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Capacitor bank for power factor correction

Calculate the kVAr your plant needs, how much the current drops, how to split an automatic bank into steps, whether any step resonates with the transformer and what voltage the capacitor sees with a detuning reactor.

IEEE 1036shunt bank compensation and resonanceIEEE 18continuous operation up to 110 % of rated voltage

Example cases
Capacitor bank for power factor correction
E1Load
kW

Demand measured at the peak hour.

V
E2Transformer and source
kVA
%
MVA

Optional. Empty = infinite source, the case with the highest resonance.

E3Automatic bank

With grounded wye the 3rd harmonic is also checked.

V

Line to line. Empty = system voltage. With a reactor the capacitor sees V / (1 − p): specify a higher voltage.

Use a decimal point. The calculation runs in your browser and updates as you type.

Required compensation

— kVAr

Rating to specify

— kVAr

Resonance, full bank

—

Capacitor voltage

— V

Load current

— A

Capacitance per phase

— µF

Resonance by steps connected
  • Resonance order h
  • Harmonics checked
  • Reactor tuning 1/√p
A red dot falls within ±0.5 of a characteristic harmonic: with that number of steps the bank amplifies that harmonic current. The ±0.5 band is a criterion of this tool, not a limit from a standard.
Power triangle
  • Before
  • With the bank
  • Bank Qc
Active power does not change: the bank only reduces the reactive power drawn from the grid, and with it the apparent power and the current.

Step-by-step calculation

What it means for your plant

    What it is for

    For a first estimate of the bank before requesting quotes: how many kVAr to buy, in how many steps to split them and whether it should be detuned. It also helps explain why a bank that worked well started to fail after variable frequency drives were installed.

    Many utilities charge for reactive energy, both for excess inductive reactive power and, in some tariffs, for capacitive reactive power when the bank overcompensates. That is why the number of steps matters as much as the total size: a large fixed bank can correct at peak hour and leave the plant capacitive at night.

    How it is calculated

    IEEE 1036bank reactive power

    Qc = P · (tan φ1 − tan φ2) · φ = arccos(PF)

    It is the power triangle, the relationship used by IEEE Std 1036 (guide for the application of shunt power capacitors) and power systems textbooks.

    Current and losses

    I = P / (√3 · V · FP)

    At constant active power and voltage, the current drops in the ratio PF1 / PF2, and the I²R losses upstream of the bank drop by 1 − (PF1 / PF2)².

    Capacitance per phase

    Wye: C = Q / (ω · VC²) · Delta: C = Q / (3 · ω · VC²)

    With ω = 2πf, Q the capacitor power and VC their line-to-line voltage. In wye each capacitor sees VC/√3; in delta it sees VC. Without a reactor, VC = V and Q = Qc.

    IEEE 1036parallel resonance

    h = √(Ssc / Qc) · Ssc = 1 / (1/Ssource + Z% / (100 · ST))

    Ssc is the short-circuit power at the bank bus (IEEE Std 1036; Dugan et al., Electrical Power Systems Quality). Without source data, Ssc = ST / (Z% / 100). In an automatic bank Qc changes with each step, so the resonance sweeps every order between the full bank and a single step; that is why the chart shows them all. With grounded wye the 3rd harmonic is also checked, because zero-sequence current has a path through the bank.

    IEEE 18110 % of rated voltage in continuous operation

    Detuning reactor

    XL = p · XC · htun = 1/√p · VC = V / (1 − p) · Qn = Qc · (1 − p) · (Vn / V)²

    The reactor tunes each step at 1/√p, below the 5th harmonic, and the resonance with the source always stays below that tuning: h = 1 / √(Qc(1 − p)/Ssc + p). The capacitor voltage rises to V / (1 − p), 7.5 % more with p = 7 %, so the capacitor is specified with a higher rated voltage Vn and with the rating Qn at that voltage. The tool warns if VC exceeds the rated voltage and flags a failure above the 110 % that IEEE Std 18 allows in continuous operation.

    Limits of the calculation

    • It is an estimate, not a study. It assumes balanced load, rated voltage and the resonance of a single bus with the transformer as the only inductance.
    • It does not consider other banks, long cables, existing filters or load damping.
    • The ±0.5 risk band around each harmonic is a warning criterion of this tool, not a limit from a standard.
    • It only checks the 110 % RMS voltage limit. The IEEE Std 18 limits of 120 % peak voltage, 135 % reactive power and 180 % current depend on the harmonic spectrum and need a measurement.
    • A capacitor rating applies at its rated voltage: installed at a lower voltage it delivers Q · (V / Vn)².
    • Before buying, measure the load profile and the harmonics and carry out the power quality study.

    Frequently asked questions

    How many kVAr do I need to correct the power factor?

    Use Qc = P · (tan φ1 − tan φ2), where P is the active power in kW, φ1 the angle of the present power factor and φ2 that of the target. For example, 500 kW from 0.78 to 0.95 needs about 237 kVAr. Use the actual measured demand, not the installed power, and check how it changes over the day to define the steps of the automatic bank.

    What is the resonance of a capacitor bank with the transformer?

    The bank and the inductance of the transformer and the source form a parallel resonant circuit. Its frequency, as a harmonic order, is roughly h = √(Scc / Qc). If it falls near a harmonic produced by the loads, such as the 5th or 7th from drives, that harmonic is amplified and can damage the capacitors, blow fuses and distort the voltage of the whole plant.

    When does a capacitor bank need detuning reactors?

    When the plant has significant non-linear loads, such as variable frequency drives, rectifiers or furnaces, or when the resonance calculation falls near a harmonic that is present. The reactor in series with each step moves the resonance below the 5th harmonic, so the bank no longer excites it. The decision is made with a harmonic measurement and a power quality study.

    We carry out your power quality study

    We measure the load profile and harmonics of your plant (in Colombia, or elsewhere on request), check the resonance with the transformer and size the compensation: steps, detuning or filters, without overcompensating.

    See the power quality studyContact us

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