Electrical Engineering is an important branch of engineering dealing with Electrical Voltage, Current in DC and AC state, Resistance, Inductance, Capacitance, Generation, Transmission and Utilisation of Electric Power, Electrical Drives etc. This study material is prepared to help those preparing for competition examination.

Part I consists of Fundamental of voltage and current, Resistance, Heating and magnetic effect of current, Magnetic material, Interaction of current-magnetic field-motion, DC motor, DC network theorems, Battery, Battery Charger etc.

Part IIconsists of AC waveform, Inductor, Transformer, Induction Motor, AC Transmission and Distribution

Fundamentals of Electricity

Electric current: Electric current is the rate of flow of charge (electron) and is also written as dQ/dt. Its unit is Ampere and symbol I. It is similar to rate of flow of water. The speed of electron in a copper conductor is just 0.58 cm/min but it is the electric field or its variation which travels at the speed of light for an electric action to perform.

Electric Potential: Electric Potential is similar to water head which makes water to flow. Electric potential is also accumulation of electric charge at one end and producing an electric field travelling at a speed of light and making the charge to flow through the conductor. Its unit is Voltage and symbol V.

Electrical Earth: Electrical Potential is measured with reference to a universal reference called earth. The earth is having very high capacitance and absorb any amount of charge without raising its potential. A leaking current is disastrous if passed through human being, and therefore, all equipment body is connected to earth. A plug is three pin terminal, of which earth is longer and thick, for the reason of easy identification, earth to connect first and should be able to carry fault current. The neutral is connected to earth at transformer end as well as utilization point.

Ohms Law: It is defined that the current through the conductor is directly proportional to voltage applied and constant of proportionality is called Resistance. It is written as V=IR. It is important that there is material which does not follow ohms law through out entire temperature range.

Electric Resistance: Flow of electron encounters resistance in its movement and loses its energy. This loss of energy is converted into heat. Unit of resistance is Ohm and symbol . For conductor, a term Conductance is also used to define the property of material which is reversal of resistance (G=1/R) having unit of Siemens.

Series and Parallel combination of Resistance

When resistances are connected in series, then equivalent resistance is given by Req=R1+R2+R3. and when connected in parallel, it is given by 1/Req= 1/R1+1/R2+1/R3.. Always remember, the resistance increases when connected in series and reduces when in parallel.

Specific Resistance or Resistivity of materials

It is the specific resistance of the material which is specific to the property of the material arising due to the composition of its atomic structure. It is constant for any material, is the symbol and unit -m and calculated by this formula R=*l/A i.e. always remember that the resistance is directly proportional to the length and inversely proportional to the area of cross-section. The resistivity of material varies very largely giving scope for different applications such as conductor, resistor, insulator, semi-conductor etc.

Conductor (x10-8ohm-meter) : Al(2.8), Brass(6-8), Carbon(3000-7000), Copper(1.72), Gold(2.44), Iron(9.8), Silver(1.64)

Insulator (x10-8ohm-meter) : Bakelite(1010), Glass(1010-1012), Rubber(1016), Mica(1015), Sulphur (1015)

Heating Element (x10-8ohm-meter): Tungsten(5.5), Nichrome(108)

Semi-Conductor: Silicon, Germanium

Effect of Current

Current is having wide range of effectin doing work namely heating, motoring, illumination, etc.Flow of electric current not only produces resistive effect but also electro-magnetic and electro-static effect. When electron is static it produces electro-static field around it and when moving, it produces electro-magnetic field around it. Electro-static and electro-magnetic field results in properties of inductance and capacitance and equipment called Inductor and Capacitor. Some important effects are explained here

Heating effect of resistance also called Joule heating

When current passes through aresistance, it results in heating and power consumed during heating is given by V*I, where voltage is the potential difference across the conductor i.e. V= I*R and I is the current through it. If we substitute the value of voltage drop across the resistor in V*I , we get the heat produced across the resistance equal to I2*R. This is also called Joules first law. The unit of power is Watt and energy is given as watt.sec.

Watt*sec. or 1 w-sec = 1 Joule and 4.2 Joules = 1 cal.

This is an important equation one should remember for conversion of electrical to mechanical and heat energy. 1 kW heater working for 10 secs. will produce heat to raise the temperature of 1 litre of water in 10 secs. by 10C. Another important point to note that heating effect is irrespective of direction of current. In alternate current, the effect of heating is same in both the positive and negative cycle.

The electric resistance changes with the rise in temperature and is directly proportional to initial resistance, rise in temperature and temperature coefficient of resistance and given by the formula R=Rt-R0=R0*t . Knowledge of temperature coefficient is important for selection of material for different applications and to provide feature for compensation of expansion which normally keeps on taking place with varying ambient temperature.

Temperature Coefficient at 200C (x10-4) for different general purpose engineering material is Al(40), Cu(39), Iron(65), Nichrome(1.5), Mercury (8.9) and Carbon (-5).The value of temperature coefficient is not constant but different at different temperature. At 500C, the value of coefficient of temperature for copper reduces from 3910-4to 3510-4. The temperature coefficient of carbon is negative, meaning thereby its resistance reduces at higher temperature.

Illumination

The lamp is the most important discovery by Thomas Edision for illuminating the space and is also the most important contribution of Electrical Engineering to mankind. Lamps provides illumination and increases effective hours of activity. It is also an important factor for mental and physical well being, mood elevation, safety and security.

Luminous Flux (lumen), Illuminace (lumen/m2 or Lux) and energy efficiency (lumen/watt) are some of the important measurement units used in specifying Illumination Engineering. Wattage/Room is the total power rating of the lamps provided in a work place and calculated as:

[Lux level required*Area of room] /[Lumen/watt] Note: This is factored by utilization and maintenance factor,shapeof the room and working plane.

