Power Factor Correction Calculator — Capacitor Bank Sizing

One formula, and then the part nobody prints

The kVAr figure is trigonometry and there is no argument about it:

Qc = P × (tan φ₁ − tan φ₂)

Every calculator on the internet stops there, and the number is correct. It is also not enough to buy anything with. A supplier quotes you a capacitor by its kVAr and its rated voltage, in a star or delta configuration, in microfarads on the datasheet — and each of those three can turn a correct kVAr figure into a bank that under-performs. That is what the rest of this page is about.

Computed without angles, deliberately

Since cos φ is the power factor, sin φ is √(1 − pf²) and tan φ falls out as:

tan φ = √(1 − pf²) / pf

Qc = P × [ √(1 − pf₁²)/pf₁ − √(1 − pf₂²)/pf₂ ]

Algebraically identical to going through arccos and tan, and used here because it has no angle in it at all — nothing to express in the wrong unit, and nothing to round through a radian. Worth doing the same in your own spreadsheet; degrees-versus-radians is the classic silent error in this calculation, and it does not announce itself, it just returns a plausible bank size.

Star and delta change the capacitance, not the kVAr

This is the part that produces wrong orders. Reactive power from a capacitor is

Q = V² · 2πf · C

where V is the voltage across that capacitor — not the system voltage, necessarily. In a delta bank each element sits across the full line voltage. In a star bank each sees the line voltage divided by √3, which is 58 % of it, and since reactive power goes with the square of voltage, each element produces only a third as much. So a star bank needs three times the capacitance for the same kVAr:

C_delta = C_star / 3     (same kVAr, same line voltage)

For 55.3 kVAr at 415 V, 50 Hz, that is 341 µF in each of three delta elements, or 1023 µF in each of three star elements. Same bank rating, same current drawn from the line, three times the microfarads — but the delta capacitors have to be insulated for 415 V rather than 240 V, which is what you pay for instead.

Delta is the usual arrangement in an LT panel. Star appears on HT banks and where the neutral point is wanted for unbalance protection.

Watch the units when reading a datasheet: manufacturers quote µF per element, but a delivery note sometimes totals all three. The calculator shows both and labels which is which, because a factor of three in the wrong direction is an easy order to place and an awkward one to return.

The de-rating that costs people money

A capacitor is manufactured for a rated voltage, and its output follows the square of the voltage it actually gets:

Actual kVAr = Rated kVAr × (V_actual / V_rated)²

Put a 25 kVAr capacitor rated at 440 V onto a 415 V system — an extremely common pairing, because 440 V units are what is stocked — and it delivers 25 × (415/440)² = 22.2 kVAr. Eleven per cent short, on every step, permanently. Fit five of them expecting 125 kVAr and you have 111, your power factor lands below target, and the penalty you bought the bank to avoid is still on the bill.

The error is always in the direction of under-correction, it never shows up on a nameplate check, and it is invisible until somebody measures. Buy on delivered kVAr at your voltage, not on the label. The calculator works out the nameplate rating you would need.

The reverse — a capacitor rated below system voltage — is worse. It delivers more than nameplate, briefly, and then fails early: dielectric life falls steeply with over-voltage, and IEC 60871 permits only narrow and time-limited excursions above rating. Never specify down.

Do not aim at unity

Target 0.95, or whatever clears your tariff threshold, and stop. Past unity the load goes capacitive and leading, and that brings voltage rise at light load, possible resonance, and under many tariffs a penalty of its own — the meter records leading kVArh as readily as lagging.

A fixed bank sized for full load will over-correct badly at three in the morning when the plant is idle but the capacitors are still connected. That is what an automatic APFC panel is for: it switches steps in and out against measured power factor. Where the base load is genuinely constant, fixed-compensate that part and switch the rest.

The calculator will tell you the resulting power factor for any bank size you are considering, including when that lands you leading. It reports leading power factor as its true magnitude — a 150 kVAr bank on this example gives 0.851 leading, not a comfortable-looking 1.000.

Measure the power factor, do not read it off a plate

A nameplate power factor is the figure at full load, and almost nothing runs at full load. A motor at a quarter of its rating can sit near 0.5 while its plate says 0.86. Size a bank from nameplates on a lightly loaded plant and you will over-correct it.

Three sources, best first: the recorded power factor across twelve months of bills; a logging meter on the incomer for a fortnight; or, failing both, nameplates with a demand factor applied and a conservative target. If you have kVA and kW but no power factor, the calculator will derive it — it is simply kW ÷ kVA.

Harmonics change the answer entirely

A capacitor is a low impedance to high frequencies. On a supply with drives, UPS or rectifier load, a plain bank can form a resonant circuit with the supply 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.

Where non-linear load is more than roughly a fifth of the plant, specify detuned reactors — typically 7 % — and rate the capacitors for the higher voltage the reactors impose on them, which is why detuned banks use 440 V or 525 V capacitors on a 415 V system by design rather than by mistake.

This calculator deliberately does not issue a resonance verdict. Doing it properly needs the source short-circuit MVA, which most people do not have to hand, and a wrong verdict would read as permission to fit plain capacitors on exactly the site that must not have them. Start with the THD loss calculator and a power quality analyser instead.

Where the bank goes

At the motor terminals it corrects everything upstream including the final cable, which is the only position that reduces internal losses as well as the bill. At the distribution board it corrects the submain and above. At the main incomer it fixes the tariff penalty and nothing else.

One caution that survives every arrangement: never connect fixed capacitors directly across a motor fed by a VFD or a soft starter. Put the bank on the supply side of the drive.

What this does not size

• Switching and protection. Capacitor duty contactors, inrush limiting, fuse ratings and discharge resistors all come from the manufacturer's datasheet. Capacitor inrush can reach a hundred times rated current on back-to-back switching, and ordinary contactors do not survive it.
• Step staging. How to split a bank into steps — and in what ratio — is an APFC controller question driven by the load profile.
• The cable and breaker to the bank. Capacitor circuits are conventionally rated well above the capacitor current for harmonic and tolerance headroom. Size that with the cable calculator against the manufacturer's stated circuit current.

Just the power triangle?

If all you want is kW, kVA and kVAr converted between each other, with the released transformer capacity, the kW / kVA / kVAr converter is the shorter page. Come here when you are specifying the capacitors themselves.