Characterization of Peltier cells for energy harvesting applications (III)

As demonstrated in the former post, the equivalent voltage source of the cell depends on the temperature difference of the surfaces and takes a value of V_o = 0.0245 \cdot \Delta T and the internal series resistor is R_s = 2.24~\Omega. Therefore, there would be different power outputs considering the resistor load and the temperature difference. The next plot shows the delivered power to a set of loads and four temperature differences \Delta T =[5,~10,~15,~20] degree Celsius. The maximum power given by the cell is delivered to a load that equals the internal resistor, R_s=R_L and takes a value of:

P_{max}=\frac{V_o^2}{4R_L}&s=1 W

potencias.png

If a difference of temperatures of 20 ºC is achieved the voltage at the load would be 245 mV and it would draw a current of 109.4 mA, the maximum power would reach 26.8 mW when connecting a load of 2.24~\Omega. Of course, all these data are hypothetical since the assumptions are in the most optimistic side considering that R_s=R_L. Even under these circumstances a voltage booster would be needed to increase the voltage to a level according to the requirements of the MCU. For instance, the ultralow power STM32L432 ARM Cortex M4 requires at least a power supply of 1.71 V. There are two options to increase the voltage, using voltage multipliers or using DC-DC converters.

Voltage multipliers

These circuits use a combination of diodes and capacitors that allows to duplicate the voltage at the input in every stage. A common setup is the Cockcroft-Walton configuration as the shown in this paper to multiply the voltage obtained from events that create pulses that can reach peaks of 1 V or more. In the case of one or two Peltier cells connected in series, this circuit is out of the question since the Schottky diodes with the lowest forward voltage drop are close to 250 mV so they would consume the voltage provided by the cell or cells.

Cockcroft-Walton_Mod.png

Voltage boosters

Voltage boosters or DC-DC step-up converters would be the most feasible solution. The working principle is easy. The inductance L is charged closing switch S storing a magnetic field. This field will maintain the current flowing towards load R when S is opened. Since the inductance is giving energy to the load the voltage at L is effectively reversed and added to v_i(t) increasing the voltage at the output, v_o(t). The switching should be done fast to avoid a total magnetic discharge of the coil when S is open and a total depletion of capacitor C when S is closed. The diode D prevents the capacitor from discharging through S.Booster.png

This idea has been implemented in integrated circuits (IC) that scavenge small quantities of energy from the source, in our case the Pletier cell, to drive the switch and are able to increase the voltage at the output upto 3.3 V or 5 V depending on the MCU connected. Some examples of these IC and their behavior under real conditions are shown in the next post.