For illumination design, following factors are considered

Economy: Price of lamp, Electricity cost and Lumen/watt),

Quality: Color Rendering Index i.e.preferredlight which is close to natural light. A CRI of sunlight is 100

Usage: Reading, Leisure, Machine Shop, safety, restaurant

Location: Street,Railway Yard, Railway Platform Covered-Uncovered Area, Circulating area around Railway Station, Concourse Area at the entranceof RailwayStation, Office, Residential lighting, Control Office,

Maintainability: Loss of illumination due to dust on the outer cover, possibility of moisture, dust and insectsenteringinto the luminary, life of the lamp including its accessories

Lux level is decided by the activity level, the nature of work, safety and security of human beings.It should be noted that this is the highest level ofilluminance to serve the purpose whenactivity levelismaximum. This is not required to be sustained throughout the switched on time. Therefore, there shall be two or three Switching circuit builtinthe design for switching on and off depending upon the activity level either manually and automatically. Thus usage and efficiencydeterminestheenergy conservationmeasures to avoid any wastage when high capacities are built in.

Energy conservation of Electric Lamp

T5 lamp with fitting replaces T8 or T12. Be careful Lumen/watt of different make also varies. Incandescent is highly energy inefficient and replaced from all locations.

CFL replaces the incandescent lamp using the same holder.

Electronic choke consumes 4w less as compared to electromagnetic choke. There are issues of reliability of electronicchokethat need to address in right earnest.

Metal halide and sodium vapor lamp takes more time to start around 3-4minutes. It is more suitable for illumination of Railway station, circulating area and yard. Avoid use of sodium vapor lamp for low height mounting at platform/yard as it may give conflict signal to loco pilot.

LED is long lasting, durable, cool (3.4 Btu/hr), mercury free, energy efficient. LED lamp is costly but still economically suited for lower wattage application in conjunction with battery (torch light, emergency light, night light, solar panel led light, focus lights, etc.). There is a caution about the reliability of driver unit and life of accessories not matching with the life of LED lamp. Large scale usage shall begin with 247 hrs air conditioned dust control area like control office, ticket counters etc.

Magnetic effect of current

Magnetic field is produced either by magnetic material or flow of charge. Magnetic field is denoted by magnitude and direction and is vector quantity. It was first demonstrated by theBiotSavart, deriving arelation betweenthe magnetic fieldgenerated by an electric current.It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The BiotSavart law is used for computing the resultant magnetic fieldBat positionrgenerated byasteadycurrentI.

Amperes Circuital Law

Amperes circuital law talks about electro-magnetic effect whereas gausss law in similar way discusses electro-statics field of charge. This law states that

The line integral of resultant magnetic field along a closed plane curve is equal to 0time the total current crossing the area bounded by the closed curve provided the electric field inside the loop remains constant Thus, this law is also used to calculate the magnetic field due to any given current distribution.

It is denoted by term H and B, both expressing in magnetic field with units of amp/meter and tesla. In a simple way to express what is H and B, than H is magnetic field and B is what is induced in a magnetic material and is given as B = 0*r*H where 0is called the permeability of free space equal to 4*10-7Henry/meter and rrelative permeability. Depending upon the value of relative permeability of material, the magnetic material are classified as Ferro-magnetic- very high r, Para-magnetic rslightly higher than 1 and dia-magnetic less than unity.

Magnetic Materials

Dia-magentic material: Diamagneticmaterials create an inducted magnetic fieldin a direction opposite to an externallyapplied magnetic field, and are repelled by the applied magnetic field. Diamagnetic materials are Bismuth, Mercury, Silver, Lead, Copper and water. Super contductors are perfect diamagnets.

Ferro-magnetic material: These materials get magnetised in the presence of magnetic field and retains it for a longer period. Ferro-magnetic material are Cobalt, Nickel, Iron, Ferro-magnetism is very important in industry and modern technology, and is the basis for many electrical and electro-mechanical devices such as electromagnets, electric motors, generators, transformers and magnetic storage such as hard discs.

Para-magnetic materials: Paramagnetic materials have a small, positive susceptibility to magnetic fields. These materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed.Paramagnetic materials are Tungsten, Aluminium, Magnesium etc.

How Current, Magnetic field and Motion interacts?

The development of a relation between current, magnetic field and motion is the foundation for motoring action. A current carrying conductor in a magnetic field experience a force and given by

Where F is the force, B is the magnetic field in the material, is current through the conductor, is the length of the conductor and is the angle between magnetic field and the current.

Flemings left-hand rule(for motors), andFlemings right-hand-rule(for generators) are a pair of visual mnemonics.These were displayedby John Fleming, in the late 19th century, as a simple way of working out the direction of motion in an electric, or the direction of electric current in an electric generator.

When current flows in a wire, and an external magnetic field is applied across that flow, the wire experiences a force perpendicular both to that field and to the direction of the current. A left hand can be held, as shown in the illustration, to represent three mutually orthogonal axes on the thumb, first finger and middle finger. Each finger is then assigned to a quantity (mechanical force, magnetic field and electric current). The right and left hand are used for generators and motors respectively.

DC Motor

Image taken from Hyper Physics

DC motor works on application of DC power supply. Working principle of DC motor and generator is shown. The current in left and right end of the coil is opposite to each other but magnetic field is perpendicular for both the parts of the coil. As the direction of flow is opposite, the force produced is also opposite which results in torque acting on the coil. The coil starts rotating and keep on reducing when it moves to the top, the torque is zero at the top and again start increasing. The reversal of current is required in the conductor after half rotating to keep the torque in one direction for which commutator and brushes are provided.

