Impulse Voltage Calculation Of Transformer

Modelling and Analysis of Non Uniform Impulse Voltage and Current Distribution of a Capacitive Transformer Winding Model Using Electro Magnetic Transients Program P. sai charan reddy Aurora’s Engineering College, Bhongiri. Abstract: Transformer plays a crucial role in electrical power transmission and distribution from the power generating stations to the load centres. Any failure in working of a healthy transformer may lead to enormous problems which can turn out to be very costly to be repaired and may ultimately result in power outages.

Recent study of modern transformer breakdown reveals that most of the transformer failures are traced to winding faults. These winding faults are mostly a result of the following cases like degradation of insulation system due to thermal, electrical and mechanical stresses, design and manufacturing errors, due to interior short circuit, over loading and line surges, improper maintenance and operation problems due to inadequate attention to loose connections. Terminal values like primary and secondary side currents and voltages convey information that can be used to analyse transformer winding faults. By simulation of the parameters such as series and shunt capacitances of windings, it would be possible to explore the behaviour of transformer winding by studying the impulse voltage distribution within the winding. Major faults in the transformer winding are due to insulation failure that results in changes in capacitance values of the transformer winding. As an effort to characterize the behaviour of transformer winding from the variations in the

parameters during faults, analysis of the non uniform impulse voltage distribution of a capacitive transformer winding model is done using Electro Magnetic Transients Program (EMTP), which is a powerful and superfast computational engine that provides significantly improved solution methods and user defined models.

I. Introduction Transformers are used to step up voltage before transmitting electrical energy over long distances. The conducting material used for the windings in a transformer depends upon the application, but in all cases the individual turns must be electrically insulated from each other to ensure that the current flows throughout every turn. Transformers are designed to withstand a variety of stresses and mechanical forces during their service life. Abnormal forces generated during shortcircuit is the main cause of deformation of winding and core. Rough transportation and unskilled handling is the other known cause. However it is an unfortunate fact that despite even the most rigorous preventative maintenance program, failures can and will occur. The mechanical force depends on configurations of windings [1]. Furthermore, it varies due to deformation and displacement of transformer windings. An increase of dielectric related failures of transformers with unknown specific reasons justifies revising capacitive model

of the transformer winding for analyzing the impulse voltage distribution for various conditions in a transformer winding using EMTP.



Insulation between layers of a winding

II.Block Diagram

Fig.2. Representation of transformer winding with various capacitances

Fig. 1. Block diagram

The capacitive winding model of a transformer winding is designed after calculating various capacitance values within a transformer. An impulse voltage is injected into the winding model. The variations in the impulse voltage distribution curves for various fault conditions within a transformer winding are analyzed to locate the fault. The above Fig.1 shows the complete block diagram of how fault analysis is done.

A. Representation Capacitances

of

Winding

Transformer winding insulation is a composite dielectric system [3], located between the electrodes, i.e., winding conductors and grounded parts of transformer. Fig.2 shows various capacitances in winding The most important components of the main transformer insulation are:  Insulation between winding and tank 

Insulation between winding and the magnetic core



Insulation between HV winding and LV winding

The main contributions to the selfcapacitance in a transformer whose winding is divided into several sections made out of different layers are the following:  Turn-to-turn capacitance (CTurn) 

Disc-to-disc capacitance (C1, C2)



Winding-to-magnetic core (C3,C4)



Inter winding interactions. (C5)

B. Winding Deformation versus Parameter Changes The transient overvoltage caused by the operation of the switches in the primary circuit will be coupled into the secondary circuits, thus the normal operation of the secondary circuits may be interfered with the over voltages. Strike of voltage surge to a transformer results in a nonlinear voltage distribution along the winding and very high stresses at the critical points on its insulation. At site, lightning impulses, switching surges and cable faults may cause the winding deformation. In addition, the winding may deform due to impact during transportation. The deformations result in the change in the capacitance values since there will be short circuit occurring between a disc of the

winding and core or between two discs of a winding.

