Chapter 39. Synchronous Motors – Electrical Technology, Vol2: Machines and Measurements, 1/e

39

Synchronous Motors

OBJECTIVES

In this chapter you will learn about:

  • The uniqueness of synchronous speed
  • Factors controlling synchronous speed
  • Constructional features of synchronous motors
  • Amortisseur winding
  • Methods of starting synchronous motors
  • Effect of changing field excitation
  • Synchronous motors V-curves
  • Synchronous capacitors
  • Power factor correction
  • Simple problems on the above topics

Synchronous motors

39.1  INTRODUCTION

The synchronous motor operates either in step or in synchronism with the frequency of the a.c. line voltage. Actual motor speed depends on the number of poles. The synchronous motor is an alternator (a.c. generator) used as a motor.

Synchronous motors are used principally in large power applications because of their high operating efficiency, reliability, controllable power factor, and relatively low sensitivity to voltage dips. They are constant speed machines with applications in mills, refineries, power plants and the like to drive pumps, compressors, fans, pulverizers and other large loads, and to assist in power factor correction. Synchronous machines designed specifically for power-factor control have no external shafts and are called synchronous condensers. They float on the bus, supplying reactive power to the system. The direction of the reactive power and, hence, the power factor of the system is adjusted by changing the field excitation of the machine. When discussing the behaviour of individual motors, it is assumed that the machine is connected to an infinite bus. The terminal voltage and frequency of the infinite bus remain constant and are unaffected by any power drawn from or supplied to the infinite bus. Large power systems in highly industrialized countries may be considered to approximate those of the infinite bus.

39.2  GENERAL

All electric motors—d.c. and a.c.—act as generators when motor action is taking place. When a dynamo (d.c. or a.c.) is connected in parallel with a bus or another source of e.m.f., it may act as: (1) a generator if it’s induced e.m.f. exceeds the bus voltage (and it generates power to the bus); or (2) as a motor, if the induced e.m.f. is less than the bus voltage (in which case it receives power from the bus).

Two factors would cause an alternator to motorize and receive power from the bus (or other alternators in parallel): (1) A decrease of field current and generated e.m.f. (below the bus voltage); and (2) A decrease in the instantaneous speed of the a.c. dynamo. When these conditions occur, the a.c. synchronous dynamo is operating as an a.c. synchronous motor.

Not only does a synchronous motor require and receive a.c. current from the bus, but also, like any (doubly exited) a.c. synchronous dynamo, it requires a d.c. excitation for its field (Figure 39.1). On large synchronous motors, the exciter (a d.c. shunt generator) is placed on the same shaft as the motor, and a small portion of the motor torque is required to generate the d.c. required for its field excitation. Due to the possibility of variation of field excitation, the a.c. synchronous motor possesses a characteristic that no other a.c. motor has—the power factor at which it operates may be varied at will.

Figure 39.1 D.c. Generator Used to Excite the Field of an a.c. Generator

An unusual characteristic of the synchronous motor is that it is not inherently self starting. Like the a.c. alternator, it must be brought up to speed by some auxiliary means and then connected across the line.

Yet another peculiarity of synchronous motors is their susceptibility to hunting, particularly when the loads are subject to sudden changes or are not uniform over one revolution, as in the case of punch press shears, compressors or pumps. The use of damper windings rotor construction has ended that problem and, at the same time, made it possible for the synchronous motor to become self-starting.

Today, the synchronous motor is widely used, and its popularity has never been greater. In certain horse power sizes and speed ranges, it outsells the poly-phase induction motor.

Poly-phase synchronous motors have the following specific advantages over poly-phase induction motors.

  1. Synchronous motors can be used for power factor correction in addition to supplying torque to drive loads.
  2. They are more efficient (when operated at unity power factor) than induction motors of corresponding horse power and voltage rating.
  3. The field pole rotors of synchronous motors can permit the use of the wider air gaps than the squirrel-cage designs that are used in induction motors, requiring less bearing tolerance and permitting greater bearing wear.
  4. They may be less expensive for the same horse power speed and voltage ratings.
39.3.  SYNCHRONOUS MOTOR CONSTRUCTION

Basically, the construction of an a.c. synchronous motor follows that of an alternator. The stator has a single phase or poly-phase winding that is identical to that of the alternator. The rotor is generally a salient pole rotor, except in types of exceedingly high speed.

