Accurate physical modeling and parameter extraction for the nonlinear current-voltage (Ⅰ-Ⅴ) chara... more Accurate physical modeling and parameter extraction for the nonlinear current-voltage (Ⅰ-Ⅴ) characteristics of photovoltaic (PV) cells and modules are essential prerequisites for the design calculation, performance analysis, and optimal control of PV generation systems. In contrast to the traditional implicit single-diode models, this paper first derives the explicit single-diode models of PV cells and modules using the Lambert Wfunction, and then proposes a simple and efficient parameter extraction method on the basis of restarting the bound constrained Nelder-Mead simplex method (rbcNM). For comparing and analyzing the accuracy of implicit and explicit single-diode models, experimental data of the two typical PV cells and modules are tested and verified. Simulation results indicate that the proposed rbcNM method can rapidly and accurately extract the optimal parameters of implicit and explicit single-diode models, the simulation data produced by the extracted parameters of rbcNM method are in very good agreement with the experimental data in all cases. Comparison results show that the accuracy of rbcNM method is quite promising and outperforms the existing methods reported in the literature. Furthermore, the accuracy of explicit single-diode models is significantly higher than that of implicit single-diode models, and thus fit the Ⅰ-Ⅴ characteristic curves better.
Abstract Fast and accurate parameter extraction of solar cell models is always desired for simula... more Abstract Fast and accurate parameter extraction of solar cell models is always desired for simulation, evaluation and maximum energy harvesting of PV systems. This paper proposes an improved shuffled complex evolution (ISCE) algorithm for parameter extraction of different PV models, including single diode model, double diode model and single diode solar module model. The novelty of proposed ISCE algorithm lies primary in the improved competitive complex evolution strategy, where three amendments are proposed to overcome the shortcomings of original SCE algorithm. (1) The expansion step and outside contraction step are inserted into to improve the probability of producing better solution. (2) The reflecting-absorbing bound- handling method is employed to enhance the chance of global search and avoid being trapped in local minima. (3) The main diagonal of simplex is adopted to overcome local roughness and drive the global search in an efficient manner. In order to test the parameter extraction performance of proposed ISCE and compare it with some state-of-the-art algorithms, the standard datasets and practical measured datasets of one solar cell and three solar modules are selected for parameter extraction of different PV models. Comparison results indicate that the proposed ISCE algorithm always exhibits the highest computational efficiency to get the most accurate parameter values among all compared algorithms. More importantly, the proposed ISCE algorithm generally promises better convergence speed and robustness than the best reported algorithms. Due to these superiorities, the proposed ISCE algorithm is quite promising and envisaged to be an accurate, efficient and reliable alternative for solving the parameter extraction problem of solar cell models.
To accurately, efficiently and reliably extract the parameters of single, double and triple diode... more To accurately, efficiently and reliably extract the parameters of single, double and triple diode solar cell models, this paper proposes a randomly initialized opposite normalized trust-region reflective (ONTRR) algorithm. The novelty of ONTRR lies primarily in two amendments to the standard TRR search. (1) Random opposite initialization is added to decrease the initial point sensitivity of TRR and thus reduce the possibility of being trapped in local optima. (2) Min-max normalization is embedded to eliminate the negative effects arising from different magnitudes of model parameter values and thus drive the derivative-dependent TRR search in an efficient manner. The proposed ONTRR algorithm is evaluated and compared to other state-of-the-art algorithms using four benchmarked I–V datasets with two commonly used objective functions. To be objective and reproducible, the comparative experiments are carried out with default random seeds for 1000 independent runs instead of the 30, 50, o...
Parameter extraction is significant for simulation analysis, evaluation, optimal control and faul... more Parameter extraction is significant for simulation analysis, evaluation, optimal control and fault detection of proton exchange membrane fuel cell (PEMFC) system. Although various techniques have been developed for parameter extraction of PEMFC, it is still challenging to quickly obtain accurate and reliable results. In this paper, a shuffled multisimplexes search (SMS) algorithm, merging the strengths of three concepts: (a) periodic shuffling multiple simplexes for an effective global exploration, (b) monitoring and revitalization of degenerate simplex to maintain the population diversity for preventing premature convergence and (c) modified simplex search algorithm to conduct a robust and powerful local exploitation, is proposed to fast and accurate extract the model parameter of PEMFC. To be objective and reproducible, the reported experimental V-I datasets of four PEMFC stacks are chosen for testing the parameter extraction performance of proposed SMS algorithm and comparing it with some state-of-the-art algorithms. The comparison results indicate that for all the four test cases, the proposed SMS consistently gets the optimal results among all compared algorithms and exhibits faster convergence speed, lesser computational CPU time (less than 0.3 s for 5000 function evaluations to converge), preferable accuracy and higher statistical robustness (the smallest standard deviation is 1.90E−16) than other algorithms. Due to these superiorities, the proposed SMS is quite promising and envisaged to be an accurate, efficient and reliable alternative for solving the parameter extraction problem of PEMFC model.
