Power flow in an Induction motor

The exact equivalent circuit model of an Induction motor is

where

R1 is the stator resistance per phase

X1 is the stator reactance per phase

R2' is the equivalent rotor resistance referred to stator per phase

X2' is the equivalent rotor reactance referred to stator per phase

Rc is the resistance representing core losses

Xm is the magnetizing reactance per phase

V1 is the per phasesupply voltage to the stator
s is the slip of the motor

Power flow in an Induction motor

From the circuit, we see that the total power input to the rotor Pg is
The power flow diagram is-

Source
http://powerlearn.ece.vt.edu/modules/PE2/index.html

How the efficiency of induction motor is measured?

Abstract
The efficiency is of paramount importance nowadays due
to increasing electrical energy demand, increasing awareness of
environmental problems as greenhouse effects and increasing
fossil fuel prices.

This paper tries to show the different results between the
standards for efficiency evaluation and the necessity of
harmonization worldwide. Then, it is going to be explained the
different standards for measurement of efficiency, and the main
differences between the standards (IEEE 112, IEC 60034-2 and
JEC-37).

To complete this study, it is going to be described the steps
in order to estimate efficiency on the jobsite and expressed the
different efficiency labels motors.

Figure 2.1 – Typical Power flow of standard motors

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Electromagnetic Induction

1. Electromagnetic Induction

2. Law of Induction

3. Direction Of Induced EMF

4. Direction Of Induced Current

5. Electromagnetic Force

6. The Magnetic Field

Electromagnetic Force

The basic principle of motor action is the so called
electromagnetic force or Lorentz force production.

Lorentz force states that "when a current carrying conductor is
placed in a magnetic field, it is subject to a force which we call
Lorentz force ".

The magnitude of the force depends upon the orientation of the
conductor with respect to the direction of the field. The force is
greatest when the conductor is perpendicular to the field and zero
when it is parallel to it. Between these two extremes, the force has
intermediate values.
The maximum force acting on a straight conductor is given by

F = Bli

Where F : Is the force acting on the conductor (N),
B : Is the flux density of the field (T), and,
l : Is the length of the conductor facing the magnetic field(m).
i: the current in the conductor (A).

The direction of the magnetic force can be determined by using
Felming left hand rule. Before going to show this rule, it is better to
explain the physical meaning of the lorentz force. This can be easly
explaind by with the help of the following two figures (Fig. And
Fig. ). For a current flowing into the page of this book, the circular
lines of force have the direction shown in Figure 2.32a. The same
figure shows the magnetic field created between the N, S poles of a
powerful permanent magnet.

The magnetic field does not, of course, have the shape shown in
the figure because lines of force never cross each other. What,
then, is the shape of the resulting field?. To answer the question,
we observe that the lines of force created respectively by the
conductor and the permanent magnet act in the same direction
above the conductor and in opposite directions below it.
Consequently, the number of lines above the conductor must be
greater than the number below. The resulting magnetic field
therefore has the shape given in Figure 2.32b.

Recalling that lines of flux act like stretched elastic bands, it is
easy to visualize that a force acts upon the conductor, tending to
push it downward.

Now let us Define Felmeng left hand rule It is illustrated in Fig.
6-9.

The direction of the force can also be determined by using the
right-hand screw rule, illustrated in Fig.2.2(b).
Turn the current vector i toward the flux vector B. If a screw is
turned in the same way, the direction in which the screw will move
represents the direction of the force f.

Note that in both cases (i.e., determining the polarity of the
induced voltage and determining the direction of the force) the
moving quantities (v and i ) are turned toward B to obtain the
screw movement.
Equations (2.1) and (2.2) can be used to determine the induced
voltage and the electromagnetic force or torque in an electric
machine. There are, of course, other methods by which these
quantities (e and f) can be determined.

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

MAGNETIC%20CIRCUITS.pdf

Electromagnetic Force, f

For the current-carrying conductor shown in Fig.3.3(a), the
force (known as Lorentz force) produced on the conductor can be
determined from the following equation:

f = Bli (3.2)

where B, l, and i are mutually perpendicular. The direction of
the force can be determined by using the Fleming’s Left Hand Rule
or right-hand screw rule as explaind in the previous chapter and
are stated in the following. The direction of the force is illustrated
in Fig.3.3(b).

Fleming’s Left Hand Rule:
“Hold out your left hand with forefinger, second finger and thumb
at right angles to one another. If the forefinger represents the
direction of the field, and the second finger that of the current, then
thumb gives the direction of the motion or force.”


Right-Hand Screw Rule:
Turn the current vector i toward the flux vector B. If a screw is
turned in the same way, the direction in which the screw will move
represents the direction of the force f.
Note that in both cases (i.e., determining the polarity of the
induced voltage and determining the direction of the force) the
moving quantities (v and i ) are turned toward B to obtain the
screw movement.

Equations (3.1) and (3.2) can be used to determine the induced
voltage and the electromagnetic force or torque in an electric
machine. There are, of course, other methods by which these
quantities (e and f) can be determined.

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

DC%20Machines2.pdf

Direction Of Induced Current

Lenz’s Law
The direction of the induced current may also be found by this
law which was formulated by Lenz.1835.

Lenz Law states, in effect, that electromagnetically induced
current always flows in such a direction that the action of the
magnetic field set up by it tends to oppose the very cause, which
produces it.