In order to eliminate hunting and to develop the necessary starting torque when an a.c. voltage is applied to this stator, the rotor poles contain pole-face conductors that are short circuited at their ends, as shown in Figure 39.2 (a). This amortisseur or damper winding consists of solid copper bars embedded at the surface of the poly-phase and short circuited at the end by means of shorting strip, as shown in Figure 39.2 (b).

Figure 39.2 Pole of an a.c. Synchronous Motor Showing Damper Winding (a) Pole of an a.c. Synchronous dynamo (b) Amortisseur, Damper, Squirrel Cage or Starter Winding

39.4  SYNCHRONOUS MOTOR OPERATION

The synchronous motor will not start by itself without a damper winding. An alternating current is applied to the stator winding as illustrated in Figure 39.3. The instantaneous direction of current in the coil sides of a given armature coil, A and B is shown.

Figure 39.3 Zero Resultant Torque Developed by Stator Conductors of a Synchronous Motor Where Rotor is at a Standstill (a) Clockwise Torque at One Instant; Rotor at Standstill (b) Counter Clockwise Torque, Next Instant; Rotor at Standstill

Both the north and south poles will be subjected to an electromagnetic torque (the left hand motor rule) moving the poles to the left (conductors to the right). The next instant, 1/120 of a second later, the frequency reverses the direction of current in the coil and the poles receive a torque in the opposite direction, as shown in the Figure 39.4.

As a result of the high inertia of the rotor, the resultant torque produced in one second is zero since the rotor has, in effect, been pushed alternately clockwise and counter clockwise, 60 times in that second, assuming a frequency of 60 Hz.

However, if by some means the rotor is moving clockwise at some speed near or at synchronous speed, as shown in Figure 39.4, the torque will be developed by coil sides A and B to cause the motor to continue to move clockwise. The space movement of the pole in electrical degrees at synchronous speed corresponds to 180° reversal of direction of current in the armature coil, and the resultant torque produced is in the same direction.

Figure 39.4 Rotor Torque in the Same Direction when Rotor is at Synchronous Speed (a) Clockwise Torque at One Instant; Rotor at Standstill (b) Clockwise Torque Produced by Instaneous Reversal of Current

The armature winding consists of many coils in series in each phase of a poly-phase synchronous dynamo. The three-phase current in the armature conductors of the stator produces a uniform rotating magnetic field rotating at a speed S = 120 f/p. The relation between the rotating field of the stator and the rotor poles is shown in Figure 39.5 (a).

The north and south poles, respectively, of the rotor, rotating at a synchronous speed, are locked in synchronism with the resultant armature synchronous rotating field of the stator. Thus, a rotor N pole is locked in synchronism with a stator S pole and vice versa, both rotating clockwise in synchronism at the synchronous speed.

If a load is placed on the shaft of a synchronous motor, the counter torque created by the load will cause the rotor to drop back momentarily, but it will continue to rotate at the same speed with respect to the rotating stator filed. The rotor speed is still at synchronous speed, however, with respect to the rotating field, but the rotor flux mutual air-gap flux is reduced slightly, as shown in Figure 39.5 (b) because of the increased air gap reluctance.

If the counter torque is so great that it exceeds the maximum torque developed, and if the rotor slips out of synchronism, the synchronous motor will stop. Thus, a synchronous motor will either run at synchronous speed or not run at all.

As the rotor is slowing down, the rotating field of the stator slips by the rotor field poles so rapidly that it is unable to lock synchronously or mesh with the rotating stator field. At one instant, a unit N pole of a rotor is attracted to an approaching S pole, producing torque in a counter clockwise direction as shown in Figure 39.5 (b). The next instant, the same N pole is attracted in the opposite direction by a passing rotor S pole, producing torque in a clockwise direction or a net torque of zero.

