Environmental Engineering Reference
In-Depth Information
U
c
dU
U
co
+I
W
e
0
Time (s)
-I
Figure 10.39 Electrochemical double layer capacitor test procedure
time constant capacitance as charge redistributes itself to longer time constant and
deeper pores in the electrode materials. Standard hold times of constant voltage
applied may vary from 6 to 8 h or more.
The negative voltage step during discharge is due to the capacitor ESR. By
measuring the voltage at open circuit and again when discharge current is applied,
the value of ESR can be derived. The capacitor is discharged at constant current
until its terminal voltage reaches zero. At this point the total available energy of the
capacitor is determined. The following expressions summarize the process to this
point:
d
U
I
ESR
¼
ð
10
:
55
Þ
ð
T
Idt
t
T
W
e
¼
U
co
1
0
Knowing the mass of the active material,
m
c
, in the capacitor permits a cal-
culation of the specific energy,
E
, of the capacitor. Also, if the capacitor has been
characterized and its capacitance is not a function of voltage, then its energy given
by (10.55) can be calculated from the known rated voltage and linear expression for
voltage slew rate as
I
C
¼
U
co
T
1
2
U
co
IT
W
e
¼
0
:
5
CU
co
W
e
¼
ð
10
:
56
Þ
W
e
m
c
E
¼
