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301
Vertically Ashfaq Ahmad
1 , Iqra Javed
2 , Waseem Nazar
1,3 The University of Lahore Department of Electronics
2 University of Management and Technology Department of Informatics and Systems
Abstract— The objective of this research is to compute the
mechanical stresses in power transformer resulting from the
currents more than rated value during its operation. Due to
this high fault current, mechanical stresses are produced
indifferent directions which may cause the damage of winding
insulation. Various techniques have been adopted to analyze
the stresses on transformer windings. For the
accomplishment of research, FEM (Finite Element Method) is
utilized for the calculation of short circuit forces. All
mechanical generated in transformers are calculated
mathematically and verified through software. For the
verification of results, real time measurements on 20MVA 132
/11.5KV power transformer are made. Various failure
mechanisms due to these forces have been discussed.
Moreover, design parameters which determine the maximum
stresses in different parts of the transformer are also the part
of research. Effects of asymmetrical current and forces in
various parts of transformer have also been narrated.
Moreover, Different properties of materials have been studied
and the usage of proper material for withstanding the
dynamic effects of short circuits is discussed. Workmanship
errors on short circuit withstand capability have also been
elucidated. Finally, a complete model for the study of dynamic
effects of short-circuits in a power transformer and
comparison with forces calculated with FEMM soft ware [13].
Keywords— Finite element method; Power transformer;
Short circuit stress; Mechanical Stresses; Axial and Radial
Stresses.
Government and utility companies have started expansion
of generation stations which include interconnections of
national grids. Due to these additions, the short circuit
current of the system has increased where many sources of
power are available to feed faulty location on the
occurrence of event. All the components in the system are
affected by this change including transformers which have
to bear heavy currents. A large number of transformers in
power system have been reported to fail due to prolonged
heavy current.
Data collected from the High Voltage testing laboratory
shows that one fifth of the transformers under test are failed
due to weak insulation which ultimately bear short-circuit
current. It is important to mention that the transformers
which have to undergo this test, are manufactured with
almost and special care in the manufacturer‘s premises
[9, 10]. Lack of insulation strength of transformers imposed
by manufacturers can cause severe damages to the
transformer as well as the system. System disruption
include following effects;
Broken pressure plates on windings
Bending of clamping structure
Bulging of tank body
Section-II discusses types of short circuits in power
system, section –III narrates the forces which are produced
due to short circuit current while remaining sections
include axial and radial forces acting on windings, and last
section describes the fem calculations results of forces
acting on transformer windings [5].
II. SHORT CIRCUIT CURRENTS
Almost all types of faults cause the sudden rise of
current in power system which results in malfunction and
inconsistent operation of installed equipment along with
severe effect on transformer insulation.
Usually, the three-phase faults are the most severe of all;
hence the transformer should be designed to withstand the
effects of symmetrical three phase faults. It must be
mentioned here that in some cases (Where a tertiary
connected winding is present), the single-phase to line fault
short-circuit current can be higher than the three-phase
fault on those windings, since it is related to very special
cases, emphasis is made on symmetrical three-phase faults
only.
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302
windings, the r.m.s value of the symmetrical short-circuits
current I shall be calculated as in equation (i) [1].
(i)
Where:
consideration, in Kilovolts
referred to the winding under consideration, in ohms per
phases
Zs: is the short-circuit impedance of the system, in ohms
per phase
As mentioned above, due to addition of more and more
generating stations within an interconnected system, the
source impedance Zs is very small and generally neglected
for calculations purpose.
Consider the circuit given alternate voltage source.
Assuming that the below with an switch is closed at t=0
instant, which simulates the short-circuit, the expression for
the current i(t) can be written as follows:
Fig 1A Sinusoidal voltage source switched on to an RL network
i(t) = Imax[sin(t-)]
t: Time, in seconds
: Time constant [L/R]
The plot of this current expression with respect to time is
as under:
Fig.2 A Sinusoidal voltage source switched on to an RL network
The mechanical strength of the transformer windings
should be such that it shall withstand the highest short-
circuit forces generated which correspond to the first
current peak in the figure above, since this current peak has
the highest magnitude due to presence of DC component in
the current pattern.
During short-circuit, a very high current flows within the
windings of the transformer. However, the duration of
short-circuit is very small, the temperature of the windings
generally do not rise high enough to damageable values.
Hence, this effect can generally be neglected.
IEC 60076-5 however, gives a formula for the
calculation of temperature rise during short-circuits. This
formula assumes that all the heat produced by the winding
during short-circuits stays in it and none is dissipated. This
is a poor assumption, but since the limit of allowable
temperature rise is high (250 o C), almost all the
transformers qualify this requirement during short-circuit
testing.
1attained by the winding after short circuit is calculated
by the equation (ii) [2].
