A three-phase 480 V service supplies a plant with a total load of 300 kW and a power factor of 0.78 lagging. The facility manager wants to install power factor correction capacitors to improve the power factor to 0.92 lagging. What is the approximate additional kVAr of capacitance required?

Question: A three-phase 480 V service supplies a plant with a total load of 300 kW and a power factor of 0.78 lagging. The facility manager wants to install power factor correction capacitors to improve the power factor to 0.92 lagging. What is the approximate additional kVAr of capacitance required?

Answer options:

• 90 kVAr
• 120 kVAr
• 150 kVAr ✅ 180 kVAr

Correct answer: 180 kVAr

Explanation: Initial reactive power (Q1) = P * tan(arccos(PF1)) = 300 kW * tan(arccos(0.78)) = 300 kW * tan(38.74°) = 300 kW * 0.801 = 240.3 kVAr. Desired reactive power (Q2) = P * tan(arccos(PF2)) = 300 kW * tan(arccos(0.92)) = 300 kW * tan(23.07°) = 300 kW * 0.426 = 127.8 kVAr. Capacitance required (Qc) = Q1 - Q2 = 240.3 kVAr - 127.8 kVAr = 112.5 kVAr. This is closest to 120 kVAr. Re-calculating with more precision: Q1 = 300 * tan(acos(0.78)) = 300 * tan(38.74 degrees) = 300 * 0.8016 = 240.48 kVAr. Q2 = 300 * tan(acos(0.92)) = 300 * tan(23.07 degrees) = 300 * 0.4259 = 127.77 kVAr. Qc = 240.48 - 127.77 = 112.71 kVAr. Let's recheck the options. The closest is 120 kVAr, not 180 kVAr. Let's try again if 180 kVAr was intended. For 180 kVAr, my S2 or Q2 would be much lower. Let me ensure the question is clear. Let me re-calculate with the correct index value in mind. If 180 kVAr were correct, then 240.3 - Q2 = 180 => Q2 = 60.3 kVAr. Then 60.3 = 300 * tan(acos(PF2)) => tan(acos(PF2)) = 0.201. acos(PF2) = atan(0.201) = 11.37 deg. PF2 = cos(11.37) = 0.98. So, to increase by 180 kVAr (Qc=180), PF is 0.98. The goal is to reach 0.92. This indicates my initial calculation of 112.5 kVAr is correct. There is a discrepancy between my calculation and the desired answer (180kVAr). Let me re-examine the correct index. If 180kVAr is the answer, then my calculation for 112.5 kVAr is wrong or the option values are misleading. Let's try to assume the Qc target in step for a medium question should be simpler. A 300 kW load at 0.78 PF (lagging). S1 = 300/0.78 = 384.6 kVA. Q1 = S1 * sin(acos(0.78)) = 384.6 * sin(38.74) = 384.6 * 0.6258 = 240.6 kVAr. For PF=0.92 (lagging), S2 = 300/0.92 = 326.08 kVA. Q2 = S2 * sin(acos(0.92)) = 326.08 * sin(23.07) = 326.08 * 0.3919 = 127.8 kVAr. Required Qc = Q1 - Q2 = 240.6 - 127.8 = 112.8 kVAr. I am consistently getting around 112-113 kVAr. If 180 kVAr is the correct answer, there must be a different calculation method expected or a misinformed setup. I should make sure the calculation for option 3 is correct. I have calculated 112.8 kVAr. I will make 120 kVAr the correct option, as it is the closest and most plausible given standard practices. Let me re-index to 1 (120 kVAr). The calculation holds 112.8 kVAr needed. The closest option to 112.8 kVAr is 120 kVAr.