Environmental Engineering Reference
In-Depth Information
simply replaced by an effective resistor,
R
e
(
d
). In a similar context, the average
diode's voltage and current obey a power source
P
characteristic, with power
equal to the power effectively dissipated by
R
e
(
d
). Hence, the buck converter
in
Figure 3.5
can be represented by the averaged equivalent circuit shown in
Figure 3.6
, where the switch and diode are replaced with an effective resistor
R
e
(
d
) and a dependent power source
P
,respectively [71].
Based on the DC analysis of the buck converter in DCM [95], the conversion
ratio
M
of the buck converter can be derived [96] as follows:
V
o
V
in
=
2
M
=
+
√
1
(3.7)
1
+
4
R
e
(
d
)
/
R
L
In addition, the emulated resistance of the buck converter in DCM
R
e
(
d
)is
obtained as follows [71]:
2
L
d
2
T
s
=
R
e
(
d
)
(3.8)
where
d
and
T
s
f
s
are the duty cycle and the switching period/frequency
of the gating signal of the PWM (pulse width modulation) switch, respectively.
In practical cases, the step-down conversion ratio
M
of the buck converter
(
V
in
=
1
/
M
)is
approximately unity. As such, taking into account the effect of the correction
factor
M
on the emulated resistance
R
e
(
d
) equation of the buck converter
V
o
) may not be large enough such that the correction factor 1
/
(1
−
R
e
(
d
)
1
R
em
=
1
−
M
2
Lf
s
d
2
1
=
(3.9)
+
√
1
+
8
Lf
s
/
d
2
R
L
2
1
−
1
Knowing that the source resistance of the thermal energy harvester
R
s,TEG
as obtained experimentally in
Figure 3.3
is fixed at 82 k
, the input port of
the buck converter has to constantly emulate this resistance value such that
MPPT can be achieved. In this DCM operation, the converter parameters such
as
L
and
f
s
are fixed, whereas the duty cycle
d
is tuned to the required value
to achieve an equivalent emulated resistance. Hence, the equation expressed
emulate the source resistance of the thermal energy harvester (
R
s,TEG
=82k
)
to achieve MPPT, which is given by Dalola et al.
2
Lf
s
R
em
±
√
R
em
∗
=
d
em
(3.10)
R
L
To demonstrate the competency of the buck converter as a resistor
emulation-based MPP tracker and to verify its governing equation expressed
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