A 6 pole, 60 hz induction motor is wye connected and has a rated slip of .03 with the follwoing parameters: Rs=0.5 ohms, Rr'=0.3ohms, Xs=J1 ohms, Xr'=J0.35 ohms, Xm=j20 ohmsand the total rotational losses=7300 watts. the motor runs from a 4160volt 3 phase line, line current = 237.59 @ -31.08 degress PF=.86 lagging, Sin=1.712 MVA, Qin=884 Kvars, RPI total=1.39Mw, RPD=1.35MW, pout=1.34MW, hp= 1.8*10^6, rpm=1200 efficiency= 91% and torque= 7.86*10^6 ft-lb at rated speed.
on the same 4160/2405 volt transformer secondary there are 4 induction motors. each one is rated at 5,000 hp with 90% efficiency and lagging power Factor of 0.8. also on the circuit is an induction motor rated at 3.53MW at power factor = .7 lagging.
Find:
a) the total secondary current and power factor.
b) repeat if one of the induction motors is replaced with a 5000 HP synchronous motor with the same efficiency but with a Power Factor =0.8 leading.