An induction motor is a common electric motor where the rotating magnetic field in the stator induces current in the rotor to generate torque. It has a simple and rugged construction, is very reliable and cost-effective. Induction motors are widely used in industrial equipment and household appliances. The current induced in the rotor depends on factors like slip and magnetic saturation, which influence the motor's speed-torque characteristics. Finite element analysis is useful for investigating these characteristics during design. While induction motors are commonly used, their modeling involves complexities like rotor skew, harmonic effects, and nonlinear materials behavior.

1. Induction Motor

2. Introduction:
• An induction motor is an AC electric motor in which the electric current in the rotor needed
to produce torque is induced by electromagnetic induction from the magnetic field of
the stator winding. An induction motor therefore does not require mechanical commutation,
separate-excitation or self-excitation for all or part of the energy transferred from stator to
rotor, as in universal, DC and large synchronous motors. An induction motor's rotor can be
either wound type or squirrel-cage type.
• Three-phase induction motors are widely used in industrial drives because they are rugged,
reliable and economical. Single-phase induction motors are used extensively for smaller
loads, such as household appliances like fans. Although traditionally used in fixed-speed
service, induction motors are increasingly being used with variable-frequency drives (VFDs) in
variable-speed service. VFDs offer especially important energy savings opportunities for
existing and prospective induction motors in variable-torque centrifugal fan, pump
and compressor load applications. Squirrel cage induction motors are very widely used in
both fixed-speed and VFD applications.

3. Torque Speed:
• For obtaining the expression for torque we consider the Thevenin’s equivalent of the actual
circuit-
• From the circuit we see that Zth=Rth+jXth is the Thevenin’s equivalent impedance.
• Now Zth is the parallel combination of the shunt branch and Z1 i.e., the stator impedance. So
from the circuit we have-
• The torque developed T is given-

4. Slip:
• An AC (Alternating Current) induction motor consists of two assemblies - a stator and a rotor. The
interaction of currents flowing in the rotor bars and the stators' rotating magnetic field generates a torque.
In an actual operation, the rotor speed always lags the magnetic field's speed, allowing the rotor bars to
cut magnetic lines of force and produce useful torque.
• The difference between the synchronous speed of the magnetic field, and the shaft rotating speed is slip -
and would be some number of RPM or frequency.
• The slip increases with an increasing load, thus providing a greater torque.

5. • It is common to express the slip as a ratio between shaft rotation speed and synchronous
magnetic field speed. The slip is often expressed as
• S = (ns - na) 100% / ns (1)
• where
• S = slip
• ns = synchronous speed of magnetic field (rev/min, rpm)
• na = shaft rotating speed (rev/min, rpm)
• When the rotor is not turning the slip is 100 %.
• Full-load slip varies from less than 1 % in high hp motors to more than 5-6 % in minor hp
motors.
• Slip and Voltage
• When the motor starts rotating the slip is 100 % and the motor current is at maximum. The
slip and motor current are reduced when the rotor starts to turn.
• Slip Frequency
• Frequency decrease when slip decrease.
• Slip and Inductive Reactance
• Inductive reactance depends on the frequency and the slip. When the rotor is not turning,
the slip frequency is at maximum and so is the inductive reactance.
• A motor has a resistance and inductance and when the rotor is turning, the inductive
reactance is low and the power factor approaches to one.
• Slip and Rotor Impedance
• The inductive reactance will change with the slip since the rotor impedance is the phase sum
of the constant resistance and the variable inductive reactance.

6. • To obtain the starting torque we put s=1 in the above equation.
• To obtain the maximum torque produced, the condition is dT/ds=0.
• Applying this condition we get smaxT that is the slip at maximum torque Tmax.
• We then put in this value of torque in the expression for torque to get the value of maximum
torque.
• Now to simplify the equation we neglect Rth and the equation for torque is obtained as-

7. • We now get the relationship between the starting torque Tstart, maximum torque Tmax and T
i.e., the torque developed at a slip say s.
• The torque equation obtained above can be expressed as-

