Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method

doi:10.1016/j.rinp.2024.107364

Results in Physics 物理学成果

Volume 57, February 2024, 107364
第 57 卷，2024 年 2 月，107364

https://doi.org/10.1016/j.rinp.2024.107364 Get rights and content 获取权利和内容

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Highlights 亮点

•
The paper introduced a modified Newton-Raphson method.
论文介绍了一种改进的牛顿-拉斐森方法。
•
The method follows predictor–corrector rule.
该方法遵循预测-修正规则。
•
The method accuracy was measured by Root Mean Squared Error.
该方法的准确性是以均方根误差来衡量的。
•
Validated of method was done against experimental values, RTC cell and PWP210 module
根据实验值、RTC 电池和 PWP210 模块对该方法进行了验证
•
MATLAB simulation was done to study effect of temperature and solar intensity.
通过 MATLAB 仿真研究了温度和太阳强度的影响。

Abstract 摘要

This paper presents a numerical method for estimating four physical parameters of a single-diode circuit model based on manufacturer’s datasheet. A system of four non-linear equations are formed based on three key points of PV characteristics. The photocurrent, saturation current, ideality factor and the series resistance are solved iteratively using the proposed method. The suggested method is validated using RTC France solar cell, Chloride CHL285P and Photowatt PWP210 modules and the results are verified with respect to the in-field outdoor measurements. The proposed method shows a good agreement with the experimental data. Lastly, The model chosen is simulated under MATLB environment to assess the effects of external physical weather conditions, that is, temperature and solar irradiance. The advantage of the proposed method with respect of existing numerical techniques is that it converged faster than the widely used Newton method. Modeling of PV cell/module is essential in predicting performance of photovoltaic generators at any operating condition.
本文介绍了一种基于制造商数据表估算单二极管电路模型四个物理参数的数值方法。根据光伏特性的三个关键点，建立了由四个非线性方程组成的系统。光电流、饱和电流、ideality 因子和串联电阻的迭代求解采用了所建议的方法。使用 RTC France 太阳能电池、Chloride CHL285P 和 Photowatt PWP210 模块对所建议的方法进行了验证，结果与现场室外测量结果一致。建议的方法与实验数据显示出良好的一致性。最后，在 MATLB 环境下模拟了所选模型，以评估外部物理天气条件（即温度和太阳辐照度）的影响。与现有数值技术相比，所提出方法的优势在于它比广泛使用的牛顿方法收敛更快。光伏电池/模块建模对于预测光伏发电机在任何运行条件下的性能都至关重要。

Keywords 关键词

Extraction of parameters

Mathematical modeling

Numerical method

Photovoltaic module

Single diode model

参数提取数学建模数值法光伏组件单二极管模型

Introduction 导言

Energy, the lifeblood of economic progress and a fundamental necessity for maintaining our quality of life and supporting all aspects of our economy, has witnessed a significant growth in demand over the past two decades [1], largely fueled by our heavy reliance on fossil fuels. However, the significant growth in energy demand has posed significant environmental challenges on a global level, emphasizing the need for immediate and decisive measures to address and mitigate its impact [2]. To address these challenges, it is imperative to adopt sustainable development strategies that offer long-term solutions. Among these strategies, renewable energy resources have emerged as highly efficient and effective alternatives [3]. In contrast to finite fossil fuel reserves, renewable energy sources like solar, wind, and hydropower have minimal adverse effects on the environment. Solar energy, in particular, has gained immense popularity worldwide due to its numerous benefits, including affordability, widespread availability, and a reduced ecological footprint [4]. This is primarily attributed to the capability of photovoltaic (PV) cell technology to directly convert sunlight into electricity [5], [6], making solar energy a promising and viable option for sustainable energy generation [7]. Despite the numerous advantages, the performance of photovoltaic (PV) modules is significantly impacted by external environmental conditions. These include solar intensity [5], ambient temperature [8], relative humidity [9], [10], wind speed [11], panel dust accumulation [12], and the tilt angle of the panel [13], [14], [15]. In light of this reality, the actual performance of PV module systems in real working environments often falls short of expectations [16]. To overcome this challenge, researchers have explored alternative methods for predicting the output characteristics and maximum power output of PV modules without relying on extensive experimental measurements. One such approach involves utilizing the manufacturer’s data, which provides information about the module’s electrical characteristics under standardized test conditions (STC) [17]. This data includes parameters like the maximum power point voltage, current, and temperature coefficients of the module. However, it is important to acknowledge that relying solely on manufacturer’s data for performance predictions may have limitations. Real-world operating conditions for PV modules can significantly differ from the standardized test conditions used to generate the manufacturer’s data [18]. Therefore, while predictive models based on manufacturer’s data can offer valuable insights, it is crucial to validate their accuracy through field measurements to ensure reliable performance predictions in actual working environments.
能源是经济进步的命脉，也是维持我们的生活质量和支持我们经济各方面发展的基本必需品，在过去二十年里，能源需求大幅增长[1]，这主要是由于我们严重依赖化石燃料。然而，能源需求的大幅增长在全球范围内带来了重大的环境挑战，强调需要立即采取果断措施来应对和减轻其影响[2]。为应对这些挑战，当务之急是采取可提供长期解决方案的可持续发展战略。在这些战略中，可再生能源已成为高效和有效的替代能源[3]。与有限的化石燃料储备相比，太阳能、风能和水能等可再生能源对环境的不利影响微乎其微。特别是太阳能，由于其众多优点，包括经济实惠、广泛可用和减少生态足迹，已在全球范围内大受欢迎[4]。这主要归功于光伏（PV）电池技术能够直接将太阳光转化为电能[5]、[6]，从而使太阳能成为可持续能源生产的一种前景广阔的可行选择[7]。尽管光伏（PV）组件具有诸多优势，但其性能受到外部环境条件的显著影响。这些因素包括太阳强度 [5]、环境温度 [8]、相对湿度 [9]、[10]、风速 [11]、面板积尘 [12] 和面板倾斜角度 [13]、[14]、[15]。鉴于这一现实，光伏组件系统在实际工作环境中的实际性能往往达不到预期[16]。为了克服这一挑战，研究人员探索了其他方法，在不依赖大量实验测量的情况下预测光伏组件的输出特性和最大功率输出。其中一种方法是利用制造商的数据，这些数据提供了模块在标准化测试条件（STC）下的电气特性信息[17]。这些数据包括模块的最大功率点电压、电流和温度系数等参数。不过，必须承认，仅依靠制造商的数据进行性能预测可能存在局限性。光伏组件的实际运行条件可能与用于生成制造商数据的标准化测试条件大相径庭[18]。因此，虽然基于制造商数据的预测模型可以提供有价值的见解，但至关重要的是要通过现场测量来验证其准确性，以确保在实际工作环境中进行可靠的性能预测。

Efforts have been made by researchers to improve the performance of solar panels, leading to the development of various PV models. Based on equivalent circuit, the models are classified as single and double diodes. While single diode model consists of five, four or three unknown parameters, double diode model has seven unknown parameters. The five parameters of sinlge diode model are the photocurrent (

I p h

), reverse saturation current (

I_{o}

), series (

R_{s}

) and shunt (

R_{s h}

) resistances, and the ideality factor (

α

). The four parameter model of a single diode assumes the shunt resistance infinity and its effect is ignored [19], [20], [21]. The three parameter model proposes that the series resistance is zero and shunt resistance is infinity leading to their neglect. On the other hand the seven estimated parameters of double diode model includes the five parameters of the single parameter model with additional of second reverse saturation current and ideality factor for the second diode [22], [23].
研究人员一直在努力提高太阳能电池板的性能，从而开发出各种光伏模型。根据等效电路，模型可分为单二极管和双二极管。单二极管模型由五个、四个或三个未知参数组成，而双二极管模型则有七个未知参数。单二极管模型的五个参数分别是光电流（

I p h

）、反向饱和电流（

I_{o}

）、串联电阻（

R_{s}

）和并联电阻（

R_{s h}

）以及表意系数（

α

）。单二极管的四参数模型假定并联电阻为无穷大，其影响被忽略 [19]、[20]、[21]。三参数模型认为串联电阻为零，并联电阻为无穷大，因此忽略了它们的影响。另一方面，双二极管模型的七个估计参数包括单参数模型的五个参数以及第二个二极管的第二个反向饱和电流和理想系数 [22]，[23]。

There are various methods developed in literature for parameter extraction of PV circuit models. These approaches can be categorized into analytical, numerical (deterministic and stochastic) and hybrid methods [22]. For example, Jakhrani et al. [23] used numerical method to determine the output current and voltage of a five-parameter model for a single diode equivalent circuit. This method however, required extensive mathematical computations. Similarly, [24] proposed a numerical approach to extract the physical parameters based on single diode model. The ideality factor and series resistance were solved numerically using only two points, at short circuit point and at maximum power point. The method proposed showed good agreement with experimental values. In addition, El Achouby et al. [25] proposed numerical method to extract the five physical parameters at standard test conditions (STC). This ideality factor was made to vary and a system of four nonlinear equations was solved. The drawback of this approach is the suitable choice of initial values of the parameters. Moreover, Elkholy and Abou El-Ela [26] took an analytical approach by solving the parameters of a single diode model based on in-field outdoor data, demonstrating good agreement between simulated and experimental measurements. However, this method was complicated due to the requirement of extensive experimental data. [27] proposed a simple fitting method for estimating parameters of a single diode model, but its validity was limited to constant solar irradiance, making it impractical for real working environments. Rasheed et al. [28] presented the Chebyshev numerical method as an alternative to the Newton–Raphson method for solving the voltage of PV cells, but the increased computational burden from calculating second derivatives posed challenges. Currently, [29] introduced a new simplified method for the iterative estimation of the five PV module parameters. This method uses some approximations to determine the values of series resistance and ideality factor. The accuracy of this method was a bit challenge due to approximations while computing series resistance and ideality factor. [30] presented a numerical method for solving the series and shunt resistances using the Newton–Raphson approach and the Lambert W- function. However, this method needs a lot of assumptions to simplify the problem in order to extract the five parameters. Lastly, Manuel Godinho Rodrigues et al. [31] conducted a comparative study using numerical simulations to evaluate the five-parameter single diode model and the more advanced seven-parameter double diode model. The double diode model accounted for additional energy losses associated with charge carrier recombination in the depletion layers, but its high complexity level limited its practicality.
文献中有多种光伏电路模型参数提取方法。这些方法可分为分析方法、数值方法（确定性和随机性）和混合方法 [22]。例如，Jakhrani 等人 [23] 使用数值方法确定了单二极管等效电路五参数模型的输出电流和电压。然而，这种方法需要大量的数学计算。同样，[24] 提出了一种基于单二极管模型提取物理参数的数值方法。仅使用短路点和最大功率点两个点对理想化系数和串联电阻进行了数值求解。所提出的方法与实验值显示出良好的一致性。此外，El Achouby 等人[25] 提出了在标准测试条件 (STC) 下提取五个物理参数的数值方法。这种表意系数是变化的，并求解了一个由四个非线性方程组成的系统。这种方法的缺点是需要选择合适的参数初始值。此外，Elkholy 和 Abou El-Ela [26] 还采用了一种分析方法，即根据现场室外数据求解单个二极管模型的参数，结果表明模拟和实验测量结果之间的一致性很好。然而，由于需要大量实验数据，这种方法比较复杂。[27] 提出了一种简单的拟合方法来估算单二极管模型的参数，但其有效性仅限于恒定的太阳辐照度，因此在实际工作环境中并不实用。Rasheed 等人 [28] 提出了切比雪夫数值方法，作为牛顿-拉斐森方法的替代方法，用于求解光伏电池的电压，但计算二次导数所增加的计算负担带来了挑战。目前，[29] 提出了一种新的简化方法，用于迭代估计五个光伏组件参数。该方法使用一些近似值来确定串联电阻和表意系数的值。由于在计算串联电阻和意向系数时使用了近似值，该方法的准确性面临一定挑战。[30] 提出了一种利用牛顿-拉斐森方法和兰伯特 W- 函数求解串联和并联电阻的数值方法。然而，这种方法需要大量假设来简化问题，以提取五个参数。最后，Manuel Godinho Rodrigues 等人[31] 利用数值模拟进行了比较研究，评估了五参数单二极管模型和更先进的七参数双二极管模型。双二极管模型考虑到了与耗尽层中电荷载流子重组相关的额外能量损失，但其高复杂度限制了其实用性。