Figure 39.5 Rotating Magnetic Field of Constant Flux Produced by the Armature Conductor of a Poly-phase Stator (a) Rotating Field of Stator with Respect to Rotor (b) Effect of Load on Flux Distribution

39.5.  STARTING SYNCHRONOUS MOTORS

The synchronous motor must be brought up to a speed sufficiently close to synchronous speed in order to lock into synchronism will the rotating field. The means by which it is brought up to speed are:

  1. A d.c. motor coupled to the synchronous motor shaft
  2. Using the field exciter generator as a d.c. motor
  3. A small induction motor of at least one pair of poles less than that of the synchronous motor
  4. Using the damper windings as a squirrel-cage induction motor

The first method is sometimes used in laboratories with synchronous motors not equipped with damper windings. Generally, the synchronous motor is intended as the constant, speed prime-mover for the d.c. generator. But in order to bring the motor up to synchronism, the d.c. generator operates as a motor, and the a.c. synchronous dynamo is synchronized to the a.c. supply as an alternator. Once in parallel with the supply, the synchronous dynamo operates as a motor. The d.c. motor will now act as a generator if its field current is increased so that its generated e.m.f. exceeds that of the d.c. bus.

The second method is actually the same as the first, except that the synchronous motor excites (a d.c. shunt generator) and is operated as a motor, and the a.c. synchronous dynamo is synchronized to the a.c. supply.

The third method—using an auxiliary induction motor with fewer poles—involves the same synchronizing procedure for the a.c. synchronous motor as an alternator. At least one pair of poles fewer is required on the induction motor to compensate for the loss in induction motor speed due to slip.

In all of the three methods, it is necessary that: (1) there is little or no load on the synchronous motor; and (2) the capacity of the starting motor (d.c. or a.c.) is between 5 and 10 per cent of the rating of the synchronous coupled to it.

By far, the most common method of starting a synchronous motor, however, is as an induction motor using the damper windings (fourth method). This method is the simplest and requires no special auxiliary machines.

39.5.1  Starting a Synchronous Motor as an Induction Motor by Means of its Damper Windings

The shorting strip in the amortisseur or damper winding, as illustrated in Figure 39.2 (a) which short circuits the rotor bars, contains holes for bolting to the next set of damper windings on the next pole. In this way, a complete squirrel-cage winding is formed. Although the bars are not of the capacity to carry the rated current continuously, they are sufficient to start the synchronous motor as an induction motor with little or no load on the motor.

It is customary to short circuit the d.c. winding during the starting period, whatever voltage and current are induced in it may then aid the damper winding in producing induction motor action. In very large synchronous motors, field-sectionalizing or field-splitting switches are used to short circuit individual field windings to prevent cumulative addition of voltages from pole-to-pole. Such induced high voltages may puncture the field insulation.

Among the advantages of synchronous motors over induction motors is the fact that the air-gap of a synchronous motor is greater. The induction winding of the rotor, therefore, develops on starting a fairly high ratio of rotor reactance to resistance. It does result in improving the no-load slip speed of the synchronous motors. Thus, when the short circuit is removed from the field and d.c. is applied to the rotor field winding, at or near synchronous speed, the rotor easily pulls into synchronism with the rotating stator field.

To summarize, when an unloaded synchronous motor is started on its damper windings: (1) the d.c. field winding is shorted, and a.c. is applied to the stator, bringing the motor up to no load-speed as an induction motor; (2) direct current is applied to the field winding, and the current is adjusted to provide minimum a.c. line current; and (3) couple the load to the motor shaft.

39.6  SYNCHRONOUS MOTOR POWER FACTOR CONTROL

Synchronous motor will run and carry its load with a wide range of rotating field d.c. excitation. Since the relation between the rotating field and stator coils is the same as in a synchronous alternator, the resulting generated voltage Egp can also vary over a wide range. The Egp voltage exactly opposes the applied voltage per phase Vp if there were no requirement to supply torque, and if Egp were adjusted to Vp. However, even in running light there is some torque requirement. When running with a normal load, there is the full normal torque requirement and, therefore, the full requirement for the stator current is required to develop the needed strength of the rotating stator magnetic field.

