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Correct extraction of the equivalent circuit model parameters of photovoltaic modules is of great significance for power prediction, fault diagnosis, and system optimization of photovoltaic power generation systems. Although there are many methods developed to extract the equivalent circuit model parameters of the photovoltaic module, it is still challenging to ensure the stability and operational efficiency of the extract method. In order to effectively extract the parameters of photovoltaic modules, this paper proposes a hybrid algorithm combining analytical methods and differential evolution algorithms for the extraction parameters of PV module. Firstly, the analytical method is applied to simplify the equivalent circuit model and improve the efficiency of the algorithm. Then, the adaptive algorithm is used to adjust the parameters of the differential evolution algorithm. Through the algorithm proposed in this paper, the parameters of the equivalent circuit model of the photovoltaic module can be extracted by the open-circuit voltage, short-circuit current, and maximum power point current and voltage provided by the manufacturer. The proposed method is applied to the extraction of the parameters of the dual-diode equivalent circuit model of different types of photovoltaic modules. The reliability and computational efficiency of the proposed algorithm are verified by comparison and analysis.

With the emphasis on environmental and energy issues, photovoltaic power generation technology is widely used. In order to predict the power generation of photovoltaic power generation systems [

The simulation models of solar cells currently widely used include single-diode models and two-diode models [

To find a fast, simple, and accurate method for modeling solar cells, Chin et al. [

Tao et al. [

In order to maintain the advantages of the differential evolution algorithm and suppress the “premature maturity” phenomenon, researchers at home and abroad have improved the differential evolution algorithm. The improved method can be divided into two types, one is the improvement of the algorithm parameters and steps, such as Qin et al. [

The aim of this paper is to develop a PV module parameter extraction algorithm that combines the analytical method with the improved differential evolution algorithm. The algorithm can accurately extract the PV module parameters based on the dual-diode circuit model and has higher computational efficiency. In the proposed algorithm, the equivalent circuit model is simplified by the analytical method to improve the efficiency of the algorithm. Then, the adaptive algorithm is used to adjust the parameters in the differential evolution algorithm to avoid the algorithm falling into local optimum and improve the convergence speed. Finally, using the above algorithm and the open-circuit voltage, short-circuit current, and maximum power point current and voltage of the photovoltaic module provided by the manufacturer, the equivalent circuit model parameters of the photovoltaic module can be extracted. The proposed method is applied to the extraction of dual-diode equivalent circuit model parameters of different types of photovoltaic modules. The comparison and analysis indicate that the proposed algorithm has high reliability and competitive computational efficiency.

The main contributions of this paper are as follows:

A hybrid algorithm combining analytical methods and differential evolution algorithms is developed for PV parameter estimation. In this method, the analytical method is applied to simplify the equivalent circuit model and improve the efficiency of the algorithm

The proposed algorithm employs an adaptive method to adjust the parameters in the differential evolution algorithm to avoid the algorithm getting into the local best and speed up the convergence of the algorithm

The proposed algorithm is applied to extract parameters of three different PV modules. The obtained results of the method proposed in this paper are compared with well-established algorithms to confirm its effectiveness

The rest of the paper is organized as follows: Section

The model of the photovoltaic module based on the two diodes is shown in Figure

Two-diode circuit model for the PV module.

The short-circuit current

In this paper, using the test data provided by the manufacturer, combined with the numerical solution method and differential evolution algorithm, a method of modeling and parameter optimization of photovoltaic cells using only PV module test parameters is proposed.

First, the manufacturer provides the short-circuit status point data into formula (

Normally,

Similarly, it is available to substitute the open-circuit voltage state point (

Set

According to the analysis of Yahya-Khotbehsara and Shahhoseini [

Substituting equation (

Similarly, substituting the maximum power state point (

At this point, there are only three unknown parameters in the PV module model:

It can also be written as

Therefore, the objective function in the differential optimization algorithm is defined as

When applying the differential evolution algorithm to search for, three parameters, in order to ensure that the solution is a feasible solution, the parameter changes must be constrained. According to the literature [

When

The algorithm flow chart proposed in this paper.

The differential evolution algorithm is an intelligent optimization algorithm with simple programming and fast convergence. It has strong adaptability to multipeak function optimization problems. It has been optimized in mechanism, image recognition, target tracking, and so on. The field is widely used. With the deepening of human research, the DE algorithm is also applied to the extraction of PV module parameters. However, since the differential evolution algorithm is a random self-heuristic search algorithm, in high-dimensional and multipeak problems, the algorithm will appear “premature,” thus falling into the local best. The basic DE algorithm flow is as follows.

