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On the root mean square error (RMSE) calculation for parameter estimation of photovoltaic models: A novel exact analytical solution based on Lambert W function
摘要： In the literature, one can find a lot of methods and techniques employed to estimate single diode solar photovoltaic (PV) cell parameters. The efficiency of these methods is usually tested by calculating the Root Mean Square Error (RMSE) between the measured and estimated values of the solar PV cell output current. In this work, first, the values of RMSE calculated using 69 different methods published in many journal papers for the well-known RTC France solar PV cell are presented and discussed. Second, a novel exact analytical solution for RMSE calculation based on the Lambert W function is proposed. The results obtained show that the RMSE values were not calculated correctly in most of the methods presented in the literature since the exact expression of the calculated cell output current was not used. Third, the precision of calculation of the methods used for analytical solving of Lambert W equation is presented and discussed. Fourth, the applicability of the proposed solution methodology in accordance with current-voltage characteristics measured in the laboratory for solar modules of Clean Energy Trainer Setup is checked. Identification of its unknown parameters is presented using three optimization techniques. Further, the proposed solution methodology is proven for Solarex MSX–60 PV module, and the most promising 5-parameter single diode parameters are estimated based on minimization of the precise RMSE values calculated. Finally, this work aimed to develop a good base for proper investigation and implementation of optimization algorithms to solve the parameter estimation problem of 5-parameter single diode PV equivalent circuits.
关键词： Root mean square error,5-parameter single diode model,PV parameter estimation,Optimization,RTC France solar cell,Lambert W function
更新于2025-09-23 15:21:01
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Exact Solution, Endoreversible Thermodynamics, and Kinetics of the Generalized Shockley-Queisser Model
摘要： We consider the generalized Shockley-Queisser (GSQ) model, which is based on a single assumption that photocarriers and emitted photons are in chemical equilibrium and described by the Boltzmann distribution functions with the same chemical potential. The model takes into account the frequency-dependent absorption (emission), photon trapping and recycling, photocarrier multiplication, and nonradiative recombination processes. For the noninteracting photocarriers, we obtain an exact analytical solution of the GSQ model. We present the conversion e?ciency and other photovoltaic (PV) characteristics in a convenient form via the Lambert W function. Photocarrier multiplication and recombination via three-body Auger processes are also directly included in this formalism. We derive universal formulas for useful energy, thermal losses, and emission losses per absorbed photon. We show that the relation between the maximal conversion e?ciency and the photo-induced chemical potential, obtained by Henry [J. Appl. Phys. 51, 4494 (1980)] for the ideal SQ limit, is also valid in the GSQ model. In the general case of interacting electrons, in particular for the Shockley-Read-Hall processes, the solution is presented in an iterative form. We analyze photocarrier kinetics and derive a general relation between the optimal photocarrier collection time and photocarrier lifetime with respect to all radiative and nonradiative processes. Finally, we analyze ?nite mobility limitations and show that PV devices with photon trapping and recycling provide the fast photocarrier collection required by the GSQ model.
关键词： photocarrier kinetics,photon trapping and recycling,photovoltaic conversion,Lambert W function,generalized Shockley-Queisser model
更新于2025-09-09 09:28:46