C. Need For Modelling To know the extent of damage and its location in the winding [2], obviously an approach that would circumvent disassembly of the winding would be most attractive. In order to carry out the research of the effect of voltage surges on the transformer winding, it is very necessary to establish a model of the transformer windings, which is helpful to provide the theoretical basis to prevent the damage of the transformer insulation and improve the design of the transformer.

such voltages. These voltages are of the nature of an impulse wave, a half cycle of voltage characterized by a rapid rise to its crest and a slow decline to zero. The more rapid the rise and the slower the decline, the more severe is the effect of the impulse voltage on the winding. When an impulse voltage is given to a winding of a transformer [5], as there is the presence of the inter winding capacitance and the capacitances to earth of the transformer windings, the upper elements of the transformer windings tend to be more heavily stressed than the lower portions. Due to the velocity of propagation, of the impulse voltage would not be evenly distributed in the winding. On the top portion of the node where the stress is low the voltage is high. The voltage at the bottom nodes gradually reduces as the stress on the each node increases and also due to velocity of propagation of the impulse wave. Hence there is an linear decrease in the voltage of an impulse in a transformer winding during impulse voltage. E. Importance Of Capacitance In

Winding Fig.3. Representation of transformer with various capacitances

Disassembling a winding is an expensive and time-consuming exercise, and this should evidently be the last resort. Therefore, the main objective is to demonstrate localization of winding deformation based on impulse voltage distribution in the transformer winding.

D. Impulse Voltage Distribution Lightning voltages are responsible for the greatest insulation stresses in a transformer winding in practice, and it is proper to consider here the transient voltage characteristics [5] of a transformer winding, as they would be exhibited under

When a step voltage impinges on the transformer winding terminals, the initial distribution in the winding depends on the capacitances between turns, between windings, and those between windings and ground. The winding inductances have no effect on the initial voltage distribution since the magnetic field requires a finite time to build up and as it is known that current in an inductance cannot be established instantaneously. Since the duration of the impulse voltage applied to the terminals of the transformer winding is very small, the voltage across the capacitance [3] builds up before an appreciable inductive current establishes in the winding. The presence of coil capacitance causes the transformer to respond as a capacitor

and not as an inductor to abrupt impulse voltages. Thus, the inductances practically do not carry any current and the voltage distribution is predominantly decided by the capacitances in the network, and the problem can be considered as entirely electrostatic without any appreciable error. In other words, the presence of series capacitances between winding sections causes the transformer to respond to abrupt impulses as a network of capacitances. By representing the transformer winding as a network of elements, the field problem is effectively converted into a circuit problem. III. MATHEMATICAL MODELLING OF TRANSFORMER WINDING A 1MVA, 33/11 KV, shell type of transformer is considered. The mathematical calculations have been done for finding out all the parameters required for modelling. Using the formulae provided in the existing literature, all the dimensions needed to calculate various types of capacitance in a transformer winding are derived. Using these dimensions of the transformer internal geometry, capacitance values can be calculated. A model of the transformer winding is then prepared by building the capacitance winding network. Rating of transformer 33/ 11 kv, 1MVA Emf per turn, Et= K S (S is in KVA) (K=1.0 for shell type transformer) Et= 1.0 1000 emf/ turn Number of turns on the H.V side (N1): 33  103 N1= 3 =600 turns _______ (1) 31.62 Number of turns in each disc on the H.V. winding = 25 turns Therefore, from equation (1) number of discs on H.V. winding = 24 discs Number of turns on the L.V side (N2): 11  10 3 N2= 3 =200 turns _______ (2) 31.62

Number of turns in each disc on the L.V. winding = 8 turns Therefore, from equation (2) number of discs on L.V. winding = 25 discs 1000 Current on H.V side = 33 =53A 3 1000 Current on L.V side = 11 =157A 3

Cross sectional area (a1) of the conductor I1 53 a1= = =24.09mm2 Current density 2.2 (3)

_

Assume current density = 2.2A/mm2 a2= I2 = 71.54 mm2 ___ Current density

Area of the iron core Ai =

(4)

Et 4.44  f  Bm

Where, Bm =1.35 wb/m2 Ai =

31.62 = 0.105 m2 4.44  50  1.35

Since, Area = d=

d2 ; diameter of the core 4

0.105 = 36 cm 0.785

_______ (5)

Fig.4. Cross-sectional view of disc configuration

From the obtained calculations, the geometrical view of transformer and its winding has been designed as shown in the Fig.5

Fig.5. Geometrical view of complete transformer

Capacitance between two discs of LV winding (C1): 2

2

A   (r2  r1 )   (26 2  20 2 )  0.0867m 2 d  ( 2  1) mm  3  10 3 m

  1.95  10 11 F / M A

 563.55  10 12 F ______ (6) D Capacitance between two discs of HV winding (C2): C1 

2

2

A   (r2  r1 )   (33 2  23 2 )  0.1759m 2 d  (5  1)mm  6  10 3 m

  1.95  10 11 F / M A C2 

D

 517.74  10 12 F _______ (7)

