Introduction

In late 1880's after Faraday published his laws of electromagnetic induction, first alternator was manufactured. The alternator by principle cannot produce a non-variable voltage with respect to time unlike a voltaic cell. Here the electrical technology was going through a great dilemma. On one hand, all electric appliances and instruments were manufactured for fixed voltage or DC voltage and on other hand, the demand of new generation or alternative voltages was in questions. The famous war of current between the father of DC voltages Thomas Edison and American engineer and manufacturer of AC voltage George Westing House was the most discussed issue in late 1880's. For a short span of time we used to use a commutator to get DC out of an alternator. It was very soon that there was a great revolution in electrical engineering as such and all equipments were redesigned and redeveloped to function in AC environment.

What is AC?

In a voltaic cell the output voltage does not vary with time. For a fixed load (i.e. for a constant current) the output voltage is constant throughout the time. In other words the voltage does not change its polarity. The voltage of this kind is the direct current voltage or DC voltage. The current is proportional to the voltage. So a DC voltage always feeds a constant unidirectional current to the circuit. Whereas, an AC voltage source changes its polarity and thus the current changes its direction accordingly. We get a variable bidirectional current from an AC source.

Introduction

Let us look at the vast stary night sky. Let us think of the galaxy full of scintillating fire balls. Let us experience a ride on a high speed Maglev train in Miyazaki, Japan. We must find one thing common in these. Everything is so very balanced yet so moving. The equilibrium state or the multiple equilibrium states are adjoined by the consequent transient states of these events. They are characterized by different force fields. We can imagine our physical existence is situated and controlled by four major force fields. They are:

• a. Gravitational force field

• b. Electrical force field

• c. Magnetic force field

• d. Atomic or Nuclear force field

Out of these four the first three are governed by inverse square law. Bodies which are inversely proportional to the distance between them and directly proportional to their dimension (i.e. mass, charge, magnetic pole intensity). The gravitational force field is both attractive and repulsive. Electrical and magnetic field generally coexist. We can call them sister fields. In most of the cases we derive one as a result of another one. Thus we can easily establish a linear relationship between them. We as an electrical engineer mostly deal with these two sister fields and their combined network. Power system is an electro-magnetic system. Thus, we should have a profound study on electric and magnetic field with prior importance. This chapter will enlighten us how these two fields work and react to each other.

Introduction

Now we are almost at the verge of finish line of our course. Let us now reminisce what have we studied so far. Let us cultivate the purpose of our study. One part of achievement of our study is of course to know the nature and the natural law and how technology has been developed on these laws to make our lives easier. But the other part of our goal is to be socially responsible towards proper utilization of electrical energy. Society expects that engineers should understand the technology at work around us. In this chapter we shall conclude our study by knowing the basic electrical technology associated with our domestic and social lives. We hope we shall be able to understand and shall make awareness among others as a responsible engineer.

Cables and Wires

Electrical cables are made of wires. Two or many wires twisted or running side by side make a cable. The wires are made of Ohmic conductors, mainly copper or aluminium, to carry the current. To carry more amount of current we need less resistive wires in order to maintain a reasonably low I2R loss. To reduce the per unit length resistance of a wire we need to increase the diameter of the wire. In short, for higher current rating of a wire we must have more amount of conductive metal. The overhead cables are naked conductors. But the underground cables or overhead cable in densely populated areas are generally covered by non-conducting insulation. The insulators are dielectric materials, usually polyurethanes; prevent two wires to get short circuited.

Introduction

In chapter 3, we have discussed about four different force fields. Magnetic force field is one of those force field exists in the universe. The Magnetostatic deals with the magnetic field. Electrical engineers are concerned about the magnetic field as much as electrical field. These two fields are associated with each other. Like electric field, magnetic field is also inverse square law field. We define different parameters of magnetic field which are analogous to electric field. These two fields are inter-related. Magnetic field plays a very important role to deliver electrical power to our useful mechanical system. This develops the importance to study both the electrical and magnetic field together. Electromagnetism is the branch of science and technology where we study the effects of magnetic field on the electric field and vice-versa. We have studied the alternating current in chapter 4. Any alternating current is associated with an alternating magnetic field. Alternating magnetic field again induces another electric field. In this chapter we shall study the properties and nature of magnetic field and also its connection to electric field. When an electric charge is in motion it produces the magnetic field.

