Research on Numerical Simulation of 3D Leakage Magnetic Field and Short-circuit Impedance of Axial Dual-low-voltage Split-winding Transformer

doi:10.4236/epe.2013.54B208

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Energy and Power Engineering, 2013, 5, 1093-1096

doi:10.4236/epe.2013.54B208 Published Online July 2013 (http://www.scirp.org/journal/epe)

Research on Numerical Simulation of 3D Leakage

Magnetic Field and Short-circuit Impedance of Axial

Dual-low-voltage Split-winding Transformer*

Yan Li, Longnv Li, Yongteng Jing, Fangxu Han

Research Institute of Special Electrical Machines, Shenyang University of Technology, Shenyang, China

Email: [email protected]

Received March, 2013

ABSTRACT

It is difficult to accurately calculate the short-circuit impedance, due to the complexity of axial dual-low-voltage

split-winding transformer winding structure. In this paper, firstly, the leakage magnetic field and short-circuit imped-

ance model of axial dual-low-voltage split-winding transformer is established, and then the 2D and 3D leakage mag-

netic field are analyzed. Secondly, th e short-circuit impedance and split parallel branch curren t distribution in different

working conditions are calculated, which is based on field-circuit coupled method. At last, effectiveness and feasibility

of the proposed model is verified by comparison between experiment, analysis and simulation. The results showed that

the 3D analysis method is a better approach to calculate the short-circuit impedance, since its analytical value is more

closer to the experimental value compared with the 2D analysis results, the finite element method calculation error is

less than 2%, while the leakage flux method maximum error is 7.2%.

Keywords: Split-winding Transformer; Short-circuit Impedance; Field-circuit Coupled; Current Distribution

1. Introduction

Short-circuit impedance is the important technical pa-

rameter of power transformer [1,2]. The value of short-

circuit impedance can influence the cost, efficiency,

voltage regulation, mechanical strength, short-circuit

current of transformer, so the deviation between meas-

ured value and rated value when the transformer leave

factory is very strict. Split-winding transformer splits one

winding into two ones, wh en one winding is short circuit

it can increase the impedance, it’s the effective and

economy method to restrict the shot-circuit current. The

application of split-winding transformer is used more and

more widely following with the increase of unit capacity

and system capacity [3-6]. So calculation of short-circuit

impedance accurately in split-winding transformer is

important in transformer design.

2D and 3D calculation model are established for a ax-

ial dual-low-voltage split-winding transformer which

type is SFFZ10-88000 kVA/220 kV based on rational

simplification and assumption. Apply field-circuit cou-

pled method to compute and analysis the leakage mag-

netic field and short-circuit impedance, it could be used

as the starting point for studying the load short circuit

current and distribution of high voltage parallel road

current. At last, finite element, computing and experi-

mental values are contrastive analyzed, then the finite-

element analysis is verified to be proper and more verac-

ity.

2. Basic Parameter and Calculation Model of

Split-winding Transformer

The structure diagram of axial dual-low-voltage split-

winding transformer is shown in Figure 1.

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

Program for LN IRT in University (LT2011002) . Figure 1. Structure diagram of winding.

Y. LI ET AL.

1094

The arrangement of winding is core---balanced wind-

ing---low voltage winding---high voltage winding

---regulating winding. Low voltage winding break up

into four equality rated capacity (LV1 , LV2, LV3, LV4).

High voltage winding adopt inlet line from central sec-

tion, the two parts (HV1, HV2) are in parallel then con-

nected in series with regulating winding (TV1, TV2).

Regulating winding all accessing is maximum tap, re-

verse accessing is minimum tap. The low and high volt-

age winding of transformer are all Y connection, a bal-

anced winding is needed to provide access of third har-

monic current for enhancing waveform quality. The basic

parameter of split-winding transformer is shown in Table

1. 3D calculation model of split-winding transformer is

shown in Figure 2.

