This experiment aims to characterize a thermoelectric cooler (TEC) for cooling electric vehicle batteries by measuring its Seebeck coefficient and coefficient of performance (COP). A small-scale system using a hot plate, TEC module, and fan will simulate an EV battery cooling system. Temperature and voltage measurements taken with and without the hot plate will be used to calculate the Seebeck coefficient and COP of the TEC and determine the uncertainty in these values. The results will help engineers evaluate TECs for optimal battery thermal management.

1. Experiment Design Proposal:
Thermoelectric Cooling of Electric
Vehicle Batteries
Kit Kerames
EGME 476B-52 Energy and Power Laboratory
California State University Fullerton
Submitted to: Darren Banks, Ph.D.
June 27, 2021
Nomenclature
Name of Factor Symbol Unit
Temperature T k
Seebeck Coefficient S V/K
Coefficient of Performance 𝛽 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠
Work W Joule
Voltage V volt
Heat Q Joule
Current I amp
Resistance 𝛺 Ohm
Average value ( )𝑎𝑣𝑒 n/a
Cold value ( )𝑐 n/a
Hot value ( )ℎ n/a
Introduction
Background
Automotive vehicles have always needed thermal management systems. With the emergence of
electric vehicles (EVs), different thermal management systems had to be put in place. One of the areas in an
EV in which thermal management is used is in the vehicle’s battery pack. EV batteries operate best within the
temperature range, 15°C–35°C [1]. Operating the batteries outside of this range can make them less efficient
or cause damage when they reach extreme temperatures. As batteries rise in temperature with operation, the
main objective of the thermal management system is to cool them. One of the methods of cooling is with a

2. thermoelectric cooler (TEC). These take advantage of the Peltier effect to draw heat from one side of the TEC
to the other, causing a refrigeration cycle to occur. The Peltier effect is the generation of a temperature
gradient when a voltage is applied across a specific type of thermocouple. This thermocouple is an electric
circuit made of two different semiconductors, a n-type and an p-type, which each transport a different charge
carrier – electrons and holes, respectively. When a current is passed through the semiconductors, it causes
the higher energy charge carriers to diffuse to one side of the semiconductor carrying heat from one side of
the device to the other [2]. A diagram of the TEC can be seen in Figure 1.
Figure 1. Diagram of the TEC used in this experiment [2].
TECs have some constraints that will be considered in this experiment. They have a maximum
operating temperature over which they will not function properly. As they approach this temperature, their
performance also decreases [3]. In this experiment, the hot side of the TEC will not exceed 80°C in order to
avoid it reaching its maximum operating temperature of 101°C [4]. Another constraint to consider is the
minimum temperature that the TEC should reach. Condensation can form on the cold side of the TEC. In order
to avoid having this condensation damage electrical equipment, the operating temperature of the cold side of
the TEC should not fall below the ambient air temperature without additional measures being taken to
mitigate condensation. In this experiment, a fan will be used as a source of forced convection in order to
reduce condensation and facilitate removal of heat from the hot side of the TEC.
When comparing a TEC to other cooling solutions, the coefficient of performance (COP) of each
option must be considered. In this context, the COP is the ratio of how much heat is transferred through the
cold surface of the TEC per unit of electrical energy used by the TEC to do so. The heat energy is supplied
mainly by the hot battery. Understanding the COP of this device, as well as the factors that effect it, can help
engineers weigh the costs and benefits of each cooling solution in order to come up with the optimal thermal

