Model Of Photovoltaic Module Research Articles

Development of thermo–electrical loss model for photovoltaic module with inhomogeneous temperature

Accurate, efficient, and reliable measurements of solar photovoltaic (PV) modules are essential for the evaluation and diagnosis of the actual operating status of PV plants. However, current online measurements and extraction models are limited because they do not account for power losses caused by inhomogeneous thermal performance of photovoltaic modules. Accordingly, this paper develops a coupled thermo–electrical loss model to access the power generation, energy losses, and degradation rate of photovoltaic modules with inhomogeneous temperature under actual operating conditions. The experiments indicate that the temperature coefficient of power dissipation and efficiency for solar cells with uneven temperature distribution PV modules are within −0.68W/oC to −0.83 W/°C and −0.46%/oC to −5.81%/oC, respectively. Additionally, the relative error values for the maximum power range from −2.54% to 4.09%, demonstrating the feasibility of the proposed model for predicting the power output behavior of operating PV modules with inhomogeneous temperature distributions. Furthermore, the daily performances of the modules indicate heat and electricity losses ranging from 0.245 kWh to 0.337 kWh, while the ratios of electrical energy dissipation to daily losses vary from 36% to 50%. To ensure the reliability of measuring degradation rates, the solar irradiance thresholds of PV module performance tests are nearly 632W/m2, 781W/m2, 875W/m2, and 875W/m2, respectively. Finally, for the long-term performance valuation, the levelized costs of electricity increase by approximately 0.011 CNY/kWh for every 5% reduction in annual power generation, and the PBP is extended by 4.81yr, 4.22yr, 3.62yr, and 7.10yr, respectively.

Research on output distribution modeling of photovoltaic modules based on kernel density estimation method and its application in anomaly identification

As the core of photovoltaic (PV) power generation systems, the safe and steady operation of PV modules is important. But faults frequently occur in PV modules with year-round outdoor exposure, reducing generation efficiency and producing safety hazards. Current fault detection methods mainly focus on PV array, while fault detection methods of module-level generally have the limitation of complexity and low precision. The implementation of PV module sensors enables online anomaly identification, but the output uncertainty and the unclear distribution characteristics of PV modules caused difficulty to anomaly identification. Based on the analysis output distribution characteristics, a novel module-level anomaly identification method is proposed. First, the output indicators were constructed considering the strong fluctuations of current and voltage, then the probability density distribution (PDD) models of the newly constructed output indicators were built using the kernel density estimation (KDE) method. The modeling results show that the PDD curves between normal and abnormal modules differed significantly, the PDD-indicators can effectively describe the difference. The quartile method was used to calculate the threshold of PDD-indicator, and then the abnormal modules could be detected. The core innovations of this study include: the PDD features between normal and abnormal PV modules were revealed, the feature extraction method was designed and successfully applied to anomaly module identification, and the case study proves the proposed method is effective.

An Improved Levenberg–Marquardt Approach With a New Reduced Form for the Identification of Parameters of the One-Diode Photovoltaic Model

Abstract Building a highly accurate model for solar cells and photovoltaic (PV) modules based on experimental data is becoming increasingly important for the simulation, evaluation, control, and optimization of PV systems. Powerful, accurate, and more robust optimization algorithms are needed to solve this problem. In this study, a new optimization approach based on the Levenberg–Marquardt algorithm (ImLM) is proposed to estimate the parameters of PV cells and modules and simulate their electrical behavior under all environmental conditions efficiently and accurately. To avoid the premature convergence of the Levenberg–Marquardt algorithm and the long computation time caused by a bad choice of initial values, we propose a new approach. This is a new reduced form leading to a nonlinear relationship of the series resistance and thus allowing to calculate the optimal initial values of the model parameters. Comparisons with other published methods show that the proposed approach gives not only a more accurate final solution but also a fast convergence speed and a better stability. Furthermore, tests on three PV modules of different technologies (multi-crystalline, thin film, and monocrystalline) reveal that the proposed algorithm performs well at different irradiations and temperatures. These results confirm that the ImLM approach is a valuable tool and can be an effective and efficient alternative for extracting PV model parameters and simulating PV module behavior under different conditions.

