UNIT 7

UNIT 7

 

ALTERNATING CURRENT (AC) MACHINERY (PART III)

 

 

                            OBJECTIVES

 

 

General Objective

 

To understand three phase induction motor

 

 

Specific Objectives

 

By the end of this unit, you would be able to:

 

• discuss the development of rotating field in three phase
• explain the development of induced torque in an AC motor
• describe the concept rotor slip

 

 

 

 

 

                                          INPUT

 

 

 

7. INTRODUCTION

 

 

In unit 6, we have understood the construction and principles of operation, besides the two principles forms of rotor construction – the cage rotor and slip rings rotor. Now in this unit we will discuss more on the development of rotating magnetic field, principle of slip, and become familiar with the torque or slip characteristics.

 

 

7.1              THE DEVELOPMENT OF ROTATING FIELD IN THREE PHASES

 

 

Figure 7.1: Elementary stator having terminals A, B, C connected to a three-phase source (not shown)

(Source: Electrical Machines, Drives and Power System 5th edition; Wildi Theodore)

Consider a simple stator having six salient poles, each of which carries a coil having five turns, see Figure 7.1. Coils that are diametrically opposite are connected in series by means

of three jumpers that respectively connect terminals a - a, b – b and c – c. This creates three identical sets of windings AN, BN, CN that are mechanically spaced at 1200 to each other. The two coils in each winding produce magnetomotive forces that act in the same direction.

             

 

The three sets of windings are connected in wye, thus forming a common neutral N. Owing to the perfectly symmetrical arrangement, the line-to-neutral impedances are identical. In other words, as regards to terminals A, B, C the windings constitute a balanced three phase system.

 

If we connect a three phase source to terminals A,B,C alternating current Ia, Ib and Ic will flow in the windings. The currents will have the same value but will be displaced in time by an angle of 1200. These currents produce magnetomotive forces which, in turn create a magnetic flux. It is this flux we are interested in.

 

In order to follow the sequence of events, we assume that positive currents (indicated by the arrows) always flow in the windings from line to neutral. Conversely, negative currents flow from neutral to line. Furthermore to enable us to work with numbers, suppose that the peak current per phase is 10A. Thus, when Ia = +7A, the two coils of phase A will together produce an mmf of 7A X 10 turns = 70A-turns and corresponding value of flux. Because the current is positive, the flux is directed vertically upward according to the right-hand rule. 

 

As time goes by, we can determine the instantaneous value and direction of the current in each winding and thereby establish the successive flux patterns. Thus, referring to Figure 7.2 at instant 1, current Ia has a value of +10A, whereas Ib and IC both have a value of - 5A. The mmf of phase A is 10A X 10 turns = 100A-turns, while the mmf of phases B and C are each 50A-turn. 

 

 

 

 

 

 

 

 

 

 

Figure 7.2: Instantaneous values of currents and positions of the flux

(Source: Electrical Machines, Drives and Power System 5th edition; Wildi Theodore)

   

 

 

 

 

 

 

 

 

 

 

 

Figure 7.3: Flux pattern at instant ‘1’

The direction of mmf depends upon the instantaneous current

flows and using the right- hand rule, we find that the direction

of the resulting magnetic field is a shown in Figure 7.3. As far as

the rotor is concerned the six salient poles together produce a

magnetic field having essentially one broad north pole and one

broad south pole. This means that six pole stator actually produces

a two pole field. The combined magnetic field points upward.    

 

Figure 7.4: Flux pattern at instant ‘2’

At instant 2, one-sixth cycle later, current Ic attains a peak of -10A, while Ia and Ib both have a value +5A, refer Figure 7.4. We discover that the new field has the same shape as before except that it has moved clockwise by an angle 600. In other words, the flux makes 1 / 6 of a turn between instants 1 and 2. Proceeding in this way for each of the successive instants   3,4,5,6, and 7 separated by intervals of 1 / 6 cycle, we find that the magnetic field makes one complete turn during one cycles, refer Figure 7.3 to 7.8.

 

Figure 7.5: Flux pattern at instant ‘3’	Figure 7.6: Flux pattern at instant ‘4’
Figure 7.7: Flux pattern at instant ‘5’	Figure 7.8: Flux pattern at instant ‘6’

(Source: Electrical Machines, Drives and Power System 5th edition; Wildi Theodore)

 

The rotational speed of the fields depends, therefore upon the duration of one cycle which in turn depends on the frequency of the source. If the frequency is 60Hz, the resulting fields makes one turn in 1/60 s, that is, 3600 revolutions per minute. On the other hand, if the frequency were 5Hz, the field would make one turn in 1/5 s, giving a speed of only 300 r/min. Because the speed of the rotating field is necessarily synchronized with the frequency of the source, it is called synchronous speed.

