Power factor correction is the engineering process of reducing unnecessary reactive power in AC electrical systems. This cheat sheet helps students connect the power triangle, AC load behavior, capacitor banks, and utility billing. It is useful for circuit analysis, energy systems, motors, transformers, and practical electrical design.
Students need it because poor power factor increases current, losses, voltage drop, and equipment loading.
The core ideas are real power P in watts, reactive power Q in vars, apparent power S in volt-amperes, and power factor PF = P/S. Inductive loads such as motors usually create lagging power factor, while capacitors supply leading reactive power that offsets it. Correction calculations often use Qc = P(tan theta1 - tan theta2), where theta comes from PF = cos theta.
Good engineering correction improves system efficiency without overcorrecting into a leading power factor.
Key Facts
- Real power is the useful average power converted to work or heat, and for single-phase AC it is P = V I PF.
- Reactive power is power that oscillates between the source and reactive components, and for single-phase AC it is Q = V I sin theta.
- Apparent power is the product of RMS voltage and RMS current, and for single-phase AC it is S = V I.
- The power triangle relationship is S^2 = P^2 + Q^2, where P is in watts, Q is in vars, and S is in volt-amperes.
- Power factor is PF = P/S = cos theta, where theta is the phase angle between voltage and current.
- For three-phase balanced loads, real power is P = sqrt(3) V_line I_line PF and apparent power is S = sqrt(3) V_line I_line.
- The capacitor reactive power needed for correction is Qc = P(tan theta1 - tan theta2), where theta1 is the original angle and theta2 is the target angle.
- Improving power factor reduces line current because I = P/(V PF) for single-phase loads when real power and voltage stay constant.
Vocabulary
- Power factor
- Power factor is the ratio of real power to apparent power, written as PF = P/S.
- Real power
- Real power is the average power that performs useful work, measured in watts.
- Reactive power
- Reactive power is the power exchanged by inductors and capacitors in an AC system, measured in vars.
- Apparent power
- Apparent power is the total RMS voltage-current product supplied to a load, measured in volt-amperes.
- Lagging power factor
- Lagging power factor occurs when current lags voltage, usually because the load is inductive.
- Capacitor bank
- A capacitor bank is a group of capacitors installed to supply leading reactive power and improve power factor.
Common Mistakes to Avoid
- Using kW and kVAR as if they are the same unit is wrong because real power and reactive power represent different parts of the power triangle.
- Forgetting to convert power units is wrong because Qc = P(tan theta1 - tan theta2) requires consistent units, such as kW with kVAR or W with VAR.
- Using PF directly as an angle is wrong because the angle must be found from theta = arccos(PF) before using tangent.
- Assuming correction changes real power is wrong because capacitors mainly reduce reactive power and current, not the useful power demanded by the load.
- Overcorrecting past the target power factor is wrong because a leading power factor can cause voltage regulation problems and penalties in some systems.
Practice Questions
- 1 A single-phase load uses 12 kW at a power factor of 0.75 lagging. What is its apparent power in kVA?
- 2 A 50 kW motor load has an original power factor of 0.70 lagging and must be corrected to 0.95 lagging. Use Qc = P(tan theta1 - tan theta2) to find the required capacitor size in kVAR.
- 3 A balanced three-phase load operates at 480 V line-to-line, draws 80 A, and has PF = 0.86. Find the real power using P = sqrt(3) V_line I_line PF.
- 4 Explain why adding capacitors to an inductive motor system can reduce current in the supply conductors even if the motor's real power output does not increase.