IEEE Power Electronics Magazine - December 2014 - 28
changes the ohmic resistance of
the active mass during discharging. These effects result in an inhomogeneous discharge of porous electrode, especially at higher currents.
Electric and Magnetic Effects
(a)
CDL
ID
IBattery
ICT
RCT
(b)
Positve Electrode
Electrolyte
Negative Electrode
(c)
Cp
RB
LB
Impedance of
Electrodes
(d)
fig 4 The equivalent circuits applicable to different dynamic effects: (a) diffusion effects,
(b) the EDL capacitor effect, (c) the porous electrode case, and (d) high-frequency operation.
(Figure adapted from [1].)
28
IEEE PowEr ElEctronIcs MagazInE
z December 2014
Compared with the slow effects of
mass transport and the EDL, much
faster phenomena are found in a
rechargeable battery. This is due to
the total ohmic resistance (the sum
of the resistances of electrolyte,
current collector, the active mass,
and the transition resistance
between the active mass and the
current collector) and the serial
inductance (based on the geometry
of the cell). For a lead-acid battery,
values between 10 and 100 nH/cell
for 100 Ah cells are reported [1].
This is in addition to the wiring of
the cell. This inductance limits the
slew rate of the current, particularly in large lead-acid systems,
and, in large packs, this inductance
can be of interest above 1-kHz frequencies. For small batteries, much
higher frequencies, such as
10-100 kHz, show the effect of
inductive components. With
increased frequencies, the penetration depth of the ions decreases
and the electrodes act like planar
electrodes. At high frequencies, the
electrode pair becomes a simple
plate capacitor equivalent. A typical value of this high-frequency
interelectrode capacitance for a
lead-acid cell is around 10 nF/cell
[1]. Another important high-frequency effect is the skin effect,
which can come into play depending on the depth of the materials in
the current collectors [1]. The generally applicable equivalent circuits
for various dynamic effects are
shown in Figure 4.
Battery Equivalent Circuit
Models and Modeling
Techniques
From an electronic engineer's
viewpoint, it is most useful to have
an equivalent circuit for a battery
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