Environmental Engineering Reference
In-Depth Information
E
c
¼
1
2
C
V
2
ð
5
:
32
Þ
whereas the capacitance C (F) of the capacitor is given by the equation:
C
¼
e
A
d
ð
5
:
33
Þ
where e (Farad per meter) is the permittivity of the material between the plates.
A is the plate area and d is the distance of separation between the plates. Modern
super capacitors have distance of separations between the plates very small and
this make them really interesting as energy storage systems. The capacitance
results from the formation on the electrode surface of a layer of electrolytic ions.
They can have high surface areas, e.g., 10
6
m
2
/kg, and this make possible to fit
capacitors of thousand of Faradays in small containers [
3
,
39
].
However, the voltages at the terminals of each capacitor can only be between 1
and 3 V, and this represents the main problem of this technology, because it limits
the amount of energy that can be stored. For this reason, more capacitors have to
be connected in series in order to store energy at a reasonable voltage, since from
Eq.
5.32
, it derives that the energy stored increases as the voltage squared.
However, being the total capacitance C of n capacitors C
1
, C
2
, C
n
connected in
series given by the formula:
C
¼
1
1
þ
1
C
2
þþ
1
C
n
ð
5
:
34
Þ
C
1
this type of connection implies a reduction of the total capacitance, in addition to
an increase of costs.
Another problem of capacitors connected in series is given by the charge
equalization between each capacitor forming the stream, since the same current
flows through the series circuit. The difference in charge of each capacitor is
generally caused by self-discharge phenomena due to small difference in the
insulation between the plates of each capacitor, or by a small difference in
capacitance among the capacitors of the same series. The consequence may be an
overcharging of some capacitors, which means a voltage value higher than 3 V,
with irreversible damages of the device.
The solution for this problem is the use of an equalisation circuit, which is
essential in systems composed by at least six capacitors in series. This equipment
monitors each capacitor testing the voltage across each pair of its terminals, and
eventually moves charge from one capacitor to another to guarantee the same
value of voltage across the series.
Equalisation circuits increase the cost of capacitor energy storage systems.
They also require energy to work. However, these circuits are very efficient and
have a very low current consumption [
40
].
Super capacitors have relatively high specific power and low specific energy,
like flywheels. For this reason both these devices can be used as energy storage
