# VK MEHTA ELECTRICAL MACHINES PDF

Chapter (1) D.C. Generators Introduction Although a far greater percentage of the electrical machines in service are a.c. machines, the d.c. machines are of. Download Principle of Electrical Machines By V.K. Mehta, Rohit Mehta – For over 15 years “Principles of Electrical Machines” is an ideal text for students who. Principles of Electrical Machines is an ideal text for students who look to gain a current and clear understanding of the subject as all theories and concep.

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Principle of Electrical Machines, 2/e. V K Mehta & Rohit Mehta. ISBN: Pages: Binding: Paperback. Language: English. Imprint: S. As an extension of Electrical machines I course this subject facilitates to. 2. Principles of Electrical Machines, V.K. Mehta, Rohit Mehta, S. Chand study of the . Principles of Electrical Machines by V. K. Mehta, , available at Book Depository with free delivery worldwide.

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Join With us. Today Updates. Statics and Dynamics By R. It is very important that brushes are in correct position relative to the field poles. By right-hand rule, the direction of e. In order to find the position of brushes, the ring diagram shown in Fig. A positive brush will be placed on that commutator segment where the currents in the coils are meeting to flow out of the segment. A negative brush will be placed on that commutator segment where the currents in the coils are meeting to flow in.

Referring to Fig. Therefore, we arrive at a very important conclusion that in a simplex lap winding, the number of brushes is equal to the number of poles.

If the brushes of the same polarity are connected together, then all the armature conductors are connected in four parallel paths; each path containing an equal number of conductors in series.

Since segments 6 and 16 are connected together through positive brushes and segments 11 and 1 are connected together through negative brushes, there are four parallel paths, each containing 10 conductors in series.

Therefore, in a simplex lap winding, the number of parallel paths is equal to the number of poles. Therefore, the armature winding has 4 parallel paths, each consisting of 10 conductors in series. As a result, the coil voltages add. The simplex wave winding must not close after it passes once around the armature but it must connect to a commutator segment adjacent to the first and the next coil must be adjacent to the first as indicated in Fig.

This is repeated each time around until connections are made to all the commutator segments and all the slots are occupied after which the winding automatically returns to the starting point.

If, after passing once around the armature, the winding connects to a segment to the left of the starting point, the winding is retrogressive [See Fig. If it connects to a segment to the right of the starting point, it is progressive [See Fig. This type of winding is called wave winding because it passes around the armature in a wave-like form. The YB must be an odd integer so that a top conductor and a bottom conductor will be joined. The YB must be an odd integer so that a top conductor and a bottom Fig.

When one tour of armature has been 2 completed, the winding should connect to the next top conductor progressive or to the preceding top conductor retrogressive.

In either case, the difference will be of 2 conductors or one slot. In Eq. If they differ by 2, they are one more and one less than YA. The two conductors which lie in the same slot are drawn nearer to each other than to those in the other slots. This means that the number of commutator segments spanned between the start end and finish end of any coil is 11 segments. Position and number of brushes We now turn to find the position and the number of brushes.

By right hand rule, the direction of e. It is clear that only two brushes—one positive and one negative—are required though two positive and two negative brushes can also be used. We find that there are two parallel paths between the positive brush and the negative brush. Thus is illustrated in Fig. Therefore, we arrive at a very important conclusion that in a simplex wave winding, the number of parallel paths is two irrespective of the number of poles. Note that the first parallel path has 11 coils or 22 conductors while the second parallel path has 10 coils or 20 conductors.

This fact is not important as it may appear at first glance. The coils m the smaller group should supply less current to the external circuit. But the identity of the coils in either parallel path is rapidly changing from moment to moment.

Therefore, the average value of current through any particular coil is the same. Sometimes the standard armature punchings available in the market have slots that do not satisfy the above requirement so that more coils usually only one more are provided than can be utilized.

These extra coils are called dummy or dead coils. The dummy coil is inserted into the slots in the same way as the others to make the armature dynamically balanced but it is not a part of the armature winding.

