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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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[IEEE 2019 29th Australasian Universities Power Engineering Conference (AUPEC) - Nadi, Fiji (2019.11.26-2019.11.29)] 2019 29th Australasian Universities Power Engineering Conference (AUPEC) - Adaptive Boosting and Bootstrapped Aggregation based Ensemble Machine Learning Methods for Photovoltaic Systems Output Current Prediction
摘要： Photovoltaics output current prediction received great deal of attention in recent years, due to the high penetration level of PV utilization. The intermittent nature of PV systems, in addition to the fast-varying irradiance levels, provoked the need for fast, accurate and reliable forecasting techniques. Machine Learning (ML) methods have been proven to effectively solve regression-based prediction problems. ML methods that utilize multiple models to construct decision trees are called Ensemble Machine Learning (EML) algorithms. This paper presents a comparison study of two EML methods namely; AdaBoost and Random Forest for photovoltaics application. A dataset of fast varying environmental conditions has been employed and the terminal current of the experimental setup has been augmented based on the mathematical model and the use of an evolutionary algorithm. The mathematical model has been examined for several irradiance and temperature levels and adjusted based on the manufacturer datasheet. Random Forest overall absolute error distribution had the lowest mean and standard deviation. Results shows the superior performance of Random Forest over AdaBoost in terms of absolute error, on the contrary, AdaBoost absolute error distribution is scattered with larger quartiles limits. Random Forest overall absolute error distribution had the lowest mean of 0.27% with a standard deviation of 0.91%, however, AdaBoost absolute error mean was as high as 34.5% with a standard deviation of 15.8% relative to the mathematical model. Accurate predictions can be integrated in an EML based maximum power point tracking (MPPT) scheme.
关键词： ensemble machine learning,adaptive boosting,photovoltaics,regression decision trees,single diode model
更新于2025-09-23 15:21:01
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Photovoltaic module model determination by using the Tellegena??s theorem
摘要： This paper proposes a generalized methodology to calculate the parameters of the single-diode or double-diode models of a photovoltaic module. The presented method relies in the solution by a simple iterative process of the set of equations obtained from the photovoltaic-module’s equivalent circuit. The use of the generalized form of Tellegen’s theorem allows the solving of the equivalent circuit’s equations in an exact way, without making considerations or approximations commonly used in previous works. The parameters of the equivalent circuit are obtained from the standard conditions of: open-circuit, short-circuit and maximum power, provided by the manufacturer in the data sheet of the photovoltaic module. The presented method is applied to obtain the models of several commercial modules. The accuracy of the obtained parameters is greater than that of the results previously determined by other authors. The curves calculated with the obtained models matches the experimental curves supplied in the manufacturer’s data.
关键词： Double-diode model,PV-Module,Single-diode model
更新于2025-09-23 15:19:57
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An Interval-Arithmetic-Based Approach to the Parametric Identification of the Single-Diode Model of Photovoltaic Generators
摘要： Parametric identi?cation of the single diode model of a photovoltaic generator is a key element in simulation and diagnosis. Parameters’ values are often determined by using experimental data the modules manufacturers provide in the data sheets. In outdoor applications, the parametric identi?cation is instead performed by starting from the current vs. voltage curve acquired in non-standard operating conditions. This paper refers to this latter case and introduces an approach based on the use of interval arithmetic. Photovoltaic generators based on crystalline silicon cells are considered: they are modeled by using the single diode model, and a divide-and-conquer algorithm is used to contract the initial search space up to a small hyper-rectangle including the identi?ed set of parameters. The proposed approach is validated by using experimental data measured in outdoor conditions. The information provided by the approach, in terms of parametric sensitivity and of correlation between current variations and drifts of the parameters values, is discussed. The results are analyzed in view of the on-site application of the proposed approach for diagnostic purposes.
关键词： parametric identi?cation,interval arithmetic,photovoltaic systems,single-diode model
更新于2025-09-23 15:19:57
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Simple and Low-Cost Photovoltaic Module Emulator
摘要： The design and testing phase of photovoltaic (PV) power systems requires time-consuming and expensive field-testing activities for the proper operational evaluation of maximum power point trackers (MPPT), battery chargers, DC/AC inverters. Instead, the use of a PV source emulator that accurately reproduces the electrical characteristic of a PV panel or array is highly desirable for in-lab testing and rapid prototyping. In this paper, we present the development of a low-cost microcontroller-based PV source emulator, which allows testing the static and dynamic performance of PV systems considering different PV module types and variable operating and environmental conditions. The novelty of the simple design adopted resides in using a low-cost current generator and a single MOSFET converter to reproduce, from a fixed current source, the exact amount of current predicted by the PV model for the actual load conditions. The I–V characteristic is calculated in real-time using a single diode exponential model under variable and user-selectable operating conditions. The proposed method has the advantage of reducing noise from high-frequency switching, reducing or eliminating ripple and the demand for output filters, and it does not require expensive DC Power source, providing high accuracy results. The fast response of the system allows the testing of very fast MPPTs algorithms, thus overcoming the main limitations of state-of-art PV source emulators that are unable to respond to the quick variation of the load. Experimental results carried on a hardware prototype of the proposed PV source emulator are reported to validate the concept. As a whole result, an average error of ±1% in the reproduction of PV module I–V characteristics have been obtained and reported.