The DE algorithm first randomly generates NP

Each element in the vector is randomly generated according to

Individuals are randomly selected in the current population, and the mutated individuals are generated by the scaling operation, thereby realizing the search for different regions in the feasible domain. The mutation formula is

In order to maintain the diversity of the population, the mutated individuals are exchanged with the original individual information to generate new individuals. The crossoperating operator can be expressed as

Comparing the appropriateness of the original individual and the candidate individual, select the moderately good individual to enter the next iterative process, so as to optimize the decision variable. The selection operator is as in

Although the basic differential evolution algorithm has a fast convergence speed, its stability and robustness are poor. In order to maintain the fastness of the parameter optimization process and maintain good stability, literature [

The specific method of parameter adaptive adjustment is as follows.

For an individual, its crossover probability

In the formula, the effect of

In the formula, the initial value of

In order to effectively extract the parameters of the PV module, the parameter setting of the differential evolution algorithm is very important. In Reference [

In order to verify the proposed method, three different photovoltaic modules were selected, including monocrystalline silicon components, polycrystalline silicon components, and thin film components. The parameters were extracted and compared by different methods. The test data was obtained from the manufacturer’s instructions. The parameters of the three components provided by the manufacturer under STC are shown in Table

Parameters of three kinds of PV module.

Parameter | Unit | SP75 | S25 | ST36 |
---|---|---|---|---|

ISC,STC | A | 4.8 | 1.5 | 2.68 |

VOC,STC | V | 21.7 | 21.4 | 22.9 |

IMPP,STC | A | 4.4 | 1.45 | 2.28 |

VMPP,STC | V | 17 | 16.5 | 15.8 |

KI | mA/°C | 2 | 0.7 | 0.32 |

KV | mV/°C | -76.0 | -76.0 | -100 |

KIP | mA/°C | 0.26 | 0.26 | 0.45 |

KVP | mV/°C | -76.0 | -76.0 | -100 |

NS | — | 36 | 36 | 42 |

The statistical results for RTC France PV cell and Photowatt-PWP 201 PV module.

PV module | Parameters | Algorithm | Mean | SD |
---|---|---|---|---|

SP75 | DE | 1.041 | 6.899 | |

SP75 | IDE | 1.054 | 1.342 | |

SP75 | DE | 2.071 | 0.024 | |

SP75 | IDE | 2.34 | 0.013 | |

SP75 | DE | 0.405 | 0.009 | |

SP75 | IDE | 0.331 | 0.006 | |

S25 | DE | 1.031 | 0.002 | |

S25 | IDE | 1.039 | 0.005 | |

S25 | DE | 2.156 | 0.046 | |

S25 | IDE | 2.257 | 0.034 | |

S25 | DE | 0.779 | 0.013 | |

S25 | IDE | 0.780 | 0.005 | |

ST36 | DE | 1.643 | 0.080 | |

ST36 | IDE | 1.679 | 0.082 | |

ST36 | DE | 2.062 | 0.015 | |

ST36 | IDE | 2.071 | 0.012 | |

ST36 | DE | 1.258 | 0.010 | |

ST36 | IDE | 1.347 | 0.009 |

Convergence graph of the parameter optimization process using DE and IDE.

Extraction parameters of SP75 module with different methods.

Method | |||||||
---|---|---|---|---|---|---|---|

DE | 4.80 | 6.33 |
1.05 |
1.042 | 2.059 | 0.394 | 633.93 |

IDE | 4.80 | 0.15 | 0.40 | 1.36 | 2.37 | 0.320 | 383.11 |

Extraction parameters of S25 module with different methods.

Method | |||||||
---|---|---|---|---|---|---|---|

DE | 1.50 | 2.542 |
1.687 |
1.031 | 2.147 | 0.779 | 2672.8 |

IDE | 1.50 | 1.043 |
2.70 |
1.097 | 2.239 | 0.833 | 1683.6 |

Extraction parameters of S25 module with different methods.

Method | |||||||
---|---|---|---|---|---|---|---|

DE | 2.68 | 2.521 |
6.53 |
2.45 | 2.82 | 0.952 | 270.51 |

IDE | 2.684 | 5.436 |
8.40 |
1.66 | 2.062 | 1.254 | 1044.6 |

Mean absolute error at different environmental conditions for three kinds of PV module.