Let us illustrate the use of dummy coils with a numerical example. Suppose the number of slots is 22 and each slot contains 2 conductors. The number of poles is 4. The extra coil or dummy coil is put in the slot.

One end of this coil is taped and the other end connected to the unused commutator segment segment 22 for the sake of appearance. Since only 21 segments are required, the two 21 and 22 segments are connected together and considered as one. On the other hand, the lap winding carries more current than a wave winding because it has more parallel paths. In small machines, the current-carrying capacity of the armature conductors is not critical and in order to achieve suitable voltages, wave windings are used.

On the other hand, in large machines suitable voltages are easily obtained because of the availability of large number of armature conductors and the current carrying capacity is more critical. Hence in large machines, lap windings are used. In general, a high-current armature is lap-wound to provide a large number of parallel paths and a low-current armature is wave-wound to provide a small number of parallel paths. A simplex wave-wound armature has two parallel paths irrespective of the number of poles.

In case of a pole machine, using simplex windings, the designer is restricted to either two parallel circuits wave or ten parallel circuits lap.

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Sometimes it is desirable to increase the number of parallel paths. For this purpose, multiplex windings are used. The sole purpose of multiplex windings is to increase the number of parallel paths enabling the armature to carry a large total current.

The degree of multiplicity or plex determines the number of parallel paths in the following manner: If an armature is changed from simplex lap to duplex lap without making any other change, the number of parallel paths is doubled and each path has half as many coils. The armature will then supply twice as much current at half the voltage. Thus a duplex wave winding has 4 parallel paths, triplex wave winding has 6 parallel paths and so on. The commutator and brushes cause the alternating e.

Further, the direction of current in coil reverses as it passes the brush. Thus when the coil approaches the contact with the brush, the current through the coil is in one direction; when the coil leaves the contact with the brush, the current has been reversed. This reversal of current in the coil as the coil passes a brush is called commutation and fakes place while the coil is short-circuited by the brush. These changes occur in every coil in turn. If, at the instant when the brush breaks contact with the commutator segment connected to the coil undergoing commutation, the current in the coil has not been reversed, the result will be sparking between the commutator segments and the brush.

The criterion of good commutation is that it should be sparkless. In order to have sparkless commutation, the brushes on the commutator should be placed at points known as neutral point where no voltage exists between adjacent segments. The conductors connected to these segments lie between the poles in position of zero magnetic flux which is termed as magnetic neutral axis M.

Equation of a D. Generator We shall now derive an expression for the e.

Generators The magnetic field in a d. Generators are generally classified according to their methods of field excitation. On this basis, d. Generators A d. The greater the speed and field current, greater is the generated e. It may be noted that separately excited d. The d. There are three types of self-excited generators depending upon the manner in which the field winding is connected to the armature, namely; i Series generator; ii Shunt generator; iii Compound generator i Series generator In a series wound generator, the field winding is connected in series with armature winding so that whole armature current flows through the field winding as well as the load.

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Since the field winding carries the whole of load current, it has a few turns of thick wire having low resistance. Series generators are rarely used except for special purposes e. The shunt field winding has many turns of fine wire having high resistance. Therefore, only a part of armature current flows through shunt field winding and the rest flows through the load.

A compound wound generator may be: Obviously, its value will depend upon the amount of current flowing and the value of contact resistance. This drop is generally small. Machine The losses in a d. All these losses appear as heat and thus raise the temperature of the machine.

They also lower the efficiency of the machine. Copper losses These losses occur due to currents in the various windings of the machine. There is also brush contact loss due to brush contact resistance i. This loss is generally included in armature copper loss.

Iron or Core losses These losses occur in the armature of a d. They are of two types viz.

Consider a small piece ab of the armature. When the piece ab is under N-pole, the magnetic lines pass from a to b. Half a revolution later, the same piece of iron is under S-pole and magnetic lines pass from b to a so that magnetism in the iron is reversed.

