The problem I am working on is: A 480 V, star connected, three phase ac generator supplies power to a delta connected load through a transmission line. The per phase impedeances of the load and of the transmission line are (16+j20) and (1+j20) respectively. Determine: (a) The line current (b) The magnitude of the line to line voltage across the load (c) The efficiency of the transmission For a I have I=480/(1+j20)=1.197-j23.94 but should I instead add both impedances together and divide 480 by them?
Yes, to find the line current you have to consider the total load plus line impedance - not just the line impedance. You may find it simpler to refer everything back to a 'per phase' representation. In that case calculate the generator line-to-neutral voltage and apply this to the line impedance plus the delta load impedance converted to its star equivalent. Remember the total impedance is a complex number addition. The subsequent complex division of the line-to-neutral voltage by the total line + load impedance will give you the line current. The rest is complex number manipulation. %Efficiency=(Real Load Power)/(Real Generator Power) expressed as a percentage.
Thanks for the advice, What I did was: Vln=480/sqrt(3) <-30 = 277.13 <-30° Zy=ZΔ/3= (16+j20)/3 = 5.3+ j6.67 <== Not sure why it needs to be converted to ZΔ Ztotal= (5.3+j6.67)+(1+j20)= 6.3+j26.67 Iline= (277.13 <-30°)/(6.3+j26.67) = (240-j138.57)/(6.3+j26.67) = -2.9 - j9.69 This doesn't seem right to me though
Your answers look fine. So how would you have otherwise determined the total load seen by the generator?