As per literature review, numerical iterative methods have been widely applied in solving the non-linear, multi-parameter and transcendental equation of PV model. Of many iterative approaches, Newton–Raphson method is the most popular in this field due to its simplicity, accuracy and quadratic convergency rate [28], [32], [33]. Despite this dominance, Newton–Raphson has convergence shortcomings especially when the initial inputs are far from the actual roots [34], [35].
根据文献综述，数值迭代法已被广泛应用于求解光伏模型的非线性、多参数和超越方程。在众多迭代法中，牛顿-拉夫逊法因其简单、精确和二次收敛率而在该领域最受欢迎 [28]、[32]、[33]。尽管牛顿-拉夫逊法占主导地位，但它也存在收敛性缺陷，尤其是当初始输入远离实际根值时[34]，[35]。

In this work, we present a modified Newton–Raphson Method proposed by [36] to estimate the parameters of single diode model. We first choose to use a simplified four parameter model of a single diode equivalent circuit. Next, we develop the corresponding mathematical equation of the model. Then, basing on three key points from manufacturer’s catalog, a system of four non-linear equations is formed and solved iteratively using the proposed method. This method advantageous than the standard Newton–Raphson one because its rate of convergence is enhanced to the order of

1 + \sqrt{2}

. Thus, it offers a quick and accurate analysis of PV module performance. Circuit modeling of PV cells, as discussed by Batzelis and Papathanassiou, El Achouby et al. [37], [25], enables PV cell simulation and performance evaluation under varying conditions, aiding in monitoring system operation, forecasting power output, calculating power losses, and developing maximum power point tracking algorithms [38]. This paper is organized as follows: Section “Introduction” presents an introductory part of the study and the reviews of different approaches of solving mathematical models of PV module. Method part is found in Section “Method” in which the model formulation procedures and parameter extraction processes are discussed. Results and Discussion are presented in Section “Results and Discussion”. Lastly, conclusion is declared in Section “Conclusion”.
在这项工作中，我们采用 [36] 提出的修正牛顿-拉斐森方法来估计单二极管模型的参数。我们首先选择使用单二极管等效电路的简化四参数模型。接着，我们建立了模型的相应数学方程。然后，根据制造商目录中的三个关键点，形成四个非线性方程组，并使用所提出的方法进行迭代求解。与标准的 Newton-Raphson 方法相比，该方法的优势在于其收敛速度提高到了

1 + \sqrt{2}

的数量级。因此，它能快速准确地分析光伏组件的性能。正如 Batzelis 和 Papathanassiou、El Achouby 等人[37]、[25]所讨论的那样，光伏电池的电路建模可以在不同条件下对光伏电池进行模拟和性能评估，有助于监控系统运行、预测功率输出、计算功率损耗和开发最大功率点跟踪算法[38]。本文的结构如下：绪论 "部分介绍了本研究的前言部分，并回顾了求解光伏组件数学模型的不同方法。在 "方法 "部分，讨论了模型制定程序和参数提取过程。结果和讨论 "部分介绍了结果和讨论。最后，在 "结论 "部分给出结论。

Method 方法

Model formulation 模型表述

PV cell is modeled as p–n junction diode because their working principle are similar. The equivalent circuit of the single diode model consists of the real diode connected in parallel with the ideal current source (

I_{p h}

), the series and the parallel resistors (

R_{s}

and

R_{s h}

) as shown in Fig. 1. Referring Fig. 1, the Kirchhoff’s law is represented by the following equation: (1)

I = I_{p h} - I_{D} - I_{s h}

Where;

I

is the current output,

I_{p h}

is the photocurrent from the source,

I_{D}

is the current through the diode and

I_{s h}

is the current through the shunt resistance. The photocurrent

I_{p h}

is the function of solar irradiation and temperature as shown in the equation [39] (2)

I_{p h} = \frac{G}{G_{r e f}} [I_{p h, r e f} + K_{i} (T - T_{r e f})]

光伏电池的工作原理与 p-n 结二极管相似，因此将其建模为 p-n 结二极管。如图 1 所示，单二极管模型的等效电路由与理想电流源（

I_{p h}

）并联的实际二极管、串联电阻和并联电阻（

R_{s}

和

R_{s h}

）组成。参照图 1，基尔霍夫定律用下式表示： (1)

I = I_{p h} - I_{D} - I_{s h}

其中，

I

为输出电流，

I_{p h}

为来自光源的光电流，

I_{D}

为通过二极管的电流，

I_{s h}

为通过并联电阻的电流。光电流

I_{p h}

是太阳辐照度和温度的函数，如公式 [39] (2)

I_{p h} = \frac{G}{G_{r e f}} [I_{p h, r e f} + K_{i} (T - T_{r e f})]

所示

Where;

G

is the solar irradiance,

G_{r e f}

is the solar irradiance at reference point,

I_{p h, r e f}

is the photocurrent at reference point,

K_{i}

is the temperature coefficient at short circuit,

T

is an operating temperature and

T_{r e f}

is the temperature at reference point The diode current is given by Shockley equation as follows [26] (3)

I_{D} = I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1]

Where:
式中：

G

为太阳辐照度，

G_{r e f}

为参考点的太阳辐照度，

I_{p h, r e f}

为参考点的光电流，

K_{i}

为短路时的温度系数，

T

为工作温度，

T_{r e f}

为参考点的温度二极管电流由肖克利方程给出，如下所示[26] (3)

I_{D} = I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1]

式中

q

– Charge of an electron

(1.602 \times 1 0^{- 19} C)

q

- 电子的电荷

(1.602 \times 1 0^{- 19} C)

α

– Diode ideality factor

α

- 二极管理想系数

K

– Boltzmann constant

(1.381 \times 1 0^{- 23} J/K)

K

- 玻耳兹曼常数

(1.381 \times 1 0^{- 23} J/K)

T_{c}

– Temperature of a cell

(K)

T_{c}

- 电池的温度

(K)

V

– Voltage output

(V)

V

- 电压输出

(V)

I_{0}

– Diode reverse saturation current

I_{0}

- 二极管反向饱和电流

The reverse saturation current depends on ambient temperature as shown in the equation [41] (4)

I_{0} = I_{0, r e f} {(\frac{T_{c}}{T_{r e f}})}^{3} exp [\frac{q E_{g}}{K α} (\frac{1}{T_{r e f}} - \frac{1}{T_{c}})]

Where (5)

I_{0, r e f} = \frac{I_{s c}}{exp (\frac{q V_{o c}}{α N_{s} K T}) - 1}

The series

(R_{s})

and shunt

(R_{s h})

resistances can be estimated from

V - I

curve as follows: (6)

R_{s} = {- \frac{d V}{d I}|}_{I = 0, V = V_{o c}} - \frac{V_{T}}{I_{s c}}

Where

V_{T} = \frac{α K T_{c}}{q}

, and (7)

R_{s h} = {- \frac{d V}{d I}|}_{I = I_{s c}, V = 0}

The current through the shunt resistance is given by the following equation [42] (8)

I_{s h} = \frac{V + I R_{s}}{R_{s h}}

The ideality factor

(α)

is given by [43], [44] as follows: (9)

α = \frac{V_{m p p} + I_{m p p} R_{s o} - V_{o c}}{V_{T} [ln (I_{s c} - I_{m p p} - \frac{V_{m p p}}{R_{s h o}}) - ln (I_{s c} - \frac{V_{o c}}{R_{s h}}) + \frac{I_{m p p}}{I_{s c} - \frac{V_{o c}}{R_{s h o}}}]}

Under varying physical conditions, [26], [45] presents the analytical formulas to determine series

R_{s}

and shunt

R_{s h}

resistances, and the ideality factor

α

as follows: (10)

R_{s} = R_{s, r e f} (\frac{T_{c}}{T_{r e f}}) [1 - β_{o c} ln (\frac{G}{G_{r e f}})]

Where,

R_{s, r e f}

is the series resistance at reference conditions and

R_{s}

is the corresponding parameter at the real experimental weather conditions.

