Question

Consider a 50 kW, 3-phase, 380 V line-to-line, 50 Hz, 6 pole Y-connected wound-rotor
induction motor. The stator winding ac resistance is 0.1 Ω/phase. The effective stator-to-rotor turns
ratio is 2. The exciting branch is negligible.
It is found that when an external resistor of 0.09 Ω/phase is connected to the rotor terminals maximum
starting torque of 1150 Nm is obtained.
a. Compute the internal mechanical power and the internal torque developed by this motor when it
drives a load at a speed of 950 rpm with the rotor terminals are short circuited (normal motor
operation). (17 pts)
b. Suppose that constant V/f ratio control is used to control the speed of this motor. Find the frequency
at which maximum torque is obtained at starting without connecting any external resistances to the
rotor (18 pts)

Answer 1

& Given question P= 50kw, U = 380v, f-50HZ, P=6, Rilph = o.Inph, Stator Potor =2, Re = 0.99948 I manset: 11 SUNM la We know relation Tem 25 Sman Here 1 Tman St Sman Tman = 1150 Sman=1 Tem Exlx Suns 1150 sti Ng = 120f P 120x5o 6 Ns = loroopm given N8 = 950 rpm Ng- No Ng S= 1000-950 2005 1000 Tem 2x140.05 (0.05)71 -0.099 11 50 internal torque Tem= 114.710m developed internal power P=Txw = 114,71 +27X 950 al1412.10 60 developed IP = 11:41 kw using Upration we know Tox (Ny-No) CSScanned with CamScanner

Tem SNs (Us, No em (Nsq Nr) stad O OSX1000 - TmanStat Ng-950 Nse 950 11417 so 1150 Ny 950 Nse-lus:90 120xf2 = 1451.30 P 120xfz - 1451.90 6 fr = 72.56 HZ 1 - at this frequency with corresponding changed voltage torque is obtained without external resistance. manimum to maintain Ulf - Const, at starting. CSScanned with CamScanner
In question additional resistance in rotor circuit will make maximum torque at starting , to get same maximum torque with out external resistance with V/f control method by changing frequency and maintain V/f= constant.required frequency is obtained.