关键词： photovoltaic emulator,single diode model,MPPT,photovoltaic panel
更新于2025-09-23 15:19:57
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Boosted mutation-based Harris hawks optimizer for parameters identification of single-diode solar cell models
摘要： In order to realize the performance of the PV model before being installed, it is often indispensable to develop reliable and accurate parameter identification methods for dealing with the PV models. Up to now, several stochastic methods have been proposed to analyze the feature space of this problem. However, some of the stochastic-based methods may present unsatisfactory results due to their insufficient exploration and exploitation inclinations, and the multimodal and nonlinearity existed in PV parameters extraction problems. In this paper, a Boosted Harris Hawk’s Optimization (BHHO) technique is proposed to achieve a more stable model and effectively estimate the parameters of the single diode PV model. The BHHO method combines random exploratory steps of evolution inspired by the flower pollination algorithm (FPA) and a powerful mutation scheme of the differential evolution (DE) with 2-Opt algorithms. The proposed strategies not only help BHHO algorithm to accelerate the convergence rate but also assist it in scanning new regions of the search basins. The results demonstrate that the proposed BHHO is more accurate and reliable compared to the basic version and several well-established methods. The BHHO method was rigorously validated by using real experimental data under seven sunlight and temperature conditions. Furthermore, the statistical criteria indicate that the proposed BHHO method has lower errors among other peers, which is highly useful for real-world applications.
关键词： I–V characteristics,Photovoltaic module,Harris hawks optimization,Parameter extraction,Single-diode model
更新于2025-09-19 17:13:59
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A Dragonfly Algorithm Application: Optimizing Solar Cell Single Diode Model Parameters
摘要： This paper provides an overview of optimizing solar cell single diode parameters using Dragonfly Algorithm. The 57 mm diameter commercial (R.T.C. France) silicon solar cell measurement data are taking as the data source for the optimization process. The results produced are compared with NM-PSO and IJAYA algorithms to observe the efficiency, accuracy and reliability of the proposed approach
关键词： Single Diode Model,Optimization,Dragonfly Algorithm,Solar Cell
更新于2025-09-19 17:13:59
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Estimation of Single-Diode and Two-Diode Solar Cell Parameters by Using a Chaotic Optimization Approach
摘要： Estimation of single-diode and two-diode solar cell parameters by using chaotic optimization approach (COA) is addressed. The proposed approach is based on the use of experimentally determined current-voltage (I-V) characteristics. It outperforms a large number of other techniques in terms of average error between the measured and the estimated I-V values, as well as of time complexity. Implementation of the proposed approach on the I-V curves measured in laboratory environment for different values of solar irradiation and temperature prove its applicability in terms of accuracy, effectiveness and the ease of implementation for a wide range of practical environment conditions. The COA-based parameter estimation is, therefore, useful for PV power converter designers who require fast and accurate model for PV cell/module.
关键词： COA,Solar cell parameters,single-diode model,two-diode model
更新于2025-09-12 10:27:22
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A new approach for parameter estimation of the single-diode model for photovoltaic cells/modules
摘要： Solar energy has become a popular renewable energy source, leading to wide use of photovoltaic (PV) cells/modules in energy production. For this reason, realistic modeling of PVs and determining the equivalent circuit parameters is of great importance in terms of planning and operation. Hence, in this study, an analytical model for identifying the single-diode equivalent circuit parameters; series resistance ( Rs ), shunt resistance ( Rp ), diode ideality factor ( a ), diode reverse-saturation current ( Io ), and photon current ( Ipv ) for PV cells/modules is developed without neglecting any term. In order to test the accuracy of the model, a number of PV modules from different manufacturers are taken into account and the results are compared with those obtained by using such analytical models given in the literature. Current-voltage (I-V ) characteristics of the PV modules, which are studied here, are also simulated by comparing with the experimental I-V curves provided by the manufacturers. Results show that the values of the parameters obtained for the PV modules are consistent with those extracted by using other analytical models. In addition, I-V curves created by using the obtained parameters are in full agreement with the experimental data. The curves also show a high degree of compatibility with the ones created by using the optimal parameters of the two-diode models given in the literature. Moreover, the proposed model provides a great advantage in estimating equivalent circuit parameters in terms of ease of use, requirements for input data, dependency on initial conditions as well as considering the parameters which are neglected in such methods given in the literature.
关键词： Photovoltaic cells/modules,single-diode model,mathematical modeling,parameter extraction
更新于2025-09-12 10:27:22
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An Efficient and Simple Method for Modelling Solar Cells
摘要： Accurate and reliable PV device modelling is a fundamental tool to optimize system performance. The regular operation of the PV system in an outdoor condition implies the need for a model that relate the environmental effects. This paper presents a new, simple, and efficient method for constructing the I-V characteristics for a PV cell incorporating the environmental conditions. The proposed model is based on the idea of dividing the voltage axis of the solar cell I-V characteristics using a fixed time interval. For each voltage interval point, a two-dimensional current matrix is calculated, corresponding different irradiance conditions and temperatures. Polynomial surface fitting is used to build sub-models for each voltage interval. The current two-dimensional matrix, for each point, is calculated by two different methods. The first method is based on linear interpolation of the measured I-V curves. The second method uses pre-extracted five parameters for the well known single diode model at a wide range of environmental conditions. The developed modelling technique provides accurate results compared with the measured data for a mono-crystalline solar cell.
关键词： solar cell,I-V characteristics,single diode model
更新于2025-09-11 14:15:04