MATLAB-Based Modeling to Study the Effects of Partial Shading on PV Array Characteristics

Geometric ModelingGeometric modeling is a crucial aspect of computer-aided design (CAD) and computer graphics. It involves the creation of digital representations of physical objects and environments using mathematical and computational techniques. This process is used in various industries, including engineering, architecture, animation, and video game development. Geometric modeling plays a significant role in the design and visualization of complex structures, products, and virtual worlds. In this article, we will explore the importance of geometric modeling, its applications, and the challenges associated with this field. One of the primary applications of geometric modeling is in the field of engineering and product design. Engineers use geometric modeling software to create 3D models of mechanical parts, components, and assemblies. These digital representations allow engineers to visualize and analyze the behavior of the designed objects under various conditions. Geometric modeling also facilitates the simulation of the manufacturing processes, such as machining and 3D printing, enabling engineers to optimize the design for production. Furthermore, geometric modeling plays acrucial role in finite element analysis (FEA) and computational fluid dynamics (CFD), allowing engineers to evaluate the structural integrity and performance of the designed components. In the architectural and construction industry, geometric modeling is utilized for creating detailed 3D models of buildings, infrastructure, and urban environments. Architects and urban planners use geometric modeling software to develop accurate representations of their designs, enabling them to assess the spatial relationships, aesthetics, and functional aspects of the proposed structures. Geometric modeling also supports the generation of construction drawings, renderings, and virtual walkthroughs, which are essential for communicating design concepts to clients and stakeholders. Additionally, geometric modeling facilitates the integration of building information modeling (BIM), enabling the coordination and collaboration of various disciplines involved in the construction process. Moreover, geometric modeling is fundamental in the field of computer graphics and animation. Artists and animators use geometric modeling tools to create virtual characters, environments, and special effects for films, video games, and simulations. By manipulating thevertices, edges, and faces of 3D models, artists can sculpt and refine the visual appearance of their creations. Geometric modeling also involves the application of texture mapping, shading, and lighting techniques to enhance the realism and aesthetic quality of the rendered images. Furthermore, geometric modeling supports the animation of characters and objects through rigging, skinning, and keyframe interpolation, enabling artists to bring their creations to life. Despite its numerous applications and benefits, geometric modeling presents several challenges and limitations. One of the primary challenges is the complexity of representing and manipulating geometric shapes with high precision and efficiency. As the demand for more intricate and detailed models increases, geometric modeling software must continually evolve to handle larger datasets and more sophisticated operations. Additionally, ensuring the accuracy and consistency of geometric models across different software platforms and file formats remains a challenge in the industry. Interoperability issues often arise when transferring geometric data between different CAD and visualization tools, leading to data loss and compatibility issues. Another challenge in geometric modeling is the representation of freeform and organic shapes. While traditional modeling techniques are suitable for creating geometric primitives and regular structures, they may not be well-suited for capturing the complexity of natural forms and artistic designs. To address this limitation, advanced geometric modeling methods, such as NURBS (non-uniform rational B-splines) and subdivision surfaces, have been developed to enable the creation of smooth and curvilinear shapes. These techniques provide artists and designers with greater flexibility and control over the form of their creations, allowing for more expressive and organic designs. Furthermore, the optimization of geometric models for real-time rendering and interactive applications poses a significant challenge in the field of computer graphics. As the demand for immersive virtual experiences and interactive simulations grows, geometric modeling techniques must be optimized to deliverhigh-performance visuals on a variety of computing platforms. This requires the development of efficient algorithms for level-of-detail (LOD) management, mesh simplification, and real-time tessellation, allowing for the dynamic adjustment of geometric complexity based on the viewing distance and hardware capabilities. Inconclusion, geometric modeling is a fundamental and versatile discipline that plays a crucial role in various industries, including engineering, architecture, and computer graphics. Its applications range from the design and analysis of mechanical components to the creation of virtual worlds and characters for entertainment and simulation. Despite its challenges, including the representation of complex shapes and the optimization for real-time rendering, geometric modeling continues to evolve with advancements in computational techniques and software development. As technology continues to progress, the future of geometric modeling holds promise for enabling more efficient and expressive digital representations of the physical world.。

