Power factor
Power factor is the ratio of true power to apparent power: PF = kW ÷ kVA. It tells you how much of the current a load draws actually does work. A purely resistive load has a power factor of 1.0, while motors and other inductive loads run lower, which means they draw more current for the same kW. Capacitors are added to raise a lagging power factor and bring the current back down.
What power factor is
Power factor is a number between 0 and 1 that compares the power a load uses to do work with the volt-amperes it draws from the supply. In a DC circuit or a purely resistive AC circuit, volts times amps equals watts. In an AC circuit with inductance or capacitance, the current shifts out of step with the voltage, and volts times amps is larger than the watts actually delivered.
Power factor is also the cosine of the phase angle between voltage and current. A load whose current lags the voltage by about 36.9° has a power factor of 0.80.
True, apparent and reactive power
Every AC load has three kinds of power:
- True power (watts, W or kW) does the work: heat, light, motion. This is what a wattmeter reads.
- Apparent power (volt-amperes, VA or kVA) is voltage times current. It is what the wires, breakers and transformers have to carry.
- Reactive power (volt-amperes reactive, VAR or kVAR) moves back and forth between the source and the magnetic or electric fields of inductors and capacitors. It does no work, but it still takes current.
This is why transformers are rated in kVA instead of kW. Their heating depends on the current they carry, no matter what the load's power factor is. See transformers.
The power triangle
The three powers form a right triangle. True power is the base, reactive power is the vertical side, and apparent power is the hypotenuse. The angle between the base and the hypotenuse is the phase angle.
kVA = √(kW² + kVAR²)PF = kW ÷ kVA = cos θ
kW = kVA × PF
Lagging and leading. Inductive loads (induction motors, magnetic ballasts, transformers) make current lag the voltage. Capacitive loads make current lead. The memory aid is "ELI the ICE man": in an inductor (L), voltage (E) comes before current (I); in a capacitor (C), current comes before voltage. Most buildings run at a lagging power factor because of motors.
How power factor affects current
For the same true power, a lower power factor means more current. Divide by the power factor when finding current from watts:
Single-phase: I = W ÷ (E × PF)Three-phase: I = W ÷ (E × 1.732 × PF)
Extra current means larger conductors, more voltage drop, more I²R heating and more capacity used in transformers and switchgear. Utilities often charge commercial customers a penalty for low power factor for the same reason. Lightly loaded induction motors have especially poor power factor, so oversizing motors makes it worse. For motor-specific rules, see motor circuits.
Correcting power factor with capacitors
Capacitors draw leading reactive current that cancels part of the lagging reactive current of motors. The kW stays the same, the kVAR drops, and so do the kVA and the line current. To find the capacitor size needed to go from one power factor to another:
Capacitor kVAR = kW × (tan θ1 − tan θ2)Here θ1 is the angle of the existing power factor and θ2 is the angle of the target. Capacitor installations are covered by NEC Article 460. For example, 460.8 sets the ampacity of capacitor circuit conductors at no less than 135% of the capacitor's rated current, and Article 460 also requires a means to discharge stored energy. When capacitors are connected on the load side of a motor overload device, the overload is sized for the improved power factor current, not the motor's full-load current.
Worked examples
Example 1: find PF and kVAR. A single-phase 240-volt load draws 30 A, and a wattmeter reads 6,120 W.
- Apparent power: 240 × 30 = 7,200 VA.
- Power factor: 6,120 ÷ 7,200 = 0.85.
- Reactive power: √(7,200² − 6,120²) ≈ 3,793 VAR, or about 3.79 kVAR.
Example 2: power triangle. A load has 12 kW of true power and 9 kVAR of reactive power.
- Apparent power: √(12² + 9²) = √225 = 15 kVA.
- Power factor: 12 ÷ 15 = 0.80.
Example 3: effect on current. A 50 kW, 480-volt, three-phase load.
- At 0.75 PF: 50,000 ÷ (480 × 1.732 × 0.75) ≈ 80.2 A.
- At 0.95 PF: 50,000 ÷ (480 × 1.732 × 0.95) ≈ 63.3 A.
- Raising the power factor cuts the line current by about 21% with no change in the work done.
Example 4: capacitor sizing. A plant uses 100 kW at 0.75 PF and wants 0.95.
- Angle at 0.75 is about 41.4°, and tan 41.4° ≈ 0.882. Existing reactive power: 100 × 0.882 ≈ 88.2 kVAR.
- Angle at 0.95 is about 18.2°, and tan 18.2° ≈ 0.329. Target reactive power: 100 × 0.329 ≈ 32.9 kVAR.
- Capacitor needed: 88.2 − 32.9 ≈ 55.3 kVAR.
- Apparent power drops from 100 ÷ 0.75 ≈ 133.3 kVA to 100 ÷ 0.95 ≈ 105.3 kVA.
You can check the volts and amps parts of these with the Ohm's law calculator, and see three-phase power for the 1.732 factor.
Common exam mistakes
- Multiplying by power factor when finding current from watts. You divide; current goes up as PF goes down.
- Mixing up kW and kVA. Wattmeters read kW. Volts times amps gives kVA.
- Adding kW and kVAR directly. They are at right angles, so use the square root of the sum of the squares.
- Forgetting 1.732 on three-phase problems.
- Thinking capacitors reduce kW. They reduce kVAR and current; the true power stays the same.
Practice questions
Frequently asked questions
What is a good power factor?
A power factor of 1.0 is ideal, and values in the 0.90s are generally considered good for commercial and industrial loads. Whether a utility charges a penalty, and at what level, depends on its rate schedule.
Why does low power factor increase current?
For a given true power, current equals watts divided by volts times power factor. A smaller power factor in the denominator gives a larger current, even though the load does the same work.
What causes a lagging power factor?
Inductive loads such as induction motors, transformers and magnetic ballasts. Their magnetic fields need reactive current, which lags the voltage. Lightly loaded motors are the worst offenders.
Do capacitors save energy?
Capacitors reduce the current on the wiring between the capacitor and the source, which lowers I²R losses and frees up capacity. They do not reduce the kW the load itself uses.
Is power factor on the journeyman exam?
Power factor is part of electrical theory, which journeyman exams commonly cover alongside kVA and current calculations. Practice them on the practice test.