Implement generic supercapacitor model
Electric Drives/Extra Sources
The Supercapacitor block implements a generic model parameterized to represent most popular types of supercapacitors. The figure shows the equivalent circuit of the supercapacitor:
The supercapacitor output voltage is expressed using a Stern equation as:
To represent the self-discharge phenomenon, the supercapacitor electric charge is modified as follows (when iSC = 0):
The constants α1, α2, and α3 are the rates of change of the supercapacitor voltage during time intervals (toc, t3), (t3, t4), and (t4, t5) respectively, as shown in the figure:
|Ai||Interfacial area between electrodes and electrolyte (m2)|
|c||Molar concentration (mol/m3) equal to c = 1/(8NAr3)|
|r||Molecular radius (m)|
|isc||Supercapacitor current (A)|
|Vsc||Supercapacitor voltage (V)|
|CT||Total capacitance (F)|
|Rsc||Total resistance (ohms)|
|Ne||Number of layers of electrodes|
|Np||Number of parallel supercapacitors|
|Ns||Number of series supercapacitors|
|QT||Electric charge (C)|
|R||Ideal gas constant|
|T||Operating temperature (K)|
|ε||Permittivity of material|
|ε0||Permittivity of free space|
Specify the nominal capacitance of the supercapacitor, in farad.
Specify the internal resistance of the supercapacitor, in ohms.
Specify the rated voltage of the supercapacitor, in volts. Typical
rated voltage is equal to 2.7 V. Default is
Specify the number of series capacitors to be represented. Default
Specify the number of parallel capacitors to be represented.
Specify the initial voltage of the supercapacitor, in volts.
Specify the operating temperature of the supercapacitor. The
nominal temperature is 25° C. Default is
When this check box is selected, loads predetermined parameters of the Stern model into the mask of the block. These parameter values have been determined from experimental tests, and they can be used as default values to represent a common supercapacitor. Experimental validation of the model has shown a maximum error of 2% for charge and discharge when using the predetermined parameters. Default is cleared
When this check box is selected, the Number of layers, Molecular radius (m), Permittivity of electrolyte material (F/m), and Estimate using test data parameters appear dimmed.
When this check box is selected, you provide test data required for the estimation of the Stern model parameters. Default is cleared. This parameter is available only if the Optimization Toolbox™ is installed.
When this check box is selected, the Charge current (A) and Voltage @ 0 s, 20 s, and 60 s [V_0, V_2, V_3] (V) parameters are enabled. The Use predetermined parameters, Number of layers, Molecular radius (m), and Permittivity of electrolyte material (F/m) parameters appear dimmed.
Specify the number of layers related to the Stern model. Default
Specify the molecular radius related to the Stern model, in
meters. Default is
Specify the permittivity of the electrolyte material, in farad/meter.
Specify the charge current during a constant current charge
test, in amperes. Default is
Specify the supercapacitor voltage, in volts, at 0 s, 20 s,
and 60 s, when the supercapacitor is charged with a constant current
equal to the value provided in the Charge current (A) parameter.
[0.161 2.7 7.8].
When this check box is selected, you provide test data required for modeling the self-discharge phenomenon. Default is selected.
Specify the current prior to an open-circuit event, in amperes.
Specify the supercapacitor voltage, in volts, at 0 s, 10 s,
100 s, and at 1000 s, when the supercapacitor is open-circuit. The
corresponding current prior to open-circuit is given in the Current
prior open-circuit (A) parameter. Default is
47.8 47.06 44.65].
When this check box is selected, the block plots a figure containing the charge curves at the specified charge currents and time units. Default is cleared.
Specify the charge currents, in amperes, used to plot the charge
characteristics. Default is
[10 20 100 500].
Specify the time units (seconds, minutes, hours) used to plot
the charge characteristics. Default is
Outputs a vector containing measurement signals. You can demultiplex these signals using the Bus Selector block.
|1||The supercapacitor current||A|
|2||The supercapacitor voltage||V|
|3||The state of charge (SOC), between 0 and 100||%|
The SOC for a fully charged supercapacitor is 100% and for an empty supercapacitor is 0%. The SOC is calculated as:
Internal resistance is assumed constant during the charge and the discharge cycles.
The model does not take into account temperature effect on the electrolyte material.
No aging effect is taken into account.
Charge redistribution is the same for all values of voltage.
The block does not model cell balancing.
Current through the supercapacitor is assumed to be continuous.
shows a simple hybridization of a supercapacitor with a battery. The
supercapacitor is connected to a buck/boost converter and the battery
is connected to a boost converter. The DC bus voltage is equal to
42V. The converters are doing power management. The battery power
is limited by a rate limiter block, therefore the transient power
is supplied to the DC bus by the supercapacitor.
 Oldham, K. B. “A Gouy-Chapman-Stern model of the double layer at a (metal)/(ionic liquid) interface.” J. Electroanalytical Chem. Vol. 613, No. 2, 2008, pp. 131–38.
 Xu, N., and J. Riley. “Nonlinear analysis of a classical system: The double-layer capacitor.” Electrochemistry Communications. Vol. 13, No. 10, 2011, pp. 1077–81.