In order to reverse continuously the molecular magnets in the armature core, some amount of power has to be spent which is called hysteresis loss. It is given by Steinmetz formula. These voltages produce circulating currents in the armature core as shown in Fig.

These are called eddy currents and power loss due to their flow is called eddy current loss. The eddy current loss appears as heat which raises the temperature of the machine and lowers its efficiency.

If a continuous solid iron core is used, the resistance to eddy current path will be small due to large cross-sectional area of the core. Consequently, the magnitude of eddy current and hence eddy current loss will be large. The magnitude of eddy current can be reduced by making core resistance as high as practical. The laminations are insulated from each other with a coating of varnish.

The insulating coating has a high resistance, so very little current flows from one lamination to the other. Also, because each lamination is very thin, the resistance to current flowing through the width of a lamination is also quite large.

Thus laminating a core increases the core resistance which decreases the eddy current and hence the eddy current loss. For this reason, lamination thickness should be kept as small as possible. Mechanical losses These losses are due to friction and windage. These losses depend upon the speed of the machine. But for a given speed, they are practically constant. Iron losses and mechanical losses together are called stray losses. The constant losses in a d. The variable losses in a d.

Field Cu loss is constant for shunt and compound generators. Consider a shunt generator delivering a load current IL at a terminal voltage V. Fig 1. Although the armature winding is not provided for the purpose of producing a magnetic field, nevertheless the current in the armature winding will also produce magnetic flux called armature flux. The armature flux distorts and weakens the main flux posing problems for the proper operation of the d.

The action of armature flux on the main flux is called armature reaction. In the previous chapter Sec 1. This phenomenon is termed as commutation. The criterion for good commutation is that it should be sparkless. In order to have sparkless commutation, the brushes should lie along magnetic neutral axis. In this chapter, we shall discuss the various aspects of armature reaction and commutation in a d.

However, current flowing through armature conductors also creates a magnetic flux called armature flux that distorts and weakens the flux coming from the poles.

This distortion and field weakening takes place in both generators and motors. The action of armature flux on the main flux is known as armature reaction.

The phenomenon of armature reaction in a d. Only one pole is shown for clarity. Referring to Fig 2.

This unequal field distribution produces the following two effects: Consequently, the increase in flux at pole tip B is less than the decrease in flux under pole tip A. As we shall see, the weakening of flux due to armature reaction depends upon the position of brushes. Clearly, it is the axis of symmetry between two adjacent poles. Clearly, no e. With no current in the armature conductors, the M. In order to achieve sparkless commutation, the brushes must lie along M. However, when current flows in armature conductors, the combined action of main flux and armature flux shifts the M.

In case of a generator, the M. In order to achieve sparkless commutation, the brushes have to be moved along the new M. Under such a condition, the armature reaction produces the following two effects: It demagnetizes or weakens the main flux.

It cross-magnetizes or distorts the main flux. Let us discuss these effects of armature reaction by considering a 2-pole generator though the following remarks also hold good for a multipolar generator. The flux across the air gap is uniform. Note that OFm is perpendicular to G. The armature conductors to the left of G.

## Principles of Electronics-S. Chand V. K. Mehta, Rohit Mehta

The direction of magnetic lines of force can be found by cork screw rule. It is clear that armature flux is directed downward parallel to the brush axis. The resultant m. Since M.

Note that M. Due to brush shift, the m. It is because some of the conductors which were earlier under N-pole now come under S-pole and vice-versa.

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The result is that armature m. Now FA can be resolved into rectangular components Fc and Fd. OFm due to main poles. It has a demagnetizing effect on the flux due to main poles. For this reason, it is called the demagnetizing or weakening component of armature reaction. It distorts the main field. For this reason, it is called the cross- magnetizing or distorting component of armature reaction. It may be noted that with the increase of armature current, both demagnetizing and distorting effects will increase.

Conclusions i With brushes located along G. There is only distorting or cross- magnetizing effect of armature reaction. Their relative magnitudes depend on the amount of shift. This shift is directly proportional to the armature current.

