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IEC 608319 min read

Worked Example: Sizing a Capacitor Bank to Raise Power Factor from 0.75 to 0.95

A 500 kW load running at a costly 0.75 power factor — sized up to a 277 kVAr delta-connected capacitor bank that cuts line current by a fifth.

Scenario

Active load500 kW, 415 V three-phase
Existing power factor0.75
Target power factor0.95
Bank connectionDelta, rated at 440 V

Step-by-step calculation

Step 1: Find the reactive power at the existing and target power factors

Q = P x tan(phi), phi = arccos(PF)
phi1 = arccos(0.75) = 41.4°; Q1 = 500 x tan(41.4°) = 441.0 kVAr phi2 = arccos(0.95) = 18.2°; Q2 = 500 x tan(18.2°) = 164.3 kVAr
Q1 = 441.0 kVAr, Q2 = 164.3 kVAr

Step 2: Find the required capacitor bank reactive power

Qc = Q1 - Q2
441.0 - 164.3
Qc = 276.6 kVAr

Step 3: Find apparent power and line current before and after correction

S = P / PF I = (S x 1000) / (√3 x V)
S1 = 500/0.75 = 666.7 kVA; I1 = 927.5 A S2 = 500/0.95 = 526.3 kVA; I2 = 732.2 A
S1 = 666.7 kVA, I1 = 927.5 A S2 = 526.3 kVA, I2 = 732.2 A

Step 4: Size the delta-connected capacitance per phase

C = (Qc x 10⁶ / 3) / (2π·f·Vcap²)
Using f = 50 Hz, Vcap = 440 V
C = 1.516 µF per phase, capacitor current Ic = 384.8 A

Step 5: Compute line current reduction and apparent-power saving

Current reduction% = (I1 - I2) / I1 x 100 kVA saving = S1 - S2
(927.5 - 732.2) / 927.5 x 100
Current reduction = 21.1%, kVA saving = 140.4 kVA

Result summary

CheckRequirementActualStatus
Required capacitor bank ratingn/a (this is the sizing result)276.6 kVAr✓ PASS
Line current after correctionn/a (informational)732.2 A, down from 927.5 A✓ PASS
A 276.6 kVAr delta-connected capacitor bank raises this load's power factor from 0.75 to 0.95, cutting line current by 21.1% (927.5 A -> 732.2 A) and freeing up 140.4 kVA of apparent-power headroom on the same supply.

Key insight: Power factor correction reduces current and apparent power without changing the actual real power (kW) the load consumes — the load still does the same 500 kW of work, but the supply, transformer and cables no longer have to carry the extra reactive current that was previously going back and forth to support that load's magnetizing/reactive needs.

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Frequently asked questions

Why does the capacitor bank need a voltage rating (440 V) higher than the system voltage (415 V)?

Capacitor banks are typically rated with some margin above nominal system voltage to account for normal voltage variation and harmonic voltage content, both of which stress a capacitor more than a purely sinusoidal signal at exactly nominal voltage — running a capacitor at or above its rated voltage for extended periods accelerates dielectric aging and shortens its service life.

Does over-correcting to unity power factor (1.0) make sense?

Not usually — pushing power factor all the way to 1.0 requires a larger capacitor bank for diminishing improvement, and slight over-correction can actually create a leading power factor during light-load periods (when the fixed capacitor bank's reactive output exceeds the load's now-smaller reactive demand), which many utilities penalize just as they penalize a lagging power factor. Most utility tariffs and this calculator's own target-PF convention aim for a value like 0.95, not 1.0.

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