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# How to determine the efficiency of an Induction Motor?

## Theory and Circuit Diagram

The no-load test or open-circuit test of an induction motor enables us to determine the efficiency and the circuit parameters of the equivalent circuit of the 3-phase induction motor. The circuit arrangement for the no-load test of the induction motor is shown in the figure.

In the no-load test, the motor is uncoupled from the load and the rated voltage at the rated frequency is applied to the stator of the motor to run it. To measure the input power, two-wattmeter method is used.

A voltmeter and an ammeter being connected as shown in the circuit diagram (see the figure). The voltmeter reads the rated supply voltage, while the ammeter measures the no-load current of the motor.

Since the no-load current of the induction motor is about 20-30% of the rated current, thus the I 2R losses in winding may be neglected. Therefore, at no-load, the total input power to the motor is equal to core loss, friction and windage losses of the motor, i.e.,

$$\mathrm{𝑃_0 = 𝑃_𝑖 = 𝑃_𝐶 + 𝑃_{𝑓𝑤}}$$

$$\mathrm{𝑃_0 = 𝑃_𝑖 = Sum\: of \:two\: wattmeter\: readings = 𝑊_1 + 𝑊_2}$$

As the power factor of the induction motor under no-load is less than 0.5, so one wattmeter will give negative reading. Therefore, it is necessary to reverse the direction of the current-coil terminals to obtain the correct reading.

Now, if

**𝑉**_{𝑖𝐿}= Input line voltage**𝑉**_{𝑖𝑝ℎ}= Input phase voltage**𝑃**_{𝑖.𝑁𝐿}= Input three phase power at no load**𝐼**_{0}= No load input line current

Then,

$$\mathrm{𝑃_{𝑖.𝑁𝐿} = \sqrt{3} 𝑉_{𝑖𝐿} 𝐼_0\:cos \varphi_0}$$

The magnetising component of the no-load current is,

$$\mathrm{𝐼_𝑚 = 𝐼_0\:sin \varphi_0}$$

The core loss component of no-load current is,

$$\mathrm{𝐼_𝑤 = 𝐼_0\: cos \varphi_0}$$

$$\mathrm{𝑅_0 =\frac{𝑉_{𝑖𝑝ℎ}}{𝐼_{𝑤}}}$$

$$\mathrm{𝑋_0 =\frac{𝑉_{𝑖𝑝ℎ}}{𝐼_𝑚}}$$

## Separation of Friction and Windage Losses

The friction and windage losses of the motor can be separated from the no-load losses (P_{0}). For this, a number of readings of P_{0} at no-load is taken at different stator applied voltages at rated frequency. A graph is plotted between the P_{0} and V as shown in the figure below.

Here, the curve is parabolic at normal voltages, since the iron losses are almost proportional to the square of the flux density and hence, the applied voltage. Now, the curve is extended to the left to cut the vertical axis at point M. At the vertical axis V = 0 and hence, the intercept OM represents the voltage independent losses which are the losses due to the friction and windage (P_{fw}).

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