Since conventional methods are incapable of estimating the parameters of Photovoltaic (PV) models with high accuracy, bioinspired algorithms have attracted significant attention in the last decade. Cuckoo Search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. In this paper, a CSbased parameter estimation method is proposed to extract the parameters of singlediode models for commercial PV generators. Simulation results and experimental data show that the CS algorithm is capable of obtaining all the parameters with extremely high accuracy, depicted by a low RootMeanSquaredError (RMSE) value. The proposed method outperforms other algorithms applied in this study.
Photovoltaic (PV) cells, normally assembled into modules or arrays on mounting systems, are capable of producing electrons when photons strike its surface. Taking the advantages of many promising features like renewability, less pollution, and ease of installation, PV generators are envisaged to be an important energy source for the future.
Due to the high initial cost of a PVsupplied system, predictive performance tools are widely used by engineers to optimize the system performance [
PV model, with the ability to predict
Analytical methods [
Cuckoo Search (CS) is a natureinspired optimization algorithm based on the fascinating breeding behavior such as brood parasitism of certain species of cuckoos. In [
The rest of the paper is organized as follows. Section
PV cells are made of a variety of semiconductor materials using different manufacturing processes. The working principle of PV cells is essentially on the basis of the PV effect, which refers to the generation of a potential difference at the
In (
SDM assumes that the superposition principle holds; that is, the total characteristic is the sum of the dark and illuminated characteristics [
The equivalent circuit of the SDM.
PV module is a particular case of the PV cells connected in series. If the number of the connected cells is up to
In this sense,
The traditional SDM ignores the operating conditions effect on these parameters. However, some studies have shown that the parameters, such as
In [
where
Based on the diode theory, Messenger and Ventre [
where
In [
where the values of the resistances
By using the aforementioned relations, the ISDM described in [
PV parameter estimation is a process that minimizes the difference between the measured data and the calculated current by adjusting the normal PV parameters. When the number of experimental data is up to
For the case of ISDM
The CS algorithm [
A cuckoo lays an egg and dumps it randomly into other bird species’ nests.
The best nests with high quality eggs will be carried forward to the next generation.
There are a fixed number of available host nests. If a host bird discovers that the eggs are not its own, it will either throw these alien eggs away, or it may abandon the nest and build a brand new nest at a nearby location.
Based on the three rules, the basic steps of CS can be summarized by the pseudocode shown in Pseudocode
Cuckoo Search via Lévy Flights
Initialization of
Choose a cuckoo egg by Lévy flights and evaluate
its fitness
Choose an egg in other’s nest randomly and
calculate its fitness
If
A fraction
replaced by new ones;
Preserve good nests (best solutions).
where
Before the searching process, the CS algorithm detects the most successful pattern as
where
After initialization, the evolution phase of the
The CS algorithm will evaluate the fitness of the random pattern. If a better solution is caught, the
With the aim of providing a thorough evaluation of the CS algorithm in estimating the PV parameters, both SDM and ISDM are considered in this paper. Two case studies are designed to estimate the CS algorithm in model parameters estimation:
a commercial 57 mm diameter solar cell (R.T.C. France [
a PV module (KC200GT Multicrystal Photovoltaic Module) operating under varied environment conditions.
During the parameter extraction process, the objective function
Statistical analysis is performed to evaluate the quality of the fitted models to the experimental data. Besides RMSE, other two fundamental measures, namely, Individual Absolute Error (IAE) and the Mean Absolute Error (MAE), are applied to evaluate in this paper. Equations (
The optimization algorithms applied in this paper are programmed in MATLAB. Similar simulation conditions, including population size, maximum generation number, and search ranges, are set to ensure a fair evaluation (population size = 25; maximum generation number = 5000).
Table
A comparison between the parameter results obtained by the CS algorithm and that of other algorithms from the SDM.
CS  CPSO [ 
GA [ 
PS [  


0.7608  0.7607  0.7619  0.7617 






1.4812  1.5033  1.5751  1.6 

0.0364  0.0354  0.0299  0.0313 

53.7185  59.012  42.3729  61.1026 
RMSE  0.0010  0.0014  0.0191  0.0149 
During the parameter estimation process for the SDM, the values of the objective function in different optimization algorithms are shown in Figure
Convergence process of different optimization algorithms during the parameter estimation process of the SDM.
Table
Parameters of the ISDM obtained by the CS algorithm.