The assumption cond itions are shown as follows:

1) The 1/2 model of whole transformer model is estab-

lished in order to reduce the computational time;

2) The eddy currents and their influence on windings

are neglec t ed;

3) The currents in the windings are equa lly distributed

along the cross section;

4) All field quantity sinusoidal variation with time, do

not consider the high-order harmonic.

The diagram of external circuit that calculating the short-

circuit impedance of transformer based on field-circuit

coupled method is shown in Figure 3. Figure 3(a) shows

the equivalent circuit diagram of crossing, Figure 3(b)

shows the equivalent circuit diagram of semi-crossing.

Table 1. Basic Parameter of Split-winding Transformer.

Parameter Value

Rated current of high voltage winding 109.95 A

Rated current of low voltage winding 2419.4 A

Rated current of regulating winding 219.9 A

Rated current of balanced winding 936.5 A

Turns of high voltage winding 773

Turns of low voltage wind in g LV1,LV3(18),LV2,LV4(19)

Turns of regula ti n g w i nd i ng 40

Turns of balanced wi n d i n g 64

Figure 2. Model of split-winding transformer.

(a) Equivalent circuit diagram of crossing

(b) Equivalent circ u i t d i a g ram of semi-crossing

Figure 3. Equivalent circuit diagram.

A,i

i,Cis the three-phase symmetrical current source

with internal impedance at the secondary side of the

transformer. A, B, C is the secondary winding consist of

HV and TV. a, b, c is the primary winding consist of LV.

3. Calculation of Short-circuit Impedance

Calculation of short-circuit impedance percentage using

analytical method can be governed by following equa-

tion:

49.6

IWD K

UeH







 (1)

where t is every turn potential, e

is rated phase

current of winding, W is total number of turns, H is av-

erage reactance height of coil, K is additional reactance

coefficient,



is low-type coefficient, is leak-

age magnetic area. D



When calculate the short circuit impedance of trans-

former by the finite element method based on

field-circuit coupled, energy of magnetic field stored in

transformer is transformed from external source during

setting up the magnetic field. Calculate the distribution of

magnetic can obtain the energy of magnetic field stored

in transformer [7,8]. When there is the current

winding, energy of magnetic field is:

WLIN

(2)

where is magnetic field energy, L is inductance of

winding, m

is phase current.

Y. LI ET AL. 1095

When resistive component of the short-circuit imped-

ance can be ignored, the short-circuit impedance of cor-

responding rated current

is:

LWI



 (3)

where

is short-circuit impedance (leakage reac-

tance),



is angular frequency of power source.

Percentage of short-ci rcuit impedance is shown as:

KNN

LI fW

UVA



  (4)

Where

U is percentage of short-circuit impedance,

is frequency, VA is capacity of single phase when

transformer working under rated operating condition.

4. Analysis of Calculation Results

The short-circuit impedance of axial dual-low-voltage

split-winding transformer is calculated and analyzed

though analytical method, 2D and 3D finite element me-

thod. The distribution of leakage magnetic vector when

the transformer is working under crossing and semi-

crossing condition are respectively shown in Figure 4(a)

and Figure 4(b).

The comparison of results about the short-circuit im-

pedance of split-winding transformer working under dif-

ferent conditions are shown in Table 2. In this table,

low-up is LV1 and LV2 in the structure diagram, low-

down is LV3 and LV4 in the structure diagram, Zd is the

short-circuit impedance of crossing, ZB is the short-cir-

cuit impedance of semi-crossing.

(a) Leakage magnetic vector distribution of crossing

(b) Leakage magnetic vector distribution of semi-crossing

Figure 4. 3D leakage magnetic field distribution (rated tap).

Table 2. Short-circuit Impedance Results of Split- winding

Transformer (%).

