Electric Machine II Notes

 

Course Description:

This course covers the electrical machines-three-phase induction motor and generator, single phase ac motors, synchronous generator and synchronous motor. It deals with the constructional details, operating principle, characteristics, testing methods of the above machines.

Course content:

Unit 1. Three Phase Induction Motor (15)

1.1 Constructional details – Yoke, stator, stator windings, and rotor – squirrel cage type and phase wound type.

1.2 Operation – Production of rotating magnetic field, operating principle, reversing the direction of rotation.

1.3 Stand still condition – equivalent circuit, starting current and starting torque.

1.4 Running condition - equivalent circuit, running current and torque.

1.5 Torque-Speed characteristics, effect of applied voltage on T-S characteristic, effect of rotor resistance on T-S characteristic.

1.6 Power stages, losses and efficiency

1.7 Starting methods – Direct On-line starting, Primary resistor method, Autotransformer method, Star-Delta method.

1.8 Speed control – Primary voltage control method, Rotor resistance control method, frequency control method, Cascade connection method.

1.9 Induction generator – principle of operation, excitation requirement, voltage build-up process, isolated and grid connected modes of operation.

 

Unit 2. Single Phase AC Motors : (8 )

2.1 Split-phase induction motor – Construction, concept of pulsating field produced by single phase winding, double revolving field theory, Torque-speed characteristic, self-starting by split-phase winding, Characteristics and

applications.

2.2 Capacitor start and induction run motor – Operating principle, Characteristics and applications.

2.3 Capacitor start and run motor- Operating principle, Characteristics and

applications

2.4 Shaded pole motor – Operating principle, Characteristics and applications

2.5 AC series motor – Operating principle, Characteristics and applications

Unit 3. Three-phase Synchronous Generator (12)

3.1 Constructional details and types.

3.2 Operation – Operating principle, emf equation, armature winding parameters and its effect on emf generation, relationship between speed, frequency and number of magnetic poles in rotor, concept of geometrical degree and electrical degree.

3.3 Advantages of stationary armature winding and rotating field winding.

3.4 Loaded operation – effect of armature winding resistance, leakage reactance, armature reaction, concept of synchronous impedance, equivalent circuit and phasor diagrams for resistive, inductive and capacitive load, voltage regulation.

3.5 Synchronizing action and synchronizing power Synchronous generator connected to infinite bus, effect of excitation.

3.6 Parallel operation and synchronization.

3.7 Related numerical problems.

 

Unit 4. Synchronous Motor (10)

4.1 Principle of operation and starting method.

4.2 General features and applications

4.3 No-load and load operation

4.4 Effect of excitation on armature current and power factor- V and inverted V curves.

4.5 Power-Angle characteristic.

Unit 1. Three Phase Induction Motor (15)

Introduction

•       The three-phase induction motors are the most widely used electric motors in industry.

•       They run at essentially constant speed from no-load to full-load.

•      However, the speed is frequency dependent and consequently these motors are not easily adapted to speed control.

•       We usually prefer d.c. motors when large speed variations are required.

•       Like any electric motor, a 3-phase induction motor has a stator and a rotor.

•   The stator carries a 3-phase winding (called stator winding) while the rotor carries a short-circuited winding (called rotor winding).

•      Only the stator winding is fed from 3-phase supply.

•    The rotor winding derives its voltage and power from the externally energized stator winding through electromagnetic induction and hence the name.

•       The induction motor may be considered to be a transformer with a rotating secondary and it can, therefore, be described as a “transformer type” a.c. machine in which electrical energy is converted into mechanical energy.

 

Advantages

(i) It has simple and rugged construction.

(ii) It is relatively cheap.

(iii) It requires little maintenance.

(iv) It has high efficiency and reasonably good power factor.

(v) It has self starting torque.

Disadvantages

(i) It is essentially a constant speed motor and its speed cannot be changed easily.

(ii) Its starting torque is inferior to d.c. shunt motor.

 

Induction Machine Construction

•       A 3-phase induction motor has two main parts

 (i) stator and (ii) rotor.

•       The rotor is separated from the stator by a small air-gap which ranges from 0.4 mm to 4  mm, depending on the power of the motor.

1. Stator

•       It consists of a steel frame which encloses a hollow, cylindrical core made up of thin laminations of silicon steel to reduce hysteresis and eddy current losses.

•        A number of evenly spaced slots are provided on the inner periphery of the laminations 

•       The 3-phase stator winding is wound for a definite number of poles as per requirement of speed.

•       Greater the number of poles, lesser is the speed of the motor and vice-versa.

•   When 3-phase supply is given to the stator winding, a rotating magnetic field  of constant magnitude is produced.

•       This rotating field induces currents in the rotor by electromagnetic induction.

Fig: Stator

2. Rotor
The rotor, mounted on a shaft, is a hollow laminated core having slots on its outer periphery. The winding placed in these slots (called rotor winding) may be one of the following two types:
(i) Squirrel cage type (ii) Wound type

      (i)            Squirrel cage rotor

•       It consists of a laminated cylindrical core having parallel slots on its outer periphery.

•       One copper or aluminum bar is placed in each slot.

•       All these bars are joined at each end by metal rings called end rings [See Fig. (8.2)].

•       This forms a permanently short-circuited winding which is indestructible.

•       The entire construction (bars and end rings) resembles a squirrel cage and hence the name.

•  The rotor is not connected electrically to the supply but has current induced in it by transformer action from the stator

  

  Fig: Squirrel Cage Rotor

  
  

(ii) Wound rotor

•      It consists of a laminated cylindrical core and carries a 3- phase winding, similar to the one on the stator.

•       The rotor winding is uniformly distributed in the slots and is usually star-connected.

•   The open ends of the rotor winding are brought out and joined to three insulated slip rings mounted on the rotor shaft with one brush resting on each slip ring.

•      The three brushes are connected to a 3-phase star-connected rheostat.

•      At starting, the external resistances are included in the rotor circuit to give a large starting torque.

•      These resistances are gradually reduced to zero as the motor runs up to speed.

1.2  Operation

Production of Rotating Magnetic Field Due to 3-Phase Currents

When a 3-phase winding is energized from a 3-phase supply, a rotating magnetic field is produced. This field is such that its poles do no remain in a fixed position on the stator but go on shifting their positions around the stator. For this reason, it is called a rotating field. It can be shown that magnitude of this rotating field is constant and is equal to 1.5 fm where fm is the maximum flux due to any phase.

To see how rotating field is produced, consider a 2-pole, 3i-phase winding as shown in Fig. (8.6 (i)). The three phases X, Y and Z are energized from a 3-phase source and currents in these phases are indicated as Ix, Iy and Iz [See Fig. (8.6 (ii))]. Referring to Fig. (8.6 (ii)), the fluxes produced by these currents are given by:

Here Øm is the maximum flux due to any phase. Fig. shows the phasor diagram of the three fluxes. We shall now prove that this 3-phase supply produces a rotating field of constant magnitude equal to 1.5 Øm.

Fig 8.6

(i) At instant 1 [See Fig. (8.6 (ii)) and Fig. (8.6 (iii))], the current in phase X is zero and currents in phases Y and Z are equal and opposite. The currents are flowing outward in the top conductors and inward in the bottom conductors. This establishes a resultant flux towards right. The magnitude of the resultant flux is constant and is equal to 1.5 Øm as proved under:

At instant 1, wt = 0°. Therefore, the three fluxes are given by;

The phasor sum of - Øy and Øz is the resultant flux Ør [See Fig. (8.7)]. It is clear that:

Ør=√( Øy²+ Øz²+2* Øy* Øz*cosΘ)=1.5Øm

 (ii) At instant 2, the current is maximum (negative) in Øy phase Y and 0.5 maximum (positive) in phases X and Y. The magnitude of resultant flux is 1.5 Øm proved under:

At instant 2, wt = 30°. Therefore, the three fluxes are given by;

The phasor sum of Øx, - Øy and Øz is the resultant flux Ør.

iii) At instant 3, current in phase Z is zero and the currents in phases X and Y are equal and opposite (currents in phases X and Y arc 0.866 ´ max. value). The magnitude of resultant flux is 1.5 Øm as proved under:

At instant 3, wt = 60°. Therefore, the three fluxes are given by;

The phasor sum of Øx, - Øy and Øz is the resultant flux Ør.

 

iv) At instant 4, the current in phase X is maximum (positive) and the currents in phases V and Z are equal and negative (currents in phases V and Z are 0.5 ´ max. value). This establishes a resultant flux downward as shown under:

At instant 4, wt = 90°. Therefore, the three fluxes are given by;

The phasor sum of Øx, - Øy and - Øz is the resultant flux Ør.

It follows from the above discussion that a 3-phase supply produces a rotating field of constant value (= 1.5 Øm, where Øm is the maximum flux due to any phase).

Speed of rotating magnetic field

The speed at which the rotating magnetic field revolves is called the synchronous speed (Ns).

where f is the frequency of the supply and P is the number of poles per phase.

Principle of Operation

Consider a portion of 3-phase induction motor as shown in Fig. (8.13). The operation of the motor can be explained as under:

(i)    When 3-phase stator winding is energized from a 3-phase supply, a rotating magnetic field is set up which rotates round the stator at synchronous speed Ns (= 120 f/P).

 

(ii)      The rotating field passes through the air gap and cuts the rotor conductors, which as yet, are stationary. Due to the relative speed between the rotating flux and the stationary rotor, e.m.f.s are induced in the rotor conductors. Since the rotor circuit is short-circuited, currents start flowing in the rotor conductors.

(iiii)     The current-carrying rotor conductors are placed in the magnetic field produced by the stator. Consequently, mechanical force acts on the rotor conductors. The sum of the mechanical forces on all the rotor conductors produces a torque which tends to move the rotor in the same direction as the rotating field.

