The sizing arithmetic for power factor correction is genuinely short — one formula and a table of coefficients. The reason installations fail is almost never the arithmetic.
It is a target chosen without reference to the tariff, a fixed bank installed on a variable load, or capacitance added to a system full of harmonics without anyone checking what resonance it would create.
The calculation
The reactive power to be supplied is the difference between what the load draws now and what it would draw at the target power factor.
Sizing a bank for a 900 kW load
Correcting from 0.78 to a target of 0.95.
- Real power at the design condition900 kW
- Existing power factor0.78
- (Existing reactive power: 900 × tan(arccos 0.78))722 kVAR
- Target power factor0.95
- (Reactive power at target: 900 × tan(arccos 0.95))296 kVAR
- (Correction required: 722 − 296)426 kVAR
- Nearest standard bank size above450 kVAR
Specify450 kVAR, automatically switched in steps
The 450 kVAR bank slightly overshoots the target at full load, which is fine. What matters is that at light load it must not be all connected — hence switched steps. Figures illustrative.
The diagram makes the essential point that arithmetic alone can obscure: the horizontal leg does not move. Real power is unchanged, because the work being done is unchanged. What shortens is the vertical leg and therefore the hypotenuse — the apparent power the system has to carry.
Choosing the target
Not unity. Almost never unity.
The economically correct target is the point at which the tariff stops charging you, plus a margin. If your tariff penalizes below 0.90, correcting to 0.93 or 0.95 captures the entire available benefit. Correcting to 0.99 costs more capacitance and earns nothing further, while increasing the risk of overcorrection when the plant is lightly loaded.
The exception is a tariff that bills demand in kVA. There, every increment of correction reduces the determinant continuously, so the target is set by economics rather than by a threshold: correct until the marginal capacitance costs more than the marginal kVA it saves. That is a different optimization and it usually lands higher, though still short of unity. The distinction between the two cases is set out in power factor penalties explained.
Sizing to the right condition
The design condition matters as much as the target, and it is where sizing goes wrong quietly.
Size to the condition the tariff measures. If power factor is assessed at the time of peak demand, size for the peak. If it is assessed as a monthly average, sizing for the peak will overcorrect for most of the month. If it is assessed continuously, the bank has to track the load — which means switching.
Establish the range, not just the maximum. The ratio between your highest and lowest reactive load determines how many switching steps you need. A plant whose reactive demand varies by a factor of three cannot be served by a two-step bank without either undercorrecting at the top or overcorrecting at the bottom.
Include the transformers. On-site transformers contribute magnetizing reactive power continuously, including at night when nothing else is running. A site whose reactive load never falls below a floor has a fixed component that can be corrected with a fixed bank, with switched steps handling the variable remainder.
Overcorrection is a real failure, not a theoretical one
A fixed bank sized for full load, left connected when the plant is idle, produces a leading power factor. The consequences are practical:
- Voltage rise at the point of connection, which can push equipment above its tolerance.
- A penalty in the other direction under tariffs that specify a band rather than a minimum.
- Interaction with generation and drives, which can behave unexpectedly on a leading supply.
The remedy is switching, controlled by a relay measuring actual power factor and connecting steps as required. It is a standard product and the incremental cost over a fixed bank is small compared with the cost of getting it wrong.
Check harmonics before you order
This is the single most important precondition and the one most often skipped.
Capacitors and the supply inductance form a resonant circuit whose frequency depends on the capacitance installed. Add capacitance and you move that frequency. If it lands near a harmonic order that your own equipment is generating — the fifth and seventh are the usual suspects where drives and rectifiers are present — currents at that frequency are amplified, and the capacitors, being a low impedance path at high frequency, absorb the result.
The symptoms are capacitor overheating, repeated fuse operation, and in bad cases equipment damage. The bank appears defective; it is not. It is doing exactly what a capacitor does in a resonant circuit.
Where drives are a significant share of load, the solution is normally detuned capacitors — a reactor in series with each step, shifting the resonant frequency below the lowest significant harmonic. It costs more and it is the difference between an installation that works and one that is switched off within the year: harmonics, resonance and why capacitors sometimes make it worse.
Before the order goes out
- Confirm the tariff's power factor mechanism, its threshold, and when it is measured.
- Confirm the benefit exists at all. If the schedule ignores power factor, there is no billing saving to fund the project.
- Measure the actual reactive load across a full operating cycle, not at one moment.
- Establish the range between minimum and maximum reactive demand, and size the switching steps to it.
- Assess harmonic content. Specify detuned equipment where drives, rectifiers or significant electronic load are present.
- Set the target just above the tariff threshold unless demand is billed in kVA.
- Confirm the protection, the discharge arrangements and the physical location with a qualified engineer. This is live switchgear work and it is not a procurement decision.
- Verify the result on the next bill against the calculation, and keep the comparison: measurement and verification.
What to expect afterward
The power factor line on the bill should move immediately and the penalty should disappear, or the kVA determinant should fall by the calculated amount. What should not change is the kilowatt demand or the kilowatt-hours consumed, and if a proposal promised that they would, the proposal was wrong: the real power doing the work is exactly what correction leaves alone.
Where a site has substantial drive load, there is a further wrinkle worth understanding before assuming a capacitor bank is needed at all, because drives interact with power factor in a way that is frequently misread: variable frequency drives and displacement power factor.
