Environmental Engineering Reference
In-Depth Information
It is also accepted practice to characterize the discharge power of the capacitor
at 95% efficiency. For constant power mode the specific power,
P
, becomes
h
¼
0
:
95
2
ð
1
hÞ
U
2
mx
ESR
dc
3
4
P
h
¼
ð
10
:
57
Þ
P
95
m
c
P
¼
where
P
95
is the discharge power at 95% efficiency. This is the specific power that
is used to characterize the capacitor
P
/
E
metric. Capacitor discharge into matched
impedance typically results in power magnitudes of ten times the value of
P
95
.
Under matched impedance discharge,
R
L
¼
ESR, the power becomes
U
2
mx
4ESR
dc
P
ML
¼
ð
10
:
58
Þ
Referring to the illustration of capacitor test data shown in Figure 10.39 and
bearing in mind the circuit topologies of this test as shown in Figure 10.40, it is
straightforward to calculate the constant current charge and discharge efficiency.
R
i
= ESR
R
i
= ESR
-
I
*
+
U
c
(
t
)
U
c
+
k
R
L
C
I
C
(a)
(b)
Figure 10.40 Constant current charge and discharge test: (a) constant current
charge, (b) constant current discharge
During the charging test shown as Figure 10.40(a) the capacitor losses are
accounted for by the dissipation into the ESR. As the stored energy increases to the
value given in (10.56), the losses increase according to (10.59). Then, on knowing
the losses, the charge efficiency will be calculated as shown in (10.59):
P
L
¼ t
C
U
co
T
2
W
e
¼
0
!
0
:
5
CU
co
ð
10
:
59
Þ
