Engee documentation

Supercapacitor

Electrochemical double-layer capacitor.

blockType: AcausalElectricPowerSystems.Passive.Supercapacitor

supercapacitor

Path in the library:

/Physical Modeling/Electrical/Passive/Supercapacitor

Description

Block Supercapacitor It is an electrochemical double-layer capacitor (ELDC), which is commonly referred to as a supercapacitor or ultracapacitor. The capacitance values of supercapacitors are orders of magnitude higher than those of conventional capacitors. Supercapacitors can provide bursts of energy because they are able to charge and discharge quickly.

You can simulate any number of supercapacitors connected in series or parallel using a single unit. Supercapacitor. To do this, set the parameters Number of series cells or Number of parallel cells a value greater than 1. The block simulates only the equations for one supercapacitor cell, but at the same time calculates:

  • Output voltage depending on the number of cells connected in series;

  • The current depends on the number of parallel connected cells.

Calculating the output of a multicellular supercapacitor based on the output for a single cell is more efficient than modeling equations for each cell individually.

The figure shows an equivalent circuit for a single cell in a supercapacitor unit. This circuit is a network of resistors and capacitors, which is commonly used to model the behavior of a supercapacitor.

supercapacitor 1

Capacitors , and they have a fixed capacity. Capacitor capacity depends on the voltage on it. Resistors , , and they have fixed resistances. The voltage across each individual fixed capacitor in the supercapacitor unit is calculated as

where

  • – voltage on the unit;

  • – the number of cells connected in series;

  • – branch number. = [1, 2, 3];

  • – current through - the 5th branch;

  • – resistance in -th branch;

  • – voltage across the capacitor in - th branch.

The equation for the current through the first branch of the supercapacitor depends on the voltage across the capacitors in this branch. If the capacitors have a positive voltage, that is

then

or

where

  • – voltage across the capacitors in the first branch;

  • – the capacity of the fixed capacitor in the first branch;

  • – voltage-dependent capacitance gain;

  • – current through the first branch.

For the other branches, the current is defined as:

where

  • – branch number. =[2, 3];

  • – capacity - th branch.

The total current through the supercapacitor unit is:

where

  • – the number of parallel connected cells;

  • – self-discharge resistance of the supercapacitor;

  • – current through the supercapacitor.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# + — positive
electricity

Details

The electrical port represents a positive terminal.

Program usage name

p

# – — negative
electricity

Details

The electrical port represents the negative terminal.

Program usage name

n

Parameters

Cell Characteristics

# Fixed resistances, [R1, R2, R3] — fixed resistance values for each branch
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Specify the resistances for the DC resistors in the individual branches of the supercapacitor as an array.

Units

Ohm | mOhm | kOhm | MOhm | GOhm
Default value

[0.2, 90.0, 1000.0] Ohm
Program usage name

R_fixed_vector
Evaluatable

Yes

# Fixed capacitances, [C1, C2, C3] — fixed capacity values for each branch
F | pF | nF | uF | mF

Details

Specify the individual capacitance values for the constant-capacity capacitors in the supercapacitor as an array.

Units

F | pF | nF | uF | mF
Default value

[2.5, 1.5, 4.0] F
Program usage name

C_fixed_vector
Evaluatable

Yes

# Voltage-dependent capacitor gain — variable capacity coefficient for the first branch
F/V

Details

Specify the variable capacity factor, , for a voltage-dependent capacitor in the first branch of the supercapacitor. For information on determining the variable capacity factor, see 1.

Units

F/V
Default value

0.95 F/V
Program usage name

voltage_dependent_capacitor_gain
Evaluatable

Yes

# Self-discharge resistance — self-discharge resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Specify the self-discharge resistance of the supercapacitor connected between the two terminals.

Units

Ohm | mOhm | kOhm | MOhm | GOhm
Default value

Inf Ohm
Program usage name

R_discharge
Evaluatable

Yes

Configuration

# Number of series cells — number of supercapacitor cells connected in series

Details

Specify the number of cells in the supercapacitor connected in series.

Default value

1
Program usage name

series_capacitor_count
Evaluatable

Yes

# Number of parallel cells — the number of parallel supercapacitor cells

Details

Specify the number of supercapacitor cells connected in parallel.

Default value

1
Program usage name

parallel_capacitor_count
Evaluatable

Yes

Examples