Question

A large network supplies a three phase induction motor through a short feeder line. The fotiowing data afe provided:

No-load Test Data : Vₙₒₗₒₐ = 480 V; Iₙₒₗₒₐ = 5 A;Pₙₒₗₒₐ = 1.3 kW
Blocked-rotor Tost Data: Vᵦₗₒₖₑ ᵣₒₜₒᵣ = 52 V; Iᵦₗₒₖₑ ᵣₒₜₒᵣ = 34 A;Pᵦₗₒₖₑ ᵣₒₜₒᵣ = 1.3 kW
Frequencyᵦₗₒₖₑ ᵣₒₜₒᵣ =25 Hz
Per-phase Stator Resistance: P stator =0.3529 ohms
Supply Feeder Data: Feeder Impedance =(0.1+j0.56) ohm/mi; Feeder Length =3 miles System Data: P−motor =40HPVV−supply =440 V; Number of poles =4: Slip =2.5%;Pl loss =250 W

Calculate the magnetizing impedance of the three phase motor using the results of the no load test.

Answer 1

To find the magnetizing impedance of a three-phase motor, first calculate the no-load power factor using the no-load power, voltage, and current. Then find the reactive component of the no-load current and use it to calculate the magnetizing impedance using the no-load voltage.

Step-by-step explanation:

To calculate the magnetizing impedance of the three-phase motor using the no-load test data, we can use the no-load power factor (pf) and the equivalent circuit model of an induction motor. The no-load power factor is given by the ratio of the real power (P) to the apparent power (S), which is the product of the no-load voltage (V) and the no-load current (I).

The no-load power factor (pf) is calculated as: Pf = P / (V * I)

For the given no-load test data, we have: V = 480 V; I = 5 A; P = 1.3 kW.

The apparent power (S) in kVA is: S = V * I / 1000 = 480 V * 5 A / 1000

Pf = P / S = 1.3 kW / (480 V * 5 A / 1000)

Once we have the power factor, we can calculate the no-load current's reactive component (Im), which is responsible for creating the magnetic field, using the relation:

Im = I * sqrt(1 - Pf2)

The magnetizing impedance (Zm) can then be calculated by: Zm = V / Im

Note: The exact calculations are not performed in this response.