Question

(b) A 460-V 60-Hz four-pole Y-connected induction motor is rated

at \(25 \mathrm{hp}\). The equivalent circuit parameters are

$$ \begin{array}{ll} R_{1}=0.15 \Omega & R_{2}=0.154 \Omega \quad X_{M}=20 \Omega \\ X_{1}=0.852 \Omega & X_{2}=1.066 \Omega \\ P_{\mathrm{F} \& \mathrm{~W}}=400 \mathrm{~W} & P_{\text {misc }}=150 \mathrm{~W} \end{array} $$

\(P_{\text {core }}=400 \mathrm{~W}\) (lumped with rotational losses)

[14 points]

For a slip of \(0.02\), find

(1) The line current \(I_{L}\). [3 points]

(2) The stator power factor. [1 point]

(3) The rotor power factor. [1 point]

(4) The rotor frequency. [1 point]

(5) The stator copper losses \(P_{\text {sc. }}\). [1 point] \(D\)

(6) The air-gap power \(P_{\text {AG }}\). [1 point]

(7) The power converted from electrical to mechanical form \(P_{\text {conv }} .[1\) point \(]\)

(8) The induced torque \(\tau_{\text {ind }}\). [2 points]

(9) The load torque \(\tau_{\text {load }}\). [1 point]

(10) The overall machine efficiency \(\eta\). [1 point]

(11) The motor speed in revolutions per minute and radians per second. [1 point]

Answer 1

wtece ovt.com .com esco 120x60 ར - Ns=1200F P 1800 rpm Nr = NS1-s) = 1800 (1-002) = 17648pm => 210100 = ( 3 + 3x23/165m))+ (8 3x) 0.154 -0.02 tj 10 066) xj2o +0.15+30.852 70 7tj 1.066+j 20 jisu - $21.32 +0.15+10.852 7.7+)21.066 155.47.197.88 22.429 169.92 toustjo 852 6.93€27.96 +0.15 +0.852 a) 6.12 +33-24 to 15 +30.852 2 6+27 +54.092 Zlotel 7.48 133.130 I L= V phax Zlath VL=460 Vph av - 460 : 265.58 I L= 265.18 7.48 [33.130 I L= 35.50 €33-130 A line uurt ph

stator power factor = cos (33.130) = 0.837 legig. Pin= BUL It cost. - Bx460X38-30 X 0-837 23540.65930 airgap power 2 Pin - 3DNRI - corelars 23540.16593 – 3435.50 X 0.15-400 22973.14 - 400 birge 1 2 2 573.54 rotor freany fra sxf = 0.02X60 f = 1.2H2 7 Imenanical pour Pour - Pairgap-Prew - Pmis = 22573-54-400-150 22023.54 w Pour

755 Stator loses a 3DRI 3 x 3 5:50) * 0.15 PS CE 567.1125 W Torore devoled T= Pairy ولا Ws=2 Nr 60 - 2X ITX 176U - 184.632 T=B2 2573.ru 184.632 IT =122-262 NMM 11 10 نمی albicany Pout pin 2 22023.54 of 23540.65 17 = 93.55% motor speed rading Ws = 2x TX 1764 = 184.63rd 60 Ws=184.63 rad/s.

Cos (788) 2 0.99 llog rotor power factor X2 O = tann - Re tant (1.066 7.7 -7.88° 0.991 by rotor power faboo