Cosφ correction: sizing the capacitor bank
Free calculator for sizing the reactive power compensation of an installation: power Q to compensate in kVAR, capacitor value C in µF (single-phase, star, delta), indicative cost and estimated ROI. In line with Swiss practice (NIBT, utility recommendations) and the principles of IEC 60831 for LV power capacitors.
Why correct the cosφ of an installation
The power factor cosφ expresses the ratio between active power P (kW), the only power actually converted into useful work, and apparent power S (kVA) actually carried by the network. The difference is carried by the reactive power Q (kVAR), which flows between the source and the inductive loads (asynchronous motors, transformers, ballasts, uncompensated drives) without producing any work. This reactive energy saturates cables, transformers and protective devices, increases Joule losses and causes additional voltage drops on the lines.
Swiss utilities (Romande Energie, Services Industriels de Genève, SIL Lausanne, IWB Basel, EWZ Zurich) bill reactive energy beyond a contractual threshold, generally a monthly average cosφ below 0.90 or even 0.93 for industrial metering. Beyond this threshold, the reactive-energy penalty can represent 5 to 15 % of the total bill for an average service-sector SME and up to 20-25 % for a poorly compensated manufacturing industry. Installing a capacitor bank therefore pursues three cumulative goals: eliminating the penalty, freeing up available power on the customer side and improving voltage quality at the end of the line.
Another often-forgotten benefit concerns the sizing of the incoming cables and the private substation transformer. A 100 kW installation at cosφ 0.70 calls for 143 kVA, i.e. 207 A in 400 V three-phase; the same installation corrected to 0.95 draws only 105 kVA, i.e. 152 A. The incoming cable and the upstream protection can stay at a smaller cross-section, and the transformer keeps a comfortable reserve for future extensions. Compensation is therefore, in most cases, more cost-effective than reinforcing the supply.
Reactive compensation calculation formulas
Sizing rests on three elementary formulas derived from the power triangle S² = P² + Q². Let cosφ₁ be the power factor before compensation and cosφ₂ the one targeted after compensation:
- Phase angles : φ₁ = arccos(cosφ₁) and φ₂ = arccos(cosφ₂).
- Reactive power to compensate :
Q = P × (tan φ₁ − tan φ₂)expressed in kVAR for P in kW. - Single-phase capacitance :
C = Q × 10⁶ / (2π · f · U²)with Q in VAR, U = 230 V, C in µF. - Star capacitance (three-phase) :
C_Y = Q × 10⁶ / (2π · f · U²)with U the line-to-line voltage. - Delta capacitance (three-phase) :
C_Δ = C_Y / 3. The delta connection is the LV industrial standard because it divides the capacitance value by 3 for the same reactive power.
Worked example: a commercial-building installation of P = 100 kW, cosφ₁ = 0.70, which we want to bring back to cosφ₂ = 0,95 at 400 V three-phase 50 Hz, requires Q = 100 × (tan 45.57° − tan 18.19°) = 100 × (1.020 − 0.329) ≈ 69 kVAR. The delta capacitance is then about 458 µF per phase. The indicative cost of a 6-step automatically regulated capacitor bank is around 5,500 to 6,500 CHF installed, excluding connection.
Compensation table by power and initial cosφ
Reactive power Q to compensate in kVAR to bring an installation back to target cosφ 0,95, the standard target value to avoid any utility penalty.
| Active P | cosφ 0,60 | cosφ 0,70 | cosφ 0,75 | cosφ 0,80 | cosφ 0,85 | cosφ 0,90 |
|---|---|---|---|---|---|---|
| 10 kW | 10,0 | 6,9 | 5,5 | 4,2 | 2,9 | 1,5 |
| 25 kW | 25,1 | 17,3 | 13,8 | 10,5 | 7,3 | 3,8 |
| 50 kW | 50,2 | 34,6 | 27,6 | 21,1 | 14,5 | 7,6 |
| 75 kW | 75,3 | 51,8 | 41,4 | 31,6 | 21,8 | 11,4 |
| 100 kW | 100,4 | 69,1 | 55,2 | 42,1 | 29,1 | 15,2 |
| 150 kW | 150,6 | 103,7 | 82,8 | 63,2 | 43,6 | 22,8 |
| 200 kW | 200,8 | 138,2 | 110,4 | 84,3 | 58,2 | 30,5 |
| 250 kW | 251,0 | 172,8 | 138,0 | 105,3 | 72,7 | 38,1 |
| 400 kW | 401,6 | 276,5 | 220,8 | 168,5 | 116,4 | 60,9 |
| 630 kW | 632,5 | 435,5 | 347,8 | 265,4 | 183,2 | 95,9 |
For a target cosφ 0,98 (high-level compensation, rare in LV due to the risk of overcompensation), multiply the values by about 1,15. For cosφ 0,90 only, multiply by 0.75.
