Calculation of Equivalent Circuit Parameters

Calculation of Equivalent Circuit Parameters

The equivalent circuit of an induction motor is shown in the Fig. 6.6.1.

On no load, slip is very very small hence R₂/s is very large compared to X₀.

Thus the resultant of parallel branches j X₀ and (R₂/s +  j X₂ )is almost equal to j X_{0 .}Thus the equivalent circuit on no load is as shown in the Fig.6.6.2.

X_nl = X₁ + X₀ = Stator self reactance  … (6.6.1)

From the no load readings,

where W₀ =  No load power input

If stator resistance R₁ is known then,

P_R = Rotational losses = W_o – Stator copper losses

Where I_o and R₁ are per phase values.

The blocked rotor test is like short circuit test on transformer. The equivalent circuit for blocked rotor test is known in the Fig. 6.6.3. As rotor is still, s = 1

The blocked rotor impedance as viewed through the stator terminals is given by,

Generally X₀ >> X₂ hence X₂ / X₀ can be neglected.

X_ie = X₁ + X₂

Generally Xj is assumed equal to X₂ as practically there is no method of separating X₁ and X₂.

But    X_nl = X₁ + X₀

Equating real parts of equation (6.6.4),

Hence equation (6.6.8) given X₀, equation (6.6.9) gives R₂ while R₁ from d.c. resistance per phase of stator winding can be obtained.

Example 6.6.1 The results of the no-load and blocked rotor tests on a 3-phase, Y-connectedc 10 kW, 400 V, 17 A, 50 Hz. 8-pole induction motor with a squirrel-cage rotor are given below.

No-load test : Line-line voltage = 400 V

Total input power = 467 W

Line current = 6.8 A

Blocked rotor tests : Line-line voltage = 180 V

Total input power = 1200 W

Line current = 17 A

The d.c. resistance of the stator measured immediately after the blocked rotor test is found to have an average value of 0.68 ohm.phase. Calculate the parameters of the circuit model of the induction motor. Draw circuit model. Calculate : i) Torque (net), ii) Stator current, iii) Power factor, iv) Efficiency.

Solution :

From no load test,

Example 6.6.2 A 3 phase, 400 V, 50 Hz star connected induction motor gave the following test results :

The ratio of standstill leakage reactance of stator and rotor is estimated as 2. If the motor is running at a speed of 960 r.p.m. Determine,

i) Net mechanical power output ii) Net torque iii) Efficiency of the motor.

Assume stator and rotor copper losses to be equal. 

Solution :

On no load, slip snl is very small hence R₂ / snl in the equivalent circuit is very large compared to Hence parallel combination of jX_m, and R₂ / snl is almost equal to jX_m

Example for Practice

Example 6.6.3 The following test results were obtained on a 7.5 kW, 400 V, 4-pole, 50 Hz, delta connected induction motor with a stator resistance of 2.1. ohm/phase.

Obtain the approximate equivalent circuit model. Also estimate the breaking torque developed when the motor running with a slip of 0.05 has two of its terminals suddenly interchanged.

[Ans.: 0.5916 <Vph, 3.829 Ω, 390.233 Ω, 42.234 Ω, 1.2916 Ω, T_breaking = 19.667 Nm]

Review Question

1. How do obtain equivalent circuit parameters from the no load test and blocked rotor test on induction motor.