(iv)    The fact that rotor is urged to follow the stator field (i.e., rotor moves in the direction of stator field) can be explained by Lenz’s law. According to this law, the direction of rotor currents will be such that they tend to oppose the cause producing them. Now, the cause producing the rotor currents is the relative speed between the rotating field and the stationary rotor conductors. Hence to reduce this relative speed, the rotor starts running in the same direction as that of stator field and tries to catch it.

Click here to watch How Induction motor works?

Direction of rotating magnetic field

The phase sequence of the three-phase voltage applied to the stator winding in Fig. (8.6 (ii)) is X-Y-Z. If this sequence is changed to X-Z-Y, it is observed that direction of rotation of the field is reversed i.e., the field rotates counterclockwise rather than clockwise. However, the number of poles and the speed at which the magnetic field rotates remain unchanged. Thus it is necessary only to change the phase sequence in order to change the direction of rotation of the magnetic field. For a three-phase supply, this can be done by interchanging any two of the three lines. As we shall see, the rotor in a 3-phase induction motor runs in the same direction as the rotating magnetic field. Therefore, the direction of rotation of a 3-phase induction motor can be reversed by interchanging any two of the three motor supply lines.

Slip

The difference between the synchronous speed Ns of the rotating stator field and the actual rotor speed N is called slip. It is usually expressed as a percentage of synchronous speed i.e.,

(i)                The quantity Ns - N is sometimes called slip speed.

(ii)             When the rotor is stationary (i.e., N = 0), slip, s = 1 or 100 %.

(iii)           In an induction motor, the change in slip from no-load to full-load is hardly 0.1% to 3% so that it is essentially a constant-speed motor.

Rotor Current Frequency

The frequency of a voltage or current induced due to the relative speed between a vending and a magnetic field is given by the general formula;

Frequency = NP/120

 where N = Relative speed between magnetic field and the winding

P = Number of poles

For a rotor speed N, the relative speed between the rotating flux and the rotor is Ns - N. Consequently, the rotor current frequency f' is given by;

i.e., Rotor current frequency = Fractional slip x Supply frequency

At any slip s,

Rotor e.m.f./phase = sE2

Rotor reactance/phase = sX2

Rotor frequency = sf

where E2,X2 and f are the corresponding values at standstill

Rotor Current

At standstill. Fig. (8.15 (i)) shows one phase of the rotor circuit at standstill. 

When running at slip s. Fig. (8.15 (ii)) shows one phase of the rotor circuit when the motor is running at slip s.

Rotor Torque

The torque T developed by the rotor is directly proportional to:

(i) rotor current

(ii) rotor e.m.f.

(iii) power factor of the rotor circuit  

\ T µE2I2 cosf2        or,  T = KE2 I2 cosf2

where I2 = rotor current at standstill                              

E2 = rotor e.m.f. at standstill    

   cos f2 = rotor p.f. at standstill

Note. The values of rotor e.m.f., rotor current and rotor power factor are taken for the given conditions.

 Analysis at Standstill Condition

Standstill condition is the instant of starting. At this instant, the speed of the rotor is zero. Therefore the relative speed Ns-N is maximum, slip is maximum(s=1) and maximum emf will induce in the rotor circuit(just like in secondary winding in a transformer) and the frequency of emf induced in rotor circuit is same as that of supply voltage frequency ‘f’ and is given by :

f= (Ns*P)/120

The equivalent circuit of the induction motor at standstill condition is very similar to the equivalent circuit of a transformer. The stator winding is analogous to the primary winding of the transformer and rotor circuit is analogous to the secondary winding of the transformer. The per phase equivalent circuit of a three phase induction motor is as shown in fig8.11.

Let E2 = rotor e.m.f. per phase at standstill

X2 = rotor reactance per phase at standstill

R2 = rotor resistance per phase

Analysis of Running Condition

The equivalent circuit of the induction motor at running condition can be written as:

Fig: Equivalent circuit of induction motor at running condition

Let the rotor at standstill have per phase induced e.m.f. E2, reactance X2 and resistance R2. Then under running conditions at slip s,

Running Torque, Tr µ E'2 I'2 cosf'2

                                µ fI'2 cosf'2                                  (Q E'2 µ f)

Torque-Slip Characteristics

If a curve is drawn between the torque and slip for a particular value of rotor resistance R2, the graph thus obtained is called torque-slip characteristic. The general equation of torque is given by:

From this equation it is clear that the torque developed by the motor depends upon the slip‘s’ provided E2 and R2 remains constant. As slip‘s’ changes with the speed, torque will also change with the speed. If the speed decreases, the value of slip‘s’ will increase, then the motor will develop more torque. But there is a limit so that after particular value of speed, the motor will not be able to produce more torque. The speed at which the torque is maximum can be determined by differentiating above equation w.r.t‘s’

Thus for maximum torque (Tm) under running conditions :

Rotor resistance/phase = Fractional slip ´ Standstill rotor reactance/phase

Hence maximum torque will develop at a speed corresponding to slip s=R2/X2. If the motor is overloaded so that speed goes below this value, the motor will not be able to develop more torque to overcome the increased load.

Effect of Change of Supply Voltage

Therefore, the starting torque is very sensitive to changes in the value of supply voltage. For example, a drop of 10% in supply voltage will decrease the starting torque by about 20%. This could mean the motor failing to start if it cannot produce a torque greater than the load torque plus friction torque.

Effect of rotor resistance on T-S characteristics

At normal running condition, Tr µ s/R₂

At starting, Ts µ R₂/s

Therefore, if we add some resistance in series with rotor winding (that we can do in case of slip-ring rotor), the starting torque will increase, but running torque will decrease. Fig below show the effect of rotor resistance on the T-S characteristics of induction motor.

Here two curves are shown- one for rotor resistance of R₂ and other for rotor resistance of 2R₂. At a particular speed N₁, the running torque is equal to OT₁ when rotor resistance is R₂. At the same speed, the running torque is only OT₂  when the rotor resistance is 2R₂. The starting torque of the motor is equal to OC with rotor resistance R₂ and the motor gives higher starting torque with rotor resistance 2R₂. Hence, external rotor resistance are used where high starting torque is required. Once the motor has picked up to its normal operating speed (N), the external rotor resistance is removed to improve the running torque.

Numericals from V.K. Mehta book Principles of Electrical Machines

Example 9.11

A 4-pole, 3-phase, 50Hz induction motor has a star connected rotor. The rotor has a resistance of 0.1 ohm per phase and standstill reactance of 2 ohm per phase. The induced emf between the slip rings is 100V. If the full load speed is 1460 rpm, calculate

     i.        The slip

   ii.        The emf induced in the rotor in each phase

 iii.        The rotor reactance per phase

  iv.        The rotor current and

   v.        Rotor power factor.

Assume slip rings are short circuited.

Example: 9.1

A 6-pole, 3 phase induction motor is connected to 50 Hz supply. If it is running at 970 rpm, find the slip. (ans=3%)

 

Example 9.2

A 3-phase induction motor is wound for 4 poles and is supplied from 50 Hz system. Calculate: i) the synchronous speed ii)the speed of the motor when slip is 4% and iii) the rotor current frequency when the motor runs at 600 rpm.(ans: 1500rpm, 1440rpm, 30Hz)

Example 9.3

A 50 Hz 4-pole 3-phase induction motor has a rotor current of frequency of 2 Hz. Determine i)the slip and ii) speed of the motor. (4%, 1440rpm)

Example 9.4

 A 500 hp, 3-phase, 440 V, 50 Hz induction motor has a speed of 950 rpm on full load. The machine has 6-poles. Calculate the full load slip and rotor frequency. (5%, 2.5 Hz)

Tutorials

1.   A 2-pole, 3-phase,50-Hz induction motor is running on no load with a slip of 4%. Calculate i) synchronous speed ii) speed of the motor (ans:  3000rpm, 2880rpm)

2.   The frequency of emf in the stator of a 4-pole,3-phase induction motor is 50Hz and that in the rotor is 1.5 Hz. Determine i) the slip  ii) speed of the motor (ans: 3%, 1455 rpm)

3.   A 3-phase, 50Hz induction motor has 8 poles. If the full-load slip is 2.5 %, determine i) synchronous speed ii) rotor speed iii) rotor frequency (ans: 750rpm, 731 rpm, 1.25Hz)

 

 

_{1.6 Power stages, losses and efficiency}

The input electric power fed to the stator of the motor is converted into mechanical power at the shaft of the motor. The various losses during the energy conversion are:

1. Fixed losses

(i) Stator iron loss

(ii) Friction and windage loss

The rotor iron loss is negligible because the frequency of rotor currents under normal running condition is small.

2. Variable losses

(i) Stator copper loss

(ii) Rotor copper loss

Fig. (8.20) shows how electric power fed to the stator of an induction motor suffers losses and finally converted into mechanical power.

The following points may be noted from the above diagram:

(i)                 Stator input, Pi = Stator output + Stator losses

                                              = Stator output + Stator Iron loss + Stator Cu loss

(ii)               Rotor input, Pr = Stator output

It is because stator output is entirely transferred to the rotor through air gap by electromagnetic induction.

(iii)            Mechanical power available, Pm = Pr - Rotor Cu loss

This mechanical power available is the gross rotor output and will produce a gross torque Tg.

(iv)            Mechanical power at shaft, Pout = Pm - Friction and windage loss

Mechanical power available at the shaft produces a shaft torque Tsh.

Clearly, Pm - Pout = Friction and windage loss

Induction Motor Torque

Rotor Output

If T_g newton-metre is the gross torque developed and N r.p.m. is the speed of the rotor, then,

Gross rotor output = 2pNT_g/60 watts

If there were no copper losses in the rotor, the output would equal rotor input and the rotor would run at synchronous speed Ns.