On the other hand, the distorting component of armature reaction distorts the main flux. However, when the brushes are shifted from the G. We shall identify the armature conductors that produce demagnetizing effect and those that produce cross-magnetizing effect. These are called demagnetizing armature conductors and constitute the demagnetizing ampere-turns of armature reaction Remember two conductors constitute a turn.

These conductors produce the cross-magnetizing or distorting effect i. Therefore, they are called cross-magnetizing conductors and constitute the cross-magnetizing ampere-turns of armature reaction. This is achieved by adding extra ampere-turns to the main field winding. When a conductor passes a pair of poles, one cycle of voltage is generated. We say one cycle contains electrical degrees. In order to neutralize the cross- magnetizing effect of armature reaction, a compensating winding is used.

A compensating winding is an auxiliary winding embedded in slots in the pole faces as shown in Fig. It is connected in series with armature in a Fig. If Z is the total number of armature conductors and P is the number of poles, then, Z No. There are two parallel paths between the brushes. Note that the currents in the coils connected to a brush are either all towards the brush positive brush or all directed away from the brush negative brush.

Therefore, current in a coil will reverse as the coil passes a brush. When commutation takes place, the coil undergoing commutation is short- circuited by the brush. The brief period during which the coil remains short- circuited is known as commutation period Tc. If the current reversal is completed by the end of commutation period, it is called ideal commutation. If the current reversal is not completed by that time, then sparking occurs between the brush and the commutator which results in progressive damage to both.

Ideal commutation Let us discuss the phenomenon of ideal commutation i. For this purpose, we consider the coil A. The brush width is equal to the width of one commutator segment and one mica insulation. Suppose the total armature current is 40 A. Since there are two parallel paths, each coil carries a current of 20 A. The commutator segment 1 conducts a current of 40 A to the brush; 20 A from coil A and 20 A from the adjacent coil as shown.

The coil A has yet to undergo commutation. There are now two parallel paths into the brush as long as the short-circuit of coil A exists. For this condition, the resistance of the path through segment 2 is three times the resistance of the path through segment 1 Q contact resistance varies inversely as the area of contact of brush with the segment.

The brush again conducts a current of 40 A; 30 A through segment 1 and 10 A through segment 2. Note that current in coil A the coil undergoing commutation is reduced from 20 A to 10 A. The brush again conducts 40 A; 20 A through segment 1 and 20 A through segment 2 Q now the resistances of the two parallel paths are equal.

Note that now. The brush conducts a current of 40 A; 30 A through segment 2 and 10 A through segment 1. Note that current in coil A is 10 A but in the reverse direction to that before the start of commutation. The reader may see the action of the commutator in reversing the current in a coil as the coil passes the brush axis. Note that now current in coil A is 20 A but in the reverse direction.

Thus the coil A has undergone commutation. Each coil undergoes commutation in this way as it passes the brush axis. Note that during commutation, the coil under consideration remains short- circuited by the brush. The horizontal line AB represents a constant current of 20 A upto the beginning of commutation.

From the finish of commutation, it is represented by another horizontal line CD on the opposite side of the zero line and Fig. The way in which current changes from B to C depends upon the conditions under which the coil undergoes commutation. If the current changes at a uniform rate i. Under such conditions, no sparking will take place between the brush and the commutator.

Practical difficulties The ideal commutation i. This is mainly due to the fact that the armature coils have appreciable inductance. When the current in the coil undergoing commutation changes, self-induced e. This is generally called reactance voltage. This reactance voltage opposes the change of current in the coil undergoing commutation. The straight line RC represents the ideal commutation whereas the curve BE represents the change in current when self-inductance of the coil is taken into account.

This results in sparking just as when any other current- carrying circuit is broken. The sparking results in overheating of commutator- brush contact and causing damage to both. At the end of commutation or short-circuit period, the current in coil A is reversed to a value of 12 A instead of 20 A due to inductance of the coil.

When the brush breaks contact with segment 1, the remaining 8 A current jumps from segment 1 to the brush through air causing sparking between segment 1 and the brush. Therefore, the time of short circuit or commutation period Tc is equal to the time required by the commutator to move a distance equal to the circumferential thickness of the brush minus the thickness of one insultating strip of mica.

