Battery efficiency and losses
Global Losses
The global battery loss (EBatLss) is defined as: $$ \text{EBatLss} = \text{EBatCh} - \text{EBatDis} - \text{ESOCBal} $$ where:
- EBatCh is the energy injected into the battery,
- EBatDis is the energy drawn from the battery,
- ESOCBal is the stored energy balance between the beginning and the end of the interval (SOCEnd − SOCBeg).
Additionally, the overall battery efficiency (EffBatE) is defined as: $$ \text{EffBatE} = \frac{\text{EBatDis} + \text{ESOCBal}}{\text{EBatCh}} $$ Note that the battery efficiency is only meaningful over a sufficiently long period, so that ESOCBal is a small contribution with respect to the EBatDis value.
Detailed Losses
The battery efficiency includes the following losses:
- Ohmic losses, due to the internal resistance,
- Current losses due to the Coulombic or Faradic efficiency,
- Self-discharge losses, which are permanent,
- Losses during overcharging conditions (gassing in lead-acid batteries, resistance increase in Li-ion batteries),
- A pseudo-loss due to the variability of the capacity.
The table below shows when each individual loss is applied. Note that the losses applied to the ESOCBal term vary depending on whether the battery is charging or discharging. This state is fixed for each simulation time step.
| Energy | Losses applied | Description |
|---|---|---|
| EBatCh | Charging energy, at VBattery | |
| Eoverload | Overload/overvoltage (gassing with lead-acid, ResInt with Li-ion) | |
| Eohmic | Internal ohmic loss: ResInt × IBattery | |
| Eefficl | Faradic (current) efficiency, reduction of the charging current | |
| ESOCBal (charging) | Stored energy: VOCbattery × IBattery × DTime / Capacity | |
| SOC state | SOCend = SOCbeg + IBattery × DTime / Capacity | |
| Eself-disch | Self-discharge permanent current (loss) | |
| ESOCBal (discharging) | Stored energy: VOCbattery × IBattery × DTime / Capacity | |
| Eohmic | Ohmic loss: ResInt × IBattery | |
| EBatDis | Discharging energy at VBattery |
Efficiency evaluation
The efficiency over a running period cannot be accurately recalculated from the accumulated values because:
- Ohmic losses are proportional to the square of the current, IBattery²
- The capacity depends on instantaneous conditions (charge/discharge rate); therefore, the SOC evolution is only valid when using instantaneous values
- The voltage is specific to each operating condition, so an average voltage cannot be used
- The temperature, which affects voltage and resistance, may vary during the period
As a result, the values shown in the final loss diagram cannot be fully consistent. The battery efficiency evaluation is therefore based on the final accumulated energy losses. In particular, due to the sensitivity to capacity variations, it may depend on the load power distribution (ESOCCharge and ESOCDischarge are not always well defined).
NB: A more detailed description is available on the page describing the use of the battery model during the simulation.