Starting of 3-Phase Induction Motors

The induction motor is fundamentally a transformer in which the stator is the primary and the rotor is short-circuited secondary. At starting, the voltage induced in the induction motor rotor is maximum (Q s = 1). Since the rotor impedance is low, the rotor current is excessively large. This large rotor current is reflected in the stator because of transformer action. This results in high starting current (4 to 10 times the full-load current) in the stator at low power factor and consequently the value of starting torque is low.

 

Methods of Starting 3-Phase Induction Motors

The method to be employed in starting a given induction motor depends upon the size of the motor and the type of the motor. The common methods used to start induction motors are:

(i)                Direct-on-line starting

(ii)              Stator resistance starting

(iii)             Autotransformer starting

(iv)             Star-delta starting

(v)               Rotor resistance starting

Methods (i) to (iv) are applicable to both squirrel-cage and slip ring motors. However, method (v) is applicable only to slip ring motors. In practice, any one of the first four methods is used for starting squirrel cage motors, depending upon ,the size of the motor. But slip ring motors are invariably started by rotor resistance starting.

 

(i) Direct-on-line starting

This method of starting in just what the name implies—the motor is started by connecting it directly to 3-phase supply. The impedance of the motor at standstill is relatively low and when it is directly connected to the supply system, the starting current will be high (4 to 10 times the full-load current) and at a low power factor. Consequently, this method of starting is suitable for relatively small (up to 7.5 kW) machines.

 

(ii) Stator resistance starting

In this method, external resistances are connected in series with each phase of stator winding during starting. This causes voltage drop across the resistances so that voltage available across motor terminals is reduced and hence the starting current. The starting resistances are gradually cut out in steps (two or more steps) from the stator circuit as the motor picks up speed. When the motor attains rated speed, the resistances are completely cut out and full line voltage is applied to the rotor.

This method suffers from two drawbacks. First, the reduced voltage applied to the motor during the starting period lowers the starting torque and hence increases the accelerating time. Secondly, a lot of power is wasted in the starting resistances.

(iii) Autotransformer starting

This method also aims at connecting the induction motor to a reduced supply at starting and then connecting it to the full voltage as the motor picks up sufficient speed. Fig. (8.31) shows the circuit arrangement for autotransformer starting. The tapping on the autotransformer is so set that when it is in the circuit, 65% to 80% of line voltage is applied to the motor.

At the instant of starting, the change-over switch is thrown to “start” position. This puts the autotransformer in the circuit and thus reduced voltage is applied to the circuit. Consequently, starting current is limited to safe value. When the motor attains about 80% of normal speed, the changeover switch is thrown to “run” position. This takes out the autotransformer from the circuit and puts the motor to full line voltage. Autotransformer starting has several advantages viz low power loss, low starting current and less radiated heat. For large machines (over 25 H.P.), this method of starting is often used. This method can be used for both star and delta connected motors.

(iv) Star-delta starting

The stator winding of the motor is designed for delta operation and is connected in star during the starting period. When the machine is up to speed, the connections are changed to delta. The circuit arrangement for star-delta starting is shown in Fig. (8.33). The six leads of the stator windings are connected to the changeover switch as shown. At the instant of starting, the changeover switch is thrown to “Start” position which connects the stator windings in star. Therefore, each stator phase gets V 3 volts where V is the line voltage. This reduces the starting current.

When the motor picks up speed, the changeover switch is thrown to “Run” position which connects the stator windings in delta. Now each stator phase gets full line voltage V. The disadvantages of this method are:

(a) With star-connection during starting, stator phase voltage is 1 3 times the line voltage. Consequently, starting torque is ( )2 1 3 or 1/3 times the value it would have with D-connection. This is rather a large reduction in starting torque.

(b) The reduction in voltage is fixed.

This method of starting is used for medium-size machines (upto about 25 H.P.).

(v)   Starting of Slip-Ring Motors

Slip-ring motors are invariably started by rotor resistance starting. In this method, a variable star-connected rheostat is connected in the rotor circuit through slip rings and full voltage is applied to the stator winding as shown in Fig. (8.34).

(i)                At starting, the handle of rheostat is set in the OFF position so that maximum resistance is placed in each phase of the rotor circuit. This reduces the starting current and at the same time starting torque is increased.

(ii)               As the motor picks up speed, the handle of rheostat is gradually moved in clockwise direction and cuts out the external resistance in each phase of the rotor circuit. When the motor attains normal speed, the change-over switch is in the ON position and the whole external resistance is cut out from the rotor circuit.

Speed Control of Induction Motor

The slip of an induction motor is very small (<3%) so that it is essentially a constant speed motor. Therefore, it is suitable for use in essentially constant speed drive systems. However, many industrial applications require several speeds or a continuously adjustable range of speeds. Traditionally, dc motors have been used in such adjustable speed applications. However, dc motors are expensive and require frequent maintenance of commutators and brushes. On the other hand, the induction motors (squirrel cage motors) are cheap, rugged, have no commutators and are suitable for high speed applications. The engineers have devised several methods to change the speed of induction motors.

The relation between motor speed (N), synchronous speed (Ns) and slip(s) is given by:

N= (1-s) Ns

N= (1-s)*(120f/P)

This equation reveals that the speed of an induction motor can be changed by the following methods:

1.     By changing the number of stator poles(P)

2.      By changing the line frequency(f)

3.      By changing the slip (s) for a given load. The slip can be changed by:

a)     By changing the applied voltage

b)    By changing resistance in the rotor circuit

c)     By inserting foreign voltage of appropriate frequency in the rotor circuit

 

 

1.  By changing the number of stator poles(P)

The synchronous speed of rotating magnetic field is inversely proportional to the number of magnetic poles in stator winding. Stator winding can be designed in such a way that they can be connected as 2-pole or 4-pole or 6-pole with the help of special switch and accordingly we can operate the motor at three different speeds, but smooth change in speed is not possible with this method.

 

2.  By changing the line frequency(f)

From the formula of the synchronous speed of the induction motor, we know that by changing the line frequency f, the synchronous speed Ns of the motor and hence the running speed N can be changed. A major difficulty with this method is that it involves the use of 3-phase variable frequency power supply.

 

3.   By changing the applied voltage

We know that the torque developed (T) by an induction motor is directly proportional to the square of applied voltage (V) i.e TaV². Therefore, by changing the applied voltage, the torque and hence speed (or slip) of the motor can be changed. Fig 10.21 shows the arrangement to control the speed of induction motor by changing the applied voltage.

Limitation: The stator voltage control method is the cheapest and the easiest method of speed control of induction motors. However, it is rarely used because of the following drawbacks:

a)     A large change in voltage is required for a relatively small change in speed.

b)    The large change in voltage results in large change in the flux density. This affects the magnetic conditions and hence performance of the motor.

1. By changing rotor circuit resistance

This method of speed control is suitable only for slip ring motors. The speed of the motor can be decreased by adding external resistance to the rotor as shown in fig. Under normal running condition, the relation between torque (T) and slip (s) of an induction motor is given by:

T a (s/R₂)

R­₂ is the rotor resistance per phase. It is clear from the above equation that for a given torque, s a R_2. Therefore slip can be increased by increasing the rotor resistance

Cascade Connection Method

In this method of speed control, two motors having different number of poles are mounted on a common shaft as shown in figure 8.16. The stator winding of the motor A is supplied by main supply voltage of frequency ‘f’. The second motor B is supplied by the voltage induced in the rotor of the first motor A through slip rings. Therefore the frequency of voltage applied to the stator of the second motor will be different from the main supply frequency. Now the two motors will try to run with two different speed corresponding to two different frequencies. As the both motors are couple to a common shaft, the system will run at a new speed.

Induction Generator

If an induction motor whose stator windings are connected to a 3-phase line is driven by a prime-mover at a speed higher than synchronous speed, it acts as a generator. It converts the mechanical energy it receives from the prime-mover into electrical energy and this electrical energy is supplied to the mains. Such a machine is called an induction generator or asynchronous generator. When speed of the generator exceeds the synchronous speed, the slip(s) becomes negative.

Fig below shows the induction generator connected to a 3-phase line. The petrol engine is the prime mover.

Need of excitement

As soon as the engine speed exceeds the synchronous speed, the motor becomes a generator, delivering active power P to the electrical systems to which it is connected. However, to create its magnetic field, the motor has to absorb reactive power Q. this power can come only from the lines. Consequently, the reactive power Q flows in the opposite direction to the active power P as shown in fig.

We have seen that an induction generator will deliver power only if it is supplied with proper reactive power to create its magnetic field. For this reason, an induction generator is generally connected to a 3-phase line. However, reactive power may be supplied by a group of capacitors connected to the terminals of the motor as shown in fig. in that case, the induction generator does not require external source for supply of reactive power.

Voltage Build up process in Induction Generator

An induction machine with capacitors connected across its terminals, when driven by a prime mover, builds up the voltage in a manner similar to that of a de shunt generator. The voltage build-up process in a dc machine depends upon the residual magnetism in the field poles and the final steady terminal voltage is determined by the resistance of the field circuit. In case of the induction generator, the residual magnetism in the magnetic circuit of the machine is sufficient to generate a small ac voltage in the stator. This small ac voltage causes the capacitor to draw a leading current or a lagging magnetizing current through the magnetizing reactance. 

When a proper value of capacitor is selected, the magnetizing current can be made sufficient to increase the existing air gap flux. With an increased air gap flux, induced voltage increases resulting in more magnetizing current to flow. This process of voltage build-up continues until induce voltage reaches a limit constrained by the saturation curve of the machine and the reactance of the capacitor. The steady state value of the emf generated corresponds to the point of intersection between magnetization curve and volt-amp characteristic of the capacitor.

