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Monitoring sealed automotive lead-acid batteries by sparse-impedance spectroscopy Proc. Indian Acad. Sci. (Chem. Sci.), Vol. 115, Nos 5 & 6, OctoberDecember 2003, pp 465472
©
Indian Academy of Sciences
465

Monitoring sealed automotive lead-acid batteries by
sparse-impedance spectroscopy
¶


B HARIPRAKASH, S K MARTHA and A K SHUKLA*
Solid State and Structural Chemistry Unit, Indian Institute of Science,
Bangalore 560 012, India
e-mail: shukla@sscu.iisc.ernet.in

Abstract.
A reliable diagnostics of lead-acid batteries would become mandatory
with the induction of an improved power net and the increase of electrically assisted
features in future automobiles. Sparse-impedance spectroscopic technique described
in this paper estimates the internal resistance of sealed automotive lead-acid batteries
in the frequency range 10 Hz10 kHz, usually produced by the alternators fitted in the
automobiles. The state-of-health of the battery could be monitored from its internal
resistance.

Keywords.
Impedance spectroscopy; sealed lead-acid batteries; state-of-health;
state-of-charge; internal resistance.
1. Introduction
The state-of-charge (SOC) of a battery is reflected by the electrical response associated
with the batterys resistance and inductance where the application of a load causes the
battery voltage to drop instantaneously. This phenomenon has been targeted by
researchers for determining the batterys resistance, and therefore, as an indicator of its
discharged capacity. Since, open-circuit-voltage of a battery is a fixed quantity and its
discharge circuit is also not altered, it is quite obvious that the internal resistance of the
battery increases with its depth-of-discharge along with its voltage on-charge. Accor-
dingly, if the discharge behaviour of the battery is known a priori then its state-of-health
can be easily estimated. It is noteworthy that with the aging of the battery, the discharge
capacity of the battery decreases owing to an increase in its internal resistance.
Accordingly, the state-of-health (SOH) of any sealed battery can be predicted from a
knowledge of its internal resistance, which could be estimated from electrochemical
impedance spectroscopy.
At present, the lead-acid battery is the most ubiquitous battery in the global
rechargeable battery market and, in terms of value, the present world market for lead-acid
batteries is about US$ 10 billion per annum.
1
The on-going electrification of automobiles
makes a reliable diagnostic necessary for the vehicles energy storage units. Since sealed

¶
Dedicated to Professor C N R Rao on his 70th birthday
*For correspondence
State-of-charge of a battery is the fraction usually expressed as percentage of the full capacity of
the battery that is still available for further discharge A measurement that reflects the state-of-health of a battery, taking into account its charge accep-
tance, internal resistance, voltage and self-discharge B Hariprakash et al
466
lead-acid batteries are supposed to become the most important battery storage technology
for the near-term future vehicles, monitoring and diagnostic algorithm for these batteries
are of great importance. Besides, with the induction of 36V/42V power net and the
increase of electrically-assisted features e.g. idle/stop operation, launch assistance etc.,
the importance of a suitable battery monitoring and management will increase even
further. In the literature, several methods are employed to monitor the SOH of various
battery systems.
225
In this article, we describe on-line monitoring of sealed automotive
lead-acid batteries by electrochemical sparse-impedance spectroscopy,
26
which is
believed to find application in future automobiles.
2. Operating principle of sealed lead-acid batteries
The conventional flooded-type lead-acid battery requires checking of the specific gravity
of the electrolyte, periodic addition of water to maintain electrolyte level above the plates
and recharge soon after discharge to prevent hard sulphation that causes loss of capacity.
The emission of acid fumes from these batteries causes corrosion of metallic parts in the
vicinity of the battery. Furthermore, seepage of acid on the top cover of the batteries
leads to leakage current resulting in increased self-discharge and ground-shunt hazard. To
overcome these problems, valve-regulated lead-acid (VRLA) or sealed lead-acid (SLA)
batteries based on a oxygen-recombination cycle have emerged. SLA batteries offer the
freedom of battery placement, cyclability without the need for addition of water or
checking the specific gravity, increased safety and superior performance in some
instances.
The electrochemical reactions taking place at the positive and negative electrodes of a
lead-acid battery are as follows.
At the positive electrode:

PbO
2
+ H
2
SO
4
+ 2H
+
+ 2<i>e
PbSO
4
+ 2H
2
O,
(E
°
= 1 69 V vs SHE). (1)

At the negative electrode:
Pb + H
2
SO
4
PbSO
4
+ 2H
+
+ 2<i>e , (E
°
= 0 36 V vs SHE). (2)
Accordingly, the net cell reaction is given by:
PbO
2
+ Pb + 2H
2
SO
4
2PbSO
4
+ 2H
2
O, (E
cell
= 2 05 V). (3)
Thermodynamic stability of the electrolyte requires that its lowest unoccupied state
have a higher energy than the highest occupied state of the reductant and its highest
occupied state have a lower energy than the lowest unoccupied state of the oxidant
(figure 1).
27
If either of these two conditions is violated, electrons may be transferred to
or from the electrolyte to reduce or oxidise it. Therefore, the requirement for
thermodynamic stability of the electrolyte restricts the cell voltage (E
cell
) to be always
less than the thermodynamic window (E
g
) of the electrolyte.
discharge
charge
discharge
charge
discharge
charge Monitoring sealed automotive lead-acid batteries
467


Figure 1.
Reaction window for an aqueous electrolyte electrochemical cell with
solid metallic reactants.




Figure 2.
Potential of Pb/PbSO
4
and PbO
2
/PbSO
4
electrodes under equilibrium and
during gas evolution.


Both PbO
2
and Pb are thermodynamically unstable in sulphuric acid solution. The
equilibrium potential of PbO
2
/PbSO
4
couple is more anodic to O
2
/H
2
O couple by 0 46 V
and the equilibrium potential of Pb/PbSO
4
is more cathodic to H
2
/H
+
couple by 0 36 V as
shown in figure 2. Hence, even under open-circuit conditions, O
2
evolution at the PbO
2

electrode and H
2
evolution at the negative electrode can occur according to the reactions,

PbO
2
+ H
2
SO
4
PbSO
4
+ H
2
O + ½ O
2
, (4)

Pb + H
2
SO
4
PbSO
4
+ H
2
. (5)

The rates of reactions (4) and (5) increase with acid concentration. Therefore, the lead-
acid cell should not work in principle but in practice however the high O
2
and H
2

overpotentials on PbO
2
and Pb enable the respective electrodes to be charged before O
2

and H
2
evolve at a substantial rate. In the lead-acid cell, it is the poor kinetics at the
electrodeelectrolyte interface that allows a cell voltage higher than the thermodynamic B Hariprakash et al
468
window (E
g
) of 1 23 V between the lowest unoccupied molecular orbital (LUMO) of the
H
2
/H
+
redox energy and the highest occupied molecular orbital (HOMO) of the O
2
/H
2
O
redox energy.
28

The positive electrode in a lead-acid cell accepts charge less efficiently than the
negative electrode. Therefore, O
2
and H
2
are evolved non-stoichiometrically during the
recharge of a lead-acid battery with O
2
evolution occurring prior to H
2
evolution. The
oxygen evolved at the positive electrode is constantly reduced at the electrode as follows.

O
2
+ 2Pb + 2H
2
SO
4
2PbSO
4
+ 2H
2
O. (6)

This feature is the mainstay of the design of SLA batteries.
29

3. Sparse-impedance spectroscopy on sealed lead-acid batteries
The electrical behaviour of battery half-cell can be described using the Randles
equivalent circuit
4,26
shown in the figure 3a. In this case, only one electrode is modelled,
but apart from different value for the parameters such as different time constants, the
basic model can be used for both the electrodes. The equivalent circuit in figure 3a shows
an ohmic resistance (R
i
), which is due to the limited conductance of the contacts, the
inter-cell connections, the electrodes and the electrolyte, and depends on the SOC of the
battery, on its previous usage and on its age. The inductance (L) in figure 3a is mainly
caused by the met