Journal of ELECTRONIC MATERIALS, Vol. 40, No. 5, 2011
DOI: 10.1007/s11664-011-1523-2
Ó 2011 TMS
A Four-Quadrant Operation Diagram for Thermoelectric
Modules in Heating–Cooling Mode and Generating Mode
W. CHIMCHAVEE1,2
1.—Electrical and Energy Engineering, University of the Thai Chamber of Commerce, 126/1,
Vibhavadee-Rangsit Road, Dindaeng, Bangkok 10400, Thailand. 2.—e-mail: wanchai_chi@utcc.
ac.th
The operation of a thermoelectric module in heating–cooling mode, generating
mode, and regenerating mode can be discussed in terms of power, cooling load,
and current. A direct current machine in motoring mode and generating mode
and an induction motor in motoring mode and regenerating mode are analogous to thermoelectric modules. Therefore, the first objective of this work is to
present the four-quadrant (4-Q) operation diagram and the 4-Q equivalent
circuits of thermoelectric modules in heating–cooling mode and generating
mode. The second objective is to present the cooling and regenerating curves of
a thermoelectric module in cooling mode and regenerating mode. The curves
are composed from the cooling powers and the generating powers, the input
and output current, the thermal resistance of the heat exchanger, and the
different temperatures that exist between the hot and cold sides of the thermoelectric module. The methodology used to present the data involved
drawing analogies between the mechanical system, the electrical system, and
the thermal system; an experimental setup was also used. The experimental
setup was built to test a thermoelectric module (TE2) in cooling mode and
regenerating mode under conditions in which it was necessary to control the
different temperatures on the hot and cold sides of TE2. Two thermoelectric
modules were used to control the temperature. The cold side was controlled by
a thermoelectric module labeled TE1, whereas the hot side was controlled by a
second thermoelectric module labeled TE3. The results include the power, the
cooling load, and the current of the thermoelectric module, which are analogous to the torque, the power, the speed, and the slip speed of a direct current
machine and an induction motor. This 4-Q operation diagram, the 4-Q
equivalent circuits, and the cooling and regenerating curves of the thermoelectric module can be used to analyze the bidirectional current and to select
appropriate operating conditions in the cooling and regenerating modes.
Key words: Four-quadrant operation diagram, four-quadrant equivalent
circuits, cooling and regenerating curve, heating–cooling mode,
generating mode, regenerating mode, thermoelectric modules,
bidirectional current
INTRODUCTION
Thermoelectric devices typically consist of a series
of n-type and p-type semiconductors electrically
(Received April 29, 2010; accepted January 17, 2011;
published online February 8, 2011)
connected at one end to form an n–p junction. Series
connection of such n–p junctions proportionally
increases the voltage of the thermoelectric device,
whereas the current remains constant throughout
the module. The n–p junctions and the p–n junctions can be split into two components, yielding an
electrical terminal for input and output power
707
708
known as a ‘‘module.’’ If direct current is delivered
to both electrical terminals of the thermoelectric
module, heat is rejected on one side. This makes the
other side cooler; this is known as ‘‘heating–cooling
mode’’ and is required for intended uses of heating
and cooling. Clearly, one side of the thermoelectric
module ventilates the heat, but the other side of the
module has a thermal energy input that causes a
temperature difference between the hot side and the
cold side. When this happens, a direct current
voltage may develop across the two terminals, creating a power generator, i.e., so-called generating
mode. Case studies of the generating mode have
been conducted in the past. In 2004, Weiling et al.
proposed that thermoelectric power generators
could be used for numerous applications.1 Mikhailovsky also explored the physical characteristics of a
100-W thermoelectric power generator that was
used with cooling water.2 In 2005, Bodnaruk published the results of an analysis of the characteristics and parameters of a thermoelectric module that
can change thermal energy into an alternating
current.3 In 2006, Rowe suggested that thermoelectric modules be used to generate power by using
waste heat recovery and renewable energy sources.4
In 2007, Zhang et al. proposed an evolution of the
thermoelectric module for generation of power in
China.5 Lidorenko et al. did the same for Russia,6
and Kajikawa did the same for Japan.7 Moreover,
Anatychuk analyzed and developed a material used
to produce the thermoelectric module by considering
other problems and provisions.8 Pustovalov also
proposed an evolution of the thermoelectric module
that has been used to generate power in space for
the past 40 years.9
In addition, Strutynska et al. proposed a physical model and analyzed the basic characteristics of
a thermal source power generator with a small
thermoelectric module that used gas and liquid
fuel.10 It was intended to be used for analysis of
power generator systems. Anatychuk et al. also
analyzed the efficiency of a thermal source power
generator system with a thermoelectric module
that used gas and liquid fuel.11 In 1997, Lau et al.