β_{o c}

is the temperature coefficient at open circuit whose value is about

0.217 K

. (11)

R_{s h} = R_{s h, r e f} (\frac{G_{r e f}}{G})

Where,

R_{s h, r e f}

is the shunt resistance at reference conditions and is the parameter at the real outdoor conditions [26]. (12)

α = α_{r e f} (\frac{T_{c}}{T_{r e f}})

Where,

α_{r e f}

is the ideality factor of the diode at reference conditions and

α

is the ideality factor at the real outdoor conditions [26]. Therefore, the final equation of a single diode five-parameter model is given as follows [25], [26], [46], [47], [48], [49] (13)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1] - \frac{V + I R_{s}}{R_{s h}}

[21] claims that the PV cell is not sensitive to shunt resistance and that it can be considered to be infinity without generating earth current leakage. In addition, a comparative study performed by [20] for different models of PV cell reveals that the effect of shunt resistance at low voltage and solar illumination is negligible. Moreover, a study by [19] shows that for higher power yield and fill factor, the shunt resistance should be large enough because low shunt resistance leads to high power loss. Therefore, the shunt resistance in this study is assumed to be infinity, hence the last term of the model equation is disregarded. By omitting this final component of the model, the influence of shunt resistance on PV module performance is ignored. The model equation remains only with four parameters

(I_{p h}, I_{o}, R_{s}, α)

. This helps to reduce the complexity of the model as given below: (14)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1]

For

N

cells, Eq. (14) becomes: (15)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{N α K T_{c}}) - 1]

反向饱和电流取决于环境温度，如公式 [41] 所示 (4)

I_{0} = I_{0, r e f} {(\frac{T_{c}}{T_{r e f}})}^{3} exp [\frac{q E_{g}}{K α} (\frac{1}{T_{r e f}} - \frac{1}{T_{c}})]

其中 (5)

I_{0, r e f} = \frac{I_{s c}}{exp (\frac{q V_{o c}}{α N_{s} K T}) - 1}

串联电阻

(R_{s})

和并联电阻

(R_{s h})

可根据

V - I

曲线估算如下： (6)

R_{s} = {- \frac{d V}{d I}|}_{I = 0, V = V_{o c}} - \frac{V_{T}}{I_{s c}}

其中

V_{T} = \frac{α K T_{c}}{q}

和 (7)

R_{s h} = {- \frac{d V}{d I}|}_{I = I_{s c}, V = 0}

通过并联电阻的电流由下式 [42] 得出 (8)

I_{s h} = \frac{V + I R_{s}}{R_{s h}}

理想系数

(α)

由 [43], [44] 得出如下： (9)

α = \frac{V_{m p p} + I_{m p p} R_{s o} - V_{o c}}{V_{T} [ln (I_{s c} - I_{m p p} - \frac{V_{m p p}}{R_{s h o}}) - ln (I_{s c} - \frac{V_{o c}}{R_{s h}}) + \frac{I_{m p p}}{I_{s c} - \frac{V_{o c}}{R_{s h o}}}]}

在不同的物理条件下，[26]、[45] 提出了确定串联

R_{s}

和并联

R_{s h}

电阻以及表意系数

α

的解析公式如下： (10)

R_{s} = R_{s, r e f} (\frac{T_{c}}{T_{r e f}}) [1 - β_{o c} ln (\frac{G}{G_{r e f}})]

其中，

R_{s, r e f}

为参考条件下的串联电阻，

R_{s}

为实际实验天气条件下的相应参数。

β_{o c}

是开路时的温度系数，其值约为

0.217 K

。 (11)

R_{s h} = R_{s h, r e f} (\frac{G_{r e f}}{G})

其中，

R_{s h, r e f}

是参考条件下的并联电阻，是实际室外条件下的参数 [26]。 (12)

α = α_{r e f} (\frac{T_{c}}{T_{r e f}})

其中，

α_{r e f}

是二极管在参考条件下的表意系数，

α

是实际室外条件下的表意系数[26]。因此，单二极管五参数模型的最终方程如下 [25]、[26]、[46]、[47]、[48]、[49] (13)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1] - \frac{V + I R_{s}}{R_{s h}}

[21] 称，光伏电池对并联电阻不敏感，可以认为其为无穷大，不会产生接地电流泄漏。此外，[20] 对不同型号的光伏电池进行的比较研究表明，在低电压和太阳光照下，并联电阻的影响可以忽略不计。此外，[19] 的研究表明，为了获得更高的功率输出和填充因子，并联电阻应该足够大，因为并联电阻过小会导致功率损耗过大。因此，本研究假定并联电阻为无穷大，从而忽略了模型方程的最后一项。通过省略模型的最后一项，并联电阻对光伏组件性能的影响被忽略。模型方程只剩下四个参数

(I_{p h}, I_{o}, R_{s}, α)

。这有助于降低模型的复杂性，如下所示： (14)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{K α T_{c}}) - 1]

对于

N

电池，公式 (14) 变为： (15)

I = I_{p h} - I_{0} [exp (\frac{q (V + I R_{s})}{N α K T_{c}}) - 1]

Determination of parameters of the model
确定模型参数

The model consists of four unknown parameters (

I_{p h}

I_{0}

a

, and

R_{s}

) whose values are required to be determined. To solve for these parameters, four equations are required. The three basic operating points on

I - V

curve of the PV cell/module give the first three equations which are Eqs. (16), (17), (18)
该模型包括四个未知参数（

I_{p h}

、

I_{0}

、

a

和

R_{s}

），需要确定其值。要求解这些参数，需要四个方程。光伏电池/模块的

I - V

曲线上的三个基本工作点给出了前三个方程，即公式 (16)、(17) 和 (18)

(a)
At the open circuit, $V = V_{o c}$ and $I = 0$ (16) $0 = I_{p h} - I_{0} [exp (\frac{q V_{o c}}{N α K T_{c}}) - 1]$
开路时， $V = V_{o c}$ 和 $I = 0$ (16) $0 = I_{p h} - I_{0} [exp (\frac{q V_{o c}}{N α K T_{c}}) - 1]$
(b)
At the short circuit, $V = 0$ and $I = I_{s c}$ (17) $I_{s c} = I_{p h} - I_{0} [exp (\frac{q I_{s c} R_{s}}{N α K T_{c}}) - 1]$
短路时， $V = 0$ 和 $I = I_{s c}$ (17) $I_{s c} = I_{p h} - I_{0} [exp (\frac{q I_{s c} R_{s}}{N α K T_{c}}) - 1]$
(c)
At the maximum power point, $V = V_{m p p}$ and $I = I_{m p p}$ (18) $I_{m p p} = I_{p h} - I_{0} [exp (\frac{q (V_{m p p} + I_{m p p} R_{s})}{N α K T_{c}}) - 1]$
在最大功率点， $V = V_{m p p}$ 和 $I = I_{m p p}$ (18) $I_{m p p} = I_{p h} - I_{0} [exp (\frac{q (V_{m p p} + I_{m p p} R_{s})}{N α K T_{c}}) - 1]$
(d)
At maximum power point $(I_{m p p}, V_{m p p})$ the slope, $\frac{d P}{d V} = 0$ , where the power $P = V I$ . Thus, we have the fourth equation as shown in Eq. (19) below (19) $\frac{I_{m p p}}{V_{m p p}} = \frac{q I_{0}}{N α K T_{c}} (1 + R_{s} \frac{I_{m p p}}{V_{m p p}}) exp (\frac{q (V_{m p p} + I_{m p p} R_{s})}{N α K T_{c}})$
在最大功率点 $(I_{m p p}, V_{m p p})$ 的斜率， $\frac{d P}{d V} = 0$ ，其中功率 $P = V I$ 。因此，我们可以得到下式 (19) 所示的第四个方程 (19) $\frac{I_{m p p}}{V_{m p p}} = \frac{q I_{0}}{N α K T_{c}} (1 + R_{s} \frac{I_{m p p}}{V_{m p p}}) exp (\frac{q (V_{m p p} + I_{m p p} R_{s})}{N α K T_{c}})$ .

If we let

I_{p h} = x_{1}

I_{0} = x_{2}

α = x_{3}

R_{s} = x_{4}

and

\frac{q}{N K T_{c}} = λ

, then the system of equations can be written as follows (20)

\{\begin{matrix} f_{1} (X) = x_{1} - x_{2} [exp (\frac{λ V_{o c}}{x_{3}}) - 1] \\ f_{2} (X) = x_{1} - x_{2} [exp (\frac{λ I_{s c} x_{4}}{x_{3}}) - 1] - I_{s c} \\ f_{3} (X) = x_{1} - x_{2} [exp (\frac{λ (v_{m p p} + x_{4} I_{m p p})}{x_{3}}) - 1] - I_{m p p} \\ f_{4} (X) = \frac{λ x_{2}}{x_{3}} (1 + \frac{x_{4} I_{m p p}}{V_{m p p}}) exp (\frac{λ (v_{m p p} + x_{4} I_{m p p})}{x_{3}}) - \frac{I_{m p p}}{V_{m p p}} \end{matrix}

To obtain the values of model parameters, the system (20) is solved simultaneously by first plugging the values of

I_{s c}

V_{o c}

I_{m p p}

and

V_{m p p}

which are always given in manufacturer’s catalog. The proposed method, modified Newton–Raphson, is used to solve this system.
如果设

I_{p h} = x_{1}

、

I_{0} = x_{2}

、

α = x_{3}

、

R_{s} = x_{4}

和

\frac{q}{N K T_{c}} = λ

，则方程组可写成 (20)

\{\begin{matrix} f_{1} (X) = x_{1} - x_{2} [exp (\frac{λ V_{o c}}{x_{3}}) - 1] \\ f_{2} (X) = x_{1} - x_{2} [exp (\frac{λ I_{s c} x_{4}}{x_{3}}) - 1] - I_{s c} \\ f_{3} (X) = x_{1} - x_{2} [exp (\frac{λ (v_{m p p} + x_{4} I_{m p p})}{x_{3}}) - 1] - I_{m p p} \\ f_{4} (X) = \frac{λ x_{2}}{x_{3}} (1 + \frac{x_{4} I_{m p p}}{V_{m p p}}) exp (\frac{λ (v_{m p p} + x_{4} I_{m p p})}{x_{3}}) - \frac{I_{m p p}}{V_{m p p}} \end{matrix}

为获得模型参数值，首先插入制造商目录中通常给出的

I_{s c}

、

V_{o c}

、

I_{m p p}

和

V_{m p p}

的值，同时求解系统 (20)。所提出的修正牛顿-拉夫逊方法用于求解该系统。

Modified Newton–Raphson method
改进的牛顿-拉斐逊法

The modified Newton–Raphson algorithm as proposed by [36] is given as follows: (21)

x_{0}^{*} = x_{0} - \frac{f (x_{0})}{f^{'} (x_{0})}

(22)

x_{1} = x_{0} - \frac{f (x_{0})}{f^{'} (\frac{1}{2} [x_{0} + x_{0}^{*}])}

This algorithm follows predictor–corrector rule in which Eq. (21) is a predictor step and Eq. (22) forms a corrector step. To start iteration two initial values,

x_{0}

and

x_{0}^{*}

are required. Given an initial value

x_{0}

, the second starting value,

x_{0}^{*}

is obtained simply by standard Newton–Raphson method (NRM) (Eq. (21)). The iteration then proceeds with the corrector step (Eq. (22)) in which the value of the derivative is evaluated at