Fig: Equivalent circuit for no load excitation circuit

 X = Total leakage reactance

i_µ= Magnetizing current

X_m = Magnetizing reactance

e = emf induced in stator

Self-excitation occurs when Xc ≤ (Xm + X)

Curve ‘a’ shown in fig 11 is the magnetization characteristics of the machine and the lines C1, C2, C3 and C4 represents the volt-amp characteristics of different rating capacitors used for excitation.

For any point on the excitation curve, e/i_µ = (X_m+X) = X_C

This equation is true for reactive volt-amp balance in the system, when the leading volt-amp rating of the capacitor is equal to the lagging or magnetizing volt-amp rating of the machine. Thus the slope of the lines gives the reactance of the capacitor required to produce the voltage corresponding to points of intersection of the lies with the magnetizing curve. As the value of the capacitor decreases, the slope of its reactance line increases resulting decrease in terminal voltage. For example, e1 and e2 are the steady state values of terminal voltage corresponding to the capacitance of C1 and C2 respectively. The curve C3 corresponds to the critical value of capacitance below which the voltage builds up in the machine does not occur.

 

 Induction generator in isolated mode of operation:

If the induction generator is operated to supply only isolated local load without connecting the inter-connected power system bus, then such operation is known as isolated mode of operation. It is clear from the T-S characteristic shown in Fig.12 that the induction generator operates at different slip (speed) at different loading condition. At full load it operates at slip 's1', whereas at no-load it operates at slip 's2'. Hence, if the water flow into the turbine is not regulated to match the varying load condition, the frequency of generated voltage varies from full load to no-load.

However, if the water flow into the turbine is not regulated (i.e. constant discharge and head is maintained) and electronic load controller is used, the speed and frequency call be made constant at the varying load conditions. The electronic load controller keeps the total load on the generator constant as shown in Fig.13.

When the consumer's load decreases or increases by some amount, the electronic control circuit will increase or decrease the power consumed by ballast load by same amount so that the total power consumption (P_L + P_B) remains constant and equal to power generated by the generator (P_G) resulting in constant speed operation at varying consumer's load conditions.

Induction generator is more robust and cheaper than synchronous generator. But an induction generator cannot generate reactive power demanded by the load. Whereas, synchronous generator can generate reactive power demanded by the load with the help of dc excitation system provided in the rotor winding. Induction generator is becoming more popular in Micro Hydro Power (MHP) plant in rural area, where the consumer's loads are mostly resistive (lighting and heating).

Induction generator in grid connected mode of operation:

If the induction generator is connected to the bus of large inter-connected grid system as shown in Fig.14, then such operation is known as grid connected mode of operation. In such operation, no Electronic load controller is required. At varying mechanical power input from the turbine, the induction generator injects varying amount of power to the grid and frequency of voltage of induction generator will be automatically constant and equal to grid voltage and frequency. The voltage and frequency of grid always remains constant, because it has frequency governors and voltage controllers in the power stations of the grid. In this mode of operation, even the excitation capacitor is not required. The grid supplies reactive power required for induction generator to maintain air-gap flux.

Synchronizing to grid:

 The synchronizing process of Induction Generator to grid is very simple with compare to that for Synchronous generator. The IG is driven by turbine keeping the switch (S1) open and speed is gradually increased by opening the turbine valve. When the speed reaches little greater than the synchronous speed, then the switch (S1) shall be closed as shown in Fig.15 , then the IG gets synchronized automatically and runs at constant speed which is little greater than the synchronous corresponding to the slip.

Unit 2: Single Phase Motors

Single-phase motors are the most familiar of all electric motors because they are extensively used in home appliances, shops, offices etc. It is true that single phase motors are less efficient substitute for 3-phase motors but 3-phase power is normally not available except in large commercial and industrial establishments. Even where 3-phase mains are present, the single-phase supply may be obtained by using one of the three lines and the neutral.

Types of Single-Phase Motors

Single-phase motors are generally built in the fractional-horsepower range and may be classified into the following four basic types:

1. Single-phase induction motors

(i) split-phase type (ii) capacitor type (iii) shaded-pole type

2. A.C. series motor or universal motor

3. Repulsion motors

(i) Repulsion-start induction-run motor

(ii) Repulsion-induction motor

4. Synchronous motors

(i) Reluctance motor (ii) Hysteresis motor

Single-Phase Induction Motors

Construction and Concept of pulsating field produced by single phase winding

A single phase induction motor is very similar to a 3-phase squirrel cage induction motor. It has (i) a squirrel-cage rotor identical to a 3-phase motor and (ii) a single-phase winding on the stator.

Unlike a 3-phase induction motor, a single-phase induction motor is not self-starting but requires some starting means. The single-phase stator winding produces a magnetic field that pulsates in strength in a sinusoidal manner. The field polarity reverses after each half cycle but the field does not rotate.

Consequently, the alternating flux cannot produce rotation in a stationary squirrel-cage rotor. However, if the rotor of a single-phase motor is rotated in one direction by some mechanical means, it will continue to run in the direction of rotation. As a matter of fact, the rotor quickly accelerates until it reaches a speed slightly below the synchronous speed. Once the motor is running at this speed, it will continue to rotate even though single-phase current is flowing through the stator winding. This method of starting is generally not convenient for large motors. Nor can it be employed fur a motor located at some inaccessible spot. This strange behavior of single-phase induction motor can be explained on the basis of double-field revolving theory.

Double-Field Revolving Theory

This theory is based on the fact that an alternating sinusoidal flux (ɸ= ɸm cos wt) can be represented by two revolving fluxes, each equal to one-half of the maximum value of alternating flux (i.e., ɸm/2) and each rotating at synchronous speed (Ns = 120 f/P, w= 2*pi*f) in opposite directions. The above statement will now be proved. The instantaneous value of flux due to the stator current of a single-phase induction motor is given by;

ɸ=ɸm coswt 

Consider two rotating magnetic fluxes ɸ1 and ɸ2 each of magnitude ɸm/2 and rotating in opposite directions with angular velocity w. Let the two fluxes start rotating from OX axis at t = 0. After time t seconds, the angle through which the flux vectors have rotated is at. Resolving the flux vectors along-X-axis and Y-axis, we have,

Thus the resultant flux vector is ɸ= ɸm cos wt along X-axis. Therefore, an alternating field can be replaced by two relating fields of half its amplitude rotating in opposite directions at synchronous speed. When the rotating flux vectors are in phase, the resultant vector is ɸ= ɸm; when out of phase by 180° , the resultant vector ɸ = 0.

(i) Rotor at standstill

The alternating flux produced by the stator winding can be presented as the sum of two rotating fluxes ɸ1 and ɸ2, each equal to one half of the maximum value of alternating flux and each rotating at synchronous speed (Ns = 120 f/P) in opposite directions. Let the flux ɸ1 rotate in anti-clockwise direction and flux ɸ2 in clockwise direction. The flux ɸ1 will result in the production of torque T1 in the anti clockwise direction and flux ɸ2 will result in the production of torque T2 In the clockwise direction. At standstill, these two torques are equal and opposite and the net torque developed is zero. Therefore, single-phase induction motor is not self-starting.

(ii) Rotor running

Now assume that the rotor is started by spinning the rotor or by using auxiliary

circuit, in say clockwise direction. The flux rotating in the clockwise direction is the

forward rotating flux ( ɸf) and that in the other direction is the backward rotating flux

( ɸb). The slip w.r.t. the forward flux will be

Where Ns = synchronous speed

N = speed of rotor in the direction of forward flux

The rotor rotates opposite to the rotation of the backward flux. Therefore, the slip

w.r.t. the backward flux will be

Thus for forward rotating flux, slip is s (less than unity) and for backward rotating flux, the slip is 2 - s (greater than unity). Since for usual rotor resistance/reactance ratios, the torques at slips of less than unity arc greater than those at slips of more than unity, the resultant torque will be in the direction of the rotation of the forward flux. Thus if the motor is once started, it will develop net torque in the direction in which it has been started and will function as a motor.

Making Single-Phase Induction Motor Self-Starting

To make a single-phase induction motor self-starting, we should somehow produce a revolving stator magnetic field. This may be achieved by converting a single phase supply into two-phase supply through the use of an additional winding. When the motor attains sufficient speed, the starting means (i.e., additional winding) may be removed depending upon the type of the motor.

Classification according to the method employed to make them self-starting

(i) Split-phase motors-started by two phase motor action through the use of an auxiliary or starting winding.

(ii) Capacitor motors-started by two-phase motor action through the use of an auxiliary winding and a capacitor.

(iii) Shaded-pole motors-started by the motion of the magnetic field produced by means of a shading coil around a portion of the pole structure.

Split-Phase Induction Motor

The stator of a split-phase induction motor is provided with an auxiliary or starting winding S in addition to the main or running winding M. The starting winding is located 90° electrical from the main winding [See Fig. (9.13 (i))] and operates only during the brief period when the motor starts up. The two windings are so resigned that the starting winding S has a high resistance and relatively small reactance while the main winding M has relatively low resistance and large reactance as shown in the schematic connections in Fig. (9.13 (ii)). Consequently, the currents flowing in the two windings have reasonable phase difference c (25° to 30°) as shown in the phasor diagram in Fig. (9.13 (iii)).

Fig 9.13

Operation

(i) When the two stator windings are energized from a single-phase supply, the main winding carries current Im while the starting winding carries current Is.

(ii) Since main winding is made highly inductive while the starting winding highly resistive, the currents Im and Is have a reasonable phase angle a (25° to 30°) between them as shown in Fig. (9.13 (iii)). Consequently, a weak revolving field approximating to that of a 2-phase machine is produced which starts the motor. The starting torque is given by;

 Ts = kIm Is sinα

where k is a constant whose magnitude depends upon the design of the motor.