calculated the performance of a thermoelectric
power generator by analyzing a finite-element
model.12 Lineykin et al., in 2005, analyzed a model
of a thermoelectric module capable of cooling and
generating power by simulating a Simulation
Program with Integrated Circuit Emphasis
(SPICE)-compatible equivalent circuit.13 Furthermore, Lobunats analyzed the performance of a
thermoelectric module that could generate heat
found in the heating–cooling system.14 In contrast,
Mitrani et al. studied the impact of temperature on
the lumped parameters of a material used for
producing thermoelectric modules. This was done
by simulating with a SPICE model.15 Additionally,
Chen et al. studied how the heat transfer properties of the thermoelectric module affect the heat
absorption within the module, which is useful
Chimchavee
information when modeling power generation with
mathematical calculations.16 In the case of the
heating–cooling mode, it appears that most of the
research studies use thermodynamic theory and
mathematical methods.17 Nevertheless, Chimchavee analyzed a thermoelectric module in cooling
mode using an electrothermal model, the so-called
CHIM model. This proposed model is based on
Kirchoff’s laws and a PSPICE program.18 In 2003–
2009, Chimchavee also analyzed a sine wave temperature generator along with the concept of a
thermoelectric module plus analysis of thermoelectric modules in heating–cooling and generating
modes using electrical circuit theory.19,20
The main points of interest are the operation of a
direct current machine in motoring mode and
generating mode at a steady state. In motoring
mode, the voltage input (V) is equal to the sum of
the electromotive force (Em) and the voltage drop
from the resistance of the conductor (IR) (Eq. 1).
The power input (Pin) is equal to the sum of the
power output (IEm) and the power loss of the conductor (I2R) (Eq. 2). In generating mode, the load
voltage (VL) is the difference between the electromotive force (Eg) and the voltage drop from the
resistance of the conductor (Eq. 3). The load power
(PL) is equal to the difference in the power output
(IEg) and the power loss of the conductor (Eq. 4).
The electromotive force created by the motor and
the generator is the product of a constant value for
the machine (K), the magnetic flux (U), and the
speed (Eq. 5). The basic equation given in Eq. 6 is
the relationship between the power (P) and the
speed (x) for the operation of an electrical
machine. From the perspective of a motor, the
torque and speed are the outputs and the power is
the input (T = P/Px). From the perspective of a
generator, the speed and the torque (T) are inputs
and the power is the output (P = Tx). In Eqs. 2
and 4–6, the torque and power equations of a direct current machine can be written in motoring
mode and generating mode, as shown in Eqs. 7 and
8. The relationship between input and output can
be explained by a four-quadrant (4-Q) operation
diagram as shown in Fig. 1. The first quadrant
represents the forward motoring mode; the torque
and power are positive, and the speed is positive.
The second quadrant represents the forward generating mode; the torque and power are negative,
and the speed is positive. The third quadrant represents the reverse motoring mode; the torque and
power are negative, and the speed is negative. The
fourth quadrant represents the reverse generating
mode; the torque and power are positive and the
speed is negative.
In the case of the motoring mode,
V ¼ Em þ IR;
(1)
Pin ¼ IEm þ I 2 R:
(2)
A Four-Quadrant Operation Diagram for Thermoelectric Modules in Heating–Cooling Mode
and Generating Mode
Fig. 1. 4-Q operation diagram of a direct current machine.
Fig. 2. Torque, power, and slip speed curves of an induction motor.
In the case of the generating mode,
VL ¼ Eg IR;
(3)
PL ¼ IEg I2 R:
(4)
The basic equation of an electrical machine is
Em ¼ Eg ¼ KUx;
(5)
P ¼ Tx:
(6)
Therefore, in motoring mode,
T ¼ KUI ¼ ðPin I 2 RÞ x;
(7)
and in generating mode,
P ¼ KUIx ¼ PL þ I 2 R :
709
(8)
The first objective of this paper is to present the
4-Q operation diagram and the 4-Q equivalent circuits for thermoelectric modules at steady state in
heating–cooling mode and generating mode, which
are analogous to the 4-Q operating diagram of a
direct current machine at steady state in motoring
mode and generating mode.
