Question

how do we calculate ii and iii) - induction motor

(25 marks) QUESTION 3 A three-phase, 400 V, 50 Hz, 4-pole, 1370 rpm, star connected, squirrei-cage induction motor has the following parameters: R, 20, R2- 3 Q, X1-X2- 3.5 and Xm=40 .Motor is controlled by a voltage source inverter at constant V/f ratio. By using IEEE equivalent circuit; Calculate the starting torque and starting current at 10 Hz To- If the torque-speed to be a straight line calculate the slip speed at rated full-load condition curve from no-load to full-load torque can be considered As in question 3a(i) above, find the speed at 30 Hz and 80% full-load torque. (15 marks)

Answer 1

3 Given dala about Induction molor-3-6) Vollage, V=40ov frequuncy, f50tz NO of poles- 4 Speed, N-1310rpm Paramelers R22 R-32 Xm-402 starling torgue and Slarling current at lo tiz The starting torque is maximum for inducbon motor when rotor resistane is equal to rotor readance at standsti re, Slip 1 RozX belauwe d Slip at toi lia condi biong The re labon beluteo Starbng forque and maximum torque and Tmax KE2 2X2 TSt kER Tst Tmax di viding Tot, ue Tmax get R2 IT Then Tst 2a max 1ta 'y taking a from ThiA E Take Tst aa

So slarBng larque, Tst= a l2 For solving and" paramelersue can ute grven Resistane andReactante pamdeos tHere k'is constant K 3X60 &U NS So for given Vale d frequency, f L0HZ R2-3XK2 NS=180xlo 300 Pm -BX9.118 X10 K2z 0082 kz 3x60 &11 K30 K 9.118X103 O.095 -3 -8.6X9.118 X10 2=0519 Substitub xi in starting lorque Equalion Tstax O2. O-549 MO.98360 starting current Ist = SE2 Condibons slip,s= I. At starling So for Caleulaling TstKR2 11 -d95X 0.021 EzI485 V 1.435 83 45 amps Tst

1 torque Speed Cuove from no laad to fullead taoue straight line caleulat sip Speced Can be Considered to be at raled full lood Condi bon when Slips=0, NENS and hente toqe TE0- , molor Can't run at Synchronous Sed Very low iey the Speed i8 very when Shp y'is Synchrmous Speed, then "The oeadāne fs very small. and Can negleded tbe lorque sip near to be for tow valuey d Slip TaS Ts Staight bre adually Sip= åk-, may at Slaring Condstions CUOve is a stp sted Ms-N 30orpm ay Calculaled abae sly suud at to H 1310-300 1010m ) for above queion find Spead at 30tHz and 80. dfel 10a.d Larque Slip= Ns- N NS 3103 8 N at 30Hz=1a0x80 11 1810 S 1310-9o 034 1310 Condi Bon ds 801. d fall load torque By The Tst Tst TH ue Sy Elobaling The lem! 0.8 Ist xTmax 0.8 Tmax TFL aats 2a st 402 0-8 (ta)C2axo-3) auCot0-34) Ho2 ey caleulabng ar1.26 TFL 2aSf full lood Sped =S Trmax ot S2

2X(-26St =a.8 -2c) 2 =0.8 -262 t 03Lay 0311 1-204 VA HaaSp O505+ 0-3742 - 0 317S4S-0 So50 St 0.053 ey full lood sltp Then Sped at max (orque Ns(l-Sm) gif0o(t-2) Y cbeqa(t-021 O.a549 Sret 457.3 n SHO