A 3-phase, wye connected load of12kW at 0.8 PF lagging is connected in parallel

Question

A 3-phase, wye connected load of12kW at 0.8 PF lagging is connected in parallel with another3-phase, wye connected load of 24 kVA at a power factor of 0.6leading. The line-to-line voltage is 440 volts.
a) Determine total complex power, power factor ( lead orlag ) , and the line current. (Answer is: ST =26.4 - j10.2 = 28.3 at angle -21.13 degrees kVA, PF = 0.933 lead,IL = 37.14 A, but please show all steps.) b) Assuming that Van is the reference phasor (0degrees), determine the line currents in each load and the totalline current in phasor form. Draw the phasor diagram (all voltagesand currents). (Answer is: IL1 = 19.68 at angle-36.87 degrees A, IL2 = 31.49 at angle 53.13 degrees A,IL = 37.14 at angle 21.13 degrees A , but pleaseshow all steps.) c) Determine the KVAR needed to make the aggregate (whichmeans total) power factor unity. Is it inductive or capacitiveKVARs? Please show all steps. Thank you. A 3-phase, wye connected load of12kW at 0.8 PF lagging is connected in parallel with another3-phase, wye connected load of 24 kVA at a power factor of 0.6leading. The line-to-line voltage is 440 volts.
a) Determine total complex power, power factor ( lead orlag ) , and the line current. (Answer is: ST =26.4 - j10.2 = 28.3 at angle -21.13 degrees kVA, PF = 0.933 lead,IL = 37.14 A, but please show all steps.) b) Assuming that Van is the reference phasor (0degrees), determine the line currents in each load and the totalline current in phasor form. Draw the phasor diagram (all voltagesand currents). (Answer is: IL1 = 19.68 at angle-36.87 degrees A, IL2 = 31.49 at angle 53.13 degrees A,IL = 37.14 at angle 21.13 degrees A , but pleaseshow all steps.) c) Determine the KVAR needed to make the aggregate (whichmeans total) power factor unity. Is it inductive or capacitiveKVARs? Please show all steps. Thank you.

Explanation / Answer

apparant power for load 1=S1=12/.8=15KVA at an angle36.87 apparant power for load 2=S2=24KVA at an angle -53.13 total apparant power being=S1+S2=S=26.4-10.2j kVA at an angle-21.13 power factor=.933(lead) line current total Iline=28.3*10^3/(3*440)=37.14A line current for load1=15*1000/(3*440)=19.68A at anangle 36.87(lagging the voltage Van) line current for load2=24*1000/(3*440)=31.49A at anangle 53.13(leading the voltage Van) accordingly will be the phasor diagram for unity power factor reactive power=active power for which we will need inductive compensation inductive compensator=10.2kVAR

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