Battery efficiency and losses
A component loss or efficiency is the difference between the energy going in and out. In the battery case, knowing the difference between the In/Out energy during a certain period is not sufficient, as the battery may hold more or less energy than in its original state.
In practice, the battery efficiency can only be reliably measured after a certain number of charging and discharging cycles, when any internal energy variation will be negligible compared to the total energy exchanged.
In simulation, the battery losses are known at any given point, so the battery efficiency is also always defined. This does not mean the instantaneous battery loss value is representative. The loss model is not symmetrical, notably with the Coulombic efficiency being only applied on the charging current. Battery losses should always be considered when the \(\Delta \textsf{SOC}\) is 0.
Global Losses
The global battery loss (EBatLss) is defined as: $$ \textsf{EBatLss} = \textsf{EBatCh} - \textsf{EBatDis} - \textsf{ESOCBal} $$ 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: $$ \textsf{EffBatE} = \frac{\textsf{EBatDis} + \textsf{ESOCBal}}{\textsf{EBatCh}} $$ 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),
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 / CapaRef | |
| SOC state | SOCend = SOCbeg + IBattery × DTime / CapaRef | |
| Eself-disch | Self-discharge permanent current (loss) | |
| ESOCBal (discharging) | Stored energy: VOCbattery × IBattery × DTime / CapaRef | |
| 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 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).