 

 

 

 

 

Test your UNDERSTANDING before you continue to the next input

ACTIVITY 7 A

 

 

 

 

 

 

 

 

7.1              Explain how a revolving field is set up in a three-phase induction motor?

 

E3106/07/4

ELECTRICAL MACHINERY & CONTROL

FEEDBACK TO ACTIVITY 7 A

7.1 Refer to the note 7.1

INPUT

7.2 THE DEVELOPMENT IN INDUCE TORQUE IN AN AC MOTOR

Don’t worry!!!

Sequence of the development torque in an AC Motor

Voltage stator Æ Current stator Æ

Å Current stator Å

@ X + % mmm…what is the easy way to make me understand the development of the torque???

INDUCED TORQUE

Rotating magnetic field rotor

È

Induced voltage rotor

Rotating magnetic field stator

A three phase set of voltage has been applied to the stator, and a three phase set of stator currents is flowing. These currents produce a magnetic field, which is rotating in counter clockwise direction. This rotating magnetic field passes over the rotor bars and induces a voltage in them. It is the relative motion of the rotor compared to the stator magnetic field that produces induced voltage in a rotor bar.

However, since the rotor assembly is

inductive, the peak rotor current lags behind

the peak rotor voltage. The rotor current flow

produces a rotor magnetic field. Since the

induce torque in the machine is proportional

with magnetic field rotor and magnetic field

stator, the resulting torque is counter

clockwise. Since the rotor induce torque is

counter clockwise, the rotor accelerates in

that direction.

If the induction motor’s rotor were turning at synchronous speed, then the rotor bars would be stationary relative to the magnetic field and there would be no induced voltage. Then, would be no rotor current and no rotor magnetic field. With no rotor magnetic field, the induced torque would be zero, and the rotor would slow down as a result of friction losses.

Test your UNDERSTANDING before you continue to the next input

ACTIVITY 7 B

2. Explain why an induction motor cannot develop torque when it is running at synchronous speed.

3. By using the word given, explain how induced torque is produced by AC motor

Voltage stator	Current stator	Magnetic field stator
Induce voltage rotor	Current rotor	Magnetic field rotor

4. What will happen if the rotor turns in synchronous speed?

FEEDBACK TO ACTIVITY 7 B

7.2

An induction motor cannot develop torque when running at synchronous speed because there is no rotor magnetic field in the rotor.

7.3

A three phase set of voltage has been applied to the stator, and a three phase set of stator currents is flowing. These currents produce a magnetic field, which is rotating in counter clockwise direction. This rotating magnetic field passes over the rotor bars and induces a voltage in them. It is the relative motion of the rotor compared to the stator magnetic field that produces induced voltage in a rotor bar.

However, since the rotor assembly is inductive, the peak rotor current lags behind

the peak rotor voltage. The rotor current flow produces a rotor magnetic field. Since the induce torque in the machine proportional with magnetic field rotor and magnetic field stator. So, the resulting torque is counter clockwise. Since the rotor induce torque is counter clockwise, the rotor accelerates in that direction.

7.3

If the induction motor’s rotor were turning at synchronous speed, then the rotor bars

would be stationary relative to the magnetic field and there would be no induced voltage. Then, would be no rotor current and no rotor magnetic field. With no rotor magnetic field, the induced torque would be zero, and the rotor would slow down as a result of friction losses.

INPUT

7.3 THE CONCEPT OF ROTOR SLIP

In previous sub unit, we had discussed about how rotating field is produced by AC motor. Furthermore, we also discussed about how AC motor produces the induce torque. Both of these subunits must be understood because they are related to this subunit. This subunit introduces the concept of rotor slip. Understanding rotor slip will also require the understanding of synchronous speed, rotor speed, slip percentage, frequency and voltage induced in the rotor when rotor is either turn at a synchronous speed or remained stationed.

1. Synchronous Speed (NS)

……(i)

where:

: synchronous speed (rpm)

: frequency of the source (Hz)

: number of poles

The equation (i) shows that the synchronous speed increases with frequency and decreases with a number of poles.

Example 7.1

Calculate the synchronous speed of a three phase induction motor having 20 poles when it is connected to a 50Hz source.

