Principles of electrical machines

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 considerable industrial importance The principal advantage of the d.c machine, particularly the d.c motor, is that it provides a fine control of speed Such an advantage is not claimed by any a.c motor However, d.c generators are not as common as they used to be, because direct current, when required, is mainly obtained from an a.c supply by the use of rectifiers Nevertheless, an understanding of d.c generator is important because it represents a logical introduction to the behaviour of d.c motors Indeed many d.c motors in industry actually operate as d.c generators for a brief period In this chapter, we shall deal with various aspects of d.c generators 1.1 Generator Principle An electric generator is a machine that converts mechanical energy into electrical energy An electric generator is based on the principle that whenever flux is cut by a conductor, an e.m.f is induced which will cause a current to flow if the conductor circuit is closed The direction of induced e.m.f (and hence current) is given by Fleming’s right hand rule Therefore, the essential components of a generator are: (a) a magnetic field (b) conductor or a group of conductors (c) motion of conductor w.r.t magnetic field 1.2 Simple Loop Generator Consider a single turn loop ABCD rotating clockwise in a uniform magnetic field with a constant speed as shown in Fig.(1.1) As the loop rotates, the flux linking the coil sides AB and CD changes continuously Hence the e.m.f induced in these coil sides also changes but the e.m.f induced in one coil side adds to that induced in the other (i) When the loop is in position no [See Fig 1.1], the generated e.m.f is zero because the coil sides (AB and CD) are cutting no flux but are moving parallel to it (ii) When the loop is in position no 2, the coil sides are moving at an angle to the flux and, therefore, a low e.m.f is generated as indicated by point in Fig (1.2) (iii) When the loop is in position no 3, the coil sides (AB and CD) are at right angle to the flux and are, therefore, cutting the flux at a maximum rate Hence at this instant, the generated e.m.f is maximum as indicated by point in Fig (1.2) (iv) At position 4, the generated e.m.f is less because the coil sides are cutting the flux at an angle (v) At position 5, no magnetic lines are cut and hence induced e.m.f is zero as indicated by point in Fig (1.2) (vi) At position 6, the coil sides move under a pole of opposite polarity and hence the direction of generated e.m.f is reversed The maximum e.m.f in this direction (i.e., reverse direction, See Fig 1.2) will be when the loop is at position and zero when at position This cycle repeats with each revolution of the coil Fig (1.1) Fig (1.2) Note that e.m.f generated in the loop is alternating one It is because any coil side, say AB has e.m.f in one direction when under the influence of N-pole and in the other direction when under the influence of S-pole If a load is connected across the ends of the loop, then alternating current will flow through the load The alternating voltage generated in the loop can be converted into direct voltage by a device called commutator We then have the d.c generator In fact, a commutator is a mechanical rectifier 1.3 Action Of Commutator If, somehow, connection of the coil side to the external load is reversed at the same instant the current in the coil side reverses, the current through the load will be direct current This is what a commutator does Fig (1.3) shows a commutator having two segments C1 and C2 It consists of a cylindrical metal ring cut into two halves or segments C1 and C2 respectively separated by a thin sheet of mica The commutator is mounted on but insulated from the rotor shaft The ends of coil sides AB and CD are connected to the segments C1 and C2 respectively as shown in Fig (1.4) Two stationary carbon brushes rest on the commutator and lead current to the external load With this arrangement, the commutator at all times connects the coil side under S-pole to the +ve brush and that under N-pole to the −ve brush (i) In Fig (1.4), the coil sides AB and CD are under N-pole and S-pole respectively Note that segment C1 connects the coil side AB to point P of the load resistance R and the segment C2 connects the coil side CD to point Q of the load Also note the direction of current through load It is from Q to P (ii) After half a revolution of the loop (i.e., 180° rotation), the coil side AB is under S-pole and the coil side CD under N-pole as shown in Fig (1.5) The currents in the coil sides now flow in the reverse direction but the segments C1 and C2 have also moved through 180° i.e., segment C1 is now in contact with +ve brush and segment C2 in contact with −ve brush Note that commutator has reversed the coil connections to the load i.e., coil side AB is now connected to point Q of the load and coil side CD to the point P of the load Also note the direction of current through the load It is again from Q to P Fig.(1.3) Fig.(1.4) Fig.