Capacitor bank sizing: reactive power, stages and protection for power factor correction

What capacitor bank sizing is

Sizing a capacitor bank is not picking a kVAr value from a catalogue and bolting it to the busbar: it is computing exactly how much reactive power an installation needs to raise its power factor from the present value to the target, then deciding how to deliver that power — as one fixed block or as several switchable stages — and how to protect and switch each block safely. The number that starts everything is the reactive power Qc; everything downstream (stages, currents, contactors, fuses, reactors, the enclosure) follows from it.

The most common field mistake is to treat power factor correction as a single number bought once. In a real plant the load breathes through the day, the network carries harmonics, and the capacitor itself draws a violent inrush every time it switches. A correct design accounts for all three.

The reactive power to install

A load that draws active power P at a lagging power factor fp₁ also draws reactive power q₁ = P·tan φ₁. To raise the power factor to fp₂ you must supply the difference locally:

Qc = P · (tan φ₁ − tan φ₂)

Here φ₁ = acos(fp₁) and φ₂ = acos(fp₂). Because a capacitor can only add capacitive reactive power, the target fp₂ must be greater than fp₁ — asking for a lower target is physically impossible and the method flags it instead of silently returning a “minimum bank”. The computed Qc is then rounded up to the nearest commercial bank value (the 2.5 / 5 / 7.5 / 10 / 12.5 / 15 / 20 / 25 / 30 / 40 / 50 … kVAr series), giving Qbank.

The obtained power factor is checked against the residual reactive power q₂ = q₁ − Qbank:

fp_obtained = P / √(P² + q₂²)

This confirms the rounded bank actually clears the target with a small margin rather than over- or under-correcting.

Fixed bank or automatic bank

A fixed bank is a single block, sensible only when the load is stable (an individual motor switched with its starter). When the load varies, a fixed bank overcorrects at light load and produces a leading power factor — itself penalised. The answer is an automatic bank: the total Qbank is split into stages that a power factor controller switches in and out to track the target.

The stages can follow two schemes:

• Equal — every stage carries the same kVAr (step = Qbank/N). Simple, robust, the default.
• Binary — stage weights follow 1 : 2 : 4 : … : 2^(N−1), so the smallest step is Qbank/(2^N − 1). Three binary stages (1+2+4) resolve in seven levels what would need seven equal stages — finer regulation with fewer contactors, at the cost of unequal hardware.

Current, contactor and fuse per stage

Each stage of Q_stage kVAr at line voltage V draws a rated three-phase current:

Icn = Q_stage · 1000 / (√3 · V)

But a capacitor is never sized for Icn. IEC 60831 combines a 1.10 overvoltage with a 1.30 factor for harmonics and capacitance tolerance, giving the sizing current:

Ic_dim = 1.43 · Icn

That is the current the cable and the general protection must carry. The per-stage switching and protection follow commercial rules:

• Contactor ≥ 1.5·Icn, in utilization category AC-6b, fitted with pre-charge resistors to tame the capacitor inrush;
• gG fuse ≈ 1.65·Icn, rounded up to the standard fuse series.

A general AC-3 motor contactor is the wrong tool here — the repeated capacitor inrush welds its contacts.

The detuning reactor and harmonics

On a clean network an undetuned bank is fine. On a network rich in harmonics — variable-speed drives, rectifiers, UPS — the bank and the supply inductance form a parallel resonance at order:

h_r = √(Scc / Qc), with Scc = √3·V·Icc

If h_r lands in the danger band (roughly 4.5 to 7.5, i.e. near the 5th or 7th harmonic), the bank amplifies that harmonic and capacitors and fuses fail early. The cure is a detuning reactor in series with each stage, sized so the series LC tunes below the lowest troublesome harmonic at order:

n = 1 / √p

For the common p = 7 %, n ≈ 3.78 — comfortably below the 5th. The reactor inductance per phase is L = XL/ω with XL = p·Xc and Xc = V²/Q_stage. The reactor, however, raises the voltage across the capacitor to:

Vc = V / (1 − p)

so the capacitor units must be rated above the line voltage (for 380 V at 7 %, Vc ≈ 409 V). Forgetting this is a classic cause of premature capacitor failure in detuned banks.

How the method assembles the bank

The calculation proceeds in steps:

1. Reactive power — from P, fp₁ and fp₂ it computes Qc and rounds up to the commercial Qbank, then checks the obtained power factor.
2. Stages — for a fixed bank, one stage; for an automatic bank, N stages with equal or binary weights, and the smallest switching step.
3. Per stage — it sizes the commercial capacitor unit, the rated and sizing currents (1.43·Icn), the AC-6b contactor (1.5·Icn), the gG fuse (1.65·Icn) and, if detuned, the reactor inductance and the elevated capacitor voltage.
4. Overall — it sums the currents to set the general protection (1.43·Ic_total) and verifies the assembly’s short-circuit withstand against Icc; it estimates the equivalent capacitance and the resonance order.
5. Enclosure — it lays the stages, controller and general device into a cabinet (à la motor control centre), returning the build dimensions for the 2D/3D drawing.

Practical design notes

• Aim for 0.92–0.95, not unity, and prefer an automatic controller so light load does not push you into a leading power factor.
• Size everything for 1.43·Icn, per IEC 60831, not for the rated current.
• Use AC-6b contactors with pre-charge — never a plain motor contactor on a capacitor.
• Detune (5.67 / 7 / 14 %) whenever the network carries harmonics, and rate the capacitors for Vc = V/(1 − p).
• Check the parallel resonance h_r = √(Scc/Qc) before committing to an undetuned bank.

Following this chain — reactive power, stages, per-stage current and protection, detuning and resonance check, then the assembly — yields a capacitor bank that meets the target power factor, survives switching and harmonics, and matches the field-validated reference sheet.