The following are the two principal methods of improving commutation: Therefore, there are two parallel paths for the current as long as the short circuit exists. If the contact resistance between the brush and the commutator is made large, then current would divide in the inverse ratio of contact resistances as for any two resistances in parallel. This is the key point in improving commutation. This is achieved by using carbon brushes instead of Cu brushes which have high contact resistance.

This method of improving commutation is called resistance commutation. The coil A is yet to undergo commutation. As the armature rotates, the brush short- circuits the coil A and there are two parallel paths for the current into the brush.

The equivalent electric circuit is shown in Fig. The values of current in the parallel paths of the equivalent circuit are determined by the respective resistances of the paths. For the condition shown in Fig. Therefore, the current distribution in the paths will be as shown. Note that current in coil A is reduced from 20 A to 10 A due to division of current in he inverse ratio of contact resistances.

If the Cu brush is used which has low contact resistance , R1 R2 and the current in coil A would not have reduced to 10 A. As the carbon brush passes over the commutator, the contact area with segment 2 increases and that with segment 1 decreases i. Therefore, more and more current passes to the brush through segment 2. This is illustrated in Figs. It may be noted that the main cause of sparking during commutation is the production of reactance voltage and carbon brushes cannot prevent it.

Nevertheless, the carbon brushes do help in improving commutation.

The other minor advantages of carbon brushes are: Commutation In this method, an arrangement is made to neutralize the reactance voltage by producing a reversing voltage in the coil undergoing commutation. The reversing voltage acts in opposition to the reactance voltage and neutralizes it to some extent. If the reversing voltage is equal to the reactance voltage, the effect of the latter is completely wiped out and we get sparkless commutation.

The reversing voltage may be produced in the following two ways: Since the short-circuited coil is now in the reversing field, the reversing voltage produced cancels the reactance voltage. This method suffers from the following drawbacks: Therefore, the brush shift will depend on the magnitude of armature current which keeps on changing.

This necessitates frequent shifting of brushes. This increases the demagnetizing effect of armature reaction and further weakens the main field.

This method is discussed in Sec. These are small poles fixed to the yoke and spaced mid-way between the main poles See Fig. They are wound with comparatively few turns and connected in series with the armature so that they carry armature current. Their polarity is the same as the next main pole ahead in the direction of rotation for a generator See Fig.

Connections for a d. The interpoles perform the following two functions: This leads to sparkless commutation. The e. Since the interpoles carry the armature current and the reactance voltage is also proportional to armature current, the neutralization of reactance voltage is automatic.

It is because the two m. Both these windings are connected in series with the armature and so they carry the armature current. However, the functions they perform must be understood clearly.

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The main function of commutating winding is to produce reversing or commutating e. The compensating winding neutralizes the cross-magnetizing effect of armature reaction under the pole faces. Because of wear in the bearings, and for other reasons, the air gaps in a generator become unequal and, therefore, the flux in some poles becomes greater than in others. This causes the voltages of the different paths to be unequal. With unequal voltages in these parallel paths, circulating current will flow even if no current is supplied to an external load.

If these currents are large, some of the brushes will be required to carry a greater current at full load than they were designed to carry and this will cause sparking. To relieve the brushes of these circulating currents, points on the armature that are at the same potential are connected together by means of copper bars called equalizer rings. This is achieved by connecting to the same equalizer ring the coils that occupy the same positions relative to the poles See Fig.

Thus referring to Fig. Therefore, the two coils are connected to the same equalizer ring. The equalizers provide a low resistance path for the circulating current. As a result, the circulating current due to the slight differences in the voltages of the various parallel paths passes through the equalizer rings instead of passing through the brushes.

This reduces sparking. For best results, each coil should be connected to an equalizer ring but this is seldom done. Satisfactory results are obtained by connecting about every third coil to an equalizer ring. In order to distribute the connections to the equalizer rings equally, the number of coils per pole must be divisible by the connection pitch.

