Bulk Capacitor Hold-Up Energy

E = 0.5 × C × (V1² − V2²)

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Formula

E = 0.5 × C × (V1² − V2²)

Description

Bulk capacitors provide energy during brief power interruptions or load transients. The usable energy is not the total stored energy but only the difference between the energy at the starting voltage and the energy at the minimum acceptable voltage. A capacitor charged to 12V that can discharge to 10V provides only 36% of its total stored energy. This formula is essential for sizing hold-up capacitors in power supplies, ride-through capacitors for motor drives, and energy storage for peak load handling.

Variables

  • E — Usable energy between V1 and V2 (J)
  • C — Capacitance (F)
  • V1 — Initial (fully charged) voltage (V)
  • V2 — Minimum acceptable voltage (V)

Practical Notes

Hold-up time = E / P_load. For a 20W load requiring 20ms hold-up from 12V to 10V: C = 2 × 0.020 × 20 / (144 - 100) = 18.2 mF. Use electrolytic or supercapacitors for bulk energy storage. Account for capacitor aging (electrolytic capacitors lose 20-30% capacitance over their lifetime) and temperature derating.

Related Formulas

Decoupling Capacitor Impedance Capacitor Ripple Current (Buck)

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