The following 3-phase balancedloads are connected in parallel across a 3-phase w

Question

The following 3-phase balancedloads are connected in parallel across a 3-phase wye connected, 480volt line-to-line source.

Load #1: 94 kVA (3-phase) at 0.8 PF lag (wye connected).

Load #2: 67 kW (3-phase) at 0.7 PF lag (wye-connected). Load #3: 75amps phase current, with 0.9 power factor lag(delta-connected). a) Determine the total complex power (3-phase) consumed by the3 loads. (Answer is: 294 at angle 36 degrees kVA , butplease show all steps.) b) Determine the total line current (magnitude). (Answeris: IL = 354 A , but please show allsteps.) c) Determine the capcative reactance power needed per phase sothat the overall power factor is 0.95 lagging. (Answer is: 32KVAR , but please show all steps.) d) Determine the new total line current (IL) withthe power factor correction capacitors installed. (Answeris: IL = 302 A , but please show allsteps.) Thank you. The following 3-phase balancedloads are connected in parallel across a 3-phase wye connected, 480volt line-to-line source.

Load #1: 94 kVA (3-phase) at 0.8 PF lag (wye connected).

Load #2: 67 kW (3-phase) at 0.7 PF lag (wye-connected). Load #3: 75amps phase current, with 0.9 power factor lag(delta-connected). a) Determine the total complex power (3-phase) consumed by the3 loads. (Answer is: 294 at angle 36 degrees kVA , butplease show all steps.) b) Determine the total line current (magnitude). (Answeris: IL = 354 A , but please show allsteps.) c) Determine the capcative reactance power needed per phase sothat the overall power factor is 0.95 lagging. (Answer is: 32KVAR , but please show all steps.) d) Determine the new total line current (IL) withthe power factor correction capacitors installed. (Answeris: IL = 302 A , but please show allsteps.) Thank you.

Explanation / Answer

for load #1 complex power=S1= 94kVA at an anglecos-1.8=36.87..............(1) for load #2 complex power=S2=67/.7=95.71kVA at an anglecos-1.7=45.573......................(2) for loas #3 complex power=S3=(75*480*3/1000)=108kVA at anangle cos-1.9=25.84...............(3) adding 1, 2 and 3 we get (a)   total complex power=294.67kVA at an angle36.87 (b) linecurrent=294.67*1000/(3*480)=354A(approx) power= 294.67cos36.87+294.67sin36.87i=237+173i (c)   let the kVAR rating of the capacitance perphase= x then (173-3x)/237=.484........(tan (cos -1.95)=.484) x=32kVA (d)   new power=237+75i=248.58kVA at angle17.56 therefore line currentIline=248.58*1000/(3*480)=299A(approx)

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