IJP International Journal of Photoenergy 1687-529X 1110-662X Hindawi 10.1155/2020/6873847 6873847 Research Article Research on Parameter Extraction Method of Photovoltaic Module Based on Improved Hybrid Algorithm https://orcid.org/0000-0002-9698-1290 Wu Haitao12 Shang Zhou3 Grancini Giulia 1 School of Robot Engineering Yangtze Normal University Chongqing 408100 Chinayznu.cn 2 School of Electrical Engineering Chongqing University Chongqing 400044 Chinacqu.edu.cn 3 Xingzhi Primary School of Shenzhen City Shenzhen 518013 China 2020 1312020 2020 14 06 2019 13 11 2019 12 12 2019 1312020 2020 Copyright © 2020 Haitao Wu and Zhou Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.

Science and Technology Research Project of Yangtze Normal University2013XJ2D004Science and Technology Research Project of the Chongqing Municipal Education CommissionKJ131321Special Financial Aid to Post-Doctor Research Fellow in ChongqingXm2014086
1. Introduction

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 , improve the performance of photovoltaic modules, and perform fault diagnosis , extracting model parameters based on an equivalent circuit model of photovoltaic modules has become one of the research hotspots .

The simulation models of solar cells currently widely used include single-diode models and two-diode models . Traditional photovoltaic module modeling uses single-diode models. In recent years, with the deepening of research, researchers have found that the two-diode model takes into account the composite effect of the electrically neutral region and the space charge region, revealing the working mechanism of photovoltaic cells, making the two-diode model more accurate than the single-diode model . However, the equivalent circuit model of the PV module based on the two-diode model is implicitly nonlinear. In equation, it is difficult to find the analytical solution by a traditional algebraic method. In recent years, researchers have proposed a large number of modeling methods of this problem. These methods can be divided into two categories: one is the numerical solution method, and the analytical solution to the model is obtained through some empirical formulas and mathematical techniques. It is shorter, because the method usually ignores some parameters or uses empirical formulas to obtain some parameters. If the parameters are improperly set in the application process, it will affect the accuracy of the modeling . The other type uses the intelligent optimization algorithm, such as the differential evolution (DE) algorithm, particle swarm optimization (PSO) algorithm, and genetic algorithm (GA). These methods do not approximate the parameters during use, which can improve the accuracy of the solution . However, these intelligent optimization algorithms are random optimization algorithms. If the algorithm parameters are set incorrectly, it will affect the stability and robustness of the solution. In addition, these algorithms take a long time to solve high-dimensional optimization problems. There are also two sources of data for PV module modeling. One is the IV data of a PV module obtained under experiment under certain conditions; the other is the standard test condition (STC) provided by the manufacturer: short-circuit current, open-circuit voltage, and voltage and current at the maximum power point. The first type of data comes from experiments. The established model is close to the actual working conditions, but the experimental workload is large, and the test process data will error due to the limitations of the test conditions, resulting in a large model error. The second is data. Standard test data from manufacturers are reliable data source, have small modeling workload, and are widely used in engineering, but this method has a small amount of data; if the modeling method is not appropriate, it will lead to large model error.

To find a fast, simple, and accurate method for modeling solar cells, Chin et al.  proposed a hybrid calculation method that combines numerical solutions with intelligent optimization algorithms to extract the parameters of the photovoltaic module circuit model using standard test data provided by the manufacturer. The solution method is used to obtain the photogenerated current in the solar cell model under standard test conditions, the two equivalent diode reverse saturation currents, and the parallel resistance. Then, the differential evolution algorithm is used to find the ideal factor and series resistance of the two diodes. This method combines two modeling methods to achieve fast and accurate modeling of solar cells. However, in order to maintain the accuracy of the modeling, the method does not make any approximations and assumptions in the numerical solution method, which leads to the complexity of the explicit expression of the parameters, which increases the difficulty of modeling and increases the calculation time. In addition, the evolutionary algorithm has the advantages of easy implementation and optimization for multipeak functions. However, in the evolutionary process of random search, the phenomenon of “premature maturity” is easy to occur, which leads to the local best, which leads to the decline of modeling accuracy.