(1.5) Thus the alternating voltage generated in the loop will appear as direct voltage across the brushes The reader may note that e.m.f generated in the armature winding of a d.c generator is alternating one It is by the use of commutator that we convert the generated alternating e.m.f into direct voltage The purpose of brushes is simply to lead current from the rotating loop or winding to the external stationary load The variation of voltage across the brushes with the angular displacement of the loop will be as shown in Fig (1.6) This is not a steady direct voltage but has a pulsating character It is because the voltage appearing across the brushes varies from zero to maximum value and back to zero twice for each revolution of the loop A Fig (1.6) pulsating direct voltage such as is produced by a single loop is not suitable for many commercial uses What we require is the steady direct voltage This can be achieved by using a large number of coils connected in series The resulting arrangement is known as armature winding 1.4 Construction of d.c Generator The d.c generators and d.c motors have the same general construction In fact, when the machine is being assembled, the workmen usually not know whether it is a d.c generator or motor Any d.c generator can be run as a d.c motor and vice-versa All d.c machines have five principal components viz., (i) field system (ii) armature core (iii) armature winding (iv) commutator (v) brushes [See Fig 1.7] Fig (1.7) (i) Fig (1.8) Field system The function of the field system is to produce uniform magnetic field within which the armature rotates It consists of a number of salient poles (of course, even number) bolted to the inside of circular frame (generally called yoke) The yoke is usually made of solid cast steel whereas the pole pieces are composed of stacked laminations Field coils are mounted on the poles and carry the d.c exciting current The field coils are connected in such a way that adjacent poles have opposite polarity The m.m.f developed by the field coils produces a magnetic flux that passes through the pole pieces, the air gap, the armature and the frame (See Fig 1.8) Practical d.c machines have air gaps ranging from 0.5 mm to 1.5 mm Since armature and field systems are composed of materials that have high permeability, most of the m.m.f of field coils is required to set up flux in the air gap By reducing the length of air gap, we can reduce the size of field coils (i.e number of turns) (ii) Armature core The armature core is keyed to the machine shaft and rotates between the field poles It consists of slotted soft-iron laminations (about 0.4 to 0.6 mm thick) that are stacked to form a cylindrical core as shown in Fig (1.9) The laminations (See Fig 1.10) are individually coated with a thin insulating film so that they not come in electrical contact with each other The purpose of laminating the core is to reduce the eddy current loss The laminations are slotted to accommodate and provide mechanical security to the armature winding and to give shorter air gap for the flux to cross between the pole face and the armature “teeth” Fig (1.9) Fig (1.10) (iii) Armature winding The slots of the armature core hold insulated conductors that are connected in a suitable manner This is known as armature winding This is the winding in which “working” e.m.f is induced The armature conductors are connected in series-parallel; the conductors being connected in series so as to increase the voltage and in parallel paths so as to increase the current The armature winding of a d.c machine is a closed-circuit winding; the conductors being connected in a symmetrical manner forming a closed loop or series of closed loops (iv) Commutator A commutator is a mechanical rectifier which converts the alternating voltage generated in the armature winding into direct voltage across the brushes The commutator is made of copper segments insulated from each other by mica sheets and mounted on the shaft of the machine (See Fig 1.11) The armature conductors are soldered to the commutator segments in a suitable manner to give rise to the armature winding Depending upon the manner in which the armature conductors are connected to the commutator segments, there are two types of armature winding in a d.c machine viz., (a) lap winding (b) wave winding Great care is taken in building the commutator because any eccentricity will cause the brushes to bounce, producing unacceptable sparking The sparks may bum the brushes and overheat and carbonise the commutator (v) Brushes The purpose of brushes is to ensure electrical connections between the rotating commutator and stationary external load circuit The brushes are made of carbon and rest on the commutator The brush pressure is adjusted by means of adjustable springs (See Fig 1.12) If the brush pressure is very large, the friction produces heating of the commutator and the brushes On the other hand, if it is too weak, the imperfect contact with the commutator may produce sparking Fig (1.11) Fig (1.12) Multipole machines have as many brushes as they have poles For example, a 4pole machine has brushes As we go round the commutator, the successive brushes have positive and negative polarities Brushes having the same polarity are connected together so that we have two terminals viz., the +ve terminal and the −ve terminal 1.5 General Features OF D.C Armature Windings (i) A d.c machine (generator or motor) generally employs windings distributed in slots over the circumference of the armature core Each conductor lies at right angles to the magnetic flux and to the direction of its movement Therefore, the induced e.m.f in the conductor is given by; e = Bl v where volts B = magnetic flux density in Wb/m2 l = length of the conductor in metres v = velocity (in m/s) of the conductor (ii) The armature conductors are connected to form coils The basic component of all types of armature windings is the armature coil Fig (1.13) (i) shows a single-turn coil It has two conductors or coil sides connected at the back of the armature Fig 1.13 (ii) shows a 4-turn coil which has conductors or coil sides Fig (1.13) The coil sides of a coil are placed a pole span apart i.e., one coil side of the coil is under N-pole and the other coil side is under the next S-pole at the corresponding position as shown in Fig 1.13 (i) Consequently the e.m.f.s of the coil sides add together If the e.m.f induced in one conductor is 2.5 volts, then the e.m.f of a single-turn coil will be = × 2.5 = volts For the same flux and speed, the e.m.f of a 4-turn coil will be = × 2.5 = 20 V (iii) Most of d.c armature windings are double layer windings i.e., there are two coil sides per slot as shown in Fig (1.14) One coil side of a coil lies at the top of a slot and the other coil side lies at the bottom of some Fig (1.14) other slot The coil ends will then lie side by side In two-layer winding, it is desirable to number the coil sides rather than the slots The coil sides are numbered as indicated in Fig (1.14) The coil sides at the top of slots are given odd numbers and those at the bottom are given even numbers The coil sides are numbered in order round the armature As discussed above, each coil has one side at the top of a slot and the other side at the bottom of another slot; the coil sides are nearly a pole pitch apart In connecting the coils, it is ensured that top coil side is joined to the bottom coil side and vice-versa This is illustrated in Fig (1.15) The coil side at the top of a slot is joined to coil side 10 at the bottom of another slot about a pole pitch apart The coil side 12 at the bottom of a slot is joined to coil side at the top of another slot How coils are connected at the back of the armature and at the front (commutator end) will be discussed in later sections It may be noted that as far as connecting the coils is concerned, the number of turns per coil is immaterial For simplicity, then, the coils in winding diagrams will be represented as having only one turn (i.e., two conductors) Fig (1.15) Fig (1.16) (iv) The coil sides are connected through commutator segments in such a manner as to form a series-parallel system; a number of conductors are connected in series so as to increase the voltage and two or more such series-connected paths in parallel to share the current Fig (1.16) shows how the two coils connected through commutator segments (A, R, C etc) have their e.m.f.s added together If voltage induced in each conductor is 25 V, then voltage between segments A and C = × 2.5 = 10 V It may be noted here that in the conventional way of representing a developed armature winding, full lines represent top coil sides (i.e., coil sides lying at the top of a slot) and dotted lines represent the bottom coil sides (i.e., coil sides lying at the bottom of a slot) (v) The d.c armature winding is a closed circuit winding In such a winding, if one starts at some point in the winding and traces through the winding, one will come back to the starting point without passing through any external connection D.C armature windings must be of the closed type in order to provide for the commutation of the coils 1.6 Commutator Pitch (YC) The commutator pitch is the number of commutator segments spanned by each coil of the winding It is denoted by YC In Fig (1.17), one side of the coil is connected to commutator segment and the other side connected to commutator segment Therefore, the number of commutator segments spanned by the coil is i.e., YC = In Fig (1.18), one side of the coil is connected to commutator segment and the other side to commutator segment Therefore, the number of commutator segments spanned by the coil = − = segments i.e., YC = The commutator pitch of a winding is always a whole number Since each coil has two ends and as two coil connections are joined at each commutator segment, Fig (1.17) Fig (1.18) ∴ Number of coils = Number of commutator segments For example, if an armature has 30 conductors, the number of coils will be 30/2 = 15 Therefore, number of commutator segments is also 15 Note that commutator pitch is the most important factor in determining the type of d.c armature winding 1.7 Pole-Pitch It is the distance measured in terms of number of armature slots (or armature conductors) per pole Thus if a 4-pole generator has 16 coils, then number of slots = 16 ∴ Also Pole pitch = 16 = slots Pole pitch = No of conductors 16 × = = conductors No of poles 1.8 Coil Span or Coil Pitch (YS) It is the distance measured in terms of the number of armature slots (or armature conductors) spanned by a coil Thus if the coil span is slots, it means one side of the coil is in slot and the other side in slot 10 1.9 Full-Pitched Coil If the coil-span or coil pitch is equal to pole pitch, it is called full-pitched coil (See Fig 1.19) In this case, the e.m.f.s in the coil sides are additive and have a phase difference of 0° Therefore, e.m.f induced in the coil is maximum If e.m.f induced in one coil side is 2-5 V, then e.m.f across the coil terminals = × 2.5 = V Therefore, coil span should always be one pole pitch unless there is a good reason for making it shorter Fractional pitched coil If the coil span or coil pitch is less than the pole pitch, then it is called fractional pitched coil (See Fig 1.20) In this case, the phase difference between the e.m.f.s in the two coil sides will not be zero so that the e.m.f of the coil will be less compared to full-pitched coil Fractional pitch winding requires less copper but if the pitch is too small, an appreciable reduction in the generated e.m.f results Synchronous speed, N s = where 120f P f = frequency