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5. Modeling and Simulation of Photovoltaic Systems 243

2
where NOCT is the normal operating cell temperature (800 W/m solar irradiance

and 20 C air temperature) and G is the actual irradiance.
Another PV array model that was experimentally validated with success and has
been used by several authors in the literature is the Sandia Array Performance Model
(SAPM). The SAPM model is an empirical model defined by the following equa-
tions [52,53].
The model uses the normalized irradiance, E e , defined as follows:
G
E e ¼ (7.23)
G ref
Then, the current and voltage of the MPP of the PV array, I mg and V mg , can be
calculated by using the following equations:
2

I mg ¼ N pm I mpo C 0 E e þ C 1 E ð1 þ a Imp ðT c T ref ÞÞ (7.24)
e
h i
2
V mg ¼ N sm V mpo þ C 2 N s dðT c ÞlnðE e Þþ C 3 N s ðdðT c ÞlnðE e ÞÞ þ b Vmp e ðT c T ref Þ
E
(7.25)
nkðT c þ 273:15Þ
dðT c Þ¼ (7.26)
q
where I mpo and V mpo are the STC PV module current and voltage at the MPP; C 0 and
C 1 are empirically determined coefficients that relate Imp to the effective irradiance,
C 0 þC 1 ¼1; a Imp is the normalized temperature coefficient for Imp; C 2 and C 3 also
are empirical coefficients that relate Vmp to the effective irradiance; d(T c ) is the ther-
mal voltage per cell at temperature T c ; q is the elementary charge; k is the Boltz-
mann’s constant; and b Vmp is the temperature coefficient for module Vmp at STC.

5.2 INVERTER MODEL
The inverters convert DC power from the PVarray on AC power that can be injected
into the grid or used to supply AC loads present in the system. The DC to AC con-
version efficiency, h inv , of the inverter is given by the following equation:

R
E AC P AC dt
h inv ¼ ¼ R (7.27)
E DC P DC dt
where P AC and E AC are the power and energy at the inverter output, respectively, and
E DC and P DC the energy and power at the inverter input, output of the PV array.
Several models can be found in the literature introducing different approaches to
estimate the energy conversion of inverters in GCPVSs [54,55]. A model that was
widely used proposed the following equation to estimate h inv by including electrical
losses of the device [56]:

P AC =P NOM
h inv ¼ (7.28)
P AC =P NOM þ k O þ k 1 ðP AC =P NOM Þþ k 2 ðP AC =P NOM Þ 2