Battery C-rate and runtime equations
Pack calculations use volts, ampere-hours, and current. Project calculations use MW and MWh. Both apply the selected SOC window, SOH, and efficiency to estimate delivered energy.
E = V × AhC-rate = I / AhP-rate = MW / MWht = Erated × ΔSOC × SOH × η / Pwhere:
- E
- Battery energy[Wh, kWh, or MWh]
- Ah
- Charge capacity[Ah]
- ΔSOC
- Upper SOC minus lower SOC as a decimal
- SOH
- Remaining state-of-health factor
- η
- Discharge efficiency
- t
- Estimated constant-power or constant-current runtime[h]
Real runtime depends on voltage sag, cell chemistry, temperature, C-rate, BMS cutoff, PCS efficiency, auxiliary power, degradation, and warranty limits.
How to calculate battery runtime
Choose pack-level V/Ah/A inputs or project-level MW/MWh inputs. Then apply upper and lower SOC limits, state of health, and discharge efficiency to estimate usable delivered energy and runtime.
- Calculate rated energy.
- Apply SOC operating window.
- Apply SOH and efficiency.
- Divide usable energy by discharge power.
- Check BMS, PCS, temperature, and warranty limits.
Pack C-rate example
A 48 V, 200 Ah pack stores 9.6 kWh nominally. At 100 A the rate is 0.5C. With an 80% SOC window, 100% SOH, and 95% efficiency, delivered energy is about 7.3 kWh and constant-voltage runtime is about 1.52 hours.
C-rate = 100 / 200 = 0.5C
Eusable = 9.6 × 0.8 × 1.0 × 0.95 = 7.30 kWh
BESS P-rate and duration
A 50 MW / 200 MWh system has a 0.25P nameplate rate and four-hour nameplate duration. Operating SOC window, degradation, PCS loss, and auxiliaries reduce delivered duration.
Why actual runtime differs
Cell voltage changes during discharge, capacity depends on temperature and rate, BMS cutoffs limit the usable window, and converters have load-dependent losses. Use guaranteed usable-energy and power curves for final project commitments.
Assumptions
- Constant discharge current or power
- SOC, SOH, and efficiency are independent planning factors
- Voltage sag, auxiliary consumption, temperature, and BMS cutoff dynamics are not modeled
Important Warnings
- Battery runtime is not perfectly linear at all C-rates, temperatures, chemistries, or ages.
- Use BMS limits, cell data, warranty conditions, PCS efficiency curves, and guaranteed usable-energy definitions for final design.