Influence of the Parameters of Disk Winding on the Impulse Voltage Distribution in Power Transformers
M. Heidarzadeh* and M. R. Besmi*(C.A.)
Abstract: Overvoltage distribution along the transformer winding must be uniform to certify the safety of the operation of the power transformer. Influence of the parameters variation on the Impulse Voltage Distribution (IVD) in disk winding transformer is going to be analyzed which hasn’t been analyzed on this type of winding in the previous papers. In this research, a transformer with disk winding and rectangular cross-section is analyzed.
Equations for capacitances between winding turns and also equations for capacitances between turns and core are deduced. Noting that the relationships presented are dependent on the parameters of the transformer winding, so with changing these parameters, the capacitances of turn –turn and turn – core and finally the capacitances of total series and parallel of the winding will be changed. The purpose of this paper is to show the effect of the variations of these parameters on the IVD in disk winding of transformer. This paper, will assess how to change the parameters of disk winding in order to achieve a uniform initial IVD along the winding and to reduce the Amplitude of Impulse Voltage Fluctuations (AIVF) in winding and which parameters have more effect in making uniform the IVD on the disk winding.
Keywords: Constant of Winding Voltage Distribution, Disk Winding, Impulse Voltage Distribution, Series and Parallel Capacitances.
1 Introduction1
Frequency pattern of impulse voltage caused by lightning contains fundamental frequencies up to several megahertz. Thus, in these high frequencies, capacitances of transformer winding should be considered in calculations. But they ignored in power frequency [1-3]. These capacitances are considered between windings and grounded components (i.e. core, tank, etc) and between disks, layers and turns. With presence of these capacitances, IVD along the winding isn’t uniform. Non-uniform IVD along the winding produces severe stress on the winding which can be resulted in electric breakdown of transformer insulation.
In power frequency, voltage distribution along the winding is uniform and there is not stress on the transformer insulation. Therefore, IVD on the winding disks must be uniform in order to reduce the AIVF.
Distribution of the impulse voltage along the winding depends on the winding capacitive network that is consisting of parallel and series capacitances [1].
Capacitors between winding turns are known as series
Iranian Journal of Electrical & Electronic Engineering, 2014.
Paper first received 7 July 2013 and in revised form 6 Oct. 2013.
* The Authors are with the Electrical and Electronic Engineering Department, Shahed University, Tehran, Iran.
E-mails: [email protected] and [email protected].
and capacitors between turns and core are known as parallel capacitors.
According to Fig. 1, the voltage of any point in capacitive network in the time of the strike of impulse voltage, U, with assuming the transformer winding is grounded is deduced from Eq. (1) [3]:
( )
x x
l l
e e
V x U
e e
α α
α α
−
−
⎛ − ⎞
= ⎜⎝ − ⎟⎠
(1) where
s p
C
= C
α
(2) In Eq. (1), U is the amplitude of the applied impulse voltage to the winding terminal, l is the total length of winding and x is the coordinates of point for calculating the voltage. Also in Eq. (2), Cs is the total series capacitance of the winding, and Cp is the total parallel capacitance of the winding.
Constant of winding voltage distribution (α) shows the rate of uniformity of IVD along the transformer winding [1]. This coefficient depends on the total series and parallel capacitance of winding. Total series capacitance of the winding is equivalent to the capacitances of turn-turn and total parallel capacitance of the winding is equivalent to the capacitances of turn- core.
144 Accordin of total se capacitance causes the cu be nonlinear winding will
By decrea winding uni reduces.
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eries capacit will decrease urve of IVD o
and also acc be increased.
asing the coef iforms but ng to Fig. 2, nalyzed for se
he winding, th acitance be sm linear. But if t acitance in cap
IVD will be l will change to ows, the initia t α [1]. Also
ient on each d fluctuations (c ues of α [1].
ng to the abov the winding ltage, the co ssible value.
