Читать книгу Thermoelectric Microgenerators. Optimization for energy harvesting - Gennady Gromov - Страница 8

Summary. In this Chapter dependences of parameters of thermoelectric generators on elements of their design are considered. The analysis is provided on the example of the known wide nomenclature range of microgenerator modules. On these examples it is given an idea, what parameters of generators and what role they play in their efficiency and in consumer properties.

Introduction

Useful formulas are illustrated on the example of series of standard TE microgenerators developed earlier [5] in the TEC Microsystems GmbH company in relation to tasks of “low power” – energy harvesting applications.

The nomenclature of thermoelectric modules of TEC Microsystems GmbH is developed with use of classification system of thermoelectric micromodules [6]. This classification allows systematizing thermoelectric micromodules on series in compliance with their parameters and features of a design (see also Chapter 12).

Thus, logical ranks of micromodules convenient for their choice for practical applications are created.

Number of thermoelements

The number of thermoelements 2N in the generator module at the specified temperature difference ∆T and Seebeck coefficient αdetermines the key characteristic – total thermoEMF E.

The value of thermoEMF E provided by the generator determines the output voltage U in the load circuit.

Depending on value of load resistance R_load the working voltageU range of generator could vary widely.

In maximum power mode

If to increase load resistance Rload in the limit we have

Value of thermoEMF E and corerspoindingly output voltage U of generators are variable; depend on the value of temperature drop ∆T. It is not so convenient for consumers of such non-stable power supply – to electronic devices.

Always it is necessary to use electronic DC-DC converter to transform the generator variable voltage to the standard supply voltage of electronic devices.

The DC-DC converters have restrictions on the minimum input voltage which they can transform. It needs to be taken into account. And thermoelectric generators selected for practical applications must be capable to give working voltage not below the minimum threshold of the applied DC-DC converter. In more detail about the choice of a DC-DC converters see Chapter 10.

Zones of applicability of modern DC-DC converters with the minimum input voltage are given in Fig. 6.1. It is, for instance, 20 mV (Linear Technology) [3], 80 mV and 250 mV (Texas Instruments) [4].

Figure. 6.1 ThermoEMF E depending on the number of pellet pairs N under various temperature differences ΔT.

Besides, low input voltage of the DC-DC converter requires to pay additional “cost”. It is the converter efficiency. The input voltage is lower – the efficiency of transformation of the DC-DC electronic scheme is lower.

In this regard it is more preferable to use generators giving the bigger thermoEMF, i.e. generators with a large number of thermoelements (see Fig. 6.1). Besides, practical tasks sometimes force to leave absolutely optimal solutions for generator. I.e. to use electric loads with a resistance bigger, than ACR, to increase the output voltage of the generator, though by reduction of generator’s efficiency.

It means to consider efficiencies of thermoelectric generator and DC-DC electrical circuit in a combination to obtain maximal output value (see Chapter 10).

Form-factor of thermoelements

The form-factor f of thermoelements of the generator module determines its total electric resistance.

where f – form-factor of a thermoelement.

Here we neglect the additional resistance of the generator module construction (conductors, places of soldering of thermoelements, resistance of barrier layers). In most cases it is valid, as this additional resistance is insignificant usually in comparison of the sum of resistance of thermoelements (6.5).

Then

The formula for maximum power P_max through the generator number of thermoelements N and their form-factor f has a finite shape

Thermal resistance

Thermal resistance Ȓ_TEG of thermoelectric generator determines its overall performance.

Formula (6.8) can be converted to a dependence of maximum power P_max vs thermal resistance Ȓ_TEG of generator.

Figure. 6.2 Power P_max of generators of different series (developed by TEC Microsystems) vs their thermal resistance Ȓ_TEG at different temperature differences ΔT: Points mark the boundaries of the applicability of these series (1MD02, 1MD03, 1MD04 and 1MD06).

This formula (6.10) and the provided graph (Fig. 6.2) are important for understanding of features of practical applications of generator modules and the choice of optimal solutions.

The power provided by the generator depends on its Figure-of-Merit Z, thermal resistance Ȓ_TEG and temperature difference ∆T.

– Figure-of-Merit Z is defined by properties of the thermoelectric material used in the generator module and a design of the module. For different designs of generators average Figure-of-Merit Z – it a little changeable size is at the level of 2.8…3.0⨯10^—3 K^-1 (Table 7.1).

