The results of the no-load and blocked-rotor tests on a 3-phase, Y-connected 10 kW, 400 V, 17 A, 50 Hz, 8 pole induction motor with a squirrel-cage rotor are given below. No-load test: Line to line voltage = 400 V Total input power = 467 W Line current = 6.8 A Blocked rotor test: Line to line

Question

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

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

Total input power = 467 W

Line current = 6.8 A

Blocked rotor test: Line to line voltage = 180 V

Total input power = 1200 W

Line current = 17 A

The dc 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 IEEE circuit model.

Using MATLAB calculate and plot against motor speed or slip the following variables:

(i) Torque (net)

(ii) Stator current

(iii) Power factor

Accepted Answer

No-Load Test

[latex] Y_{0}=\frac{6.8}{400 / \sqrt{3}}=0.0294 \mho [/latex]

[latex] G_{i w f}=\frac{467-3(6.8)^{2} imes 0.68}{(400)^{2}}=2.33 imes 10^{-3} \mho [/latex]

[latex] B_{m}=\sqrt{Y_{0}^{2}-G_{i w f}^{2}}=2.93 imes 10^{-2} \mho [/latex]

[latex] X_{m}=34.12 \Omega[/latex]

The IEEE circuit model is given in the Fig. 9.68 (c).

Blocked-Rotor Test

[latex] Z=\frac{180 / \sqrt{3}}{17}=6.113 \Omega[/latex]

[latex] R=\frac{1200 / 3}{(17)^{2}}=1.384 \Omega[/latex]

[latex] X=\sqrt{Z^{2}-R^{2}}=5.95 \Omega[/latex]

[latex] R=R_{1}+R_{2}^{\prime}[/latex]

[latex] R_{2}^{\prime}=1.384-0.68=0.704 \Omega[/latex]

[latex] X_{1}=X_{2}^{\prime}=\frac{X}{2}=2.975 \Omega[/latex]

Performance Calculation

s = 0.05

[latex] \bar{Z}_{f}=\left(\frac{R_{2}^{\prime}}{s}+j X_{2} ight) \|\left(j X_{m} ight)[/latex]

[latex] =\left(\frac{0.704}{0.05}+j 2.975 ight) \|(j 34.12)[/latex]

[latex] =(14.08+j 2.975) \|(j 34.12)[/latex]

[latex] =\frac{14.39 \angle 11.9^{\circ} imes 34.12 \angle 90^{\circ}}{39.677 \angle 69.2^{\circ}}[/latex]

[latex] =12.375 \angle 32.7^{\circ}[/latex]

= 10.414 + j 6.685

[latex] \bar{Z}_{( ext {total })}=0.68+j 2.975+10.414+j 6.685[/latex]

[latex] \simeq 14.7 \angle 41.3^{\circ} \Omega[/latex]

[latex] |\bar{Z}|_{ ext {(total) }}=14.7 \Omega[/latex]

(a) Stator Current

[latex] I_{1}=\frac{400}{\sqrt{3} imes 14.7}=15.69 A[/latex]

(b) Power Factor

[latex] p f=\cos \left(14.3^{\circ} ight)=0.751[/latex] (lagging)

(c) Efficiency`

Power input [latex] =3 V_{p h} I_{p h} \cos \phi[/latex]

[latex] =3\left(\frac{400}{\sqrt{3}} ight) imes 15.69 imes 0.751=8163.4 W[/latex]

Air-gap power [latex] =3 I_{1}^{2} R_{f}=3(15.69)^{2} imes 10.374=7661.5 W[/latex]

[latex] \omega_{s}=\frac{120 f}{P}=750 rpm[/latex]

[latex] P_{m}( ext { gross })=(1-s) P_{g}=0.95 imes 7661.5=7278.4 W[/latex]

[latex] P_{m}( ext { net })=P_{m}( ext { gross })-P_{r}[/latex]

Where Pm (net) = Pm (gross) – Pr

[latex] P_{r}=P_{0}-3 I_{0}^{2} R_{1}=372 W[/latex]

(d) Torque

[latex] \omega=\omega_{s}(1-s)=750 imes 0.95=712 rpm[/latex]

[latex] T_{( ext {net })}=\frac{P_{m( ext { net })}}{\omega}=\frac{6906.4}{712}=9.7 Nm[/latex]

Efficiency [latex] =\frac{P_{m(n e t)}}{P_{ ext {input }}}=\frac{6906.4}{8163.4}=0.846[/latex]

% Efficiency = 84.6%

Question 9.20: The results of the no-load and blocked-rotor tests on a 3-ph...

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