There are three types of DC motor namely, Shunt Motor, Compound Motor and Series Motor. In earlier days, before the advent of AC induction motor, Shunt and Compound motors were used for constant speed motors. The most important advantage of DC series motor is its ability to produce large starting torque and making it suitable for an application which requires high starting torque such as traction, hoist etc. This application was widely used till the advent of electronics drives to get the similar characteristics from induction motor.

The standard equations of DC motors are

From this, following interpretation emerges to be remembered are

Shunt and Compound DC Motor: In these motors, the field and armature is connected in parallel to the applied voltage. Speed is directly proportional to voltage. Torque is proportional to armature current. These motors found wide application in 20th century for all fixed speed application and almost constant torque. But with the development of three phase induction motor, application of this motor is now obsolete.

Series Motor: The field is connected in series to the armature and field is current is regulated by insertion of permanent and speed regulation field diverter. Speed is inversely proportional to flux and during start if does not have a mechanical load, the speed will shot up. The DC series motor therefore, always starts on load. Torque is proportional to square of the armature current before saturation. Series motor has wide applications for traction, crane, hoists etc. But now with the development of solid state technology to derive similar characteristics from Induction motor, series motor is also now obsolete except for maintenance for the life cycle of the motors in service.

Always remember that when high starting torque is the requirement, series DC motor had been the choice.

DC Network Theorems

A network always is required to calculate the electrical parameters in a circuit consisting of voltage and current source, resistance connected in different combination, etc. In order to simply and systematise methods for solving these circuits, different theorems has been developed and one should be aware of it. These are

Kirchhoffs law: There are two laws namely Current Law and Voltage Law. Current law states that the algebraic sum of the current meeting at a point is zero and voltage law states that the algebraic sum voltage source and drop in a closed circuit is always zero. Algebraic sum meansdirection is taken into consideration.

Thevenin Theorem: It provides a mathematical technique for replacing a given network into a single voltage source and series resistance as seen through the two output terminals.

Norton Theorem: On similar lines to Thevenin Theorem, Norton theorem converts the network by a current source and parallel resistance.

Delta/star Transformation: In many networks, by converting star into delta or vice-versa, the solution of the circuit becomes simpler.

Storage Electric Battery

Batteryis a device which converts stored chemical energy into electrical energy and vice versa. Faradays through his experiment has given two laws to govern the phenomenon of electrolysis. These are called Faradays Laws of Electrolysis.

Ist Law: The mass of ions liberated at an electrode is directly proportional to the quantity of electricity passes through the electrolyte

IInd Law: The masses of ions of different substances liberated by the same quantity of electricity are proportional to the their chemical equivalent weights.

There are two types of batteries namely

Primary: Energy is stored in the composition of electrodes and when used, the electrode material undergoes an irreversible change. These are disposable type batteries and discarded when used. Applications are where usage is limited such as flashlights and other portable devices.

Secondary: these are rechargeable batteries which can charged and recharged multiple times ( theoretically infinite time but cycle is limited due to permanent damage of electrode)

Each cell has a positive terminal, or cathode,and a negative terminal, or anode. Electrolytesallow ions to move between the electrodes and terminals, which allows current to flow out of the battery to do work.

The common examples are (a) lead-acid batteries used in vehicles (b) lithium ion batteries used for portable electronics. Batteries come in many shapes and sizes, from miniature cells used to power hearing aids, blood sugar/ BP metersand wristwatches to battery banks the size of rooms that provide standby power for telephone exchangesand computer data centres. Secondary Batteries are having wide range industrial application. InIndian Railways, the most important application is for train lighting and air conditioning of coaches.

Lead Acid battery

The main active materials required to build a lead-acidbatteryare

1. Lead peroxide (PbO2), Positive Plate, it is PbO2when fully charged and converts to PbSO4when discharged,

2. Sponge lead (Pb), Negative Plate, it is Pb when fully charged and converts to PbSO4when discharged

3. Dilute sulfuric acid (H2SO4), electrolyte with specific gravity of 1.265 when fully charged and 1.120 when discharged. During discharge process, H2SO4gets converted into water therefore, drop in specific gravity. The measure of the specific gravity is the best method of finding out the charge of the battery.

4. The open-circuit voltage is 2.1 when fully charged and drops to 1.98 when fully discharged.

5. High Specific gravity is used for specific application such as 1.3 (heavy cycle battery for traction application), 1.26 (automotive batteries), 1.25 (UPS and standby) and 1.215 (general purpose).

6. High Specific gravity has the advantage of more capacity, less space, higher momentarily discharge rate but at the loss of shorter life.

7. In general, lower temperature improves efficiency of electrical appliance. But for battery, it is the operating range of temperature to be maintained. Lower range reduces it capacity and higher reduces its life. Mobility of ion reduces at lower temperature, thus the reduced capacity.

8. Rate of Charging current is important and depends upon temperature and state of charge.

9. The specific gravity increases due to loss of water due to normal evaporation. It is important to maintain the water level.

10. Batteries, when stored for a long period undergoes capacity reduction due to the presence of generally irreversibleside reactionsthat consume charge carriers without producing current. This is called internal self-discharge. A tickle charge is necessary to compensate for the internal self discharge.

In order to improve performance of battery, following development has taken place

1. Use of sintered porous plug in which when the water evaporate, it travels through the porous sintered holes, and condensate thus saving loss of water and reducing maintenance need.