(ii)
Where
Celsius
t: is the duration, in seconds (s)
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conductor, whose magnitude is given by equation (iii).
F=B.I.L sinα (iii)
I: Current in the conductor, in Amps
L: length of current carrying element, in meters
α: angle between flux density vector and current vector
This force is called the electromagnetic force because
it is produced both by combined effect or electric current
and magnetic flux. [12] The direction of this force can be
easily computed using the well-Known Left-hand rule.
A. Electromagnetic Forces
components if we model it in 3D cylindrical coordinates.
r-component
z-component
-component
The r-component of the electromagnetic forces results in
the radial forces that act on the windings [8]. The z-
component is the originator of the axial forces that act on the windings. Finally, the -component can cause twisting
motion of the windings, but it is never present because the
center axis of the windings is always coinciding with each
other.
forces is by solving equation (iii), using data of the
transformer from the design calculation sheets. This
calculation, however, assumes a lot of data which can
sometimes result in a very safe calculation and, else wise,
could result in unsafe margins during calculations.
B. Approximations in analytical formula
The analytical method of calculating the short-circuit
forces assumes certain data, most prominent of which are:
Conductors are tightly wound radially on top of each
other and thus the radial short-circuit forces act over
the average circumference of the windings.
Presence of axial cooling ducts can result in
appreciable error in the short-circuit forces
calculations which is ignored in the analytical formula
[8].
change which is again ignored in the analytical
formula of short-circuit forces calculations.
Portion of windings under the yoke have a different
leakage field pattern compared to portion outside the
window. Again this phenomenon is ignored in the
analytical formula.
windows is ignored in the analytical formula.
Combined (axial and radial) forces at the winding
ends which are the major cause of tilting of the
conductors are neglected in analytical formula.
Axial imbalance of windings during manufacturing is
neglected in the analytical method of forces
calculation. This imbalance usually occurs during
shifting over of windings over the core where the
centerline of windings is not exactly the same.
Axial imbalance within the winding (which is
normally due to presence of radial spacers in the
windings) is ignored. During manufacturing of
winding on the winding machines, height of windings
has to be maintained by placement of radial spacers
within it. The position of placement of these stabilization spacers can shift the centerline of the
winding which cannot be ignored.
IV. FINITE ELEMENT MODELING
Finite element method (FEM) is a numerical method
mainly used for solving Differential and Integral Equations.
Essence of this method is to divide the application
domain in very small sub domain elements called as finite
elements. Problem is subdivided into Finite size sub
problems and is independently dealt to find complete
problem solution.
incorporating the Finite Element Method Solution. In this
thesis, a software tool titled meshing and finite element
solver has been used [3]. The model has been drawn using
MATLAB with complete computation of leakage flux and
therefore short-circuit forces.
In transformers, finite element method can be used to
calculate the following quantities:
Electric field analysis
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Finite Element modeling is a highly accurate method of
calculating the transformer parameters. The FEM formation
makes use of the fact that poison‘s partial-differential
equation is satisfied when total magnetic energy function is
a minimum [4].
1- The geometry to solve (which is basically the core
and set of transformer winding represented simple as
rectangular blocks) can be drawn using most CAD
programs. In this work, Auto Cad 2010 is used to
drawn the geometry in .dxf format.
2-
Fig. 3 Geometry of the transformer
3- Once the geometry is ready, it is then divided in to
finite elements i.e. small elements. The smaller the
size of each mesh or element, the higher will be the
accuracy of the results can be obtained if problem is
divided into number small problems. Different models
and geometries of transformer for the application and
calculations are given in fig 4, 5, 6 and 7. while fig. 8
and 9 gives flux plots of transformer which are
important to obtain while calculating short circuit
effect on power transformer windings.
Fig. 4 Meshing of the transformer geometry
4- The properties of each of the blocks drawn, is then
assigned along with the boundary conditions. Since
core has a very high relative permeability value, it
will not store any appreciable energy. Hence, it
doesn‘t matter whether core is given a relative
permeability of 10,000 or 100,000. When assigning
the properties to the windings, it must be made sure
that the ampere-turns of all the winding regimes must
be equal and opposite, so that no mutual component
of flux in the core should exist.
5- The space filled with oil is assigned a relative
permeability of 1, including the windings.
6- The geometry is solved in the FEM solver and the
flux leakage plot obtained:
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305
MOVEMENT
performed.
mm, 10-mm, 15-mm is chosen for vertical respectively.
The results and geometry model for these movements
are given as below in fig.6.
Fig. 6 Geometrical model
displaced in vertically as shown below
Fig. 7 Mesh model
Fig. 8 Flux plot
fluxes obtained from FEM measured forces obtained from
FEMM by setting properties of core, oil, LV, HV windings
etc. It also includes comparison plots of forces obtained by
mat lab.
of FEMM.