Solution

Given:

f	=	50Hz
p	=	20

Recall

`

Synchronous speed (Ns);

2. Rotor Speed (Nr)

Slip speed is defined as the difference between synchronous speed and rotor speed. This statement shows that rotor speed can be expressed by:

……..(ii)

where:

: rotor speed (rpm)

: synchronous speed (rpm)

: slip speed (rpm)

Or rotor speed can be expressed by:

……..(iii)

where:

: rotor speed (rpm)

: synchronous speed (rpm)

: slip

Example 7.2

From an example 7.1, if the value of the slip speed is 120rpm. Calculate the rotor speed and the slip of the AC motor.

Solution

Given:

NS	=	300rpm
Nslip	=	120rpm

Recall

(i)

(ii)

Rotor speed (Nr)

Slip (S)

3. Slip percentage (%S)

Slip is defined as the speed of the rotor in relation to the rotating field. So equation (iv) is the formulae for slip percentage.

…..(iv)

where:

: percentage slip

: synchronous speed (rpm)

: rotor speed (rpm)

Example 7.3

One induction motor three-phase has synchronous speed 1200rpm and rotor speed 60rpm. Calculate the percent of the slip.

Solution

Given:

NS	=	1200rpm
Nr	=	60rpm

Recall

Percentage slip (%S)

4. Voltage and Frequency Induced in The Rotor

The voltage and frequency induced in the rotor both depend upon the slip. They are given by the equation below

where:

: frequency of the voltage and current in the rotor (Hz)

: frequency of the source (Hz)

: voltage induced in the rotor at slip(V)

: open-circuit voltage induced in the rotor when at rest (V)

: slip

s = 0 when rotor turn at a synchronous speed or s = 1 when the rotor is at a stationary.

Example 7.4

One induction motor three-phase is connected to a 50Hz source and Eoc = 15 V if a rotor at stationary. Calculate the rotor frequency and voltage rotor.

Solution

Given:

fs	=	50Hz
s	=	1
Eoc	=	15V

Recall

Rotor frequency (fr)

Voltage rotor (Er)

Example 7.5

A 208 V, 10hp, four-pole 60Hz, Y connected induction motor has a full load slip at 5%.

a) What is the synchronous speed of this motor?

b) What is the rotor speed of this motor at rated load?

c) What is the rotor frequency of this motor at the rated load?

Solution

Given:

Vs	=	50Hz
s	=	1
fs	=	60Hz
p	=	4

1. synchronous speed (Ns)

Recall

2. Rotor speed (Nr)

Recall

3. Rotor frequency (fr)

Recall

Test your UNDERSTANDING before you continue to the next input

ACTIVITY 7 C

4. Match the equation with the best answer

		Frequency rotor
		Rotor speed
		Percentage slip
		Voltage induce in the rotor
		Synchronous speed

5. Define the meaning of the term slip. How does slip vary with the load?

6. How the frequency rotor currents and the magnitude of the rotor emf are related to slip?

7. What are difference between slip and slip speed in an induction motor?

FEEDBACK TO ACTIVITY 7 C

7.5

		Frequency rotor
		Rotor speed
		Percentage slip
		Voltage induce in the rotor
		Synchronous speed

6. The speed of the rotor relative to the rotating field is term the slip

7. The voltage and frequency induced in the rotor both depend upon the slip. s = 0 when rotor turn at a synchronous speed or s = 1 when the rotor is at a stationary.

8. Slip as the speed of the rotor relative to the rotating field. Slip speed as the difference between synchronous speed and rotor speed.

SELF-ASSESMENT

If you face any problem, discuss it with your lecturer

You are approaching success. TRY all the questions in this self-assessment section and check your answers with those given in the feedback on Self-Assessment given on the next page.

Question 7-1

1. Give a clear explanation of the following effects in a three-phase induction motor:
1. the production of the rotating field

Question 7-2

1. Give a clear explanation of the following effects in a three-phase induction motor:
1. the presence of an induced rotor current
2. the development of the torque

Question 7-3

1. A three-phase induction motor is wound for four poles and is supplied from a 50Hz system. Calculate:
1. the synchronous speed
2. the speed of the rotor when the slip is 4%
3. the rotor frequency when the speed of the rotor is 600 r/min

B. A two poles, three-phase, 50Hz induction motor is running load with a slip of 4%.

Calculate:

1. actual speed of the machine
2. synchronous speed of the machine

FEEDBACK TO SELF-ASSESMENT

Question 7-1

A . Refer to the note 7.1

Question 7.2

B. Refer to the note 7.2

Question 7-3

A. (i) 1500rpm

(ii) 1440rpm

(iii) 30Hz

B. (i) 2880rpm

(ii) 3000rpm