\frac{1}{2} (x_{0} + x_{0}^{*})

, which is a more appropriate value to use than that at

x_{0}

. For

k \geq 1

: (23)

x_{k}^{*} = x_{k} - \frac{f (x_{k})}{f^{'} (\frac{1}{2} [x_{k - 1} + x_{k - 1}^{*}])}

(24)

x_{k + 1} = x_{k} - \frac{f (x_{k})}{f^{'} (\frac{1}{2} [x_{k} + x_{k}^{*}])}

The initial values were carefully selected with the help of physical analytical formulas developed by Elkholy and Abou El-Ela [26]. The system Eq. (20) was then implemented in MATLAB under standard settings, and the findings are discussed in the next section.
[36] 提出的修正牛顿-拉夫逊算法如下： (21)

x_{0}^{*} = x_{0} - \frac{f (x_{0})}{f^{'} (x_{0})}

(22)

x_{1} = x_{0} - \frac{f (x_{0})}{f^{'} (\frac{1}{2} [x_{0} + x_{0}^{*}])}

该算法遵循预测-修正规则，其中式（21）为预测步骤，式（22）为修正步骤。开始迭代需要两个初始值，即

x_{0}

和

x_{0}^{*}

。在给定初始值

x_{0}

的情况下，第二个起始值

x_{0}^{*}

可以通过标准牛顿-拉斐森方法 (NRM) 简单获得（式 (21)）。然后迭代进入修正器步骤（式 (22)），在该步骤中，导数值在

\frac{1}{2} (x_{0} + x_{0}^{*})

处求值，该值比

x_{0}

处的值更合适。对于

k \geq 1

: (23)

x_{k}^{*} = x_{k} - \frac{f (x_{k})}{f^{'} (\frac{1}{2} [x_{k - 1} + x_{k - 1}^{*}])}

(24)

x_{k + 1} = x_{k} - \frac{f (x_{k})}{f^{'} (\frac{1}{2} [x_{k} + x_{k}^{*}])}

初始值是在 Elkholy 和 Abou El-Ela [26] 提出的物理分析公式的帮助下精心选择的。然后，在标准设置下用 MATLAB 实现了公式 (20) 系统，并在下一节中对结果进行了讨论。

Results and discussion 结果和讨论

In order to verify the proposed method, an outdoor experiment was performed at Arusha Technical College Solar Center using polycrystalline PV module (CHL285P) connected to a PROVA 210 module analyzer. The output current and voltage were obtained at different temperatures and solar irradiances including the standard conditions (irradiation level

1000 {W/m}^{2}

, Air Mass of 1.5 and cell temperature 25 °C). For more validation, two extra experimental case studies, Silicon solar cell RTC France at 33 °C and Silicon Module PWP201 operating at 45 °C, were selected. The accuracy of the proposed approach and the degree of precision of the applied mathematical model were evaluated using two statistical indicators. These are Absolute Error

(ɛ_{absolute})

and the Root Mean Squared Error (RMSE) as defined by [25], [50], [51]. (25)

ɛ_{absolute} = | I_{measured} - I_{model} |

(26)

RMSE = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(I_{i, measured} - I_{i, model})}^{2}}

为了验证所提出的方法，在阿鲁沙技术学院太阳能中心进行了一次室外实验，使用的是与 PROVA 210 模块分析仪相连的多晶光伏模块（CHL285P）。在不同温度和太阳辐照度（包括标准条件（辐照度

1000 {W/m}^{2}

，空气质量为 1.5，电池温度为 25 °C）下获得了输出电流和电压。为了进行更多验证，还选择了两个额外的实验案例研究，即 33 °C 下的硅太阳能电池 RTC France 和 45 °C 下的硅模块 PWP201。建议方法的准确性和应用数学模型的精确度通过两个统计指标进行评估。这两个指标是绝对误差

(ɛ_{absolute})

和均方根误差 (RMSE)，定义见 [25]、[50]、[51]。 (25)

ɛ_{absolute} = | I_{measured} - I_{model} |

(26)

RMSE = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(I_{i, measured} - I_{i, model})}^{2}}

Table 1 summerizes the datasheet of each experimental case study used in this study in order to validate the method presented [22], [24].
表 1 列出了本研究中使用的每个实验案例的数据表，以验证所介绍的方法 [22], [24]。

Table 1. Manufacturer’s catalog for CHL285P module, France Solar cell (RTC) and Photowatt PWP210.
表 1.CHL285P 模块、法国太阳能电池 (RTC) 和 Photowatt PWP210 的制造商目录。

Specification 规格	CHL285P	France solar (RTC) 法国太阳能 (RTC)	PWP210
Cell type 细胞类型	Polycrystalline 多晶体	NA	Polycrystalline 多晶体
$V_{o c}$ [V] $V_{o c}$ [V］	41.25	0.5728	16.778
$I_{s c}$ [A] $I_{s c}$ [A］	9.54	0.76	1.03
$V_{m p p}$ [V] $V_{m p p}$ [V］	32.76	0.45	12.60
$I_{m p p}$ [A] $I_{m p p}$ [A］	9.13	0.691	0.898
$P_{m a x}$ [W] $P_{m a x}$ [瓦]	300	11.315	0.311
Ref. temp. [°C] 参考温度[°C]	STC	33	45
No. of cells 细胞数	60	1	36
Dimensions 尺寸	$1640 \times 992 \times 35 mm$	57 mm diameter 57 毫米直径	–

Chloride CHL285P PV module
氯化物 CHL285P 光伏组件

The proposed iterative method is executed in MATLAB to extract the four unknown parameters (

I_{p h}

I_{o}

α

R_{s}

) of presented model using the information provided in Table 1. The results obtained are then compared with values from standard Newton–Raphson method and another current numerical approach by [24] as shown in Table 1. It can be observed from Table 1 that the proposed method has least value of root mean squared error (RMSE) and less number of iterations than the rest in comparison. This implies that the modified Newton–Raphson method is quicker and accurate than the widely used standard Newton method (see Table 2).
利用表 1 中提供的信息，在 MATLAB 中执行所提议的迭代法来提取模型的四个未知参数（

I_{p h}

、

I_{o}

、

α

、

R_{s}

）。如表 1 所示，将所得结果与标准 Newton-Raphson 方法和另一种当前的数值方法[24]的值进行比较。从表 1 中可以看出，与其他方法相比，拟议方法的均方根误差（RMSE）最小，迭代次数最少。这意味着改进的牛顿-拉斐森方法比广泛使用的标准牛顿方法更快、更准确（见表 2）。

Using the values of four calculated parameters of the model in discussion, it was possible to plot

I - V

and

P - V

characteristic curves. The output calculated characteristics of a test PV module obtained at standard conditions were then compared with experimental curves at reference condition as shown in Fig. 2, Fig. 3. It was discovered from these curves that the model curve passes through the points of the experimental curve. This demonstrates good agreement between theoretically estimated and experimental results. Fig. 4 shows the plot of absolute error for output current versus output voltage for three methods in comparison.
利用讨论中模型的四个计算参数值，可以绘制出

I - V

和

P - V

特性曲线。如图 2 和图 3 所示，将标准条件下测试光伏组件的输出计算特性与参考条件下的实验曲线进行比较。从这些曲线中可以发现，模型曲线经过了实验曲线的各个点。这表明理论估算结果与实验结果非常吻合。图 4 显示了三种比较方法的输出电流与输出电压绝对误差图。

Table 2. Comparison of proposed method with other numerical approaches.
表 2.拟议方法与其他数值方法的比较。

Parameters 参数	Proposed 建议	Standard NRM 标准 NRM	Benahmida [24]
$I_{p h}$ (A)	9.257012	9.257011	9.257009
$I_{o} (μ A)$	3.3193	3.3190	3.3191
$α$	1.206302	1.206301	1.206302
$R_{s} (Ω)$	0.355201	0.355201	0.355202
Iterations. 迭代。	8	10	9
RMSE	0.02	0.028	0.032

RTC France solar cell 法国 RTC 太阳能电池

For RTC solar cell, the optimal parameters obtained using different numerical techniques are presented in Table 3. The cell parameters estimated using modified Newton–Raphson method have the least RMSE value giving its superiority over others in comparison.
表 3 列出了使用不同数值技术获得的 RTC 太阳能电池最佳参数。与其他方法相比，使用修正牛顿-拉夫逊法估算的电池参数的 RMSE 值最小。

Table 3. Parameter values using two methods for RTC France solar cell.
表 3.采用两种方法计算的法国 RTC 太阳能电池参数值。

Empty Cell	Standard NRM 标准 NRM	Benahmida [24]	Proposed method 建议的方法
$I_{p h}$ [A] $I_{p h}$ [A］	0.7611	0.7611	0.7611
$I_{o} [μ A]$	0.3479	0.3477	0.3469
$R_{s} [Ω]$	0.0348	0.0349	0.0347
$α$	1.4876	1.4877	1.4875
RMSE	0.004015	0.004938	0.003417
Iterations 迭代	7	7	6

Photowatt PWP201

The proposed method is again applied to the PWP201 module to extract the module parameters. The extracted values are then compared to the standard Newton–Raphson method (NRM) and the work [24]. Table 4 shows the results attained for each approach. As it is be seen, the proposed numerical method gives lower RMSE value compared to other methods (see Fig. 5, Fig. 6).
提议的方法再次应用于 PWP201 模块，以提取模块参数。然后将提取的值与标准牛顿-拉夫逊法（NRM）和研究成果 [24] 进行比较。表 4 显示了每种方法得出的结果。可以看出，与其他方法相比，拟议的数值方法的 RMSE 值更低（见图 5、图 6）。

Table 4. Parameter values using two methods for Photowatt PWP210 solar module.
表 4.采用两种方法计算的 Photowatt PWP210 太阳能模块参数值。