Figure 39.6 shows the various phasor relations for different d.c. field excitation values. When the field is of such strength that Egp approximates Vp, the condition is called normal field excitation, as shown in Figure 39.6 (a). Under these conditions, Egp swings around just enough so that the phasor sum of Egp and Vp, which is the resultant voltage Ev, is sufficiently large to produce the required armature or stator current Ia. In a normal stator winding, the resistance Ra is held as low as possible in order to reduce the I2R losses. The dominant part of the winding impedance is the inductive reactance. The angle between the ER and Ia phases is nearly but not quite 90°. The whole winding impedance triangle fits into this corner of the phasors and is suggested by the dotted line in Figure 39.6 (a). By adjusting d.c. excitation to the correct amount, the armature current Ia may be made to be exactly in phase with the supplied voltage Vp. This is the situation for the unity power factor, shown in Figure 39.6 (a).

Assuming the same motor load, which will mean the same required input power or VpIa cos θ, but with substantially less d.c. field excitation, the situation shown in Figure 39.6 (b) arises. Since less field excitation means less Egp, the phasor sum of a normal Vp and a low Egp will take a direction of Er, as represented in Figure 39.6 (b). Since the requirement is for the same value of effective stator power. Ia must be larger in order that Ia cos θ matches the original value of Ia as represented in Figure 39.6 (a). This means that the Er phasor must grow proportionately. For Er to increase with shorter Egp, the angle α2 must be larger than that of the original α1. The only way that a small Egp can contribute to a larger Er is for this angular relation to change. The same phase angle between Er and Ia will still hold, since the same winding impedance is effective. Externally, under these conditions, the motor becomes a lagging power factor load on the power supply. The percentage of lag or the cosine of angle θ depends on how short Egp is allowed to become as the field excitation is reduced. Internally, the phasor relation shown in Figure 39.6 (b) is created by the increased field magnetization that results from a lagging power factor stator current.

The opposite situation holds if the d.c. field excitation is increased. This results an Egp voltage greater than the Vp voltage, and creates the phasor relation as illustrated in Figure 39.6 (c). Under the same load condition, the stator power drawn from the line must be the same, so that again Ia cos θ must match the original Ia as can be seen in Figure 39.6 (a).

The phases’ relation then becomes changed by the larger Egp. The resultant phasor voltage, Er is pulled around counter clockwise as shown in Figure 39.6 (c). Since the Er phasor has rotated, so must the Ia phasor, as the angle between them is still set by the winding impedance triangle. The result is a strong leading load power factor with the over-excited field adjustment.

Figure 39.6 Effect of Changing Field Excitation on Synchronous Motor Power Factor (a) Normal Excitation Unity Power Factor EgpVp (b) Under Excitation Lagging Power Factor Egp < Vp (c) Over Excitation, Leading Power Factor Egp > Vp

When the synchronous motor is deliberately adjusted this way, it draws a leading Ia current from the line by contributing an internal Ia sin θ reactive current component. At comparable leading and lagging power factors, the Ia stator current is the same. The benefit is that the created Ia sin θ component is opposite in phase to whatever Ia sin θ components may exist with the rest of the installation that the synchronous motor serves. Substantial system power factor improvement is achieved commercially by the over-excited large synchronous motors while they work.

When a synchronous motor is used solely to produce a large leading Ia sin θ current component, it is called a synchronous capacitor. This name comes from effect, which is the same as if a giant capacitor were placed across the line. When the motor carries a normal mechanical load, it is also normally used as a synchronous power factor corrector when it is deliberately over excited.

39.7   SYNCHRONOUS MOTOR V CURVE

The power factor response of a synchronous motor under various d.c. field excitation currents while holding a constant power is shown by the V-curve test. The curves are so named because of their distinctive shape when plotted. A synchronous motor that is to be tested is connected to instrumentation and a variable load, as shown in Figure 39.7. The two Wattmeter method is shown, but any of the acceptable Wattmeter circuits are applicable, bearing in mind that the three-phase loads are balanced.

Figure 39.7 Circuit Connection for V Curves of Synchronous Motor

Three voltmeters are shown but only one reading is needed if the balance is shown. The motor is tested by applying a load and varying the d.c. field excitation in logical steps. Data for all meters are recorded at each step so that volt-amperes and power can be determined. This allows the power factor of the motor to be determined for each field current setting for each load.

Figure 39.8 shows a typical family of V curves. The curves may be taken over more closely spaced increments to truly define the curve shapes, depending on the ease of load control and the period of time available.

