Page 66 - Applied Photovoltaics

P | c V I c R c I
m mp mp s mp
§ c I ·
| P ¨ 1 mp R ¸
mp ¨ s ¸
c V
© mp ¹
§ I ·
| P 1 ¨ sc R . ¸
mp ¨ s ¸
© V oc ¹
If the characteristic resistance of a solar cell is defined as (Green, 1982)

V
R oc (3.17)
ch
I sc
it is possible to define a ‘normalised R s ’ such that
R
r s (3.18)
s
R
ch
Hence
FF | 0 FF 1 r s (3.19)

or, empirically but more accurately
2
r
1
FF s FF 0 | 1 . 1 r s (3.20)
s
4 . 5
which is valid for r s < 0.4 and v oc > 10.
Similarly, for shunt resistance, it is possible to define

R
r sh (3.21)
sh
R
ch
Then, as before
§ 1 ·
¨
FF | FF 1 ¸ (3.22)
0 ¨ ¸
© r sh ¹
or, again more accurately (Green, 1992)
ª v 7.0 FF º
FF FF 1 oc 0 » (3.23)
«
sh 0
¬ v oc r sh ¼
which is valid for r sh > 0.4.
In the presence of both series and shunt resistances, the I-V curve of a solar cell is
given by

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