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 α determines 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 Rload the working voltage U 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 Pmax through the generator number of thermoelements N and their form-factor f has a finite shape
Thermal resistance
Thermal resistance ȒTEG of thermoelectric generator determines its overall performance.
Formula (6.8) can be converted to a dependence of maximum power Pmax vs thermal resistance ȒTEG of generator.
Figure. 6.2 Power Pmax of generators of different series (developed by TEC Microsystems) vs their thermal resistance ȒTEG 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 ȒTEG 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 ȒTEG. 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 mopt~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 (Th+Tc)/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