Fig.6. Top view of transformer winding

Capacitance between LV winding and core (C3): 2l  12.79  10 12 F r C3= ln( 2 ) r1 _______ (8) where, r =18cm,r =20cm and l =11mm Capacitance between HV winding and core (C4) : 2l  4.298  10 12 F C4= ln( r2 ) r1 ______ (9) where, r =18cm,r =23cm and l = 8.6mm 1

2

1

2

Capacitance between LV and HV winding (C5 ): 2l  10.99  10 12 F r C5= ln( 2 ) r1 _____ (10) where, r =26cm,r =29cm and l = 9.8mm 1

2

Fig.7. Various winding capacitances representation

From the above data which has been acquired, the transformer winding is made into a network of capacitances as shown in Fig.7 From the equations 6, 7, 8, 9, 10:  C1 : Capacitance between two LV windings = 563.55  10 12 F 

C2 : Capacitance between two HV windings = 571.74  10 12 F



C3 : Capacitance between LV winding and core = 12.79  10 12 F



C4 : Capacitance between winding and core 2l  4.298  10 12 F r2 ln( ) r1

HV =



C5 : Capacitance between winding and HV winding 10.99  10 12 F

LV =

IV. EMTP Winding

Model

of

Transformer

The complete winding of transformer is made into a capacitive winding network considering the capacitances between the two discs, capacitance between the windings and also between the core and winding forming a capacitive transformer winding network as shown in Fig 8. Twenty five discs in LV winding and twenty four discs in HV winding are considered. Each disc is represented with each node as shown. This forms a discs configuration of the LV and the HV winding in the manner of 1:1 as represented in the Fig.7. An impulse voltage is injected at node 2 to observe voltage distribution throughout the winding for normal and various fault conditions. A resistor is placed between node 27 and the ground for measurement of impulse voltage distribution with in the transformer winding.

Fig.8. Capacitive winding model

V.Simulation Results and Analysis A.Impulse Voltage Distribution When an impulse voltage is given to a winding of a transformer, as there is the presence of the inter winding capacitance and the capacitances to earth of the transformer windings, the upper elements of the transformer windings tend to be more heavily stressed than the lower portions. Due to the velocity of propagation, of the impulse voltage would not be evenly distributed in the winding. On the top

portion of the node where the stress is low the voltage is high. Hence there is a linear decrease in the voltage of an impulse in an transformer winding during impulse voltage. B.Results Of Capacitive Winding Model Various results have been observed when the impulse voltage is given to the capacitive transformer winding model under different fault conditions.

1. Impulse Voltage Distribution under Normal Condition The simulation has been done by injecting an impulse voltage at node 2. The change in the voltages at different nodes has been tabulated in Table 5.1 from the tabulated values a graph has been plotted shown in Fig.9.

Table 1 Impulse voltage distribution under normal conditions NODES

VOLTAGE

2

95710

5

56833

7

40848

12

18869

17

9149

26

907.3

27

0.00184

• The graph shows the impulse voltage distribution of a transformer winding at normal condition. • It is observed that the voltage injected at the node2 (95,710V) has decreased gradually and dropped to (0.00184V) at node27.

2. Results under short circuit between core and winding The below table 2 depicts the different voltages at different nodes during fault condition which occurred between winding and the core and a graph is plotted for this fault condition shown in Fig. 10.

Table 2 Impulse voltage distribution during S.C between core and winding NODES

VOLTAGE

2

95710

5

0.000389

7

1030

12

1525.5

17

1119.8

26

149.54

27

0.00302

Fig.10. Voltage distribution during Short circuit between core and disc Fig.9 Impulse Voltage Distribution at Normal Conditions

• This graph shows the impulse voltage distribution of the transformer winding for short circuit of a disc with the core.

• The voltage has dropped drastically at the node5 (0.000389V) that has been shorted to core (ground). • The injected impulse voltage has been diverted to ground at the particular disc5 that has been shorted to core.

C. Results under Short Circuit between Two Discs of Winding

Fig.11. Voltage distribution during inter disc short circuit

• This Fig.11 shows the impulse voltage distribution of the transformer winding for short circuit between two discs (5 and 6). • The voltage has flattened at the node 5-6 during inter-disc short circuit when compared to the normal impulse voltage distribution.

The table 3 shows the different voltages at different nodes during a short circuit condition between two discs. Fig.11 shows impulse voltage distribution under these fault condition.

• This indicates that almost same voltage flows through the two different nodes which are shorted.

Table 3 Impulse voltage distribution during S.C between two discs

The simulation performed under various fault conditions are shown in table 4. i.e impulse voltage distribution under normal conditions, short circuit between two discs and short circuit between core and disc. From these values a graph is plotted shown in Fig.12 under various conditions.