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4 a e s l f f d e e n e r s y s s
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with unlimi ular cross-sect quivalent to t -plane capac
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the king orm the s on per, ding and also ffect this for been disk ding ical ware ulse is y of
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s.
win [14 and Fig int the adj coa wir cal
Ci
equ wid and sid coa two adj in t Co
cen the coa tran oth dis ass ass ass com com
Ctt
wit Eq two cal
Ctt
In next steps nding parame 4-19], distance d core are div g. 5, distance o 3 regions. F e first turn, se jacent turns ating of the se
The capacita re (capacitan lculated from
0
. . .
ic r
ε ε π
=
Parameters o uation, DT is t dth of turn’s d t is the thic de and εr is t ating of each w
In transform o turns is usu jacent turns in the second reg
oil r oil =ε0.ε ( ).
In Eq. (5), p nters of the c e height of t ating and εr(oil)
The distanc nsformer win her insulation stance of betw sociated with sociated with sociated with
mposition th mbination is s
This series c
oi ic
oil ic
t C C
C C
2 .
= +
It is importan th the first and qs. (4) and (5)
o adjacent tur lculated:
= roil t
p ε ε0. ( ).
s Eq. (3) will eters will be e between two vided into dif
between two First region i econd region and the third econd turn.
ance for the nce of the fi Eq. (4) that is .D wT.
t of Eq. (4) are the average di
cross-section ckness of the the relative pe
wire.
mer windings, ually oil. The n the area of c gion) from Eq
t h p
w DT
2 . .
−
−
π
p is winding ross-sections turn’s cross-s
l) is the relativ e between tw nding, in addi
s, which is i ween two adja h the first re the second r h the third r hat the ori shown in Fig.
ombination ca
il
nt to note that d third region
in Eq. (6), the rns (turn–turn
⎜⎝
⎛ −
−
−
T
t h p
π D 1 2
. .
l be more acc included. In o adjacent tur fferent parts.
o adjacent tur s the insulatin
is the insula d region is t insulating coa irst and third s deduced usin e shown in F iameter of the without insul insulating co ermittivity of
the insulation e capacitance covered by oil q. (5) is calcul
pitch or dista of the adjace section witho ve permittivity wo adjacent tion to the oi gnored from acent turns, th gion and the region and th region, make
entation of 6.
an be shown a t the capacity s are equal. B e total capacit capacitor) us
⎟⎠
⎞
r oil r
w
ε ( )ε
curate so that n this method rns or the turn According to rns is divided ng coating of ation between the insulating ating of each d regions) is ng Eq. (3).
(4) Fig. 4. In this
turn, w is the lating coating oating on one the insulating n between the between two l (capacitance
ated:
(5) ance between ent turns, h is out insulating y of oil.
turns in the il can include them. In the he capacitance e capacitance e capacitance up a series this series as Eq. (6):
(6) of associated By substituting tance between sing Eq. (7) is (7) t d n o d f n g h s
s e g e g e o e
n s g e e e e e e s s
d g n s )
146 Iranian Journal of Electrical & Electronic Engineering, Vol. 10, No. 2, June 2014 Fig. 5 Regions between two adjacent turns.
Fig. 6 Series combination of capacitances in the distance of between two adjacent turns.
2.2 Parallel Capacitance
For calculation of parallel capacitance (turn-core capacitor), like section 2.1 the curvature of the turns are ignored. Also the core is considered as a plane. Also the core is considered as a plane. Also in this section the basic equation is Eq. (3) which will be more accurate later. In this method [14-19], the distance between the turn and the core is divided into two regions. According to Fig. 7, first region is the insulating coating of the turn and the second region is the insulation between turn and core (oil).
In this section, for calculation of the capacitance of first region (the capacitance of insulating coating of the turn) is used from Eq. (8):
t h Cic r .DT.
.
0. ε π ε
=
(8)
Fig. 7 Regions between turn and core.
Fig. 8 Series combination of capacitances in the distance of between turn and core.
Capacitance of second region (i.e. the region filled with oil) is calculated according to the Eq. (9):
w t Z
h Coil roil DT
−
= −
2) (
. . .
. ( )
0
ε π
ε (9) Parameters of Eq. (9) are shown in Fig. 4. In this equation, Z is distance between the center of turn’s cross-section and the outer surface of the core.
According to Fig. 8, in the distance between the turn and core capacitance associated with the first region make a series combination with the capacitance associated with the second region.
This series combination can be shown as Eq. (10):
oil ic
oil ic
tc C C
C C C
= +.
