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46 CHAPTER 1 Solar Cells and Arrays: Principles, Analysis, and Design

Table 1.1 Summary of Mathematical Equations for the Solar Cell or Module
!
qðVþIR s Þ
I ¼ I ph I s e nk B T 1 VþIR s
R sh

3 qE g
1 1
T nk B T T STC
I ph ¼ I phðSTCÞ þ K I ðT T STC Þ I s ¼ I sðSTCÞ T STC e

G I SCðSTCÞ
I sðSTCÞ ¼ !
I phðSTCÞ ¼ I SCðSTCÞ G STC
qV ocðSTCÞ
e nk B T STC 1
V oc ¼ V ocðSTCÞ þ K v ðT T STC Þ
where, E g is the band gap energy of the semiconductor; G is the surface irradiance of the cell; G STC is
2
the irradiance under STC (¼1000 W/m ); I s(STC) is the nominal saturation current; I SC(STC) is the short
circuit current per cell at T STC ; k B is the Boltzmann’s constant; K I is the temperature coefficient of short-
circuit current; K v is the temperature coefficient of open-circuit voltage; n is the diode ideality factor;
STC is standard test conditions (T STC ¼ 25 C); T is the absolute temperature in K.

R sh ,and n. In this section, we present two methods that can be implemented using
Ò
Matlab to extract the mentioned parameters. The extraction is mainly based on
the manufacturer’s specification datasheets or experimental data. Most solar cell
manufacturers include in the datasheet, at the least, information about the
following at STC:
• short circuit current, I sc , and short circuit current/temperature coefficient K i
• open circuit voltage, V oc , and open circuit voltage/temperature coefficient K v
• MPP: the optimum operating point at V ¼ V mp and I ¼ I mp .
Table 1.2 shows the steps and equations used for extracting the single-diode
model parameters using two methods. The first method relies on estimating the ide-
ality factor n, while the other is performed by getting an initial value for the shunt
resistance [39,40].
6.1.3 PSpice Model of the Solar Cell
The PSpice model of the subcircuit of an ideal solar cell can be implemented as fol-
lows [37]. First, all parameters are defined:

.param Isc_STC ¼ 3.87, Ns ¼ 36, n ¼ {ncell*Ns}, ncell ¼ 1.35, G ¼ 1000
þ Rs ¼ 0.1606, Rsh ¼ 385.86, Ki ¼ 2.6e 3Kv ¼ 0.08, Voc_STC ¼ 21.

Temperature and temperature-dependent parameters are also included. For
example:

.param Tmod ¼ 25
.param Io ¼ {((RshþRs)*Isc_STC Voc)/(Rsh*exp(Voc/(n*Vtn)))}
.param Iph_STC ¼ {(Isc_STC*(1 þ Rs/Rsh) þ Io*(exp(Iscn*Rs/(n*Vtn)) 1))}
.param Iph ¼ {Iph_STCþKi*(Tmod-25)}, Voc ¼ {Voc_STC þ Kv*(Tmod-25)}
þ Vtn ¼ {0.0257*(Tmod þ 273)/298}