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EnergyCalcHQ
S = P / cos φ

kW, kVA and kVAr Converter

Convert between real, apparent and reactive power, and size the capacitor bank needed to lift power factor to a target — with the current reduction and released transformer capacity shown.

Load

Capacitor required
47.4kVAr
To move from 0.78 to 0.95. Line current falls from 178 A to 146 A.
Apparent power now128.2kVA
Apparent power corrected105.3kVA
Reactive power now80.2kVAr
Reactive power after32.9kVAr
Line current now178.4A
Line current after146.4A
kVA released22.9kVA

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The three powers

An AC circuit carrying an inductive load moves three different quantities, related by a right triangle:

  • Real power, kW — does the work. This is what the energy meter bills you for in units.
  • Reactive power, kVAr — magnetises motors and transformers. It does no work but it flows back and forth through your cables every cycle.
  • Apparent power, kVA — the vector sum. This is what the transformer, the cable and the switchgear must actually carry.
S = P / cos φ
Q = P × tan(arccos φ)
S² = P² + Q²

Why correcting power factor pays

It pays three times over, and only the first is obvious:

  1. The penalty goes away. Most Indian utilities levy a power factor penalty below 0.90 and pay an incentive above 0.95. For an industrial connection this alone often repays a capacitor bank within a year.
  2. Transformer and cable capacity is released. A 100 kW load at 0.78 PF draws 128 kVA. At 0.95 it draws 105 kVA. That is 23 kVA of headroom recovered without buying anything — the difference between needing a bigger transformer and not.
  3. Losses fall. Cable loss goes with the square of current. Cutting current by 18 % cuts copper loss by about a third, every hour the plant runs.

Sizing the capacitor

Qc = P × (tan φ₁ − tan φ₂)

where φ₁ is the present angle and φ₂ the target. The calculator does this and reports the difference in kVAr, which is what you order.

Do not overcorrect

Pushing past unity into leading power factor causes real problems: voltage rise at light load, resonance with system inductance, and in some tariffs a penalty for leading PF just as there is for lagging. Target 0.95, not 1.0.

This matters most on plants whose load varies. A fixed bank sized for full load will overcorrect badly at night. Use an automatic power factor correction panel that switches steps in and out, or split the bank so the base load is fixed-compensated and the variable part is switched.

Where to connect it

MethodCorrects losses inBest for
At the motor terminalsEverything upstream, including the final cableLarge motors that run continuously
At the distribution boardSubmain and aboveGroups of smaller motors
At the main incomerOnly the utility sideRemoving the tariff penalty only

Correcting at the incomer fixes the bill but not the internal losses. Correcting at the load fixes both, and lets you use smaller cable on new installations.

One caution: do not connect fixed capacitors directly across a motor fed by a VFD or fitted with a soft starter. Use a separate switched bank on the supply side.

Measure it before you size anything

A nameplate power factor is the figure at full load. Almost nothing runs at full load, and the gap is large: a motor at a quarter of its rating can sit near 0.5 while its plate says 0.86. Sizing a capacitor bank from nameplates on a lightly loaded plant overcorrects badly.

Three sources, best first: the recorded power factor on twelve months of bills, a logging meter on the incomer for a fortnight, or — failing both — nameplates with a demand factor applied and a target set conservatively.

Generators change the answer

An alternator is rated in kVA at 0.8 power factor, so poor power factor hits its current limit while the engine still has kilowatts to give. Correcting releases real capacity on a DG-fed site.

But a fixed bank sized for mains running will overcorrect a lightly loaded generator into leading power factor, where the automatic voltage regulator hunts and the output becomes unstable. Interlock the bank to the changeover, or use a controller that knows which source is live. This is a two-wire job that is forgotten on most retrofits.

Capacitors and harmonics

A capacitor is a low impedance to high frequencies, and a bank connected to a supply with drive or rectifier load can resonate with the system inductance and amplify a harmonic that was previously tolerable.

The symptoms arrive in a recognisable order: capacitors running hot, fuses failing for no visible reason, then capacitors failing repeatedly. If non-linear load is more than about a fifth of the plant, specify detuned reactors — typically 7 % — and rate the capacitors for the higher voltage the reactors impose on them.

Reading the result

The kVAr figure is what you order. The released kVA is what you tell the finance department, because demand is billed on apparent power and that number comes off the bill every month whether or not a penalty ever applied.