Impedance-Based Simulation Models of Supercapacitors and Li-Ion ...

BULLER et al.: IMPEDANCE-BASED SIMULATION MODELS OF SCs AND Li-ION BATTERIES 745
Fig. 8.
Current profile for the verification of the SC model.
Fig. 10. Comparison of the measured voltage response and the data obtained
from different simulation models.
TABLE I
COMPARISON OF MEASURED AND SIMULATED EFFICIENCY DATA.WORKING
POINT: 1.5 V, ROOM TEMPERATURE, CYCLE DEPTH 615% Q
Fig. 9.
Measured and simulated voltage response to the current profile.
V. VERIFICATION AND APPLICATION OF THE MODELS
As a final step, the results of the simulation models are compared
with measured data in the time domain. Both, the SC
model as well as the model of the Li-ion battery have been verified
in detail [1]. In this section, some examples of these verification
measurements are given.
For the verification of the SC model, the current profile depicted
in Fig. 8 has been employed [2]. The imposed charging
and discharging pulses model a highly dynamic load at the beginning
as well as deeper charging and discharging periods at
the end of the evaluation. The corresponding voltage curves are
depicted in Fig. 9. The measured and the calculated data show
excellent agreement.
The influence of the porous structure of the SC electrodes
can be illustrated by means of a comparison of the full simulation
model with the voltage response of the simplified model
which only consists of a series connection of the ohmic resistance
and the capacitance of the SC. For this comparison,
Fig. 10 provides an enlarged view of the first current pulses of
the verification profile. Once more, the excellent agreement of
the measured and simulated voltage data becomes obvious. In
addition, remarkable deviations due to the neglect of porosity
are observed for the simplified model. For low frequencies, i.e.,
for comparably long relaxation times, these deviations could be
overcome by replacing the ohmic resistance by the larger dc
resistance with being the resistance of the
electrolyte in the pores of the electrodes [2]. In this case however,
the fast voltage transients would not be well represented
anymore.
One advantage of SCs used as energy storage devices is their
good energy efficiency. This efficiency is also influenced by
the porous structure of the electrodes which means that the increasing
real part of the impedance with decreasing frequency
has to be taken into account.
To compare measured and simulated efficiency data, an SC
is partly charged and discharged with constant dc currents of
various amplitudes. The cycle depth is chosen to be 540 A s
which corresponds approximately to . For each current
amplitude, the charge/discharge cycle is repeated ten times
but only the last five cycles, which start and finish at the same
internal conditions (quasi-stationary), are used for the efficiency
calculation. In a second step, the same current profile is simulated
by means of the newly developed capacitor model. Measured
and simulated efficiency data are compared in Table I.
Again, very good agreement is observed.
Next, a simulation example of the Li-ion battery model is
presented. For the model verification, the dynamic discharge
current profile depicted in Fig. 11 has been selected. The
comparison of the simulated and the measured voltage response
to this current profile at a state of charge of 77.5% and
room temperature is shown in Fig. 12. Excellent agreement
of the measured and the simulated voltage curves is found.
The outstanding accuracy of the simulation model is due to
the exact representation of the complex battery impedance
including all important nonlinearities.
An important precondition for the high quality of the simulation
results is the nearly perfect reproducibility of the battery
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