### Equivalent circuit, output power and fill factor

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1) Equivalent circuit Figure 1 shows the equivalent circuit of a solar cell under stable illumination. It consists of the following circuit elements: a current source capable of generating a photocurrent I_{L}, a diode V_{D} under forward bias, a resistor R_{sh} in parallel with the diode, a capacitor C_{f}, and a resistor Rs in series with the output. The photocurrent l_{L} provides the forward current I_{D}=I_{0} (e^{eUj/AKT}-1) of the diode, the bypass current l_{Rp} and the load current I.

2) Output power According to Figure 1, under the illumination, the output power P of the solar cell obtained on the load R_{L} is:

When the load RL changes from zero to infinity, the I-U characteristic curve of the solar cell as shown in Figure 2 can be drawn. Any point on the curve is called the working point, the line connecting the working point and the origin is the load line, and the inverse of the slope of the load line is equal to RL. When the load resistance R_{L} is adjusted to a certain value R_{m}, the optimal operating point M (also called the maximum power point) of the solar cell can be obtained on the curve, and the product of the corresponding operating current I_{m} and operating voltage U_{m} reaches the maximum value.

P_{m}=I_{m}U_{m} (1-2)

I_{m} is called the optimum working current, U_{m} is the optimum working voltage, R_{m} is the optimum load resistance, and P_{m} is the maximum output power.

3) Fill factor Fill factor (FF) is an important parameter to evaluate the quality of solar cells, which is defined as the ratio of the maximum output power P_{m} of the solar cell to the product of open circuit voltage and short circuit current (U_{oc}I_{sc}).

Under a certain light intensity, the larger the FF, the higher the output power. FF is closely related to incident light intensity, reverse saturation current, curve factor and series/parallel resistance.

Usually the I-U characteristic curve relationship is obtained by using a single-diode equivalent circuit, and assuming that the parallel resistance R_{sh} is infinite and the series resistance R_{s}=0 in the ideal situation. But in fact, the carrier recombination current in the base region, the emitter region and the space charge region is distinguished, and the two-diode equivalent circuit with two diodes is used to fit the actual I-U characteristic curve better,as shown in Figure 3. In the figure, I_{D}_{1} represents the saturation current of the body region or surface through the recombination of trap energy levels, and the corresponding diode curve factor A=1; I_{D2} represents the saturation current recombined in the depletion region or grain boundary of the PN junction, and the corresponding diode curve factor A=2.