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ee341_h03_Wi2012_Solution - ECE 341 HW3 Winter 2012 Problem...

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ECE 341 HW3 Winter 2012 Problem 1: A three-phase line feeds three balanced three-phase loads that are connected in parallel. The first three-phase load is absorbing a total of 156 kW and 117 kVAr. The second three-phase load is delta connected and has a phase impedance of 144-j42 ohm. The third three-phase load is at 115kVA at 06 PF leading. The line impedance between the source and the load is 0.6+j0.3 ohm. If the line to neutral voltage at the load end of the line is 2400 V. What is the magnitude of the line- line voltage at the source? (8 pts.) ) ( t v a ) ( t v b ) ( t v c A N V AN =2400 V 0.6 + j 0.3 ohm Load 1 Load 2 Load 3 V ab =? V Solution: Load 1 : S 1 =52+j39 kVA, i 1 = [(52000+j39000)/2400]*=21.7-j15 A Load 2 : Convert the Delta connection to Wye connection, Z 2y =(144-j42)/3=48-j14 ohm i 2 =2400/(48-j14)=46.08+j13.44 A Load 3 : With a leading power factor, the reactive power has a negative value S 3 =[115×0.6-j115sin( (0.6))]/3=23-j30.667 KVA i 3 =[(23000-j30667)/2400]*=9.58+j12.78 A In the per phase analysis, Load 1, 2, and 3 are connected in parallel, thus, the current that
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