Empty Cell	Newton–Raphson method 牛顿-拉斐逊法	Benahmida [24]	Proposed method 建议的方法
$I_{p h}$ [A] $I_{p h}$ [A］	1.033	1.034	1.033
$I_{o} [μ A]$	2.5671	2.7253	2.2989
$R_{s} [Ω]$	1.2316	1.2092	1.1958
$α$	1.3132	1.3249	1.3043
RMSE	0.002621	0.002410	0.001934
Iterations 迭代	9	9	8

Analysis of output characteristics
输出特性分析

Effects of irradiation on PV module
辐照对光伏组件的影响

In order to investigate the impact of variations of solar irradiation, a proposed model was simulated under MATLAB/Simulink environments using information given in a test polycrystalline (CHL285P) module described in Table 1. Simulation model that calculates photocurrent was built based on Eq. (2) to obtain the theoretical characteristics. Simulations were performed at five different solar irradiances while keeping temperature constant (25 °C). Both Current–Voltage

(I - V)

and Power–Voltage

(P - V)

curves were plotted and compared with experimental measurements at different irradiances. From Fig. 7 it was observed that, PV module current is proportional to variation of solar illuminance. A significant decrease of short-circuit current was observed on decreasing the solar irradiance. It was further noticed that, open-circuit voltage also decreases on reducing irradiance value, but the decrease is slight. Fig. 8 shows that the maximum power is also directly proportional to solar irradiance. A huge fall of power generated is observed on reducing the sun intensity while the open-circuit voltage change is minimal.
为了研究太阳辐照变化的影响，利用表 1 所述的测试多晶 (CHL285P) 模块中提供的信息，在 MATLAB/Simulink 环境下模拟了所提出的模型。根据公式 (2) 建立了计算光电流的仿真模型，以获得理论特性。模拟在五种不同的太阳辐照度下进行，同时保持温度恒定（25 °C）。绘制了电流-电压

(I - V)

和功率-电压

(P - V)

曲线，并与不同辐照度下的实验测量结果进行了比较。从图 7 可以看出，光伏组件电流与太阳照度的变化成正比。在太阳辐照度降低时，短路电流明显下降。此外，辐照度降低时，开路电压也会降低，但降低幅度很小。图 8 显示，最大功率也与太阳辐照度成正比。当太阳辐照度降低时，发电功率会大幅下降，而开路电压的变化却很小。

Effects of temperature on PV module
温度对光伏组件的影响

Simulation of the proposed model was performed under MATLAB/Simulink to study the impact of temperature variation at constant solar illumination level of

1000 {W/m}^{2}

. A simulating model block was constructed based on Eq. (4) in order to obtain the theoretical characteristics. The inputs of simulating model were obtained from manufacturer’s catalog of a test module described in Table 1. Current–Voltage

(I - V)

and Power–Voltage

(P - V)

curves were obtained at five different temperatures and the resulting curves were compared with in-field characteristics. It was observed from Fig. 9 that as temperature of the module increases, the open-circuit voltage decreases significantly whereas short-circuit current increases slightly. Significant decrease in open-circuit voltage is due to the decrease in bandgap of PV material that is caused by increase in temperature as reported by [52]. In Fig. 10, it was observed that the increase in temperature of the PV module lowered the power produced, and thus it was concluded that, raise in temperature reduces the efficiency of PV panel as argued by [25]. Therefore, variation of temperature is inversely proportional to open-circuit voltage and output power.
在 MATLAB/Simulink 下对所提出的模型进行了仿真，以研究

1000 {W/m}^{2}

恒定太阳光照度下温度变化的影响。根据公式 (4) 构建了一个仿真模型块，以获得理论特性。仿真模型的输入数据来自表 1 所示测试模块的制造商目录。在五个不同的温度下，得到了电流-电压

(I - V)

和功率-电压

(P - V)

曲线，并将得到的曲线与现场特性进行了比较。从图 9 中可以看出，随着模块温度的升高，开路电压显著降低，而短路电流略有增加。正如文献 [52] 所述，开路电压显著降低的原因是温度升高导致光伏材料带隙减小。从图 10 中可以看出，光伏组件的温度升高会降低发电量，因此得出结论，温度升高会降低光伏板的效率，正如文献[25]所指出的那样。因此，温度变化与开路电压和输出功率成反比。

Conclusion 结论

This paper has presented a modified Newton–Raphson method to extract and evaluate the physical parameters of photovoltaic generators. The equivalent single-diode circuit with four parameters was applied for modeling the electrical behavior of the PV module. This method follows predictor–corrector rule in which two initial values are required. The first starting value is carefully selected whereas the second one is evaluated using standard Newton–Raphson method. The suggested iterative method converges faster than the normal Newton–Raphson method with order of

(1 + \sqrt{2})

. The application of this method for the RTC France solar cell, PWP201 and the CHL285P panels returned less error and a good agreement with the experimental measurements. The paper offers a significant contribution to the prediction of photovoltaic module performances, which is a critical stage in the analysis of any PV system. The suggested method can turn it into an alternative tool for designers looking for a simple and effective model for modeling PV devices linked with power converters. Therefore, our contribution could serve as a starting step toward constructing a full solar PV power conversion system for a high grid application.
本文介绍了一种改进的牛顿-拉斐森方法，用于提取和评估光伏发电机的物理参数。四参数等效单二极管电路被用于光伏组件电气行为的建模。该方法遵循预测-修正规则，需要两个初始值。第一个初始值经过精心选择，而第二个初始值则使用标准的牛顿-拉斐森方法进行评估。所建议的迭代法比普通的牛顿-拉夫逊法收敛更快，阶数为

(1 + \sqrt{2})

。将该方法应用于法国 RTC 太阳能电池、PWP201 和 CHL285P 面板，结果误差较小，与实验测量结果吻合良好。本文为光伏组件性能预测做出了重要贡献，这是任何光伏系统分析的关键阶段。所建议的方法可将其转化为一种替代工具，帮助设计人员寻找一种简单有效的模型，用于对与功率转换器相连的光伏设备进行建模。因此，我们的贡献可以作为构建高电网应用的完整太阳能光伏发电转换系统的第一步。

CRediT authorship contribution statement
CRediT 作者贡献声明

Nsulwa John Mlazi: Writing – original draft, Validation, Software, Methodology, Investigation, Conceptualization. Maranya Mayengo: Writing – review & editing, Supervision. Geminpeter Lyakurwa: Writing – review & editing, Supervision. Baraka Kichonge: Writing – review & editing, Supervision.
恩苏尔瓦-约翰-姆拉齐写作--原稿、验证、软件、方法、调查、构思。马兰亚-马延戈写作--审阅和编辑、指导。Geminpeter Lyakurwa：写作--审阅和编辑、指导。巴拉卡-基琼格写作--审核与编辑、监督

Declaration of competing interest
利益冲突声明

The authors declare no conflict of interest.
作者声明没有利益冲突。

Acknowledgments 致谢

The authors are grateful to the referees for their insightful remarks and suggestions for improving the paper.
作者感谢审稿人对本文提出的深刻见解和改进建议。