(iii) When the motor reaches about 75% of synchronous speed, the centrifugal switch opens the circuit of the starting winding. The motor then operates as a single-phase induction motor and continues to accelerate till it reaches the normal speed. The normal speed of the motor is below the synchronous speed and depends upon the load on the motor.

Characteristics and application

(i) The starting torque is 1.5 to 2 times the full-loud torque and the  starting current is 6 to 8 times the full-load current.

(ii) Due to their low cost, split-phase induction motors are most popular single-phase motors in the market.

(iii) Since the starting winding is made of fine wire, the current density is high and the winding heats up quickly. If the starting period exceeds 5 seconds, the winding may burn out unless the motor is protected by built-in-thermal

relay. This motor is, therefore, suitable where starting periods are not frequent.

(iv) An important characteristic of these motors is that they are essentially constant-speed motors. The speed variation is 2-5% from no-load to full load.

(v) These motors are suitable where a moderate starting torque is required and where starting periods are infrequent e.g., to drive: (a) fans (b) washing machines (c) oil burners (d) small machine tools etc.

The power rating of such motors generally lies between 60 W and 250 W.

Capacitor-Start and induction run Motor

The capacitor-start motor is identical to a split-phase motor except that the starting winding has as many turns as the main winding. Moreover, a capacitor C is connected in series with the starting winding as shown in Fig. (9.14 (i)). The value of capacitor is so chosen that Is leads Im by about 80° (i.e., ~ 80°) which is considerably greater than 25° found in split-phase motor [See Fig. (9.14 (ii))]. Consequently, starting torque (Ts = k Im Is sin ) is much more than that of a split-phase motor Again, the starting winding is opened by the centrifugal switch when the motor attains about 75% of synchronous speed. The motor then operates as a single-phase induction motor and continues to accelerate till it reaches the normal speed.

Characteristics

i. Although starting characteristics of a capacitor-start motor are better than those of a split-phase motor, both machines possess the same running characteristics because the main windings are identical.

ii. The phase angle between the two currents is about 80° compared to about 25° in a split-phase motor. Consequently, for the same starting torque, the current in the starting winding is only about half that in a split-phase motor. Therefore, the starting winding of a capacitor start motor heats up less quickly and is well suited to applications involving either frequent or prolonged starting periods.

Fig 9.14

iii. Capacitor-start motors are used where high starting torque is required and where the starting period may be long e.g., to drive: (a) Compressors (b) large fans (c) pumps (d) high inertia loads

The power rating of such motors lies between 120 W and 7-5 kW.

Capacitor-Start Capacitor-Run Motor

This motor is identical to a capacitor-start motor except that starting winding is not opened after starting so that both the windings remain connected to the supply when running as well as at starting. Two designs are generally used.

i. In one design, a single capacitor C is used for both starting and running as shown in Fig.(9.15 (i)). This design eliminates the need of a centrifugal switch and at the same time improves the power factor and efficiency of the motor.

Fig 9.15

ii. In the other design, two capacitors C1 and C2 are used in the starting winding as shown in Fig. (9.15 (ii)). The smaller capacitor C1 required for optimum running conditions is permanently connected in series with the starting winding. The much larger capacitor C2 is connected in parallel with C1 for optimum starting and remains in the circuit during starting. The starting capacitor C1 is disconnected when the motor approaches about 75% of synchronous speed. The motor then runs as a single-phase induction motor.

Characteristics

i. The starting winding and the capacitor can be designed for perfect 2-phase operation at any load. The motor then produces a constant torque and not a pulsating torque as in other single-phase motors.

ii. Because of constant torque, the motor is vibration free and can be used in: (a) hospitals (6) studios and (c) other places where silence is important.

Shaded-Pole Motor

The shaded-pole motor is very popular for ratings below 0.05 H.P. (~ 40 W) because of its extremely simple construction. It has salient poles on the stator excited by single-phase supply and a squirrel cage rotor as shown in Fig. (9.16).

A portion of each pole is surrounded by a short-circuited turn of copper strip called shading coil.

Fig 9.16

Operation

The operation of the motor can be understood by referring to Fig. (9.17) which shows one pole of the motor with a shading coil.

i. During the portion OA of the alternating-current cycle [See Fig. (9.17)], the flux begins to increase and an e.m.f. is induced in the shading coil. The resulting current in the shading coil will be in such a direction (Lenz’s law) so as to oppose the change in flux. Thus the flux in the shaded portion of the pole is weakened while that in the unshaded portion is strengthened as shown in Fig. (9.17 (ii)).

ii. During the portion AB of the alternating-current cycle, the flux has reached almost maximum value and is not changing. Consequently, the flux distribution across the pole is uniform [See Fig. (9.17 (iii))] since no current is flowing in the shading coil. As the flux decreases (portion BC of the alternating current cycle), current is induced in the shading coil so as to oppose the decrease in current. Thus the flux in the shaded portion of the

Fig 9.17

iii. The effect of the shading coil is to cause the field flux to shift across the pole face from the unshaded to the shaded portion. This shifting flux is like a rotating weak field moving in the direction from unshaded portion to the shaded portion of the pole.

iv. The rotor is of the squirrel-cage type and is under the influence of this moving field. Consequently, a small starting torque is developed. As soon as this torque starts to revolve the rotor, additional torque is produced by single-phase induction-motor action. The motor accelerates to a speed slightly below the synchronous speed and runs as a single-phase induction motor.

Characteristics

i. The salient features of this motor are extremely simple construction and absence of centrifugal switch.

ii. Since starting torque, efficiency and power factor are very low, these motors are only suitable for low power applications e.g., to drive: (a) small fans (6) toys (c) hair driers (d) desk fans etc.

The power rating of such motors is upto about 30 W.

A.C. Series Motor or Universal Motor

Construction

The construction of an a.c. series motor is very similar to a d.c. series motor except that above modifications are incorporated [See Fig. (9.20)]. Such a motor can be operated either on a.c. or d.c. supply and the resulting torque-speed curve is about the same in each case. For this reason, it is sometimes called a universal motor.

Operation

When the motor is connected to an a.c. supply, the same alternating current flows through the field and armature windings. The field winding produces an alternating flux that reacts with the current flowing in the armature to produce a torque. Since both armature current and flux reverse simultaneously, the torque always acts in the same direction. It may be noted that no rotating flux is produced in this type of machines; the principle of operation is the same as that of a d.c. series motor.

Characteristics

The operating characteristics of an a.c. series motor are similar to those of a d.c. series motor.

i. The speed increases to a high value with a decrease in load. In very small series motors, the losses are usually large enough at no load that limit the speed to a definite value (1500 - 15,000 r.p.m.).

ii. The motor torque is high for large armature currents, thus giving a high starting torque.

iii. At full-load, the power factor is about 90%. However, at starting or when carrying an overload, the power factor is lower.

Applications

The fractional horsepower a.c. series motors have high-speed (and corresponding small size) and large starting torque. They can, therefore, be used to drive: (a) high-speed vacuum cleaners (b) sewing machines (c) electric shavers (d) drills (e) machine tools etc.

Unit 3: Three phase synchronous generator

Introduction

Three phase synchronous generator is also known as alternator. An alternator operates on the same fundamental principle of electromagnetic induction as a d.c. generator. Like a d.c. generator, an alternator also has an armature winding and a field winding. But there is one important difference between the two. In a d.c. generator, the armature winding is placed on the rotor in order to provide a way of converting alternating voltage generated in the winding to a direct voltage at the terminals through the use of a rotating commutator. The field poles are placed on the stationary part of the machine.

Construction of Alternator

An alternator has 3,-phase winding on the stator and a d.c. field winding on the rotor. The main parts of alternator are:

1. Stator or armature

2. Rotor

3. Excitor

Fig: Construction of alternator

1. Stator

It is the stationary part of the machine and is built up of sheet-steel laminations having slots on its inner periphery. A 3-phase winding is placed in these slots and serves as the armature winding of the alternator. The armature winding is always connected in star and the neutral is connected to ground.

2. Rotor

The rotor carries a field winding which is supplied with direct current through two slip rings by a separate d.c. source or excitor. Rotor construction is of two types, namely;

(i) Salient (or projecting) pole type

(ii) Non-salient (or cylindrical) pole type

(i) Salient pole type

In this type, salient or projecting poles are mounted on a large circular steel frame which is fixed to the shaft of the alternator. Low and medium-speed alternators (120-400 r.p.m.) such as those driven by diesel engines or water turbines have salient pole type rotors due to the following reasons:

a. The salient field poles would cause .an excessive windage loss if driven at high speed and would tend to produce noise.

b. Salient-pole construction cannot be made strong enough to withstand the mechanical stresses to which they may be subjected at higher speeds.

Fig: Salient pole rotor

(ii) Non-salient pole type / Cylindrical type rotor:

This type of rotor has got smooth magnetic poles in the form of a closed cylinder as shown in fig. construction of this type of rotor is more compact and robust with compared to salient pole rotor. This type of rotors are generally used in the generators driven by high speed prime movers like steam turbine, gas turbine.

Fig: Cylindrical type rotor

3. Excitor

It is a self-excited dc generator mounted on the shaft of the alternator. This will provide dc current required to magnetize the magnetic poles of the rotor. The dc current generated by the exciter is fed to the field winding of the alternator through slip ring and carbon brush arrangement.

Principle of Operation

The rotor winding is energized from the d.c. exciter and alternate N and S poles are developed on the rotor. When the rotor is rotated in anti-clockwise direction by a prime mover, the stator or armature conductors are cut by the magnetic flux of rotor poles. Consequently, e.m.f. is induced in the armature conductors due to electromagnetic induction. The induced e.m.f. is alternating since N and S poles of rotor alternately pass the armature conductors. The direction of induced e.m.f. can be found by Fleming’s right hand rule and frequency is given by;

Where N = speed of rotor in r.p.m.