In Figure 39.8 (a) the no-load curve drops to a minimum but not zero. The minimum current can be related to a minimum power necessary to overcome the fixed internal losses, such as the rotational losses that are always present. The shape of the curves clearly shows that for each load, there is a distinct minimum armature phase current Ia at a specific d.c. field current If. This specific field current is known as normal excitation. Unless otherwise specified, the labelled d.c. field current for a synchronous motor will be the current that produces minimum armature winding current in the region of 80 per cent to full load.

Figure 39.8 (b) shows the same data plotted as load power factor versus d.c. field current. These curves show that a synchronous motor can be over excited and carry a substantial leading power factor. This process is limited by the maximum current rating of the stator windings. Even though the increasing d.c. field current brings higher and higher leading power factors, the main stator current is increasing at the same time. The current handling capability of the motor is fairly well taxed for full-load currents at 100 per cent PF.

If it is desired to carry a strong leading PF for load power factor improvement of a factory, and at the same time, to power the factory air compressors, conveyor systems, etc., the synchronous may well need to be a larger size. This is because a synchronous motor may be rated at unity PF or pole at 80 per cent PF at a given load. The name plate usually states the load and power factor conditions. If a more leading PF is desired, it can be met by a motor of one or more frame sizes larger than the basic power requirement ordinarily needed.

The V-curve intersection with the normal excitation line in Figure 39.8 (a) illustrates the phasor relation in Figure 39.6 (a). The V-curve intersection with 0.8 PF lagging dotted line in Figure 39.8 (a) illustrates a phasor relation like that shown in Figure 39.6 (b). The intersection of a load curve with 0.8 PF leading line in Figure 39.8 (a) is illustrated as a phasor relation in Figure 39.6 (c).

Figure 39.8 Synchronous Motor V Curves (a) Armature Current vs Field Current (b) Power Factor vs Field Current

 

Example 39.1

A factory has an average total electrical load of 41300 kW at 0.810 PF lagging. Part of the load is incurred by a large three-phase induction of 5073 kW, which operates at 0.730 PF lagging and at 92 per cent efficiency. The motor is in need of rewinding and requires extensive mechanical rebuilding so that replacement is scheduled. Two different synchronous motors are investigated, one to carry the same 6800 hp (5073 kW) load at unity PF and the same efficiency. The other one is a larger frame unit and carries the same load at the same efficiency and at 0.780 PF leading. Calculate the following:

  1. Overall system power factor using unity PF motor.
  2. Overall system power factor using the 0.780 leading PF motor.
  3. The difference in required kilovolt-ampere rating of the two motors.

Solution:

  1. The original system kilowatt power will be expected to remain through these alternatives since the motor load and efficiency remain the same. In that case the kilovolt-amperes and kilovolt-amperes reactive are
    cos θ = 0.810, θ = 39.9°, sin θ = 0.586
    (50988) (0.586) = 29 900 kVAr originally

     

    The original motor kVA and kVAr are

    cos θ = 0.730 (motor), θ = 43.1°, sin θ = 0.683
    (7953) (0.683) = 5159 kVAr motor

     

    The original and still factor load less than motor is

    41300 kW – 5514 kW = 39790 kW

    The kVAr component is

    2990 kVAr = 5159 kVAr = 24740 kVAr

     

    The unity PF motor will then create a total factory kW the same as the original or 41300 kW, but no more kVAr than the factory without the motor or 24740 kVAr.

    The total factory power factor will then be

    which corresponds to θ = 30.92°; thus
    cos θ = 0.858 or 85.8 per cent PF

     

  2. A synchronous motor with the same horse power (or kW) and a 0.780 PF leading will have the same kW as the other motors, but will contribute a leading kVAr component
    cos θ = 0.780, θ = 38.74°, sin θ = 0.626
    (7069) (0.626) = 4424 kVAr leading

     

    The total plant kW is the same 41300 kW, but the kVAr is less:

    24740 kVAr – 4424 kVAr = 20316 kVAr

     

    The total plant power factor is then

    cos 26.19° = 9.897 or 89.7 per cent PF

     

  3. Step (1) requires a kVA rating the same as its kW rating owing to unity PF: 5514 kVA. The step (2) situation requires 7069 kVA;
    7069 – 5514 = 1555 kVA

The motor that produces the improvement in plant PF from 85.8 per cent to 89.7 per cent requires an additional kVA rating of over 1500 kVA. This means a substantially large size is needed to decrease the added heat, since 100-92 or 8 per cent of this difference is lost heat in the stator windings.

