WHAT IS Electrical Power System Quality With Terms and Definitions

Listed below is the most important terms you should know before studying  about electrical power system quality.

What is..

Aswell
is defined as an increase to between 1.1 and 1.8 pu in rms voltage or current at the power frequency for durations from 0.5 cycle to 1 min.  DC Offset is defined of the presence of a dc voltage or current in an ac power system

Harmonics
are sinusoidal voltages or currents having frequencies that are integer  multiples of the frequency at which the supply system is designed to  operate termed the fundamental frequency; usually 50 or 60 Hz.

Interharmonics
is a Voltages or currents having frequency components that are not integer multiples of the frequency at which the supply system is designed to operate e.g., 50 or 60 Hz 


Impulsive Transient
 is a sudden, non–power frequency change in the steady-state condition of  voltage, current, or both that is unidirectional in polarity primarily  either positive or negative.

Interruption
is occurs when the supply voltage or load current decreases to less than  0.1 pu for a period of time not exceeding 1 min. Long-duration variation is encompass root-mean-square rms deviations at power frequencies for longer than 1 min. Notching is a periodic voltage disturbance caused by the normal operation of power electronic devices when current is commutated from one phase to another.

Noise 
is defined as unwanted electrical signals with broadband spectral content  lower than 200 kHz superimposed upon the power system voltage or current  in phase conductors, or found on neutral conductors or signal lines.


Oscillatory Transient 
is a sudden, non–power frequency change in the steady-state condition of  voltage, current, or both, that includes both positive and negative polarity values.

Overvoltage
is an increase in the rms ac voltage greater than 110 percent at the  power frequency for a duration longer than 1 min.


Power frequency variations 
are defined as the deviation of the power system fundamental frequency  from it specified nominal value e.g., 50 or 60 Hz.

Sustained Interruption 
is When the supply voltage has been zero for a period of time in excess  of 1 min in which a long-duration voltage variation is considered.

Short-duration voltage variations 
are caused by fault conditions, the energization of large loads which  require high starting currents, or intermittent loose connections in  power wiring.

Sag 
is a decrease to between 0.1 and 0.9 pu in rms voltage or current at the  power frequency for durations from 0.5 cycle to 1 min.

Transients 
has long been used in the analysis of power systemvariations to denote an  event that is undesirable and momentary in nature.

Undervoltage 
is a decrease in the rms ac voltage to less than 90 percent at the power  frequency for a duration longer than 1 min.

Voltage Imbalance 
or is also called voltage unbalance this is sometimes defined as the  maximum deviation from the average of the three-phase voltage or currents, divided by the average of the three-phase voltages or  currents, expressed in percent.

Voltage fluctuations 
are systematic variations of the voltage envelope or a series of random  voltage changes, the magnitude of which does not normally exceed the voltage ranges specified by ANSI C84.1 of 0.9 to 1.1 
pu.

Waveform distortion 
is defined as a steady-state deviation from an ideal sine wave of power  frequency principally characterized by the spectral content of the  deviation.

What is the working principle of a transformer Questions and Answers

20 Questions :

1. If a transformer is not marked, how could you test it for polarity?
2. A 10-kVA rating, that are connected in a closed delta arrangement, you would have a capacity of 30 
K VA. If one transformer is taken out of the bank, what would be the output capacity of the remaining 10
K VA transformers?
3. When connecting transformers in parallel, what factors must be taken into consideration?
4. What is a split-coil transformer?
5. Where may autotransformers be used?
6. What is the purpose of the markings on transformer leads?
7. In a bank of three single-phase transformers that are connected in a delta, each transformer delivers 240 volts at 10 amperes. What are the line voltages and line currents?
8. If you have a bank of three single-phase transformers that are connected in a closed delta arrangement, and one transformer burns up, how would you continue operation on the remaining two transformers?
9. What special precaution must be taken when using a booster transformer?
10. What is a three-phase transformer?
11. If transformers with different electrical characteristics are connected in parallel, what will happen?
12. Describe a current transformer.
13. What precautions must be taken when working with current transformers? Why?
14. What is an induction regulator?
15.Is it possible to connect two single-phase transformers to secure a three-phase output from a three-phase input?
16. When connecting an ordinary transformer as a booster transformer, what important factors must be considered?
17. When you use a bank of two single-phase transformers in an open delta arrangement, do they supply their full output rating?
18. How are current transformers rated?
19. Describe a potential transformer.
20. What is the phase relation between the three phases of a three-phase circuit?