P = number of rotor poles

The magnitude of the voltage induced in each phase depends upon the rotor flux, the number and position of the conductors in the phase and the speed of the rotor.

Fig 10.4

Fig. (10.4 (i)) shows star-connected armature winding and d.c. field winding. When the rotor is rotated, a 3-phase voltage is induced in the armature winding. The magnitude of induced e.m.f. depends upon the speed of rotation and the d.c. exciting current. The magnitude of e.m.f. in each phase of the armature winding is the same. However, they differ in phase by 120° electrical as shown in the phasor diagram in Fig. (10.4 (ii)).

E.M.F. Equation of an Alternator

Let Z = No. of conductors or coil sides in series per phase

Ø= Flux per pole in Weber

P = Number of rotor poles

N = Rotor speed in r.p.m.

Z=2*T

T=no of turns of coil

In one revolution (i.e., 60/N second), each stator conductor is cut by PØWeber

i.e.,

dØ= PØ;

dt = 60/N

Average e.m.f. induced in one stator conductor

                                       Er.m.s./phase=4.44fØT

Armature winding parameters

Besides the factors indicated by the above equation, there are some other factors which affects the magnitude of emf induced in stator windings. The factors are –pitch factor and distribution factor.

i. Pitch factor: (also known as chord factor)

A coil whose sides are separated by one pole pitch (i.e., coil span is 180° electrical) is called a full-pitch coil. But in actual machine, the span may be less than 180o electrical. Such winding is known as “short-pitched winding”. The e.m.f. induced in a short-pitch coil is less than that of a full pitch coil. The factor by which e.m.f. per coil is reduced is called pitch factor Kp. It is defined as:

Since EAB = ECD, EAD = 2E cos /2

Kp = cos/ 2

For a full-pitch winding, Kp = 1. However, for a short-pitch winding, Kp < 1.

ii. Distribution factor(Kd): (also called breadth factor)

In an actual machine, the stator windings are not concentrated in a slot. The windings are uniformly distributed over many number of slots to form polar group under each pole. The distribution factor Kd is defined as:

Note that numerator is less than denominator so that Kd < 1.

Effect of windage parameters on emf generation

If Kp and Kd are the pitch factor and distribution factor of the armature winding, then,

Er.m.s. / phase = 2.22KpKd fØZ volts

Sometimes the turns (T) per phase rather than conductors per phase are specified, in that case, eq. (ii) becomes:

Er.m.s. / phase = 4.44KpKd fØT volts

The line voltage will depend upon whether the winding is star or delta connected.

Relationship between speed, frequency and number of magnetic poles in rotor

The frequency of induced e.m.f. in the armature conductors depends upon speed

and the number of poles.

Let N = rotor speed in r.p.m.

P = number of rotor poles

f = frequency of e.m.f. in Hz

No. of cycles/revolution = No. of pairs of poles = P/2

No. of revolutions/second = N/60

No. of cycles/second = (P/2)*(N/60) = N P/120

But number of cycles of e.m.f. per second is its frequency.

f = NP/120

It may be noted that N is the synchronous speed and is generally represented by Ns. For a given alternator, the number of rotor poles is fixed and, therefore, the alternator must be run at synchronous speed to give an output of desired frequency. For this reason, an alternator is sometimes called synchronous generator.

Concept of geometrical degree and electrical degree

Fig 9.7 shows a four pole synchronous generator. If the rotor is rotated at the same speed as in fig 9.6, during the 3600 geometrical degree rotation of rotor (or during the time of generating one cycle of emf in 2-pole machine) two cycle of emf will generate in the 4-pole machine. The frequency of emf generated in 4-pole machine will be double of frequency of emf in 2-pole machine (f = PN/120 = (4*3000)/120=100 Hz). If emf of 50 Hz is to be generated from the 4-pole machine, the rotor has to be rotated at a lower speed of 1500 rpm. The relation between electrical degree and geometrical degree is given by:

Electrical degree = (P/2)*Geometrical degree

Advantages of stationary armature

The field winding of an alternator is placed on the rotor and is connected to d.c. supply through two slip rings. The 3-phase armature winding is placed on the stator. This arrangement has the following advantages:

i. It is easier to insulate stationary winding for high voltages for which the alternators are usually designed. Ii is because they are not subjected to centrifugal forces and also extra space is available due to the stationary arrangement of the armature.

ii. The stationary 3-phase armature can be directly connected to load without going through large, unreliable slip rings and brushes.

iii. Only two slip rings are required for d.c. supply to the field winding on the rotor. Since the exciting current is small, the slip rings and brush gear required are of light construction.

iv. Due to simple and robust construction of the rotor, higher speed of rotating d.c. field is possible. This increases the output obtainable from a machine of given dimensions.

Alternator on Load

Fig. (10.14)

Fig. (10.14) shows Y-connected alternator supplying inductive load (lagging p.f.). When the load on the alternator is increased (i.e., armature current Ia is increased), the field excitation and speed being kept constant, the terminal voltage V (phase value) of the alternator decreases. This is due to

(i) Voltage drop IaRa where Ra is the armature resistance per phase.

(ii) Voltage drop IaXL where XL is the armature leakage reactance per phase.

(iii) Voltage drop because of armature reaction.

(i) Armature Resistance (Ra)

Since the armature or stator winding has some resistance, there will be an IaRa drop when current (Ia) flows through it. The armature resistance per phase is generally small so that IaRa drop is negligible for all practical purposes.

(ii) Armature Leakage Reactance (XL)

When current flows through the armature winding, flux is set up and a part of it does not cross the air-gap and links the coil sides as shown in Fig. (10.15). This leakage

flux alternates with current and gives the winding self-inductance. This is called armature leakage reactance. Therefore, there will be IaXL drop which is also effective in reducing the terminal voltage.

(iii) Armature reaction (phasor diagram for different cases remains)

The load is generally inductive and the effect of armature reaction is to reduce the generated voltage. Since armature reaction results in a voltage effect in a circuit caused by the change in flux produced by current in the same circuit, its effect is of the nature of an inductive reactance. Therefore, armature reaction effect is accounted for by assuming the presence of a fictitious reactance XAR in the armature winding. The quantity XAR is called reactance of armature reaction. The value of XAR is such that IaXAR represents the voltage drop due to armature reaction.

Equivalent Circuit

Fig. (10.16) shows the equivalent circuit of the loaded alternator for one phase. All the quantities are per phase. Here

E0 = No-load e.m.f.

E = Load induced e.m.f. It is the induced e.m.f. after allowing for armature reaction. It is equal to phasor difference of E0 and IaXAR.

V = Terminal voltage. It is less than E by voltage drops in XL and Ra.

E = V + Ia (Ra + j XL)

and E0 = E+ Ia ( jXAR )

Fig.(10.16)

Synchronous Reactance (Xs)

The sum of armature leakage reactance (XL) and reactance of armature reaction (XAR) is called synchronous reactance Xs [See Fig. (10.17 (i))]. Note that all quantities are per phase.

Xs = XL + XAR

Fig.(10.17)

The synchronous reactance is a fictitious reactance employed to account for the voltage effects in the armature circuit produced by the actual armature leakage reactance and the change in the air-gap flux caused by armature reaction. The circuit then reduces to the one shown in Fig. (10.17 (ii)).

Synchronous impedance, Zs = Ra + j Xs

The synchronous impedance is the fictitious impedance employed to account for the voltage effects in the armature circuit produced by the actual armature resistance, the actual armature leakage reactance and the change in the air-gap flux produced by armature reaction.

E0 = V + IaZs = V + Ia (R + j Xs)

Voltage Regulation

The voltage regulation of an alternator is defined as the change in terminal voltage from no-load to full-load (the speed and field excitation being constant) divided by full-load voltage.

Note that E0 - V is the arithmetic difference and not the phasor difference. The factors affecting the voltage regulation of an alternator are:

(i) IaRa drop in armature winding

(ii) IaXL drop in armature winding

(iii) Voltage change due to armature reaction

We have seen that change in terminal voltage due to armature reaction depends upon the armature current as well as power-factor of the load. For leading load p.f., the no-load voltage is less than the full-load voltage. Hence voltage regulation is negative in this case. The effects of different load power factors on the change in the terminal voltage with changes of load on the alternator are shown in Fig. (10.19). Since the regulation of an alternator depends on the load and the load power factor, it is necessary to mention power factor while expressing regulation.

Fig.(10.19)

Synchronizing Action

When two or more alternators have been connected in parallel, they will remain in stable operation under all normal conditions i.e., voltage, frequency, speed and phase equality will continue. In other words, once synchronized properly, the alternators will continue to run in synchronism under all normal conditions. If one alternator tries to fall out of synchronism, it is immediately counteracted by the production of a synchronizing torque which brings it back to synchronism. This automatic action is called the synchronizing action of the alternators.

Synchronizing Power

When two alternators are operating in parallel, each machine has an inherent tendency to remain synchronized. Consider two similar single-phase alternators

1 and 2 operating in parallel at no-load [See Fig. (10.45)]. Suppose, due to any reason, the speed of machine 2 decreases. This will cause E2 to fall back by a phase angle of a electrical degrees as shown in Fig. (10.46) (though still E1 = E2). Within the local circuit formed by two alternators, the resultant e.m.f. Er is the phasor difference E1 - E2. This resultant e.m.f. results in the production of synchronizing current Isy which sets up synchronizing torque. The synchronizing torque retards machine 1 and accelerates machine 2 so that synchronism is reestablished. The power associated with synchronizing torque is called synchronizing power.