A modified stochastic fractal search algorithm for parameter estimation of solar cells and PV modules

In this work, a modified stochastic fractal search algorithm is proposed for effectively estimate the unknown model parameters of the single diode model and the double diode model of solar cells and photovoltaic modules. This algorithm modifies the diffusion process and the update processes of the original stochastic fractal search algorithm and employs a population size reduction mechanism and thus simplifies the implementation of the original algorithm and achieves better performance for the parameter estimation of solar cells and PV modules. Firstly, the algorithm is tested on three widely used estimation benchmark cases and compared with other seven state-of-the-art algorithms. The proposed algorithm shows its advantages in the aspects of accuracy, convergence speed, and stability over the other studied algorithms. In 100 independent runs with the maximum number of fitness function evaluations equal to 50000, the proposed algorithm achieved the best known solutions with 100% probability and the standard deviation of the 100 RMSE values is of the order of 10−17. Then, the proposed algorithm is used to estimate the unknown single diode model parameters and double diode model parameters of three different types of PV modules, i.e. Multi-crystalline S75, Mono-crystalline SM55, and Thin-film ST40 under different irradiance and temperature conditions, and the algorithm also achieves sufficiently accurate models. The root mean square of the error (RMSE) values between the obtained models and the actual current data are of the order of 10−2 or 10−3. In view of its effectiveness and practicability, the proposed algorithm can be used as a new tool for the parameter estimation of solar cells and PV modules.

Adaptive Harris hawks optimization with persistent trigonometric differences for photovoltaic model parameter extraction

In this paper, an adaptive Harris hawk optimization with persistent trigonometric (sine–cosine)-differences (ADHHO) is proposed for parameter identification of Photovoltaic (PV) systems. In the optimized version of HHO, we innovatively propose the persistent-trigonometric-differences mechanism for improving the global search capability of HHO; moreover, we improve the energy factor in the original algorithm so that ADHHO obtains a better balance between exploration and exploitation. Note that the proposed method can obtain lower CPU time in parameter extraction for the three-diode and PV module models with an enhanced parameter extraction performance. To validate the performance of ADHHO, we verified the parameter extraction capability of the single-diode model (SDM), double-diode model (DDM), triple-diode model (TDM), and PV module model (PVM), respectively. Further, we verified the parameter extraction effect of ADHHO in three commercial cells with different light intensity and temperature conditions. Experiments show that the method proposed in this paper can reasonably simulate the output performance of solar PV cells and can be used as a trustworthy method for the extraction of unknown parameters of solar PV systems.

ELECTRICAL PARAMETERS ESTIMATION OF SINGLE DIODE PV MODULE MODEL USING HYBRID METAHEURISTIC ALGORIHM

In this paper, an improved hybrid algorithm called differential evolution with integrated mutation per iteration (DEIM) is proposed to extract five parameters of single-diode PV module model obtained by combining differential evolution (DE) algorithm and electromagnetic-like (EML) algorithm. The EML algorithm's attraction-repulsion idea is employed in DEIM in order to enhance the mutation process of DE. The proposed algorithm is validated with other methods using experimental I-V data. The results of presented method reveal that simulated I-V characteristics have a high degree of agreement with experimental ones. The proposed model has an average root mean square error of 0.062A, an absolute error of 0.0452A, a mean bias error of 0.006A, a coefficient of determination of 0.992, a standard test deviation around 0.04540, and 15.33sec as execution time. The results demonstrate that the proposed method is better in terms of the accuracy and execution time (convergence) when compared with other methods where provide less errors.