Equalizer rings are not used in wave winding because there is no imbalance in the voltages of the two parallel paths. This is due to the fact that conductors in each of the two paths pass under all N and S poles successively unlike a lap winding where all conductors in any parallel path lie under one pair of poles. Therefore, even if there are inequalities in pole flux, they will affect each path equally.

Chapter 3 D. Generator Characteristics Introduction The speed of a d.

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For general-purpose operation, the prime mover is equipped with a speed governor so that the speed of the generator is practically constant.

Under such condition, the generator performance deals primarily with the relation between excitation, terminal voltage and load. These relations can be best exhibited graphically by means of curves known as generator characteristics.

These characteristics show at a glance the behaviour of the generator under different load conditions. Generator Characteristics The following are the three most important characteristics of a d. Open Circuit Characteristic O. This curve shows the relation between the generated e. It is also known as magnetic characteristic or no-load saturation curve. Its shape is practically the same for all generators whether separately or self-excited.

The data for O. E is less than E0 due to the demagnetizing effect of armature reaction. Therefore, this curve will lie below the open circuit characteristic O. The internal characteristic is of interest chiefly to the designer.

It cannot be obtained directly by experiment. It is because a voltmeter cannot read the e. The internal characteristic can be obtained from external characteristic if winding resistances are known because armature reaction effect is included in both characteristics. The terminal voltage V will be less than E due to voltage drop in the armature circuit.

## Principle of Electrical Machines, 2/e

Therefore, this curve will lie below the internal characteristic. This characteristic is very important in determining the suitability of a generator for a given purpose. It can be obtained by making simultaneous measurements of terminal voltage and load current with voltmeter and ammeter of a loaded generator.

Generator The O. The field winding of the d. The generator is run at fixed speed i. The field current If is increased from zero in steps and the corresponding values of generated e.

E0 read off on a voltmeter connected across the armature terminals. On plotting the relation between E0 and If, we get the open circuit characteristic as shown in Fig. This is due to the residual magnetism in the field poles. It is because in this range, reluctance of iron is negligible as compared with that of air gap.

The air gap reluctance is constant and hence linear relationship. Consequently, the curve deviates from linear relationship. The reader may note that the O. Generator The obvious disadvantage of a separately excited d. But since the output voltage may be controlled more easily and over a wide range from zero to a maximum , this type of excitation finds many applications.

The O. Note that if the value of constant speed is increased, the steepness of the curve also increases. When the field current is zero, the residual magnetism in the poles will give rise to the small initial e.

In order to determine the external characteristic, the circuit set up is as shown in Fig. As the load current increases, the terminal voltage falls due to two reasons: Due to these reasons, the external characteristic is a drooping curve [curve 3 in Fig.

Note that in the absence of armature reaction and armature drop, the generated e.

The internal characteristic can be determined from external characteristic by adding ILRa drop to the external characteristic. It is because armature reaction drop is included in the external characteristic. If the generator is run at a constant speed, some e. This small e. This process continues and the generator builds up the normal generated voltage following the O.

The field resistance Rf can be represented by a straight line passing through the origin as shown in Fig. The two curves can be shown on the same diagram as they have the same ordinate [See Fig. Mehta, Rohit Mehta, S. Chand Publishing. Access Content. Have you ever thought, What is electrical current? What are amps? View Video. Return Doc. EEE Course Title: Principles of Elctrical Machines: Doc Retrieval. The principal advantage of the d. Retrieve Doc. TV room, washing machines, and dining etc.

Read Article. Document Retrieval.It may be noted that as the load is added, the increased amount of flux causes the speed to decrease more than does the speed of a shunt motor. This is achieved by adding extra ampere-turns to the main field winding. When a conductor passes a pair of poles, one cycle of voltage is generated. Generator The d. Eb in a shunt motor are almost constant under normal conditions.

If the e. Related Searching Keywords. Consequently, the increase in flux at pole tip B is less than the decrease in flux under pole tip A.