Compensation bank: fixed or automatically regulated?
The choice between fixed compensation and automatic compensation dépend exclusivement de la variabilité de la charge réactive. Une compensation fixe est constituée d'un ou plusieurs condensateurs câblés en parallèle de la charge, en service permanent. Elle convient lorsque la puissance réactive consommée est stable, par exemple en pied d'un transformateur dont la charge varie peu, sur un moteur dédié à compensation individuelle, ou sur une ligne d'éclairage à ballasts ferromagnétiques. Son coût est faible (1 500 à 3 000 CHF pour 25 à 50 kVAR), sa maintenance se limite à un contrôle visuel annuel.
La compensation automatique régulée pilote 4 à 12 gradins de condensateurs via un régulateur électronique mesurant le cosφ en temps réel sur le départ. Elle s'impose dès que la charge varie significativement dans la journée — typiquement une PME industrielle ou un commerce avec démarrages de groupes froid, presses, compresseurs et ascenseurs en cycles intermittents. Sans régulation, une batterie fixe surdimensionnée surcompenserait à charge réduite, faisant remonter le cosφ capacitif au-dessus de 1, ce que les distributeurs facturent désormais comme l'inductif. Le coût d'une batterie automatique 50 à 100 kVAR oscille entre 4 000 et 7 000 CHF, plus la pose et le câblage. Pour les installations soumises à des harmoniques importantes (variateurs de fréquence, redresseurs, fours à induction, onduleurs PV), prévoir des cellules à anti-harmonic reactor (« detuned », tuned to 134 or 189 Hz) to avoid resonance with the network.
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FAQ — cosφ correction and capacitor banks
From what cosφ should you compensate?
Almost all Swiss utilities bill reactive energy as soon as the average monthly cosφ falls below 0,90. Some utilities tolerate 0.85 on small subscriptions, then switch to 0.90 or 0.93 as soon as the subscribed power exceeds 50 kW. A compensation project is triggered as soon as the bill shows a significant « reactive energy » line item, or if the periodic reading of the average cosφ stays below 0.92.
What is the difference between a fixed and an automatic capacitor bank?
Une batterie fixe délivre une puissance réactive capacitive constante en permanence ; elle convient à une charge stable. Une batterie automatique régule la puissance fournie par paliers grâce à un régulateur qui enclenche et déclenche les gradins en suivant le cosφ instantané. Elle est indispensable dès que la charge varie de plus de 30 % au cours d'une journée. Le surcoût (≈ +30 à +50 %) se rentabilise par la suppression du risque de surcompensation, désormais facturée par la plupart des GRD comme l'inductif.
What is the return on investment of compensation?
For an industrial SME of 100 kW at cosφ 0.75, the monthly reactive-energy bill is typically between 200 and 500 CHF depending on the utility. With an automatic 60 kVAR bank at about 5 500 CHF installed, the ROI ranges from 11 to 28 months. Added to this are the indirect gains: reduced Joule losses (1 to 3 %), freed-up capacity on the incoming feed and the transformer, improved voltage at the end of the line.
Where should the capacitor bank be installed?
Three positions are possible. Central compensation upstream of the main LV distribution board, just after the metering: the standard case for small and medium installations. Group compensation on each distribution board: relieves the cables between the main panel and the zone, recommended for elongated buildings. Individual compensation directly at the motor terminals: relieves all the upstream cabling but costs more in capacitor units; reserved for high-power motors running continuously.
Should anti-harmonic reactors be provided?
Oui, dès que le réseau alimente des charges polluantes : variateurs de fréquence, redresseurs, alimentations à découpage importantes, fours à induction, onduleurs photovoltaïques. Sans self, la batterie entre en résonance avec l'inductance du réseau amont, ce qui amplifie certains rangs harmoniques (5 et 7) et provoque le claquage des condensateurs en quelques mois. Une batterie « detuned » avec selfs à 134 Hz (p=7 %) ou 189 Hz (p=14 %) déplace la résonance et garantit la longévité.
Must the capacitor bank be declared under the OIBT?
Yes. Any capacitor bank constitutes a modification of the installation within the meaning of the OIBT and must appear in the safety report (RDS). Cable cross-sections, upstream protective devices (aM fuses preferable to gG for inrush-current withstand), earthing and marking must comply with NIBT 2020.
Additional tools and resources
- Electrical power calculation (P, Q, S, cosφ) — convert between active, reactive and apparent power.
- Joule loss calculation — quantify the energy savings from compensation.
- NIBT 2020 cable sizing calculation — check the supply cable cross-section after compensation.
- NIBT 2020 standard — protection rules, minimum cross-sections and chapter 5.5 on compensation.
- ElectroCAD Tools for AutoCAD — schematics, parts lists and BOMs with built-in compensation.
- All ElectroCAD calculation tools