3. management system. Therefore, objectives of this experiment will be to use measured temperatures and
voltages to calculate the Seebeck coefficient of the TEC, and to use that coefficient along with the measured
values to calculate the COP of a TEC under the operating conditions of an EV.
Theory
The Seebeck coefficient, 𝑆, is used to characterize the TEC. 𝑆 is defined as,
𝑆 =
∆𝑉
∆𝑇
(1)
For a refrigeration cycle, the COP, 𝛽, is defined as,
𝛽 =
𝑄𝐶
𝑊
(2)
where 𝑄𝑐 is the rate at which heat energy enters the cold side of the TEC and 𝑊 is the electric power used to
run the TEC. 𝑄𝑐 can approximately be expressed as,
𝑄𝑐 = 𝐼𝑆𝑇𝑐 (3)
assuming all heat energy entering the TEC exits through the hot plate. 𝑇𝑐 is the temperature of the cold side of
the TEC. The electric power to run the TEC is,
𝑊 = 𝐼∆𝑉 (4)
Combining equations (2), (3), and (4) yields,
𝛽 =
𝑆𝑇𝑐
∆𝑉
(5)
The maximum COP occurs at 𝛽𝑚𝑎𝑥 such that,
𝛽𝑚𝑎𝑥 =
𝑇𝑐
∆𝑇
(6)
[2]
Procedure
Materials
Object name Manufacturer Model name
Hot plate Cole-Parmer Thermo Scientific Cimarec Stirring Hot Plate
7x7" Ceramic; 120 VAC
Multimeter Cen-Tech 11 Function Digital Multimeter With Audible
Continuity; Leads included
Adjustable power supply Siglent Technologies SPD1168X
Thermoelectric cooler Sheetak SKTC1-127-06

4. 2-channel thermocouple
thermometer
Cole-Parmer Traceable Two-Channel Thermocouple
Thermometer with Offset and Calibration
Table fan Honeywell Comfort Control Oscillating Table Fan Adjustable
Tilt Head with 3 Speeds
Experiment overview
Instead of using an actual EV and battery pack in the system being tested, a small-scale system will be
used. A hot plate will be the source of heat instead of a battery, a single TEC module will be used for cooling,
and a table fan will produce the forced convection that would be used in an EV. A diagram of the test set-up
can be seen in Figure 2. A problem with using a battery as a heat source is that it charges and discharges at a
non-constant rate making it difficult to maintain an optimal operating temperature without additional
equipment when compared to using a hot plate. A hot plate will be able to provide a constant heat flux to the
TEC while maintaining the same, constant operating temperature that a battery would ideally be kept at
(30°C). The TEC will be run close to its maximum operating temperature (101°C) to simulate the most
energy-demanding conditions of a TEC being used in an EV. This setup will allow the experiment to be done at
a lower cost, making it easily reproducible.
Figure 2. Diagram of experimental setup.
Steps
Part 1: Measurements without the hot plate (used to calculate 𝑆).
1. Measure and record ambient air temperature with thermocouple thermometer.
2. Attach two thermocouples to the TEC, one to the top surface and one to the bottom.
3. Attach the TEC to the power supply, and place it down on a heat-resistant surface.
4. Turn the power supply on to any value between 5–10V, and take note of which sides of the TEC feel
hot and cold (being mindful not to burn yourself if it has been kept on for a long time).