Different Physical Parameters Related to Magnetic Field

Magnetic field

We have already defined the electric field and field intensity with respect to a positive unit electric charge. When an electric charge is in motion it creates a magnetic field. The magnetic field also exerts a force on the charge. So a charge Q with velocity V will experience force F both by the electric field B and magnetic field B. The combined force which will be acted upon the charge Q is known as Lorentz force.

We know the force experienced by charge Q in electric field Ē;.

Introduction

The recorded observations related to various electrical events and facts are found dating back to the fifth century BC. The lighting in a stormy night, or the attraction between a rubbed amber and cat's fur have always provoked human curiosity. But, it was merely a subject of the philosopher's mind, rather than the business of technology. It was only in the mid-sixteenth century that scientists developed techniques to store electrical charge. Suddenly, like a flash of thunder, everything was changed. We were able to convert a spontaneous event into a continuous operation. The technology had shifted from the era of the mechanical intentions to the era of electrical progression. We can call it a paradigm shift of technology.

Like any other paradigm shift, this change did not occur overnight. We have achieved the great electrical inventions through gradual efforts by scientists. Different theories and formulae had made it possible. In this chapter, we are going to discuss these preliminary concepts and related theories to begin with, starting with static electrical charges to laws of current electricity. We shall also observe that the application of these theories requires a great deal of measurement and quantification of various electrical parameters, such as electrical potential, current flow and resistance. Let us explore this world of electricity from the perspective of an electrical engineer.

Introduction

Our discussion on electrical engineering has been so far pivoted upon two major aspects. First, the electrical and magnetic field and the correlation between them. Second, the different types of electrical circuits through which a continuous flow of electric charge can be established. We by this time have acquired the knowledge that the electric and magnetic fields complement each other. They often co-exist in a material. The most obvious supposition from the above discussion is the analogy between magnetic and electric field knowing the facts of electrical circuit we can imagine the existence of magnetic circuit following the similar laws to electric circuit laws.

In the first half of seventeenth century the idea of magnetic circuit was developed. When two magnetic coils are placed in close vicinity to each other, the coils get magnetically coupled. The same flux is linked with both coils. Thus, there must be a magnetic connection between two magnetically coupled coils. The connection between the coils is certainly not via an electrical circuit. The magnetic connection is made by another circuit. There is no material link between two magnetically coupled coils. So no electron flow is practically possible. We can only think of a circuit through which magnetic flux can be flowed and linked the two coils. This circuit is named as magnetic circuit. In this chapter, we shall discuss more on different phenomena and laws of magnetic circuit.

Science is abstract. Mathematics is the language of science. The challenge of an engineer is to solve the real practical problems of life by applying knowledge of science. This book is fully devoted towards extending the knowledge of science to solve the real-life engineering problems in electrical engineering. Our intention has been to introduce practical electrical engineering challenges to budding engineers and enable them to solve the challenges of technology in a proper way.

We believe the book will be helpful to all the students of engineering of all streams at degree and diploma level. The chapters are organized to meet the requirements of the syllabus of introductory lessons on basic electrical engineering of all universities. We hope the beneficiaries will get to know the subject in an interactive fashion through the numerous solved problems included in the book.

We have tried to explain the theory so that the theorems become tangible and problems become explicit. The book is enriched with its overwhelming pedagogy and practical knowledge. The emphasis is placed on better illustrative understanding of theory related to day-to-day life experiences. The book is expected to be a complete guideline of fundamental knowledge on basic electrical engineering. This knowledge is essential for not only core electrical engineering students but also students from other streams of technical education dealing with power and energy.

Introduction

In the next few chapters we shall be engaged in discussions on electrical machines. An electrical machine is an ‘electro-mechanical’ rotating device. Well, is it perfect to call an electrical machine an ‘electro-mechanical’ device? Partly yes, but not exactly. We may better call it an ‘electromagnetic-mechanical’ device. Now what is it all about? A machine is a system which transforms energy. Generally, a machine transforms electrical energy of an electric circuit to a mechanical system via a magnetic circuit or vice-versa. So we can simply draw the transformation of energy in an electric machine by a single line diagram as follows:

Fig. 8.1a represents the action of a generator while Fig. 8.1b shows the action of a motor. Thus, electric machines are of two types namely generator and motor.