of supply in Hz P = number of poles An important drawback of a synchronous motor is that it is not self-starting and auxiliary means have to be used for starting it 11.2 Some Facts about Synchronous Motor Some salient features of a synchronous motor are: (i) A synchronous motor runs at synchronous speed or not at all Its speed is constant (synchronous speed) at all loads The only way to change its speed is to alter the supply frequency (Ns = 120 f/P) (ii) The outstanding characteristic of a synchronous motor is that it can be made to operate over a wide range of power factors (lagging, unity or leading) by adjustment of its field excitation Therefore, a synchronous motor can be made to carry the mechanical load at constant speed and at the same time improve the power factor of the system (iii) Synchronous motors are generally of the salient pole type (iv) A synchronous motor is not self-starting and an auxiliary means has to be used for starting it We use either induction motor principle or a separate starting motor for this purpose If the latter method is used, the machine must be run up to synchronous speed and synchronized as an alternator 11.3 Operating Principle The fact that a synchronous motor has no starting torque can be easily explained (i) Consider a 3-phase synchronous motor having two rotor poles NR and SR Then the stator will also be wound for two poles NS and SS The motor has direct voltage applied to the rotor winding and a 3-phase voltage applied to the stator winding The stator winding produces a rotating field which revolves round the stator at synchronous speed Ns(= 120 f/P) The direct (or zero frequency) current sets up a two-pole field which is stationary so long as the rotor is not turning Thus, we have a situation in which there exists a pair of revolving armature poles (i.e., NS − SS) and a pair of stationary rotor poles (i.e., NR − SR) (ii) Suppose at any instant, the stator poles are at positions A and B as shown in Fig (11.2 (i)) It is clear that poles NS and NR repel each other and so the poles SS and SR Therefore, the rotor tends to move in the anticlockwise direction After a period of half-cycle (or ½ f = 1/100 second), the polarities of the stator poles are reversed but the polarities of the rotor poles remain the same as shown in Fig (11.2 (ii)) Now SS and NR attract 294 each other and so NS and SR Therefore, the rotor tends to move in the clockwise direction Since the stator poles change their polarities rapidly, they tend to pull the rotor first in one direction and then after a period of half-cycle in the other Due to high inertia of the rotor, the motor fails to start Fig.(10.2) Hence, a synchronous motor has no self-starting torque i.e., a synchronous motor cannot start by itself How to get continuous unidirectional torque? If the rotor poles are rotated by some external means at such a speed that they interchange their positions along with the stator poles, then the rotor will experience a continuous unidirectional torque This can be understood from the following discussion: (i) Suppose the stator field is rotating in the clockwise direction and the rotor is also rotated clockwise by some external means at such a speed that the rotor poles interchange their positions along with the stator poles (ii) Suppose at any instant the stator and rotor poles are in the position shown in Fig (11.3 (i)) It is clear that torque on the rotor will be clockwise After a period of half-cycle, the stator poles reverse their polarities and at the same time rotor poles also interchange their positions as shown in Fig (11.3 (ii)) The result is that again the torque on the rotor is clockwise Hence a continuous unidirectional torque acts on the rotor and moves it in the clockwise direction Under this condition, poles on the rotor always face poles of opposite polarity on the stator and a strong magnetic attraction is set up between them This mutual attraction locks the rotor and stator together and the rotor is virtually pulled into step with the speed of revolving flux (i.e., synchronous speed) (iii) If now the external prime mover driving the rotor is removed, the rotor will continue to rotate at synchronous speed in the clockwise direction because the rotor poles are magnetically locked up with the stator poles It is due to 295 this magnetic interlocking between stator and rotor poles that a synchronous motor runs at the speed of revolving flux i.e., synchronous speed Fig.(11.3) 11.4 Making Synchronous Motor Self-Starting A synchronous motor cannot start by itself In order to make the motor self-starting, a squirrel cage winding (also called damper winding) is provided on the rotor The damper winding consists of copper bars embedded in the pole faces of the salient poles of the rotor as shown in Fig (11.4) The bars are short-circuited at the ends to form in effect a partial Fig.