Equivalent Circuits for Solar Cells

The current-voltage characteristic of an ideal solar cell in (4.57) can be seen as the sum of the currents from a diode in the dark j q = jrev[exp(el//A T) — l] and from a current source contributing jig = jsc. This leads to the equivalent circuit of an ideal solar cell sketched in Fig. 4.10, consisting of an ideal diode and a current source in parallel. 

The simplest extension to real device operation in a stationary state consists in introducing losses via a series resistance Rs, which represents contact resistances, Ohmic losses in the front contact grid and in the rear contact, and a parallel resistance Rp, which includes any current bypassing the membranes (junction), and even shunt currents through short-cuts. 

The total current density for the real diode is now composed of three contributions, the photoinduced short-circuit current, the diode current and the shunt current through Rp  

The j/V curve is substantially modified by these two resistors, since the series resistor consumes the voltage V(RS) = jRs, whereas the shunt adds the current density jp = (V — jRs)/Rv to the output current density. 

For only small deviations from the ideal values Rs = 0, and Rp — oo, the influence of both losses on the j/V curve can be derived analytically by differentiating (4.94) with respect to V. In particular modes of operation such as V(j = 0) = K,c (open circuit) and V(j = jsc) = 0 (short circuit), and provided that Rs -C Rp [a reasonable assumption since Rs and Rp designate the departure from i s,ideal = 0, and i p,ideal oo, respectively], we find 

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Fig. 4.10. Equivalent circuits for solar cells. Left ideal solar cell consisting of a current source — jsc shunted by a diode. Right real solar cell with additional shunt resistor Rp and series resistor Rs...

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