5. 5. Record the temperature of each surface once they reach a constant value. If any temperature exceeds
80°C, turn the voltage down until the maximum temperature is below 80°C.
6. Connect 2 leads to the multimeter then measure and record the voltage across the TEC (make sure
the meter dial is set to measure voltage in volts).
7. Repeat steps 5 and 6 four more times changing the voltage to any other value between 5–10V.
8. Leave all components attached with the voltmeter on when beginning part 2.
Part 2: Measurements with the hot plate (used to calculate 𝛽).
1. Turn hot plate to its minimum temperature of 30°C.
2. Place the cold side of the TEC on the hot plate with a thermocouple thermometer between the
surfaces.
3. Place the fan about 0.5m away from the TEC, turn it on its lowest setting, and aim it such that it blows
air parallel to the hot surface of the TEC (make sure that its oscillation mode is set to “off”).
4. Adjust the voltage on the power supply until the hot side of the TEC remains as close as possible to a
constant temperature of 80°C (as measured by one of the thermocouples).
5. Record the temperatures on each side of the TEC. The hot side should measure close to 80°C, but
does not have to be exact as long as it is remaining relatively constant (within ±3°C). Any
temperature below 30°C is an acceptable measurement for the cold side.
6. Measure and record the voltage across the TEC using the multimeter.
7. Set the multimeter to measure current in amps, then measure and record the current across the TEC.
8. Repeat steps 5–7 four more times.
9. Turn of the hot plate, turn off the voltmeter, then put all equipment away once it cools to a safe
temperature for storage.
Results
Before 𝑆 and 𝛽 are found, average values, 𝑉
𝑎𝑣𝑒 and 𝑇𝑎𝑣𝑒 must be calculated for measurements with and
without the hot plate as follows:
𝑥𝑎𝑣𝑒 = ∑
𝑥𝑖
𝑛
𝑛
𝑖=1
(7)
where 𝑛 is the number of measurements, and 𝑥 represents an arbitrary measured quantity. 𝑛 = 5 for all
calculations in this experiment, as there are five trials for each measurement in the procedure. The same
formula as in Equation 7 can be used to find the average values for all measurements.
Calculating S
To calculate 𝑆, the 𝑉 and 𝑇 values that were measured without the hot plate must be used. 𝑆 can be calculated
from Equation (1) as follows :
𝑆 =
∆𝑉
∆𝑇
=
𝑉
𝑎𝑣𝑒
𝑇ℎ,𝑎𝑣𝑒 − 𝑇𝑐,𝑎𝑣𝑒
𝑇ℎ,𝑎𝑣𝑒 and 𝑇𝑐,𝑎𝑣𝑒 are the average hot and cold temperatures measured without the hot plate, respectively.
Calculating 𝜷
To calculate 𝛽, the 𝑉 and 𝑇 values that were measured with the hot plate must be used. Equation (6) can be
used to calculate 𝛽 as follows,
𝛽 =
𝑆𝑇𝑐
∆𝑉
=
𝑆𝑇𝑐,𝑎𝑣𝑒
𝑉
𝑎𝑣𝑒
A typical COP for this application should be 𝛽 ≈ 0.7 [3].

6. Error Analysis
Both the 95% confidence interval (CI) and error propagation must be calculated and compared. The larger
value will be used as a measure of uncertainty.
Case 1: Using a CI
To calculate the confidence interval, the sample standard deviation, σs, must first be found using,
𝜎𝑠 = √
∑ (𝑥𝑖 − 𝑥𝑎𝑣𝑒)2
𝑛
𝑖=1
𝑛 − 1
(8)
The error expressed in the confidence interval, ϵ, can be found using the Microsoft Excel function,
=CONFIDENCE(𝛼, 𝜎𝑠,𝑛)
where 𝛼 is the significance level. At a 95% confidence level, 𝛼 = 1 − 0.95 = 0.5.
𝜖 should be rounded to the least number of decimals in the measurements.
Case 2: Error propagation
Using error propagation, the uncertainty, 𝜔𝑓, in any function f(x,y) will be [2],
𝜔𝑓 = √(𝜔𝑥
𝜕𝑓
𝜕𝑥
)
2
+ (𝜔𝑦
𝜕𝑓
𝜕𝑦
)
2 (9)
where 𝜔𝑥 and 𝜔𝑦 are the uncertainties in individual measurements for two different variables. This
uncertainty will be equal to the quantity of 5 in the place value below the rightmost significant digit.
For example, if a measurement for temperature reads, “49.4”, the uncertainty would be 𝜔𝑇 = 0.05.
For 𝑥𝑎𝑣𝑒, Equation (9) reduces to,
𝜔𝑥𝑎𝑣𝑒
=
𝜔𝑥
√𝑛
(10)
Using Equations (9) and (10), the final uncertainty in ∆𝑇 will be,
𝜔∆𝑇 = √(𝜔𝑇ℎ,𝑎𝑣𝑒
𝜕𝑓
𝜕𝑇ℎ
)
2
+ (𝜔𝑇𝑐,𝑎𝑣𝑒
𝜕𝑓
𝜕𝑇𝑐
)
2
= √(𝜔𝑇ℎ,𝑎𝑣𝑒
)
2
+ (𝜔𝑇𝑐,𝑎𝑣𝑒
)
2
where ∆𝑇 = 𝑇ℎ,𝑎𝑣𝑒 − 𝑇𝑐,𝑎𝑣𝑒. 𝜔∆𝑇 can be used to find the uncertainty in 𝑆 as follows,
𝜔𝑆 = √(𝜔𝑉𝑎𝑣𝑒
1
∆𝑇
)
2
+ (𝜔∆𝑇
𝑉
𝑎𝑣𝑒
(∆𝑇)2
)
2
To find the uncertainty in 𝛽, first the uncertainty in the function, 𝑔(𝑆,𝑇) = 𝑆𝑇𝑐,𝑎𝑣𝑒, must be found:
𝜔𝑔 = √(𝜔𝑆𝑇𝑐,𝑎𝑣𝑒 )
2
+ (𝜔𝑇𝑐,𝑎𝑣𝑒
𝑆 )
2

