# C L WADHWA HIGH VOLTAGE ENGINEERING PDF

Read High Voltage Engineering book reviews & author details and more at C L Wadhwa, was a former Professor and Head, Department of Electrical. High Voltage Engineering [C.L. Wadhwa] on *FREE* shipping on qualifying offers. The book provides a clear, systematic and exhaustive. The book provides a clear, systematic and exhaustive exposition of various discussions of High Voltage Engineering. Generation of a.c., d.c. and impulse.

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Skip to main content. Log In Sign Up. No part of this ebook may be reproduced in wadhea form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. Awdhwa inquiries should be emailed to rights newagepublishers. My father, who taught me modesty and tolerance.

My wife, a symbol of mutual trust and mutual respect. My daughter and son, volrage exhibited a high degree of patience. My students, who made me learn the subject.

The Almighty, who has created such a beautiful world. The author developed interest in the field of High Voltage Engineering when he was a student at the Govt. It used to be thrilling wadhws observe large metal spheres flashing over, corona phenomenon on a wire placed along the axis of a cylinder and then recording the corona loss, controlling the wave shapes of impulse voltages etc. The author has taught the subject at the Delhi College of Engineering for quite a number of years and while preparing lecture notes he referred to some of the books and journals and some literature from the internationally famed manufacturers of High Voltage equipments e.

In this edition, zeroth chapter on Electric Stress estimation and c ontrol has been added where in different methods viz. Chapter 1 deals with the breakdown of gases, liquids, and solid materials. Even though it has not been possible to explain the physical phenomenon associated with breakdown of enigneering materials, with accuracy and precisiveness, an attempt has been made to bring out some of the theories advocated by researchers in this field in a simple lucid and organised way.

Chapters 2 and 3 discuss the generation of high d. Some of the latest circuits have been discussed and rigorous math- ematical treatment of the circuit has been given to make the subject ebgineering interesting and to make the student understand the subject better. Measurement of transient voltage and currents and high voltage and current require dif- ferent skills and equipment as compared with common a.

Chapter 4 discusses various techniques and circuits for measurement of such quantities. The measurements using high voltage Wwdhwa bridge, transformer ratio arm bridge and partial discharges yield information regarding the life expectancy and the long term sta- bility or otherwise of the insulating materials.

These techniques have jigh discussed elabo- rately in Chapter 6. These tests are very important both during design and operation of the equipments. Electrical transients last for a very short duration but these play a very important role in the insulation design of power system.

Chapter 7 takes a view of various types of tran- sients in power system and suggests classical and more modern statistical methods of coordinating the insulation requirements of various equipments of the system and the devices required for protection of these equipments.

In this edition of the book following articles have been added in chapter 1 of the book: A suitable number of problems voltagge been solved to help understand the relevant theory. At the enginneering, a large number of multiple choice questions have been added to help the reader to test himself. An engineeding bibliography will help the reader to locate detailed information on various topics of his interest.

There are very few High Voltage Laboratories all over the world and the reader may not have an opportunity to visit such a laboratory. Therefore, a few photoplates have been added at suitable locations in the book to give a physical feel of various equipments in a well equipped high voltage laboratory.

The author feels that with the inclusion of photoplates of high voltage equipments the student as well the practising engineers would be greatly benefited. I also wish my express my gratitude to my wife Usha, daughter Meenu and son Sandeep for their patience and encouragement during the preparation of the book.

Any constructive suggestion for the improvement of the book will be gratefully acknowl- edged. Impulse Voltage 81 3. The electric field intensity can be obtained from the potential by gradient operation on the potential i. However it is not a simple job as the exact distribution of charges for a particular potential at a point is not readily available.

Following methods are normally used for determination of the potential distribution i Numerical methods ii Electrolytic tank method.

### High Voltage Engineering by C.L. Wadhwa

From equation 11 it is clear that the potential at point O is the average of the potential at the four neighbouring points. The iterative method uses equation 11 to determine the potential at the corner of every square sub- division in turn and then the process is repeated over the entire region until the difference in values is less than a prespecified voltagee.

The method is found suitable only for two dimensional symmetrical field where a direct solution is possible. In order to work for irregular three dimensional field so that these nodes are fixed upon boundaries, becomes extremely difficult.

Also to solve for such fields as very large number of V x, y values of potential are required which needs very large computer memory and computation time and hence this method is normally not recommended for a solution of such electrostatic problems. This means that this voltage distribution under given conditions of electrode surface should make the enclosed energy function to be a minimum for a given dielectric volume v.

Let us assume an isotropic dielectric medium and an electrostatic field without any space charge. The potential V would be determined by the boundaries formed by the metal electrode surfaces. In this method also the field between electrodes is divided into discrete elements as in FDM. The shape of these elements is chosen to be triangular for two dimensional representation and tetrahe- dron for three dimensional field representation Fig.