2. Development of Vent Regulated Lead Acid/Maintenance Free Battery: The most important advantage of VRLA battery is it ability to mount in any orientation, not requiring monitoring of electrolyte level etc. The term maintenance free could not succeed effectively. VRLA batteries have been shown to reach catastrophic failure and are prone to thermal runaway. A common cause of failure is overheating and dust obstructing the valve, preventing release of gases. They are widely used in large portable electrical devices, off grid powersystems and similar roles, where large amounts of storage are needed at a lower cost than other low-maintenance technologies likelithium ion.

3. There are two primary types of VRLA batteries namelygel cellsandAGM. Gel cells add silica dust to the electrolyte, forming a thick putty-like gel. Absorbed Glass Mat (AGM) is fitted with fibreglassmesh between the battery electrodes which serves to contain the electrolyte. Both designs offer advantages and disadvantages compared to conventional batteries, as well as each other.

Comparison of different other types of Batteries

Nickel Cadmium(NiCd) The NiCd is used where long life, high discharge rate and cost advantage is important. Main applications are two-way radios, bio-medical equipment, professional cameras and power tools. The NiCd contains toxic metals and is environmentally unfriendly.

Nickel-Metal Hydride(NiMH) It has a higher energy density compared to the NiCd at the expense of reduced cycle life. NiMH contains no toxic metals. Applications includemobile phones and laptop computers.

Lithium Ion(Liion) This is the fastest growing battery system. Liion is used where high-energy density and lightweight is of prime importance. The technology is fragile and a protection circuit is required to assure safety. Applications include notebook computers andmobile phones.

Lithium Ion Polymer(Liion polymer) It offers the attributes of the Li-ion in ultra-slim geometry and simplified packaging. Main applications aremobile phones.

Capacity of Battery

The capacity of battery is given Ah say 100 or 200 Ampere.Hour and discharge rate like C10 or C20. A 100 Ah battery will deliver 10 A current for 10 hours before voltage threshold is achieved. A battery bank contains many cells of output voltage 2.1 V and therefore, a 24 V battery bank will contain 12 cells. Generally 12 or 24 V battery back is used for different application.

Back up time

It is important to know the calculation of back up time for emergency application. For this purpose, calculate the house hold load in Watts and find out diversity factory which is around 0.5 to 0.7. Select VA rating of inverter. VA rating is important as it is the current handling capacity of the inverter. Therefore VA ratings of inverter shall match with Watts*Pf of the load. Select inverter type which is Quasi Sine Wave, Square wave and Pure sine wave. Sine wave is best as it produces rotating field in the rotating machine of one speed resulting smooth running of motor like fan, Refrigerator, AC etc.

Select the battery bank of 12V than the back time will be

Back up time in Hours = (Ah)x(12V)x(PF)x(0.8)/(Load VA) where efficiency of battery and inverter has to be taken into consideration.

Basics of Capacitor

A capacitor is a device having two conductive plates separated by an insulator medium. As soon as electric potential is applied across the capacitor plates, electric field sets in, making the charge to flow. Due to the presence of insulator media, the current cannot flow through, and thus the charge keeps accumulating at the conductive plates. The two plates always occupies opposite charge because of gain of charge at one plate always results in the loss of charge on the other plate.

Image from Electrical-tutorial

The plates accumulate charge till such time the opposing potential developed across it stops the flow of charge. Now if the applied potential drops, the accumulated charge starts flow in the reverse direction to balance the voltage across it equal to the applied voltage. Thus the function of a capacitor is to store and release charge as per the requirement of the circuit. It is a temporary storage device. Charge Q is given as a multiple of Capacitance and Voltage across the capacitor i.e Q=CV. As the charge is held in a electric field, it posses electrostatic energy. Therefore, capacitor is an energy storage device.

A capacitor stores charge in an electric field. The insulating material provided in between the plates plays an important role, as it holds the potential across the capacitor. The insulating material is also called die-electric and its strength, say Udwith unit V/m, is vital in the design of capacitors.

The unit of capacitor is Farad and generally in the range of pF to mF only. The capacitance depends on its ability to accept charge. This is directly proportional to the area of the plates and dielectric constant of the medium, whereas inversely proportional to thickness between the plates.

1. More area provides the ability to hold more charge, therefore directly proportional

2. Less thickness results in the opposite polarity plates closure thus attracting the charge.

3. Higher the dielectric constant more is the polarization of the dipole which produces its own electric field opposite to the applied field. This reduces resultant voltage across the capacitor and as we know C is inversely proportional to V, thus C increases. Dielectric constant of important materials is Vacuum =1, Glass = 5 to 10, Mica = 3 to 6, Plastic = 2 to 4, Al2O3= 10, Tantalum Oxide TA2O5= 26, Barium Titanate = BATiO3= 1000 30000

Important relations to remembered about capacitors are as follows:

1. Q = C*V

2. C = r* 0*A/d

3. E = CV2or *A*d*Ud2thus energy storage depends on the Dielectric volume and square of dielectric strength.

4. The equivalent value of two or more capacitors connected in series or parallel is given by

Parallel Combincation Ceq= C1+ C2+ C3

Series Combination 1/Ceq= 1/C1+1/C2+ 1/C3

Application of Capacitor in Electrical Engineering

Capacitor is having wide range of application in the management of electrical power

1. Power factor compensation: This is the most important application of capacitor in electrical circuits. A part of the electrical load is always inductive and draws current from the utility but without requiring doing any useful work. By providing a capacitor network, the needofreactivecurrentfortheinductiveloadis met locally. The utility imposes penalty for low power factor also.Important formulas in this regard are

Total Power drawn from utility kVA = V*A

Total Active power from utility kW = V*A*Cos

Total Reactive Power from utility kVAh = V*A*Sin

Power factor = kW/kVA = Cos = PF

Capacitor bank required to compensate and improving power factor angle from 1to 2is given by = kW(Tan 1-Tan 2)

A reactor is also used along with capacitor bank to control switching surges.