Tao et al.  used the adaptive differential evolution algorithm to extract the parameters of the PV module based on the two-diode model, but it is modeled by the IV data obtained by the experiment, and the dimensionality of the solution is not caused by the dimension reduction processing of the model. It is higher, is more computational, and has time-consuming modeling. The adaptive differential evolution algorithm used in this paper only makes the scaling factor adaptively adjust with evolutionary algebra. Although this method can avoid the phenomenon of “premature,” the search efficiency and robustness of the algorithm are not improved much.

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 2 introduces the photovoltaic module model based on two diodes. Section 3 describes PV module modeling and parameter optimization problem. Section 4 introduces the principles of the improved differential evolution algorithm. Section 5 presents experimental results and discussion. Section 6 concludes this paper.

2. The Photovoltaic Module Model Based on Two Diodes

The model of the photovoltaic module based on the two diodes is shown in Figure 1. Its mathematical model is as shown in equation (1). (1)I=IPVIo1eV+IRs/Nsn1Vt1Io2eV+IRs/Nsn2Vt1V+IRsRsh,where I is the output current (A) for the photovoltaic module; V is the output voltage (V) for the photovoltaic module; IPV is the photogenerated current (A); Io1 and Io2 are the two equivalent diode reverse saturation currents (A), respectively; n1 and n2 are the ideality factor of the two-diode model; Rs is the equivalent series resistance of the photovoltaic cell (Ω); Rsh is the equivalent parallel resistance of the photovoltaic cell (Ω); and VthT is the thermal temperature coefficient of the photovoltaic cell; its equation is (2)VthT=kTq,where k is the Boltzmann constant (1.38×1023 J/K), T is the absolute temperature (K) for the photovoltaic cell, and q is the electron charge (1.6×1019C).

Two-diode circuit model for the PV module.

The short-circuit current ISC, open-circuit voltage VOC, and maximum power point voltage VMPP and current IMPP at different temperatures and different solar radiation intensities can be obtained by the parameters of the standard test conditions provided by the manufacturer and according to (3)ISC=ISC,STCGGSTC1+KITTSTC,(4)VOC=VOC,STC+VthlnGGSTC+KVTTSTC,(5)VMPP=VMPP,STC+VthlnGGSTC+KVPTTSTC,(6)IMPP=IMPP,STCGGSTC1+KIPTTSTC,where ISC,STC, VOC,STC, IMPP,STC, VMPP,STC, GSTC, and TSTC are the short-circuit current, open-circuit voltage, maximum power point current, maximum power point voltage, solar radiation intensity, and temperature measured under standard test conditions; KI, KV, KIP, and KVP are the short-circuit current, open-circuit voltage, maximum power point current, and maximum power point voltage; and G and T are the radiation intensity and temperature of the photovoltaic module. The manufacturer does not provide the seven parameters IPV, Io1, Io2, n1, n2, Rs, and Rsh contained in equation (1), so the purpose of modeling the PV module was to estimate the above seven parameters from the data provided by the manufacturer. The seven parameters in (1) make the voltage-current curve of the PV module obtained by equation (1) consistent with the measurement curve provided by the manufacturer.

3. PV Module Modeling and Parameter Optimization

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 (1): (7)ISC,STC=IPV,STCIo1,STCeISC,STCRs,STC/Nsn1,STCVth,STC1Io2eISC,STCRs,STC/Nsn2,STCVth,STC1ISC,STCRs,STCRsh,STC,where n1STC and n2STC are the two-diode quality factors in the photovoltaic cell circuit models under standard test conditions, Rs,STC is the equivalent series resistance of the photovoltaic cell under test conditions, Rsh,STC is the equivalent parallel resistance of the photovoltaic cell under the test conditions, and Vth,STC is the thermal temperature coefficient of the photovoltaic cell under test conditions; the mathematical expression is (8)Vth,STC=kTSTCq.

