Exercise 01

On the nameplate of a three-phase squirrel-cage induction motor, we read the following indications: 230/400V; 50hz; 70/40A; cos(φ) = 0.86 and n = 725 rpm.

Knowing that the resistance of a stator winding is R₁ = 0.15 Ω, that the stator iron losses are 500W and that the electric network phase-to-phase voltage is 400V, Find:

1. The stator winding coupling mode

2. The synchronism speed and the number of pole pairs

3. The stator copper losses

4. The motor slip

5. The rotor copper losses

6. The efficiency of the motor if the mechanical losses are negligible

Exercise 02

A four pole induction motor, stator coupled in triangle, operates under the following conditions: line voltage : U=400V, frequency f=60hz, useful power P_U=5kW, rotation speed n=1710 rpm, cos(φ) = 0.9 and line current intensity I=10A.

The stator resistance measured between two phase wires is 0.8 Ω.

For this operation, we will assume that the iron losses are equal to the copper losses in the stator. Calculate:

1. The motor slip

2. The useful torque T_U

3. The current intensity in each phase of the stator

4. The stator copper losses

5. The power absorbed by the motor.

6. The rotor copper losses

7. The motor efficiency

Exercise 03

A three-phase four-pole induction motor is supplied by a 400V line voltage at 50hz. The stator resistance measured between two phase wires is 0.9 Ω for a star-connected stator winding. In no-load operation, the motor absorbs a current of 9.1A and a power of 420W.

1. Determine the stator iron losses and the mechanical losses assuming them to be equal.

2. At rated load, the useful power on the rotor shaft is 7kW, the power factor is 0.85 and the efficiency is equal to 87%. Determine:

            2.1 The intensity of absorbed current

            2.2 The stator copper losses

            2.3 The rotor copper losses

            2.4 The motor speed and slip

            2.5 The useful torque