0　引言当今世界，能源体系和发展模式正在进入非化石能源主导的崭新阶段，可再生能源将逐步成为支撑经济社会发展的主力能源，大力发展可再生能源已经成为全球能源转型和应对气候变化的重大战略方向和一致宏大行动。

在这种趋势下，光伏发电技术有了快速的发展[1]，但光伏发电具有间歇性、波动性和随机性的特点，会对电网稳定运行造成不利影响[2]。

因此，提高光伏出力预测的准确性对电网安全及新能源发展具有重要作用[3]。

光伏预测通常可分为物理方法、数理统计方法和人工智能算法三类[4]。

其中物理方法是结合天气预报信息和地理信息进行建模，对数据依赖比较严重[5]。

数理统计方法是以历史数据构建模型，建模简单，数据需求少，但对非线性拟合能力和高维数据处理能力差。

近年来随着人工智能的发展，越来越多基于人工智能算法的光伏出力预测模型出现[6]，该方法具有数据需求少、输入特征灵活、对高维非线性样本拟合能力好等优势，是光伏出力预测的有效方法，如深度学习模型（ANN）[7]、非线性自回归神经网络（NARNN）[8]、长短期记忆神经网络（LSTM）[9]等。

由于光伏出力数据受天气影响很大，许多学者提出“相似日”概念，将光伏出力按日过程进行筛选和分类，对不同分类样本分类建模，有效提高光伏出力预测模型的精度。

K-means聚类是一种经典的聚类算法，闰钇汛等[10]采用K-means聚类方法选取相似日，提高了预测精度。

但传统K-means聚类的相似日受出力大小的影响，对不同的出力大小也会分为不同天气类别，如在同样晴天的状况下，其辐射量不同也会导致出力大小的差异，而在不利天气情况下其出力均值也许与辐射量低的晴天出力大小相似，这样分类不一定符合同样的天气状况，因此需要提出一种更符合相似日的聚类方法。

为提高相似日的聚类效果，提高光伏出力预测效果，本文提出基于相似日相关性聚类的LSTM短期光伏出力预测模型。

首先，根据相关性筛选出与光伏出力相关程度较高的气象数据；然后，根据相关性选取变化趋势相似的相似日聚类中心；最后，对不同相似日建立不同的LSTM训练模型，并与K-means聚类模型进行对比，结果显示基于相似日相关性聚类方法有效提高了光伏出力预测精度。

局部遮阴下光伏系统MPPT研究与优化吴琨;王磊;王秋实;陈东【摘要】In order to solve the problem of unstable operation and output power decreasing of photovoltaic (PV) cells caused by partial shade due to leaves,buildings,clouds,etc,propose a maximum power point tracking (MPPT) of the shading condition PV systems based on GPPSO,and use it for MPPT of the complex shading condition PV systems.Results show that double optimized algorithm effectively improves the local accurate searching and global convergence ability of optimization space,in the process of the optimal solving of objective function,precision and convergence speed are improved obviously,which can rapidly adapt to environmental shade changes,can accurately track the maximum power point in complicated environment,and improve efficiency of PV systems.%为了解决光伏发电系统中,光伏电池在环境中被树叶、建筑物、云层等遮挡造成局部阴影,导致光伏电池出现运行不稳定和输出功率降低的问题,提出了一种基于改进自适应动态惯性权重并引入粒子寻优目标适应度评判系数的优化粒子群算法(GPPSO).将GPPSO应用于复杂自然环境条件下的最大功率点跟踪(MPPT),结果表明:双重优化后的算法有效提高了局部精确搜索和寻优空间全局收敛能力,在目标函数最优求解过程中,精度和收敛速度都明显提高,较快地适应环境遮阴变化,能够在复杂的自然环境中准确地对光伏发电系统最大功率点进行跟踪,提高光伏系统发电效率.【期刊名称】《传感器与微系统》【年(卷),期】2017(036)007【总页数】4页(P38-41)【关键词】光伏系统;遮阴条件;改进粒子群优化算法;最大功率点跟踪效率【作者】吴琨;王磊;王秋实;陈东【作者单位】辽宁工程技术大学电气与控制工程学院,辽宁葫芦岛125105;浙江艾罗电源有限公司,浙江杭州310000;辽宁工程技术大学电气与控制工程学院,辽宁葫芦岛125105;辽宁工程技术大学电气与控制工程学院,辽宁葫芦岛125105【正文语种】中文【中图分类】TM46作为一种新兴的清洁、可再生绿色能源，太阳能已经在世界范围内受到高度重视并取得了长足进展，基于太阳能的光伏发电有望成为缓解全球性能源危机和日益严重的环境问题的关键技术之一[1]。

