Efficiency - Battery Design

When you charge and then discharge a battery cell you lose energy, the ratio of the amount of discharge to charge energy is the efficiency.

If we put 11 Wh into a battery cell when charging and recover 10 Wh when discharging the energy efficiency = 10 / 11 = 90.9%

Typical energy efficiencies:

Lead acid ~70%

Coulombic Efficiency

Also known as Faradaic Efficiency, this is the charge efficiency by which electrons are transferred in a battery. It is the ratio of the total charge extracted from the battery to the total charge input to the battery over a full cycle.

Coulombic efficiency values:

Lead acid ~85%
Lithium ion >99%

High coulombic efficiency usually indicates a long battery cycle life.

Q_n=Q_0 CE^n

Coulombic Efficiency, CE [%]	Cycles, n
99	35
99.9	356
99.95	713
99.99	3566

Table shows number of cycles to 70% state of health.

n=\frac{ln(Q_n/Q_0)}{ln(CE)}=\frac{ln(0.7)}{ln(CE)}

Initial Coulombic Efficiency

The ratio of the first discharge capacity to the first charge capacity in a battery, representing the percentage of charge recovered after the initial cycle.

Voltaic Efficiency

This is the ratio of the average discharge voltage to the average charge voltage over a cycle. The charging voltage is always higher than the rated voltage to activate the chemical reaction within the battery and hence losses.