Battery efficiency and losses

The battery efficiency is defined as:

\(Effic = (EDischarge + ESOCbal) / ECharge\)

where

• ECharge and EDischarge are energies injected and drawn from the battery,
• ESOCBal is the stored energy between the beginning and the end of the interval (SOC variation).

The battery efficiency is only pertinent over a sufficiently long period, so that the ESOCbal is a little contribution with respect to the EDischarge value.

The efficiency calculation involves taking all losses into account:

At a given time step, the battery current is either positive, or negative, i.e. the battery is either charging or discharging. A time step is one hour of simulation, or a fraction of hour if we have a control condition change during the hour (charging OFF, discharging OFF, etc).

The efficiency includes the following losses:

• The ohmic loss, due to the internal resistance,
• The loss of current due to the Coulombic or Faradic efficiency,
• The self-discharge loss, permanent,
• Losses during the overcharging conditions (Gassing in Lead-acid, resistance increase in Li-Ion).
• A pseudo loss, due to the variability of the capacity.

Efficiency evaluation

The efficiency over a running period cannot be accurately recalculated from the accumulated values because:

• The ohmic losses are proportional to the square of the current, IBattery²
• The capacity is dependent on the instantaneous conditions (charge/discharge rate), therefore the SOC evolution is only valid with instantaneous values,
• The voltage is specific to each operating condition, we cannot use an average voltage,
• The temperature, acting on the voltage or the resistance, may vary during the period.

Therefore the results in the final loss diagram cannot be quite consistent. The battery efficiency evaluation is made on the final accumulated values (loss energies). Namely due to the sensitivity to the capacity variations, it may vary depending on the load power distribution (ESOCCharge and ESOCDischarge are not well defined).

NB: You will find a more detailed description on the page describing the use of the battery model during the simulation.