For an induction motor, the input and the output
at steady state in motoring mode and regenerating
mode are important; the power is related to the slip
speed (S) when there is constant power loss of the
rotor conductor (I22R2). The slip speed is the difference between the synchronous speed (xs) and the
rotor speed (xr); to be valuable, the maximum value
of the slip speed should be equal to one unit when
the rotor speed is equal to zero, as shown in Fig. 2
and Eqs. 9 and 10. The power and slip speed curves
are defined at the origin where the slip speed is
equal to zero or the synchronous speed. The induction motor is operated in motoring mode when the
slip speed is positive and in regenerating mode
when the slip speed is negative. The first quadrant
represents the motoring mode; the rotor speed is
slightly more than the synchronous speed, the
power is positive, and the slip speed is positive. The
third quadrant represents the regenerating mode;
the rotor speed is more than the synchronous
speed, the power is negative, and the slip speed is
negative.21 For example, an electric car accesses
the motoring mode when operated in acceleration
mode, and it accesses the regenerating mode when
it is operated in deceleration mode. The energy
produced in the regenerating mode can be stored in
batteries.
The second objective of this paper is to present the
cooling and regenerating curves of the thermoelectric cooling system at steady state in cooling mode
and regenerating mode to discuss the relationship
between the power, the cooling load, and the current
analogies to the power and slip speed curves of an
induction motor at steady state in motoring mode
and regenerating mode.
ð1 SÞ
;
S
(9)
S ¼ ðxs xr Þ=xs :
(10)
P ¼ I22 R2
The analogies between the mechanical system,
the electrical system, and the thermal system used
in this paper are presented in Table I.22 The power,
the cooling load, and the current are the inputs and
the outputs of thermoelectric modules, being analogous to the power, the speed, and the slip speed,
which are the inputs and the outputs of a direct
current machine and an induction motor. These
analogies can be used to design a system with an
optimized capacity for storing energy in the battery
and to protect the thermoelectric module from
thermal oscillations.
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Chimchavee
Table I. Electrical–thermal–mechanical analogies
Mechanical
System
Electrical
System
Thermal
System
Torque (T)
Speed (x), slip
speed (S)
Power (P)
N/A
N/A
Voltage (V)
Current (I)
Temperature (T)
Heat flow (Q)
Power (P)
Conductivity (K)
Resistance (R)
N/A
Conductivity
Resistance (R)
BASIS FORMULA AND MODEL
The thermoelectric module consists of a heating–
cooling mode and a generating mode. The basic
device comprises a power source or a thermal
source, the thermoelectric modules, and the heat
exchanger on the cold side and on the hot side
(Fig. 3). The analysis will neglect the leakage loss
(Qa, W). When Qin is the thermal input (W), PL is
the power output (W), and Tin is the temperature
input for the generating mode, when expressing
temperatures in Kelvin (K). Pin is the power input
for the heating–cooling mode (W). In the heating–
cooling mode, an electrical current (I) introduced to
the thermoelectric module at the cold junction that
the cooling load (Qc) will be pumped from the
atmosphere (Ta) to the thermoelectric module via
the heat exchanger (Rc) and emit heat to the
atmospheric at the hot junction with the other heat
exchanger (Rh). On the other hand, in generating
mode, thermal energy (Qh) is inputed to the thermoelectric module on the other side, which creates a
temperature increase on the surface (Th) via the
heat exchanger (Rh) and the heat ventilator (Qc) on
the other side of the thermoelectric module. The
temperature at the surface (Tc) rises and reaches
atmospheric temperature through the thermal
resistance of the heat exchanger (Rc). This may
cause a difference in temperature between the two
sides of the thermoelectric module, which generates
a direct current to the load. Equations 11–23 illustrate the relationship between the two modes.23,24
In the heating–cooling mode, the power input is
the sum of the Seebeck power (aIDT) and the
electrical loss or Joule heat (I2R) in the thermoelectric module. In the generating mode, the power
output is the difference between the Seebeck
power and the electrical loss in the thermoelectric
module.