39.8  SYNCHRONOUS CAPACITORS

A number of specialized synchronous motors are deliberately manufactured without any shaft extensions at all. They are intended to be used solely for power factory correction. Also, they are incapable of driving a mechanical load. Any over-excited synchronous motor that is not used to drive a load may be classed as a synchronous capacitor.

Although there is no mechanical load on a synchronous capacitor to contribute to the armature current, the V-curves of Figure 39.8 show that when over-excited, even at no load, the stator armature current is high. This is not a disadvantage, considering that the synchronous capacitor armature current may be raised to its rated value at an extremely low leading PF for use in power factor correction.

As shown in Figure 39.9 when a synchronous motor is over-excited without load, the resultant phase impedance Er is quite high, despite the very small torque angle α, producing a relatively large leading armature current Ia, which is practically at 90° with respect to the bus phase voltage.

Figure 39.9 Synchronous Capacitor Phase Relationships

Synchronous capacitors are preferred for power factor correction over commercial capacitors. The former can be constructed much less expensively in extremely high kVA (and even MVA) ratings as well as in high voltages (100 kV to 800 kV), as compared to fixed commercial capacitor of the same voltage and kVA rating. Such synchronous capacitors, driving no mechanical load whatsoever, merely float on the transmission lines of a power system for purposes of power factor improvement.

39.8.1  Power Factor Correction Advantages

Loads having moderate to low lagging or leading power factors (below 0.65) result in a severe loss of electrical power to the utility supplying power to a given industrial or commercial occupancy. Lower power factors require the utility to increase their capacity or apparent power in order to supply a higher current for the lower power factor loads. This added capacity (and higher current) is needed all along the line, from the generating station, through the transformers and the transmission lines, to the load. The cost of this additional added capacity is kept to a maximum by means power factor correction.

Many other advantages also emerge from power factor correction. These are:

  1. Since the power capacity and line current are both lower, the power losses (I2R) in the lines are reduced.
  2. Similarly, the line volt drop across the line impedance is reduced, making the voltage regulation task easier in maintaining rated voltage to occupancies supplied by the utility.
  3. Transmission efficiency from source to load is increased.
  4. Utility costs are decreased, reflecting a savings (theoretically) to the consumer.

Almost all commercial, industrial, and residential loads tend to have lagging power factors (i.e., current lags voltage) due to inductive reactive loads (motors, fluorescent lights, etc.). Consequently, power factor correction consists of adding capacitive loads in parallel with existing inductive loads to raise the power factor.

It is customary not to attempt any correction of the power factor of a system all the way to unity power factor. The economic reason placing a limit on maximum power factor correction can be inferred from the data in Table 39.1 for a 10000 kVA system. A 10000 kVA system operating at 0.6 PF is capable of delivering only 6000 kW; whereas, at unity PF it could deliver 10000 kW at the same current and at the same line drop. Any increase in output, however, is at the expense of reactive kilovolt-ampere. In improving the PF from 0.65 to 0.70, for example, there is an increase in output of 500 kW at a correction cost of 460 kVAr. In improving the PF from 0.80 to 0.85, the increase in 500 kW is made at a higher correction cost of 730 kVAr. At each successively higher power factor level, the kVAr cost is greater for a further improvement of 0.05 in the power factor. In improving the power factor from 0.95 to unity, the 500 kW increase in output entails a correction cost of 3120 kVAr. Thus, it is economically prohibitive generally to range the power factor beyond 0.85 lagging.

 

Table 39.1 Total Reactive Kilovolt-amperes of Correction Required at Various Power Factors

Example 39.2

A 3-phase synchronous motor of 8000 Watt 1100 V has synchronous reactance of 8 Ω per phase. Find the minimum current and the corresponding induced e.m.f. for full load condition. The efficiency of the machine is 0.8. Neglect armature resistance.

