Supercapacitor

Generic supercapacitor model

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Libraries:
Simscape / Electrical / Specialized Power Systems / Sources

Description

The Supercapacitor block implements a generic supercapacitor model. This figure shows the equivalent circuit of the supercapacitor:

The capacitors C₁, C₂, and C₃ have fixed capacitances. The capacitance of capacitor C_v depends on the voltage across it. The resistors R₁, R₂, and R₃ have fixed resistances.

The equation for the current through the first branch of the supercapacitor depends on the voltage across the capacitors in the branch,

$$i_1=\{\begin{array}{cc}\left(C_1+K_v{V}_{C_1}\right)\frac{d{V}_{C_1}}{dt}& \text{if }{V}_{C_1}>0\\ C_1\frac{d{V}_{C_1}}{dt}& \text{if }{V}_{C_1}<0\end{array}$$

where:

• V_C1 is the voltage across the capacitors in the first branch.

• C₁ is the capacitance of the fixed capacitor in the first branch.

• K_v is the voltage-dependent capacitance gain.

• i₁ is the current through the first branch.

This equation defines the current through the remaining branches:

$i_n=C_n\frac{d{V}_{C_n}}{dt},$

where n is the number of the branch in the range [2,3] and C_n is the capacitance of the nth branch.

The block derives the values of the resistors (R₁, R₂, and R₃), capacitors (C₁, C₂, and C₃), and K_v from the block parameters by using the methodology in [1].

Ports

Conserving

V+ — Positive terminal

specialized electrical

Specialized electrical conserving port associated with the supercapacitor positive terminal.

V- — Negative terminal

specialized electrical

Specialized electrical conserving port associated with the supercapacitor negative terminal.

Output

m — Measurement signals

vector of three elements

Measurement signals. You can demultiplex these signals using the Bus Selector block.

Signal	Definition	Units	Symbol
1	Supercapacitor current	A	Current
2	Supercapacitor voltage	V	Voltage
3	State of charge (SOC), in the range [0,100]	%	SOC

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Parameters

Rated capacitance (F) — Nominal capacitance of supercapacitor

99.5 (default)

Nominal capacitance of the supercapacitor, in farad.

Equivalent DC series resistance (Ohms) — Internal resistance of supercapacitor

8.9e-3 (default)

Internal resistance of the supercapacitor, in ohms.

Rated voltage (V) — Rated voltage of supercapacitor

48 (default)

Rated voltage of the supercapacitor, in volts. Typical rated voltage is equal to 2.7 V.

Number of series capacitors — Number of series capacitors

18 (default)

Number of series capacitors to be represented.

Number of parallel capacitors — Number of parallel capacitors

1 (default)

Number of parallel capacitors to represent.

Initial voltage (V) — Initial voltage of supercapacitor

0 (default)

Initial voltage of the supercapacitor, in volts.

Operating temperature (Celsius) — Operating temperature of supercapacitor

25 (default)

Operating temperature of the supercapacitor. The nominal temperature is 25° C.

Stern

Number of layers — Number of layers

1 (default)

Number of layers related to the Stern model.

Molecular radius (m) — Molecular radius

1e-9 (default)

Molecular radius related to the Stern model, in meters.

Permittivity of electrolyte material (F/m) — Permittivity of electrolyte material

6.0208e-10 (default)

Permittivity of the electrolyte material, in farad/meter.

Self-discharge

Current prior open-circuit (A) — Current prior to open-circuit event

10 (default)

Current prior to an open-circuit event, in amperes.

Voltage @ 0 s, 10 s, 100 s, and 1000 s [V_oc, V_3, V_4, V_5] (V) — Supercapacitor voltage at 0 s, 10 s, 100 s

[48 47.8 47.06 44.65] (default)

Supercapacitor voltage, in volts, at 0 s, 10 s, 100 s, and at 1000 s, when the supercapacitor is open-circuit. Specify the corresponding current prior to open-circuit in the Current prior open-circuit (A) parameter.

References

[1] Zubieta, L. and R. Bonert. "Characterization of Double-Layer Capacitors for Power Electronics Applications." IEEE Transactions on Industry Applications, Vol. 36, No. 1, 2000, pp. 199-205.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2013a

R2024b: Internal implementation has changed

The internal implementation of the Supercapacitor block has changed. The block no longer models the self-discharge effects and the ability to load predetermined parameters or test data of the Stern model.

As a result of this change, these parameters have been removed:

• Use predetermined parameters

• Estimate using test data (requires the Optimization Toolbox)

• Charge current (A)

• Voltage @ 0 s, 20 s, and 60 s [V_0, V_2, V_3] (V)

• Simulate self-discharge

• Plot charge characteristics

• Charge current [i_1, i_2, i_3, ...] (A)

• Time units