Estimation for Model Parameters and Maximum Power Points of Photovoltaic Modules Using Stochastic Fractal Search Algorithms

The performance of a photovoltaic (PV) power generation system could be improved through the optimal control and operation of a PV module which is one of the fundamental components of this system. Thus, an appropriate PV module model along with precise knowledge of its parameters is necessary. This paper proposes a novel technique to estimate the source current, the saturation current of diodes, the shunt resistance, the series resistance, the ideality coefficient of diodes and the maximum power points (MPPs) of PV modules at the same time. This estimation problem can be described by the minimization of the root mean squared error (RMSE) of the powers obtained from the PV module through estimation and experiment. The improved stochastic fractal search (ISFS) algorithm is proposed to solve this minimization with two modifications. The first replaces the logarithmic function with the exponential function in the standard deviation of the diffusion technique to improve the exploration ability efficiently in the search space. The second utilizes the sine map instead of the uniform distribution in both the diffusion and update techniques for improving the performance of the ISFS algorithm. Numerical results demonstrate the remarkable ability of the ISFS algorithm in obtaining both the model parameters and MPPs of the PV module with high accuracy. The comparison shows that the ISFS algorithm outperforms other meta-heuristic algorithms such as a stochastic fractal search (SFS) algorithm, a particle swarm optimization (PSO) algorithm, and an improved particle swarm optimization (IPSO) algorithm in the proposed parameter estimation application.

Fault classification for photovoltaic module based on maximum power point and machine learning techniques

Photovoltaic (PV) module is the key component in the solar energy system. Fault classification for photovoltaic module is necessary for safety, efficiency and reliability of photovoltaic systems. When faults of PV module occurred, the current-voltage characteristics (I-V curves) of PV module are changed leads to the shift in voltage and current of the maximum power point (MPP). In this paper, fault classification for photovoltaic module based on MPP and machine learning techniques is proposed. Through analysing the location of the MPP in I-V parameters plane, faults of PV module during performance of could be identified and classified. The parameters of voltage and current of PV module in the faults (line-to-line fault, shading, open circuit in one array, open circuit, short circuit during different irradiation levels) are collected by simulations in Simulink/MATLAB software. Then, these parameters would be processed and built into a dataset. This dataset would be fed into fault classification model for PV module using machine learning algorithms included Support Vector Machine (SVM) and k-means. The desired results of machine learning models would be accurately classified faults using parameters of voltage and current of the MPP and survey the fault diagnosis through the borderline of each classification group of the models. The result shows that the fault classification capability and accuracy of the machine learning model using SVM algorithm (98,9%) are better than the k-means algorithm (61,1%).

Extraction of Photovoltaic Cell and Photovoltaic Module Parameters Using African Vultures Optimization Algorithm

In order to characterize the actual electrical behavior of photovoltaic cells and photovoltaic modules, it is required to construct the equivalent circuit models effectively, and to identify the unknown model parameters properly. This improves the design, control and performance of photovoltaic systems. In this study, African vultures optimization was applied to solve the parameter extraction problem encountered in single diode- and double diode-based photovoltaic cell modeling and single diode-based photovoltaic module modeling. African vultures optimization algorithm efficiently balances the optimization process by using two different strategies in the exploration phase and four different strategies in the exploitation phase. The root mean squared error between simulated and measured output current was computed to evaluate the parameter extraction performance. In addition, the obtained results were compared with different parameter extraction methods commonly-used in the literature. It has been shown that the African vultures optimization algorithm is a stable and reliable technique for the extraction of photovoltaic cell and module parameters.

Solar photovoltaic model parameter estimation based on orthogonally-adapted gradient-based optimization

Solar photovoltaic (PV) model parameter estimation research is a growing field of interest. To establish accurate and reliable PV models, including single diode, double diode, three diode and PV module models, a new method is proposed in this paper. Gradient-based optimization (GBO) is designed to be used in conjunction with orthogonal learning, namely, orthogonal learning gradient-based optimization (OLGBO). In OLGBO, the orthogonal learning (OL) mechanism improves the speed rate and accuracy of GBO, achieving an adaptive conversion between exploitation and exploration. Therefore, the proposed OLGBO is evolved into a way for unknown parameter estimation of different PV models. Compared with the RLGBO and basic GBO methods, OLGBO achieves a smaller root-mean-square error (RMSE) and standard deviation (STD). In addition, OLGBO is compared with other algorithms, and the outcomes also demonstrate that the OLGBO method has a better excellent effect than selected state-of-the-art methods at certain temperatures and light conditions. Thus, all the evidences indicates that OLGBO can be a fast, promising, reliable, and feasible optimization method for dealing with unknown parameter identification problems in photovoltaic models.

