Problem #$3-$ Induction Motor Characterization $(38$ points$)$

A three$-$phase, Y$-$connected, $4160V,60Hz,2250hp$ squirrel$-$cage induction motor is used in a chiller compressor to provide chilled water that is in turn used for air conditioning in a building complex. A line$-$to$-$neutral DC test shows $V_{DC}=9V$ and $I_{DC}=250A.$ The motor is tested to later determine its efficiency curve and the following test results are reported using the two$-$Wattmeter method.

No load test: $P_{3,NL}=83,350W,V_{NL}=4160V,I_{NL}=22A.$

Locked$-$rotor test: $P_{3,LR}=5,000W,V_{LR}=175V,I_{LR}=232A.$