Method | Modules | Irradiance (W/m^{2}) |
Temperature (°C) | MSE |
---|---|---|---|---|

DE | SP75 | 1000 | 25 | 0.015 |

DE | SP75 | 600 | 25 | 0.023 |

DE | SP75 | 1000 | 20 | 0.039 |

DE | SP75 | 1000 | 60 | 0.063 |

IDE | SP75 | 1000 | 25 | 0.023 |

IDE | SP75 | 600 | 25 | 0.034 |

IDE | SP75 | 1000 | 20 | 0.139 |

IDE | SP75 | 1000 | 60 | 0.099 |

DE | S25 | 1000 | 25 | 0.013 |

DE | S25 | 600 | 25 | 0.011 |

DE | S25 | 1000 | 20 | 0.011 |

DE | S25 | 1000 | 60 | 0.018 |

IDE | S25 | 1000 | 25 | 0.012 |

IDE | S25 | 600 | 25 | 0.012 |

IDE | S25 | 1000 | 20 | 0.016 |

IDE | S25 | 1000 | 60 | 0.026 |

DE | ST36 | 1000 | 25 | 0.026 |

DE | ST36 | 600 | 25 | 0.011 |

DE | ST36 | 1000 | 20 | 0.031 |

DE | ST36 | 1000 | 60 | 0.019 |

IDE | ST36 | 1000 | 25 | 0.028 |

IDE | ST36 | 600 | 25 | 0.043 |

IDE | ST36 | 1000 | 20 | 0.034 |

IDE | ST36 | 1000 | 60 | 0.036 |

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Set the absolute error

With the CPU: Intel i5-4210U@2.39 GHz, memory: 12 GB computing environment, using the method proposed in this paper and the method of [

Time on extracting parameters from three kinds of PV modules by different methods.

Method | Modules | Irradiance (W/m^{2}) |
Temperature (°C) | Time (ms) |
---|---|---|---|---|

DE | SP75 | 1000 | 25 | 2.845 |

DE | SP75 | 600 | 25 | 2.745 |

DE | SP75 | 1000 | 20 | 2.796 |

DE | SP75 | 1000 | 60 | 3.124 |

IDE | SP75 | 1000 | 25 | 1.975 |

IDE | SP75 | 600 | 25 | 1.854 |

IDE | SP75 | 1000 | 20 | 1.842 |

IDE | SP75 | 1000 | 60 | 2.026 |

DE | S25 | 1000 | 25 | 2.762 |

DE | S25 | 600 | 25 | 2.975 |

DE | S25 | 1000 | 20 | 2.874 |

DE | S25 | 1000 | 60 | 2.975 |

IDE | S25 | 1000 | 25 | 1.696 |

IDE | S25 | 600 | 25 | 1.852 |

IDE | S25 | 1000 | 20 | 1.796 |

IDE | S25 | 1000 | 60 | 1.927 |

DE | ST36 | 1000 | 25 | 2.951 |

DE | ST36 | 600 | 25 | 3.246 |

DE | ST36 | 1000 | 20 | 2.987 |

DE | ST36 | 1000 | 60 | 2.994 |

IDE | ST36 | 1000 | 25 | 1.786 |

IDE | ST36 | 600 | 25 | 1.954 |

IDE | ST36 | 1000 | 20 | 1.997 |

IDE | ST36 | 1000 | 60 | 1.849 |

Figures

Absolute error comparison of SP75 modules with different extraction methods under STC.

Absolute error comparison of S25 module with different extraction methods under STC.

Absolute error comparison of ST36 modules with different extraction methods under STC.

This paper proposes a hybrid photovoltaic module parameter extraction algorithm that combines the analytical method with the improved differential evolution algorithm. It only needs four parameters that are the open-circuit voltage, short-circuit current, and maximum power point current and voltage of the photovoltaic module provided by the manufacturer; then, the parameters of the photovoltaic module based on the dual-diode equivalent circuit model are extracted. In the proposed algorithm, the equivalent circuit model is simplified by the analytical method to improve the efficiency of the algorithm. Then, the adaptive algorithm is used to adjust the parameters in the differential evolution algorithm to avoid the algorithm falling into local optimum and improve the convergence speed. In this paper, a comprehensive experimental test is carried out on the algorithm to study the performance of the algorithm on the parameter extraction of different types of photovoltaic modules. Compared with other recent methods, experimental and statistical analysis proves the superiority of the proposed algorithm in terms of accuracy, reliability, and computational efficiency.

The experimental data used to support the findings of this study are included within the article.

The authors declare no conflict of interest.

H.W. and Z.S. conceived the paper and designed and performed the simulations; H.W. wrote and revised the paper; H.W. and Z.S. finally analyzed the data.

This research was supported by the Special Financial Aid to Post-Doctor Research Fellow in Chongqing (grant Xm2014086); Science and Technology Research Project of the Chongqing Municipal Education Commission (grant KJ131321), and Science and Technology Research Project of Yangtze Normal University (grant 2013XJ2D004).