



σε Tσε T

μT0

()







 



 



 



 











(2)



, then





μ()T0





(3)

The governing equations in non-eddy zone is





μH

()0



  (4)

where, Hs is the magnetic field produced by source cur-

rent in infinite space, T is electric vector potential,



scalar magnetic potential, is conductivity, is di-

electric constant,

σε

is permeability.

The calculation process is treated as follows:

1) According to structural symmetry, the half trans-

former model is taken into calculation (as shown in Fig-

ure 1);

2) Circulation and eddy current in winding, and eddy

current in core is neglected;

Using wire winding, and the current density is uniform

in the winding.

 (5)

where J is winding current density, N is winding turns, S

is sectional area, I is winding current;

*This work was supported by NSFC, under Project 51177103 and

Program for LNIRT in University (LT2011002).

Y. LI ET AL.

1106

3) Material of iron core is according to rolling direc-

tion and orthogonal opposite treated. The material of tank,

draw plate and clamping part are treated according to

each direction same treated. The basic magnetization

characteristic curve is used here and hysteresis charac-

teristic is neglected.

4) The Newton-Raphson algorithm is used to solve the

magnetization characteristic of core silicon steel sheet

and tank steel plate for their characteristic are nonlinear

relation.

5) The eddy zone produce skin effect, and mesh gen-

eration should take current density radial distance.







 (6)

where



is penetration depth,

is frequency,



conductivity,



is permeability. According to field

value some gradient descent discipline to stratify, pene-

tration depth chooses 0.22, 0.51, 0.92, 1.6 and 5 times to

mesh generation.

3. Field Analysis

To analysis short-circuit electromagnetic force, the flux

leakage magnetic distribution should be studied first.

As shown in Figure 2 that winding average flux den-

sity along circumferential distribution, winding end

magnetic density is affected by upper and lower iron yok,

the inner magnetic density is higher than the outers’. The

radiation component Br value is impacted greatly from

24.35mT to 27.8mT. The axis component Bz value varies

from 58.4mT to 61.6mT, and both of their two sides are

more than that at the middle part. The middle of the

winding does not change greatly for its far distant form

clamping part and iron yoke.

For the anglicizing of the structure eddy current loss,

the surface field and eddy current distribution are the

emphases.

As shown in Figure 3 that the magnetic curve of outer

tank side winding end part is bend, and the vortex center

is formed for the leakage flux concentrated into the tank

surface.

tank

Draw

Plate Pp

champing

Figure 1. Transformer calculation model.

Figure 2. Winding average fl ux density along circumferential

distribution.

Vo rtex

center ble

stress

requireme

nts g7

Figure 3. The surface of the oil tank eddy current distribu-

tion.

According to the CIGRE recommended document , the

transformer metal structure of local overheating criteria,

through calculation, the tank surface magnetic field

strength of the tangential component maximum value

was 48.22A • cm-1, does not exceed the standard value of

60 A • cm-1, therefore, the additional fuel tank shield is

not necessary.

4. Short Circuit Strength

The national standard GB1094.5-2008, in the new ver-

sion, the allowable stress requirements of .conventional,

non - viscous, sticky wire and CTCs (continuous trans-

posed conductor) are different from the original design.

Now, take average ring stress t1



, warping free limit

stress cr



, the inner winding radial bending stress sav



axial compressive stress act



, conductor axial bending

stress AL



, and wire inclination critical stress _cr tilt



for example [3,4]

According to the national standard GB1094.2-2008,

the first peak of asymmetric short-circuit current is





峰 (7)

where, i is rated current effective value, k

U is short

circuit impedance, 2k is peak factor, in this paper

Y. LI ET AL. 1107

the transformer is valued 2.55.

According to the Lorenz formula, the winding elec-

tromagnetic force can be calculated., The SSZ11-50000/

110 transformer short-circuit force calculated values and

national standard GB1094.5-2008 requirements short-

circuit mechanical strength are shown in Table 1.

Through calculation, the low-voltage windings of

power transformer SSZ11-50000/110 meet the national

standard GB1094.5-2008 to withstand short-circuit me-

chanical strength requirements.

5. Eddy Current Loss

Eddy current density can be calculated by the following

formula

e(σV



 



(8)

Eddy current loss

eσ

pJdv

(9)

where, Je is eddy current density，pe is Eddy current loss,

Ais magnetic vector potential，V is electric scalar po-

tential.