Due to its property of blocking DC and passing through AC by offering lower impedance, it is widely used for filtering and coupling in electrical and electronic circuits.

The most important application is providing stabilised DC link voltage to get any combination of several phases, variable voltage, variable frequency, controlling power factor etc. This conversion would not have been possible without the help of capacitor. This has changed the complete domain of electrical drives bringing efficiency, simplicity, improvements, size reduction etc.

Transient storage device of energy and release at the instant demand in electric power application.

Indirect Capacitance: Capacitance arise accumulation of charge on any metallic surface. Such situation exists in all scenarios and therefore, stray capacitance. Cables, long transmission lines etc. always has stray capacitance.

Maintenance, Reliability and Life of Capacitance

Capacitor is filled with a dielectric and its performance is largely dependent on voltage applied and temperature. Both are detrimental to the life of the dielectric.

1. Maintenance: Capacitor is a passive item with the application of electrical stress. There is no natural maintenance need except check on the capacitance at the interval. The interval for check shall be decided based on the application and implication for a reduction in capacitance value and expected life.

2. Reliability: The reliability of capacitor is generally very highexcept if it has to work in the harsh environment of voltage, frequency and temperature. The harsh environment shall be compensated by over ratingthe capacitance the capacitor to take care.

3. Life: The life is generally given asabout 5-8 years but found lasting more than 10 years.

4. Modern days capacitors are provided with over pressure dis connector switch, which disconnects the capacitor from the circuit when there is building up of pressure.

Safety with Capacitors

1. In a circuit, the capacitor remains charged and disconnected, some charge always remainsand can cause shock to human beings. It is important to discharge all high value capacitors for safe touch.

2. The human body always has some charge and transfers to printed circuit board if touched with bare hands requiring safety measures while working with PCBs.

There was a hostile war betweenAC and DC at the end of 19th century between The Edison Company, the original company holding patent for DC system and The Westinghouse Company using patents filed by Tesla for AC system. The war was similar to what existed in 21st century between Appleand Microsoft.Finally, the entire 20th and now 21st century belongs to AC system. In fact, there existed AC vs DC war in the selection process of traction voltage, and if interested, read moreon theeternal war between AC and DC

The entire scenario of electric power generation, transmission, distribution and utilization is on AC system with few exceptions. DC utilization is limited to low power devices (solid state electronics), Battery Storage and devices working on it, 750/1500 V DC Electric Traction for metro transport, HVDC transmission etc.

However, understanding AC is important for all aspects of electrical engineering

Waveform

There is a circular motion during which power is induced. The magnitude of induction various continuously during the cycle resulting sinusoidal waveform. The sinusoidal waveform results varying magnetic field around it, making the transformation of voltage simple and wide range of application. Power generation, conversion, transmission, distribution and utilisation is simple when it is AC. Voltage and current are written as v=VPeakSin and i=IPeakSin. is a function of time and frequency, and written as t or 2ft. The varying nature of power supply with positive and negative cycle brings some interesting behaviors which are not there with DC. The factors such as Period (T), Frequency (f), Instantaneous Value (v,i), Peak Value (V,I), Peak to Peak value (2V, 2I), Root mean square and Average value are important one should understand of a periodical waveform.

Period: Time take to complete a cycle is called Period and denoted by T, unit as sec or s, and as shown in the diagram.

Frequency: No of cycles per second is frequency and also calculated as f=1/T.

Instantaneous Value: It is the value at any instant on the cycle, denoted by small v or i and written as v=VSin(2ft);

Peak to Peak Value:As it suggests, it is generally twice the peak voltage/current when it is same in both part of the cycle.

Root mean square (RMS): As the instantaneousvaluevaries continuously, the RMS value is to understand the work output. Its value is Vrms=V/2. 2 is called the crest factor. For 230V rms voltage system, the VPeakis 2302=325V. The crest factor is 3 and 1 for triangular and square waveform.

Average value:Average value is an indicator of the total charge flow in a complete cycle. Vavg=2VPeak/, or it is Vavg= 0.637VPeak

Form Factor:It is the ratio of RMS value and Average value i.e.Vrms/Vavg.For sinusoidal waveform the form factor is/22 which is equal to 1.11. It is said that this is one of the reason for defining standards of voltage as multiple of 1.1, beside other reasons of the factor of 4.44 in the induced voltage etc.

Behavour of AC circuits

AC power supply circuits behave differently as compared to DC power supply and its circuits. The voltage and current moves in phase in DC circuits whereas in AC it is either lagging or leading. This is because of the action arising due tothe electro-static and electro-magnetic effect 0fthe static and moving charge (electron) and its reaction. This makes the study very interesting,study of systems through mathematical modelling, derivation and integration, and difficult also. Step by step study simplifies the complications involved in it.

Purely electrical resistive circuits behaves similar to what is there in DC system but magnetism get involved when studying AC system.

Understanding Magnetic Circuits

Magnetic circuits is having similarly with resistivecircuit following Ohms law and makes the understanding easy. A table below compares the two class of circuits and its similarities.