(10) It should be noted that in this section, there is only one capacitor Cic but in section of 2.1 there were two capacitors Cic which were series. So by substituting Eqs.
(8) and (9) in Eq. (10), the total capacitance between the turn and core (turn-core capacitor) using Eq. (11) is calculated:
( )
⎟⎠
⎜ ⎞
⎝⎛ −
−
−
=
r oil r T oil
r tc
w t Z
h C D
ε ε ε π
ε
) ( )
( 0
2 1 . . .
. (11)
Eqs. (4) - (11) are based on references [14-19].
3 Study of Capacitive Network of the Disk Winding In Fig. 9, view of a disk winding is shown. In this type of winding, each disk has several turns that are placed in one horizontal plane. In this winding, the turns
Fig. 9Disk winding with 4 disks that each disk has 5 turns.
of first disk are wrapped from outside to inside and next disk is wrapped in different direction (from inside to outside) and this procedure is repeated to final disk.
The advantages of disk winding is that they can be used in high power and high voltage transformers and provide high cooling capability, mechanical strength and good impulse voltage distribution.
Capacitive network of the disk winding is shown in Fig. 10. In this capacitive network, there are two kinds of series capacitors and one kind of parallel capacitor.
Series capacitors are as follow:
1- Turn-Turn capacitors, between adjacent turns in one disk (Ctt(st)).
2- Turn-Turn capacitors, between adjacent turns in two adjacent disks (Ctt(sd)).
Also Turn-Core capacitors (Ctc) in disk winding are as a parallel capacitor.
Series capacitors in the capacitive network of the disk winding from Eq. (7) and parallel capacitors from Eq. (11) are calculated. Proportional to change in each parameter of the winding, one or more parameters in Eqs. (7) and (11) will be changed and caused to change the capacitive network of the winding. With variations in the capacitive network of the winding, the IVD and AIVF on the winding and also the impulse voltage on each disk will be changed.
4 Impulse Voltage Distribution Analysis on the Disk Winding
A typical transformer with disk winding is considered for this section. The parameters of the transformer winding are introduced in Table 1.
The results of the change in winding parameters according to VOLNA software are shown in the following tables and figures. Figures 11-14 which are based on Fig. 2 show how the IVD on the winding changes as the parameters of winding change. Tables 2- 5 show the change of impulse voltage on each disk of the winding as the winding parameters variation (voltage on each disk is a percent of applied impulse voltage).
By increasing the distance of the core outer surface from the winding (Bcw), DT in Eqs. (7) and (11) and also Z in Eq. (11) will be increased. This variation causes to increase the proportion of total series to total parallel capacitances. According to Fig. 11, these variations will be caused the IVD on the winding to be uniform and it will be also decreased α. Also from Table 2 it can be seen that with increasing Bcw, the impulse voltage on each disk was decreased. Thus the risk of electrical breakdown is reduced in the winding insulation.
Table 1Parameters of simulated disk winding.
20 Number of disks (N)
4 Number of turns in each disk (n)
Paper=4.2 oil=2.25 Relative permittivity of insulation
9.5 mm Height of turn’s cross-section without
insulating coating (h)
6.5 mm Width of turn’s cross-section without
insulating coating (w)
0.5 mm Thickness of paper insulation of the
conductor in one side(t)
500 mm Diameter of core (Dc)
30 mm Distance of the outer surface of the core
to winding (Bcw)
4.5 mm Length of the channel between
winding’s disks (Hch)
Table 2Changes of the impulse voltage on the disks caused by the changes of Bcw.
Impulse voltage on the disks [%]
Bcw=80 mm Bcw=50
mm Bcw=30
mm Bcw=10
mm Disk
Number
96.82 97.02
97.79 100.21
1
96.06 96.33
97.19 100.29
2
90.76 91.43
93.31 100.85
3
89.99 90.70
92.75 100.90
4
83.99 84.78
88.67 100.00
5
83.08 83.88
88.07 99.87
6
75.80 77.53
83.11 96.85
7
74.70 76.69
82.36 96.27
8
66.02 69.99
76.04 90.77
9
64.72 69.00
75.07 89.85
10
56.96 61.17
67.41 81.54
11
55.87 59.99
66.26 80.23
12
46.89 51.36
56.71 68.99
13
45.57 50.09
55.24 67.31
14
34.97 39.40
44.11 53.32
15
33.40 37.75
42.47 51.28
16
21.73 24.90
28.93 34.44
17
20.04 23.01
26.86 32.15
18
8.17 9.42
11.13 13.76
19
6.48 7.48
8.85 11.01
20 Fig. 10Capacitive network of the disk winding.
148 Iranian Journal of Electrical & Electronic Engineering, Vol. 10, No. 2, June 2014 Table 3 Changes of the impulse voltage on the disks caused
by the changes of Hch.