Solution:

The current in the motor is minimum when the power factor is unity,

That is, when cos θ = 1.
Motor input = (motor output) /efficiency
Pi = 8000/0.8 = 10000 W = 10 kW

For unity factor

Example 39.3

A 3-phase, 400 V synchronous motor takes 52.5 A at a power factor 0.8 leading. Determine the induced e.m.f. and the power supplied. The motor impedance per phase is (0.25 + j 3.2) Ω.

Solution:

For leading power factor

= (171.6)2 + (306 + 0.57)2
Ef = 391.3 V

Example 39.4

Find the three highest speeds at which synchronous motor generator sets could run to link up with a 25 Hz and a 60 Hz system.

Solution:

f = (RPS) × pole pair

Equating the two, we have

That is, the pole pairs of 60 Hz = 2.4 pole pairs of 60 Hz; both must be integers. So, the first three values of P25 will be 5, 10 and 15 and the corresponding RPM will be and

SUMMARY
  1. A synchronous motor is a machine that converts a.c. electric power, to mechanical power at a constant speed called synchronous speed.
  2. A synchronous motor is a doubly excited machine.
  3. The synchronous motor is an alternator (a.c. generator) used as a motor.
  4. Synchronous motors are constant speed machines.
  5. Synchronous machines designed specifically for power factor correction have no external shafts and are called synchronous condensers.
  6. The float on the bus supply reactive power to the system.
  7. The direction of the reactive power is adjusted by changing the field excitation of the machine.
  8. When discussing individual motors, it is assumed that the machine is connected to an infinite bus.
  9. The exciter (a d.c. shunt generator) is placed on the same shaft as the motor and a small portion of the motor torque is required to generate the d.c. required for its field excitation.
  10. A synchronous motor is not inherently self starting.
  11. The stator has a single phase or poly-phase winding that is identical to that of the alternator.
  12. The rotor is generally a salient pole rotor, except in types of exceedingly high speed.
  13. In order to eliminate hunting and develop the necessary starting torque when an a.c. voltage is applied to the stator, the rotor poles contain pole-face conductors that are short circuited at their ends.
  14. The synchronous motor will not start by itself without a damper winding.
  15. The name plate usually states the load and power factor condition.
  16. Any over-excited synchronous motor that is not used to drive a load may be classed as a synchronous capacitor.
  17. Synchronous capacitors are preferred for power factor correction over commercial capacitors.
  18. Power factor correction consists of adding capacitive loads in parallel with existing inductive loads to raise the power factor.
MULTIPLE CHOICE QUESTIONS (MCQ)
  1. An alternator operates on the principle of
    1. Electromagnetic induction
    2. Self induction
    3. Mutual induction
    4. (c) or (b)
  2. The starter core of a synchronous machine is built up of
    1. Stainless steel laminations
    2. Silicon steel laminations
    3. Cast iron laminations
    4. Cast steel laminations
  3. In a salient pole field structure, the pole shoes cover about
    1. One-third of pole pitch
    2. One-half of pole pitch
    3. Two-third of pole pitch
    4. Whole of the pole pitch
  4. For a two-layer winding, the number of stator slots is equal to the number of
    1. Poles
    2. Conductors
    3. Coil sides
    4. Coils
  5. The rating of a universal machine is usually governed by the
    1. Speed
    2. Temperature rise
    3. Weight
    4. None of these
  6. The synchronous reactance of the machine is the
    1. Reaction due to armature reaction of the machine
    2. Reactance due to leakage flux
    3. Combined reactance due leakage flux and armature reaction
    4. Reactance due to armature reaction or leakage flux
  7. A poly-phase field is
    1. Pulsating and stationary
    2. Pulsating and rotating
    3. Constant amplitude and rotating at synchronous speed
    4. Constant in amplitude and stationary in space
  8. When does a synchronous motor operate with leading power factor current?
    1. While it is under excited
    2. While it is critically excited
    3. While it is over excited
    4. While it is heavily loaded
  9. A salient pole synchronous motor is running on no-load. If it’s excitation is cut off, it will