Accurate modeling plays an important role in solar cell simulation. In order to reveal the applic... more Accurate modeling plays an important role in solar cell simulation. In order to reveal the applicability and superiority of Special Trans function based single diode model (SBSDM), this paper presents a comprehensive comparison of SBSDM, Lambert W function based single diode model (LBSDM) and exponential-type single diode model (SDM). The performance difference of SBSDM, LBSDM and SDM is verified and compared in two aspects: (1) different fitness to the measured I-V data of solar cells and (2) different parameter extraction performance. To be objective and reproducible, the reported parameter values of standard datasets and measured datasets are employed to validate the fitness difference of the three models. The comparison results indicate that SBSDM always exhibits better fitness than LBSDM and SDM in representing the I-V characteristics of various solar cells and can provide a closer prediction to actual maximum power points. With the help of a ranking based branch selection strategy, a modified Nelder-Mead simplex (MNMS) algorithm is proposed to test the parameter extraction performance of SBSDM, LBSDM and SDM. The comparison results reveal that the time computational efficiency of SBSDM is inferior to SDM but superior to LBSDM. SBSDM always achieves superior accuracy and convergence speed than LBSDM and SDM, although lacking enough statistical robustness. Due to these superiorities, SBSDM is quite promising and envisaged to be the most valuable model for solar cell parameter extraction and PV system simulation.
Accurate modeling and parameter extraction of solar cells play an important role in the simulatio... more Accurate modeling and parameter extraction of solar cells play an important role in the simulation and optimization of PV systems. This paper presents a Lambert W-function based exact representation (LBER) for traditional double diode model (DDM) of solar cells, and then compares their fitness and parameter extraction performance. Unlike existing works, the proposed LBER is rigorously derived from DDM, and in LBER the coefficients of Lambert W-function are not extra parameters to be extracted or arbitrary scalars but the vectors of terminal voltage and current of solar cells. The fitness difference between LBER and DDM is objectively validated by the reported parameter values and experimental I-V data of a solar cell and four solar modules from different technologies. The comparison results indicate that under the same parameter values, the proposed LBER can better represent the I-V and P-V characteristics of solar cells and provide a closer representation to actual maximum power points of all module types. Two different algorithms are used to compare the parameter extraction performance of LBER and DDM. One is our restart-based bound constrained Nelder-Mead (rbcNM) algorithm implemented in Matlab, and the other is the reported R cr-IJADE algorithm executed in Visual Studio. The comparison results reveal that, the parameter values extracted from LBER using two algorithms are always more accurate and robust than those from DDM despite more time consuming. As an improved version of DDM, the proposed LBER is quite promising for PV simulation and thus deserves serious attention.
Abstract This letter presents a response to the comments of Mehrzad Alizadeh on the proper applic... more Abstract This letter presents a response to the comments of Mehrzad Alizadeh on the proper application of generalized steady-state electrochemical model (GSSEM) of proton exchange membrane fuel cells (PEMFC). In order to rectify his/her misconceptions, this letter firstly introduces the actual application situation of GSSEM in literatures, then analyzes the universality and root reason why the results of GSSEM are physically inconsistent, and finally points out the negative effect of using his/her potential modification of GSSEM for PEMFC parameter extraction.
Due to the environmental degradation and depletion of conventional energy, much attention has bee... more Due to the environmental degradation and depletion of conventional energy, much attention has been devoted to wind energy in many countries. The intermittent nature of wind power has had a great impact on power grid security. Accurate forecasting of wind speed plays a vital role in power system stability. This paper presents a comparison of three wavelet neural networks for short-term forecasting of wind speed. The first two combined models are two types of basic combinations of wavelet transform and neural network, namely, compact wavelet neural network (CWNN) and loose wavelet neural network (LWNN) in this study, and the third model is a new hybrid method based on the CWNN and LWNN models. The efficiency of the combined models has been evaluated by using actual wind speed from two test stations in North China. The results show that the forecasting performances of the CWNN and LWNN models are unstable and are affected by the test stations selected; the third model is far more accurate than the other forecasting models in spite of the drawback of lower computational efficiency.
