Reactive power: why 1000 W at cos φ 0.8 loads the wiring like 1250 VA
With an inductive load, part of the current does nothing but build and release a magnetic field. It adds no active energy, yet the conductor still has to carry it. What W, var and VA actually mean — and when it genuinely matters to you.
The symptom: two different power figures on the nameplate
You buy a UPS and see "1500 VA / 900 W". You pick up a motor and its nameplate says 1.1 kW and cos φ 0.8. The inverter manufacturer talks about apparent power, the salesman about watts, and the electricity bill about kilowatt-hours.
This is not sloppy labelling. These are three different quantities. With an almost purely resistive load — a heating element or a traditional incandescent bulb — they are nearly equal. With a motor, a transformer or a discharge lamp they drift well apart.
The difference can be large. A 1000 W load at cos φ 0.8 loads the installation as if it were 1250 VA. The conductor and the inverter have to carry that current, even though no extra energy corresponds to it. Protective devices, however, are not selected by the same VA-to-amps conversion — the characteristics of the whole circuit decide that.
Three powers, one triangle
Active power in watts is the part that turns into motion, heat or light. It is what you pay for on a domestic tariff, and it is what determines how long a battery will last.
Reactive power in vars does no work. It circulates between the source and the load: in one quarter of the cycle it charges the motor's magnetic field, in the next it flows back to the grid. The balance over a full cycle is zero, but the current flows the whole time.
Apparent power in volt-amperes is the product of voltage and current — what the conductor actually sees. Pythagoras ties them together:
S² = P² + Q²
For a 1000 W load at cos φ 0.8 that works out to 1250 VA of apparent power and 750 var of reactive power. At 230 V it means a current of 5.43 A instead of 4.35 A — a quarter more in the same conductor, for the same work done.
Where the current nobody uses comes from
A motor does not turn current into motion directly. It first has to build a magnetic field in its winding — and that field must be fed, whether or not the shaft is loaded.
The magnetising current flows even when the motor runs at no load. That is why an underloaded motor has the worst cos φ of its whole operating range: it draws little active power, yet has to magnetise just the same. A motor picked "with a generous margin" makes things worse, not better.
The same logic applies to transformers, ballasts in discharge luminaires and contactor coils. A heating element, an incandescent bulb and a kettle have nothing to magnetise — their cos φ is close to one and all three powers are practically equal. This does not extend to LED luminaires or fluorescent lamps: there, an electronic circuit sits between the mains and the light source, and the picture is different.
cos φ is not always the power factor
Here begins the territory where even trade publications get it wrong.
cos φ describes the phase shift between voltage and current. It makes sense when the current is a sine wave — that is, with motors, transformers and other linear loads.
The power factor is a broader concept: the ratio of active to apparent power, regardless of the waveform. Switch-mode power supplies, inverters, chargers and some LED lighting draw a distorted current — not a sine wave, but short pulses at the voltage peak. There, cos φ alone overstates the result, because it ignores the harmonics.
The practical conclusion: a calculation based on cos φ is correct for a motor or a transformer. For a computer power supply or a converter, treat it as an optimistic estimate and check the real power factor in the device's documentation.
Compensation: capacitors, and what they will not fix
A motor's reactive power can be produced on the spot instead of being drawn from the grid. A capacitor draws reactive power of the opposite sign, so connected in parallel with the motor it reduces what flows through the supply conductor.
An example with numbers. A plant draws 10 kW at cos φ 0.7 and wants to reach 0.95 at 400 V and 50 Hz. That leaves 6915 var to be compensated. In a delta connection this takes 45.86 µF per phase, and in a star connection 137.57 µF — three times more. Anyone who quotes a single figure without naming the connection is wrong in two cases out of three. The current in the supply conductor drops by 26.3 percent as a result.
What such a result does not tell you. It does not know whether your installation carries harmonics — and with non-linear loads a capacitor bank can resonate with the supply inductance and make things worse instead of better. It does not replace choosing the working voltage, the capacitor class or checking the manufacturer's conditions. The microfarad figure is a theoretical calculation for the stated connection, not a shopping list.
When this concerns you
The first case is sizing an inverter or a UPS. This equipment is rated in volt-amperes precisely because current, not energy, is the limit. A 600 W linear load at cos φ 0.45 needs about 1333 VA. The "1000 W" printed on an inverter is therefore not enough to judge by: compare its continuous and peak ratings given in VA, its permitted current, and the data of your load.
The second is a charge for reactive power. A network operator or a tariff may bill for reactive energy drawn beyond an agreed level. We give no thresholds or rates here, because they depend on the country, the tariff and the contract — check them in your own contract and on your bill, not in a calculator that does not know where you are. Whether such a charge applies at all, and from what level, follows from the contract and the operator's rules for the specific connection. A general article — this one included — is not a basis for assessing your own bill.
The third is conductor sizing. A conductor is sized for current, and the current follows from the apparent power. The same 1000 W load needs a conductor rated for 5.43 A at cos φ 0.8 and for 4.35 A at cos φ equal to 1.
Sources
- Fluke 39/41B — the difference between cos φ at the fundamental frequency and the full power factor including harmonics
- Fluke — fifth-harmonic resonance: when capacitors make things worse
- Polish tariff regulation (Dz.U. 2019 item 503) — an example of national rules on reactive energy billing; check the equivalent with your own operator