Data availability 数据可用性

Data will be made available on request.
数据将应要求提供。

References

[1]
Mutezo G., Mulopo J.
A review of africa’s transition from fossil fuels to renewable energy using circular economy principles
Renew Sustain Energy Rev, 137 (2021), Article 110609
View PDF View article View in Scopus Google Scholar
[2]
Wu Xuan, Chen George Y., Owens Gary, Chu Dewei, Xu Haolan
Photothermal materials: A key platform enabling highly efficient water evaporation driven by solar energy
Mater Today Energy, 12 (2019), pp. 277-296
View PDF View article Google Scholar
[3]
Jaiswal Krishna Kumar, Chowdhury Chandrama Roy, Yadav Deepti, Verma Ravikant, Dutta Swapnamoy, Jaiswal Km Smriti, et al.
Renewable and sustainable clean energy development and impact on social, economic, and environmental health
Energy Nexus, 7 (2022), Article 100118
View PDF View article View in Scopus Google Scholar
[4]
Kabir Ehsanul, Kumar Pawan, Kumar Sandeep, Adelodun Adedeji A., Kim Ki-Hyun
Solar energy: Potential and future prospects
Renew Sustain Energy Rev, 82 (2018), pp. 894-900
View PDF View article View in Scopus Google Scholar
[5]
Hayat Muhammad Badar, Ali Danish, Monyake Keitumetse Cathrine, Alagha Lana, Ahmed Niaz
Solar energy—A look into power generation, challenges, and a solar-powered future
Int J Energy Res, 43 (3) (2019), pp. 1049-1067
Crossref View in Scopus Google Scholar
[6]
Shaikh Mohd Rizwan Sirajuddin, et al.
A review paper on electricity generation from solar energy
(2017)
Google Scholar
[7]
Javed Muhammad Shahzad, Ma Tao, Jurasz Jakub, Amin Muhammad Yasir
Solar and wind power generation systems with pumped hydro storage: Review and future perspectives
Renew Energy, 148 (2020), pp. 176-192
View PDF View article View in Scopus Google Scholar
[8]
Dwivedi Pushpendu, Sudhakar K., Soni Archana, Solomin Evgeny, Kirpichnikova I.
Advanced cooling techniques of PV modules: A state of art
Case Stud Therm Eng, 21 (2020), Article 100674
View PDF View article View in Scopus Google Scholar
[9]
Hasan Khaled, Yousuf Sumaiya Binty, Tushar Mohammad Shahed Hasan Khan, Das Barun K., Das Pronob, Islam Md Saiful
Effects of different environmental and operational factors on the PV performance: A comprehensive review
Energy Sci Eng, 10 (2) (2022), pp. 656-675
Crossref View in Scopus Google Scholar
[10]
Tripathi Abhishek Kumar, Ray Shashwati, Aruna Mangalpady, Prasad Sandeep
Evaluation of solar PV panel performance under humid atmosphere
Mater Today Proc, 45 (2021), pp. 5916-5920
View PDF View article Google Scholar
[11]
Cordero R.R., Damiani Alessandro, Laroze David, Macdonell Shelley, Jorquera Jose, Sepúlveda Edgardo, et al.
Effects of soiling on photovoltaic (PV) modules in the Atacama Desert
Sci Rep, 8 (1) (2018), p. 13943
View in Scopus Google Scholar
[12]
Andrea Yotham, Pogrebnaya Tatiana, Kichonge Baraka
Effect of industrial dust deposition on photovoltaic module performance: Experimental measurements in the tropical region
Int J Photoenergy, 2019 (2019), pp. 1-10
Crossref Google Scholar
[13]
Babatunde A.A., Abbasoglu Sj, Senol M.
Analysis of the impact of dust, tilt angle and orientation on performance of PV plants
Renew Sustain Energy Rev, 90 (2018), pp. 1017-1026
View PDF View article View in Scopus Google Scholar
[14]
Mamun M.A.A., Islam M.M., Hasanuzzaman M., Selvaraj Jeyraj
Effect of tilt angle on the performance and electrical parameters of a PV module: Comparative indoor and outdoor experimental investigation
Energy Built Environ, 3 (3) (2022), pp. 278-290
View PDF View article View in Scopus Google Scholar
[15]
Yunus Khan T.M., Soudagar Manzoore Elahi M., Kanchan Mithun, Afzal Asif, Banapurmath Nagaraj R., Akram Naveed, et al.
Optimum location and influence of tilt angle on performance of solar PV panels
J Therm Anal Calorim, 141 (2020), pp. 511-532
Crossref View in Scopus Google Scholar
[16]
Ameur Arechkik, Berrada Asmae, Bouaichi Abdellatif, Loudiyi Khalid
Long-term performance and degradation analysis of different PV modules under temperate climate
Renew Energy, 188 (2022), pp. 37-51
View PDF View article View in Scopus Google Scholar
[17]
Singh Rashmi, Sharma Madhu, Yadav Kamlesh
Degradation and reliability analysis of photovoltaic modules after operating for 12 years: A case study with comparisons
Renew Energy, 196 (2022), pp. 1170-1186
View PDF View article View in Scopus Google Scholar
[18]
Ustun Taha Selim, Nakamura Yasuhiro, Hashimoto Jun, Otani Kenji
Performance analysis of PV panels based on different technologies after two years of outdoor exposure in Fukushima, Japan
Renew Energy, 136 (2019), pp. 159-178
View PDF View article View in Scopus Google Scholar
[19]
Islam Nazrul, et al.
Modeling of photovoltaic module under varying solar irradiance
Department of Electrical and Electronic Engineering (EEE) (2014)
Google Scholar
[20]
Zina Boussada, Mouna Ben Hamed, Lassad Sbita
Photovoltaic cell mathematical modelling
Int J Eng Res Technol (IJERT), 6 (6) (2017), pp. 884-887
Google Scholar
[21]
Zhang Peng
Modeling and simulation of PV engineering mathematical model parameters calculation based on Newton-Raphson method
Int J Grid Distrib Comput, 9 (8) (2016), pp. 209-222
Crossref View in Scopus Google Scholar
[22]
El-Dabah Mahmoud Abbas, El-Sehiemy Ragab Abdelaziz, Ebrahim Mohamed Ahmed, Alaas Zuhair, Ramadan Mohamed Mostafa
Identification study of solar cell/module using recent optimization techniques
Int J Electr Comput Eng, 12 (2) (2022), p. 1189
Crossref View in Scopus Google Scholar
[23]
Jakhrani Abdul Qayoom, Samo Saleem Raza, Kamboh Shakeel Ahmed, Labadin Jane, Rigit Andrew Ragai Henry
An improved mathematical model for computing power output of solar photovoltaic modules
Int J Photoenergy, 2014 (2014)
Google Scholar
[24]
Benahmida Abdelaaziz, Maouhoub Noureddine, Sahsah Hassan
Numerical approach for extraction of photovoltaic generator single-diode model parameters
Comput Sci Inf Technol, 2 (2) (2021), pp. 58-66
Crossref Google Scholar
[25]
El Achouby H., Zaimi M., Ibral A., Zegoudi O., Assaid E.M.
New analytical expressions of photovoltaic solar module physical parameters: Effects of module temperature and incident solar irradiance
IOP conference series: Materials science and engineering, vol. 948, no. 1, IOP Publishing (2020), Article 012009
Crossref View in Scopus Google Scholar
[26]
Elkholy A., Abou El-Ela A.A.
Optimal parameters estimation and modelling of photovoltaic modules using analytical method
Heliyon, 5 (7) (2019), Article e02137
View PDF View article View in Scopus Google Scholar
[27]
Zhang Chunfu, Zhang Jincheng, Hao Yue, Lin Zhenhua, Zhu Chunxiang
A simple and efficient solar cell parameter extraction method from a single current-voltage curve
J Appl Phys, 110 (6) (2011), Article 064504
View in Scopus Google Scholar
[28]
Rasheed Mohammed, Alabdali Osama, Shihab Suha
A new technique for solar cell parameters estimation of the single-diode model
J Phys Conf Ser, 1879 (3) (2021), Article 032120
Crossref View in Scopus Google Scholar
[29]
Stornelli Vincenzo, Muttillo Mirco, De Rubeis Tullio, Nardi Iole
A new simplified five-parameter estimation method for single-diode model of photovoltaic panels
Energies, 12 (22) (2019), p. 4271
Crossref View in Scopus Google Scholar
[30]
Ghani Faisal, Rosengarten Gary, Duke Mike, Carson J.K.
The numerical calculation of single-diode solar-cell modelling parameters
Renew Energy, 72 (2014), pp. 105-112
View PDF View article View in Scopus Google Scholar
[31]
Manuel Godinho Rodrigues Eduardo, Godina Radu, Marzband Mousa, Pouresmaeil Edris
Simulation and comparison of mathematical models of PV cells with growing levels of complexity
Energies, 11 (11) (2018), p. 2902
Crossref Google Scholar
[32]
Liang Yu, Shi Zhenjun, Chung Peter W.
A hessian-free Newton–Raphson method for the configuration of physics systems featured by numerically asymmetric force field
Math Comput Simulation, 140 (2017), pp. 1-23
View PDF View article View in Scopus Google Scholar
[33]
Salimi Mehdi, Lotfi Taher, Sharifi Somayeh, Siegmund Stefan
Optimal Newton–Secant like methods without memory for solving nonlinear equations with its dynamics
Int J Comput Math, 94 (9) (2017), pp. 1759-1777
Crossref View in Scopus Google Scholar
[34]
Gholami Ali, Aghamiry Hossein S.
Iteratively re-weighted and refined least squares algorithm for robust inversion of geophysical data
Geophys Prospect, 65 (S1) (2017), pp. 201-215
Crossref View in Scopus Google Scholar
[35]
Mujahed Murad Mohammed, Elshareif Elgilani Eltahir
Internal rate of return (IRR): A new proposed approach
Leadership, innovation and entrepreneurship as driving forces of the global economy: Proceedings of the 2016 international conference on leadership, innovation and entrepreneurship, Springer (2017), pp. 761-767
Crossref View in Scopus Google Scholar
[36]
McDougall Trevor J., Wotherspoon Simon J.
A simple modification of Newton’s method to achieve convergence of order 1+ 2
Appl Math Lett, 29 (2014), pp. 20-25
View PDF View article View in Scopus Google Scholar
[37]
Batzelis Efstratios I., Papathanassiou Stavros A.
A method for the analytical extraction of the single-diode PV model parameters
IEEE Trans Sustain Energy, 7 (2) (2015), pp. 504-512
Google Scholar
[38]
Vergura S., Pavan A. Massi
On the photovoltaic explicit empirical model: Operations along the current-voltage curve
2015 International conference on clean electrical power, IEEE (2015), pp. 99-104
Crossref View in Scopus Google Scholar
[39]
Motahhir Saad, El Hammoumi Aboubakr, El Ghzizal Abdelaziz
Photovoltaic system with quantitative comparative between an improved MPPT and existing INC and P&O methods under fast varying of solar irradiation
Energy Rep, 4 (2018), pp. 341-350
View PDF View article View in Scopus Google Scholar
[40]
AlRashidi Mohammed R., El-Naggar K.M., AlHajri Mohamad F.
Parameters estimation of double diode solar cell model
Int J Electr Comput Eng, 7 (2013), pp. 118-121
Google Scholar
[41]
Ramos-Hernanz Josean, Lopez-Guede Jose Manuel, Zulueta Ekaitz, Fernandez-Gamiz Unai
Reverse saturation current analysis in photovoltaic cell models
WSEAS Trans. Power Syst., 12 (2017), pp. 231-237
Google Scholar
[42]
Petreus Dorin, Ciocan Ionut, Farcas Cristian
An improvement on empirical modelling of photovoltaic cells
2008 31st International spring seminar on electronics technology, IEEE (2008), pp. 598-603
View in Scopus Google Scholar
[43]
Chan Daniel S.H., Phang Jacob C.H.
Analytical methods for the extraction of solar-cell single-and double-diode model parameters from IV characteristics
IEEE Trans Electron Devices, 34 (2) (1987), pp. 286-293
View in Scopus Google Scholar
[44]
Phang J.C.H., Chan D.S.H., Phillips J.R.
Accurate analytical method for the extraction of solar cell model parameters
Electron Lett, 10 (20) (1984), pp. 406-408
Crossref View in Scopus Google Scholar
[45]
Tossa Alain K., Soro Y.M., Azoumah Y., Yamegueu D.
A new approach to estimate the performance and energy productivity of photovoltaic modules in real operating conditions
Sol Energy, 110 (2014), pp. 543-560
View PDF View article View in Scopus Google Scholar
[46]
Dzimano Gwinyai J.
Modeling of photovoltaic systems
[Ph.D. thesis]
The Ohio State University (2008)
Google Scholar
[47]
Edouard Mboumboue, Njomo Donatien
Mathematical modeling and digital simulation of PV solar panel using Matlab software
Int J Emerg Technol Adv Eng, 3 (9) (2013), pp. 24-32
Google Scholar
[48]
Reis LRD, Camacho Jose Robert, Novacki DF. The Newton Raphson method in the extraction of parameters of PV modules. In: International conference on renewable energies and power quality, vol. 1, no. 15. 2017, p. 634–9.
Google Scholar
[49]
Zaimi M., El Achouby H., Zegoudi O., Ibral A., Assaid E.M.
Numerical method and new analytical models for determining temporal changes of model-parameters to predict maximum power and efficiency of PV module operating outdoor under arbitrary conditions
Energy Convers Manage, 220 (2020), Article 113071
View PDF View article View in Scopus Google Scholar
[50]
Kumar Manish, Kumar Arun
An efficient parameters extraction technique of photovoltaic models for performance assessment
Sol Energy, 158 (2017), pp. 192-206
View PDF View article View in Scopus Google Scholar
[51]
Maouhoub Noureddine
Photovoltaic module parameter estimation using an analytical approach and least squares method
J Comput Electron, 17 (2) (2018), pp. 784-790
Crossref View in Scopus Google Scholar
[52]
Cho Y., Yamaguchi A., Uehara R., Yasuhara S., Hoshina T., Miyauchi M.
Temperature dependence on bandgap of semiconductor photocatalysts
J Chem Phys, 152 (23) (2020)
Google Scholar