Fig.(10.45)

Fig.(10.46)

Alternator on Infinite Busbars

The behaviour of alternators connected to an infinite busbars is as under:

(i) Any change made in the operating conditions of one alternator will not change the terminal voltage or frequency of the system. In other words, terminal voltage (busbars voltage) and frequency are not affected by changing the operating conditions of one alternator. It is because of large size and inertia of the system.

(ii) The kW output supplied by an alternator depends solely on the mechanical power supplied to the prime mover of the alternator. An increase in mechanical power to the prime mover increases the kW output of the alternator and not the kVAR. A decrease in the mechanical power to the prime mover decreases the kW output of the alternator and not the kVAR.

(iii) If the mechanical power to the prime mover of an alternator is kept constant, then change in excitation will change the power factor at which the machine supplies changed current. In other words, change of excitation controls the kVAR and not kW.

The change of driving torque controls the kW output and not kVAR of an alternator.

The change of excitation controls the kVAR and not the kW output of an alternator.

Effect of change of field excitation

Suppose the alternator connected to infinite bus bars is operating at unity p.f. It is then said to be normally excited. Suppose that excitation of the alternator is increased (overexcited) while the power input to the prime mover is unchanged. The active power output (W or kW) of the alternator will thus remain unchanged i.e., active component of current is unaltered. The overexcited alternator will supply

lagging current (and hence lagging reactive power) to the infinite bus bars. Fig. (10.50) shows the phasor diagram of an overexcited alternator connected to infinite bus bars. The angle d between E and V is called power angle.

Fig.(10.50)

Now suppose that excitation of the alternator is decreased below normal excitation (under-excitation) while the power input to the prime mover is unchanged. Therefore, the active power output (W or kW) of the alternator will remain unchanged L e., active component of current is unaltered. The under excited alternator supplies leading current (and hence leading reactive power) to the infinite bus bars. It is because when an alternator is under excited, it must deliver leading current since leading current produces an aiding m.m.f. to increase the under excitation.

Fig.(10.51)

Conclusion. An overexcited alternator operates at lagging power factor and supplies lagging reactive power to infinite bus bars. On the other hand, an under excited alternator operates at leading power factor and supplies leading reactive power to the infinite bus bars.

Hunting

Sometimes an alternator will not operate satisfactorily with others due to hunting. If the driving torque applied to an alternator is pulsating such as that produced by a diesel engine, the alternator rotor may be pulled periodically ahead of or behind its normal position as it rotates. This oscillating action is called hunting.

Parallel Operation of Alternators

It is rare to find a 3-phase alternator supplying its own load independently except under test conditions. In practice, a very large number of 3-phase alternators operate in parallel because the various power stations are interconnected through the national grid. Therefore, the output of any single alternator is small compared with the total interconnected capacity. For example, the total capacity of the interconnected system may be over 40,000 MW while the capacity of the biggest single alternator may be 500 MW. For this reason, the performance of a single alternator is unlikely to affect appreciably the voltage and frequency of the whole system. An alternator connected to such a system is said to be connected to infinite bus bars. The outstanding electrical characteristics of such bus bars are that they are constant-voltage, constant frequency bus bars.

Advantages of Parallel Operation of Alternators

i. Continuity of service.

ii. Efficiency

iii. Maintenance and repair.

iv. Load growth.

Conditions for Paralleling Alternator with Infinite Bus bars

In order to connect an alternator safely to the infinite bus bars, the following conditions are met:

1. The terminal voltage (r.m.s. value) of the incoming alternator must be the same as bus bars voltage.

2. The frequency of the generated voltage of the incoming alternator must be equal to the bus bars frequency.

3. The phase of the incoming alternator voltage must be identical with the phase of the bus bars voltage. In other words, the two voltages must be in phase with each other.

4. The phase sequence of the voltage of the incoming alternator should be the same as that of the bus bars.

Methods of Synchronization

The method of connecting an incoming alternator safely to the live bus bars is called synchronization. The equality of voltage between the incoming alternator and the bus bars can be easily checked by a voltmeter. The phase sequence of the alternator and the bus bars can be checked by a phase sequence indicator. Differences in frequency and phase of the voltages of the incoming alternator and bus bars can be checked by one of the following two methods:

(i) By Three Lamp (one dark, two bright) method

(ii) By Synchroscope

Click here to get notes on synchronization

nit 4: Synchronous Motor

Construction

A synchronous motor is a machine that operates at synchronous speed and converts electrical energy into mechanical energy. It is fundamentally an alternator operated as a motor. Like an alternator, a synchronous motor has the following two parts:

1. a stator

2. a rotor

The stator is wound for the same number of poles as the rotor poles. As in the case of an induction motor, the number of poles determines the synchronous speed of the motor:

Synchronous speed,

Ns =120f/ P

where f = frequency of supply in Hz

           P = number of poles

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.

An important drawback of a synchronous motor is that it is not self-starting and auxiliary means have to be used for starting it.

Operating principle

Synchronous motor is not self-starting. When the stator windings are supplied by three phase voltage, rotating magnetic field will produce. At the same time if the rotor field windings are excited by current, the rotor poles will get magnetized. But the interaction between stator magnetic field and rotor magnetic will not be able to produce a continuous rotation. This facts can be explained as follows:

(i) At starting, the position of rotor poles could have many alternative positions relative to the stator poles as shown in fig 9.19. If the relative position between rotor poles and stator poles at the starting is as shown in fig 9.19(a), the like poles will get repel and the tendency of the rotor will be to rotate in anti-clock wise direction. But after sometime, the Npole of the stator and S-pole of the rotor comes face to face. Then these opposite poles will try to get attract with each other, then the tendency of the rotor will be to rotate in clockwise direction. But the heavy mass of the rotor cannot response to such a quick reversal of direction of rotation. Hence the motor remains at rest.

(ii) If the relative position between rotor poles and stator poles at the starting is as shown in Fig.9.19(b), the unlike poles will get attract and the tendency of the rotor will be to rotate in clockwise direction alone with the stator poles, But the heavy mass of the rotor cannot pick up the synchronous speed immediately. Therefore after some time, N-pole of the stator and N-pole of the rotor comes face to face. Now the like poles repels each other and the tendency of the rotor will be to rotate in anticlockwise direction. But the heavy mass of the rotor cannot response to such a quick reversal of direction of rotation. Hence the rotor remains at rest.

(iii) If the relative position between rotor poles and stator poles at the starting is as shown in Fig.9.19(c), the like poles will get repel and the tendency of the rotor will be to rotate in anti-clockwise direction, But-after some time, the N-pole of the stator and S-pole of the rotor comes face to face. Then these opposite poles will try to get attract with each other, then the tendency of the rotor will be to rotate in clockwise direction. But the heavy mass of the rotor c n not response to such a quick reversal of direction of rotation. Hence the rotor remains at rest.

Hence. at any position, the motor is not self-starting. If the rotor is rotated up to or near to the synchronous speed (before supplying voltage to the rotor) by some auxiliary means without exciting the rotor field winding and then stator and field are excited by their respective supply, the rotor pole will get magnetically locked up into synchronism with the stator poles. Then the rotor rotates continuously and the auxiliary means is removed.

Starting Methods:

It has been explained that a synchronous motor must be accelerated up to the synchronous speed by some auxiliary means before exciting the stator and field.

Various methods are available for starting the synchronous motor. Methods are as follows

i) A dc motor coupled to the shaft of synchronous motor.

ii) Using field exciter of synchronous as dc motor

iii) A small induction motor of at least one pair of poles less than the synchronous motor.

iv) Using damper winding as a squirrel cage induction motor

(i) A dc motor coupled to the shaft of synchronous motor:

This method is sometime used in the laboratories with synchronous motors without damper windings. The unexcited rotors is rotated by means of a dc motor coupled to the shaft of the synchronous motor. The speed of the dc motor is adjusted by is field regulator. As the speed reach near to synchronous speed, the field winding of the synchronous motor is excited by the dc current and the dc motor is switched off. Then the motor continuously rotates with synchronous speed.

(ii) Using field exciter of synchronous as dc motor:

The second method is similar to the first method except that the exciter of the synchronous motor (i.e. a dc shunt generator) is operated as dc motor for the time being and as the speed reaches close to the synchronous speed. The dc machine is again used as exciter.

(iii) A small induction motor of at least one pair of poles less than the synchronous motor.

This third method using an auxiliary induction motor with at least one pair of pole less involves the same synchronizing process as that of the first method.

(iv) Using damper winding as a squirrel cage induction motor

Most of the modern synchronous motors are started with the help of the damper findings. Fig.9.20 shows the constructional detail of a rotor pole having damper winding.

It should be noted that the shorting strip, which short circuits the rotor bars, contains holes for bolting to the next set of damper winding on the next pole. In this way, a complete squirrel cage winding is formed. Although the bar's' are not of the capacity to carry the rated synchronous motor load, they are sufficient to start the motor as induction motor—Star-Delta or auto transformer' methods are used to reduce the starting current drawn by the motor. It is practically impossible to start a synchronous motor with its field excited. Even with un-excited condition, the rapidly rotating magnetic field of the stator will induce extremely high voltage in many turns of the field winding. Therefore., it is better to short circuit dc field winding during the starting period; whatever voltage and current are induced in it may then aid in producing induction motor action.

All the above methods shall be used with the synchronous motor without load. In order to start the synchronous motor with load, phase wound damper winding shall be used so that external resistance can be inserted to produce high starting torque. Fig.9.21 shows the schematic diagram of phase wound damper winding for starting synchronous motor.

Such motor will have rotor with five slip ring. Two for the dc field excitation and three for ac star connected wound damper winding The motor is started with full external resistance per phase and dc field circuit open As the motor approaches synchronous speed, the starting resistance is reduced and, when the field voltage is applied, the motor pulls into synchronism. 

