PhD Thesis - Cranfield University

Chapter 7
( 45)(
12.
5 ⋅10
=
2
= 281.
2 µ H
−6
)
Similarly, the inductance required for the same ripple current limit at minimum Vuc dis is,
( Vuc
L =
dis
min)( ∆t
∆I
( 20)(
33.
5⋅10
=
2
= 335 µ H
−6
mac
)
)
189
(7-46)
The sizing methodology yields a minimum required inductance value of 335 µH. However,
unlike the battery system, the duty cycle range of the ultracapacitor boost converter
0 ≤ T 4 ≤
( . 25 D 0.
67 ) has a possible duty cycle condition of 0.5. In this event, the previously
assumed inductance value is not the minimum required value.
Rewriting (7-5) and (7-7) for the ultracapacitor parameters,
∆i
L f sw = Vout
−V
)
uc
uc
( 1−
DT
4
in
(7-47)
V = V 1−
D )
(7-48)
in
out ( T 4
Solving for current ripple gives,
−
Vout
DT
4 ( 1 DT
4 )
∆ iuc
=
(7-49)
Luc
f sw
From (7-49), the maximum current ripple will occur when the duty cycle assumes a value of
0.5. The value of the inductance required to achieve the same ripple current limit of 2A is
then calculated by setting D T4 = 0.5 in (7-49) and solving for L uc,