Capacitor Bank Sizing for 1200 kW Load: kVAr Calculation, Power Factor, Harmonics

User question

what is capacitor bank size for 1200 KW load

Artificial Intelligence Response

Direct answer to the question

• You can’t pick a capacitor bank size from kW alone. You must know:
  • Existing power factor PF1
  • Target power factor PF2 (often 0.95–0.98, utility dependent)
  • System voltage and frequency (in the U.S., typically 480 V, 60 Hz)
• Use: Qc [kVAr] = P [kW] × (tanφ1 − tanφ2), where φ = cos⁻¹(PF)

Key points

• For a 1200 kW load:
  • From PF 0.80 to 0.95 ⇒ Qc ≈ 505 kVAr → select ~525 kVAr automatic bank
  • From PF 0.75 to 0.95 ⇒ Qc ≈ 664 kVAr → select ~700 kVAr automatic bank
  • From PF 0.70 to 0.95 ⇒ Qc ≈ 830 kVAr → select ~850 kVAr automatic bank
  • From PF 0.90 to 0.95 ⇒ Qc ≈ 187 kVAr → select ~200 kVAr automatic bank

Detailed problem analysis

• Theory
  • Real power P = 1200 kW (given). Reactive power Q is what capacitors supply to raise PF.
  • Power triangle relationships:
  • PF = cosφ
  • tanφ = Q/P
  • Required correction: Qc = P(tanφ1 − tanφ2)
• Worked examples (1200 kW)
  • PF 0.80 → 0.95:
  • φ1 = cos⁻¹(0.80) = 36.87°, tanφ1 ≈ 0.750
  • φ2 = cos⁻¹(0.95) = 18.19°, tanφ2 ≈ 0.329
  • Qc = 1200(0.750 − 0.329) ≈ 505 kVAr
  • PF 0.75 → 0.95:
  • tanφ1 ≈ 0.882; Qc ≈ 1200(0.882 − 0.329) ≈ 664 kVAr
  • PF 0.70 → 0.95:
  • tanφ1 ≈ 1.020; Qc ≈ 1200(1.020 − 0.329) ≈ 830 kVAr
  • PF 0.90 → 0.95:
  • tanφ1 ≈ 0.484; Qc ≈ 1200(0.484 − 0.329) ≈ 187 kVAr
• Practical sizing
  • Round up to next standard rating and use an automatic (stepped) APFC bank for varying load.
  • Typical step plan examples:
  • ~525 kVAr bank: 25 + 50 + 50 + 100 + 100 + 200 kVAr
  • ~700 kVAr bank: 50 + 50 + 100 + 100 + 200 + 200 kVAr
• Current of the bank (useful for switchgear/cable sizing)
  • Istep = Qstep / (√3 × Vline)
  • Example at 480 V:
  • 525 kVAr bank ⇒ I ≈ 525,000 / (1.732 × 480) ≈ 632 A
  • 700 kVAr bank ⇒ I ≈ 700,000 / (1.732 × 480) ≈ 841 A
  • Apply 1.3–1.5× margin for capacitive overcurrent and harmonics when selecting feeders and protective devices.

Current information and trends

• Many U.S. utilities incentivize or require PF ≥ 0.95; penalties may apply below 0.90.
• Detuned (reactor‑protected) capacitor banks are now the default in facilities with VFDs/LED/UPS due to harmonics.
• Hybrid solutions (detuned capacitors + active harmonic filter) are increasingly specified for high-THD plants.

Supporting explanations and details

• Why automatic banks: load and PF vary over time; stepped banks prevent over‑ or under‑compensation and avoid a leading PF at light load.
• Harmonics and detuning:
  • Use 5.67–7% detuning (tuned ≈ 189–210 Hz at 60 Hz) to avoid resonance with 5th harmonic.
  • For severe nonlinearity, pair with an active filter or consider a hybrid APFC panel.
• Capacitor voltage rating:
  • On 480 V systems, use capacitors rated ≥ 480 V; with detuning, many spec 525 V elements to handle the inductor‑induced voltage rise.
• Converting kVAr to capacitance (for reference)
  • Three‑phase delta bank: Cphase = Qc / (6π f Vline²)
  • Three‑phase wye bank: Cphase = Qc / (2π f Vphase²), with Vphase = Vline/√3

Ethical and legal aspects

• Comply with applicable standards: IEEE 18/1036 (application/testing), NEC/UL for installation and component listing, IEC 60831 for LV power capacitors.
• Provide proper labeling, lockout/tagout, and ensure discharge resistors reduce terminal voltage <50 V within 1 minute before access.

Practical guidelines

• Confirm:
  • Present PF (minimum, average, and worst-case)
  • Target PF required by your utility
  • System voltage and short-circuit level
  • Harmonic levels (THDv/THDi) and nonlinear load share
• Specify:
  • Automatic, multi-step, detuned APFC bank
  • Capacitor duty contactors (inrush-rated), current‑limiting fuses, and EMC‑rated wiring
  • Ambient rating and ventilation for the enclosure
• Commissioning/tests:
  • Verify step kVAr, step currents, temperature rise, and that PF controller tracks within set deadband.
  • Post‑install harmonic scan to confirm no resonance.

Possible disclaimers or additional notes

• Numbers above assume balanced three‑phase conditions; unbalance or significant harmonic content can change the required kVAr.
• Do not chase unity PF at all times; aim for 0.95–0.98 to avoid leading PF and overvoltage at light load.

Suggestions for further research

• If harmonics are high, evaluate active harmonic filters vs. larger detuning.
• For rapidly fluctuating loads (welders, cranes), consider thyristor‑switched capacitors (TSC) for sub‑cycle response.
• Review utility tariff PF clauses and demand ratchets to quantify savings vs. capex.

Brief summary

• Capacitor bank size for a 1200 kW load depends on PF correction needed: Qc = 1200 × (tanφ1 − tanφ2).
• Typical results to reach PF 0.95: ~505 kVAr from 0.80 PF, ~664 kVAr from 0.75 PF, ~830 kVAr from 0.70 PF.
• Use an automatic, detuned, multi‑step bank; select the next standard rating up (e.g., 525 kVAr, 700 kVAr, 850 kVAr).

If you share your present PF, target PF, system voltage, and whether you have significant VFD/UPS/LED loads, I’ll size the bank precisely and propose an optimal step configuration.

Disclaimer: The responses provided by artificial intelligence (language model) may be inaccurate and misleading. Elektroda is not responsible for the accuracy, reliability, or completeness of the presented information. All responses should be verified by the user.