The shape and size of these finite elements is suitably chosen and these are irregularly distrib- uted within the field. It is to be noted that wherever within the medium higher electric stresses are expected e. Let us consider an element e1 as shown in Fig.

There will ll a large no. Having obtained the potential of the nodes of these elements, the potential distribution within each elements is required to be obtained. Equation 16 implies that electric field intensity hlgh the element is con- stant and potentials at any point within the element are linearly distributed. Thus partially differentiating equation 21 with respect to Vi and making use of equations 19 and Of course while seeking the final solution the boundary conditions must be satisfied and hence this would require some iterative method for the exact solution.

The second approach could be to formulate energy function in terms of the unknown nodal voltage. This energy function is subjected to certain constraints in terms of boundary conditions. The objective then is to min. For this various mathematical programming techniques like, Fletcher Powell technique, Fletcher technique, direct search techniques, self scaling variable metric techniques can be used.

A computer program can be engineerjng and accuracy of the result can be obtained depending upon the convergence critsion fed into the computer. The finite element method is useful for estimating electric fields at highly curved and thin elec- trode surfaces with composite dielectric materials especially when the electric hlgh are uniform or weakly non-uniform and can be expressed in two voltagf geometrics. The voltxge is normally not recommended for three dimensional non-uniform fields.

These charges could be in the form of point, line or ring, depending upon the shape of hhigh electrode under consideration. It could be a suitable combination of these fictitious charges. The posi- tion voltabe type of simulation charges are to be determined first and then the englneering on the electrode surface is determined by goltage potential function of these individual charges. In order to determine the magnitude of these charges n no.

The sum of the potentials due to fictitious charge distribution at any contour points enginneering correspond to the conductor potential Vc which is known a priori.

It is found these are also dependent upon various distance of these jigh from the point under considera- tion where potential is to be obtained and the permittivity of the medium as in case of a point charge and hence potential co-efficients are constant number and hence the potential due to various types of charges are a linear function of charges wadbwa this is how wadhsa get the potential at a point due to various charges as an algebraic sum of potential due to individual charges.

A few contour points must also be taken at the electrode boundaries also and the potential due to the simulated charge system should be obtained at these points and this should correspond to the equipotentials or else, the type and location of charges should be changed to acquire the desired shape and the given potential. Vn at the given discrete points. Next, it is necessary to check whether the type and location of charges as obtained from the solution of equation 28 satisfies the actual boundary conditions every where on the electrode surfaces.

It is just possible that at certain check points the charges may not satisfy the potential at those points. This check for individual point is carried out wqdhwa equation If simulation does not meet the accuracy criterion, the procedure is repeated by changing either the number or type or location or all, of the simulation charges till adequate charge system simulation is obtained.

Once, this is achieved, potential or engineeging field intensity at any point can be obtained. The field intensity at a point due to various charges is obtained by vector addition of intensity due to individual charges at that point.

However, it is desirable to votage the individual directional components of field intensity separately. In this method it is very important to select a suitable type of simulation charges and their location for faster convergence of the solution e. However, for fields with axial symmetry having projected wadywa structures, ring charges are found better.

Experi- ence of working on such problems certainly will play an important role for better and faster selection. The procedure for CSM is summarised as follows: Choose a suitable vlotage and location of simulation charges within the electride system.

Select some contour point on the surface of the electrodes. A relatively larger no. Calculate the pij for different charges and locations contour points and assemble in the engimeering of a matrix. Obtain inverse of this matrix and calculate the magnitude of charges simulation. Test whether the solution so obtained is feasible or not by selecting some check points on the conductor surface.

If the solution is feasible stop and calculate the electric field intensity at requisite point. If not, repeat the procedure by either changing the type or location of the simulation charges.

## High Voltage Engineering

CSM has proved quite useful for estimation of electric field intensity for two and three dimen- sional fields both with or without axial symmetry. It is a simple method and is found computationally efficient and provides accurate results.

However, it is difficult to apply this methods for thin electrodes e. Also, it is found difficult to apply this method for electrodes with vo,tage irregular enngineering complicated bounda- ries with sharp edges etc. However, as mentioned earlier a good experience of selecting type and location of simulation charge may solve some of these problem.

In actual practice the existing surface charge on the electrode configuration is simulated by integration of ring charges placed on the electrode contour and dielectric boundaries.

This results into a physically correct reproduction of the whole electrode configuration. The electrode contours are segmented as shown in Fig.

Surface charges can be simulated either by line or ring charges. Ring charge simulation is found to be more useful for fields with symmetry of rotation.