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

The equivalent circuit starts with the photogenerated current, which could be
assigned to a G-device which is a voltage-controlled current source. Then the circuit
may look like:

*vbias is added to trace the load current
vbias 1 0 dc 0
*to define the photogenerated current
virrad 2 0 dc {G}
*the PV module is to be defined as a subcircuit model
xPV 0 1 2 PV_mod

The subcircuit net list could be written as follows:

.subckt PV_mod 100 103 102
girrad 100 101 value ¼ {(Iph/1000)*V(102)}
d1 101 100 diode
.model diode d(is ¼ {Io}, N ¼ {n}, LEVEL ¼ 3)
rs 101 103 {Rs}
rsh 101 100 {Rsh}
.ends PV_mod

Finally, many analysis could be done using .TEMP (to sweep the temperature) or
.dc (to sweep the voltage) and so on. For example, the following order will sweep the
DC bias voltage to get the IeV characteristics.

.dc vbias 0 21 0.01

Also, we can sweep any parameter to examine its effect on the IeV characteris-
tics. For example, the following orders will sweep the irradiance and the cell ideality
factor, respectively, to get different curves at the same time.

.step param G list 1000 800 600 400 200
.step param ncell list 1.2 1.35

6.1.4 Case Studies
Here, we consider two case studies to validate the modeling and extraction tech-
niques provided in the previous subsections. The first case study is the Photowatt-
PWP 201 solar module. The module is composed of 36 solar cells connected in
series (N s ¼ 36) and measured at 45 C [41]. This example has been widely used

by different authors as benchmark to check for parameter extraction validity. The
second case study is the BP MSX-60 solar module, which consists of 36 series solar
cells [42]. The measurements of the Photowatt-PWP 201 and the datasheet specifi-
cations of the BP MSX-60 are given in Table 1.3.