Parameter extraction of photovoltaic models using a memory-based improved gorilla troops optimizer

The parameter extraction of the PV model is a challenging issue owing to its multi-model and nonlinear characteristics. Moreover, these characteristics of the problem render the algorithms tackling it susceptible to being stuck in local optima. Nevertheless, it is imperative to accurately estimate the parameters due to their significant impact on the efficiency of the Photovoltaic (PV) system in terms of current and power generation. Hence, this paper proposes a new metaheuristic algorithm called the Memory-based Improved Gorilla Troops Optimizer (MIGTO). Furthermore, the Explorative Gorilla with an Adaptive Mutation Mechanism (EGAMM) and the Gorilla memory-saving technique are two major improvements that support the MIGTO superiority. EGAMM primarily comprises two main operators (explorative gorilla operator, adaptive mutation operator). The explorative gorilla operator enhances the search capability to explore new gorillas’ positions in the search space to escape from local optima with a small probability of 0.1. Otherwise, MIGTO updates the new gorilla position using the adaptive mutation operator by selecting two random gorillas. Additionally, the GMS technique promotes the quality of the gorillas by keeping a history of the previous positions to be compared to the current ones. Several experiments are conducted between MIGTO and other well-known metaheuristic algorithms. The experimental results and statistical analyses prove the outperformance of MIGTO in effectively extracting the parameters of different PV models, including the single diode model, the double diode model, the triple diode model, and the photovoltaic module model. Additionally, the performance of the algorithms is tested using the manufacturer’s datasheet.

A novel levy flight trajectory-based salp swarm algorithm for photovoltaic parameters estimation

Simulation and optimization of photovoltaic (PV) systems are recently urging as a hotspot in the field of renewable energy. For this, different models have been introduced to simulate the behavior of real PV cells and modules. An accurate estimation of unknown parameters of PV models is necessary to achieve a good performance of photovoltaic systems. This paper presents a new metaheuristic algorithm called Levy flight trajectory-based salp swarm algorithm (LSSA), which estimated single diode (SD), double diode (DD) and PV module models parameters. Compared with the original salp swarm algorithm (SSA), LSSA benefits from enhanced population diversity due to Levy flight trajectory characteristic of long jump steps. In order to validate its efficiency, the proposed technique was compared with other well-known meta-heuristics for estimating PV parameters in the SD, DD and PV modules. The experimental and comparative results demonstrated that LSSA was able to find extremely accurate solutions with high reliability and offers very competitive results for the problem of estimating PV parameters.

Parameter estimation of photovoltaic modules using analytical and numerical/iterative approaches: A comparative study

Modeling photovoltaic (PV) modules is fundamental for analyzing their efficiency and performance under different operating conditions. Generally, photovoltaic module modeling is based on a suitable equivalent circuit and a set of parameters representing the PV module's properties. Defining these parameters is not a trivial task, as they are usually not included in the technical documentation of the module. Therefore, the need to find suitable values for the model parameters becomes imperative. In this paper, we will test and compare two methods of extracting single-diode model (SDM) parameters: analytical and numerical, under standard test conditions (STC conditions). We examined the performance of six techniques: three analytical and three numerical. Except for Saleem technique, which tends to underestimate the I-V and P-V curves in the MPP zone, the results demonstrated that both approaches (analytical and iterative/numerical) are valid and accurate for predicting the I-V and P-V curves under STC conditions.