Answers Above Questions:

1.Connect the transformer as shown in Figure 6-7. If it has subtractive polarity, V will be less than the voltage of the power source; if it has additive polarity, V will be greater than the voltage of the power source.
2.Each transformer would deliver 8.66 kVA, and you would have a bank capacity of 17.32 k VA.
3.Their electrical characteristics, such as voltage ratio, impedance percentage, and voltage regulation.
4.A transformer that has the coils on the low or high side in separate winding's so that they can be connected in series or parallel for higher or lower voltages, as desired.
5.(a) Where the system being supplied contains an identified grounded conductor that is solidly connected to a similar identified
6.They are there for standardization, so that transformer polarities are recognizable for any type of use.
7.The line voltages are each equal to 240 volts; however, the line current in each phase would be the current of each transformer multiplied by 1.732 (the square root of 3), or 17.32 amperes.
8.By merely disconnecting the leads to the disabled transformer.
9.There must be no fusing in the high side, or primary. Because the booster transformer is similar to a current transformer, an extremely high voltage could be built up on the secondary side if the fuse should blow.
10.A transformer that is the equivalent of three single-phase transformers, which are all wound on one core and enclosed within one common case.
11.They won’t distribute the load equally; one transformer will tend to assume more of the load than the other. This leads to overheating and, in severe cases, the destruction of the transformers.
12.A current transformer has a primary of a few turns of heavy conductor capable of carrying the total current, and the secondary consists of a number of turns of smaller wire. The primary winding is connected in series with the circuit carrying the current that is to be measured.
13.The secondary must never be opened when the primary circuit is energized. If it is necessary to disconnect an instrument while the circuit is energized, the secondary must be short-circuited. If the secondary is opened while the circuit is energized, the potential on the secondary might reach dangerously high values. By short-circuiting the secondary, damage is avoided and the voltage on the secondary is kept within safe limits.
14.This device is similar to a booster transformer. It has a primary and a secondary winding, which are wound on separate cores. The primary can be moved in either direction; this is usually done by an electric motor. In turning, the primary bucks or boosts the line voltage, as required. The amount of bucking or boosting is anticipated by the current being drawn by the line.
15.Yes, they would have to be connected in an open delta.
16.The high side of the transformer must be able to handle the approximate voltage of the line; the low side must have a voltage of approximately the value by which you wish to boost the line voltage and must also have a current capacity that is sufficient to carry the line current.
17.No. Each transformer is only capable of supplying 86.6 percent of its output rating.
18.They are rated at 50 to 5, 100 to 5, etc. The first number is the total current that the transformer is supposed to handle, and the second figure is the current on the secondary when the fullloadcurrent is flowing through the primary. For example, a 50- to-5 rating would have a multiplier of 10 Kilo.
19.A potential transformer is built like the ordinary isolation transformer, except that extra precautions are taken to ensure that the winding ratios are exact. Also, the primary winding is connected in parallel with the circuit to be measured.
20.They are 120 electrical degrees apart.

