t m0 x15 h19 y6f ff4 fsb fc0 sc0 ls0">B
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.
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
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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