Impulse voltage on the disks [%]
Hch=20 mm Hch=10
mm Hch=4.5
mm Hch=0
mm Disk
Number
99.99 99.99
97.79 99.99
1
100.57 99.08
97.19 91.85
2
100.57 99.08
93.31 91.85
3
100.32 97.943
92.75 83.56
4
100.32 97.94
88.67 83.56
5
97.76 94.67
88.07 74.93
6
97.76 94.67
83.11 74.93
7
91.91 89.17
82.36 65.94
8
91.91 89.17
76.04 65.94
9
83.37 80.59
75.07 56.41
10
83.37 80.59
67.41 56.41
11
71.57 69.39
66.26 46.84
12
71.57 69.39
56.71 46.84
13
56.77 55.42
55.24 35.74
14
56.77 55.42
44.11 35.74
15
39.59 39.16
42.47 23.66
16
39.59 39.16
28.93 23.66
17
20.96 20.57
26.86 11.71
18
20.96 20.57
11.13 11.71
19
2E-07 2E-07
8.85 2E-07
20
Table 4 Changes of the impulse voltage on the disks caused by the changes of t.
Impulse voltage on the disks [%]
t=1.5 mm t=1.0
mm t=0.5
mm t=0.125
mm Disk
Number
98.33 98.07
97.79 97.53
1
97.90 97.56
97.19 96.77
2
95.25 94.41
93.31 91.63
3
94.87 93.95
92.75 90.90
4
91.53 90.30
88.67 85.56
5
91.01 89.76
88.07 84.78
6
86.68 85.21
83.11 78.90
7
86.02 84.50
82.36 78.04
8
79.93 78.27
76.04 71.32
9
78.99 77.31
75.07 70.33
10
71.00 69.60
67.41 62.46
11
69.82 68.40
66.26 61.29
12
59.79 58.56
56.71 52.47
13
58.27 57.07
55.24 51.16
14
46.16 45.48
44.11 40.09
15
44.49 43.86
42.47 38.40
16
30.69 30.04
28.93 25.47
17
28.56 27.91
26.86 23.57
18
11.90 11.58
11.13 9.72
19
9.46 9.21
8.85 7.73
20
As it is seen from Fig. 12, with decreasing the length of the channel between winding’s disks (Hch), the IVD along the winding will be more uniform, that means the
AIVF on the winding will be decreased. This is because by reducing the Hch, P in Eq. (7) will be reduced and the total series capacitance will be increased. The decrease of impulse voltage on each disk with decreasing Hch in the Table 3 can be observed.
Decreasing the thickness of paper insulation of the conductor (t) has a little effect on the IVD of the disk winding. Since in the capacitive network of disk winding the number of series capacitances is more than the parallel capacitances, the decrease of t has more effect on the value of total series capacitance. So with the decrease of t, the proportion of total series to total parallel capacitances will increase and according to Fig.
13, the IVD along the winding become linear but it is not significant. Also according to Table 4, the impulse voltage on disks will decrease by decreasing t.
To analyze IVD on the winding with respect to changing the dimensions of conductor cross-section, it has been tried to consider the area of conductor cross- section to be constant but with changing its height (h) and width (w). According to Fig. 14, the most uniform IVD on the disk winding can be seen that when the cross-section of each turn of disk has its maximum h and its lowest w. Also Table 5 shows the impulse voltage variation on each disk of winding for various values of w and h.
Table 5 Changes of the impulse voltage on the disks caused by the changes of w and h.
