IEEE Power Electronics Magazine - December 2014 - 27

Effects caused by
Porous Electrodes
Porous electrodes are complex
components. The diffusion of
ions through the porous electrodes is one of the main limiting
factors in batteries. In addition,
the porous structure changes

during discharging, as the volume of
the discharged active mass in most
systems is much higher than the volume of the charged active mass.
This results in a reduction in the porosity during discharging, which, in
turn, leads to lower diffusion. In
general, the active mass of the electrode depends on whether it is the
cathode or the anode. In many systems, the conductivity of the discharged active mass differs from
that of the charged active mass. This

Compared with the
slow effects of mass
transport and the EDL,
much faster
phenomena are found
in a rechargeable
battery.

1

Negative Electrode

0.1

Results for a 12-V Vented Lead-Acid Battery

Positive Electrode

0.01
0.1

1

10
100
Frequency (Hz)

1,000

10,000

(a)
Cdl, p

Cdl, n
RHF

Lp

Ln

Zw, p

-

Zw, n

Rt, p

Rt, n
(b)

Im (Z)/mX

Normalized Battery Current

surface can be simplified by several
assumptions.
1) Electrodes are multiple spherical
particles of identical size and
dynamics
2) The particle material is spatially
homogeneous.
3) The electrodes are of perfect
conductivity.
4) The film growth caused by aging
only happens on the anode surface.
5) The electrolyte, separator, and current collectors are lumped pure
resistors.
Such a set of simplifications
allows us to simplify the cell
based on identical particles, as
shown in Figure 2(c) and (d).
This simplification allows for
the development of a set of mathematical relationships between
the internal dynamics and external measurements to include the
EDL effect. For a lead-acid cell,
the typical double-layer capacitance of the positive electrode
divided by the battery capacity
(in Ah) is from approximately 7
to 70  F/Ah, while, for the negative electrode, it is from 0.4 to
1 F/ Ah. The analytical details are
available in [6], and an overview
on different dynamic effects is
given in [1].
Figure 3(a) shows the frequency response of the two electrodes of a lead-acid batter y
caused by the double-layer effect.
As can be seen, cutoff frequencies for the positive and negative
electrodes are approximately 10
and 100 Hz, respectively, indicating that alternative currents with
a frequency above 100 Hz do not
flow through  the charge transfer
reaction due to filtering by the
double-layer capacitor.

4

f = 0.001
x
fc

2

R2

f=1
x

f = 10 x
f = 100x

f = 0.01
x

f = 0.1 x

RHF x 2

R1

4

Re (Z)/mX
(c)

fig 3 An automotive battery: (a) the frequency response of the two electrodes due to the
double-layer effect (adapted from [1]), (b) the equivalent circuit (adapted from [4]), and (c) a
Nyquist plot (adapted from [4]).

December 2014

z	IEEE PowEr ElEctronIcs MagazInE

27



Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - December 2014

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