Characterization of Peltier cells for energy harvesting applications (II)

With the setup described in the last post, the temperature of one of the surfaces of the cells can be controlled with an electrical current, the other surface is cooled passively with a heatsink. The resistors and the two temperature sensors are connected to the same voltage source taking advantage of the wide range of voltages supported by the LM35. The outputs of the LM35 are connected directly to two multimeters to measure the differences of temperature achieved between the two surfaces. Now, the process is easy: the resistors are heated with different currents and the output voltages of the cell and the temperatures are registered. This will solve the voltage source of the equivalent electric circuit of the cell in open circuit or the Thévenin voltage. The results are represented in the next Figure showing a perfect linearity between temperature and voltage.

VthVsT.png

I_s = [0.49~0.59~0.69~0.79] A
V_s = [12.3~14.6~17.3~20] V

V_o = [62.4~140.5~252.5~414~580~775] mV

T_h = [24.8~30.2~38.4~55.0~66.5~82.7] degree Celsius
T_c = [22.5~24.5~28.0~38.0~42.9~51.0] degree Celsius

Where, I_s and V_s are the current and voltage applied by the power supply to the resistors, respectively; V_o is the output of the cell and T_h and T_c are the temperatures of the hot and cold sides of the cell, respectively. The plot shows that V_o = 0.0245 \cdot \Delta T with the slope in V / ºC.

The next test will determine the equivalent series resistance, R_s, of the cell loading it with a known resistor, R_L = 13.5~\Omega. In this case, the current given by the cell provokes a voltage drop in the internal resistor R_s so the voltage applied to R_L, V_L, is smaller than the open circuit voltage, V_o > V_L.  A new set of measurements is conducted injecting the same current to the heating resistors to determine this voltage and, then, the internal resistance of the cell:

V_L = [51.9~121.1~ 211.7~ 344.1~ 486~ 639] mV

T_h = [27.6~ 33.2~ 40.7~ 53.0~ 65.0~ 79.3] degree Celsius
T_c = [25.5~ 27.7~ 30.7~ 36.7~ 41.9~ 48.6] degree Celsius

VLVsT

The blue plot represents the voltage in open circuit, V_o, and the red plot the voltage at the load, V_L. Dividing this voltage by the load resistor yields the current given by the cell, I_L. Therefore, the internal resistor is calculated applying Ohm’s Law knowing that the voltage drop is V_o - V_L and the current is I_L. This is done for several points along the experimental results in the plot giving a constant value for the resistor, R_s = 2.24~\Omega. The same process is repeated for another cell of the same type and the result for R_s differ from the first cell giving R_s = 4.75~\Omega. Even when the former internal resistor is double the latter one, the results have been re-checked and confirmed and are in agreement to other results found in the literature.

Once the cell has been characterized, it is possible to determine the current that it will give to a known load. The next step is to devise a method to store the energy delivered by the cell or to explore the possibility of boosting the voltage to drive an MCU (microcontroller unit) directly. This will be explained in the next post.

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