Transformer Principles Questions and Answers For Engineering Students and Workers

QUESTIONS:

1. What is the difference between the primary and the secondary of a transformer?
2. What is an oil-immersed transformer?
3. What is a transformer?
4. What factors affect the amount of induced electromotive force emf in a transformer?
5. Why is oil used in a transformer?
6. Is it possible to connect two single-phase transformers to secure a three-phase output from a three-phase input?
7. What is an air-core transformer?
8. What are eddy currents?
9. What means can be taken to keep eddy currents at a minimum?
10. Is hysteresis objectionable?
11. Are transformers normally considered to be efficient devices?
12. What factors constitute the major losses produced in transformers?
13. There are two basic types of transformers. What are they?
14. Is there a definite relationship between the number of turns and voltages in transformers?
15. What are instrument transformers?
16. Ordinarily, what is the phase relationship between the primary and secondary voltages of a transformer?
17. Is it possible to have the primary and secondary of a transformer in phase?
18. How are the leads of a transformer marked, according to ANSI (American National Standards Institute)?
19. What is mutual inductance?
20. What is a booster transformer?

ANSWERS:

1. The primary of the transformer is the input side of the transformer and the secondary is the output side of the transformer. On a step-down transformer, the high-voltage side is the primary and the low-voltage side is the secondary; on a step-up transformer, the opposite is true
2. The core and coils are immersed in a high-grade mineral oil, which has high dielectric qualities.
3. A device that transforms electrical energy from one or more circuits to one or more other circuits at the same frequency but usually at a different voltage and current. It consists of a core of soft-iron laminations surrounded by coils of copper-insulated wire.
4. The strength of the magnetic field, the speed at which the conductors are cut by the magnetic field, and the number of turns of wire being cut by the magnetic field.
5. To increase the dielectric strength of the insulation, to keep down the possibility of arcing between coils, and to dissipate heat to the outer case so that the transformer can carry heavier loads without excessive overheating.
6. Yes, they would have to be connected in an open delta.
7. A transformer that does not contain oil or other dielectric
compositions but is insulated entirely by the winding insulations and air.
8. Circulating currents induced in conductive materials (usually
the iron cores of transformers or coils) by varying magnetic
fields.
9. The iron used in the core of an alternation-current transformer
is laminated, or made up of thin sheets or strips of iron,
so that eddy currents will circulate only in limited areas.
10. Yes, it is a loss and affects the efficiency of transformers.
11. Yes, they have one of the highest efficiencies of any electrical device.
12. Power loss of the copper I2R losses, eddy currents, and hysteresis losses.
13. The isolation type, in which the two windings are physically isolated and electrically insulated from each other, and the autotransformer type, in which there is only one coil with a tap or taps taken off it to secure other voltages the primary is part of the secondary and the secondary is part of the primary.
14. Yes, the voltage varies in exact proportion to the number of turns connected in series in each winding.
15. In the measurement of current, voltage, or kilowatt-hours on systems with high voltage or high current, it is necessary to use a device known as an instrument transformer, which reproduces in its secondary circuit the primary current or voltage while preserving the phase relationship to measure or record at lower voltages
or lower amperages, and then to use a constant to multiply the readings to obtain the actual values of voltage or current. Current transformers CTs are used to measure the current, and potential transformers PTs are used to register the potential.
16. They are 180º out of phase.
17. Yes, by changing the connections on one side of the transformer.
18. The high side of the transformer is marked H1, H2, etc. The low side of the transformer is marked X1, X2, etc.
19. The linkage of flux between two coils or conductors, caused by the current flowing within one or both of the coils or conductors.
20. A transformer arrangement that is often used toward the end of a power line in order to raise the voltage to its desired value. These are often called “Buck-boost” transformers.

Transformer Built In Protection and Cooling Tutorials

Protection Devices Built In For Safe Operation of A Transformer

Conservator

It is a sort of a drum, mounted on the top of transformer. A level indicatoris fixed to it. Conservator is connected through a pipe to the transformer containing oil. This oil expanse and contracts depending upon the heat produced so the oil level in the conservator rises and falls. Pipe connected to the conservator is left open to the atmosphere through a breather so that extra air any go out or come in.

Breather

Is is a box containing calcium chloride to absorb moisture of air entering the conservator as it sis well known fact that the insulating property of the transformer oil is lost even if a small amount of moisture enters in it, so the dry air is allowed to pass in through this breather.