Well, are we absolutely right? Yes, partially but not completely. In the next chapter, this myth of machine as ‘electro-mechanical’ convertor will be destroyed. We shall see that a transformer does not really have a mechanical part and yet it is an electrical machine (static). A transformer transforms electrical energy of one electric circuit to another via a magnetic circuit.

Fig. 8.2 is showing the action of a transformer. Thus, a transformer can be called an ‘electro-magneto-electrical’ static device.

In chapter 4 we have seen that when a conducting coil is rotated in a magnetic field, an AC voltage will be induced in the coil. Similarly, if we supply AC voltage to the same coil it will show the motoring action.

Introduction

In previous chapters we have read that a motional emf is induced when a conductor coil is moved in a constant magnetic field. There must be a relative motion between the steady magnetic field and the conductor to get the generated emf This mechanism is reciprocal. That means we can even get the movement if we apply the emf in the same manner. Thus, we can conclude that a dynamic machine is applied to convert the electrical energy to mechanical energy and vice-versa. We have already come to know about DC machine and induction machine. In DC machine, the single phase power is commutated via a commutator to convert AC to DC and vice-versa. Whereas in induction motor we use a shorted three phase winding as stator winding. An induction machine runs at a speed lesser than the synchronous speed. If we energize the field from a DC source and the armature current is supplied from an AC source the rotor will rotate at exactly the same speed of the synchronous speed of the supply frequency. This motor is synchronous motor. We can consider a synchronous machine as a DC motor without commutator and supplied from an AC source.

Construction of Synchronous Machine

We know there must be a relative rotational motion between the rotor and the stator in order to develop a rate of change of flux in the machine. The rate of change of flux is essential to produce electrical energy and generate the voltage difference. In DC motor we have seen the field excitation is given to the stator coil while the current carrying conductor is the rotor winding or armature winding.

Necessity of Measurement

We have so far discussed a major section of electrical technology. We have theorized different electrical, electro-mechanical (dynamic machines: motor, generator) and electro-magnetic (static machine: transformer) systems. From these theories we have derived a large number of equations. From these equations we have generated numerical problems and we have found the solutions. At this stage the most obvious question that should incite a rational mind is ‘Why’? Why we have taken all these efforts? If we think quietly, we should realize that one of the most important mottos of human science and technology is to quantify different physical or social parametres which can affect our system. The quantification implies the estimation of the parametres in terms of number system. We, the human mind cannot think much without numbers. So our constant effort has been to put everything into number which does or may have any impact on our lives. Not only the physical parametres but also some social parametres are weighed in terms of number. Like in democracy the opinions of people are counted by votes. The wealth is counted by currency. The merit of a student is estimated by the marks awarded to him in examination. Even in today's life your popularity is counted by the number of ‘likes’ offered by your friends in social networking media. In technical industry, the same effort is strongly needed for two aspects. One, the economic aspect and the other is the scientific aspect. The economy and cost is immensely related to the production of an industry at different level.

Introduction

A motor is probably the most utilized invention of mankind after the ignition of fire. We always wanted to increase the energy of a motor. Electricity is the most trusted source of energy in science and technology. Electrical energy can be efficiently applied to run a motor. We have seen in chapter 8 how a DC voltage source can operate a DC motor. In the era of AC generation, use of DC motors became quite obsolete. We know an AC generation is generally essentially of three phase. A motor which can be operated by three phase power can make the coordination between power and motor useful. We have also seen that a three phase current can induce a rotating magnetic field. This phenomenon was first discovered by French physicist Francois Arago in 1824. This Arago's rotation helped the engineers to design a rotating machine which takes power from a three-phase AC power supply. The most used motor in technology of these days is the three phase induction motor. The induction motor operates on the principle of transformer emf induced in rotor three phase circuit due to three phase power supplied in stator winding. In this chapter we shall solely concentrate on three phase induction motor.

To understand the working principal of three phase induction motor, let us consider a magnetic strip of alternating poles situated sequentially. Let us consider another bar magnet is placed above the magnetic strip without any physical contact. The strip and the bar are magnetically coupled. This is depicted in Fig. 10.1.