Calculation

conditions Calculation MeasuredError/%

Analytical 9.92 0.7

2D 9.76 0.9

3D 9.83

9.85

0.2

Analytical 18.5 0.27

2D 18.59 0.22

(high/low-up) 3D 18.63

18.55

0.43

Analytical 18.5 0.16

2D 18.65 0.97

RATE D

TAP

(high/low-down) 3D 18.63

18.47

0.87

Analytical 10.08 0.5

2D 9.96 1.2

3D 10.03

10.08

0.5

Analytical 18.87 0.53

2D 18.86 0.48

(high/low-up) 3D 18.8

18.77

0.16

Analytical 18.87 1

2D 18.9 1.18

MA X

TAP

(high/low-down) 3D 18.92

18.68

1.28

Analytical 9.61 3.3

2D 9.87 0.7

3D 10

9.94

0.6

Analytical 17.36 7.2

2D 18.87 0.85

(high/low-up) 3D 18.82

18.71

0.59

Analytical 17.36 6.5

2D 18.78 1.13

MI N

TAP

(high/low-down) 3D 18.82

18.57

1.34

Figure 5. End winding magnetic flux density distribution

along circle direction.

The distribution of magnetic flux density along circle

direction of upper end of the winding under crossing

condition is shown in Figure 5. The distribution of mag-

netic flux density is uneven along the circle direction of

Y. LI ET AL.

1096

Table 3. Current calculation of HV parallel branch (-show

phase contrast).

Calculation conditions High voltage

up/A High voltage

down/A

Zd 109.95 110.14

ZB(high/low-up) 111.02 -1.08

Rated tap

ZB(high/low-down) -1.11 111.02

Zd 104.62 104.88

ZB(high/low-up) 108.62 -3.66 Max tap

ZB(high/low-down) -3.67 108.62

Zd 129.13 129.67

ZB(high/low-up) 120.92 8.46 Min tap

ZB(high/low-down) 8.45 120.93

winding from the figure, the magnetic flux density in the

core window is larger than that out of the core window.

The comparative analysis of the analytical method, 2D

finite element method, 3D finite element method and

measured values shows that the 3D finite element calcu-

lation value is more close to the measured value. Due to

short-circuit impedance is decided by the value and re-

gularity of distribution of leakage magnetic field, ana-

lytical method can not calculate the leakage magnetic

accurately. 2D finite element method can not figure up

the uneven of the distribution of magnetic field along the

circle direction of winding. So the 3D finite element me-

thod is the best choice when calculating short-circuit

impedance.

5. Analysis of Current Distribution

In this paper, the high voltage winding is connected in

parallel, then series connected with regulating winding,

current excitation is applied at high voltage side when

calculating short-circuit impedance from Figure 1. The

problem of current distribution is analyzed in different

conditions, the calculation results of 3D finite element

method are shown in Table 3.

Table 3 shows that the high voltage parallel branch

current in crossing is not much different and equal divi-

sion when in the three conditions; current in

semi-crossing is different and distribution uneven. The

reason for this phenomenon is that: under the

semi-crossing, the two low voltage winding impedances

are different in the up and down two parallel branches,

and the magnetic field is mutual affected. At last, a circle

flowing the two low-voltage winding is emerged to

counteract the imbalance of impedance.

6. Conclusions

In this paper, an axial dual-low-voltage split-winding

transformer is selected as the research object, calculation

model of the equivalent circuit and the leakage magnetic

field is established. Analytical method, 2D and 3D finite

element method are used to calculate the short-circuit

impedance of transformer in different conditions, then

get the following conclusions:

1) The error of 3D finite element and measured values

is in 2%. The maximum error of analytical method

achieves 7.2%. The 3D finite element method is more

accurate than the 2D one and analytical method.

2) The current distribution can be accurately obtained

by 3D field-circuit coupled finite element analysis me-

thod though the analysis of current distribution of high

voltage parallel branch, then the precise short-circuit

impedance is gained. All of these can be the reference

frame in the short-circuit design of split-winding trans-

former.

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