(11.4) squirrel cage winding The damper winding serves to start the motor (i) To start with, 3-phase supply is given to the stator winding while the rotor field winding is left unenergized The rotating stator field induces currents in the damper or squirrel cage winding and the motor starts as an induction motor (ii) As the motor approaches the synchronous speed, the rotor is excited with direct current Now the resulting poles on the rotor face poles of opposite polarity on the stator and a strong magnetic attraction is set up between them The rotor poles lock in with the poles of rotating flux Consequently, the rotor revolves at the same speed as the stator field i.e., at synchronous speed (iii) Because the bars of squirrel cage portion of the rotor now rotate at the same speed as the rotating stator field, these bars not cut any flux and, therefore, have no induced currents in them Hence squirrel cage portion of the rotor is, in effect, removed from the operation of the motor 296 It may be emphasized here that due to magnetic interlocking between the stator and rotor poles, a synchronous motor can only run at synchronous speed At any other speed, this magnetic interlocking (i.e., rotor poles facing opposite polarity stator poles) ceases and the average torque becomes zero Consequently, the motor comes to a halt with a severe disturbance on the line Note: It is important to excite the rotor with direct current at the right moment For example, if the d.c excitation is applied when N-pole of the stator faces Npole of the rotor, the resulting magnetic repulsion will produce a violent mechanical shock The motor will immediately slow down and the circuit breakers will trip In practice, starters for synchronous motors arc designed to detect the precise moment when excitation should be applied 11.5 Equivalent Circuit Unlike the induction motor, the synchronous motor is connected to two electrical systems; a d.c source at the rotor terminals and an a.c system at the stator terminals Under normal conditions of synchronous motor operation, no voltage is induced in the rotor by the stator field because the rotor winding is rotating at the same speed as the stator field Only the impressed direct current is present in the rotor winding and ohmic resistance of this winding is the only opposition to it as shown in Fig (11.5 (i)) In the stator winding, two effects are to be considered, the effect of stator field on the stator winding and the effect of the rotor field cutting the stator conductors at synchronous speed Fig.(11.5) (i) The effect of stator field on the stator (or armature) conductors is accounted for by including an inductive reactance in the armature winding This is called synchronous reactance Xs A resistance Ra must be considered to be in series with this reactance to account for the copper losses in the stator or armature winding as shown in Fig (11.5 (i)) This 297 resistance combines with synchronous reactance and gives the synchronous impedance of the machine (ii) The second effect is that a voltage is generated in the stator winding by the synchronously-revolving field of the rotor as shown in Fig (11.5 (i)) This generated e.m.f EB is known as back e.m.f and opposes the stator voltage V The magnitude of Eb depends upon rotor speed and rotor flux φ per pole Since rotor speed is constant; the value of Eb depends upon the rotor flux per pole i.e exciting rotor current If Fig (11.5 (i)) shows the schematic diagram for one phase of a star-connected synchronous motor while Fig (11.5 (ii)) shows its equivalent circuit Referring to the equivalent circuit in Fig (11.5 (ii)) Net voltage/phase in stator winding is Er = V − Eb Armature current/phase, I a = where phasor difference Er Zs Zs = R 2a + X s2 This equivalent circuit helps considerably in understanding the operation of a synchronous motor A synchronous motor is said to be normally excited if the field excitation is such that Eb = V If the field excitation is such that Eb < V, the motor is said to be under-excited The motor is said to be over-excited if the field excitation is such that Eb > V As we shall see, for both normal and under excitation, the motor has lagging power factor However, for over-excitation, the motor has leading power factor Note: In a synchronous motor, the value of Xs is 10 to 100 times greater than Ra Consequently, we can neglect Ra unless we are interested in efficiency or heating effects 11.6 Motor on Load In d.c motors and induction motors, an addition of load causes the motor speed to decrease The decrease in speed reduces the counter e.m.f enough so that additional current is drawn from the source to carry the increased load at a reduced speed This action cannot take place in a synchronous motor because it runs at a constant speed (i.e., synchronous speed) at all loads What happens when we apply mechanical load to a synchronous motor? The rotor poles fall slightly behind the stator poles while continuing to run at 298 synchronous speed The angular displacement between stator and rotor poles (called torque angle α) causes the phase of back e.m.f Eb to change w.r.t supply voltage V This increases the net e.m.f Er in the stator winding Consequently, stator current Ia ( = Er/Zs) increases to carry the load Fig.(11.6) The following points may be noted in synchronous motor operation: (i) A synchronous motor runs at synchronous speed at all loads It meets the increased load not by a decrease in speed but by the relative shift between stator and rotor poles i.e., by the adjustment of torque angle α (ii) If the load on the motor increases, the torque angle a also increases (i.e., rotor poles lag behind the stator poles by a greater angle) but the motor continues to run at synchronous speed The increase in torque angle α causes a greater phase shift of back e.m.f Eb w.r.t supply voltage V This increases the net voltage Er in the stator winding Consequently, armature current Ia (= Er/Zs) increases to meet the load demand (iii) If the load on the motor decreases, the torque angle α also decreases This causes a smaller phase shift of Eb w.r.t V Consequently, the net voltage Er in the stator winding decreases and so does the armature current Ia (= Er/Zs) 11.7 Pull-Out Torque There is a