Introduction

Alternating current and voltage are having three parameters – magnitude, frequency and phase. We have to apply the rated constant magnitude and rated constant frequency voltage input to each and every electrical appliance for its proper functioning. The frequency and voltage value are specified on the label of the appliance. But for an electrical appliance there is generally no specification mentioned regarding the phase. Now the question is what is the phase of our supply voltage? Do we always use a single phase supply? We shall see that on AC generation is essentially polyphased. The optimum value of number of phase for the standard power system is three. We shall also see the load to this three phase system is also three phase. Though our domestic appliances are mostly single phase systems, we may have three phase load too. Though our domestic voltage supply is single phase, we need the three phase supply for industrial plants. In this chapter we shall focus on these different aspects of three phase system.

Concept of Three Phase Voltage

In the chapter 4, we have seen an AC voltage is sinusoidal in nature.

The AC voltage is having peak voltage Vm and frequency f = 1/T. This voltage is a simple single phase voltage we have chosen the reference point at 0 so the phase of the voltage is zero.

Introduction

The technological advancement has been achieved so far by faming the energy in the most useful manner. From transportation to cotton mill, from airline to emergency medical services every modern amenity demands energy to operate. For the last two hundred years or more, we have used fossil fuels as the major source of energy. The valuable fossil fuels are in the form of coal and petroleum oil and gas. The most useful form of energy that can be widely used is electrical energy. Electrical energy is the most convenient form of energy to transmit across a long distance via current carrying conductor. We, the modern people, are completely dependent on electricity. The prime source of power of any modern civilization is electricity. The power flows from the generating end to the user via a very complex network, spread over thousands of kilometers, across different states and nations. This whole system through which these transactions of energy occur is known as power system. Power system deals with the power in the form of electricity. Power system plays a major big role in technological development and economy of the world. In this chapter we shall build a general idea about how the electrical power is generated and travelled a long distance before its utilization.

Basic Structure of Power System

We have already discussed that power system starts at the generating station and ends at the electrical load of the users. A lot of things happen in between the source and utilization of the power. We can segregate the whole path of the power flow into three different operational divisions. These three divisions constitute the complete operation of the power system. Let us elaborate our discussion on these three divisions of power system – generation, transmission and distribution.

Introduction

The seventeenth century was the century for theorization of electricity. The electrical technology became more and more advanced and complex. Direct current technology was dominating the new inventions. It was very necessary to mathematize the different parameters of these complex electrical connections and circuits. We had to develop a new mathematical model to calculate and determine the voltage, current power etc. of a circuit at different branches and nodes without measuring it directly. Some important theorems regarding electrical circuit were mutated during the last half of the century. These theorems work good with some constrain in the nature of the circuit. Before the semiconductor circuits or electronic circuits came into the picture these theorems were successfully used to determined different parameters of an electrical circuit. In this chapter let us find out and discuss about some of those electrical circuit theories.

Basic Concepts: Electric Circuit, Loop, Mesh etc.

• a. Electric circuit: An electric circuit or electric network is a combination of different electric components (discussed in the next topic) via loop and branches of conductors.

• b. Node: A node is a junction of an electric circuit where two or more circuit components are connected together.

• c. Branch: Branch is the part of the circuit which lies between two junctions or nodes in an electric circuit.

• d. Loop: Loop is the closed path in an electric circuit in which no element or node is connected more than once.

• e. Mesh: Mesh is such a loop that does not involve no other loop in it. So every mesh is a loop but all loops are not meshes.

Introduction

In the previous chapter we got a brief idea of electric machine. In case of a generator, the mechanical input is transformed into electrical output via a magnetic circuit whereas in case of a motor the energy flow is just reversal. But they all transform one energy form to another energy form via magnetic transformation. It will not be very wrong if we call all machines are transformers. But in electric engineering we exclusively specify a special type of electric (static) machine as the transformer. A motor or a generator transforms the electrical energy to mechanical energy and vice-versa. We have seen the energy flow diagram of these in Fig. 8.1a and Fig. 8.1b. In these cases the quality of the energy parameters is completely transformed. We get mechanical energy parameters, like torque and speed transformed as electrical parameters like voltage and current in generator. We get the reversed effect in motor. Transformer is such a static machine that transforms one form of electrical energy to another form of electrical energy. There is no qualitative transformation in the energy parameters. We obtain voltage and current output from voltage and current input. Only the quantity of the parameters get changed due to this transformation. That is, the input voltage level is different from the output voltage value in a transformer. Being a non-perpetual machine the transformer ought to follow the energy conservation law. The electric energy is measured by the product of voltage and current. Thus, in a transformer V×I of input side should be equal to the V×I of the output side.