IEEE Power Electronics Magazine - December 2014 - 26

heat generated within the battery. The dynamics of these
temperature variations can range from seconds to several hours.

Mass transport Effects

Within a battery, the transport of ions is due to diffusion
caused by the gradient in concentration and migration due
to forces of electric fields within the chemical system, and
these cases may act in different directions. Migration is
long-term Effects
often hindered by solvated molecules that cover the ion. In
Aging, reversible, cycling, and SOC effects are considered
most cases, diffusion is largely responsible for the mass
longer-term phenomena, and their dynamics occur within
transport. Diffusion occurs at different inside locations of
minutes to years of time durations. These are related to the
an electrochemical cell: more details
operation regime of the battery.
are summarized in [24].
Inside a battery, there are three
aging Effects
Rechargeable
batteries
separate
primary parts, which are
Aging influences the battery performainly
responsible
for the chemical
mance and the output parameters sigand supercapacitors are
reactions. They are the positive and
nificantly. The time domain for battery
two complementary
negative electrodes and the elecaging is typically in the range of
device families that are
trolyte. A porous separator is in the
months to years.
middle of the battery between the
growing rapidly.
two electrodes. Figure 2(a) shows a
reversible Effects
typical case of an Li-ion cell, with a
Most electrochemical storage systems
porous negative electrode made of
show reversible effects. These occur
graphite and a porous positive electrode with a polypropylduring cyclic operations and can be regenerated by special
ene separator immersed in the electrolyte. More details of
charge-discharge regimes. For example, vented lead-acid
such a simple schematic, used in the estimation of capacity
batteries show acid stratification that can be removed by
fade models for Li-ion batteries, are discussed in [3].
an extended charge. In nickel-cadmium cells, the memFigure 2(b) portrays the three locations where diffusion
ory effect is another example, which can be cleared by
can take place. As the battery has two electrodes, the difapplying one or more full charge-discharge cycles. Time
fusion within the porous electrode and within the active
constants of a few hours to one year are effective in
mass occur in both electrodes. In such a case, the diffusion
these processes.
occurring can be described by Fick's first law [1], [24], and
temperature is a key influencing factor.
cycling and soc Effects
The time constant representing the diffusion also
If a battery is charged or discharged, its SOC is changed,
depends on the electrolyte concentration, the electrode
and this itself is a dynamic characteristic of a battery. In
thickness, and the structure to a great degree, with typical
addition, the open circuit or the terminal voltage itself is a
time constants in the range of seconds to minutes [1]. Elecfunction of the SOC. The time domain of SOC change or
trochemical impedance spectroscopy (EIS), or measuring
cycling depends on the operational conditions with a time
the response of a battery to an excitation of a small amplidomain from several minutes to days.
tude signal of a voltage or a current to estimate the small
During the cycling process, the battery heats up due
signal impedance of the cell, is frequently used to analyze
to internal heat sources such as ohmic heating or any
the dynamic behavior of the batteries due to mass transother chemical reactions. The ohmic heat can be heavily
port effects [1], [4].
influenced by the charge/discharge current profiles. If we
assume that there will be only Joule loss, heating power can
be estimated by
Double-layer Effects
The electrical double-layer (EDL) effect is a phenomenon
present in supercapacitors and batteries. When two elecPloss = R int I 2eff ,
(2)
trodes are placed in an electrolyte, due to the action of the
electrolyte, two charged layers develop on both ends of the
where Ploss is the power dissipated due to ohmic resiselectrolyte, which is equivalent to two capacitors in series,
tances due to an overall internal effective resistance of R int
and this is called a double-layer capacitor. Due to the large
and the I eff is the effective current based on the wave
surface areas of porous electrodes, a high-capacitance surshape. As per the GSM example in Figure 1(b), the root
face layer is formed next to the electrodes and creates the
mean square (rms) value of the current is estimated as 0.73
double-layer effect [5].
A and the average current is 0.42 A. With a form factor of
Recent research publications [6] indicate that electro1.73, which is the heat generated due to the rms current
chemistry-based impedance models for battery chemistries,
due to pulse transmission, it generates 3# bigger power,
such as Li-ion, can be developed to achieve a better undercalculated based on the average current of the waveform.
standing of battery dynamics. In this process, the charge
More discussion on the subject of waveform parameters
transfer reaction happening on the electrode/electrolyte
can be found in [2].

IEEE PowEr ElEctronIcs MagazInE

z December 2014

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