Solar Cell Equivalent Circuit:

Solar cell is a current source, the electronic characteristic of which can be represented by an equivalent circuit as shown in figure below.

Equivalent Circuit

An ideal solar cell equivalent circuit consists of a current source (Iph ) and a diode. But in practice there are two extra resistances, one in series (Rs) and the other in parallel (Rsh). The series resistance is because of the fact that a solar cell is not a perfect conductor and represents the ohmic loss. The parallel resistance is caused by the recombination of electron-hole pair or leakage current from one terminal to the other due to poor insulation at edges.

From the equivalent circuit diagram,

Iph – Id – Ish = I

Where,

I_d = I_o*[exp(q*V_d / nkT) – 1]

V_d = V + I*R_s

I_sh = V_d / R_sh

Hence, I_ph – I_o*[exp(q*( V + I*R_s ) / nkT) – 1] – (V + I*R_s ) / R_sh = I

Iph = Current produced by the solar cell       Id = Diode current

I_sh = Shunt or leakage current                      I = Load current

I_o = Reverse saturation current of diode      q = Charge of an electron

V = Voltage across load                               n = Diode quality factor

k = Boltzmann’s constant                            T = Absolute temperature of the cell

Generally, series resistance is of very low value and shunt resistance is of very high value. Ideally, Rs = 0 & Rsh =  ∞. A shunt resistance of a few hundred ohms does not reduce the output power of the solar cell appreciably.  In reality, Rsh is much larger than a few hundred ohms and can in most cases be neglected.  The series resistance, however, can drastically reduce output power.

Short circuit current (I_sc) and Open circuit voltage (V_oc): Two quantities of interest for solar cell i.e. I_sc & V_oc can be calculated from the above equivalent circuit equation by neglecting R_sh .

Putting I = 0, V_oc = (nkT/q)*ln(I_ph/I_o +1)

Putting V = 0, I_sc = I_ph – I_o*[exp(qI_scR_s / nkT) – 1]

If we further neglect R_s i.e. R_s = 0, then

Isc = Iph