Power factor correction with capacitor banks

Reference notes

Use Next → on the narrator above to step through power-factor correction with capacitor banks: why it pays back, how to size kVAR, the four bank types, placement trade-offs, harmonic resonance and detuning, and simple-payback economics.

Why correct PF?

• Utility demand-charge avoidance: most large-customer tariffs penalize PF below 0.90 or 0.95. The penalty is usually applied per kVAR of reactive demand, often a few dollars per kVAR-month.
• Freed-up kVA capacity: lower kVAR at the same kW means lower kVA = smaller line current. This frees headroom on the existing transformer and feeders without new copper.
• Loss reduction: I²R losses on the customer's own distribution scale as I² = (S/V_LL)², so a 20% drop in kVA = ~36% drop in losses on that section.
• Voltage support: less reactive current = less X·sin θ drop in the feeder = bus voltage closer to nominal.

Typical industrial PF-correction project: customer at 0.78 PF lagging corrected to 0.95 lagging, with payback under 18 months from demand-charge avoidance alone.

Sizing the capacitor bank

Real power P does not change with capacitor compensation — only Q does. Before correction Q_old = P · tan θ_old; after Q_new = P · tan θ_new. The capacitor supplies the difference:

Worked example: 800 kW at 0.78 PF lagging → 0.95 PF lagging.

• tan θ_old = √(1 − 0.78²) / 0.78 ≈ 0.802
• tan θ_new = √(1 − 0.95²) / 0.95 ≈ 0.329
• Q_cap = 800 · (0.802 − 0.329) ≈ 378 kVAR → round up to a standard 400 kVAR bank.

Bank types

• Fixed shunt bank: always energized in shunt with the load. Cheapest, but supplies the same kVAR regardless of load. Risk: light-load voltage rise.
• Switched shunt bank (manual or contactor): multiple groups in shunt, each on a contactor. Operator energizes groups as load varies.
• Automatic: PF-sensing relay (ANSI 55) energizes shunt groups in steps based on measured PF, with a deadband around the target to prevent hunting. Standard for modern industrial installations.
• Synchronous condenser: over-excited synchronous motor running unloaded; its excitation field current is adjusted to supply continuously variable kVAR. Older utility-substation technology; mostly replaced by SVCs / STATCOMs today.

Placement

Three classical locations, ordered by loss-reduction benefit:

1. At the load (e.g., capacitor at each motor's terminals): eliminates reactive current all the way upstream. Best loss reduction; most expensive to install.
2. At the busbar: serves multiple loads from a single bank. Moderate loss reduction; simpler switching.
3. At the substation: cheapest $/kVAR. Only addresses utility-side demand penalty; reactive current still flows through customer's internal distribution.

Harmonic resonance

A capacitor bank Q_cap on a bus with short-circuit MVA S_SC forms a parallel resonant circuit with the source inductance. The resonant frequency is:

If f_r happens to land near a harmonic injected by VFDs or rectifiers (5th and 7th are the usual suspects on 6-pulse drives, 11th and 13th on 12-pulse), the harmonic voltage at the bus is amplified — sometimes ten-fold or more, causing damaged capacitors, tripped drives, and overheating transformers.

The fix is a detuning reactor in series with each capacitor, sizing the LC pair to resonate at a frequency just below the lowest troublesome harmonic — typically 4.7×f_1 (just under the 5th) for 6-pulse drive environments. The detuned LC presents low impedance to the harmonic instead of amplifying it.

Three-phase bank topology

Two common 3-φ topologies:

• Y-connected with grounded neutral: each capacitor at V_LN = V_LL/√3. Per-phase Q = ω·C·V_LN². Lower voltage stress per unit; lower cost per kVAR. Used on MV systems.
• Δ-connected: each capacitor at V_LL. Per-phase Q = ω·C·V_LL² — three times the kVAR per microfarad versus Y. Common on LV systems where the higher voltage stress is tolerable.

Both deliver the same TOTAL 3-φ kVAR at the same applied V_LL — the difference is in unit cost and the failure-mode behaviour (unbalanced fault detection differs between the two topologies).

Economic analysis

Typical LV-bank installed cost: $25–$50 per kVAR. Annual demand-charge avoidance: $30–$60 per kVAR-year (utility-specific). Loss reduction: a few percent of the existing distribution losses. Most industrial PF-correction projects show simple payback under 2 years.

Over-correction caveat: pushing past the utility's deadband to leading PF often triggers a leading-PF penalty too. And during low-load periods a fixed over-sized bank can lift the bus voltage above 1.05 pu — damaging customer equipment. Use automatic switching, or size for slightly under-correction (e.g., target 0.95 instead of 0.98).

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