Power Factor Correction Calculator: kVAR, Savings & Resonance

Fundamental compensation and current

For a balanced three-phase load, $\varphi_1=\cos^{-1}(\mathrm{PF}_1)$ and $\varphi_t=\cos^{-1}(\mathrm{PF}_t)$. The ideal net bank is

The evaluated bank gives $Q_2=Q_1-Q_b$, $S_2=\sqrt{P^2+Q_2^2}$ and $\mathrm{PF}_2=P/S_2$. Supply current is $I=S/(\sqrt3 U_{LL})$, with power converted explicitly to VA. The motor/load itself keeps its original PF; improvement applies upstream of the capacitor connection. Source: Schneider Electric Electrical Installation Guide 2016, chapter L, attached s1 page 8 (printed L8).

Capacitors with or without series reactors

The branch equations below are derived here from $X_C=1/(\omega C)$ and $X_L=\omega L$, with $p=X_L/X_C$ and $\omega=2\pi f$:

Here Q is in var, C in F, and U in V. For a plain bank, p is zero. The selected branch sees $U_C=U_{branch}/(1-p)$, carries $I_{branch}=\omega C U_C$, and needs $L=p/(\omega^2 C)$. Capacitor-element reactive power is $Q_C=Q_b/(1-p)$. The series tuning order is $h_t=1/\sqrt p$ and frequency $f_t=f h_t$. Schneider L24 (s1 page 24) gives the common 5.7%, 7%, 14% candidates and notes the increased capacitor voltage. Calculated voltage is fundamental stress only; select a suitable rated assembly with harmonic and tolerance margins.

Resonance screen

Use Ssc in kVA and Q in kvar at the same bus. This is Schneider's undetuned, predominantly inductive source approximation (s1 page 23, L23). For a detuned candidate, this tool shows a hypothetical plain bank at the same net kvar, not an actual network pole. Other banks are included here only: the entered present PF already reflects existing correction. The nearest of harmonics 3, 5, 7, 11, 13, 17, 19, 23 and 25 is reported. A 10% relative band is an author-selected screening aid, not a standard acceptance limit. Tune below the lowest significant harmonic; the spectrum and network study decide suitability.

Losses and user-entered tariffs

Three-phase feeder copper loss is $3I^2R_{phase}$. Its relative reduction is $1-(I_2/I_1)^2$; annual saved feeder energy is the difference in kW times entered hours. At the load bus, kVAh charges are $r_S S H$; excess-kvarh charges are $r_Q\max(Q-aP,0)H$, where a is the contract's free kvarh/kWh allowance. Before-minus-after gives gross annual tariff saving. No tariff schedule is embedded; CU denotes the same user-chosen currency throughout. Do not add feeder energy savings to the displayed charge saving without modelling the meter location.

Direct motor-terminal constraint

Using the no-load magnetising Q0 supplied by the user, capacitor-element kvar is limited to $0.9Q_0$. Automatic mode therefore caps net output at $0.9Q_0(1-p)$ and shows any target shortfall. This is a conservative extension of the 90% no-load rule to a detuned assembly. Schneider L20 (s1 page 20) uses approximately $0.9\sqrt3 U I_0$ for a nearly reactive no-load current; ABB paper 8, printed page 15, states the 90% Q0 rule. Manual mode rejects an excessive bank.

Target sweeps

The kvar sizing curve shows the ideal requirement without a motor ceiling. The current curve instead evaluates automatic bank sizing at each requested target and applies the same motor no-load ceiling used by the result cards. In motor mode it therefore plateaus when additional compensation is disallowed. These curves compare prospective automatic banks even when an entered bank is being evaluated.

• Balanced three-phase RMS quantities and a constant operating point. The power factors are lagging fundamental displacement factors, not distorted true PF.
• P is electrical input power at the capacitor bus, constant before and after; source voltage and feeder resistance stay fixed. Installation calculations do not include motor efficiency or a shaft-power conversion.
• The entered bank rating is its net fundamental output at the stated bus voltage and frequency, including the selected reactor. It is not automatically corrected from a capacitor nameplate at another voltage.
• Each star phase or delta branch has identical C and, where selected, identical series L. Reactors and capacitors are ideal for sizing; losses, tolerances, saturation and harmonic currents are excluded.
• The resistance is one upstream phase conductor, not a three-phase sum or loop resistance. Only that upstream segment benefits.
• No-load magnetising kvar must come from a measurement or the motor manufacturer at the entered voltage and frequency. The equations for capacitance, branch voltage, loss and conservation are derived here from elementary circuit relationships.
• Annual hours describe an equivalent steady load; rates and the reactive allowance are user data. The default allowance and prices are illustrative, with no jurisdiction or utility implied.

Use for preliminary engineering sizing and teaching on balanced 45–65 Hz three-phase systems. Commercial capacitor stages, insulation level, switching inrush, discharge, protection, conductor sizing and installation arrangements need separate selection. At medium voltage, equipment and switching requirements need a specialist design.

The undetuned resonance approximation neglects damping, other network branches, generators, cables and harmonic source impedances. It does not calculate amplification, THD, filter absorption or the poles of a detuned network. Evaluate every bank switching state and the full measured spectrum, including harmonics outside the screened list. Unknown spectra need measurement; an order outside the illustrative 10% band is not a safety clearance. Triplen behaviour depends on the connection and grounding. With no connected bank, undefined resonance and inductance are shown as gaps.

Motor no-load limiting is necessary but does not certify freedom from self-excitation. Manufacturer limits take precedence; high-inertia loads, residual speed, shared banks, supply loss and coordinated capacitor/motor switching need an engineering review. Automatic sizing may intentionally leave the requested PF unmet. An entered bank that creates leading operation or exceeds the motor ceiling is rejected.

Feeder-loss estimates assume a modest voltage drop; a warning asks for a fuller model above 10% calculated feeder loss. No net equipment energy saving, payback, demand-charge saving or guaranteed bill reduction is claimed. Metering intervals, variable loads, step controllers, capacitor/reactor losses and utility billing rules can change the result.

Method sources: Schneider Electric Electrical Installation Guide 2016, chapter L, cross-checked against the open wiki on 2026-10-28, and ABB Technical Application Paper 8. This is not a compliance calculator tied to a particular code edition or tariff date. Check against the standard in force and the current contract. Installation work belongs to a qualified person.