1
Abstract-- in this paper, voltage distribution and maximum
electric field intensity in power transformer windings, using
various electric shields are studied. The study covers disk type
and layer type windings. According to the results, disk-type
windings with inter-turn shields have the best voltage
distribution under lightning impulse conditions.
Keywords - transformer winding, lightning overvoltages, high
voltage shields, voltage distribution, potential gradient
I. INTRODUCTION
xcessive voltage of network over its nominal rate is called
overvoltage, which may appear in transient or temporary
form in electrical network. One the most important types
of transient overvoltages are caused by lightning. It is not
distributed uniformly in transformer winding and produces
significant voltage gradient at the beginning of the winding,
which can result in electric breakdown of transformer
insulation. Standard lightning waveform is determined by rise
time T
1
, the time which waveform reaches to 90% of its peak
value and back time T
2
which waveform passes the peak value
and is reduced to half of the peak. Thus, lightning waveform is
introduced by
2 1
/ T T . In lightning waves, T
2
in more than 54%
of the cases is greater than 40 μs, and T1 in more than 70% of
the cases is more than 1.2 μs. therefore, standard lightning
voltage waveform is defined as s s μ μ 50 / 2 . 1 which is used in
voltage impulse tests.
Frequency of lightning impulses can reach hundreds of
thousand kHz. Thus, substantial capacitance of winding
cannot be ignored despite normal 50Hz situations. According
to equivalent circuit of Fig. 1, parallel and series capacitances
are considered between windings and grounded components
(i.e. core, tank, etc) and between disks, layers and turns,
respectively. Just after the application of a step voltage to the
winding, voltage distribution is completely controlled by
capacitance values. Charging current of the first capacitances
is more than that of the second ones due to the current paths.
Therefore, voltage drop on different capacitances is different.
Thus the voltage distribution is not uniform at all. Complete
capacitance network is very complicated. Differential equation
of voltage location in each point of winding with this
capacitive model is as follows:
0 v
Į
v/dx d
2
2
2 2
= -
A
(1)
If winding end is grounded, the answer is:
() ( ) Į sinh
Įx
sinh U x v
A
= (2)
Where, U is the amplitude of the applied voltage at the
winding terminal, v(x) is the voltage at any point of the
winding, l is the winding length and α is the winding
capacitance index, which is defined as:
S
P
C
C
= α (3)
Where, Cp and Cs are the whole winding parallel and series
capacitance, respectively. According to the above equations,
greater series capacitance results in more uniform impulse
voltage distribution and then lower stress on winding
insulation. Greater α results in more uniform field and less
insulation damage in insulation system [1-5].
Increasing the series capacitance of the winding highly
uniforms this distribution. Normally transformer
manufacturers reach to this aim by interleaving the winding
turns. This method is costly and time consuming. In [6], the
electrostatic shielding, used in disc windings to increase the
windings series capacitance, and for linearization of its
impulse voltage distribution is introduced and its impact on
the modification of impulse voltage distribution is compared
with the disc winding without shielding.
Figure 1- equivalent circuit of a single layer winding.
Also in [7], an electrostatic shielding is introduced in the disk
winding to increase the winding equivalent series capacitance,
and consequently linearize the impulse voltage distribution. Its
impact on impulse voltage distribution is evaluated by
Comparative Study of the Effect of Various
Shields on Lightning Electric Field in Power
Transformer Windings
M. R. Meshkatodini, A. Shahmohammadi, M. Majidi and M. Karami,
Electrical Engineering Faculty, Power and Water University of Technology, Tehran, Iran,
E
Paper accepted for presentation at the 2011 IEEE Trondheim PowerTech
978-1-4244-8417-1/11/$26.00 ©2011