Performance Estimation Modeling via Machine Learning of an Agrophotovoltaic System in South Korea

The Agrophotovoltaic (APV) system is a novel concept in the field of Renewable Energy Systems. This system enables the generation of solar energy via photo-voltaic (PV) modules above crops, to mitigate harmful impact on food production. This study aims to develop a performance evaluation model for an APV system in a temperate climate region, such as South Korea. To this end, both traditional electricity generation models (solar radiation-based model and climate-based model) of PV modules and two major machine learning (ML) techniques (i.e., polynomial regression and deep learning) have been considered. Electricity generation data was collected via remote sensors installed in the APV system at Jeollanam-do Agricultural Research and Extension Services in South Korea. Moreover, economic analysis in terms of cost and benefit of the subject APV system was conducted to provide information about the return on investment to farmers and government agencies. As a result, farmers, agronomists, and agricultural engineers can easily estimate performance and profit of their APV systems via the proposed performance model.

A novel two step method to extract the parameters of the single diode model of Photovoltaic module using experimental Power–Voltage data

Accurate modeling of the Photovoltaic (PV) module is required to find the location of the fault in the PV array. It also helps in designing a precise MPPT algorithm and avoiding uncertainties in the Micro-grids. This paper uses a Two-Step Linear Least Square Error (LLSE) method to extract the parameters of the PV module. The proposed method utilizes the experimental data of the Power–Voltage (P–V) curve to estimate the PV module parameters. The proposed method does not require any datasheet information and avoids initial guesses of parameters. To validate the proposed method, three different PV modules, Mono-crystalline STM6-40/36, Poly-crystalline SMP6-120/36, PWP-201, and one Real-Time Clock France solar cell have been considered. The performance of the proposed method was studied using the Root Mean Square Error, Mean Absolute Error (MAE), Normalized Root Mean Square Error (NRMSE), and Normalized Mean Absolute Error (NMAE). The proposed LLSE method exhibited the low Root-Mean-Square-Error (RMSE) for all three PV modules and the R.T.C France solar cell.

A reinvigorated strategy for the analysis of optimal parameters for modeling of Solar Photovoltaic modules under variable conditions

In today’s world, Solar Photovoltaic energy sources have accredited robustness and reliability in the context of generation, transmission, and distribution of power for the end-users and utility customers. The accurate parameters analysis of Solar PV modules is necessary for the proper assessment, simulation, and optimization of power from Solar PV systems. The main goal of this paper is to apply a suitable approach to identify unspecified parameters of the PV module and at the same time to minimize (%) relative error and computation time to get better-optimized parameters for modeling of PV module. This paper presents a hybrid of a mathematical and iterative approach to analyze the appropriate parameters of the Solar PV model. Here, Root finding algorithms have been applied to extract the optimal unknown parameters of the PV modules by MATLAB programming. These algorithms are demonstrated on three distinct types of PV modules (Thin film, Monocrystalline, and Multicrystalline type) at standard test conditions and nominal operating conditions. These algorithms provide high precision and consume minimal time with ease of implementation. Extraction of parameters and simulation of the model is performed for validation based on datasheets of distinct types of PV modules using MATLAB/ SIMULINK software. The extracted precise parameters give rise to output characteristics of PV modules under variable environmental and electrical conditions. Relative error analysis has been evaluated to distinguish between different techniques applied for parameter extraction of PV modules. The relative error (%) of the proposed techniques for parameters extraction of PV modules varies from −0.5% to ＋0.5%, which shows the supercilious characteristic of the proposed techniques. Future exploration headings concerning the optimization of power from the Solar PV system are suggested.

Orthogonal learning-based Gray Wolf Optimizer for identifying the uncertain parameters of various photovoltaic models

Defining the optimal parameters for the photovoltaic (PV) system model is essential for the design, evolution, development, estimation, and analysis of the PV power system. Therefore, it is crucial to properly identify the best parameters of the PV models based on modern computational techniques. As a result, this research proposes a new Orthogonal-Learning-Based Gray Wolf Optimizer (OLBGWO) for identifying uncertain parameters in PV cell models using a local exploratory approach. The orthogonal-learning-based (OLB) technique enhances the exploitation and exploration capabilities of the original Gray Wolf Optimizer (GWO) and modified vector parameter called a, which promotes a highly reliable balance between the exploitation and exploration phases of the algorithm. During the iterative procedure of OLBGWO, the OLB methodology is employed to obtain the optimal solution for the weaker populations and guides the population to examine the prospective search area. Additionally, in OLBGWO, an exponential decay function is used to reduce the value of vector a. The proposed approach is used to solve the PV system's parameter estimation problem. The presented OLBGWO algorithm estimates the uncertain parameters of the single-diode model (SDM), double-diode model (DDM), and PV module model. The OLBGWO's performance is compared to those of other competing algorithms to demonstrate its superiority. The simulation results demonstrate that the OLBGWO algorithm provides fast convergence speed while maintaining high solution accuracy.