NODES

VOLTAGE

2

95710

5

53865

7

45622

12

20826

17

10009

26

983.4

27

0.00203

D. Comparison of the Results

Fig.12 Impulse voltage distribution at various conditions

Table 4 Impulse voltage distribution under various conditions NORMAL CONDITION NODES

VOLTAGE(V)

INTER DISC S.C

S.C BETWEEN CORE AND DISC

VOLTAGE(V)

VOLTAGE(V)

2

95710

95710

95710

5

56833

53865

0.000389

7

40848

45622

1030

12

18869

20826

1525.5

17

9149

10009

1119.8

26

907.3

983.4

149.54

27

0.00184

0.00203

0.302

Examining the output plots of all the three cases, at a time, shows the variations for each case. This makes it easy to identify the condition of the transformer winding like normal condition or inter disc short circuit or the core and the disc short circuit for an injected impulse voltage. E. Current distribution. On application of impulse voltage wave on the transformer winding model, the current through the winding is distributed. A series combination of resistor and inductor is placed between node 27 and the ground for measurement of current. Under normal condition current through this series combination is 1.722A.when the fault is occurred its value changes. Also changes with the type and location of fault and shown in the table 5.

Fig.13. Current through series combination during inter disc short circuit.

In Fig.13 shows the Current through series combination during inter disc short circuit of the transformer winding for short circuit between two discs (5 and 6). 

Under this condition the current valve changes from 1.722A to 1.920A.



Short circuit between two discs will increase the current valve.

Fig.14. Current through series combination during Short circuit between core and disc

In Fig.14 shows the Current through series combination of the transformer winding during short circuit of a disc with the core.  Under this condition the current valve drastically changes from 1.722A to 0.29009A. 

The current is diverted towards the ground through the fault .So, current valve has been drastically reduced.

Table 5 Current distribution under various conditions Fault location

Faulted condition current through RL(amps)

Node 05 to Core

0.29009

Node 16 to Core

0.50220

Node 27 to Core

0.001748mA

Node 05 to Node 06

1.920

Node 15 to Node 16

1.850

Node 26 to Node 27

2.137

VI. Conclusion Winding deformations or displacements in a transformer may occur during transport or after some use at a site or due to shortcircuit forces. Every transformer winding has a unique signature that is sensitive to changes in the parameters of the winding, namely resistance, inductance, and capacitance. The values of series and ground capacitances have been chosen so as to facilitate the experimental verification. Strike of a lightening stroke to the high voltage terminal of a power transformer results in a non linear voltage distribution along the winding and very high stresses at critical points on its insulations. The magnitude of the series capacitance of the windings has the main role on this impulse voltage distribution. The capacitive winding model of a transformer is very sensitive to any deformation or displacement of the winding since major faults in the transformer winding are due to insulation failure that results in changes in capacitance values of the transformer winding.

The EMTP model of a transformer is a very simple and effective method for diagnosing transformer condition. The technique is also very reliable for detecting any short circuit between winding and to the core quickly, prior to any major operation that is carried out on the transformer. Results from a measurement can be analyzed through several techniques via graphical presentation. However, reference is needed for better interpretation. The reference can either be from historical data of the same transformer or from a new transformer. The interpretation of the results is meanwhile a great help in determining further action to be taken especially for suspected transformers. The task of localizing discrete changes is demonstrated using a model winding and an actual transformer winding. The localization accuracy achieved was reasonably good in all the experimental cases presented. Capacitive winding model can be a very effective tool for condition monitoring. It can avoid catastrophic failure in transformers and also help maintenance engineer to estimate time and cost for repairing the transformer after the fault before undertaking maintenance.

References [1] Aravind Singh “High frequency simulation of transformer windings for diagnostic tests”, a master thesis for the University of British Columbia, Feb. 2006. [2] M. Heindl, S. Tenbohlen and R. Wimmer “Transformer modeling based on standard frequency response measurements” XVII

International symposium on high voltage engineering, Germany, August 22-26, 2011.

Conference on Electrical Engineering, 2008, No. O-141.

[3] Luca Dalessandro “Self-capacitance of highvoltage transformers” IEEE transactions on power electronics,. vol. 22, no. 5, September 2007

[5] “Surge wave distribution over the power transformer continuous disc winding”, Elektrotehniski Vestnik,. 78(3): 106-111, May 2011

[4] Bhageri, Mehdi and Vakilian “Simulation and comparison of impulse voltage distribution in continuous, intershield and interleaved disc winding in power transformer”, The International

[6] A text book on EMTP by Dr. Hermann W. Dommel