光伏电池阵列模型的 Matlab 设计与仿真余基映;张腾;谭兴毅【摘要】利用 Matlab 软件平台搭建了光伏电池阵列的仿真电路模型，研究了光照因素、温度因素及光伏电池内部参数对光伏阵列电气特性的影响，并针对动态光照条件下光伏阵列的输出特性进行仿真和计算。

研究结果表明：光照强度、温度和串联电阻的变化对光伏阵列开路电压、短路电流、伏安特性、输出功率及最佳工作点具有显著影响，光伏阵列的仿真模型可以较好实现光伏阵列的动态仿真。

%A circuit simulation model of photovoltaic array was developed based on Matlab / Simulink soft-ware,the effects of solar insolation,temperature and photovoltaic cell parameters on electrical behavior of photovoltaic array were analyzed,and the output characteristics of photovoltaic array under dynamic irra-diance condition were simulated and calculated. The simulation results indicated that irradiance,tempera-ture and series resistor have significant impact on open-curcuit voltage,short-circuit current,volt-am-pere characteristic,output power and optimum working point of photovoltaic array. The developed model is capable of accomplishing dynamic simulation of photovoltaic array.【期刊名称】《湖北民族学院学报（自然科学版）》【年(卷),期】2016(034)001【总页数】4页(P64-67)【关键词】光伏电池阵列;仿真;输出特性【作者】余基映;张腾;谭兴毅【作者单位】湖北民族学院科技学院，湖北恩施 445000;湖北民族学院理学院，湖北恩施 445000;湖北民族学院理学院，湖北恩施 445000【正文语种】中文【中图分类】TM914光伏发电技术是基于光伏效应实现太阳能转化为电能的发电方式，目前已被广泛应用于太空卫星、电信基站及偏远山区等领域，并逐步成为解决未来能源危机和生态环境问题的有效途径[1-5].光伏阵列作为电能供应装置是构成光伏系统的核心部件，其输出特性的研究对于提高太阳能利用效率和光伏发电系统输出功率具有关键性作用.利用计算机技术建立光伏阵列仿真模型可以方便地模拟和评估不同光照及温度条件任意排列方式光伏阵列的输出电气特性，具有很好的实用价值和应用前景.Matlab软件因具有高效的计算性能而备受国内外研究者青睐，被广泛应用于光伏系统的设计和性能仿真研究[6-9].目前，普遍采用单二极管等效电路模型来建立光伏电池仿真模型[10-13]，该等效电路模型由线性直流源和单个二极管并联组成，没有考虑半导体耗尽层中因能量激发所产生电子恢复运动[14]，因而欠缺通用性.本文基于双二极管等效电路模型[15]建立光伏电池单体模型，增加的二极管用来等效光伏电池漏电流特性，可以提升仿真效率和计算精度.利用Matlab软件仿真模块simElectronics组件库搭建光伏阵列物理特性的通用仿真模型，该仿真模型以光照强度、环境温度及光伏电池内部参数为输入条件，仿真得到光伏阵列的输出V-I特性和V-P特性.通过模拟变化的光照条件，得到光伏阵列输出电气特性的动态仿真结果.双二极管等效电路模型如图1所示，因此，输出电流I满足式(1)，其中Iph为光生电流，Rs、Rp表示光伏电池等效串联电阻、并联电阻，N1、N2代表二极管D1、D2理想因子，Is1、Is2代表二极管D1、D2反向饱和电流，Vt表示光伏电池热电压，满足：Vt = kT/q，k为波尔兹曼常量，q为元电荷，T为光伏电池温度.