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Capacitor bank kVAr sizing is the engineering calculation that determines the reactive power compensation (in kVAr) required to raise a facility’s power factor from an existing lagging value to a target value, based on the active power load and the two corresponding power factor angles. This guide walks through the governing formula, a complete worked example for a medium-voltage industrial load, a comparison table of sizing steps, and the selection pitfalls engineers should watch for. It is written for plant electrical engineers, EPC contractors, and procurement teams across the Middle East and Gulf region (including Egypt and Saudi Arabia), North Africa, CIS, and Sub-Saharan Africa who need to specify power factor correction equipment correctly the first time.
Capacitor banks are frequently paired with medium-voltage switchgear for protection and switching, coordinated with [protection relays](/what-is-a-medium-voltage-protection-relay-mv-protection-relay/) for overcurrent and capacitor-specific protection, and installed downstream of distribution transformers where the reactive demand originates.
Why kVAr sizing matters
A plant operating at a low (poor) power factor draws more apparent current from the utility than the active power it actually consumes. This excess current increases I²R losses in cables and transformers, causes avoidable voltage drop, and in most tariff structures triggers a reactive-energy penalty on the utility bill. Correct capacitor bank sizing solves this by injecting leading reactive power (kVAr) that cancels part of the lagging reactive power drawn by inductive loads such as motors, transformers, and reactors — without over-sizing the bank, which can lead to overvoltage, leading power factor penalties, or harmonic resonance with the supply network.
Undersized banks fail to reach the target power factor and leave penalty exposure on the table. Oversized banks push the power factor into leading territory at light load, which many utilities penalize just as heavily as a lagging power factor, and can also elevate the risk of resonance with background harmonics from variable-frequency drives and other non-linear loads.
The sizing formula
The standard first-principles method for capacitor bank sizing uses the active power of the load (kW) and the trigonometric relationship between active power, reactive power, and apparent power.
Step 1 — Determine the load active power (kW). This is taken from the metered or calculated real power draw of the facility, typically from the utility bill, a power quality logger, or the transformer loading study.
Step 2 — Determine the existing (uncorrected) power factor, cos φ₁. This is read from the utility bill or measured directly with a power quality analyzer.
Step 3 — Determine the target power factor, cos φ₂. This is usually the minimum power factor required by the utility tariff to avoid penalties, or a plant-internal target (commonly close to unity, but never exceeding it in a purely capacitive-correction scheme).
Step 4 — Apply the sizing formula:
Qc = P × (tan φ₁ − tan φ₂)
Where: – Qc = required capacitor bank reactive power (kVAr) – P = active load power (kW) – φ₁ = power factor angle corresponding to the existing (uncorrected) power factor – φ₂ = power factor angle corresponding to the target power factor
The angles φ₁ and φ₂ are obtained from the respective power factor values using φ = arccos(cos φ), and tan φ is then calculated from that angle. This is the standard power-triangle method taught in IEEE and IEC-aligned power system engineering references and is the basis for every capacitor bank sizing calculation, regardless of voltage class.
Worked example — sizing a capacitor bank for an 11 kV industrial load
Consider a facility supplied at 11 kV with an active demand of 1000 kW, currently operating at a lagging power factor of 0.75. The utility tariff requires a minimum power factor of 0.95 to avoid reactive energy penalties.
Step 1: Load data P = 1000 kW cos φ₁ = 0.75 (existing) cos φ₂ = 0.95 (target)
Step 2: Find the angles φ₁ = arccos(0.75) ≈ 41.4° φ₂ = arccos(0.95) ≈ 18.2°
Step 3: Find the tangents tan φ₁ = tan(41.4°) ≈ 0.882 tan φ₂ = tan(18.2°) ≈ 0.329
Step 4: Apply the formula Qc = P × (tan φ₁ − tan φ�2) Qc = 1000 × (0.882 − 0.329) Qc = 1000 × 0.553 Qc ≈ 553 kVAr
So, for example, a 1000 kW load correcting from 0.75 to 0.95 power factor requires approximately 553 kVAr of capacitive compensation. In practice this would be rounded up to a standard bank size — for example a 600 kVAr bank built from multiple steps — to provide a small safety margin and allow staged switching.
Cross-check using apparent power: At cos φ₁ = 0.75, the apparent power S₁ = P / cos φ₁ = 1000 / 0.75 ≈ 1333 kVA. For an 11 kV three-phase supply, the uncorrected line current is approximately I₁ = S₁ / (√3 × V) = 1333 / (1.732 × 11) ≈ 70 A.
After correction to 0.95 power factor, the new apparent power S₂ = P / cos φ₂ = 1000 / 0.95 ≈ 1053 kVA, giving a corrected current of I₂ = 1053 / (1.732 × 11) ≈ 55.3 A.
This illustrates the practical benefit of the calculation: the same 1000 kW of useful work is now delivered with roughly 15 A less line current, which directly reduces cable and transformer loading and losses — the real-world payoff of correct capacitor bank sizing.
