Week 8 Challenge

UC (Ultra Capacitor) Model

Ultracapacitors are electrical energy storage devices that have the ability to store a large amount of electrical charge. Capacitors store energy as a result of their ability to store charge with the amount of charge stored on a capacitor depending on the voltage, V applied across its plates, and the greater the voltage, the more charge will be stored by the capacitor as, Q proportional to V.

For modelling the capacitor following parameter are required

• SOC of the capacitor: The stored charge in an ultracapacitor is characterized by a normalized measure called the state of charge, SOC [0,1]. The state of charge of 0 represents no stored charge and 1 corresponds to full charge.
• Q, charge of capacitor
• OCV, open circuit voltage of capacitor.
• Icap, capacitor current.

The following equations will help in modelling the capacitor.

• `SOC = int(I*eta)/Qdt`
• `Q = C*OCV`
• `OCV = int(I/C)dt`
• `I_(CAP) = frac(SOC.V_(max) - sqrt((SOC.V_(max))^2-((4.R.PUC)/eta)))(2.R)`

Where,

`eta`- efficiency

`R` - lumped resistance of capacitor

`PUC` - requested power from UC

`V_(max)` - maximum voltage of capacitor

`C` - capacitance of the capacitor

The modelling of the UC is done in MATLAB Simulink with the required mathematical equation.

The main subsytem consist of SOC estimation and UC model

The SOC estimation consist of following model

The UC model consist of Current, OCV and charge calculation

1. Current calculation

Using matlab function block

Mathematical relation in function block for calculation of current

2. OCV calculation

The initial voltage is taken as Vmax*Initial_SOC of UC.

3. Charge, Q calculation

The model has simulated for 598s, and a power input is given through a drive cycle input (EUDC) with a gain of4. The result obtained for the above model is as shown below.

OBSERVATION:

• The current is increasing proportionally (sqaure) of the power demanded.
• The SoC and the OCV of the UC decreases as the power drawn from the UC increases.
• The UC instantly provides the demand power without any lag, this shows the UC has greater power density.

CONCLUSION:

The UC model has developed based on the relations between different parameters. The result shows the good power density of the UC. The voltage and SOC of the UC are nearly linear and thus SOC estimation can be done with help of voltage.