Temperature Gauge

It is fitted to a transformer which indicates the temperature of transformer oil.Explosion Vent

It protects the transformer tank from the gases induced by any type  of short circuit in the transformer.

Pipes

These are fitted for cooling the transformer oil. The hot oil circulates through these pipes where it becomes cool due to the air touching.

Important Facts About Transmission and Distribution Transformer

1. Eddy current losses in a transformer are minimised by laminating the core, the lamination being insulated from each other by a light coat of core plate varnish.

2. The basic property of the transformer is that it changes the voltage level of an alternating current signal without changing power, frequency or shape.

3. The primary and secondary voltages are 180 degree out of phase in transformer.

4. Eddy current lossesin transformer core are reduced by decreasing the thickness of laminations.

5. The resistance of low voltage side of a transformer is less than the resistance of its high voltage side.

6. The efficiency of a transformer is normally in the range of ninety ot ninety eight percent.

7. The reactance of transformer is determined by its leakage flux.

8. The principle of working of a transformer is mutual induction.

9. Transformer is used to change the valuesof voltage.

10. The path of the magnetic flux in a transformer has low reactance.

11. Electric power is transformed from one coil to the other coil in a transformer magnetically.

12. Ideal transformer assumptions do not include zero reactance of windings.

13. Preferably, the resistance between the primary and the secondary of a transformer should be as low as possible.

14. The main function of the iron core in a transformer is to decrease the reluctance of the magnetic path.

15. Magnetic circuit is common in the two windings of a transformer.

16. A transformer operates at power factor depending on the power factor of the load.

17. The lamination are made from nickel alloy steel stampings.

18. The steel for construction of transformer core is made so as to have high permeability and low hysteresis.

19. The special silicon stell in used for laminations because hysteresis losses are reduced.

20. Power transformer are designed to have maximum efficiency at near full load.

Cooling Of Transformer

Natural Cooling

The cooling is provided through natural circulation of air. The surface area of the core and the transformer winding are sufficient to dissipate the heat generated. It is used for small transformer from ten kva to fifteen kva.

Natural Oil Cooling

The transformer is placed in tank filled with oil known as transformer oil. The oil used in the tank not only helps cooling the transformer but also provides insulating for the winding. The oil takes the heat produced by the transformer, the oil circulate through the pipes and tank. The hot oil becomes lighter in weight and goes up from where comes down through pipes to the bottom of the tank after cooling. The oil level should never fall below the upper ends of pipes.

Oil Blast Cooling

In this method radiator tanks are provided to the side walls of the main tank. The oil circulators through these radiators from the main tank. The radiator tanks are cooled by air blast. The system of cooling is known as oil blast type. It is used for transformer rated above five hundred kva.

Force Water Cooling

The winding of transformer is placed inside the tank containing oil and cold water is passed through the copper pipe spiral kept in the transformer oil. The cold water absorbs and carrier away the heat of the oil. The pressure of the water is not kept greater than the pressure of the oil in the tank because in case of leakage in the pipe, the water will enter into the oil. It is used for transformer having output greater than five hundred KVA.

Force Air Cooling

In this method the air is first filtered to eliminate moisture and dust particless and this filetered air under pressure is forced to passed through the winding care of the transformer and the dusts provided in them. This method is used where there 

is a scarcity of water.

Power Transformer Tutorials Links

IIEE-ICA Electrical EngineeringTechnical Manuals free pdf ebooks

Last Augusts 25-27, 2011 The International Copper Association – South East Asia and Institute of Integrated Electrical Engineers of the Philippines, Inc. gaves us a Three free books with CD of free ebooks a pdf file on the 15th Southern Mindanao Regional Conference. The three free books all about the abstract for the presentation of the contents of three technical manuals through the initiative of international copper association southern (ICASEA) and administered, executed, and implemented of ICA, a non-profit organization promoting the efficient use of copper in the industry. The main objective of ICASEA is to advance copper as the material of choice for current makets and new applications given its superior attributes in terms of technical performance, aesthetic value, sustainability, essentiality for life, and its contribution to a higher standard of living listed below are the following
which is ready to download a pdf file.

