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# Power density Ultracapacitor

The power density of a capacitor is the amount of power it can produce for a given volume. For instance, capacitors have a greater power density than batteries as they are able to deliver energy much faster than batteries can. A small capacitor can have a much higher power density than a large battery, even though a battery may have a higher energy density. In other words, power is the rate of using energy. The power density of a capacitor is usually expressed as potential energy per gram or per unit volume.

The energy stored in the Capacitor: E=½ CV2 where C is the capacitance (F) and V is the charging voltage.

##### Energy needed: 85 kWhCharging voltage V=600

Relative permittivity k=16 million (This is the highest value for dielectric constant reported in open literature.

Area of a single layer capacitor
A=20cm x 20 cm=400 cm2
Thickness of the dielectric
t=20 x10-6

For a unit of 85 kWh the total capacitance (called geometrical capacitance) is:

• C= 2E/V2 = 2 x 85 000 x 3600/(600)2= 1,700 F
• Capacitance 1 layer:  (=Ԑ0*kA/t): 0.2832 F/layer
• Energy density: 5,900 Wh/lit
• Specific Energy Density:  1,734 Wh/kg
• Gravimetric Power Density Ultracapacitor | frequency is 1:  7,780 W/kg
• Total weight energy storage device  stacked layers only:  49 kg

There are many advantages of solid state devices over Li-Ion batteries (no environmental pollution, millions of charging and discharging cycles and very fast charging to mention a few) the only disadvantage of super capacitor is the inability to hold the steady voltage during the discharging cycle under load.

The voltage in super capacitor will decrease steadily and the rate of voltage decrease depends on the load.

Higher loads will cause the voltage to drop faster. The solution to this problem is to fabricate higher power unit with high energy density.

#### Ceramic-based single layer energy storage device.

With such high power density (high kWh/kg) super capacitors, it would be possible to put on board several units and discharge one unit after another until the voltage in each unit drops below a certain value.

In this way it will be possible to keep the voltage high during the entire life of the battery set. This can easily be done using today’s modern electronics.

Due to the nature of material (the charge is stored on the surface of the dielectric/metal) charging the capacitor depends on the power to be stored. If the power is low (several kWh) charging is done in seconds.

If the energy is high, e.g. 50 or 80 kWh, charging can take several minutes provided the charging station has high enough voltage and current. Charging of several layers, as already demonstrated in our lab, have shown a full charge of the layers in less than a second.

#### Self-discharging Li-Ion batteries:

Self-discharging of Li-Ion Battery discharges is about 5 percent in the first 24 hours and then loses 1–2 percent per month; the protection circuit adds another 3 percent per month. In general, the self-discharge of all battery chemistries increases at higher temperature, and the rate typically doubles with every 10°C (18°F).

A noticeable energy loss occurs if a battery is left in a hot vehicle. High cycle count and aging also increase self-discharge of all systems.

#### Predicted self-discharging of UltraCaps’s ESD:

The self-discharging of super capacitor is similar to Li-Ion Battery except that the temperature effect is smaller and the device should be able to hold the charge for up to 20-30 days. EEStor claims their unit to be able to hold the electricity for 2 to 3 months.

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