As shown in Figure 4, the maximum point appears in

the main empty path up(down) direction, base on design

experience ,the structural overheating criterion is shown

in Table 2

Table 1. SSZ11-50000/110 anti short-circuit stability.



(MPa) cr



(MPa) sav



(MPa)

Calculation value 38.24 11.70 66.01

National standard ≤49 ≤98 ≤126

act



(MPa) AL



(MPa) tiltcr_



(MPa)

Calculation value 50 75.51 28.32

National standard ≤80 ≤126 ≤98

side

outside

Figure 4. The eddy current loss density distribution of Clamp

part.

Table 2. Large transformer partial overheat judgment.

Structure part maximum loss density / kW·m-3

tank 1800

champ 1800

Through calculation, the highest tank eddy current loss

density is 1066.3 kW • m-3. And the clamp part maxi-

mum loss density is 2100.5 kW • M-3, which exceed the

empirical criterion. Through taking effective measures,

the possible overheating is prevented.

6. Surface Impedance Method

When eddy current loss in transformer is under calcula-

tion, if more structures exists namely the vortex area ac-

counts for a larger proportion of the solution domain, it

will lead to a large amount of computer memory occu-

pied.

After taking into the consideration of the skin effect,

the refinement of mesh in the penetration depth is also

needed. Even using hierarchical subdivision method, a

smaller grid is still needed to meet the needs of accuracy.

Taking TEAM Problem 21B as an example [5], the

relations of steel plate maximum length and the calcu-

lated value eddy current loss is shown as Figure 5.

When the maximum length of the element is 5 mm, it

will cost one hour to reach the experimental values to

meet the precision need, and the method can not be ap-

plied in the calculation model because the structure size

growth several times which makes the calculation up to

tens of hours.

When the skin depth is small, the surface of eddy re-

gion is regarded as the impedance boundary conditions

for solving domain, and the finite element method are

still used in other domains that can obviously reduce the

problem scale.

The surface impedance eddy zone definition











 (10)

where

is surface impedance, is tangential

component of electric field intensity,

is tangential

component of magnetic field intensity,



is penetration

depth.

Solid line: the calculated values; dotted line: measured value

Figure 5. 21B relations of maximum element length and

calculation value.

Y. LI ET AL.

1108

Table 3. Eddy current loss calculation.

Unit: W SSZ11-50000/110 transformer problem21B

tank champ draw champ

Calculation value 9853.9 13054.57 4369.9 8.14

Measured value —— 8.09

After using surface impedance method, the calculation

time has been significantly decreased, and the eddy cur-

rent loss calculation is shown in Table 3.

7. Conclusions

The method is used in this paper to calculate the

parameters of SSZ11-50000/110 transformer, and the

conclusion can be summarized as follows:

T

1) The short-circuit mechanical strength meets the new

requirements; the tangential component of structure sur-

face field is lower than the local overheating criterion.

According to the design experience, surface eddy current

density of the clamp part greatest is too high, and there is

a risk of local overheating, for which the shielding

equipment is considered installing in the clamps.

2) The end winding leakage flux along the circumfer-

ential distribution is not uniform for the effect of iron

yoke. The calculation of the winding end axial magnetic

flux density is influenced by structure and should not be

ignored when the short-circuit force is calculated.

3) By using hierarchical subdivision method for the

calculation of transformer structure eddy current losses is

time-consuming and difficult to ensure the accuracy. And

using the finite element method of surface impedance

boundary can solve this problem effectively.

REFERENCES

[1] “Transformer design principle of,” China Electric Power

Press.

[2] C. Y. Liu, “Calculation Method and Practice of Trans-

former Design,” Liaoning Science and Technology Press.

[3] J. Liu and A. H. Zhang, “Transformer Simulation and

Evaluation of Power Winding Short-circuit Dynamic Sta-

bility,” Transformer, Vol. 49, No. 6, 2012, pp.14-25.

[4] GB1094.5-2008. Requirements Short-circuit Mechanical

Strength

[5] S. M. Yang, Z. G. Cheng and X. Q. Zhu, “The Stray Loss

in Steel Measurement Technology,” Chinese Journal of

Scientific Instrument.