kW, kVA and kVAr Converter

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.

What this converter does not decide

The arithmetic above gives you a kVAr figure and what it is worth. Four questions stand between that figure and a purchase order, and none of them is trigonometry:

• How far to correct. Not to unity — a bank sized for full load is still connected when the plant is idle, and leading power factor is metered and penalised much as lagging is.
• Fixed or switched. Which follows from how much the load varies across a day, not from its size.
• Plain or detuned. Decided by how much of the plant is drives, UPS and rectifier load, and the wrong answer here destroys capacitors rather than merely underperforming.
• Where it connects. At the incomer it fixes the bill; at the load it fixes the bill and the losses in everything between.

All four are worked through on the capacitor bank calculator, which also converts the kVAr into the microfarads and the rated voltage a supplier actually quotes against.

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.

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.

Two power factors, and only one of them is cos phi

The figure this page works with is displacement power factor: the cosine of the angle between voltage and current, which is what a capacitor bank corrects. On a purely linear load — motors, transformers, incandescent lighting — that is the whole story and true power factor equals it.

Non-linear loads add a second term. A VFD, a rectifier or a switch-mode supply draws current in a distorted waveform, and the harmonic content contributes to rms current without contributing to real power. True power factor becomes the displacement factor multiplied by a distortion factor of roughly one over the square root of one plus THD squared.

The practical consequence catches people out. A six-pulse VFD can show a displacement power factor near 0.98 and a true power factor around 0.7, because its current is drawn in phase but in pulses. Adding capacitors will not improve it, and may make things considerably worse by forming a resonant circuit with the supply inductance. The fix for distortion is a reactor, a filter or a higher pulse count — never a capacitor.

How the penalty is actually charged

Whether poor power factor costs money, and how much, depends on which mechanism your tariff uses, and Indian state utilities use at least three.

The simplest is a straightforward penalty band: below a threshold — commonly 0.90 or 0.95 — a percentage surcharge is applied to the demand or energy charge, rising in steps as the measured factor falls. Many tariffs pair it with an incentive above the threshold, so correcting past the trigger point continues to pay for a while and then stops.

The second bills kVA demand rather than kW. Nothing is called a penalty at all; poor power factor simply raises recorded demand, and the maximum demand charge follows it. This is often the largest of the three and the least visible on a bill.

The third meters reactive energy in kVArh and charges for it directly, sometimes with separate rates for lagging and leading. That last detail matters for anyone with a fixed capacitor bank: a plant that is correctly corrected at full load can go capacitive overnight when the motors stop, and be charged for leading kVArh it did not know it was producing. Automatic power factor correction with contactor stages exists mainly to avoid that.