Answer to Question #203136 in Electrical Engineering for Renoir

Question #203136

A 208 V, 60 Hz, 4 poles, star connected SCIM gave the following test results

N.L. test: 450W, 208V, 1.562A, B.R. Test : 59.4W, 27V, 2.77A

The stator winding resistance between any two terminals=2.4Ω.

a. Compute the equivalent circuit parameters of the motor.

b. Determine the shaft torque and the efficiency of the motor if it is running at its rated speed of

1710rpm.


1
Expert's answer
2021-06-07T05:46:27-0400

No-load test

"cos \\phi _o= \\frac{1200}{\\sqrt{3}*208*22}=0.151 \\implies \\phi _o =cos^{-1}0.151 =81.29^0"

"I_w=I_{oc}cos \\phi_o=22*0.151=3.33A"

"I_{\\mu}=I_{oc}sin \\phi_o=22*sin 81.29=21.746 A"

"R_c=\\frac{V_{oc}(ph)}{I_w}=\\frac{208}{\\sqrt{3}*3.33}=36.053 \\Omega"

"X_m=\\frac{V_{oc}ph}{I_{\\mu}}=\\frac{208}{\\sqrt{3}*21.746}=5.22 \\Omega"

Locked rotor test

"Z_{eq}=\\frac{V_{sc}ph}{I_{sc}}=\\frac{24.6}{\\sqrt{3}*64.5}=0.22 \\Omega"

"R_{eq}=\\frac{2200}{3*64.5^2}=0.176 \\Omega"

"X_{eq}=\\sqrt{Z_{eq}^2-R_{eq}^2}=\\sqrt{0.22^2-0.176^2}=0.131 \\Omega"

"X_1=X_2'= \\frac{0.131}{2}=0.0655 \\Omega"

"T_{sh}=\\frac{60}{2 \\pi N_s}* Shaft power output=\\frac{60}{2 \\pi *1440}*42.536*1000=282.07 Nm"

d. Total power output = 42.536 kW

Total power input = "3v_{pm}I_s cos\\phi_s=3(230.94)(73.137) cos 22.06 W= 46.961 kW"

"Efficiency = \\frac{42.536}{46.961}*100=90.577 \\%"

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