Inductor

Inductance is the property that opposes any change. This opposition is due to inducement of opposing reaction. When voltage applied to an inductor withamplitude changing with time, the current does not change simultaneously but with a delay. There are three laws which describes the theory behind this

The symbol of inductance is L in the honour of Lenz and unit Henry in the honour of Joseph Henry. Henry discovered electromagnetic induction independently and at the same time of Faraday.He also described that the inductance is one henry, if current varying at the rate of one ampere per second will induce one volt in the inductor. Inductor consists of number of turn, Length and Area of the core and permeability of the magnetic material and derives as follows:

Similar toelectro-motive force (emf or voltage) we have magneto-motive force (mmf) equal to No. of turns x current flowing through it i.e. N*I and unit A-t. This magento-motive force produces magnetic field intensity H equal to A-t/meter or N*I/ l (where l is path length in meters). This magnetic field intensity produces flux (in webers) equal to B*A. Flux linkage with the coil is given by N and inductance by flux linkage per unit current i.e. L=N /I

Now substituting the value of =BA, B=H, and H= N*I/ l, we get L=(*N2*A)/l

Therefore, Inductance is proportional to the square of the number of turns and area of the core but inversely propotional to the length of the core. It only says that the more closely packed turns will give more inductance.

Application of Inductor

Inductors along with capacitors are used in electrical system to contain, maneuver and tame the behavior of alternating voltage and current. There is one strong limitation of using inductor is ofsize in reference to both weight and volume and therefore, capacitor is preferred unless unavoidable.

Filters:Inductors are used as in filters along with capacitors and resistors. The impedance of capacitor decreases whereas that of inductor increases with increasing frequency. The combination can be designto pass or block one particularly range of frequency.

Sensors: Inductors can provide contact less sensor for sensing magnetic field and ferro-magnetic materials.

Energy Storage:Energy stored in a inductor is LI2 but it stored only when the circuit is active and discharges immediately when source is removed. However, this is used in switched mode power supply.

Choke:Chokes were used widely along with a starter for producing high voltage to ignite the discharge tube for illumination by florescence effect. Due to energy loss, now the chokes have been replaced by electronic choke.

Transformer and Motor: These two items are independent equipment but works on the principle of induction and will be discussed separately.

Transformer

Transformer is the most important application of electro-magnetic induction and transfer of power from one independent circuit to another through a magnetic media. There is a primary and secondary winding on a common core. The primary produces magnetic flux equal to number of turns which induces emf in the secondary current in proportion to the number of turns in secondary winding. Now by balancing volt-ampere and ampere-turns of primary with that of secondary, assuming no losses and an ideal transformer, we get

Np*Ip=Ns*Isand Vp*Ip=Vs*Is; and this derives the very fundamental transformer equation

Np/ Ns=Is/ Ip= Vp/ Vs

The turns ration is inversely proportional to the current ratio but directly proportional to the voltage ratio.

Transformer Losses

Losses in the transformer are simply a waste of energy into heat than its management to dissipate is an important factor to consider for selection of transmission voltages. Forenergy conservation, handling transformer losses is a priority item.

There are two types of losses namely Hysteresis, Eddy and load current joules heating losses.

Hysteresis Losses:During sinusoidal application of voltage, the magnetic field (H=NI/l)varies with time. This magnetic field induces flux in the core. During reversal of the magnetic field, the reduction in the flux does not follow the same path and retains some flux called retentivity or remanence.There is a loss of energy in a cycle and the area demonstrates the loss of energy per cycle. When H is in AT/m, B in Wb/m2than work done due to hysteresis is in joule/m3/cycle as per the diagram shown below. Alternatively, hysteresis losses is also given by Wh= kh*Bmax1.6*f*v watt (where B is the maximum flux density, f is frequency and v is the volume of core). The hysteresis loop of three materials has been shown of which the loop 1 ishard steel suitable for permanent magnet, loop 2 is wrought iron and cast steel for core of electromagnets and loop 3 is of alloyed sheet steel suitable for making transformer and motor core.

Eddy Current Losses: When there exists magnetic field in a core, the induction takes place between two winding but also inside the core making closed loops of tiny current around flux lines. There is heating loss due to the flow of these current paths. There is very complex function to evaluate the eddy losses and is given by We= ke*Bmax2f2*t2Wattt (where f is frequency and t thickness of the core).It is for this reason that the core is made of very small thickness stamping which are insulated with each other to break the path of the current.

Load Current Joule Heating Losses:This is arising due to the passing of no load and load current through the primary and load current through secondary winding. Total losses due winding resistance is =Ip2Rp+Is2Rs.

Frictional Heating: The core is made of stampings and the varying magnetic field results in expansion and contraction, the effect called magnetostriction. This is also the reason for producing humming sound in a transformer.

Mechanical Losses: Mechanical losses are not only in motor but in transformer arising due to fluctuating forces between primary and secondary winding inciting vibrations within nearby metalwork.

Stray Losses:Leakage inductance does not contribute to losses but when it intercepts nearby conductive material such as its tank etc., it give rises to eddy current losses, though very small.

Transformer is a device which converts electrical energy into electrical energy, and therefore,all losses in primary as well secondary is mainly on account of joule heating by a current irrespective of active or reactive. For this reason, transformers is rated as kVA and not kW.

The important parameters finds mentioning on the name plate of a transformer are No. of phases (mainly 3 but in some cases one), kVA or MVA, frequency (50 Hz), Primary and Secondary voltage, Tap voltages if provided, Connection diagram, type of transformer i.e. star, delta or scott , type of insulating oil, phasor diagram etc.

Delta connections are generally used for transformer used in transmission and star at distribution point of the transformer. Delta connection in transmission line also saves on running fourth conductor.Scott connection converts three phase into two phase, very important application in traction power supply system.

Methods of cooling Transformer:The efficiency of transformer varies from 98 to 95 % depending on its rating. 1000 kVA transformer with 98% efficiency will use 20 kVA for heating. Just imagine a heater of 20 kVA capacity in a closed chamber, the temperature it will produce. This temperature is harmful to its insulation, and therefore, methods of removing this heat is very important subject in designing of transformers. The transformer cooling design depends on the capacity, efficiency etc. The various methods are

ONAN: Oil natural and air natural ONAF: Oil natural and air forced OFAF: Oil forced and air forced OFWF (This system is used for cooling inElectric Locomotive): Oil forced and water forced and ODWF: Oil directed and water forced.