In the case of the heating–cooling mode,
COP ¼ Qc =Pin ;
(11)
1
Qc ¼ aITc DTK I 2 R;
2
(12)
1
Qh ¼ aITh DTK þ I 2 R;
2
(13)
Fig. 3. Configurations of thermoelectric modules in heating–cooling
mode and generating mode.
V ¼ aDT þ IR;
(14)
Pin ¼ Qh Qc ¼ aIDT þ I2 R:
(15)
In the case of the generating mode,
g ¼ PL =Qh ;
(16)
Qh ¼ PL þ Qc ;
(17)
1
Qh ¼ aITh þ DTK I 2 R;
2
(18)
1
Qc ¼ aITc þ DTK þ I 2 R
2
(19)
VL ¼ aDT IR;
(20)
PL ¼ aIDT I22 R:
(21)
The following relationships were assumed:
Voc ¼ aDT;
(22)
VL ¼ IRL :
(23)
The COP is the coefficient of performance of the
cooling mode. g is the generation efficiency of the
generating mode. Qc is the cooling load and
the ventilation heat (W) at the cold side. Qh is the
rejected heat and the thermal input at the hot side
(W). a is the Seebeck coefficient of the thermoelectric module (V/K). Th is the temperature at the hot
side (K). Tc is the temperature at the cold side (K).
DT is the difference in temperature between the hot
side and the cold side of the thermoelectric module
(K). K is the thermal conductance of the thermoelectric module (W/K). R is the inner electrical
resistance of the thermoelectric module (X). V is the
voltage input (V). Voc is the Seebeck voltage and the
open-circuit voltage (V). VL is the load voltage (V).
A Four-Quadrant Operation Diagram for Thermoelectric Modules in Heating–Cooling Mode
and Generating Mode
I is the input and output current (A). RL is the
resistance load (X).
FOUR-QUADRANT OPERATION ANALYSIS
This study designed and analyzed a 4-Q operation
diagram for a thermoelectric module operated in
heating–cooling mode and generating mode by referencing basic electrical theory and the concept of
an equivalent circuit (Fig. 3 and Eqs. 11–23). It was
assumed that the ground was 0 K. The approach
can be modeled as an electrical equivalent circuit in
heating–cooling mode and generating mode with
electrothermal coupling by making use of analogies
between the thermal and electrical systems.
Figure 4 shows that, for the electrothermal model of
the thermoelectric heating–cooling system, the
CHIM model is the equivalent circuit of the thermoelectric module.18,19 Figure 5 shows the analysis
model of the thermoelectric generating system. The
electrothermal coupling is the power coupling
between the thermal domain and the electrical
domain. Therefore, the Seebeck power and the
electrical loss can be transferred to the electrical
domain. Rl is the thermal leakage resistance (K/W)
between the hot side and the cold side of the thermoelectric module. Rc is the thermal resistance of
the heat exchanger on the cold side (K/W). Rh is the
thermal resistance of the heat exchanger on the hot
side (K/W). Rpc is the thermal resistance of the
cooling load (K/W). Qj is the Joule heat of the thermoelectric module (W). G is the thermal gain factor.
In Figs. 4 and 5, aITc equals Rpc, aITh equals GTh,
and I2R equals Qj. These relationships can be drawn
as the analysis model in heating–cooling mode and
generating mode, which is shown in Fig. 6.20 The
heat flow and the electrical current appear to move
in different directions, or bidirectional current.
Their relationships are given in Eqs. 11–23.
In Fig. 6, in heating–cooling mode, when a voltage (V) is supplied and heat (Qh) is rejected, I and Qc
have an inner flow direction, whereas Qh has an
outer flow direction. In generating mode, when heat
(Qh) is supplied and heat (Qc) is rejected, I and Qc
have an outer flow direction. These variables represent the relationship between the voltages, the
power, the cooling load, and the current of the
thermoelectric module. The voltage and power
Fig. 4. Electrothermal model for the thermoelectric heating–cooling
system.
711
inputs are shown in Eqs. 12, 14, and 15 in heating–
cooling mode. The voltage and power outputs are
shown in Eqs. 18, 20, and 21 in generating mode.
Equations 14 and 15 of the thermoelectric module in
heating–cooling mode are analogous to Eqs. 1 and 2
of the direct current machine in motoring mode.
