Can I use measured true power factor with harmonics?

No. The angle relation PF=cos phi is limited here to fundamental displacement power factor under the stated sinusoidal assumptions.

Is the capacitance output a safe capacitor-bank selection?

No. Rated voltage, kvar steps, duty, switching, discharge, protection, harmonics, resonance, temperature and product standards require separate engineering.

Why are delta and wye capacitances different?

Each delta element sees line-to-line voltage; each wye element sees line-to-neutral voltage in the ideal balanced system.

What target power factor should I choose?

This worksheet does not choose one. Use the applicable utility contract, measured load profile and controlled system study.

Ideal fundamental-frequency arithmetic — not bank sizing

Fundamental Displacement-PF Compensation Arithmetic

Calculate ideal capacitive kvar and ideal element capacitance for controlled sinusoidal single-phase or balanced three-phase conditions. The input is lagging fundamental displacement power factor, not unspecified true power factor.

Qc=P(tanφ1−tanφ2)1φ / 3φ Δ / 3φ YRMS voltageNo safe-bank verdict

Ideal capacitive reactive-power change

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Ideal capacitance per element

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Apparent power before / after

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Ideal line current before / after

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Ideal current change

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Fundamental arithmetic only.

φi=acos(DPFi); Qc=P·(tanφ1−tanφ2)
S=P/DPF; I1φ=P/(V·DPF); I3φ=P/(√3·VLL·DPF)
C1φ=Qc/(ωV²); CΔ,element=Qc/(3ωVLL²); CY,element=Qc/(ωVLL²)

P is kW, Qc is kvar, S is kVA, DPF is lagging fundamental displacement power factor, V is RMS volts, I is amperes, ω=2πf, and C is converted from farads to microfarads. The wye relation uses ideal Vphase=VLL/√3.

Qc is a positive ideal capacitive change only when 0<DPF1<DPF2≤1. No leading target is represented. Current/apparent-power values assume unchanged P and V and exclude distortion/unbalance.

Not a capacitor-bank selection. Do not purchase, connect or switch equipment from this arithmetic alone. System short-circuit impedance, harmonic spectrum/resonance, load profile, voltage rise, inrush, switching transients, discharge, protection, detuning/reactors, capacitor current/voltage duty, tolerances, temperature, enclosure and applicable installation rules are not modeled.

Power-factor definition

IEC TR61000-1-7:2016 explicitly separates fundamental power factor caused by fundamental phase displacement from non-fundamental power factor caused by distortion in non-sinusoidal single-phase systems. Therefore `acos(PF)` is not applied here to an unspecified true PF reading.

Equipment and harmonic boundaries

IEC61921:2017 edition2 applies to low-voltage AC shunt capacitor banks for power-factor correction and includes assembly verification context.It is not replaced by this worksheet.IEEE519-2022 is active and sets harmonic-control goals at the point of common coupling;exact limits and study procedures remain licensed.The US Department of Energy warns that capacitors and system inductance can create damaging harmonic resonance.

NEEDS_LICENSED_SOURCE: applicable utility contract/target and billing interval;meter definition;harmonic and resonance study;selected equipment rating/steps/duty;IEC61921 verification;IEEE519 limits;protection,switching,discharge,installation and commissioning rules.

Sources d'information

IEC TR61000-1-7:2016; IEC61921:2017; IEEE519-2022; US DOE motor-driven systems guide; NIST SI guidance.