IEEE Systems, Man and Cybernetics Magazine - January 2023 - 60

performed to confirm the effectiveness of the proposed
control system.
The structure of this article is as follows. First of all,
the section " Materials and Methods " describes the Peltier
element used in the system and explains the structure and
measurement method of a calorimeter
that uses a Peltier element.
The section " The Modeling of the
Calorimeter " describes modeling
the system using heat transfer phenomena.
The section " The Modeling
of the System " provides a
description of the control system
design for the calorimeter. The section
" Control System Design " presents
the results of experiments.
Finally, the section " Conclusions "
discusses the conclusions.
Materials and Methods
This section describes the calorimeter
using a Peltier element. The
section " The Configuration of the
Peltier Element " describes a Peltier
element. The section " The Configuration of the Calorimeter
Using the Peltier Element " explains the configuration
of the calorimeter. Finally, the section " The Measurement
Principle of the Calorimeter " explains the measurement
method of the system.
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.
The Configuration of the Peltier Element
Figure 1 shows the configuration of the Peltier element.
This element is one of the thermal-electric conversion
elements, which has the characteristic of absorbing heat
on one side and dissipating heat on the other side when
current is applied to the element.
The endothermic and exothermic
surfaces can be swapped by
switching the current direction
flowing to the element. In addition,
the amount of heat absorption
can be adjusted by controlling the
magnitude of the current flowing
to the element.
This temperature difference
inside the element is caused by
the Peltier effect. The Peltier
effect is a phenomenon in which
different metals or semiconductors
are electrically connected
in series, and when current is
applied, one side dissipates heat,
and the other side absorbs heat.
The amount of heat in a Peltier
element includes heat transfer due to the Peltier effect,
heat conduction from the heat-dissipating side to the
heat-absorbing side, and Joule heat generated inside the
element. The relationship between the endothermic
capacity of a Peltier element uc
expressed as [22]
and the current Ip
uS ()TIcp cp
hc
Endotherm
N-Type Semiconductor
Copper Electrode
N
P
Radiation
N P
Ceramic Substrate
P-Type
Semiconductor
where ST Ipc p
=- -- pp
p
R TT rI
1
2
1
2
is
(1)
is the quantity of heat transferred from
the heat-absorbing side to the heat-dissipating side by
the Peltier effect, and /( )()
p p
2
is Joule heat generated by the electric current
1RT Tph c
- is the heat conduction
due to the difference in temperature between the
heat-absorbing and heat-dissipat ing sides. Also,
() / r I12
Figure 1. The configuration of the Peltier element.
Table 1. The parameters of
the Peltier element.
Parameter
Sp
rp
Th
Tc
Rp
Description
Seebeck coefficient
Unit
[V/K]
Internal resistance of the Peltier element []X
Temperature on the radiation side
Temperature on the heat-absorbing side
[K]
[K]
Thermal resistance of the Peltier element [K/W]
60 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE January 2023
uS ()TIhp hp
where ST Iph p
=- -+
p
R TT rI
1
hc p p
2
2
1
(2)
is the quantity of heat transferred from the
heat-dissipating side to the heat-absorbing side by the Peltier
effect. Table 1 shows the parameters that were used in
(1) and (2).
flowing through the internal resistance of the Peltier
element. Joule heat due to the current is assumed to be
generated uniformly in the device, and since the heatabsorbing
side is considered here, the amount of heat is
half of the total amount.
Similarly, the relationship between the amount of radiation
of the Peltier element uh
and the current Ip
expressed as [22]
is
IEEE Systems, Man and Cybernetics Magazine - January 2023

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