Equations 20 and 21 of the thermoelectric module in
generating mode are analogous to Eqs. 3 and 4 of
the direct current machine in generating mode. To
visualize the analogy between the thermoelectric
module and the direct current machine, Figs. 3 and
6 can be used to create the 4-Q operation diagram
and the 4-Q equivalent circuits for the thermoelectric module in heating–cooling mode and generating
mode, which are illustrated in Figs. 7 and 8,
respectively.
In Figs. 7 and 8, the vertical axis shows the
cooling load (Qc) and the power generation (PL). The
horizontal axis shows the current input (I) and
the output. The first quadrant represents operation
in the forward heating–cooling mode, which supplies the electrical current (I) to a positive pole,
resulting in heat flow to the top. The cooling load
(Qc) has a positive direction, passing through the
thermoelectric module and the heating and venting
(Qh) to exit at the bottom. The third quadrant represents operation in the reverse heating–cooling
mode, which supplies the current (I) to a negative
pole, causing the heat to flow to the bottom, which
has a negative cooling load (Qc). This will pass the
heat ventilation of the thermoelectric module (Qh) to
the top. The fourth quadrant represents operation
in the reverse generating mode in which heat (Qh) is
Fig. 5. Analysis model of the thermoelectric generating system.
Fig. 6. Analysis model in heating–cooling mode and generating
mode.
712
Chimchavee
Fig. 7. 4-Q operation diagram of thermoelectric modules.
Fig. 8. 4-Q equivalent circuits of thermoelectric modules.
input to the top and heat is ventilated (Qc) to the
bottom. This will generate an electrical current (I)
that flows to a negative pole and a load that
has positive power, whereas the second quadrant
represents operation in the forward generating
mode in which heat (Qh) is input to the bottom and
A Four-Quadrant Operation Diagram for Thermoelectric Modules in Heating–Cooling Mode
and Generating Mode
heat is ventilated (Qc) to the top, causing a current
(I) to be generated. The current flows to a positive
pole and to the load that has negative power.
We present a 4-Q operation diagram and a 4-Q
equivalent circuit for thermoelectric modules at
steady state (Figs. 7, 8) and discuss the relationship
of the power, voltage, cooling load, and current in
heating–cooling mode to the analogous power, voltage, current, and speed which can be represented by
a 4-Q operation diagram of a direct current machine
in motoring mode and generating mode (Fig. 1).
Equations 12, 14, 15, 18, 20, and 21, which describe
the voltage, power, cooling load, and current, are
the inputs and outputs of a thermoelectric module,
and are analogous to Eqs. 1–4, 7, and 8, which
describe the voltage, current, power, and speed as
the inputs and outputs of a direct current machine.
EXPERIMENTAL RESULTS FOR COOLING
AND REGENERATING CURVES
Application of several thermoelectric modules
that use a parallel pattern in thermal oscillation
will always occur in the cooling mode and the
regenerating mode. Both phenomena may cause
energy to be transferred between the inner modules
of the system. Therefore, a control system is
required to protect the thermoelectric module, such
as n–p or p–n connectors, from melting. Moreover,
the large thermoelectric cooling system can store
energy when the current stops charging the thermoelectric module. This causes a temperature difference that is capable of generating power. If a
control system is used, it may stop heat ventilation
on the hot side, and it may emit heat on the cold
side. This is the regenerating mode of the thermoelectric module. An experiment is used to discuss
the cooling and regenerating curves, analogous to
the torque, power, and slip speed curves of the
induction machine. The experimental design consists of a laboratory-scale thermoelectric module, i.e.,
Melcor CP 1.4-127-045L (40 mm 9 40 mm 9 3.3 mm,
713
Imax = 8.5 A, Vmax = 15.4 V, Qmax = 72 W, DTmax =
67 K, n = 127 couple, g = 0.171 cm, a0 = 22,224,
a1 = 930.6, a2 = 0.9905, r0 = 5112, r1 = 163.4, r2 =
0.6279, k0 = 62605, k1 = 277.7, k2 = 0.4131). Three
sets were used (each set is equal to one module). The
first thermoelectric module (TE1) was operated as
the cooling load (QcTEC) for the cooling mode and as
the heating ventilator (QcTEG) for the regenerating
mode, and it was used to control the temperature on
the cold side. The next thermoelectric module (TE3)
was operated as a heating ventilator (QhTEC) for the
cooling mode and as a thermal source (QhTEG) for
the regenerating mode, and it was used to control
the temperature on the hot side of the final thermoelectric module (TE2). TE2 requires testing of the
cooling mode and the regenerating mode. Figure 9
shows a block diagram of the thermoelectric module
used for testing the system.