Normally, Io1,STCeISC,STCRs,STC/Nsn1,STCVth,STC10,Io2,STCeISC,STCRs,STC/Nsn2,STCVth,STC10, Rs,ref<<Rp,ref, then equation (1) can be simplified to (9)IPV,STCISC,STC.

Similarly, it is available to substitute the open-circuit voltage state point (Voc,ref, 0) into equation (1): (10)IPV,STCIo1,STCeVOC,STC/Nsn1,STCVth,STC1Io2eVOC,STC/Nsn2,STCVth,STC1VOC,STCRsh,STC=0.

Set (11)XOCi=eVOC,STC/Nsni,STCVth,STC,i=1,2,(12)XMPPi=eVMPP,STC+IMPP,STCRs,STC/Nsni,STCVth,STC,i=1,2.

According to the analysis of Yahya-Khotbehsara and Shahhoseini , in general, Io2,STC is three to four times Io1,STC; it can be expressed by the following formula: (13)Io2,STC=T2/53.77Io1,STC.

Substituting equation (13) into equation (10) and because of the expression that can be obtained (14)Io1,STCISC,STCXOC11+T2/5/3.77XOC21,(15)Io2,STC=T2/53.77ISC,STCXOC11+T2/5/3.77XOC21.

Similarly, substituting the maximum power state point (VMPP,STC, IMPP,STC) into equation (1) is available: (16)IMPP,STC=IPV,STCIo1,STCXMPP11Io2XMPP21VMPP,STC+IMPP,STCRs,STCRsh,STC,(17)Rs,STC=VMPP,STC+IMPP,STCRs,STCIPV,STCIo1,STCXMPP11Io2XMPP21IMPP,STC.

At this point, there are only three unknown parameters in the PV module model: n1,STC, n2,STC, and Rsh,STC. Effectively reduce the dimension of the differential evolution algorithm to solve the problem. In order to use the differential evolution algorithm to solve the remaining unknown parameters, it is necessary to define a suitable objective function. By observing the IV curve of the PV module, it can be found that there is a “knee point,” that is, the maximum power point, and the position of the maximum power point is affected by three parameters: n1,STC, n2,STC, and Rsh,STC, so the PV of the PV module can be optimized by optimizing three parameters. The gradient of the curve at the maximum power point is minimal. According to the above analysis, the output power of the maximum power state point is 0: (18)dIVdV=IMPP,STC+VMPP,STCdIdV=0.

It can also be written as (19)IMPP,STCVMPP,STC+dIdVMPP=0.

Therefore, the objective function in the differential optimization algorithm is defined as (20)J=IMPP,STCVMPP,STC+dIdVMPP,(21)dIdVMPP=Io1,STCα1XMPP1Io2,STCα2XMPP21/Rsh,STC1+Io1,STCα1Rs,STCXMPP1+Io2,STCα2Rs,STCXMPP2+Rs,STC/Rsh,STC,where (22)α1=1NSn1,STCVth,STC,(23)α2=1NSn2,STCVth,STC.

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 , the constraints are as follows:

When Rsh<Rsh,min, or Rsh>Rsh,max, or Io1<0, or Io2<0, or Io2<0, (24)J=Jrej,where Rsh,min and Rsh,max are the minimum and maximum values of Rsh,STC, respectively. If the parameter search range exceeds the above constraint range, the objective function will be set to Jrei=10. Figure 2 is the algorithm flow chart, where VTR is the preset value of the objective function.

The algorithm flow chart proposed in this paper.

4. Improve Differential Evolution Algorithm

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.

4.1. Initialization

The DE algorithm first randomly generates NP D-dimensional decision vectors, where the ith vector is expressed as (25)Xi,G=x1,i,G,x2,i,G,x3,i,G,,xD,i,G,where G is the current algebra and D is the dimension of the vector.

