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.
Understanding Power Factor Correction Reference
An induction motor needs a magnetic field before it can produce steady torque. During each AC cycle, energy enters the motor windings to build that field, then much of it returns as the field weakens. This back and forth exchange makes the current peak later than the voltage peak.
The source, cables, and transformer must carry that current even though only part of it becomes shaft output, heat, or light. The same effect appears in transformers, welding sets, fluorescent lighting with magnetic ballasts, and many industrial control systems. A resistor behaves differently because its current rises and falls in step with voltage.
A correction capacitor is connected across a load or group of loads. It stores energy in an electric field, while an inductor stores energy in a magnetic field. Their current timing is opposite.
The capacitor can provide much of the magnetic-field current close to the motor, so less of that current has to travel from the supply. Capacitor banks may use fixed units for steady loads or switched steps for changing loads. Their rating depends on system voltage, frequency, and required reactive power.
A capacitor designed for one voltage can fail if used at a higher voltage. Switching can create large brief currents, so practical banks need fuses, contactors, discharge resistors, and suitable protection.
Correction does not reduce the real energy needed by a motor to lift a load or turn a pump. It reduces current in upstream equipment. Lower current can reduce heating in cables and transformers because resistive heating depends on current squared.
It can free capacity in a switchboard or transformer without installing a larger unit. This matters most in factories and large buildings where electricity bills may include a charge for peak demand or apparent power.
A household energy meter usually records real energy, so a small home motor rarely justifies a separate correction capacitor. Engineers compare equipment cost, expected demand charges, operating hours, and maintenance before selecting a bank.
Students should keep load type, measurement point, and operating condition clear. A motor nameplate power factor applies near a stated load, not at every speed or torque. Lightly loaded motors often have poorer power factor.
In three-phase work, use line voltage and line current consistently, since mixing line values with phase values causes major errors. Harmonic currents from variable speed drives, computers, and LED drivers need special care. Ordinary capacitors can combine with system inductance and create resonance, which may amplify harmonics instead of reducing them.
Good designs often use detuned reactors or harmonic-rated capacitors. A target slightly below unity is common because too much capacitance can produce leading power factor when motors are switched off.