2.4.2 Connecting a load resistor RL across the output terminals of the module

If we set the load resistance RL to the value of the internal resistance of the thermoelectric module RM of 4.6491 Ohms, the load resistance becomes:

$$R\_L = 4.6491 \Omega$$

2.4.3 The closed-circuit voltage V

The open-circuit voltage Voc was calculated in 2.4.1, and in this case, when a load resistor RL is connected across the output terminals of the thermoelectric module, the closed-circuit voltage V is:

$$V = 5.544\,\text{V}$$

## 2.4.4 The circuit current I

With a load resistance RL connected across the output terminals of the module, the current I can be found by (Eq. (27)) as:

Thermoelectric Energy Harvesting DOI: http://dx.doi.org/10.5772/intechopen.85670

where α<sup>m</sup> is the module's average Seebeck coefficient, σ<sup>m</sup> is the average electrical

conductivity, and λ<sup>m</sup> is the module average thermal conductivity, at a specific

2.4 A numerical analysis of a thermoelectric power generation module

Tm <sup>¼</sup> Th <sup>þ</sup> Tc

Tm <sup>¼</sup> <sup>400</sup> <sup>þ</sup> <sup>300</sup> 2

Tm ¼ 350 Kelvin

2.4.1 The thermoelectric module open-circuit voltage Voc

According to [12], with an average module temperature of 350 K, the module thermoelectric parameters are; a Seebeck coefficient α<sup>m</sup> of 0.05544 V/K; a module resistance RM of 4.6491 Ohms; and a thermal conductivity KM of

The thermoelectric module open-circuit output voltage Voc can be found by

Voc ¼ αmð Þ¼ Th � Tc 0:05544 � ð Þ 400 � 300 Voc ¼ 5:544 V

If we set the load resistance RL to the value of the internal resistance of the

RL ¼ 4:6491Ω

The open-circuit voltage Voc was calculated in 2.4.1, and in this case, when a load resistor RL is connected across the output terminals of the thermoelectric module,

V ¼ 5:544 V

With a load resistance RL connected across the output terminals of the module,

2.4.2 Connecting a load resistor RL across the output terminals of the module

thermoelectric module RM of 4.6491 Ohms, the load resistance becomes:

If we consider a thermoelectric module, [12] have published some general material properties data for a 127 thermoelectric couple module. For the purpose of this analysis, we will use a hot side temperature TH of 400 K, and a cold side temperature TC of 300 K. The Seebeck coefficient and module resistance is temperature dependent, hence, their values should be calculated at the average module

<sup>2</sup> measured in kelvin

(36)

operating temperature.

A Guide to Small-Scale Energy Harvesting Techniques

temperature Tm given by:

0.4422 W/K.

using (Eq. (26)) as:

2.4.3 The closed-circuit voltage V

the closed-circuit voltage V is:

the current I can be found by (Eq. (27)) as:

2.4.4 The circuit current I

22

$$I = \frac{V}{R\_M + R\_L} = \frac{5.544}{4.6491 + 4.6491} = \frac{5.544}{9.2982}$$

$$I = 0.596 \text{ A}$$

2.4.5 The load current IL and the voltage generated at the load VL

The load current IL is the same value as the circuit current I, hence:

$$I\_L = 0.596 \text{ A}$$

The voltage generated at the load can be found by (Eq. (29)) as:

$$V\_L = I\_L \times R\_L = 0.596 \times 4.6491$$

$$V\_L = 2.7710 \text{V}$$

2.4.6 The electrical power generated at the load PL

The electrical power generated by the module at the load can now be found by (Eq. (30)) as:

$$P\_L = I\_L^2 \times R\_L = 0.596^2 \times 4.6491$$

$$P\_L = 1.6514 \text{ W}$$

or by using (Eq. (31)) as:

$$P\_L = V\_L \times I\_L = 2.7710 \times 0.596$$

$$P\_L = 1.6515 \text{W}$$

#### 2.4.7 The efficiency of the thermoelectric module η

The cooling power at the hot side of the thermoelectric couple Qh can be found by (Eq. (33)) as:

$$\begin{aligned} \mathbf{Q}\_h &= (a\_m)IT\_h - (T\_c - T\_h)(K\_m) - \frac{I^2(R\_m)}{2} \\\\ \mathbf{Q}\_h &= ((0.05544) \times 0.596 \times 400) - ((300 - 400)(0.4422)) - \frac{0.596^2(4.6491)}{2} \\\\ \mathbf{Q}\_h &= 13.2169 - (-100 \times (0.4422)) - \frac{0.3552 \times (4.6491)}{2} \\\\ \mathbf{Q}\_h &= 13.2169 + 44.22 - 0.8257 \\\\ \mathbf{Q}\_h &= 56.62 \text{W} \end{aligned}$$

Hence, the efficiency of the thermoelectric module η can now be found by Eq. (32) as:

$$\eta = \frac{P\_L}{Q\_h} = \frac{1.6515}{56.62}$$


#### Table 1.

Summary of performance characteristics of a 127 couple thermoelectric module obtained by theoretical calculation.

η ¼ 0:0292

Thermoelectric module efficiency with a temperature difference ΔT between 0 and 100 K (theoretical results).

or η ¼ 0:0292 � 100 ¼ 2:92%

thermoelectric power generation with a temperature difference ΔT varied between

A summary of the performance characteristics of the 127 couple thermoelectric module obtained by theoretical calculation is shown in Table 1. The temperature difference ΔT, which is equal to TH�TC, has been varied between 0 and 100 kelvin, in 10 kelvin steps, and the results calculated. The thermoelectric module's power generated at the load PL, voltage VL, current IL, and efficiency η, is shown in Figures 5–7 respectively. The results demonstrate the theoretical electrical power generated by a 127 couple thermoelectric module is typically in the mW to watt range when the module is subject to a temperature difference from 10 to 100 K.

2.4.8 Numerical analysis of the 127 couple thermoelectric module configured for

3. Thermoelectric power generation and energy harvesting system

Thermoelectric power generation systems have typically needed to have a very high temperature gradient across the thermoelectric module(s) in order to achieve a useful electrical power output. This limitation has been a barrier to the successful application of this technology for power generation, and limited the technologies use to mainly niche applications, for example, in deep-space spacecraft power. However, with parallel developments in the area of electrical energy storage in supercapacitors, and low power DC to DC converters and boost converters, it is possible to develop a thermoelectric energy harvesting system that will operate from very low temperature gradients of around 1 K and be able to output useful power levels. This was previously very difficult to achieve and would have required several thermoelectric modules to be connected electrically in series, and thermally in parallel, increasing the overall system weight, size, and cost, and would only

0 and 100 K

Thermoelectric Energy Harvesting

DOI: http://dx.doi.org/10.5772/intechopen.85670

Figure 7.

25

#### Figure 5.

Power generated at the load PL with a temperature difference ΔT between 0 and 100 Kelvin (theoretical results).

#### Figure 6.

Voltage VL and Current IL generated at the load with a temperature difference ΔT between 0 and 100 Kelvin (theoretical results).

Figure 7. Thermoelectric module efficiency with a temperature difference ΔT between 0 and 100 K (theoretical results).

η ¼ 0:0292

$$\text{or } \eta = 0.0292 \times 100 = 2.9296$$