Accurate physical modeling and parameter extraction for the nonlinear current-voltage (Ⅰ-Ⅴ) chara... more Accurate physical modeling and parameter extraction for the nonlinear current-voltage (Ⅰ-Ⅴ) characteristics of photovoltaic (PV) cells and modules are essential prerequisites for the design calculation, performance analysis, and optimal control of PV generation systems. In contrast to the traditional implicit single-diode models, this paper first derives the explicit single-diode models of PV cells and modules using the Lambert Wfunction, and then proposes a simple and efficient parameter extraction method on the basis of restarting the bound constrained Nelder-Mead simplex method (rbcNM). For comparing and analyzing the accuracy of implicit and explicit single-diode models, experimental data of the two typical PV cells and modules are tested and verified. Simulation results indicate that the proposed rbcNM method can rapidly and accurately extract the optimal parameters of implicit and explicit single-diode models, the simulation data produced by the extracted parameters of rbcNM method are in very good agreement with the experimental data in all cases. Comparison results show that the accuracy of rbcNM method is quite promising and outperforms the existing methods reported in the literature. Furthermore, the accuracy of explicit single-diode models is significantly higher than that of implicit single-diode models, and thus fit the Ⅰ-Ⅴ characteristic curves better.
Abstract Fast and accurate parameter extraction of solar cell models is always desired for simula... more Abstract Fast and accurate parameter extraction of solar cell models is always desired for simulation, evaluation and maximum energy harvesting of PV systems. This paper proposes an improved shuffled complex evolution (ISCE) algorithm for parameter extraction of different PV models, including single diode model, double diode model and single diode solar module model. The novelty of proposed ISCE algorithm lies primary in the improved competitive complex evolution strategy, where three amendments are proposed to overcome the shortcomings of original SCE algorithm. (1) The expansion step and outside contraction step are inserted into to improve the probability of producing better solution. (2) The reflecting-absorbing bound- handling method is employed to enhance the chance of global search and avoid being trapped in local minima. (3) The main diagonal of simplex is adopted to overcome local roughness and drive the global search in an efficient manner. In order to test the parameter extraction performance of proposed ISCE and compare it with some state-of-the-art algorithms, the standard datasets and practical measured datasets of one solar cell and three solar modules are selected for parameter extraction of different PV models. Comparison results indicate that the proposed ISCE algorithm always exhibits the highest computational efficiency to get the most accurate parameter values among all compared algorithms. More importantly, the proposed ISCE algorithm generally promises better convergence speed and robustness than the best reported algorithms. Due to these superiorities, the proposed ISCE algorithm is quite promising and envisaged to be an accurate, efficient and reliable alternative for solving the parameter extraction problem of solar cell models.
To accurately, efficiently and reliably extract the parameters of single, double and triple diode... more To accurately, efficiently and reliably extract the parameters of single, double and triple diode solar cell models, this paper proposes a randomly initialized opposite normalized trust-region reflective (ONTRR) algorithm. The novelty of ONTRR lies primarily in two amendments to the standard TRR search. (1) Random opposite initialization is added to decrease the initial point sensitivity of TRR and thus reduce the possibility of being trapped in local optima. (2) Min-max normalization is embedded to eliminate the negative effects arising from different magnitudes of model parameter values and thus drive the derivative-dependent TRR search in an efficient manner. The proposed ONTRR algorithm is evaluated and compared to other state-of-the-art algorithms using four benchmarked I–V datasets with two commonly used objective functions. To be objective and reproducible, the comparative experiments are carried out with default random seeds for 1000 independent runs instead of the 30, 50, o...
Parameter extraction is significant for simulation analysis, evaluation, optimal control and faul... more Parameter extraction is significant for simulation analysis, evaluation, optimal control and fault detection of proton exchange membrane fuel cell (PEMFC) system. Although various techniques have been developed for parameter extraction of PEMFC, it is still challenging to quickly obtain accurate and reliable results. In this paper, a shuffled multisimplexes search (SMS) algorithm, merging the strengths of three concepts: (a) periodic shuffling multiple simplexes for an effective global exploration, (b) monitoring and revitalization of degenerate simplex to maintain the population diversity for preventing premature convergence and (c) modified simplex search algorithm to conduct a robust and powerful local exploitation, is proposed to fast and accurate extract the model parameter of PEMFC. To be objective and reproducible, the reported experimental V-I datasets of four PEMFC stacks are chosen for testing the parameter extraction performance of proposed SMS algorithm and comparing it with some state-of-the-art algorithms. The comparison results indicate that for all the four test cases, the proposed SMS consistently gets the optimal results among all compared algorithms and exhibits faster convergence speed, lesser computational CPU time (less than 0.3 s for 5000 function evaluations to converge), preferable accuracy and higher statistical robustness (the smallest standard deviation is 1.90E−16) than other algorithms. Due to these superiorities, the proposed SMS is quite promising and envisaged to be an accurate, efficient and reliable alternative for solving the parameter extraction problem of PEMFC model.
