Environmental Engineering Reference
In-Depth Information
during discharge. The extent of charge loss and diffusion into the bulk of the plate
are shown to be discharge rate and duration dependent. A bar chart illustrates the
dynamics of discharge, and an integral over the plate results in a measure of
remaining energy for the next discharge. The model is more accurate than SOC
based modelling. A lumped parameter description of the model is proprietary and
unavailable.
Another lumped parameter battery model that has been shown to correlate well
for both NiMH and lithium ion performance is described in Figure 10.46 [32]. This
model derives from the highly porous surfaces of these advanced batteries and
provides a reduced order model of a highly distributed equivalent circuit.
R
dist
R
electrolyte
+ V
o
V
oc
C
dist
Figure 10.46 Advanced battery lumped parameter model
In Figure 10.46 the equivalent circuit of a highly distributed model, or
Randle's equivalent, consists of a series resistance (may also model inductance) - a
parallel network representing the distributed double layer capacitance and charge
transfer resistance and the internal potential. The series resistance is the sum of
contact, inter-cell connections, electrodes and electrolyte. The model parameter is
given as electrolyte based because this constituent exhibits the strongest contribu-
tion to series resistance and moreover it is previous history, SOC and temperature
dependent. Charge stored in the interface and phase boundary is modelled as a
double layer capacitor. The kinetics of the main reaction is modelled as a non-linear
charge transfer resistance. Not shown in the model, but easily included in series
with the charge transfer resistance, shown as
R
dist
, is a model of the diffusion
process modelled as a Warburg impedance
Z
w
, if included.
Advanced battery development for hybrid vehicles has received considerable
impetus from the US Department of Energy and the Office of Transportation
Technologies in cooperation with industry. Chester Motloch
et al
. [33] note that