Power Transformer
This manual shows how a transformer can be put to use appropriately in a particular situation. The purpose of this manual is to facilitate the physical understanding, selection, ordering, operation, and maintenace of transformer. The target readers are personnel involved in the various stages of a transformer's sevice life from planning the investment to the disposal of the transformer after use.

Electrical Motors and Drives
This manual deals primarily with small and medium sized induction motors which are the most common type of alternating current motor including asynchronous motor starting systems. They are internationally standardized and are efficienctly in long production runs. The combination of new materials and more sophistacated methods for calculation, design and production have made the modern three phase induction motors a robust and realible prime mover.

Power Cables and Wire
Power Cable and Wires technical manual was written to address the needs of by consumers, specifiers, and purchasers to have a ready reference guide in correctly specifying or ordering the appropriateness of cables and or wires, from the conductor to the insulator, are each discussed in this manual so as to educate or inform the reader of its fundamental use or purpose to the final product.

Free Tutorials On Electrical Engineering Question and Answer

1.What are taps and when are they used?
Taps are provided on some transformers on the high voltage winding to correct for high or low voltage conditions and still deliver full rated output voltages at the secondary terminal.  Standard tap arangements are at two and one-half and five percent of the rated primary voltage for both high and low voltage conditions.
2.What is the difference between “Insulating”, “Isolating” and “Shielded Winding” transformers?
Insulating and isolating are identical.  These terms are used to describe the isolation of the primary and secondary windings or isolation between the two.  A shielded transformer is designed with a metallic shield between the primary and secondary windings to attenuate transient noise.
3.Can transformers be operated at voltages other  than nameplate voltages?
In some cases, transformers can be operated at voltages below the nameplate rated voltage.  In NO case should a transformer be operated at a voltage in excess of its nameplate rating unless taps are provided for this purpose.
4.Can 60 Hz transformers be operated at 50 Hz?
Transformers 1 kVA and larger rated at 60 Hz should not be used on 50 Hz service due to the higher losses and resultant heat rise.  However, any 50 Hz transformer will operate on a 60 Hz service.
5.Can transformers be used in parallel?
Single phase transformers can be used in parallel only when their impedances and voltages are equal.  If unequal volatages are used, a circulating current exists in the closed network between the two transformers which will cause heating and result in a shorter life of the transformer.
6.Can transformers develop three phase power from a single phase source?
No. Phase converters or phase shifting devices such as reactors and capacitors are required to convert single phase power to three phase.
7.What is meant by regulation in a transformer?
Voltage regulation in transformers is the difference between the no load voltage and the full load voltage.  This is usually expressed in terms of percentage.
8.What is temperature rise in a transformer?
- Temperature rise in a transformer is the temperature of the windings and insulation above the existing ambient or surrounding temperature.
9.What is “Class” in insulation?
Insulation class was the orioginal method used to distinguish insulating materials operating at different temperature levels.Letters were used for different designations.
10.Why should dry type transformers never be over-loaded?
Overloading of a transformer results in excessive temperature. This excessive temperature causes overheating which will result in rapid deterioration of the insulation and cause complete failure of the transformer coils.
11.What is meant by “impedance” in transformers?
Impedance is the current limiting characteristic of a transformer and is expressed in percentage.
12.Why is impedance important?
It is used for determining the interrupting capacity of a circuit breaker or fuse employed to protect the primary of a transformer.
For Example:
1. Determine a minimum circuit breaker trip rating and interrupting capacity for a 10 kVA single phase transformer with 4% impedance to be operated from a 480V, 60 Hz source.
13.What is polarity when associated with a transformer?
Polarity is the instantaneous voltage obtained from the primary winding in relation to the secondary winding.
14.What is exciting current?
It is the current or amperes required  for excitation. The exciting current on most lighting and power transformers varies from approximately 10% on small sizes of about 1 kVA and smaller to approximately 0.5% to 4% on larger sizes of 750 kVA.