Accurate modeling plays an important role in solar cell simulation. In order to reveal the applic... more Accurate modeling plays an important role in solar cell simulation. In order to reveal the applicability and superiority of Special Trans function based single diode model (SBSDM), this paper presents a comprehensive comparison of SBSDM, Lambert W function based single diode model (LBSDM) and exponential-type single diode model (SDM). The performance difference of SBSDM, LBSDM and SDM is verified and compared in two aspects: (1) different fitness to the measured I-V data of solar cells and (2) different parameter extraction performance. To be objective and reproducible, the reported parameter values of standard datasets and measured datasets are employed to validate the fitness difference of the three models. The comparison results indicate that SBSDM always exhibits better fitness than LBSDM and SDM in representing the I-V characteristics of various solar cells and can provide a closer prediction to actual maximum power points. With the help of a ranking based branch selection strategy, a modified Nelder-Mead simplex (MNMS) algorithm is proposed to test the parameter extraction performance of SBSDM, LBSDM and SDM. The comparison results reveal that the time computational efficiency of SBSDM is inferior to SDM but superior to LBSDM. SBSDM always achieves superior accuracy and convergence speed than LBSDM and SDM, although lacking enough statistical robustness. Due to these superiorities, SBSDM is quite promising and envisaged to be the most valuable model for solar cell parameter extraction and PV system simulation.
Accurate modeling and parameter extraction of solar cells play an important role in the simulatio... more Accurate modeling and parameter extraction of solar cells play an important role in the simulation and optimization of PV systems. This paper presents a Lambert W-function based exact representation (LBER) for traditional double diode model (DDM) of solar cells, and then compares their fitness and parameter extraction performance. Unlike existing works, the proposed LBER is rigorously derived from DDM, and in LBER the coefficients of Lambert W-function are not extra parameters to be extracted or arbitrary scalars but the vectors of terminal voltage and current of solar cells. The fitness difference between LBER and DDM is objectively validated by the reported parameter values and experimental I-V data of a solar cell and four solar modules from different technologies. The comparison results indicate that under the same parameter values, the proposed LBER can better represent the I-V and P-V characteristics of solar cells and provide a closer representation to actual maximum power points of all module types. Two different algorithms are used to compare the parameter extraction performance of LBER and DDM. One is our restart-based bound constrained Nelder-Mead (rbcNM) algorithm implemented in Matlab, and the other is the reported R cr-IJADE algorithm executed in Visual Studio. The comparison results reveal that, the parameter values extracted from LBER using two algorithms are always more accurate and robust than those from DDM despite more time consuming. As an improved version of DDM, the proposed LBER is quite promising for PV simulation and thus deserves serious attention.
Abstract This letter presents a response to the comments of Mehrzad Alizadeh on the proper applic... more Abstract This letter presents a response to the comments of Mehrzad Alizadeh on the proper application of generalized steady-state electrochemical model (GSSEM) of proton exchange membrane fuel cells (PEMFC). In order to rectify his/her misconceptions, this letter firstly introduces the actual application situation of GSSEM in literatures, then analyzes the universality and root reason why the results of GSSEM are physically inconsistent, and finally points out the negative effect of using his/her potential modification of GSSEM for PEMFC parameter extraction.
Due to the environmental degradation and depletion of conventional energy, much attention has bee... more Due to the environmental degradation and depletion of conventional energy, much attention has been devoted to wind energy in many countries. The intermittent nature of wind power has had a great impact on power grid security. Accurate forecasting of wind speed plays a vital role in power system stability. This paper presents a comparison of three wavelet neural networks for short-term forecasting of wind speed. The first two combined models are two types of basic combinations of wavelet transform and neural network, namely, compact wavelet neural network (CWNN) and loose wavelet neural network (LWNN) in this study, and the third model is a new hybrid method based on the CWNN and LWNN models. The efficiency of the combined models has been evaluated by using actual wind speed from two test stations in North China. The results show that the forecasting performances of the CWNN and LWNN models are unstable and are affected by the test stations selected; the third model is far more accurate than the other forecasting models in spite of the drawback of lower computational efficiency.
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