The testing system can control the operation of
TE1 and TE3 to keep the temperature difference
between the cold and hot sides (DT) of TE2 constant
by alternating the electrical pole charges on both
thermoelectric modules. To test the system in cooling mode, a current was inputed to the pole of TE2.
In regenerating mode, an electrical load was connected to the pole of TE2. The experimental data
were measured using a Testo454 (error ±0.1°C) and
a METRA Hit29s (error ±0.2%). The cooling load
(Qc) was calculated by Eq. 4, which explains the
cooling and regenerating curves of the thermoelectric module in cooling and regenerating mode as
illustrated in Fig. 10. At the origin, the input and
output current are equal to zero. The thermoelectric
module is operated in cooling mode when the current is positive and in regenerating mode when the
current is negative. In cooling mode, the horizontal
axis is the input current (A) and the vertical axis is
the cooling load (W). In regenerating mode, the
horizontal axis is the output current (A) and the
vertical axis is the output power (W).25 The first
quadrant represents the cooling and current curves
for operation in cooling mode, when the current
Fig. 9. Block diagram of the thermoelectric module used to test the system.
714
Chimchavee
P & Qc
(W)
80
Cooling Mode
70
Rh=0.05ºK/W
60
Rh=0.20ºK/W
50
40
Rh=0.35ºK/W
30
20
10
I (A)
0
-2
0
2
4
6
8
10
-10
Regenerating Mode
Fig. 10. Cooling and regenerating curves of the thermoelectric
module.
input for the thermal resistance of the heat exchanger at Kh is equal to 0.05 K/W, 0.20 K/W, and
0.35 K/W. The third quadrant represents the power
and current curves for operation in regenerating
mode, when the load resistance (RL) for DT is equal
to 10 K, 20 K, and 30 K. The COP of the cooling
mode was approximately 0.72 when Kh was 0.20 K/
W and I was 7 A. The system efficiency of the
regenerating mode was approximately 5.12% when
DT was 30 K and I was 0.26 A.
The relationship between the power, the cooling
load, and the current of the thermoelectric cooling
system in cooling mode and regenerating mode is
shown in Fig. 10. The analogy to the power and slip
speed curves of an induction motor in motoring
mode and regenerating mode is shown in Fig. 2.
Equations 12 and 21 represent the power, cooling
load, and current, which are inputs and outputs of
the thermoelectric module, analogous to Eq. 9,
which represents the power and slip speed and the
inputs and outputs of an induction motor.
CONCLUSIONS
The 4-Q operation diagram and the 4-Q equivalent circuits of thermoelectric modules at steady
state in heating–cooling mode and generating mode
are analogous to the 4-Q operation diagram of a
direct current machine in motoring mode and generating mode. The first quadrant represents the
forward heating–cooling mode of the thermoelectric
modules, which is analogous to the forward motoring mode of a direct current machine. The second
quadrant represents the forward generating mode
of the thermoelectric modules, which is analogous to
the forward generating mode of a direct current
machine. The third quadrant represents the reverse
heating–cooling mode of the thermoelectric modules, which is analogous to the reverse motoring
mode of a direct current machine. Finally, the
fourth quadrant represents the reverse generating
mode of the thermoelectric modules, which is analogous to the reverse generating mode of a direct
current machine. The cooling and regenerating
curves of the experiment in cooling mode and
regenerating mode are analogous to the power and
slip speed curves of an induction machine in
motoring mode and regenerating mode. The first
quadrant represents the cooling mode of the thermoelectric modules, which is analogous to the
motoring mode of an induction machine. The third
quadrant represents the regenerating mode of the
thermoelectric modules, which is analogous to the
regenerating mode of an induction machine.
Because the electrical system and the thermal system of thermoelectric modules are analogous to the
mechanical system and the electrical system of a
direct current machine and an induction machine,
the 4-Q operation diagram, the 4-Q equivalent
circuits, and the cooling and current curves of the
thermoelectric module can be used to analyze the
bidirectional current and to design a thermoelectric
cooling system that operates in both cooling and
regenerating modes.
ACKNOWLEDGEMENTS
This research was completed with the support of
funding from the Research Support Office at the
University of the Thai Chamber of Commerce.
The author would like to express special gratitude
to the university.
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