Forces at the winding centre are purely radial.
Inner winding is subject to buckling effect.
Outer winding tends to stretch out.
Forces at the winding ends have both axial and radial
direction [7, 11].
given below which are extracted from [6,7].The minimum
flux density is shown with light color while maximum flux
density is present at top middle and bottom turns of
winding. Different colors show the level of flux produce in
windings followed by measurement of H.V and L.V forces
at bottom and in different positions in windings with the
help of FEM. Results are concluded by comparing the
results of FEMM and measurements made mathematically.
In given below flux density plots as in fig. 9, various levels
of flux densities are presented by different colors.
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VI. VERTICAL WINDING FORCES
different displacement is given below in fig. 10.
Fig. 10 Comparison of LV forces in winding
From the above plot in fig. 10, it is clear that in early
turns the negative forces are dominant and in middle of the
turns the forces approach to zero because of cancelation of
effect of the negative and positive forces. This force
applied on winding pattern is same for the displacements of
0-mm, 2-mm and 15-mm. The only difference is the
windings having less displacement has tendency of
negative forces to approach from negative to zero more
quickly and forces approach from zero to positive more
slowly and vice versa. The left side of the above plot of
fig.10 is the forces plot when high voltage winding
displaced at 5-mm and 10-mm, it is clear that in early turns
the negative forces are dominant and the middle turn forces
approach negative to positive, in the last turns again
negative forces are dominant.
different displacement is given below in fig. 11.
Fig. 11 Comparison of HV forces in windings
From above plot it is clear that in early turns the
negative forces are dominant and in middle of the turns the
forces approach to zero because of cancelation of effect of
the negative and positive forces. This force applied on
winding pattern is same for the displacements of 0-mm, 2-
mm and 15-mm. The only difference is the windings
having less displacement has tendency of negative forces to
approach from negative to zero more quickly and forces
approach from zero to positive more slowly and vice versa.
The left side of the above plot of fig.11 is the forces plot
when high voltage winding displaced at 5-mm and 10-mm,
it is clear that in early turns the negative forces are
dominant and the middle turn positive forces are dominant,
in the last turns forces are approach positive to negative
and saturated.
plots of LV and HV forces in windings at different
displacement. The Fig.12 and Fig.13 shows the individual
plots of forces in winding at different displacements 0-mm,
2-mm, 5-mm, 10-mm and 15-mm respectively.
Fig.12 Individual LV forces in winding at different displacement
Fig.13 Individual HV forces in winding at different displacement
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The comparison plot of LV forces at bottom of windings
at different displacement is given below in fig. 14.
Fig. 14 Comparison of LV forces At windings
From the above plot it is clear that accumulated forces
are minimal in upper and bottom turns. Whereas
accumulated force is maximum at middle turns of
windings. The accumulated force increases from zero to a
constant maximum value earlier at winding having less
displacement and decreases from maximum value to zero
late in bottom turns and vice versa for windings with more
displacement. This force applied on winding pattern is
same for the displacements of 0-mm, 2-mm and 15-mm.
The forces plot when high voltage winding displaced at 5-
mm and 10-mm, it is clear that in early turns the positive
forces are dominant and the middle turn negative forces are
dominant, and in the last turns forces are approaches to
zero and saturated
The comparison plot of HV forces at bottom of windings
at different displacement is given below in fig.15.
Fig. 15Comparison of HV forces at windings
From the above plot it is clear that accumulated forces
are minimal in upper and bottom turns. Whereas
accumulated force is maximum at middle turns of
windings.
maximum value earlier at winding having less
displacement and decreases from maximum value to zero
late in bottom turns and vice versa for windings with more
displacement.
This force applied on winding pattern is same for the
displacements of 0-mm, 2-mm and 15-mm. The forces plot
when high voltage winding displaced at 5-mm and 10-mm,
it is clear that in early turns the positive forces are
dominant and the middle turn negative forces are dominant,
and in the last turns forces are approaches to zero. The Fig.16 and Fig.17 shows the individual plots of
forces at winding on different displacements 0-mm, 2-mm,
5-mm, 10-mm and 15-mm.
VII. CONCLUSIONS
prolonged high currents in power transformer windings
have been evaluated. High temperatures generated inside
transformer may puncture its insulation which causes
breakdown. As Power transformer is very expensive power
system apparatus which is needed to be protected with first
priority. That is why its failure avoided and comprehensive
analysis is done to cater all drastic situations which may
cause its complete failure. This research will enable the
transformer manufacturers for careful design of transformer
and the power utility authorities to ensure its safe operation
in power system.
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308
REFERENCES
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withstand short circuit.
Version 4.2 Online available: http://femm.foster-miller.com.
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