A utility company's billing statement includes a power factor penalty. The facility has an average active power demand of 533.5 kW and an average power factor of 0.70 lagging. If the target power factor to avoid penalties is 0.90 lagging, what is the minimum additional reactive power (in kVAR) that needs to be supplied by power factor correction capacitors to meet the target PF, assuming the active power remains constant?

Question: A utility company's billing statement includes a power factor penalty. The facility has an average active power demand of 533.5 kW and an average power factor of 0.70 lagging. If the target power factor to avoid penalties is 0.90 lagging, what is the minimum additional reactive power (in kVAR) that needs to be supplied by power factor correction capacitors to meet the target PF, assuming the active power remains constant?

Answer options:

• 153.1 kVAR
• 204.2 kVAR ✅ 285.9 kVAR
• 306.3 kVAR

Correct answer: 285.9 kVAR

Explanation: Active power (P) = 533.5 kW. Initial PF = 0.70 (θ1 = arccos(0.70) ≈ 45.57°, tan(θ1) ≈ 1.0202). Target PF = 0.90 (θ2 = arccos(0.90) ≈ 25.84°, tan(θ2) ≈ 0.4843). Initial reactive power (Q1) = P × tan(θ1) = 533.5 kW × 1.0202 ≈ 544.28 kVAR. Target reactive power (Q2) = P × tan(θ2) = 533.5 kW × 0.4843 ≈ 258.38 kVAR. The reactive power to be supplied by capacitors (ΔQ) = Q1 - Q2 = 544.28 kVAR - 258.38 kVAR = 285.9 kVAR.