CHARACTERISTICS OF SOLAR CELLS

CHARACTERISTICS OF SOLAR CELLS

Equivalent Circuit Of  A Solar Cell

To understand the electronic behavior of a solar cell, it is useful to create a model which is electrically equivalent, and is based on discrete electrical components whose behavior is well known.

 Fig3.1.1 Equivalent Circuit Of Solar Cell

An ideal solar cell may be modeled by a current source in parallel with a diode; in practice no solar cell is ideal, so a shunt resistance and a series resistance component are added to the model. The resulting equivalent circuit of a solar cell is shown. Also shown,  the  schematic representation of a solar cell for use in circuit diagrams

1 Characteristic equation

From the equivalent circuit it is evident that the current produced by the solar cell is equal to that produced by the current source, minus that which flows through the diode, minus that which flows through the shunt resistor

I = I_L − I_D − I_SH

Where,

I =output current (amperes)

IL = output generated current (amperes)

ID = diode current (amperes)  

ISH = shunt current (ampers)

The current through these elements is governed by the voltage across them:

Vj = V+IRS

Where,

Vj = voltage across both diode and resistor RHS (volts)

V =  voltage across the output terminals (volts)

I =output current (amperes)

Rs = series resistance (Ω)

By the Shockley diode equation, the current diverted through the diode is:

Where,

Io = reverse saturation current (amperes)

n = diode ideality factor (1 for an ideal diode)

q = elementary charge

k =  Boltzmann's constant

T = absolute temperature

By Ohm's law, the current diverted through the shunt resistor is:

Substituting these into the first equation produces the characteristic equation of a solar cell, which relates solar cell parameters to the output current and voltage:

An alternative derivation produces an equation similar in appearance, but with V on the left hand side. The two alternatives are identities; that is, they yield precisely the same results. In principle, given a particular operating voltage V the equation may be solved to determine the operating current I at that voltage. However, because the equation involves I on both sides in a transcendental function the equation has no general analytical solution. However, even without a solution it is physically instructive. Furthermore, it is easily solved using numerical methods. Since the parameters I₀, n, R_S, and R_SH cannot be measured directly, the most common application of the characteristic equation is nonlinear regression to extract the values of these parameters on the basis of their combined effect on solar cell behavior.

2 Open-circuit voltage and short-circuit current

When the cell is operated at open circuit, I = 0 and the voltage across the output terminals is defined as the open-circuit voltage. Assuming the shunt resistance is high enough to neglect the final term of the characteristic equation, the open-circuit voltage V_OC is:

Similarly, when the cell is operated at short circuit, V = 0 and the current I through the terminals is defined as the short-circuit current. It can be shown that for a high-quality solar cell (low R_S and I₀, and high R_SH) the short circuit current I_SC is:

The values of I₀, R_S, and R_SH are dependent upon the physical size of the solar cell. In Comparing otherwise identical cells, a cell with twice the surface area of another will, in Principle, have double the I₀ because it has twice the junction area across which current can leak. It will also have half the R_S and R_SH because it has twice the cross-sectional area

Through which current can flow. For this reason, the characteristic equation is frequently written in terms of current density, or current produced per unit cell area:

where,

J =  current density (amperes/cm2)

JL = photo generated current density (amperes/cm2)

Jo = reverse saturation current density (amperes/cm2)

rs = specific series resistance (Ω-cm2)

rSH = specific shunt resistsnce (Ω-cm2)

formulation has several advantages. One is that since cell characteristics are referenced to a common cross-sectional area they may be compared for cells of different physical dimensions. While this is of limited benefit in a manufacturing setting, where all cells tend to be the same size, it is useful in research and in comparing cells between manufacturers. Another advantage is that the density equation naturally scales the parameter values to similar orders of magnitude, which can make numerical extraction of them simpler and more accurate even with naive solution methods.

This formulation has several advantages. One is that since cell characteristics are referenced to a common cross-sectional area they may be compared for cells of different physical dimensions. While this is of limited benefit in a manufacturing setting, where all cells tend to be the same size, it is useful in research and in comparing cells between manufacturers. Another advantage is that the density equation naturally scales the parameter values to similar orders of magnitude, which can make numerical extraction of them simpler and more accurate even with naive solution methods.

A practical limitation of this formulation is that as cell sizes shrink, certain parasitic effects grow in importance and can affect the extracted parameter values so very small cells may exhibit higher values of J₀ or lower values of r_SH than larger cells that are otherwise identical. In such cases, comparisons between cells must be made cautiously and with these effects in mind

3I-V Curve of Solar Cell

PV cells can be modeled as a current source in parallel with a diode. When there is no light present to generate any current, the PV cell behaves like a diode. As the intensity of incident light increases, current is generated by the PV cell, as illustrated in Figure.

1 Curve of PV Cell and Associated Electrical Diagram

2 V-I and P-V curve of solar cell                                                                      

3 I-V curve of an illuminated PV cell

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