limit to the mechanical load that can be applied to a synchronous motor As the load increases, the torque angle α also increases so that a stage is reached when the rotor is pulled out of synchronism and the motor comes to a standstill This load torque at which the motor pulls out of synchronism is called pull—out or breakdown torque Its value varies from 1.5 to 3.5 times the full— load torque When a synchronous motor pulls out of synchronism, there is a major disturbance on the line and the circuit breakers immediately trip This protects the motor because both squirrel cage and stator winding heat up rapidly when the machine ceases to run at synchronous speed 299 11.8 Motor Phasor Diagram Consider an under-excited ^tar-connected synchronous motor (Eb < V) supplied with fixed excitation i.e., back e.m.f Eb is constantLet V = supply voltage/phase Eb = back e.m.f./phase Zs = synchronous impedance/phase (i) Motor on no load When the motor is on no load, the torque angle α is small as shown in Fig (11.7 (i)) Consequently, back e.m.f Eb lags behind the supply voltage V by a small angle δ as shown in the phasor diagram in Fig (11.7 (iii)) The net voltage/phase in the stator winding, is Er Armature current/phase, Ia = Er/Zs The armature current Ia lags behind Er by θ = tan-1 Xs/Ra Since Xs >> Ra, Ia lags Er by nearly 90° The phase angle between V and Ia is φ so that motor power factor is cos φ Input power/phase = V Ia cos φ Fig.(11.7) Thus at no load, the motor takes a small power VIa cos φ/phase from the supply to meet the no-load losses while it continues to run at synchronous speed (ii) Motor on load When load is applied to the motor, the torque angle a increases as shown in Fig (11.8 (i)) This causes Eb (its magnitude is constant as excitation is fixed) to lag behind V by a greater angle as shown in the phasor diagram in Fig (11.8 (ii)) The net voltage/phase Er in the stator winding increases Consequently, the motor draws more armature current Ia (=Er/Zs) to meet the applied load Again Ia lags Er by about 90° since Xs >> Ra The power factor of the motor is cos φ 300 Input power/phase, Pi = V Ia cos φ Mechanical power developed by motor/phase Pm = Eb × Ia × cosine of angle between Eb and Ia = Eb Ia cos(δ − φ) Fig.(11.8) 11.9 Effect of Changing Field Excitation at Constant Load In a d.c motor, the armature current Ia is determined by dividing the difference between V and Eb by the armature resistance Ra Similarly, in a synchronous motor, the stator current (Ia) is determined by dividing voltage-phasor resultant (Er) between V and Eb by the synchronous impedance Zs One of the most important features of a synchronous motor is that by changing the field excitation, it can be made to operate from lagging to leading power factor Consider a synchronous motor having a fixed supply voltage and driving a constant mechanical load Since the mechanical load as well as the speed is constant, the power input to the motor (=3 VIa cos φ) is also constant This means that the in-phase component Ia cos φ drawn from the supply will remain constant If the field excitation is changed, back e.m.f Eb also changes This results in the change of phase position of Ia w.r.t V and hence the power factor cos φ of the motor changes Fig (11.9) shows the phasor diagram of the synchronous motor for different values of field excitation Note that extremities of current phasor Ia lie on the straight line AB (i) Under excitation The motor is said to be under-excited if the field excitation is such that Eb < V Under such conditions, the current Ia lags behind V so that motor power factor is lagging as shown in Fig (11.9 (i)) This can be easily explained Since Eb < V, the net voltage Er is decreased and turns clockwise As angle θ (= 90°) between Er and Ia is constant, therefore, phasor Ia also turns clockwise i.e., current Ia lags behind the supply voltage Consequently, the motor has a lagging power factor 301 (ii) Normal excitation The motor is said to be normally excited if the field excitation is such that Eb = V This is shown in Fig (11.9 (ii)) Note that the effect of increasing excitation (i.e., increasing Eb) is to turn the phasor Er and hence Ia in the anti-clockwise direction i.e., Ia phasor has come closer to phasor V Therefore, p.f increases though still lagging Since input power (=3 V Ia cos φ) is unchanged, the stator current Ia must decrease with increase in p.f Fig.(11.9) Suppose the field excitation is increased until the current Ia is in phase with the applied voltage V, making the p.f of the synchronous motor unity [See Fig (11.9 (iii))] For a given load, at unity p.f the resultant Er and, therefore, Ia are minimum (iii) Over excitation The motor is said to be overexcited if the field excitation is such that Eb > V Under-such conditions, current Ia leads V and the motor power factor is leading as shown in Fig (11.9 (iv)) Note that Er and hence Ia further turn anti-clockwise from the normal excitation position Consequently, Ia leads V From the above discussion, it is concluded that if the synchronous motor is under-excited, it has a lagging power factor As the excitation is increased, the power factor improves till it becomes unity at normal excitation Under such conditions, the current drawn from the supply is minimum If the excitation is further increased (i.e., over excitation), the motor power factor becomes leading Note The armature current (Ia) is minimum at unity p.f and increases as the power factor becomes poor, either leading or lagging 302 11.10 Phasor Diagrams With Different Excitations Fig (11.10) shows the phasor diagrams for different field excitations at constant load Fig (11.10 (i)) shows the phasor diagram for normal excitation (Eb = V), whereas Fig (11.10 (ii)) shows the phasor diagram for under-excitation In both cases, the motor has lagging power factor Fig (11.10 (iii)) shows the phasor diagram when field excitation is adjusted for unity p.f operation Under this condition, the resultant voltage Er and, therefore, the stator current Ia are minimum When the motor is overexcited, it has leading power factor as shown in Fig (11.10 (iv)) The following points may be remembered: (i) For a given load, the power factor is governed by the field excitation; a weak field produces the lagging armature current and a strong field produces a leading armature current (ii) The armature current (Ia) is minimum at unity p.f and increases as the p.f becomes less either leading or lagging Fig.(11.10) 11.11 Power Relations Consider an under-excited star-connected synchronous motor driving a mechanical load Fig (11.11 (i)) shows the equivalent circuit for one phase, while Fig (11.11 (ii)) shows the phasor diagram Fig.(11.11) 303 Input power/phase, Pi = V Ia cos φ Mechanical power developed by the motor/phase, (i) (ii) Pm = Eb × Ia × cosine of angle between Eb and Ia = Eb Ia cos(δ − φ) Armature Cu loss/phase = I 2a R a = Pi − Pm Output power/phasor, Pout = Pm − Iron, friction and excitation loss (iii) (iv) Fig (11.12) shows the power flow diagram of the synchronous motor Fig.(11.12) 11.12 Motor Torque Gross torque, Tg = 9.55 where Pm N-m Ns Pm = Gross motor output in watts = Eb Ia cos(δ − φ) Ns = Synchronous speed in r.p.m Shaft torque, Tsh = 9.55 Pout N-m Ns It may be seen that torque is directly proportional to the mechanical power because rotor speed (i.e., Ns) is fixed 11.13 Mechanical Power Developed By Motor (Armature resistance neglected) Fig (11.13) shows the phasor diagram of an under-excited synchronous motor driving a mechanical load Since armature resistance Ra is assumed zero tanθ = Xs/Ra = ∞ and hence θ = 90° Input power/phase = V Ia cos φ Fig.(11.13) 304 Since Ra is assumed zero, stator Cu loss (I 2a R a ) will be zero Hence input power is equal to the mechanical power Pm developed by the motor Mech power developed/ phase, Pm = V Ia cos φ (i) Referring to the phasor diagram in Fig (11.13), AB = E r cos φ = I a X s cos φ AB = E b sin δ Also ∴ or E b sin δ = I a X s cos φ I a cos φ = E b sin δ Xs Substituting the value of Ia cos φ in exp (i) above, Pm = V Eb Xs per phase = VEb Xs for 3-phase It is clear from the above relation that mechanical power increases with torque angle (in electrical degrees) and its maximum value is reached when δ = 90° (electrical) Pmax = V Eb Xs per phase Under this condition, the poles of the rotor will be mid-way between N and S poles of the stator 11.14 Power Factor of Synchronous Motors In an induction motor, only one winding (i.e., stator winding) produces the necessary flux in the machine The stator winding must draw reactive power from the supply to set up the flux Consequently, induction motor must operate at lagging power factor But in a synchronous motor, there are two possible sources of excitation; alternating current in the stator or direct current in the rotor The required flux may be produced either by stator or rotor or both (i) If the rotor exciting current is of such magnitude that it produces all the required flux, then no magnetizing current or reactive power is needed in the stator As a result, the motor will operate at unity power factor 305 (ii) If the rotor exciting current is less (i.e., motor is under-excited), the deficit in flux is made up by the stator Consequently, the motor draws reactive power to provide for the remaining flux Hence motor will operate at a lagging power factor (iii) If the rotor exciting current is greater (i.e., motor is over-excited), the excess flux must be counterbalanced in the stator Now the stator, instead of absorbing reactive power, actually delivers reactive power to the 3-phase line The motor then behaves like a source of reactive power, as if it were a capacitor In other words, the motor operates at a leading power factor To sum up, a synchronous motor absorbs reactive power when it is underexcited and delivers reactive power to source when it is over-excited 11.15 Synchronous Condenser A synchronous motor takes a leading current when over-excited and, therefore, behaves as a capacitor An over-excited synchronous motor running on no-load in known as synchronous condenser When such a machine is connected in parallel with induction motors or other devices that operate at low lagging power factor, the leading kVAR supplied by the synchronous condenser partly neutralizes the lagging reactive kVAR of the loads Consequently, the power factor of the system is improved Fig (11.14) shows the power factor improvement by synchronous condenser method The − φ load takes current IL at low lagging power factor cos φL The synchronous condenser takes a current Im which leads the voltage by an angle φm The resultant current I is the vector sum of Im and IL and lags behind the voltage by an angle φ It is clear that φ is less than φL so that cos φ is greater than cos φL Thus the power factor is increased from cos φL to cos φ Synchronous condensers are generally used at major bulk supply substations for power factor improvement Advantages (i) By varying the field excitation, the magnitude of current drawn by the motor can be changed by any amount This helps in achieving stepless control of power factor (ii) The motor windings have high thermal stability to short circuit currents (iii) The faults can be removed easily 306 Fig.