Equivalent diagram

 No-load and Loaded operation:

It had already been explained that a synchronous motor is not self-starting. It had to be speeded up to synchronous speed by some auxiliary means, the supply to the rotor winding of the rotor had to be switched on, then the rotor poles will get magnetically locked up with stator poles. However the engagement between the stator and rotor poles is not absolutely rigid one. As the load on the motor increases, the rotor progressively tends to fall back in phase (but net in speed) by some angle, but the motor still continue to with the synchronous speed.

At no-load, if there is no power loss in the motor, the stator poles and rotor poles will be along the same axis and phase difference between the applied voltage ‘V’ and the back emf (developed in the armature winding) will be exactly 180⁰ (See Fig9.22(a) ). But this not possible in practice because some power loss takes place due to iron loss and friction loss. Hence the rotor pole lags by some angle 'a' with the stator pole and the phasor diagram will be as shown in Fig.9.22(b) The current drawn by armature at no-load is given by

I­_a = (V-E_b)/Z_s = E_R/Z_s

E_R = Net voltage across the armature

Z_s = Synchronous impedance per phase 

In case of dc motor, the speed of the armature decreases with increase in load due to which the back emf decrease and then the armature current will increase to overcome the increased load. But in case of synchronous motor, the speed does not change with load When the load on a synchronous motor increases, the rotor poles lags the stator poles by larger angle ‘a’ and the phase between V and E_b will increase (note that magnitude of E_b will remain constant) so that the net voltage E_R will increase and the armature current will increase.

Effect of Excitation

The dc current supply to the rotor field winding is known as excitation in synchronous motor. As the speed of synchronous motor is constant, the magnitude of back emf remains constant provided the flux per pole produced by the rotor does not change. If the magnitude of back emf can be changed by field excitation. If the excitation is changed at a constant load, the magnitude of armature current and power factor will change. By changing the excitation, the motor can be operated at both lagging and leading power factor. This fact can be explained as follows:

The value of excitation for which the magnitude of back emf Eb is equal to applied voltage V is known as 100% excitation. If the excitation is more than 100%, then the motor is said to be over excited and if the excitation is less than 100%, then the motor is said to be under excited.

Consider a synchronous motor operating with a constant load. Fig 9.23(a) shows the phasor diagram for the case of 100% excitation i.e. when E_b= V (in magnitude). The armature current Ia lags behind V by a small angle Ø. ϴ is the phase angle between Ia and E_R, whose magnitude is given by ϴ = tan^-1(Xs /Ra ). Since Xs and Ra are constant, angle ϴ also remains constant.

If the motor is under excited, the magnitude of Eb will be less than V. Therefore the resultant of Eb and V (i.e. E_R) will shift upward by some angle, then the direction Ia will also shift by same angle so that angle ϴ again remains constant as shown in fig.9.23 (b). Here the magnitude of Ia has increased and Ia lags V by greater angle so that power factor is decreased, but the active component Ia cos ϴ remains same so that output power also remains constant.

Fig.9.23(c) represents the condition for over excited motor (i.e. when Eb>V). Therefore the resultant voltage vector E_R is pulled in the anti-clockwise and Ia also is shifted in anti-clockwise direction. It is seen that now motor is drawing a leaking current. It may also happen for same value of excitation, that Ia may be in phase with V. i.e. power factor is unity as shown in fig-.9.23(d). At this instant the current drawn by motor is minimum.

The following two important points shall be understand clearly from the above discussion."

i) The magnitude of armature current varies with excitation. The current has larger values at both low and high values of excitation. In between. it has minimum value corresponding to a certain excitation for which  power factor is unity  The variation of Ia with excitation are shown in fig.9.24 which are known as 'V' curves.

ii) For the same input, armature current varies between a wide range and power factor also vary accordingly with excitation. When over excited motor runs with leading power factor and the motor runs with lagging power factor when under excited. The variations power factor with excitation is also shown in Fig 9.24 and known as inverted 'V' curve. It would be noted that minimum armature current corresponding to unity power factor. 

Power angle Characteristic of Cylindrical Rotor Machines:

Fig.9.25 (a) shows the circuit diagram and phasor diagram of a synchronous machine in generating mode and Fig.9.25 (a) shows the 'circuit diagram and phasor diagram of a synchronous machine in motoring mode. The machines are assumed to be connected to the infinite bus bar having a voltage of ‘Vt’ and resistance of the stator winding is neglected and only the reactance of the machine has been considered.

 

From the eqn (9.8) it is clear that the electrical power of the machine P, is proportional to Sind, where 5 is the phase angle between V_t and E_b. This angle 5 is known as power angle. The eqn (9-8) can be represented by a curve as shown in Fig.9.26.

 Maximum power occurs at d = 90°. At no-load the machine operates at d = 0 (but > 0). As the load increases, d will increase and more electrical power will exchange. If the machine is overloaded so that d > 90°, then the machine will lose the synchronism, the machine will lose the synchronism, the machine will not be able to exchange the more power and the machine will lose stability. d =90⁰ is the steady state stability. The machine is normally operated at d much less than 90⁰. This is to prevent the machine from going into an unstable region during transient power swing.

Notes on special motors (Control system syllabus)

Servo motors

A servo system is one in which the output is some mechanical variable like position, velocity or accelerators. Such systems are automatic control systems in which output is some mechanical function such as controlling the position of the shaft, controlling angular speed of the shaft etc. As seen earlier, the motors used in such control systems are driven by the signal which is derived based on the error information supplied to the controller. These motors used in such servo systems or servomechanism are called as servomotors. These motors are low power rating motors and can drive the load directly, hence these motors are usually coupled to the load through a gear train for power matching purpose. 

Figure 1 Servo mechanism

The servomotors are basically classified depending upon the nature of the electric supply used for its operation. The electric supply can be a.c. or d.c. in nature hence basic classification is obviously a.c. servomotors and d.c servomotors.

Types

      1.            AC Servomotors

      2.            DC Servomotors

a.       Field Controlled DC Servomotors

b.      Armature Controlled DC Servomotors

c.       Permanent Magnet Armature Controlled DC servomotors

 

Stepper motor (stepping motors or step motors)

A stepper motor is an electromagnetic motor that rotates by a specific number of degrees in response to an input electrical signal. Typical step sizes are 2, 2.5, 7.5 and 15 degrees for each electrical pulse. It is to be noted that there is no continuous energy conversion (electrical to mechanical) so that motor does not rotate continuously as in a conventional electric motor.

Construction of Permanent magnet stepper motor

It consists of stator and rotor. Fig shows a two phase, two pole PM stepper motor. The stator coils are grouped to form 2 phase winding i.e. phase A winding and phase winding B winding. The phase winding terminals are brought out for dc excitation.

Figure 2  Construction and operation of PM stepper motor

Operation of PM stepper motor

For this stepper motor, the number of rotor poles Nr=2 and number of phases m=2

Step angle,a=360/(m*Nr)=90 degree/step

        I.            When only phase A  winding is excited by a contant curresnt as shown in fig I, stator tooth 1 becomes south pole. This makes the north pole of the PM rotor to align (parallel) with the south pole (stator tooth 1) of the stator. The rotor will remain locked in this position as long as phrase A winding remains energized. Under this condition step angle a=0.

     II.            If phase A winding is de-energised and phase B winding is energersed as shown in fig ii, stator tooth 2 becomes south pole. As a result, the north pole of the PM rotor aligns with the south pole of the stator. Thus the rotor has displaced 90 degree in the anticlockwise direction.

   III.            If phase B is de-energised and phase A is excited with reverse current ( current in it is opposite to the case I above) , the rotor will further rotate 90 degree in anticlockwise direction as shown in fig iii.

  IV.            So far the rotor has completed one half revolution. However, if we continue the appropriate switching, the rotor will complete one revolution in 90 degree steps.

We can change the step angle (a) of a stepper motor by changing the number of rotor poles Nr and the number of phases (m).

Driving Circuit of Stepper motor

A Stepper Motor Driver is a circuit or device that provides the necessary current and voltage to a Stepper Motor so that it has a smooth operation. A Stepper Motor is a type of DC Motor that rotates in steps. The main difference between a simple DC Motor and a Stepper Motor is that through a Stepper Motor, we can achieve precise positioning with the help of digital control. A Stepper Motor rotates precisely by synchronizing the pulse signals from a controller, which are given through a Driver. A Stepper Motor Driver is a circuit that takes the pulse signals from a controller and converts them in to Stepper Motor Motion.

Two axis AC machine

It is known that in case of non-salient pole type synchronous machine, the air gap is uniform. Due to uniform air gap, the field flux as well as armature flux vary sinusoidally in the air gap. In non-salient rotor machine, air gap length is constant and reactance is also constant. Due to this the mmfs of armature and field act upon the same magnetic circuit all the time hence can be added vectorically. But in salient pole type machines the length of the air gap varies and the reluctance also varies. Hence the armature flux and field flux cannot vary sinusoidally in the air gap. The reluctances of the magnetic circuits on which mmfs act are different in case of salient pole motors.

Hence the armature and field mmfs cannot be treated in a simple way as they can be in a non-salient pole machines. In two axis machine, the armature mmf can be divided into two components.

      1.            Components acting along the pole axis called direct axis.

      2.            Component acting at right angles to the pole axis called quadrature axis.

The component acting along direct axis can be magnetizing or demagnetizing. The component acting along quadrature axis is cross magnetizing. These components produce the effects of different kinds.

Let Fi be the mmf wave produced by field winding, then it always acts along the direct axis. This mmf is responsible to produce an excitation emf Ef which lags Ff by an angle 90 degree.

When armature carries current, it produces its own mmf wave F_AR. This can be resolved in two components, one acting along d-axis (cross-magnetising). Similarly, armature current Ia also can be divided into two components, one along direct axis and along quadrature axis.