Frequently Asked Question 
What is Transformer and How does it Works?, Why Do Transformer Hum?, How Can Reduce airborne noise and many more other question.

Free pdf file Transformer Question and Answer
Almost anything that you want to answer with regard specifically.

 Power Transformer?
How to Determine Secondary AC (RMS)Current Ratings

World's Largest-Biggest Cast Resin Transformer Made By Seimens

source

Above shown picture was the world's largest cast resin transformer developed by Siemens power transmission and distribution at a power range up to rated of 40 MVA, it has 4.8 meters long, 2-8 meters wide, 4.7 meters high and weighing of 50 metric tons.


What is Cast resin Transformer
Its answer the question how this transformer made up from birth to complete.
http://ttransfo.com/transformers/resin_transformers.htm

Why Cast Resin Transformers?
You will able to learn the transformer characteristics, reduced cost, maintenance free, power reserves, planning flexibility and safety and reliability, design details, the high-voltage winding and low voltage winding, core and coil clamps.


Cost Saving when Using
It reduced transmission losses, approach for analysis, schematic example.
http://www.automation.siemens.com/mcms/totally-integrated-power/en/power-distribution-benefits/cost-savings/cast-resin-transformer/Pages/default.aspx


More About The Topics From T&D World
http://tdworld.com/projects_in_progress/business_in_tech/siemens-cast-resin-transformer/

Need to Know About Dry Type Electrical Transformers

What is Dry type transformer? and How does it works? why is it very significant especially in the load side of customers. I always ask that question many times, especially if I have a customers in their applied load is 440 volts. One of their primary purpose instead of buying a new one distribution transformer which very expensive to their part they only buy a Dry Type transformer to convert from 440 to 220 volts, to supply electrical lighting outlet and convenience outlet. If you need more details I have prepared links and free pdf file if you want to download.

Electricity forums
Dry type transformers require minimum maintenance to provide many years of reliable trouble free service.


Natural Resource Canada
Transformers reduce the voltage of the electricity supplied by your utility to a level suitable for use by the electric equipment in your facility.


ABB
These dry type transformers meet strict parameters with respect to electrical system demands and functioning in areas with extreme climatic conditions.


Aluminum Winding DT transformers
The HV windings are wound from aluminium foil interleaved with an insulating foil.


MTCTransformers
MTC engineers have a thorough knowledge of the applications that our products support, and they create unique designs to support our customers’ special requirements. Our product offerings range from 1 KVA, 600 V to 10000 KVA, 34500V.

Electrical ebooks Practical Transformer Handbook, Power Generation Technologies

Power Generation Technologies
This book is primarily about the ways of generating electricity. It does not cover the means of transporting electricity and delivering it to those who wish to use it. Nor does it treat, except obliquely, the political issues that attach themselves to electricity supply. What it does attempt, is to provide an explanation of all the myriad ways that man has devised to produce this most elusive of energy forms. The book is divided into chapters with one chapter devoted to each type of electricity generation. The explanations provided are thorough and
technical where necessary but do not resort to overly technical language where this can be avoided. Readers, who are seeking a full analysis of the thermodynamics of the heat engine, or the differential equations for solving the problem of turbine flow, will need to look elsewhere.
http://www.mediafire.com/?qytynfoknqu