(11.14) Disadvantages (i) (ii) (iii) (iv) There are considerable losses in the motor The maintenance cost is high It produces noise Except in sizes above 500 RVA, the cost is greater than that of static capacitors of the same rating (v) As a synchronous motor has no self-starting torque, then-fore, an auxiliary equipment has to be provided for this purpose 11.16 Applications of Synchronous Motors (i) Synchronous motors are particularly attractive for low speeds (< 300 r.p.m.) because the power factor can always be adjusted to unity and efficiency is high (ii) Overexcited synchronous motors can be used to improve the power factor of a plant while carrying their rated loads (iii) They are used to improve the voltage regulation of transmission lines (iv) High-power electronic converters generating very low frequencies enable us to run synchronous motors at ultra-low speeds Thus huge motors in the 10 MW range drive crushers, rotary kilns and variable-speed ball mills 307 11.17 Comparison of Synchronous and Induction Motors S Particular No Speed Power factor Excitation Economy Self-starting Construction Starting torque 3-phase Induction Motor Remains constant (i.e., Ns) from Decreases with load no-load to full-load Can be made to operate from Operates at lagging lagging to leading power factor power factor Requires d.c excitation at the No excitation for the rotor rotor Economical fcr speeds below Economical for 300 r.p.m speeds above 600 r.p.m Self-starting No self-starting torque Auxiliary means have to be provided for starting Complicated Simple More less Synchronous Motor 308 [...]... 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 The arrowhead marked “rotation” in Fig (1.30) (i) shows the direction of motion of the conductors By right hand rule, the direction of e.m.f in each conductor will be as shown In order to find the position of brushes,... YC = 2 N C ± 2 N C ± 1 No of commutator seg ± 1 = = P P/2 Number of pair of poles YC = Now ∴ 2N C ± 2 Z ± 2 = = YA P P (Q Commutator pitch, YC = YA = 2NC = Z) YB + YF 2 In a simplex wave winding YB, YF and YC may be equal Note that YB, YF and YB are in terms of armature conductors whereas YC is in terms of commutator segments 1.15 Design of Simplex Wave Winding In the design of simplex wave winding,... the number of parallel paths is equal to the number of poles (i) (ii) Fig (1.25) Fig (1.26) Conclusions From the above discussion, the following conclusions can be drawn: (i) The total number of brushes is equal to the number of poles (ii) The armature winding is divided into as many parallel paths as the number of poles If the total number of armature conductors is Z and P is the number of poles,... 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... 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: (i) A lap winding has pole times the degree of plex parallel paths Number of parallel paths,... number of armature conductors P = number of poles A = number of parallel paths = 2 for wave winding = P for lap winding N = speed of armature in r.p.m Eg = e.m.f of the generator = e.m.f./parallel path Flux cut by one conductor in one revolution of the armature, dφ = Pφ webers Time taken to complete one revolution, dt = 60/N second Pφ N dφ Pφ e.m.f generated/conductor = = = volts dt 60 / N 60 e.m.f of. .. B 2max f 2 t 2 V where Fig (1.38) watts Ke = Constant depending upon the electrical resistance of core and system of units used Bmax = Maximum flux density in Wb/m2 f = Frequency of magnetic reversals in Hz t = Thickness of lamination in m V = Volume of core in m3 It may be noted that eddy current loss depends upon the square of lamination thickness For this reason, lamination thickness should be kept... (1.19) Fig (1.20) 1.10 Types of D.C Armature Windings The different armature coils in a d.c armature Winding must be connected in series with each other by means of end connections (back connection and front connection) in a manner so that the generated voltages of the respective coils will aid each other in the production of the terminal e.m.f of the winding Two basic methods of making these end connections... 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 (ii) A wave winding has two times the degree of plex parallel paths Number of parallel paths, A = 2 × plex Note that the number of parallel paths in a multiplex wave winding depends upon the degree of plex and not on the number of poles Thus a duplex... connections (back as well as front connection) between a conductor at the top of a slot and one at the bottom of a slot (iii) The number of commutator segments is equal to the number of slots or coils (or half the number of conductors) No of commutator segments = No of slots = No of coils It is because each coil has two ends and two coil connections are joined at each commutator segment (iv) The winding must ... top of a slot and one at the bottom of a slot (iii) The number of commutator segments is equal to the number of slots or coils (or half the number of conductors) No of commutator segments = No of. .. upon the electrical resistance of core and system of units used Bmax = Maximum flux density in Wb/m2 f = Frequency of magnetic reversals in Hz t = Thickness of lamination in m V = Volume of core... number of poles (ii) The armature winding is divided into as many parallel paths as the number of poles If the total number of armature conductors is Z and P is the number of poles, then, Number of