Thermoelectric Microgenerators. Optimization for energy harvesting. Gennady Gromov

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      In a case of non-zero parasitic thermal resistance the optimal case is the equality Ȓ’_TEG=Ȓ_c. This is equivalent to the ideal case of half temperature difference on the generator module (ΔT=½ΔT_s). The dependence of the power from the temperature difference is quadratic. This explains the ¼ of the optimum output power (5.18—5.19).

      The construction of thermoelectric generators allows quite easily manage their thermal resistance. Namely, to obtain the optimal solution for the thermal resistance (thermal resistance change) there is a direct way to change the height and/or cross-sections of thermoelements of generator module.

      Heat runs directly in thermoelectric generator through the thermoelements. Their thermal resistance is fundamental in the total thermal resistance of TE generator. Therefore, variation in height and cross section of thermoelements allows optimizing thermal resistance of the TE generator for maximum efficiency.

      Thermal resistance of working generator

      It must be noted that in the working generator module the effective thermal resistance, namely, the ratio of temperature difference to transported heat power differs from the thermal resistance related to the heat conductivity (Chapter 2). And approach of optimization on thermal resistance needs to be applied to the effective thermal resistance, i.e. taking into account ratios (2.24)-(2.26).

      In contrast to thermal resistance of thermal conductivity Ȓ_TEG the effective thermal resistance Ȓ’_TEG of working thermoelectric generator depends on the operating mode (2.28).

      – When an open electrical circuit the m=∞ and Ȓ’_TEG=Ȓ_TEG.

      – At maximum efficiency mode the value m_opt≈1.4 is given by the expression (4.2). If ZT≈1, the effective thermal resistance Ȓ’_TEG turns out to be approximately 29% less then thermal resistance of thermal conductivity Ȓ_TEG.

      – In maximum power mode m=1 and the effective thermal resistance of approximately a third less than Ȓ_TEG.

      Since the heat resistances at maximum power (5.20) and maximum efficiency (5.21) modes differ slightly, it is often convenient to perform all calculations and modeling for maximum power mode with m=1.

      Chapter 6. Design optimization

      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 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 R_load 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.

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