International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)

301

Short Circuit Stress Calculation in Power Transformer Using

Finite Element Method on High Voltage Winding Displaced

Vertically Ashfaq Ahmad

1, Iqra Javed

2, Waseem Nazar

3

1,3The 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.

I. INTRODUCTION

Due to continuous growth in demand of electricity,

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 manufacturers 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;

Deformation of LV and HV windings

Broken pressure plates on windings

Bending of clamping structure

Bulging of tank body

Collapse of bushings

Short-Circuited tapping leads

Rest of the paper organized as follows;

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.

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)

302

A. Value of symmetrical short-circuit current

For three-phase transformers with two separate

windings, the r.m.s value of the symmetrical short-circuits

current I shall be calculated as in equation (i) [1].

(i)

Where:

U: is the rated voltage of the winding under

consideration, in Kilovolts

Zt: is the short-circuit impedance of the transformer

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.

B. Nature of short-circuit current

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-)]

Where:

Imax: Maximum value of the current i

t: Time, in seconds

: Phase angle of the circuit impedance [tan-1(L/R)]

: 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.

C. Thermal withstand during short-circuit

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

oC), almost all the

transformers qualify this requirement during short-circuit

testing.

According to IEC 60076-5, the average temperature

1attained by the winding after short circuit is calculated

by the equation (ii) [2].

(ii)

Where

o: is the initial winding temperature, in degrees

Celsius

J: is the short-circuit current density,

t: is the duration, in seconds (s)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)

303

III. SHORT-CIRCUIT FORCES

When a current carrying conductor lies in a magnetic

field, a force is produced upon that current carrying

conductor, whose magnitude is given by equation (iii).

F=B.I.L sin (iii)

Where:

B: flux density, in Tesla

I: Current in the conductor, in Amps

L: length of current carrying element, in meters

: 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

In transformers, electromagnetic forces may have three

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.