Environmental Engineering Reference
In-Depth Information
Activation polarization
E
oc
Concentration polarization
Ohmic polarization
Useful power
E-discharged
Current
Figure 10.4 Voltage-current behaviour of electrochemical cells
power delivered by the cell. The normal operating voltage, shown as the region
dominated by ohmic polarization, will generally have a very shallow slope until its
end of life. The terminology 'end of useful life' is used to quantify primary cells. In
secondary cells this metric defines the lower limit of state of charge (SOC), typi-
cally 10%, at which point the cell must be recharged. In lithium ion cells, for
example, the discharge must stop before the cell terminal voltage reaches
approximately 68% of open circuit potential. Going below this potential invites the
onset of side reactions if the anode current collector metal (copper) and the elec-
trolyte may irreversibly damage the cell. Typical lower bounds on discharge of
lithium ion cells are 2.5-2.2 V or 2.0 V depending on specific chemistry.
A useful relation for predicting the end of life of an electrochemical cell is the
Peukert equation. This is an empirical relationship in which the current discharged
over a time interval is shown to equal a constant:
I
n
t
¼
k
ð
10
:
14
Þ
which is generally plotted according to (10.15) for values of
n
¼
1.0 for Pb-acid
and NiCd, and
n
¼
0.95 for Li systems:
Log
ð
t
Þþ
n
Log
ð
I
Þ¼
k
ð
10
:
15
Þ
More will be said later of useful life, discharge characteristics, and gravimetric
and energy metrics for several common battery systems used in hybrid propulsion.
A great deal has been written on battery electrochemistry, reliability and modelling.
Principal considerations should be given to long term mechanical and chemical
stability, temperature range of operation (in the case of automotive systems being
30 to
þ
70
C), self-discharge (shelf life), cell reversal, cost, cycle life (ability to
reform electrode materials during recharge) and how well the battery can tolerate
overcharge and overdischarge, both of which are abuse conditions. Battery ambient
temperature is probably the most problematic on this list of attributes because
