Thermoelectric Microgenerators. Optimization for energy harvesting. Gennady Gromov

      d)

      Figure. 7.1 Temperature dependences of thermoelectric materials properties: Seebeck coefficient (a), electric conductivity (b), thermal conductivity (c) and Figure-of-Merit (d).

      In calculated parameters of thermoelectric microgenerators average characteristics of pair of thermoelements of n-and p-types are applied. Therefore temperature dependences of properties of materials of both n-and p-types and these average dependences are given in Fig. 7.1. Average dependences characterize properties of p-n pair of such thermoelements. In mathematical formulas for parameters of thermoelectric generators such average properties on p-n to pair of thermoelements are just used.

      On the presented temperature dependences it is necessary to make several important remarks.

      Voltage

      Voltage U provided by generator linearly depends on thermoEMF E, defined by Seebeck coefficient α.

      According to temperature dependence α=f(T) (Fig. 7.1a) with increasing of temperature the thermoEMF E, although not significantly, but is growing.

      Maximum power

      Maximum power of generator can be written as

      where N×f – the product of the number N of pairs of thermoelements on the geometrical form-factor f is the specified value.

      The factor α²×σ in thermoelectricity is often called as a “power factor”. This factor is significant both for applications in the field of cooling, and in the generator direction. For generators – it shows dependence of the maximum power of P_max of generator on parameters α and σ of thermoelectric material (7.5).

      Since both parameters α and σ have temperature dependencies, with multidirectional (Fig. 7.1a and 7.1b, respectively), to understand the temperature dependence of maximum power P_max you must be aware of the temperature dependence of α²×σ that is presented in Fig.7.2.

      Figure. 7.2 Dependence of α²×σ on temperature.

      Follows from this temperature dependence that useful power decreases with growth of temperature.

      Coefficient of performance

      In the first approximation energy conversion efficiency (4.1) can be expressed as the following

      Apparently from a formula (7.6) at the given temperature difference (for example, single ΔT=1℃) efficiency η approximately linearly depends on Figure-of-Merit Z. But this dependence becomes complicated existence of a factor – fractions with Figure-of-Merit parameter.

      We will consider the modes of the maximum efficiency m≈1.4 and maximum power mode m=1. Simplified formulas for the efficiency for such modes are the following, respectively.

      Fractional factors in both formulas (7.7) and (7.8) – Figure-of Merit factors, have temperature dependences, as shown in Fig. 7.3.

      Figure. 7.3 Dependence of Figure-of-Merit on temperature.

      The key parameter of material (its Figure-of Merit Z) influencing efficiency has obviously expressed maximum near room temperatures (Fig. 7.1g) – in the range of 280—290K.