Researchers at the University of Yaounde I in Cameroon have proposed to use the Duffing oscillator to amplify very low-voltage output with low solar radiation levels at dawn and sunset.
The Duffing oscillator, or Duffing equation, is a differential equation used to model certain damped and driven oscillators. Named after the German engineer Georg Duffing, the system was originally utilized to resolve complex physical questions and to analyze anharmonic oscillations. Once it became popular, it was used to model stiffening springs, beam buckling, nonlinear electronic circuits, superconducting Josephson parametric amplifiers, and ionization waves in plasmas.
“It corresponds to a second-order non-linear differential equation with or without forcing,” the scientists explained. A forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables.
“The response of the Duffing oscillator highly depends on the nature of the forcage. For a zero or constant input signal, a constant response amplitude is obtained as output. For an alternative or variable input signal, a variable response amplitude is obtained at the output, exhibiting sometimes chaotic behaviors well analyzed in the literature,” they added.
The scientists used Fortran 95 software to simulate a system consisting of a Duffing oscillator, an inverter that reverses the negative voltage of one of the outputs of the oscillator, and a voltage adder to add both positive and reverse negative voltages of the two oscillator outputs. The oscillator is able to amplify and self-regulate the voltage generated by the PV modules using its amplifier circuit and its nonlinear element.
Image: University of Yaounde I, Heliyon, Common License CC BY 4.0
The proposed Duffing oscillator amplifier was connected to a solar cell to quantify the voltage amplification ratio. The group also included a U4 OPAMP current driver and compared the performance of this experimental setup with that of a solar cell connected to a conventional DC-DC boost converter.
“The disadvantage of the DC-DC boost chopper is its constant and limited ratio of output and input voltages, called amplification factor,” the academics specified. “We replace the DC-DC boost chopper with a new block, the electrical Duffing oscillator, to handle this limitation.”
The team conducted both theoretical and experimental investigations and visualized the results on a digital oscilloscope. “From this experimental prototype, by varying the values of the input voltage, we obtain data on the output voltage and therefore the amplification,” it emphasized.
Image: University of Yaounde I, Heliyon, Common License CC BY 4.0
The analysis showed that the Duffing oscillator can amplify the very low solar cell voltages better than the DC-DC boost chopper. The oscillator's ability to self-regulate the voltage of the solar cell was confirmed by the fact it has a high amplification factor for low voltages and a low amplification factor when input voltage increases.
The experimental investigation also showed that the output voltage can reach to 7.03V for an input voltage of 0.43V, which represents a gain of 24.3 decibels (dB).
“Solar cell technology could therefore benefit greatly from the proposed device to solve the problem of low efficiency at low input voltages,” the scientists concluded.
Their findings are available in the study “Amplification of very low output voltages of PV panels using a Duffing oscillator,” which was recently published in Heliyon.
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I don’t see an input and output on the circuit. I can see that boosting the voltage to a more useful level could help with threshold light conditions. Of course the wattage will be low and can’t be increased by a passive circuit.