7. Finally, uncertainty in 𝛽 = 𝛽(𝑔, 𝑉) is,
𝜔𝛽 = √(𝜔𝑔
1
𝑉
𝑎𝑣𝑒
)
2
+ (𝜔𝑉𝑎𝑣𝑒
𝑆𝑇𝑐,𝑎𝑣𝑒
(𝑉
𝑎𝑣𝑒)2
)
2
When presenting results, 𝜔 should be rounded up to the nearest, single significant digit. In the case of that
digit being rounded to 1, round 𝜔 up to the nearest second significant digit so that there are two significant
digits in total.
Depending on whether 𝜖 or 𝜔 is bigger, the final reported quantities should be in the form,
𝑓 ± 𝜖𝑓 or 𝑓 ± 𝜔𝑓
For example, if the confidence interval produced the larger uncertainty, the calculated COP would be
presented as,
𝛽 ± 𝜖𝛽
Estimated Uncertainty
For average measured values of 𝑇ℎ,𝑎𝑣𝑒 = 353𝐾, 𝑇𝑐,𝑎𝑣𝑒 = 298𝐾°𝐶, and 𝑉
𝑎𝑣𝑒 = 10.0𝑉, the uncertainty in each
measurement would be, 𝜔𝑇 = 0.5𝐾 and 𝜔𝑉 = 0.05𝑉,
⇒ 𝜔𝑇,𝑎𝑣𝑒 =
0.5𝐾
√5
and 𝜔𝑉 =
0.05𝑉
√5
⇒ 𝜔∆𝑇 =
0.5𝐾
√5
The uncertainty in 𝑆 would then be,
⇒ 𝜔𝑆 = √(
0.05𝑉
√5
1
55𝐾
)
2
+ (
0.5𝐾
√5
10.0𝑉
(55𝐾)2
)
2
= 0.0009 𝑉/𝐾
The uncertainty 𝜔𝑔 would be,
𝜔𝑔 = √((0.0009 𝑉/𝐾)(298𝐾))2 + ((0.5𝐾)(0.7 𝑉/𝐾 ))
2
= 0.3 𝑉
⇒ 𝜔𝛽 = √(0.3𝑉
1
10.0𝑉
)
2
+ (0.05𝑉
(0.7𝑉/𝐾)298𝐾
(10.0𝑉)2
)
2
= 0.11
The final value for COP in this case would be written as,
𝐶𝑂𝑃 = 𝛽 ± 0.11

8. References
[1] A. Pesaran, Ph. D., G.-H. Kim and S. Santhanagopalan, "Addressing the Impact of Temperature Extremes
on Large Format Li-Ion Batteries for Vehicle Applications," National Renewable Energy Laboratory,
2013. [Online]. Available: https://www.nrel.gov/docs/fy13osti/58145.pdf. [Accessed June 2021].
[2] D. Banks, Ph. D., "Thermo-Electrics Guide," California State University Fullerton, 2021.
[3] Y. Lyu, A. Siddiquea, S. Majidb, M. Biglarbegiana, S. Gadsdena and S. Mahmud, "Electric vehicle battery
thermal management system with thermoelectric cooling," Energy Reports, vol. 5, pp. 822-827, 2019.
[4] Digi-Key, 2021. [Online]. Available: https://www.digikey.com/en/products/detail/sheetak/SKTC1-127-
06-T100-SS-TF00-ALO/12087879. [Accessed June 2021].