Impulse voltage on the disks [%]
w=9.5, h=6.5
mm w=6.5,
h=9.5 mm w=30.875,
h=2 mm w=2,
h=30.875 mm Disk
Number
96.97 97.79
98.15 97.98
1
96.19 97.19
97.54 97.32
2
90.95 93.31
93.25 92.66
3
90.22 92.75
92.62 91.97
4
85.06 88.67
87.93 86.35
5
84.31 88.07
87.26 85.49
6
78.54 83.11
82.12 78.76
7
77.68 82.36
81.35 77.77
8
70.92 76.04
75.26 70.37
9
69.92 75.07
74.35 69.28
10
62.16 67.41
66.99 60.85
11
61.00 66.26
65.88 59.59
12
51.92 56.71
56.96 49.77
13
50.55 55.24
55.60 48.32
14
40.05 44.11
44.74 37.65
15
38.51 42.47
43.10 36.15
16
26.01 28.93
29.70 24.13
17
24.11 26.86
27.72 22.34
18
9.93 11.134 11.90
9.17 19
7.90 8.85
9.62 7.287
20
In Fig. 15, the maximum and minimum of impulse voltage on the second disk of the winding for various parameters (in Table 1), has been shown. These values have been taken from Tables 2-5 for the second disk.
As it is observed from Fig. 15, the decrease of Hch
has the most impact on decreasing of impulse voltage on the second disk.
Fig. 11 Changes of IVD on the winding caused by the changes of Bcw.
Fig. 12Changes of IVD on the winding caused by the changes of Hch.
Fig. 13Changes of IVD on the winding caused by the changes of t.
Fig. 14Changes of IVD on the winding caused by the changes of w and h.
Fig. 15 Max and min of the impulse voltage on the second disk for the various parameters.
5 Conclusions
In this paper, a typical transformer with disk winding and with the introduced parameters was modeled using software VOLNA and then with changing the parameters of the winding by this software, the variations of the impulse voltage distribution on the winding and the rate of the variation of impulse voltage on each disk of the winding were analyzed. In this study, a disk winding with rectangular cross-section was considered.
In the curves obtained from the software, reducing the amplitude of impulse voltage fluctuations means to reduce the constant of winding voltage distribution and reduction in these two factors means a more uniform impulse voltage distribution along the winding.
In this paper was shown that a change in each parameter of the winding causes the capacitive network and the proportion of total series to parallel capacitance to change and this will cause a change in impulse voltage distribution of the winding.
It was observed that the thickness of paper insulation of the conductor has lowest effect on impulse voltage distribution of the winding but the increase of the distance of the core outer surface to the winding and the
150 Iranian Journal of Electrical & Electronic Engineering, Vol. 10, No. 2, June 2014 decrease of the length of the channel between disks will
improve impulse voltage distribution along the winding.
This result was also obtained that if in the cross- section of each turn of disk the height (on metal) be maximum and the width (on metal) be minimum, the most uniform of the impulse voltage distribution on the disk winding will obtained.
References
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[3] S. V. Kulkarni and S. A. Khaparde, Transformer Engineering Design and Practice, New York Marcel Dekker, INC., 2004.
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Naderi, “Impulse voltage distribution in intershield disk winding VS interleaved and continuous disk winding in power transformer”, IEEE International Conf. on Power and Energy, pp. 387-392, December 2008.
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Heidarzadeh, “Influence of electrostatic shielding of disc winding on increasing the series capacitance in transformer”, IEEE Lausnne Powertech, pp. 1780-1784, 2007.
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Mojtaba Heidarzadeh was born in Sari, Iran, in 1986. He received the B.Sc.
degree in electrical engineering from Babol Noshirvani University of Technology, Iran, in 2009. Now, he studies M.Sc in electrical engineering at Shahed University, Iran. His research interests are high voltage engineering and transformer calculations. Now, he is working at the Department of Transformer, Iran Transformer Research Institute, in section of transformer calculations.
Mohammad Reza Besmi was born in Tehran, Iran, in 1959. He received the B.Sc. degree in electrical engineering from Amirkabir University, Iran, in 1989, the M.Tech degree in electrical engineering from University of Indian Institute of Technology, Delhi in June 1992 and the Ph.D. degree in electrical engineering from Newcastle upon Tyne University in September 1996. From 1997 to 1999, he was with the Niroo Research Institute in Iran. He is currently Assistant Professor of Electrical Engineering Department. His current research work is in special electrical machine design.