Practical Transformer Handbook: for Electronics, Radio and Communications Engineers
This book takes a somewhat different tack; it deals largely with transformers more relevant to electronic technology, control techniques, instrumentation, and to unusual implementations of transformers and transformer-like devices. In sodoing, the author feels that the highest usefulness will ensue from emphasis on the practical aspects of such transformers and their unique applications. For, if properly done, those readers wishing to probe further will have been guided along appropriate paths to extended investigation. The underlying objective is to stimulate the creativity of engineers, hobbyists, experimenters and inventors, rather than to provide a conventional classroom-like text. It is to be hoped that a readable and interesting exposition of the topic will help dispel much of the prevalent notion that transformers are mundane devices of a mature technology with little prospect of further evolutionary progress. To this end, it should be easy to show that the traditional treatment of transformers,
althogh providing a solid academic-foundation, tends to confine the modern practitioner to a bygone era.
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ebook for download The J & P Transformer Book, The Method of Moments in Electromagnetics

The J & P Transformer Book, Twelfth Edition
Primarily the objective has been to provide a description of the principles of transformer design and construction, testing operation and maintenance, as well as specification and procurement, in sufficient depth to enable those engineers who have involvement with transformers in a system design, installation or maintenance capacity to become ‘informed users,’ and it is hoped that, in addition, all of that valuable operational guidance contained in earlier editions has been retained and made more relevant by being brought fully into line with current thinking. Above all, the hope is that the successful formula which has led to the enormous popularity of earlier editions has not been lost and it is hoped that the information contained in this edition will prove even more useful to today’s engineers than those editions which have gone before.
http://www.mediafire.com/?t1kzmn0ykmv



The Method of Moments in Electromagnetics
This book is for a one- or two-semester course in computational electromagnetics and a reference for the practicing engineer. It is expected that the reader will be familiar with time-harmonic electromagnetic fields and vector calculus, as well as differential equations and linear algebra. The reader should also have some basic experience with computer programming in a language such as C or FORTRAN or a mathematical environment such as MATLAB. Because some of the expressions in this book require the calculation of special functions, the reader at least should be aware of what they are and be able to calculate them. This book comprises nine chapters:

Chapter 1 presents a very brief overview of computational electromagnetics and some commonly used numerical techniques in this field.
Chapter 2 begins by reviewing some necessary background material on timeharmonic electromagnetic fields. We next develop expressions for radiation and scattering, vector potentials, and the two- and three-dimensional Green’s functions. We then discuss surface equivalents and derive the electric and magnetic field integral equations for conducting surfaces.
Chapter 3 introduces the solution of integral equations by converting the problem into a linear system. The method of moments is formalized, and commonly used two-dimensional basis functions are covered. We then discuss the solution of matrix equations, Gaussian elimination, LU decomposition, condition numbers, iterative solvers, and preconditioning.
Chapter 4 is dedicated to scattering and radiation by thin wires. We derive the thin wire kernel and the Hall´en and Pocklington thin wire integral equations, and show how to solve them. We then apply the MOM to thin wires of arbitrary shape, and consider several practical thin wire problems.
Chapter 5 applies the moment method to two-dimensional problems. The
electric and magnetic field integral equations are applied to problems of TM and
TE polarization, and expressions are summarized that can be applied to general twodimensional
boundaries.
Chapter 6 considers three-dimensional objects that can described as bodies of
revolution. The application of the MOM to this problem follows the treatment of
Harrington and Mautz, with additional derivations and discussion. We then look at
the radar cross section predictions of rotationally symmetric objects and compare
them to measurements.
Chapter 7 covers three-dimensional surfaces of arbitrary shape. We discuss
modeling of surfaces by triangular facets, and devote significant effort to summarizing
the expressions used to evaluate singular potential integrals over triangular
elements. We then consider several radar cross section problems and the input
impedance calculations of some three-dimensional antennas.
Chatper 8 introduces the fast multipole method and its use with iterative
solvers and the moment method. We cover the addition theorem, wave translation,
and single- and multi-level fast multipole algorithms. The treatment is concise and
contains all the information required to succesfully implement the FMM in a new or
existing moment method code.
Chapter 9 discusses some commonly used methods of numerical integration
including the trapezoidal and Simpson’s rule, area coordinates, and Gaussian quadrature
in one dimension and over planar triangular elements.
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