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.

i

3. Calculation of Short-circuit Impedance

Calculation of short-circuit impedance percentage using

analytical method can be governed by following equa-

tion:

6

49.6

10

N

K

t

f

IWD K

UeH

(1)

where t is every turn potential, e

N

I

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

N

I

in

winding, energy of magnetic field is:

m

W

2

1

2

m

WLIN

(2)

where is magnetic field energy, L is inductance of

winding, m

W

N

I

is phase current.

Copyright © 2013 SciRes. EPE

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

N

I

is:

2

2

K

mN

Z

LWI

(3)

where

K

Z

is short-circuit impedance (leakage reac-

tance),

is angular frequency of power source.

Percentage of short-ci rcuit impedance is shown as:

4

N

m

K

KNN

LI fW

Z

U

Z

UVA

(4)

Where

K

U is percentage of short-circuit impedance,

f

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

Zd

3D 9.83

9.85

0.2

Analytical 18.5 0.27

2D 18.59 0.22

ZB

(high/low-up) 3D 18.63

18.55

0.43

Analytical 18.5 0.16

2D 18.65 0.97

RATE D

TAP

ZB

(high/low-down) 3D 18.63

18.47

0.87

Analytical 10.08 0.5

2D 9.96 1.2

Zd

3D 10.03

10.08

0.5

Analytical 18.87 0.53

2D 18.86 0.48

ZB

(high/low-up) 3D 18.8

18.77

0.16

Analytical 18.87 1

2D 18.9 1.18

MA X

TAP

ZB

(high/low-down) 3D 18.92

18.68

1.28

Analytical 9.61 3.3

2D 9.87 0.7

Zd

3D 10

9.94

0.6

Analytical 17.36 7.2

2D 18.87 0.85

ZB

(high/low-up) 3D 18.82

18.71

0.59

Analytical 17.36 6.5

2D 18.78 1.13

MI N

TAP

ZB

(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

Copyright © 2013 SciRes. EPE

Y. LI ET AL.

Copyright © 2013 SciRes. EPE

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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