– Temperature difference ∆T for a specific case is the value set up by the heat source and the environment.

– The only changeable parameter is the thermal resistance Ȓ_TEG. It can vary widely for a particular design of TE generator just by changing the form-factor – by height and cross-section of thermoelements and number of the thermoelements.

Fig. 6.2 shows the broad range of applicability of modules of given nomenclature. It is due to an opportunity in these series to change form-factor (cross-section and height) of thermoelements and its number.

Coefficient of performance

In accordance with (2.21) the efficiency of the thermoelectric microgenerator in the modes of the maximum power (m=1) or maximum efficiency when m_opt~1.4 (4.5) is determined only by the performance of the thermoelectric material – Figure-of-Merit Z, temperature difference on the generator module ∆T and averaged working temperature (T_h+T_c) /2.

For practical estimates the efficiency values at averaged temperature 320K and typical values of Figure-of-Merit Z (Chapter 7, Table 7.1) of generator micromodules are given in Table 6.1.

Table 6.1 Efficiency of generator modules depending on temperature difference (at average temperature 320K).

For the small temperature differences it is possible with good precision to consider that every degree of temperature difference provides: in the mode of the maximum power the efficiency ~ 0.047%, and in the mode of the maximum efficiency ~ 0.048% of the efficiency.

It should be noted, at increasing of average temperature the efficiency falls down (see Chapter 7). For example, in Chapter 4 it has been shown that at average temperature 300K by one degree of temperature difference the efficiency is about 0.05% (Table 4.1).

From Table 6.1 it follows that at a temperature slightly above (320K) – efficiency per one degree is slightly lower (~ 0.047%). It is explained by temperature dependences of thermoelectric material of the generators (Chapter 7, Fig. 7.3).

Heat flow density

At given efficiency the total converted power will be determined by heat flow Q_c passing through the generator module. And it is set by the capacity of the heat source and the heat transport “capacity” (inverse of thermal resistance) of the generator itself. These characteristics must be coordinated.

For coordination it is useful to operate with value of heat flow density on unit of the heat giving surface and heat flow density which is passed by unit of generator surface.

Heat flow density (2.26) is given by the formula:

where x – packing density of pellets in TE generator module; k – thermal conductivity of the thermoelements (pellet) thermoelectric material.

where δ – distance between thermoelements, a – cross-section of the thermoelement.

For practical estimates the data for heat flow density for various types of generator micromodules are provided in Table 6.4.

Thus, at the given temperature difference and the given characteristic of heat conductivity of material of the generator module, heat flow density depends on density of packing of thermoelements in the module design (6.11). The more densely they are packed (less gap between thermoelements), the generator is more powerful.

Density of heat flow passing through the generator characterizes its specific power. This specific characteristic allows calculating of absolute values of a heat flow through the chosen generator module.

Comparison of heat flow density of the heat giving surface and density of a heat flow via the generator gives the answer to a question whether it is necessary in a design of the generator device the big surface of heat collecting. I.e. whether it is necessary to collect and concentrate heat on the generator for his effective work.

Table 6.2. The density of heat flow through different types of generator micromodules at various temperature differences.

From Table 6.2 it is seen that heat flow density via the generator micromodule can reach several units of W/cm². To provide such power densities may require heat flow concentrators from heat source (case of low power heat source).

This is important issue for energy harvesting tasks, where low-power heat sources usually have very small values of heat flow power density.

Illustrative example – recycling of the human body heat. Heat flow density of such kind of heat “source” is small compared with tabular values for the microgenerators (Table 6.2) – no more than 10^—1…10^—2 W/cm². Clearly, the generator device in such tasks should include heat flow concentrators. Moreover, the area of such a hub should significantly exceed size of the generator micromodule.

Another example is soil generators which utilize heat flowing in the upper layers of soil in the daily cycle. Here the heat flows have values at the level of 100W/m² (0.01W/cm²). It also requires the concentration of heat for the supply to generator micromodule.

Another important task is to effectively dissipate heat passed through the generator. If this is not achieved, the useful heat, transported through generator system, limited to a size not more than wasted on a radiator.

Here it is also important to the specific characteristics of the density of heat flow through the radiator -" flow capacity” of the radiator. It is necessary to calculate the dimensions of the radiator (see Chapter 9). In many practical cases, dimensions of a heat sink should be also noticeably larger than the generator micromodule.