    1. Continue running at synchronous speed
    2. Continue running at a speed slightly less than synchronous speed
    3. Stop
    4. None of these
  10. The speed of a synchronous motor can be varied by varying its
    1. Excitation
    2. Supply voltage
    3. Supply frequency
    4. Load
  11. If the field of a synchronous motor is under excited, the power factor will be
    1. Lagging
    2. Leading
    3. Unity
    4. More than unity
  12. A synchronous motor will deliver maximum power when
    1. Load angle is equal to internal angle θ
    2. Input power factor is unity
    3. Load angle is 45°
    4. Load angle is 0°
  13. Synchronous motors when operated at power factor ranging from lagging through unity to leading for voltage control are called
    1. Voltage boosters
    2. Synchronous reactors
    3. Mechanical synchronizers
    4. None of these
  14. Synchronous condenser means
    1. A synchronous motor with capacitor connected across terminals to improve PF
    2. A synchronous motor operating at full load with leading PF
    3. An over-excited synchronous motor partially supplying mechanical load, and also improving the PF of the system to which it is connected
    4. An over-excited synchronous motor operating at no load with leading PF used in large power station for improvement of PF
  15. A synchronous motor may fail to pull in synchronism owing to
    1. Excessive load
    2. Low excitation
    3. High friction
    4. Any of these
  16. Which of the following used for synchronizing three-phase generator is considered the best one?
    1. Three dark lamp method
    2. Two bright and one dark lamp method
    3. Synchroscope
    4. None of these
  17. An infinite bus bar has
    1. Constant voltage
    2. Constant frequency
    3. Infinite voltage
    4. Both (a) and (b)
  18. Which of the following synchronous motors is cost comparable to that of an induction motor?
    1. High kW output high speed
    2. High kW output low speed
    3. Low kW output low speed
    4. Low kW output high speed
ANSWERS (MCQ)
  1. (a)
  2. (b)
  3. (c)
  4. (d)
  5. (b)
  6. (c)
  7. (c)
  8. (c)
  9. (b)
  10. (c)
  11. (a)
  12. (a)
  13. (b)
  14. (d)
  15. (d)
  16. (c)
  17. (d)
  18. (b)
CONVENTIONAL QUESTIONS (CQ)
  1. Name two factors that will cause an alternator to ‘motorize’.
  2. Give the equation that determines the average speed of a synchronous motor.
  3. Explain why a synchronous motor is not inherently self starting.
  4. Explain why a synchronous motor will run at synchronous speed or not at all.
  5. Give four methods used for starting synchronous motors. Which of the four methods is the most commonly used and why?
  6. How can the speed of a synchronous motor be adjusted?
  7. How does an amortisseur winding reduce hunting caused by pulsating loads?
  8. State how a synchronous motor can be started, stopped and reversed
  9. What are the two components of synchronous motor torque? What are they due to?
  10. Give one inherent advantage of synchronous motor over an induction motor as a source of mechanical power
  11. What is a synchronous capacitor and how can it be distinguished from a synchronous motor?
  12. Is there an economic limit to improvement of PF? If so, what is it?
  13. In addition to correction of PF and a source of mechanical power, give an additional application of the synchronous motor
  14. What is meant by the torque angle of a synchronous motor? What factors affect the magnitude of this angle?
  15. Differentiate between pull-in torque, pull-out torque and locked, rotor torque.
  16. Determine the speed of a 40-pole synchronous motor operating from a 3-phase, 50 Hz, 4600 V system.
  17. A 3-phase 50 hp, 2300 V, 60 Hz synchronous motor is operating at 90 r.p.m. Determine the number of poles in the rotor.
  18. Calculate (a) the frequency of the voltage that must be applied to the stator of a 10 pole, three-phase, 40 V synchronous motor, required to operate at 1200 r.p.m. (b) the number of pole required for a 220 V, three-phase synchronous motor to operate at a speed of 500 r.p.m. when 50 Hz is applied to the stator (c) The full load speed of 36 pole, 60 Hz, 220 V synchronous motor in r.p.m. and rad/second.
ANSWERS (CQ)

2.  S = (120f)/P

16.  150 RPM

17.  80 poles

18.  (a) 100 Hz (b) 12 poles (c) 16 poles, 20.9 rad/s.