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244 CHAPTER 7 Strategies for Fault Detection and Diagnosis

where K 0 , K 1 , and K 2 are mathematical coefficients and P NOM is the nominal power
of the inverter.
Another empirical model useful in simulations of inverter for GCPVS applica-
tions was proposed by Sandia: the Sandia Inverter Performance Model (SIPM)
[57]. The inverter performance is characterized by the following equations:

P ACo 2
P AC ¼ CðA BÞ ðP DC BÞþ CðP DC BÞ (7.29)
A B
A ¼ P DCo ½1 þ C 1 ðV DC V DCo ފ (7.30)

B ¼ P so ½1 þ C 2 ðV DC V DCo ފ (7.31)
C ¼ C o ½1 þ C 3 ðV DC V DCo ފ (7.32)
where V DC is the input voltage, P ACo is the maximum AC-power rating of the
inverter at nominal operating condition, P DCo and V DCo are the DC-power and
DC-voltage levels, respectively, at which the AC-power rating is achieved at the
reference operating condition, P so is the DC-power required to start the inversion
process, and C o, C 1 , C 2 , and C 3 are empirical coefficients.

5.3 PARAMETER EXTRACTION TECHNIQUES
As discussed in the previous sections, the models of PV modules, arrays, and in-
verters used in the simulation of the PV system behavior include a set of several
model parameters. Some of the model parameters can be esteemed in the character-
ization process of PV modules and inverters. However, others are empirical param-
eters obtained by fitting techniques to experimental curves. To obtain accurate
simulation results, the estimation of the model parameters is crucial. Parameter
extraction techniques are used for this purpose. The parameter extraction techniques
evaluate the model parameters described in the previous sections, using measured
data of solar irradiance and module temperature together with DC and AC output
currents and voltages as inputs.
The parameter extraction techniques can be based on different optimization al-
gorithms applied to linear and nonlinear systems. These algorithms define objective
functions for optimization of fittings. One of the most widely used algorithms for
dealing with data-fitting applications is the LevenbergeMarquardt algorithm
(LMA) [29]. Bio-inspired methods based on the Genetic Algorithm (GA) [58], Par-
ticle Swarm Optimization (PSO) [59,60], Simulated Annealing (SA) [61], Harmony
Search (HS) [62], Pattern Search (PS) [63], Differential Evolution (DE) [64], and
Artificial Bee Colony (ABC) [65,66] have proven to be useful in modeling PV sys-
tems because of their good accuracy degree [67,68].

5.4 SIMULATION TOOLS

Several simulation tools and different computational environments are available for
the simulation of PV systems independently of the models used for this purpose. As