Working of Generic Photovoltaic Cell

 Introduction : Generic Photovoltaic Cell

When the p-n junction is exposed to sunlight, photons are absorbed by the semiconductor material. As the photon is absorbed, electron-hole pair is formed. If these mobile charge carriers reach the vicinity of the junction, the electric field in the depletion region will push the holes into the p-side and the electrons into the n-side. The p-side of the junction collects holes, and the n-side of junction collects electrons; thus, voltage is generated that can be used to deliver current to a load.

If electrical (metallic grid) contacts are attached to the top, and ohmic contact is attached to the bottom of the cell, electrons will flow out of the n-type into the connecting wire, through the load, and back to the p-side. Since wire cannot conduct holes, it is only the electrons that actually move around the circuit. When they reach the p-side, they recombine with holes completing the circuit. By convention, positive current flows in the opposite direction to electron flow, so the current arrow in the figure shows current going from the p-side to the load and back into the n-side.

Fig 1: Working of Generic Photovoltaic Cell

Fig 2: Electron flows from n-side contact, through load, and back to the p-side where it recombines with holes. 

Equivalent Circuit for a Photovoltaic Cell

A equivalent circuit model for a PV cell consists of a real diode in parallel with an ideal current source. The ideal current source delivers current in proportion to the solar flux ( irradiance ) to which it is exposed.

 

Fig 3: Simple eq. ckt of PV cell consist of a current source driven by sunlight in parallel with practical diode. 

There are two particular interests with photovoltaic equivalent circuit.

1. the current that flows when the terminals are shorted together (the short-circuit current, I_SC) and

2. the voltage across the terminals when the leads are left open (the open-circuit voltage, V_OC).

     

                           Fig 4 : Open circuit voltage

         Fig 5 : Short circuit current

When the leads of the equivalent circuit for the PV cell are shorted together, no current flows in the (real) diode since V_d = 0, so all of the current from the ideal source flows through the shorted leads. Since that short-circuit current must equal ISC, the magnitude of the ideal current source itself must be equal to I_SC. Now we can write a voltage and current equation for the equivalent circuit of the photovoltaic cell shown in fig 3. 

I= I_SC − I_d                                     ---------------------------------1

We have diode equation,

I_d = I₀(exp (qVd /nkT) − 1)      ---------------------------------2

Where, n is diode ideality factor.

Equation 1 becomes,

I = I_SC − I₀(exp (qVd /kT) − 1)     ------------------------------3

When the leads from the PV cell are left open, I = 0 and we can solve eq-3 for the open-circuit voltage V_OC:

V_OC = (kT/ q) ln [(I_SC /I₀) + 1]    ------------------------------4

 

Where, Id is the diode current in the direction of the arrow,

 V_d is the voltage across the diode terminals from the p-side to the n-side (V),

I₀ is the reverse saturation current (A),

q is the electron charge (1.602 × 10−19 C),

k is Boltzmann’s constant (1.381 × 10−23 J/K), and

T is the junction temperature (K).

 

Fig 6: I -V curve of PV cell under dark and illuminated cell.

In both of these equations, short-circuit current, ISC, is directly proportional to solar insolation, which means that we can now quite easily plot sets of PV current–voltage curves for varying sunlight. Also, quite often laboratory specifications for the performance of photovoltaics are given per cm² of junction area, in which case the currents in the above equations are written as current densities.

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