8. •
• Initially when the motor starts, the slip is high. So k2/s=0. Hence the torque
produced is proportional to the speed Nm. However when the motor attains stable
speed, slip is negligible.Hence k3.s =0 and the torque is inversely proportional to
the speed Nm . From these relationships, the general shape of speed -torque
characteristics of Induction motor can be obtained.
•

9. Characteristic of Induction motor:
• The induction motor is classified into a single-phase motor and a three-phase motor
according to the using power source. This motor always uses both auxiliary winding and
condenser not only when starting but also during operation. Generally speaking, its starting
torque is not so great, but its structure is simple and reliable. In addition, its connection is
simple. It is suitable to use in houses and on factories.
• For a single-phase induction motor, be sure that the condenser indicated in the name plate
should comply with the capacity of the motor. it is not possible to reverse the direction of
rotation within a short time during operation because of the inertia torque exerting adversely
against the direction the motor is supposed to change to. Thus, stop the motor first and
change the rotational direction next. The power source of a single-phase motor includes U
(100V 60.60Hz), C (200V 50/60Hz, 220V 50/60Hz, 230V 50Hz). Refer to (Fig. 1).

10. • The three-phase induction motor has simpler connection, and higher efficiency and reliability
than the single-phase motor, because it can be driven by a three-phase power source
directly. The three-phase motor is popular as a general-purpose motor. It is possible to use
the motor for continuous rated operation and it is designed to be used in a single direction.
The number of rated revolution of the motor varies depending on the load imposed on it. It is
suitable for such operation that does not need the speed control. The power source for a
three-phase motor includes H (220V 50/60Hz), M (380V 50/60Hz), Z (440V 50/60Hz). Refer to
(Fig. 2).
More Further, The Induction motor is the most widely used machine. Its characteristic features
are:
-Simple and rugged construction
-Low cost and minimum maintenance
-High reliability and sufficiently high efficiency
-Needs no extra starting motor and need not be synchronized

11. Basic Equation of Induction Motor:

13. Analysis:
• An induction motor is a motor in which a rotating magnetic
field in the stator coils causes induced current to flow in an
auxiliary conductor. This current and magnetic field exert
force on the auxiliary conductor in the rotation direction
and cause the motor's rotor to rotate. Induction motors are
widely used in everything from industrial machines to
home appliances because they have a simple construction
and are small, light, affordable, and maintenance-free.
In an induction motor, the current induced by the auxiliary
conductor exerts a large influence on its characteristics. It
also causes strong magnetic saturation in the vicinity of the
gap, in particular. This is why a magnetic field analysis
based on the finite element method (FEM) is useful when
investigating the motor's characteristics for a design study.
This Application Note explains an analysis that confirms the
Speed-Torque curve and current density distribution of an
induction motor.

14. Conclusion:
• In general, there is a lot of subtlety involved in the design and modeling of induction
machines. This present document only scratches the surface of induction motor modeling.
Among the issues that have been neglected in the current analysis are:
• A design feature that is common in induction motor design but not addressed in the present
analysis is rotor skew. The reason for this skew is so that the rotor bars see flux linkage that
has less harmonic content.
• Harmonic effects are neglected in motionless analysis. The higher harmonics can create
forces (and losses) that are not anticipated by the simple model presented here.
• “Deep bar” rotors. To get better starting torque behavior, many induction motors are
designed with more complicated (e.g. two layer) rotor bar topologies. These are not well-
modeled by the circuit that has been presented here. A network of additional inductors and
resistors on the rotor branch of the circuit is required to model these bars. A similar
impedance-fitting approach could be used to identify values for impedances in such a
network model.
• Nonlinear materials. Generally, induction motors are designed to run near saturation. Some
induction motor designs have covered rotor slots (to reduce harmonic content of the flux in
the gap) that must saturate so that leakage flux is not excessive.

15. References:
• References of induction motor
• http://homepages.engineering.auckland.ac.nz/~kacprzak/PE2.html
• http://en.wikipedia.org/wiki/Induction_motor
• http://www.kocomotion.de/fileadmin/pages/10_PRODUKTE/GGM/Datenblaetter/K9Ix40Nx.
pdf
• http://www.uotechnology.edu.iq/dep-
eee/lectures/3rd/Electrical/Machines%202/IV_I.Machines.pdf