Each element in the vector is randomly generated according to (26)Xj,i,G=XL+rand0,1XHXL,where XH and XL are the upper and lower bounds of the search space, respectively, and rand0,1 is a random number that is uniformly distributed between 0 and 1.

4.2. Mutation Operation

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 (27)Vi,Gen=Xr1,Gen+FXr2,GenXr3,Gen,where r1, r2, and r3 are random integers, and r1r2r3.

4.3. Cross Operation

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 (28)Uj,i,Gen=Vj,i,Gen,ifrand0,1CRorj=jrand,Xj,i,Gen,otherwise,where jrand is a random number in 1,D, ensuring that at least one of the candidate individuals is from the information of the mutated individual, preventing the occurrence of invalid evolution. At the same time, the individual values are also constrained in the crossover operation. Avoid crossing the boundary and producing nonfeasible solutions.

4.4. Select Operation

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 (29)Xi,Gen=Ui,Gen,ifJUi,Gen<JXi,Gen,Xi,Gen,otherwise.

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  proposed an adaptive differential evolution algorithm, in which the scaling factor, crossover probability, and optimization strategy can be adaptively selected according to the objective function information to improve the performance of the algorithm. The scaling factor and crossfactor generation probability of each individual obey the Cauchy distribution and the normal distribution. The parameter success rate of the last iteration adjusts the control parameters of the probability distribution model so that the parameters are adaptively adjusted and the performance of the differential evolution algorithm is improved.

For an individual, its crossover probability CRi follows a normal distribution: (30)CRi=minmaxrandniμCR,0.1,0,1.

In the formula, the effect of min and max is to limit CR to 0,1, the initial value of μCR is 0.5, and it is updated after each iteration: (31)μCR=1cμCR+cmeanASCR,where SCR is a successful set of crossover probabilities, meanA is the arithmetic mean operation, and c is the weighting factor. The scaling factor F is generated as follows: (32)Fi=minmaxrandciμF,0.1,0,1.

In the formula, the initial value of μF is set to 0.5 and is updated as follows after each iteration: (33)μF=1cμF+cmeanLSF,where meanL is the Lehmer mean, calculated as (34)meanLSF=FSFF2FSFF.

5. Experimental Results and Discussion

In order to effectively extract the parameters of the PV module, the parameter setting of the differential evolution algorithm is very important. In Reference , the scaling factor and the initial value of the crossover probability are set to 0.5 and 0.8, respectively. The choice of the crossover strategy is in the literature . For the adaptive selection method, the search range of decision variables is as follows: n10.5,2, n22,4, and Rs0.01,3; the size of the population is set to 30; and the maximum number of iterations is set to 1000.

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 1. Under the MATLAB platform, the parameters in the diode model corresponding to the three components are extracted by the differential evolution (DE) algorithm  and the improved differential evolution (IDE) algorithm proposed in this paper, respectively. In order to make a fair comparison between the algorithm proposed in this paper and the algorithm in the literature , the two algorithms were run independently 30 times each to obtain their statistical results. Table 2 shows the statistical results of the experiment. The convergence curves of the two algorithms are shown in Figure 3. The parameters are shown in Tables 35. These tables show that the method used in this paper can accurately solve the parameters of monocrystalline silicon components, polycrystalline silicon components, and thin film components. It can be seen from Table 6 that the average absolute value of SP75 monocrystalline silicon modules extracted by this method under STC is absolute. The error is 0.015, the average absolute error of S25 polysilicon component under STC is 0.013, the average absolute error of ST36 thin film component under STC is 0.026, and the average absolute error is within 0.05. The calculation results of the above three components are, respectively, obtained. Substituting (1), using the Newton iteration method, can solve the IV characteristic curve of PV modules under different temperatures and different light intensities as shown in Figures 49. It can be seen from the figures that the parameters extracted by the literature  and the proposed method under the STC can well fit the output IV characteristic curves of the three PV modules, but for the method proposed in this paper, the accuracy of the fitting is higher than that of the literature .