在Matlab/Simulink环境下搭建光伏阵列仿真模型如图2所示，光伏阵列由36块光伏电池单体组成，图3给出了光伏阵列子系统中各模块连接方式.光伏阵列由6个光伏组件构成，每个光伏组件由6个光伏电池串联而成，光伏阵列的光照条件参数由Signal Builder模拟产生，光伏电池单体模型基于双二极管等效电路模型建立，仿真计算过程采用变步长Ode45(Dormand-Prince)算法，仿真运行速度快.2.1 光伏阵列光照及温度特性仿真设定光伏电池仿真参数如表1所示，在环境温度为25℃条件下，改变光照强度Ir 值分别为0.25、0.75和1.25 kW/m2得到光伏阵列V-I和V-P特性曲线如图4所示，表2列出光伏阵列不同光照强度时开路电压Voc、短路电流Isc及最大输出功率Pm等参数.由图4可以看出，随着光强增大，短路电流Isc和开路电压Voc 增大，光伏阵列输出电流与输出功率显著上升，这是由于光强增加有利于提高光伏电池内部载流子迁移率及光子吸收系数[16]，从而提升光伏阵列转换效率.固定光照强度值为1 kW/m2，得到温度T分别为15℃、25℃和35℃时光伏阵列V-I和V-P特性曲线如图5所示，表3列出了不同温度时光伏阵列的输出特性参数.由图5可得，不同温度下光伏阵列短路电流Isc基本不变，可见光生电流受温度因素影响较小.随着温度升高，光伏阵列输出电流与输出功率明显下降，其中开路电压Voc和最大输出功率Pm同时减小，该仿真结果与文献[17]中光伏电池温度特性的实验研究结果基本一致.从不同条件下的仿真结果可以看出，光照强度和温度与光伏阵列的输出电气特性密切相关，随着光强和温度的变化，最大功率点(Um，Pm)发生明显改变.由表3和表4仿真数据结果可见，光强值变化量为500 W时，最佳工作电压Um值平均变化幅度约为0.19 V，温度变化量为10℃时，最佳工作电压Um值变化平均幅度约为1.33 V，可见，温度改变对最佳工作点(Um，Im)影响较大.该仿真结果可应用于光伏系统中最佳工作点跟踪技术[18-20]，实际光伏系统中可根据外部环境变化来实时调整光伏阵列工作点以满足负载需求.2.2 串联电阻对光伏阵列输出特性的影响按照表1设定的仿真参数，改变光伏电池组件串联电阻Rs大小依次为：0.01、0.025和0.05 时，光伏阵列输出特性参数、V-I特性及V-P特性曲线分别如表4和图6所示，可见，光伏电池串联电阻影响光伏阵列输出伏安特性和输出功率.从仿真结果可以看出，串联电阻增大时光伏阵列输出电流和输出功率降低，且伏安特性曲线由非线性关系变为线性关系，短路电流Is值呈现减小趋势，开路电压Voc基本不变，最佳工作点(Um，Im)位置变化明显，最大输出功率Pm随串联电阻减小而增大.因此，针对光伏电池的生产工艺而言，较低的串联电阻更有利于提升光伏阵列的输出功率和光伏转换效率[21].2.3 光伏阵列动态仿真设定温度为25 C，光伏阵列其它参数的设定参照表1，采用自定义的函数来模拟光照条件的变化，图7(a)给出光伏阵列光照强度随时间的变化情况，光照强度值变化依次为：0.75、0. 5、1、0.25、1.25 kW/m2.仿真得到光伏阵列的输出电压、输出电流和输出功率的变化曲线如图7(b)(d)所示，光照强度值发生变化时光伏阵列的响应时间依次为：8.6×10-3 、8.4×10-3 、9.9×10-3 、6.3×10-3 s.因此，该模型能够快速有效地模拟光照条件变化时光伏阵列输出电压、输出电流和输出功率的动态特性，可应用于实际光伏系统的工程设计.通过搭建光伏电池阵列的Matlab通用仿真电路模型，得到了不同条件下光伏阵列的输出电气参数，研究了光伏阵列的光照特性和温度特性，并对光伏阵列进行了动态模拟仿真.研究结果表明：光伏阵列的输出电流、输出功率与光照强度呈正相关，与温度呈负相关.短路电流和开路电压随光照强度增强而增大，温度的变化对光伏阵列短路电流无明显影响，开路电压随温度升高而减小，温度和串联电阻对光伏阵列最佳工作点影响较为显著.光伏阵列的Matlab仿真模型仿真速度快，输出特性与实际光伏阵列特性基本一致，能够动态模拟仿真外部光照条件变化时光伏阵列输出的电气特性，可为实际光伏系统的理论研究和工程应用提供平台.。