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Photovoltaic power has emerged as an important component global energy revolution, providing a renewable and sustainable alternative for electricity generation. This paper describes how to use Monte Carlo optimisation (MCO) to estimate and extract the intrinsic electrical parameters of single, double, and triple diode designs, as well as make parallel resistance modifications. The above method was used to solve challenges related to nonlinear and complex solar cell equation. The function’s objective is to minimize the discrepancy between the experimental and calculated current values. Three different technologies are implemented to retrieve the fundamental parameters: RTC France solar cell, the Photowatt-PWP201 PV module, and the Schutten Solar STM6-40/36 monocrystalline solar module. In addition, the restricted objective function is computed using the experimental current–voltage curve. The extracted parameters using MCO are compared to contemporary research publications on metaheuristic optimization algorithms, iterative approaches, and analytical methods. In the end, to evaluate the algorithm’s effectiveness, statistical measurements such as Individual Absolute Error (IAE), Relative Error (RE), Mean Absolute Error (MAE), SD, TS, NFM, ACF, and RMSE are calculated to ensure the correctness of the generated parameters. The comparative study shows that the results generated by the MCO approach exhibit lower errors compared to other algorithms where RMSE reaches 0.0058.
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Citation Excerpt :
While current solar technologies offer many advantages, they also have certain weaknesses and drawbacks linked to optimizing energy extraction from solar panels. These include intermittency of power production, performance degradation under specific challenging conditions, high initial costs, non-linearity of photovoltaic characteristics [3]. A photovoltaic generator (PVG) can function across a broad range of output voltages and currents, but its maximum power delivery capacity is constrained to a single point Pmpp(Impp,Vmpp), which is subject to variations based on temperature and solar irradiance [4].
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2024, Energy Conversion and Management
The growing use of photovoltaic energy necessitates accurate modeling of modules, particularly in non-linear current–voltage characteristics, despite challenges in finding ideal circuit model parameters. Several meta-heuristic techniques have been developed to determine these parameters. This work presents a new method that combines the Crayfish Optimization Algorithm (COA) with fractional-order chaos maps (FC-maps), a recent development in the area. The goal of this addition is to adaptively adjust the COA settings. Moreover, the COA algorithm has been improved with the dimension learning-hunting (DLH) search scheme, inspired by crayfish hunting. This method establishes neighborhoods for each crayfish, enhancing local and global search efforts while preserving diversity. First, benchmark functions are used to conduct a thorough mathematical assessment of the improved COA (ICOA). Subsequently, the ICOA is combined with the Newton-Raphson numerical method to estimate PV parameters. Six cell and module types, including RTC France, Photowatt-PWP201, and STP6-120/36, are investigated using various PV models within the single-diode and double-diode models. The root mean squared error (RMSE) for RTC France, PWP201, and STP6-120/36 that our system employing (SDM, DDM) obtained is as follows, based on the experimental findings: (7.844017E-04, 7.520345E-04), (2.084019E-03, 2.067626E-03), and (1.441938E-02, 1.432568E-02), respectively. A statistical analysis between several well-established metaheuristic methods was conducted to showcase the superior performance of the ICOA. The results unequivocally exhibit that the ICOA excels in accurately estimating the best PV parameters when compared to the other techniques. In conclusion, ICOA surpasses alternative algorithms in terms of precision, consistency, and convergence.
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View all citing articles on Scopus

[1] [1]
Mutezo G., Mulopo J.
A review of africa’s transition from fossil fuels to renewable energy using circular economy principles
Renew Sustain Energy Rev, 137 (2021), Article 110609
View PDF View article View in Scopus Google Scholar

[2] [2]
Wu Xuan, Chen George Y., Owens Gary, Chu Dewei, Xu Haolan
Photothermal materials: A key platform enabling highly efficient water evaporation driven by solar energy
Mater Today Energy, 12 (2019), pp. 277-296
View PDF View article Google Scholar

[3] [3]
Jaiswal Krishna Kumar, Chowdhury Chandrama Roy, Yadav Deepti, Verma Ravikant, Dutta Swapnamoy, Jaiswal Km Smriti, et al.
Renewable and sustainable clean energy development and impact on social, economic, and environmental health
Energy Nexus, 7 (2022), Article 100118
View PDF View article View in Scopus Google Scholar

[4] [4]
Kabir Ehsanul, Kumar Pawan, Kumar Sandeep, Adelodun Adedeji A., Kim Ki-Hyun
Solar energy: Potential and future prospects
Renew Sustain Energy Rev, 82 (2018), pp. 894-900
View PDF View article View in Scopus Google Scholar

[5] [5]
Hayat Muhammad Badar, Ali Danish, Monyake Keitumetse Cathrine, Alagha Lana, Ahmed Niaz
Solar energy—A look into power generation, challenges, and a solar-powered future
Int J Energy Res, 43 (3) (2019), pp. 1049-1067
Crossref View in Scopus Google Scholar

[6] [6]
Shaikh Mohd Rizwan Sirajuddin, et al.
A review paper on electricity generation from solar energy
(2017)
Google Scholar

[7] [7]
Javed Muhammad Shahzad, Ma Tao, Jurasz Jakub, Amin Muhammad Yasir
Solar and wind power generation systems with pumped hydro storage: Review and future perspectives
Renew Energy, 148 (2020), pp. 176-192
View PDF View article View in Scopus Google Scholar

[8] [8]
Dwivedi Pushpendu, Sudhakar K., Soni Archana, Solomin Evgeny, Kirpichnikova I.
Advanced cooling techniques of PV modules: A state of art
Case Stud Therm Eng, 21 (2020), Article 100674
View PDF View article View in Scopus Google Scholar

[9] [9]
Hasan Khaled, Yousuf Sumaiya Binty, Tushar Mohammad Shahed Hasan Khan, Das Barun K., Das Pronob, Islam Md Saiful
Effects of different environmental and operational factors on the PV performance: A comprehensive review
Energy Sci Eng, 10 (2) (2022), pp. 656-675
Crossref View in Scopus Google Scholar

[10] [10]
Tripathi Abhishek Kumar, Ray Shashwati, Aruna Mangalpady, Prasad Sandeep
Evaluation of solar PV panel performance under humid atmosphere
Mater Today Proc, 45 (2021), pp. 5916-5920
View PDF View article Google Scholar

[11] [11]
Cordero R.R., Damiani Alessandro, Laroze David, Macdonell Shelley, Jorquera Jose, Sepúlveda Edgardo, et al.
Effects of soiling on photovoltaic (PV) modules in the Atacama Desert
Sci Rep, 8 (1) (2018), p. 13943
View in Scopus Google Scholar

[12] [12]
Andrea Yotham, Pogrebnaya Tatiana, Kichonge Baraka
Effect of industrial dust deposition on photovoltaic module performance: Experimental measurements in the tropical region
Int J Photoenergy, 2019 (2019), pp. 1-10
Crossref Google Scholar

[13] [13]
Babatunde A.A., Abbasoglu Sj, Senol M.
Analysis of the impact of dust, tilt angle and orientation on performance of PV plants
Renew Sustain Energy Rev, 90 (2018), pp. 1017-1026
View PDF View article View in Scopus Google Scholar

[14] [14]
Mamun M.A.A., Islam M.M., Hasanuzzaman M., Selvaraj Jeyraj
Effect of tilt angle on the performance and electrical parameters of a PV module: Comparative indoor and outdoor experimental investigation
Energy Built Environ, 3 (3) (2022), pp. 278-290
View PDF View article View in Scopus Google Scholar

[15] [15]
Yunus Khan T.M., Soudagar Manzoore Elahi M., Kanchan Mithun, Afzal Asif, Banapurmath Nagaraj R., Akram Naveed, et al.
Optimum location and influence of tilt angle on performance of solar PV panels
J Therm Anal Calorim, 141 (2020), pp. 511-532
Crossref View in Scopus Google Scholar

[16] [16]
Ameur Arechkik, Berrada Asmae, Bouaichi Abdellatif, Loudiyi Khalid
Long-term performance and degradation analysis of different PV modules under temperate climate
Renew Energy, 188 (2022), pp. 37-51
View PDF View article View in Scopus Google Scholar

[17] [17]
Singh Rashmi, Sharma Madhu, Yadav Kamlesh
Degradation and reliability analysis of photovoltaic modules after operating for 12 years: A case study with comparisons
Renew Energy, 196 (2022), pp. 1170-1186
View PDF View article View in Scopus Google Scholar

[18] [18]
Ustun Taha Selim, Nakamura Yasuhiro, Hashimoto Jun, Otani Kenji
Performance analysis of PV panels based on different technologies after two years of outdoor exposure in Fukushima, Japan
Renew Energy, 136 (2019), pp. 159-178
View PDF View article View in Scopus Google Scholar

[19] [19]
Islam Nazrul, et al.
Modeling of photovoltaic module under varying solar irradiance
Department of Electrical and Electronic Engineering (EEE) (2014)
Google Scholar

[20] [20]
Zina Boussada, Mouna Ben Hamed, Lassad Sbita
Photovoltaic cell mathematical modelling
Int J Eng Res Technol (IJERT), 6 (6) (2017), pp. 884-887
Google Scholar

[21] [21]
Zhang Peng
Modeling and simulation of PV engineering mathematical model parameters calculation based on Newton-Raphson method
Int J Grid Distrib Comput, 9 (8) (2016), pp. 209-222
Crossref View in Scopus Google Scholar

[22] [22]
El-Dabah Mahmoud Abbas, El-Sehiemy Ragab Abdelaziz, Ebrahim Mohamed Ahmed, Alaas Zuhair, Ramadan Mohamed Mostafa
Identification study of solar cell/module using recent optimization techniques
Int J Electr Comput Eng, 12 (2) (2022), p. 1189
Crossref View in Scopus Google Scholar

[23] [23]
Jakhrani Abdul Qayoom, Samo Saleem Raza, Kamboh Shakeel Ahmed, Labadin Jane, Rigit Andrew Ragai Henry
An improved mathematical model for computing power output of solar photovoltaic modules
Int J Photoenergy, 2014 (2014)
Google Scholar

[24] [24]
Benahmida Abdelaaziz, Maouhoub Noureddine, Sahsah Hassan
Numerical approach for extraction of photovoltaic generator single-diode model parameters
Comput Sci Inf Technol, 2 (2) (2021), pp. 58-66
Crossref Google Scholar