Step-by-step sizing table
| Step | Parameter | Formula | Example value |
|---|---|---|---|
| 1 | Active load power, P | From metering/bill | 1000 kW |
| 2 | Existing power factor, cos φ₁ | Measured | 0.75 |
| 3 | Target power factor, cos φ₂ | Utility/plant target | 0.95 |
| 4 | Existing angle, φ₁ | arccos(cos φ₁) | ≈ 41.4° |
| 5 | Target angle, φ₂ | arccos(cos φ₂) | ≈ 18.2° |
| 6 | Correction factor | tan φ₁ − tan φ₂ | ≈ 0.553 |
| 7 | Required kVAr, Qc | P × correction factor | ≈ 553 kVAr |
| 8 | Selected bank size | Rounded up, staged | ≈ 600 kVAr |
| 9 | Current before correction, I₁ | S₁/(√3×V) | ≈ 70 A |
| 10 | Current after correction, I₂ | S₂/(√3×V) | ≈ 55.3 A |
Selection criteria and common pitfalls
Load profile, not just peak demand. A capacitor bank sized only for peak load may leave the plant over-compensated during low-load periods (night shift, weekends). This is why many medium-voltage installations use multi-step or automatically switched banks, controlled by a power factor relay, rather than a single fixed block of kVAr.
Harmonic environment. Facilities with significant variable-frequency drives, rectifiers, or other non-linear loads should evaluate the risk of harmonic resonance between the capacitor bank and the system inductance before finalizing the kVAr value and bank configuration. In harmonic-rich networks, detuned or filter reactors are commonly added in series with the capacitors.
Switching and protection coordination. Capacitor banks draw significant inrush current on energization and must be matched with switching devices and protection relays rated for capacitive switching duty, coordinated with the upstream switchgear and protection relay settings.
Voltage rise effect. Injecting reactive power raises the local busbar voltage slightly; on long or heavily loaded feeders this voltage rise should be checked against the allowable voltage band, particularly when the bank is sized at the higher end of the calculated range.
Transformer loading interaction. Since capacitor banks reduce the net reactive current drawn from the supply, they also reduce the effective loading on the upstream transformer, which can be factored into long-term capacity planning.
Avoid over-correction. Sizing the bank to reach a power factor above unity (over-compensation) should be avoided in standard fixed- or stepped-capacitor schemes, as many utilities penalize leading power factor just as they penalize lagging power factor.
Standards and compliance notes
Capacitor bank design, testing, and protection coordination are addressed by the IEC 60871 series for shunt power capacitors for AC power systems. Protection relay functions used to supervise capacitor banks (overcurrent, unbalance, overvoltage) follow general IEC protection relay standards, and the switching devices used to energize/de-energize banks should be rated for capacitive switching duty per the relevant IEC switchgear standard for the voltage class. Where a specific IEC clause number is not confirmed for a given project, the sizing methodology itself (the P × (tan φ₁ − tan φ₂) formula) remains an IEEE/IEC-aligned first-principles calculation independent of any single product standard.
Related guides
See also our guides on medium voltage switchgear, gas-insulated switchgear and ring main units.
What is the formula for capacitor bank kVAr sizing?
The standard formula is Qc = P × (tan φ₁ − tan φ₂), where P is the active load in kW, φ₁ is the angle of the existing power factor, and φ₂ is the angle of the target power factor.
How do I find tan φ from a power factor value?
First find the angle φ = arccos(cos φ), then compute tan φ from that angle. For example, a power factor of 0.75 corresponds to φ ≈ 41.4°, and tan(41.4°) ≈ 0.882.
Can I size a capacitor bank just from the utility bill?
Yes — the utility bill typically provides active energy (kWh) and the measured or average power factor, from which an equivalent kW demand and cos φ₁ can be estimated for a first-pass sizing calculation before field verification.
Should I always round the calculated kVAr up?
In most installations the calculated value is rounded up slightly and matched to standard capacitor unit or step sizes, giving a small margin while avoiding significant over-correction toward a leading power factor.
Why does my corrected power factor matter for cable and transformer sizing?
Because reducing reactive current lowers the total line current for the same active power delivered, as shown in the worked example where current dropped from roughly 70 A to roughly 55 A — this reduces I²R losses and frees up transformer and cable capacity.
Do harmonics affect capacitor bank sizing?
Yes — in facilities with significant non-linear loads, the sizing calculation should be followed by a harmonic resonance check, and detuned reactors may be required in series with the bank to avoid amplifying existing harmonic distortion.
Is a fixed or automatically switched capacitor bank better?
It depends on load variability: facilities with a stable, continuous load can often use a fixed bank sized to the dominant operating point, while facilities with fluctuating load benefit from multi-step, relay-controlled banks that adjust kVAr output as demand changes. “`
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