# Shakshat Virtual Lab

# INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI

# LIST OF SYMBOLS

*f _{r}* = rated electrical frequency of the motor

V_{1,rl} = the line-to-neutral voltage

*l*_{1,rl} = the line current

P* _{nl}* = the poly-phase electrical input power

I^{2}R = no-load rotor loss

P* _{rot}* = rotational loss

*J* = rotor Inertia

*n _{ph}* = number phase

*w _{m}* = rotor speed

*T _{rot}* = rotor torque

*R _{c}* = core loss resistance

*P _{core}* = no-load core loss

*S _{nl}* = total apparent power input at no load

*R _{1}* = resistance of the motor

*X _{1}* = reactance of the motor

*X _{2}* = rotor leakage reactance

*X _{m}* = megnetizing reactance

*X _{11}* = self-reactance of the rotor

*X _{nl}* = apparent reactance

*Q _{nl}* = reactive power at no load

# THEORY

The no load test on an induction motor gives information with respect to exciting current and no-load losses. The test is performed at rated frequency and with balanced poly-phase voltages applied to the stator terminals. Readings are taken at the rated voltage, after the motor runs long enough for the bearings to be properly lubricated.

At no load, the rotor current is only the very small value needed to produce sufficient torque to overcome the friction and windage losses associated with rotation. The no-load rotor I^{2}R loss is, therefore, negligibly small. Unlike the continuous magnetic core in a transformer, the magnetizing path in an induction motor includes an air gap which significantly increases the required exciting current. Thus, in contrast to the case of a transformer, whose no-load primary I^{2}R loss is negligible, the no-load stator I^{2}R loss of an induction motor may be appreciable because of this larger exciting current. Neglecting rotor I^{2}R losses, the rotational loss P_{rot} for normal running conditions can be found by subtracting the stator I^{2}R losses from the no-load input power.

The total rotational loss at rated voltage and frequency under load usually is considered to be constant and equal to its no-load value.

Various tests can be performed to separate the friction and windage losses from the core losses. For example, if the motor is not energized, an external drive motor can be used to drive the rotor to the no-load speed and the rotational loss will be equal to the required drive-motor output power. Alternatively, if the motor is operated at no load and rated speed and if it is then suddenly disconnected from the supply, the decay in motor speed will be determined by the rotational loss as

Hence, if the rotor inertia *J* is known, the rotational loss at any speed wm can be determined from the resultant speed decay as

Thus, the rotational losses at rated speed can be determined by evaluating the above equation as the motor is first shut off when it is operating at rated speed. If the no-load rotational losses are determined in this fashion, the core loss can be determined as

Here, *P _{core}* is the total no-load core loss corresponding to the voltage of the no-load test (typically rated voltage). Under no-load conditions, the stator current is relatively low and, to a first approximation, one can neglect the corresponding voltage drop across the stator resistance and leakage reactance. Under this approximation, the voltage across the core-loss resistance will be equal to the no-load line-to-neutral voltage and the core-loss resistance can be determined as

Provided that the machine is operated close to rated speed and rated voltage, the refinement associated with separating out the core loss and specifically incorporating it in the form of a core-loss resistance in the equivalent circuit will not make a significant difference in the results of an analysis. Hence, it is common to ignore the core-loss resistance and to simply include the core losses with the rotational losses.

Because the slip at no load, *S _{nl}*, is very small, the reflected rotor resistance

*R*/

_{2}*S*is very large. The parallel combination of rotor and magnetizing branches then becomes

_{nl}*jX*shunted by the rotor leakage reactance

_{m}*X*in series with a very high resistance, and the reactance of this parallel combination therefore very nearly equals

_{2}*X*.Consequently the apparent reactance

_{m}*X*measured at the stator terminals at no load very nearly equals

_{nl}*X*+

_{1}*X*, which is the self-reactance

_{m}*X*of the stator; i.e.

_{11}The self-reactance of the stator can therefore be determined from the no-load measurements. The reactive power at no load *Q _{nl}* can be determined as

where *S _{nl}* = n

_{ph}V

_{1,nl}

*I*

_{1,nl}is the total apparent power input at no load.

The no-load reactance *X _{nl}* can then be calculated from

*Q*and

_{nl}*I*as

_{nl}Usually the no-load power factor is small ( i.e., *Q _{nl}* >>

*P*) so that the no-load reactance very nearly equals the no-load impedance.

_{nl}