This statement will be clarified with reference to Figs.1.15 and
Fig.1.16. It is found that when N-pole of the bar magnet
approaches the coil, the induced current setup by the induced EMF
flaws in the anti-clockwise direction in the coil as seen from the
magnet side. The result is that the face of the coil becomes a Npole
and so tends to retard the onward approach of the N pole' of
the magnet (tike poles repel each other). The mechanical energy
spent in overcoming this repulsive force is converted into electrical
energy, which appears in the coil.

When the magnet is withdrawn as in Fig.1.16, the induced
current flows in the clockwise direction, thus making the face of
the coil (facing the magnet) a S-pole. Therefore, the N-pole of the
magnet has to be withdrawn against the attractive force of the
S-pole of the coil. Again the mechanical energy required to
overcome this force of attraction is converted into electric energy.

It can be shown that the Lenz's law is a direct consequence of law
of conservation of energy. Imagine for a moment that when N pole
of the magnet (Fig.1.16) approaches the coil, induced current flows,
in such a direction as to make the coil face a S-pole. Then due to
inherent attraction between unlike poles, the magnet would be
automatically pulled towards the coil without the expenditure of
any mechanical energy. It means that we would be able to create
electric energy out of nothing, which is denied by the inviolable

Law of Conservation of Energy. In fact, to maintain the sanctity of
this law, it is imperative for the induced current to flow in such a
direction that the magnetic effect produced by it tends to, oppose
the very cause, which produces it. In the present case it is the
relative motion of the magnet with respect to the coil which is the
cause of the production of the induced current. Hence, the induced
current always flows in such a direct as to oppose this relative
motion (i.e., the approach or withdrawal of the magnet).


Source ( pdf )
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MAGNETIC%20CIRCUITS.pdf

Direction Of Induced EMF

There exists a definite relation between the direction of the
induced current, the direction of the flux and the direction of
motion of the conductor. The direction of the induced current may
be found easily by applying either Fleming's Right-hand Rule or
Lenz's Law. Fleming's rule is used where induced EMF is due to,
flux cutting (i.e. dynamically induced. EMF) and Lenz's when it is
due to change by flux linkages (i.e. statically induced Emf).

Fleming's Right-Hand Rule
“Hold out your right hand with forefinger, second finngure, and
thumb at right angles to one another. If the forefinger represents
the direction of the field, and the thumb represents the direction of
the motion then, the second finger represents the direction of the
induced emf in the coil”.

Fleming's Right-hand Rule can be explained as shown in Figure

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

MAGNETIC%20CIRCUITS.pdf

Law of Induction

Faraday's Laws

First Law states:
Whenever the magnetic flux linked with a circuit changes, an
EMF is always induced in it. Whenever a conductor cuts magnetic
flux, an EMF is induced in that conductor.

Second Law states:
The magnitude of the induced EMF is equal to the rate of change
of flux-linkages.

Explanation. Suppose a coil has N turns and flux through it
changes from an initial value of 1 φ webers to the final value of 2 φ ,
webers in time t seconds. Then remembering that by flux-linkages
is meant the product of number of turns by the flux linked with the
coil, we have the following relation:

Initial flux linkages = 1φ N . And final flux linkages = 2 φ N
Then the induced EMF is

Usually a minus sign is given to the right-hand side expression to
signify the fact that the induced EMF sets up current in such a
direction that magnetic effect produced by it opposes the very cause
producing it.

Source ( pdf )
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MAGNETIC%20CIRCUITS.pdf

Electromagnetic Induction

Electromagnetic Induction

In 1820 Oersted discovered the magnetic effect of an electric
current, and the first primitive electric motor was built in the
following year. Faraday's discovery of electromagnetic induction in
1831 completed the foundations of electromagnetism, and the
principles were vigorously exploited in the rapidly growing field of
electrical engineering. By 1890 the main types of rotating electrical
machine had been invented, and the next forty years saw the
development of many ingenious variations, along with refinement
of the basic types. This was the golden age of machine
development. Many machines are now obsolete which were once
made in large numbers. Thus the cross-field DC machines, or rotary
amplifiers, have been replaced by solid-state power amplifiers;
while the Schrage motor and other ingenious variable-speed AC
machines have given way to the thyristorcontrolled DC motor and
the inverter-fed induction motor.
When a conductor moves in a magnetic field, an EMF is
generated; when it caries current in a magnetic field, a force is
produced. Both of these effects may be deduced from one of the
most fundamental principles of electromagnetism, and they provide
the basis for a number of devices in which conductors move freely
in a magnetic field. It has already been mentioned that most
electrical machines employ a different form of construction.


Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/
MAGNETIC%20CIRCUITS.pdf


Induced Voltage

An expression can be derived for the voltage induced in a
conductor moving in a magnetic field. As shown in Fig.3.2a, if a
conductor of length l moves at a linear speed v in a magnetic field
B, the induced voltage in the conductor can be obtained with the
help of fraday’s law as shown in the following equation:

e = Blv (3.1)

where B, l, and v are mutually perpendicular. The polarity
(Direction) of the induced voltage can be determined from the
so-called Fleming's Right-Hand Rule as explained in the previous
chapter. The direction of this force is shown in Fig.3.2(b).

Fleming's Right-Hand Rule
“Hold out your right hand with forefinger, second finger, and
thumb at right angles to one another. If the forefinger represents
the direction of the field, and the thumb represents the direction of
the motion then, the second finger represents the direction of the
induced emf in the coil”.

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

DC%20Machines2.pdf