Moisture in transformer:The paper insulation and oil media for insulation and cooling is having tendency to absorb moisture. The moisture ingress results in loss of break down voltage of transformer oil. During variation of load on the transformer, its temperature also changes along with volume. In order to accommodate, this volume changed, a conservator is provided. The air volume above the conservator also changes, during which the air exchanges with environment which may have moisture. A silica gel breather is used which absorbs moisture of the air before it exchanges with the conservator air.

Moisture reduces dielectric strength of paper and oil and mechanical strength of paper, Temperature reduces life of oil and oxygen results in oxidation of paper insulation thus increasing the acidity of transformer oil. Therefore, moisture, oxygen and temperature are enemy of transformer.

Transformer Protection: The two very important protection of transformer are

1. Buchholz Relay: This relay acts on sudden increase of oil pressure. The oil pressure will increase if there is excessive heating due to over loading or flow of excessive fault current in the transformer. This also protects the transformer from explosion.

2. Differential Relay: The differential relay monitors the difference of primary and secondary current taking into consideration the transformer ratio.

Condition Monitoring of Transformer:It is not possible to open and check the condition of transformer very frequently. Therefore, checking the acidity, breakdown voltage and Dissolved gas analysis (DGA) are the common methods followed to assess the inside condition of transformer.

Types of Transformer:The main function of a transformer is to transform voltage through electro-magnetic induction. But there are many types of transformers depending upon application. These are

1. Transmission transformer: High power rating and the load current does not vary widely

2. Distribution Transformer: Medium rating but the load current varies widely

3. Traction Transformer: Medium rating of 3MVA to 8 MVA with very wide current variation, high harmonics etc.

4. Current Transformer: It is used for high current measurement and for circuit protection. A safety measure is necessary for current transformer where the secondary is not made to open circuit which may result very high voltage.

5. Potential Transformer: Similar to Current Transformer, Potential transformers is for voltage measurement and protection towards over and under voltage.

% Impedance:Percentage impedance is an important term used understand the behavior of transformer during short circuit conditions. Percentage impedance is defined as the percent voltage required to maintainfull load under short circuit condition of secondary. On base values , it can also be written as %Z = (kVb)2/ (kVAb)2 and short circuit current is equal to (Il* 100/%Z ), so therefore,%Z defines the level of fault current. It does not mean that we design transformer for high percentage impedance, because it will be at the cost of efficiency of transformer. So somewhere a optimization of transformer losses anditsimpedance is done. This calls for Short circuit analysis in association with codes and standards of a country.

Utilization of Electrical Energy

The most important advantage is the simplicity in transmission, transformation, conversion into different wave forms, utilisation for any application to help mankind resulted in its very quick spread and today it is impossible to imagine life sustainability without it. When we study its utility, it is important to keep these aspects in mind. Electrical energy can be converted into any other form of energy. Conversion to heat, illumination and chemical were discussed in Part I. Now we discuss its conversion into mechanical energy.

He was Tesla, who first demonstrated three phase induction motor in the year 1987. A three phase supply is fed to stator winding which is uniformly distributed through its periphery forming number of poles results in producing a rotating magnetic field of constant value but rotating at a constant speed called synchronous speed Ns= 120*(frequency in cps)/No. of poles in the air gap between rotor and stator. When it sweeps past the rotor surface and cuts the rotor conductor, it induces emf in the rotor bars which are short circuited at the end through an end-ring. The induction of emf, its direction and resultant force are the result of Fardays, Lenzs and Flemings RHR/LHR.A short circuit current flows through the rotor bars whichexperience a force and starts rotating in the direction of rotating field to neutralize the cause which produced emf in the rotor bar. By doing so, rotor tries to pick up the speed near to Nsand rotor current reduces (ideally to zero) to the level necessary to meet the demand of losses and mechanical load on the shaft. This speed is called Nrand that derives a new term called Slip between synchronous speed of flux and mechanical rotation of rotor.

Slip (s) =[(Ns Nr)*100]/Ns

It is the slip which defines all parameter in the rotor such as torque, rotor current frequency, rotor speed.

This is the basic principle of Induction motor and called so as it works on the principle of induction similar to transformer where secondary is fixed whereas in the motor, it is allowed to rotate freely. Following types of motorwere developed on this principle

1. Synchronous Motor: The rotor speed is equal to synchronous speed but when slip is zero, the torque is also zero, therefore, external source is used to drive the rotor to synchronous speed. The initial development of this motor was for power factor compensation but also used assynchronous traction motor.There is further development to provide permanent magnet in the rotor and thus developmentpermanent magnet synchronous motorwith reduced size and increased efficiency.

2. Asynchronous Motor: Induction motor is also called asynchronous motor as rotor speed is not fully synchronized. This the motor widely used for fixed speed application. With the development variable voltage variable frequency drives, it could be possible to get need base variable speed thus saving on energy. Now,induction motoris also usedextensively for applications requiring high starting torque such as traction, hoist, crane etc. Earlier, slip-rings were used to insert external resistance for using induction motor for hoist application, now it is no more.

3. Compensated and repulsion motors are used for specific application in lower wattage range.

4. Single Phase AC motor: Single phase motors are widely used for household and industrial for fractional horse power application.Minimum two phases are required to produce rotating field andstarting torque. For this, single phase is split into two by using a starting capacitor and additional auxiliary winding. There aremany combinations of this motor for specific applications.

