IEEE Systems, Man and Cybernetics Magazine - January 2023 - 61

The Configuration of the Calorimeter
Using the Peltier Element
Figure 2 is a configuration of a calorimetry system that
uses a Peltier element. The DUT is the power conversion
device to be measured. The entire calorimeter consists of
Styrofoam insulation to reduce heat leakage from temperature
differences between the internal and external parts of
the chamber. The Peltier element is placed with the endothermic
side down, and heat inside the chamber is transferred
to the outside by passing a current. Temperature
sensors are installed inside and outside the chamber, on
both sides of the Peltier element.
The Measurement Principle of the Calorimeter
The first step is to drive the DUT placed in the chamber. At
this time, inside the chamber, the temperature rises
because the power conversion device generates heat due
to the power loss. The inside of the chamber is cooled by
passing electric current through the Peltier element. When
the temperatures inside and outside the container match,
there is no heat leakage Pwall
through the container to the
outside of the system, expressed as [5]
P
TT
wall =
where Tin
Tamb
in - amb
Rwall
(3)
is the temperature internal to the chamber,
is the temperature of ambient air, and Rwall
is the
thermal resistance of the wall of the chamber. At a state
of equilibrium, the quantity of heat emitted from the
power conversion equipment is equal to the quantity of
heat absorbed by the Peltier element. Therefore, the
power loss of the power conversion device can be determined
by measuring the current flowing through the Peltier
element and the temperatures of both sides of the
device and estimating the quantity of heat absorbed by
the element from (1).
The Modeling of the Calorimeter
This section describes the modeling of the calorimeter.
The section " Heat Transfer Phenomena " provides an explanation
of the heat transfer phenomena used in modeling,
and the section " The Modeling of the System " describes
the modeling of the calorimeter.
Heat Transfer Phenomena
Heat transfer phenomena can be classified into heat conduction,
heat transfer, and radiation. First, heat conduction
is the transfer of heat energy in a solid, and when a
temperature difference is given to an object of heat conduction
area []A m2
and length of object [],L m the thermal
resistance is expressed as
R
1 =
L
Am
where []m W/mK is the thermal conductivity.
(4)
Figure 2. The configuration of the calorimeter using
the Peltier element.
January 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 61
Next, heat transfer is the heat transfer between a fluid
and a solid, and the thermal resistance at a surface area
S []m2
is expressed as
R Sh
1
2 =
where []h W/mK2
is the heat transfer coefficient.
Radiation is the heat energy transfer by electromagnetic
waves, and in the case of radiation from surface A with
surface temperature []KTA
perature [],KTB
the thermal resistance is expressed as
Rf ()()TT TT
r=+v AB AB
2
2
+
v =
10 []),W/mK
-82 4
where v is the Stefan-Boltzmann constant (.567 #
and f is the suface emissivity.
Heat capacity []C J/K represents the quantity of heat
necessary to raise the temperature of an object and is
determined by its physical properties and geometry. For an
object of volume [],V m3
c J/kg K
density [],kg/m3
t
heat [],
$
p
= t
and specific
the heat capacity C is expressed as
Cc .Vp
(7)
The Modeling of the System
If the direction of heating the internal part of the chamber
is defined as a positive current, the equations for heat conduction
at the Peltier element heat dissipation surface, the
cooling surface, the inside of the chamber, and the DUT
are expressed as follows:
dt
dT
dt
dT
h TT SI
= CR
h
hh
dt
dT
dt
dT
c =+ + hc
p
SI
c
C Tc
p
in
=
CR
TT
c
r =- - in
C
Q
in TT
dd d
r
CR .
c - in
in
2Cc
cp
+
+ CR
TT
-
ambin
in
rI TT TT
CR + CR
C Th
2
p
h
-
CR
TT
wd
r
- in
in
+
rI TT
2Ch
2
amb - -+ + ch
-
p
CR
hp
in - c
cc
C
Q
Fc
in
(11)
(9)
(10)
(8)
to surface B with surface tem(6)
(5)
Radiation
Fan
Chamber
Th
Tc
Heat
Sink
Peltier Element
Endotherm
Tin
Tamb
Radiation
DUT
IEEE Systems, Man and Cybernetics Magazine - January 2023

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