Page 160 - A Comprehensive Guide to Solar Energy Systems

Chapter 8 • Photovoltaics: The Basics 161

FIGURE 8.6 The equivalent circuit. (A) An ideal PV cell. (B) A real PV cell.

If the surface of the PV cell is irradiated with a constant irradiance, then J PV is the den-
sity of the current generated in the volume of the cell structure. In the irradiated area A ill
of the cell structure (a part of the total cell area A may be shaded by metallic contacts), the
current I PV = A ill J PV is generated. The voltage V j across the junction is influenced by the load
resistance R L . Then, a part of photo-generated current I d flows through the diode and a
part of generated current I sh flows through the parallel resistance R p , I sh = V j /R p . The output
current I can be expressed by

I = I PV − I d − I . (8.15) I=IPV−Id−Ish.
sh
The analytical solution is relatively easy for solar cells with Pn junction. From Pn junc-
tion theory, it follows that the voltage V j across the junction and the junction current den-
sity J are connected by the equation
     
J = J 01  exp  qV j  −  + J 02  exp  qV j  −  1 , (8.16)
1


2
  ζ kT     ζ kT   J=J01expqVjζ 1 kT−1+J02expqVjζ 2
1
1 1 
 D n D p kT−1,
= n q +
2
where ζ 1 and ζ 2 are so-called diode factors (1 ≤ ζ 1 ≤ 2, ζ 2 ≥ 2); J 01 i   J01=ni2qDnLn1pp0+DpLp1nn0
p
n
 Lp p0 Ln n0 
qn d
= i represent diffusion and generation-recombination components of the Pn
and J 02 J02=qnidτsc
τ sc
junction reverse current density. In eq. (8.16), the full form of the Pn junction I–V charac-
teristics including generation-recombination processes in the Pn junction space charge
region has been used. usually, the simplified form of I–V characteristics is used, which is a
relatively good approximation (e.g., in the case of crystalline silicon) for V j > 0.4 V,
  
J = J 01  exp  qV j  −  1 . (8.17)

  ζ kT   J=J01expqVjζ 1 kT−1.
1
If V is the output voltage and I is the output current and R s is the series resistance, there
is a voltage V + IR s across the Pn junction forward biasing the diode. Therefore, if A is the
total solar cell area, the output current, eq. (8.15), is given by
  V + R I     V + R I   V + R I
I = A J − I 01  exp  q s  −  − I1 02  exp  q s  −  −1 s , (8.18)
illPV
2
1
  ζ kT     ζ kT   R p I=AillJPV−I01expqV+RsIζ 1 kT−1−I
02expqV+RsIζ 2 kT−1−V+RsIRp,
where J PV is density of current generated in the volume of the cell structure, A ill ≤ A is the
illuminated area of the cell, I 01 = AJ 01 and I 02 = AJ 02 .