Battery Run Time (DoD/Efficiency)
Run time from capacity, load, depth of discharge and system efficiency
Calculation
Quick Introduction
Real battery run time is determined by more than rated Ah alone. Usable depth of discharge and total system efficiency significantly affect available energy.
This calculator helps estimate run time, required battery capacity, or admissible load for a target autonomy period.
Sizing schema:
1) Define average load power
2) Set DoD and overall efficiency
3) Solve for run time or required Ah
Formulas (MathJax)
\[E_{nom}=U\cdot C_{Ah}\]
\[E_{usable}=E_{nom}\cdot\frac{DoD}{100}\cdot\frac{\eta}{100}\]
\[t=\frac{E_{usable}}{P}\]
\[C_{Ah}=\frac{P\cdot t}{U\cdot(DoD/100)\cdot(\eta/100)}\]
Symbol Legend
- \(U\): battery voltage [V]
- \(C_{Ah}\): battery capacity [Ah]
- \(P\): average load power [W]
- \(DoD\): depth of discharge [%]
- \(\eta\): total efficiency [%]
- \(E\): energy [Wh]
- \(t\): run time [h]
Examples
Example 1: \(U=12\,V\), \(C=100\,Ah\), \(P=120\,W\), \(DoD=80\%\), \(\eta=90\%\) ⇒ \(E_{usable}=864\,Wh\), run time \(t\approx7.2\,h\).
Example 2: target \(t=10\,h\) at \(P=150\,W\), \(U=24\,V\), \(DoD=70\%\), \(\eta=92\%\) ⇒ required capacity \(\approx97\,Ah\).
Detailed Description & Summary
The energy-balance model gives a practical first estimate for off-grid systems, backup power, and mobile storage design. For detailed engineering, include temperature effects, battery aging, current-dependent capacity, and transient peaks.
For longer service life, many battery chemistries are operated with conservative DoD values instead of full discharge cycles.
Summary
- Computes run time from capacity, load, DoD, and efficiency
- Determines required Ah for a target autonomy
- Calculates maximum admissible load for a required run time
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