Batteries, Machines and Electricity Systems
Real, Reactive and Apparent Power
Understand power factor and what local capacitors change in the supply.
You are applying “Real, Reactive and Apparent Power” to a real system and need the concept, assumptions and verification boundary to stay clear.
Distinguish real, reactive and apparent power; calculate sinusoidal power triangles; separate true power factor from displacement factor; and understand why capacitor correction requires harmonic, resonance, switching and protection studies.
- Select or check first
- Power factor is a ratio, not an efficiency. True power factor is P/S. It describes how effectively RMS volt-amperes deliver average watts at the measurement point. It does not by itself state a motor's shaft efficiency or identify whether low power factor comes from phase displacement, waveform distortion, or both.
- Controlling assumption
- Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
- Top risk
- Harmonics can turn correction into resonance. Capacitance and the network's inductance form resonant circuits. Nonlinear loads can excite those frequencies and magnify current or voltage. Manufacturer guidance calls for detuned or filtered solutions where required.
- Proof
- Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Start with the basics Optional foundation before “Real, Reactive and Apparent Power”
Electrical-engineering basics
Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.
- Voltage
- Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
- Current
- Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
- Resistance and impedance
- Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
- Power and heat
- Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
- Rating versus operating point
- A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.
How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.
On this page
AC equipment can require current that does not translate entirely into average useful energy transfer. Real power P is the average rate of net energy conversion into shaft work, heat, light or other output. Reactive power Q describes the sinusoidal exchange of stored energy between source and electric or magnetic fields. Apparent power S is based on RMS voltage and current and represents the electrical loading that conductors and equipment must carry.
The familiar power triangle belongs to a sinusoidal case
Diagram description
The figure explicitly limits the triangle and normalized waveforms to the sinusoidal case. It also distinguishes true PF = P/S from displacement PF = cos φ when distortion is present.
Single-phase sinusoidal power
S = V_rms I_rms; P = S cosφ; Q = S sinφ; S² = P² + Q²
These equations apply to sinusoidal voltage and current with one phase angle φ. P is measured in watts, Q in vars and S in volt-amperes. Sign conventions for leading and lagging Q must be stated; the article uses positive Q for an inductive lagging load.
- V_rms
- RMS voltage, V
- I_rms
- RMS current, A
- φ
- current phase displacement relative to voltage
- P
- real power, W
- Q
- reactive power, var
- S
- apparent power, VA
A sinusoidal load taking 10 kVA at 0.80 lagging displacement factor uses 8 kW and 6 kvar because sin(arccos 0.80) = 0.60.
| Quantity | What it tracks | Why it matters |
|---|---|---|
| Real power P | Average net energy conversion per second | Energy use and useful-plus-loss conversion |
| Reactive power Q | Sinusoidal field-energy exchange | Current, voltage drop and equipment loading |
| Apparent power S | RMS voltage-current product | Cable, transformer, generator and switchgear loading |
| Power factor PF | P divided by S | How much apparent loading corresponds to real power |
Distorted current breaks the simple cos φ shortcut
With nonlinear loads, current can contain harmonics even when its fundamental component is nearly in phase with the voltage. True power factor still uses total real power divided by total apparent power under the applicable measurement definition, while cos φ describes only the fundamental displacement relationship. A meter may therefore report PF and cos φ as different values. The simple right triangle cannot represent all harmonic interactions.
True and displacement power factor
PF_true = P/S; DPF = cosφ₁
The subscript 1 refers to the fundamental-frequency components. Under clean sinusoidal conditions the two coincide. Under distortion they may differ, so correction decisions need waveform and harmonic measurements rather than one angle alone.
- PF_true
- true power factor
- DPF
- displacement power factor
- φ₁
- fundamental voltage-current displacement angle
Local capacitors can offset inductive reactive demand
Diagram description
The vectors are conceptual and not a sizing or connection diagram. The plate requires harmonic, switching and protection assessment and warns about overcorrection and resonance.
Sinusoidal correction target
Q_c = P(tanφ₁ − tanφ₂)
This is an initial balanced sinusoidal calculation at a stated operating point. It does not select capacitors, steps, voltage rating, detuning reactors, switching devices or protection. Load variation and utility rules determine whether a fixed or automatically stepped scheme is appropriate.
- Q_c
- capacitor-bank reactive-power magnitude, var
- P
- real load power, W
- φ₁
- initial displacement angle
- φ₂
- target displacement angle
For a steady 100 kW sinusoidal load moving from 0.80 to 0.95 lagging displacement factor, the arithmetic target is about 42 kvar. That number is not an installation prescription.
| Effect | Possible result | Boundary |
|---|---|---|
| Reactive current from upstream | Reduced when local capacitive kvar offsets inductive kvar | Depends on load and correction state |
| Feeder and transformer current | Can fall for the same real load | Harmonic RMS current may remain |
| Voltage drop and I²R loss | May decrease upstream of the bank | System impedance and operating point matter |
| Motor real power and efficiency | Not automatically improved | Capacitors do not remove motor copper, iron or mechanical loss |
| Utility billing | May improve where tariffs penalize low PF or kvar | Rules are utility- and contract-specific |
A capacitor bank is a switched energy-storage system
| Check | Hazard or failure controlled |
|---|---|
| Load profile and target PF | Overcorrection during light load and leading operation |
| Harmonic spectrum and system impedance | Series or parallel resonance and capacitor overcurrent |
| Switching frequency and inrush | Contactor, fuse, bus and capacitor transient stress |
| Voltage, temperature and tolerance | Premature ageing or dielectric failure |
| Discharge and re-energization timing | Trapped charge and high closing transients |
| Protection, enclosure and earthing | Fault energy, arc, touch and fire hazards |
Why correcting to exactly unity is not always the target
Load and system conditions change. A bank sized for one operating point can drive the installation leading when inductive demand falls, cause voltage rise, or switch excessively. Utilities and equipment makers may specify a target band below unity. The engineering goal is compliant, stable operation across the load profile—not the prettiest single meter reading.
Use Capacitors in Series and Parallel for voltage, energy and balancing fundamentals. For inductive switching protection at component scale, see Zener References and Inductive Clamp Paths.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Real, Reactive and Apparent Power?
Power factor is a ratio, not an efficiency. True power factor is P/S. It describes how effectively RMS volt-amperes deliver average watts at the measurement point. It does not by itself state a motor's shaft efficiency or identify whether low power factor comes from phase displacement, waveform distortion, or both.
Which assumption can change the conclusion?
Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
What can go wrong if I copy the example directly?
Harmonics can turn correction into resonance. Capacitance and the network's inductance form resonant circuits. Nonlinear loads can excite those frequencies and magnify current or voltage. Manufacturer guidance calls for detuned or filtered solutions where required.
How do I verify the result in the real system?
Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Sources and further reading
- Power Factor PF and cos φ Measurement — MicroLogic X User GuideSchneider Electric · 2026-10-13Manufacturer documentation reviewed for P/S power factor, fundamental cos φ and their different interpretation with harmonic current.
- Power Factor Correction and Harmonic Filtering in Electrical PlantsABB · 2026-10-13Manufacturer application guide reviewed for power-triangle quantities, capacitor kvar calculation, correction configurations and harmonic considerations.
- Film Capacitors — Power Factor Correction Installation and Maintenance InstructionsABB · 2026-10-13Manufacturer safety instructions reviewed for harmonic distortion, detuning, resonance avoidance, current limits, discharge and protection.
- Electrical Distribution Fundamentals Design GuideSchneider Electric · 2026-10-13Reviewed for the need to custom-engineer passive harmonic filters and avoid resonance.