5. Liner Induction Motor: Linear induction motor is one in which stator is split open which result in linear motion of the rotor. These

Birmingham_International_Maglev (Image wikipedia)

motors have opened a scope for research and application in the field of contact less high speed and energy efficient motion.The worlds first commercial automated maglev system was a low speed maglev shuttle that ran from the airport terminal of Birmingham International Airportto the nearby Birmingham International railway stationbetween 19841995. In India, Dr. Somnath Mahindra at BHU/Varanasi is working in this project with a working model exisitng at IRIEEN/Nasik.

AC Transmission and Distribution

AC power is generated at Power Generating Stations and the size of the machine goes up to 1000 MW. The voltage selection is based on the current levels and the dielectric strength of the insulating material for the winding and generally ranges between 6 kV to 30 kV. For a 660 MW machine operating at 23.5 kV voltage at 0.85 power factor will draw a current of 19000 A in each phase. This power is transmitted to load center which may be located at a distance of about 100-500 kms. Transmitting power at generating voltage will result heavy energy losses and voltage drop in the transmission line. We know P=3*V*I*PF and higher voltage and unity power factor will reduce current, and for this reason, the transmission voltage is increased to 132, 220, 400 kV and also 760 kV (HVDC) depending on the economics of capital cost and transmission losses. There exists grid networking for different voltages for utilisation of power generating at any station for any consumer.

Cost of Electrical Energy:The cost of electrical energy dependson the capital cost of generating station, variable cost of fuel, transmission and distribution, operation and maintenance cost. There are two parts of any costing namely Fixed and Variable cost as follows

Fixed Cost: This includes the cost of land, building, equipment, machinery and complete related infrastructure in generation, transmission and distribution to the consumer end, interest, depreciation etc. There is generating station usingclean fuelnamely wind, solar, hydro and bio-mass whereas others using non-renewable sources of energy namely thermal, nuclear etc. The fixed cost per MW also varies considerably with present order of minimum for thermal power generation and going up forhydro, nuclear, wind andsolar and variable cost in same but reverse order . Thepresent trend is showing a downward trend for capital cost ofsolar and the day is not far when solar will dominate the energy scenario. There is associated advantage of water management with hydro but with issues of environmental clearances for hydro as well as nuclear.Three nuclear accidents have influenced the discontinuation of nuclear power: the 1979, Three Mile Island partial nuclear meltdownin the United States, the 1986 Chernobyl disasterin the USSR, and the 2011 Fukushima nuclear disasterin Japan. This prompted many countries to phase out nuclear plants namely Sweden(1980),Italy(1987), Belgium(1999), and Germany(2000). Austria and Spainhave enacted laws to stop construction on new nuclear power stations. Several other European countries have debated phase-outs.

Variable Cost: The cost of fuel and operation & maintenance results variable cost.

Tariff:On lines of the cost of power generating station, the energy cost also consists of fixed cost, variable cost (depending on the energy consumed), penalty for

1. Low power factor: Low power factor at the consumer end cost the generating and transmission company for reactive power and not consumed and therefore penalty is imposed. Such penalty is generally for HT consumer. In order to charge the LT consumer, some utilities bills for kVA and not kW. (one unit is kWh but charged for kVAh which is about 5-10% more)

2. Poor Load factor: Load factor is defined as Average Load/Maximum load in a given time period. There are certain utility which imposes penalty if this value goes below 0.25 (DVC), 0.35 (BSEB) etc.

3. Fuel surcharge and other taxes etc.

Factors:Power plant dont run to the maximum capacity all the time due to varying demand during the 24 hours time period. The maximum demand is during night time between 18-22 hours and very low between 00-05 hours. Therefore while working out the economics various demands are to be considered like

Connecting load: It is the total sum of all the loads connected on the system. All the loads will not be ON at any instant of time and it is the diversity factor resulting into the actual demand on the system.

Maximum Demand: It is the maximum load which a consumer uses at any time during the 24 hours period.

Average load: The consumer does not consume power depending on the maximum demand but average consumption in kWh may be only 40-45% of the maximum demandand is called load factor.

Based on these aspects, power generating company monitors the following factors.

1. Availability factor: The total time it is available to produce electricity over a month (say) divided by the total time during the period

2. Capacity factor: Actual output over a period of time to its potential period of delivering the output

3. Utilization factor: The time period for which the equipment is in use to the total time period it could have been use.

4. Demand factor: It is average demand divided by the maximum demand possible

5. Load factor: It is the average load on the system divided by the maximum load in given period of time

6. Diversity factor: It is the percent of time for which a machine or any equipment is on full or rated load.

7. Coincidence factor: It is the reciprocal of the diversify factor and as per IEC coincidence and simultaneity factors are same.

Power Transmission:Transmission voltages are very high as compared to generation and distribution voltage to reduce I2R joule losses.

Distribution System:Distribution system starts by stepping down the transmission voltage of 132 kV and above to 33 kV at 33 kV substation and than at 11 kV distribution network before being transformed to 415/230 V network at consumer end. Distribution at consumer end is of three types namely

1. AC single phase where there only single phase loads and limited to few kW

2. 3 Phase, 3 wire where there three phase loads only

3. 3 phase, 4 wire for all types of load and where the load is high.

The distribution network is eitherradial having advantage of simplicity and low cost but during failure there is no alternative feed arrangement orring main having the advantage of reliability and reduced losses but with complex switchgear arrangement.

Material Selection for transmission line:Thematerial selection is based on economics and technical suitability. High electrical conductivity, low specific gravity (weight), low cost and high tensile strength are the key requirements. The most commonly material used are Cu, Al, Al conductor reinforced with steel (ACSR), galvanised steel and Cd-Cu. Kelvin law is relevant to assess themost economical size of conductor. It states that the variable part of the annual charges is equal to the cost of energy losses per year.