Parameter extraction of single‐diode photovoltaic module using experimental current–voltage data

SummaryAccurate modeling of photovoltaic (PV) module allows proper load scheduling and avoids the uncertainties in grid. This paper uses forward‐backward linear least square error (FB‐LLSE) curve fitting method to estimate the parameters of PV module. The proposed method does not require any data sheet information and initial values of parameters. The proposed method utilizes the experimental data on I–V curve to extract the parameters of PV module. To validate the proposed method, three different PV modules, namely, Mono‐crystalline STM6‐40/36, Poly‐crystalline SMP6‐120/36, PWP‐201, and one Real Time Clock (R.T.C.) France solar cell has been considered. The obtained results are compared with three existing methods in the literature. The performance of the proposed FB‐LLSE method is studied with root mean square error (RMSE), mean absolute error (MAE), normalized root mean square error (NRMSE), and normalized mean absolute error (NMAE). The calculated with proposed FB‐LLSEM is reduced by 10%, 7%, 2.26%, and 1.89%, respectively, for PWP‐201, STMP‐120/36, SMP6‐40/36, and R.T.C France solar cell when compared to the LLSEM method available in the literature. The proposed FB‐LLSE method is found to exhibit low value of RMSE for all three PV modules and one PV cell.

Spiral-based chaotic chicken swarm optimization algorithm for parameters identification of photovoltaic models

Photovoltaic (PV) systems are becoming increasingly significant because they can convert solar energy into electricity. The conversion efficiency is related to the PV models’ parameters, so it is crucial to identify the parameters of PV models. Recently, various metaheuristic methods have been proposed to identify the parameters, but they cannot provide sufficient accurate and reliable performance. To address this problem, this paper proposes a spiral-based chaos chicken swarm optimization algorithm (SCCSO) including three strategies: (1) the information-sharing strategy provides the latest information of the roosters for searching global optimal solution, beneficial to improve the exploitation ability; (2) the spiral motion strategy can enable hens and chicks to move toward their corresponding targets with a spiral trajectory, improving the exploration ability; and (3) a self-adaptive-based chaotic disturbance mechanism is introduced around the global optimal solution to generate a promising solution for the worst chick at each iteration, thereby improving the convergence speed of the chicken flock. Besides, SCCSO is used for identifying different PV models such as the single-diode, the double-diode, and PV module models. Comprehensive analysis and experimental results show that SCCSO provides better robustness and accuracy than other advanced metaheuristic methods.

An online optimization method for extracting parameters of multi-parameter PV module model based on adaptive Levenberg-Marquardt algorithm

This paper proposes a novel method to estimate the optimal parameters of a single-diode photovoltaic (PV) module model as well as the active power of PV generation. First, a multi-parameter PV module model is established considering the changes of temperature and solar irradiance; thus, the model is adaptive to different environmental conditions. Second, the model parameter estimation is designed as an optimization problem. An online optimization scheme that only requires the normal operation information is proposed, which avoids the need for an offline experiment to determine the current–voltage (I-V) curve as in conventional PV modeling methods. Third, the adaptive Levenberg-Marquardt (ALM) method with an adaptative damping factor selection strategy is developed to solve the parameter optimization problem, which overcomes the singular issue of traditional LM methods. Moreover, the global sensitivity analysis (GSA) is leveraged to identify critical parameters affecting the PV generation output power, which provides information on model simplification. Finally, the proposed method is tested on data from real-world PV systems in Bend, Oregon, USA, under diverse conditions and scenarios. It is revealed that compared with commonly used methods, the proposed method obtains more accurate PV module parameters and offers PV generation outputs closer to the true outputs.