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 n1 DE 1.041 6.899E-4
SP75 n1 IDE 1.054 1.342E-6
SP75 n2 DE 2.071 0.024
SP75 n2 IDE 2.34 0.013
SP75 Rs DE 0.405 0.009
SP75 Rs IDE 0.331 0.006
S25 n1 DE 1.031 0.002
S25 n2 IDE 1.039 0.005
S25 n2 DE 2.156 0.046
S25 n2 IDE 2.257 0.034
S25 Rs DE 0.779 0.013
S25 Rs IDE 0.780 0.005
ST36 n1 DE 1.643 0.080
ST36 n1 IDE 1.679 0.082
ST36 n2 DE 2.062 0.015
ST36 n2 IDE 2.071 0.012
ST36 Rs DE 1.258 0.010
ST36 Rs 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 Ipv (A) Io1 (μA) Io2 (μA) n1 n2 Rs (Ω) Rsh (Ω)
DE 4.80 6.33E-10 1.05E-5 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 Ipv (A) Io1 (μA) Io2 (μA) n1 n2 Rs (Ω) Rsh (Ω)
DE 1.50 2.542E-10 1.687E-6 1.031 2.147 0.779 2672.8
IDE 1.50 1.043E-3 2.70E-3 1.097 2.239 0.833 1683.6

Extraction parameters of S25 module with different methods.

Method Ipv (A) Io1 (μA) Io2 (μA) n1 n2 Rs (Ω) Rsh (Ω)
DE 2.68 2.521E+2 6.53E+2 2.45 2.82 0.952 270.51
IDE 2.684 5.436E-1 8.40E+1 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/m2) 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

IV characteristics under varying irradiance for SP75 monocrystalline module (T=25°C).

IV characteristics under varying irradiance for S25 polycrystalline module (T=25°C).

IV characteristics under varying irradiance for ST36 thin film module (T=25°C).

IV characteristics under varying temperature for SP75 monocrystalline module (G=1000 W/m2).

IV characteristics under varying temperature for S25 polycrystalline module (G=1000 W/m2).

IV characteristics under varying temperature for ST36 thin film module (G=1000 W/m2).

Set the absolute error e1 to (35)e1=Is,iIc,i,where Is,i is the experimental data and Ic,i is the data obtained by simulation; the mean absolute error (MAE) expression is (36)MAE=1Ni=1Nei,(37)RMSE=1Ni=1Nei2,where N is the number of sampling points. The average absolute error of the photovoltaic modules in various environmental conditions is calculated according to equation (36) as shown in Table 6. It can be seen from the table that the average absolute error simulated by the parameters extracted by the proposed method under different environmental conditions is close to that of the literature , which proves the effectiveness of the proposed method.

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  to extract the two diodes of SP75, S25, and ST36 three photovoltaic modules under different environmental conditions, the time taken for the model parameters is shown in Table 7. It can be seen from the table that the time taken to extract parameters using this method in the same computing environment is smaller than that in the literature , indicating that the calculation speed can be improved after appropriate approximation.

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

Method Modules Irradiance (W/m2) 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 1012 shows the absolute error comparison of the parameters of three different modules under STC using the literature  and the extraction method of this paper. It can be seen from the figures that for the SP75 monocrystalline silicon module and the S25 polysilicon module, the absolute error of the two methods is basically the same in the constant current region of the photovoltaic module, but in the constant voltage region, the accuracy of the proposed method is higher than that of the literature  method. However, for the ST36 thin film module, the method of  is higher than the method proposed in this paper, indicating that the conclusion of Yahya-Khotbehsara and Shahhoseini  for three to four times is not applicable to the thin film module.

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.

6. Conclusion

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.

Data Availability

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

Conflicts of Interest

The authors declare no conflict of interest.

Authors’ Contributions

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.

Acknowledgments

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).