[25] [25]
El Achouby H., Zaimi M., Ibral A., Zegoudi O., Assaid E.M.
New analytical expressions of photovoltaic solar module physical parameters: Effects of module temperature and incident solar irradiance
IOP conference series: Materials science and engineering, vol. 948, no. 1, IOP Publishing (2020), Article 012009
Crossref View in Scopus Google Scholar

[26] [26]
Elkholy A., Abou El-Ela A.A.
Optimal parameters estimation and modelling of photovoltaic modules using analytical method
Heliyon, 5 (7) (2019), Article e02137
View PDF View article View in Scopus Google Scholar

[27] [27]
Zhang Chunfu, Zhang Jincheng, Hao Yue, Lin Zhenhua, Zhu Chunxiang
A simple and efficient solar cell parameter extraction method from a single current-voltage curve
J Appl Phys, 110 (6) (2011), Article 064504
View in Scopus Google Scholar

[28] [28]
Rasheed Mohammed, Alabdali Osama, Shihab Suha
A new technique for solar cell parameters estimation of the single-diode model
J Phys Conf Ser, 1879 (3) (2021), Article 032120
Crossref View in Scopus Google Scholar

[29] [29]
Stornelli Vincenzo, Muttillo Mirco, De Rubeis Tullio, Nardi Iole
A new simplified five-parameter estimation method for single-diode model of photovoltaic panels
Energies, 12 (22) (2019), p. 4271
Crossref View in Scopus Google Scholar

[30] [30]
Ghani Faisal, Rosengarten Gary, Duke Mike, Carson J.K.
The numerical calculation of single-diode solar-cell modelling parameters
Renew Energy, 72 (2014), pp. 105-112
View PDF View article View in Scopus Google Scholar

[31] [31]
Manuel Godinho Rodrigues Eduardo, Godina Radu, Marzband Mousa, Pouresmaeil Edris
Simulation and comparison of mathematical models of PV cells with growing levels of complexity
Energies, 11 (11) (2018), p. 2902
Crossref Google Scholar

[32] [32]
Liang Yu, Shi Zhenjun, Chung Peter W.
A hessian-free Newton–Raphson method for the configuration of physics systems featured by numerically asymmetric force field
Math Comput Simulation, 140 (2017), pp. 1-23
View PDF View article View in Scopus Google Scholar

[33] [33]
Salimi Mehdi, Lotfi Taher, Sharifi Somayeh, Siegmund Stefan
Optimal Newton–Secant like methods without memory for solving nonlinear equations with its dynamics
Int J Comput Math, 94 (9) (2017), pp. 1759-1777
Crossref View in Scopus Google Scholar

[34] [34]
Gholami Ali, Aghamiry Hossein S.
Iteratively re-weighted and refined least squares algorithm for robust inversion of geophysical data
Geophys Prospect, 65 (S1) (2017), pp. 201-215
Crossref View in Scopus Google Scholar

[35] [35]
Mujahed Murad Mohammed, Elshareif Elgilani Eltahir
Internal rate of return (IRR): A new proposed approach
Leadership, innovation and entrepreneurship as driving forces of the global economy: Proceedings of the 2016 international conference on leadership, innovation and entrepreneurship, Springer (2017), pp. 761-767
Crossref View in Scopus Google Scholar

[36] [36]
McDougall Trevor J., Wotherspoon Simon J.
A simple modification of Newton’s method to achieve convergence of order 1+ 2
Appl Math Lett, 29 (2014), pp. 20-25
View PDF View article View in Scopus Google Scholar

[37] [37]
Batzelis Efstratios I., Papathanassiou Stavros A.
A method for the analytical extraction of the single-diode PV model parameters
IEEE Trans Sustain Energy, 7 (2) (2015), pp. 504-512
Google Scholar

[38] [38]
Vergura S., Pavan A. Massi
On the photovoltaic explicit empirical model: Operations along the current-voltage curve
2015 International conference on clean electrical power, IEEE (2015), pp. 99-104
Crossref View in Scopus Google Scholar

[39] [39]
Motahhir Saad, El Hammoumi Aboubakr, El Ghzizal Abdelaziz
Photovoltaic system with quantitative comparative between an improved MPPT and existing INC and P&O methods under fast varying of solar irradiation
Energy Rep, 4 (2018), pp. 341-350
View PDF View article View in Scopus Google Scholar

[40] [40]
AlRashidi Mohammed R., El-Naggar K.M., AlHajri Mohamad F.
Parameters estimation of double diode solar cell model
Int J Electr Comput Eng, 7 (2013), pp. 118-121
Google Scholar

[41] [41]
Ramos-Hernanz Josean, Lopez-Guede Jose Manuel, Zulueta Ekaitz, Fernandez-Gamiz Unai
Reverse saturation current analysis in photovoltaic cell models
WSEAS Trans. Power Syst., 12 (2017), pp. 231-237
Google Scholar

[42] [42]
Petreus Dorin, Ciocan Ionut, Farcas Cristian
An improvement on empirical modelling of photovoltaic cells
2008 31st International spring seminar on electronics technology, IEEE (2008), pp. 598-603
View in Scopus Google Scholar

[43] [43]
Chan Daniel S.H., Phang Jacob C.H.
Analytical methods for the extraction of solar-cell single-and double-diode model parameters from IV characteristics
IEEE Trans Electron Devices, 34 (2) (1987), pp. 286-293
View in Scopus Google Scholar

[44] [44]
Phang J.C.H., Chan D.S.H., Phillips J.R.
Accurate analytical method for the extraction of solar cell model parameters
Electron Lett, 10 (20) (1984), pp. 406-408
Crossref View in Scopus Google Scholar

[45] [45]
Tossa Alain K., Soro Y.M., Azoumah Y., Yamegueu D.
A new approach to estimate the performance and energy productivity of photovoltaic modules in real operating conditions
Sol Energy, 110 (2014), pp. 543-560
View PDF View article View in Scopus Google Scholar

[46] [46]
Dzimano Gwinyai J.
Modeling of photovoltaic systems
[Ph.D. thesis]
The Ohio State University (2008)
Google Scholar

[47] [47]
Edouard Mboumboue, Njomo Donatien
Mathematical modeling and digital simulation of PV solar panel using Matlab software
Int J Emerg Technol Adv Eng, 3 (9) (2013), pp. 24-32
Google Scholar

[48] [48]
Reis LRD, Camacho Jose Robert, Novacki DF. The Newton Raphson method in the extraction of parameters of PV modules. In: International conference on renewable energies and power quality, vol. 1, no. 15. 2017, p. 634–9.
Google Scholar

[49] [49]
Zaimi M., El Achouby H., Zegoudi O., Ibral A., Assaid E.M.
Numerical method and new analytical models for determining temporal changes of model-parameters to predict maximum power and efficiency of PV module operating outdoor under arbitrary conditions
Energy Convers Manage, 220 (2020), Article 113071
View PDF View article View in Scopus Google Scholar

[50] [50]
Kumar Manish, Kumar Arun
An efficient parameters extraction technique of photovoltaic models for performance assessment
Sol Energy, 158 (2017), pp. 192-206
View PDF View article View in Scopus Google Scholar

[51] [51]
Maouhoub Noureddine
Photovoltaic module parameter estimation using an analytical approach and least squares method
J Comput Electron, 17 (2) (2018), pp. 784-790
Crossref View in Scopus Google Scholar

[52] [52]
Cho Y., Yamaguchi A., Uehara R., Yasuhara S., Hoshina T., Miyauchi M.
Temperature dependence on bandgap of semiconductor photocatalysts
J Chem Phys, 152 (23) (2020)
Google Scholar

Outline 概要

Cited by (9) 引用 (9)

Figures (10) 数字 (10)

Tables (4)

Results in Physics 物理学成果

Highlights 亮点

Abstract 摘要

Keywords 关键词

Introduction 导言

Method 方法

Model formulation 模型表述

Determination of parameters of the model
确定模型参数

Modified Newton–Raphson method
改进的牛顿-拉斐逊法

Results and discussion 结果和讨论

Chloride CHL285P PV module
氯化物 CHL285P 光伏组件

RTC France solar cell 法国 RTC 太阳能电池

Photowatt PWP201

Analysis of output characteristics
输出特性分析

Effects of irradiation on PV module
辐照对光伏组件的影响

Effects of temperature on PV module
温度对光伏组件的影响

Conclusion 结论

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明

Acknowledgments 致谢

Data availability 数据可用性

References

Cited by (9)

Maximum power point tracking controller with online adaptive reference voltage generator for disturbance rejection

Optimizing photovoltaic parameters with Monte Carlo and parallel resistance adjustment

Design and implementation of temperature-parametric for maximum power point tracking of photovoltaic systems: Experimental validation using PI controller

Assessing the accuracy of analytical methods for extracting parameters of different PV module technologies under clear and cloudy sky conditions

Improved crayfish optimization algorithm for parameters estimation of photovoltaic models

Parameter Extraction of Triple-diode Photovoltaic Model via RIME Optimizer with Neighborhood Centroid Opposite Solution

Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method基于修正牛顿-拉斐逊法的太阳能光伏组件数学建模与参数提取

Highlights 亮点

Abstract 摘要

Keywords 关键词

Introduction 导言

Method 方法

Model formulation 模型表述

Determination of parameters of the model确定模型参数

Modified Newton–Raphson method改进的牛顿-拉斐逊法

Results and discussion 结果和讨论

Chloride CHL285P PV module氯化物 CHL285P 光伏组件

RTC France solar cell 法国 RTC 太阳能电池

Photowatt PWP201

Analysis of output characteristics输出特性分析

Effects of irradiation on PV module辐照对光伏组件的影响

Effects of temperature on PV module温度对光伏组件的影响

Conclusion 结论

CRediT authorship contribution statementCRediT 作者贡献声明

Declaration of competing interest利益冲突声明

Acknowledgments 致谢

Data availability 数据可用性

References

Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method
基于修正牛顿-拉斐逊法的太阳能光伏组件数学建模与参数提取

Determination of parameters of the model
确定模型参数

Modified Newton–Raphson method
改进的牛顿-拉斐逊法

Chloride CHL285P PV module
氯化物 CHL285P 光伏组件

Analysis of output characteristics
输出特性分析

Effects of irradiation on PV module
辐照对光伏组件的影响

Effects of temperature on PV module
温度对光伏组件的影响

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明