## 35 Super Capacitors

Capacitors are devices in which two conducting plates are separated by an insulator. An example is shown in Figure 3.4. A DC voltage is connected across the capacitor, one plate

Opposite charges on plates attract each other, thus storing energy

Positive charge

Negative charge

DC voltage

Figure 3.4 Principle of the capacitor being positive the other negative. The opposite charges on the plates attract and hence store energy. The charge Q stored in a capacitor of capacitance C Farads at a voltage of V Volts is given by the equation:

As with flywheels, capacitors can provide large energy storage, although they are more normally used in small sizes as components in electronic circuits. The large energy-storing capacitors with large plate areas have come to be called super capacitors. The energy stored in a capacitor is given by the equation:

where E is the energy stored in Joules. The capacitance C of a capacitor in Farads will be given by the equation:

d where e is the is the permittivity of the material between the plates, A is the plate area and d is the separation of the plates. The key to modern super capacitors is that the separation of the plates is so small. The capacitance arises from the formation on the electrode surface of a layer of electrolytic ions (the double layer). They have high surface areas, e.g. 1 000 000m2kg-1, and a 4000F capacitor can be fitted into a container the size of a beer can.

However, the problem with this technology is that the voltage across the capacitor can only be very low, between 1 to 3 V. The problem with this is clear from equation (3.5), it severely limits the energy that can be stored. In order to store charge at a reasonable voltage many capacitors have to be connected in series. This not only adds cost, it brings other problems too.

If two capacitors C1 and C2 are connected in series then it is well known1 that the combined capacitance C is given by the formula:

c Ci c2

So, for example, two 3 F capacitors in series will have a combined capacitance of 1.5 F. Putting capacitors in series reduces the capacitance. Now, the energy stored increases as the voltage squared, so it does result in more energy stored, but not as much as might be hoped from a simple consideration of equation (3.5).

Another major problem with putting capacitors in series is that of charge equalisation. In a string of capacitors in series the charge on each one should be the same, as the same current flows through the series circuit. However, the problem is that there will be a certain amount of self-discharge in each one, due to the fact that the insulation between the plates of the capacitors will not be perfect. Obviously, this self-discharge will not be equal in

1 Along with all the equations in this section, a fully explanation or proof can be found in any basic electrical circuits or physics textbook.

all the capacitors; life is not like that! The problem then is that there may be a relative charge build-up on some of the capacitors, and this will result in a higher voltage on those capacitors. It is certain that unless something is done about this, the voltage on some of the capacitors will exceed the maximum of 3 V, irrevocably damaging the capacitor.

This problem of voltage difference will also be exacerbated by the fact that the capacitance of the capacitors will vary slightly, and this will affect the voltage. From equation (3.4) we can see that capacitors with the same charge and different capacitances will have different voltages.

The only solution to this, and it is essential in systems of more than about six capacitors in series, is to have charge equalisation circuits. These are circuits connected to each pair of capacitors that continually monitor the voltage across adjacent capacitors, and move charge from one to the other in order to make sure that the voltage across the capacitors is the same.

These charge equalisation circuits add to the cost and size of a capacitor energy storage system. They also consume some energy, though designs are available that are very efficient, and which have a current consumption of only 1 mA or so. A good review and more detailed explanation of equalisation circuits in capacitor storage systems can be found in Harri and Egger (2001).

A super capacitor energy storage system is shown in Figure 3.5. In this picture, which is of the capacitors used in the bus that was shown in Figure 1.18, we can see capacitors

Figure 3.5 A bank of super capacitors, together with charge equalisation circuits. This is the system from the bus of Figure 1.18 (photograph kindly supplied by MAN Nutzfahrzeuge AG.)

Parry People Mover

Potential operating area for supercapacitors and flywheels

□ Q4___Sodium metal chloride

□ Aluminium air

0.1 1 10 100 1000 Specific energy/Wh/kg

Figure 3.6 Ragone plot of batteries, supercapacitors and flywheels connected in series, and also the charge equalisation circuits mentioned above. A Ragone plot comparing supercapacitors with batteries is shown in Figure 3.6.

In many ways the characteristics of supercapacitors are like those of flywheels. They have relatively high specific power and relatively low specific energy. They can be used as the energy storage for regenerative braking. Although they could be used alone on a vehicle, they would be better used in a hybrid as devices for giving out and receiving energy rapidly during braking and accelerating afterwards, e.g. at traffic lights. Super-capacitors are inherently safer than flywheels as they avoid the problems of mechanical breakdown and gyroscopic effects. Power electronics are needed to step voltages up and down as required. Several interesting vehicles have been built with super capacitors providing significant energy storage, and descriptions of these can be found in the literature. Furubayashi et al. (2001) describe a system where capacitors are used with a diesel IC engine. Lott and Spath (2001) describe a capacitor/zinc-air battery hybrid, and Biichi et al. (2002) describe a system where capacitors are used with a fuel cell.

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