Power factor correction

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How much capacitor correction raises your power factor to a target, and what the low power factor costs on your tariff.

Correction needed

236.8kVAR

Raising 500 kW from 0.78 to 0.95 takes about 236.8 kVAR of correction.

U.S. Department of Energy · Washington State University Energy Program and the Northwest Energy Efficiency Alliance

Cross-checked · The spec's 236.8 kVAR, 641.0 and 526.3 kVA, and $1,384.62 penalty cases pass, and a target below the current power factor returns no correction. Two published worked examples (DOE and WSU/NEEA) are reproduced within 1 kVAR. What this means

Screening estimate: a capacitor bank's size, steps, and placement, and any harmonic or resonance risk, are an electrical engineer's decision. · Example values · Review pending Report a problem

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How we got this

Method

Correction in kVAR is kW × (tan(arccos(PF now)) − tan(arccos(PF target))); apparent power is kW ÷ PF; line current is kVA × 1,000 ÷ (√3 × V) for three-phase service. On a tariff that bills demand scaled to a power-factor threshold, billing kW is kW × threshold ÷ PF when PF is lower.

Steps

Power factor now: 0.78, as entered.
Correction: 500 kW × (tan(arccos 0.78) − tan(arccos 0.95)) = 500 × (0.8023 − 0.3287) = 236.8 kVAR.
Apparent power: 641 kVA now, 526.3 kVA after; current falls by 138 A at 480 V three-phase.
Tariff: billing demand is 500 kW × 0.9 ÷ 0.78 = 576.9 kW, a power-factor penalty of 76.9 kW, or $1,384.62 a month at $18.00/kW. Correcting to 0.95 removes it.
The saving is the tariff's power-factor effect only; it leaves out the cost of the equipment and its installation, and any reduction in losses.
Choose the bank's size, steps, and placement with an electrical engineer, who also checks for harmonics and resonance; no public-domain list of standard bank ratings is cited here, so size up to the next rating your supplier offers.

Assumptions

The power factor entered (or computed from kVAR or kVA) is the one the utility bills on; a bill or the meter shows it.
Correction is sized for the kW entered, usually the demand-setting load.

Sources

U.S. Department of Energy, Energy Efficiency and Renewable Energy, "Reducing Power Factor Cost", Motor Challenge fact sheet, Power triangle example: 100 kW and 100 kVAR, corrected to 0.95 with a 67 kVAR capacitor
Washington State University Energy Program and the Northwest Energy Efficiency Alliance, "Energy Efficiency Factsheet: Reducing Power Factor Cost" (published by Clark Public Utilities), Factsheet, Figure 4: a 100 kW load at 0.70 corrected to 0.95 with a 69 kVAR capacitor

Known limits

The power factor is entered or derived from one kW and kVAR or kVA pair; a file with reactive readings gives a better basis.
Only a tariff rule that scales billing demand to a power-factor threshold is priced here; kVA billing and per-kVAR charges are priced in the workbench's bill.
Harmonics, resonance, and switching transients are not assessed.