0.7361 

1.5009  0.0355  57.8394  0.0031  1.0020 
A comparison between the errors of ISDM and SDM. The parameters are extracted by the CS algorithm.
No 






1 

0.7640  0.7639  0.0001  0.0001 
2 

0.7620  0.7626  0.0006  0.0007 
3 

0.7605  0.7614  0.0009  0.0009 
4  0.0057  0.7605  0.7602  0.0003  0.0003 
5  0.0646  0.7600  0.7592  0.0008  0.0009 
6  0.1185  0.7590  0.7583  0.0007  0.0010 
7  0.1678  0.7570  0.7574  0.0004  0.0001 
8  0.2132  0.7570  0.7565  0.0005  0.0009 
9  0.2545  0.7555  0.7555  0.0000  0.0004 
10  0.2924  0.7540  0.7540  0.0000  0.0003 
11  0.3269  0.7505  0.7517  0.0012  0.0009 
12  0.3585  0.7465  0.7476  0.0011  0.0009 
13  0.3873  0.7385  0.7402  0.0017  0.0016 
14  0.4137  0.7280  0.7273  0.0007  0.0006 
15  0.4373  0.7065  0.7066  0.0001  0.0005 
16  0.4590  0.6755  0.6748  0.0007  0.0002 
17  0.4784  0.6320  0.6304  0.0016  0.0011 
18  0.4960  0.5730  0.5717  0.0013  0.0009 
19  0.5119  0.4990  0.4994  0.0004  0.0005 
20  0.5265  0.4130  0.4137  0.0007  0.0005 
21  0.5398  0.3165  0.3176  0.0011  0.0007 
22  0.5521  0.2120  0.2127  0.0007  0.0001 
23  0.5633  0.1035  0.1033  0.0002  0.0008 
24  0.5736 


0.0011  0.0008 
25  0.5833 


0.0014  0.0014 
26  0.5900 


0.0005  0.0009 
 
MAE  0.0007  0.0007  
RMSE  0.0010  0.0010 
In this section, the validity of the CS algorithm is evaluated using KC200GT PV module operating under different environment conditions. The estimated parameters, both in the SDM and ISDM, are shown in Table
Parameters of the KC200GT PV module obtained by the CS algorithm.
SDM parameters (extracted by the CS algorithm)






8.1729  4.23 
1.0090  0.2665  140.4875 
ISDM parameters (extracted by the CS algorithm)








8.1847  5.12 
1.0170  0.2574  117.9224  0.0028  1.2474 
Figure
The simulated
Figure
A comparison of the individual absolute errors among different PV modeling methods: (a) under different irradiance levels; (b) under different temperature levels.
To further validate the accuracy of the CS algorithm, the extracted parameters are compared to the ones obtained using GA in Figure
A comparison of the individual absolute errors between CS and GA based ISDM: (a) under different irradiance levels; (b) under different temperature levels.
In this work, the Cuckoo Search (CS) algorithm is applied to estimate the parameters of two PV models, namely, Single Diode Model (SDM) and its improved version (ISDM). The feasibility of the proposed method has been validated by estimating the parameters of two commercial PV generators. The simulation and experimental results showed that the CS algorithm is capable of not only extracting all the parameters of the SDM under a certain condition but also successfully estimating all the parameters of ISDM under different operating conditions. In statistical analysis, CS algorithm recorded the lowest RMSE value compared to other algorithms such as GA, PSO and PS.
By using the parameters extracted at the STCs, the
The authors are grateful to Professor XinShe Yang for the sharing of Cuckoo Search source code online. Without his generosity, this work would not be possible. This research is supported by the National Natural Science Foundation of China under Grant 61070085.