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Analysis of safe electricity consumption on load side based on attack and defence game model 基于攻防博弈模型的负荷侧安全用电分析
Pub Date : 2024-04-01 DOI: 10.1049/tje2.12380
Xiaodong Wang, Feixiang Gong, Songsong Chen, Bowen Zheng, Ping Zhang, Liye Zhao, Linru Jiang, Dongdong Zhang, Pengcheng Du
With the improvement of digitalization and intelligence in the power system, the safe operation of the power system is facing enormous challenges. The safe use of electricity on the load side is the key to achieving safe and reliable power system operation. The detection party needs amounts of human and material resources when the power network is attacked. In response to the current difficulties of low detection ability and high detection costs, this paper proposes an attack and defence game model that considers the differences between different nodes, ensuring the safety and economy of electricity consumption while reducing energy waste. At first, the structure of smart meters and the attack characteristics of intruders are summarized, and a basic attack and defence game model is constructed. The Nash equilibrium is then solved, and the optimal strategy for the game between the defender and the intruder is given to balance the relation between detection performance and energy consumption. In response to the differences generated by each node, strategies for attackers to launch attacks on different nodes and the setting of optimal thresholds for other nodes in the defence system are explored. Finally, case studies verify that the proposed model could reduce the cost of intruder detection while ensuring a specific detection rate.
随着电力系统数字化、智能化水平的提高,电力系统的安全运行面临着巨大的挑战。负荷侧的安全用电是实现电力系统安全可靠运行的关键。当电网受到攻击时,检测方需要大量的人力和物力。针对目前检测能力低、检测成本高的困难,本文提出了一种考虑不同节点差异的攻防博弈模型,在保证用电安全和经济性的同时,减少能源浪费。首先,总结了智能电表的结构和入侵者的攻击特点,构建了基本的攻防博弈模型。然后求解纳什均衡,给出防御方与入侵方博弈的最优策略,以平衡检测性能与能耗之间的关系。针对每个节点产生的差异,探讨了攻击者对不同节点发起攻击的策略,以及防御系统中其他节点最佳阈值的设置。最后,案例研究验证了所提出的模型可以降低入侵者检测成本,同时确保特定的检测率。
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引用次数: 0
A comprehensive study on the aerodynamic influence of stationary and moving obstacles on an isolated phantom DJI 3 UAV propeller 静止和移动障碍物对孤立幻影大疆 3 无人机螺旋桨气动影响的综合研究
Pub Date : 2024-04-01 DOI: 10.1049/tje2.12374
C-F. Hage, T. Sophy, E. Aglzim
Unmanned aerial vehicle (UAV) technology is experiencing strong growth in many fields such as military and civil. When operating around obstacles and in the proximity of walls or moving objects, the UAV is constrained to thrust and power consumption variation induced by several aerodynamic effects that can lead to severe flight instability. In this paper, a methodology based on multiple reference frames (MRF) is developed and applied to computational fluid dynamics (CFD) simulations on a Phantom DJI 3 propeller to reproduce the effect of fixed and moving wall proximity on the propeller aerodynamic performances. When hovering (3000 rpm) at 0.2 m above a moving obstacle (15 m/s), the results have shown a huge decrease in the thrust by 11.3% when compared to fixed obstacle thrust. This effect, however, is reduced when the propeller is hovering at 5000 rpm and neglected at 9550 rpm. Finally, the moving obstacle had a significant impact on the propeller's aerodynamic performance, resulting in a decrease in thrust force and power consumption at low hovering rotational velocities. Especially, when the obstacle is moving at a fast speed, the UAV could properly use high rotational velocity to maintain high power loading and ensure hovering stability.
无人驾驶飞行器(UAV)技术在军事和民用等许多领域正经历着强劲的增长。当无人飞行器在障碍物周围、墙壁或移动物体附近运行时,其推力和功耗会受到多种空气动力效应的限制,从而导致严重的飞行不稳定性。本文开发了一种基于多参考框架(MRF)的方法,并将其应用于 Phantom DJI 3 螺旋桨的计算流体动力学(CFD)模拟,以再现固定墙壁和移动墙壁对螺旋桨气动性能的影响。当在移动障碍物(15 米/秒)上方 0.2 米处悬停(3000 转/分)时,结果显示与固定障碍物推力相比,推力大幅下降 11.3%。然而,当螺旋桨以每分钟 5000 转的转速悬停时,这种影响会减小,而在每分钟 9550 转时,这种影响会被忽略。最后,移动障碍物对螺旋桨的气动性能有显著影响,导致低悬停转速时推力和功率消耗下降。特别是当障碍物以较快的速度移动时,无人机可以适当地利用高转速来维持较高的功率负荷,确保悬停稳定性。
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引用次数: 0
Automatic constraint programming solver selection method based on machine learning for the cable tree wiring problem 基于机器学习的电缆树布线问题自动约束编程求解器选择方法
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12368
Zhixin Zhang, Chenglong Xiao, Shanshan Wang, Weilun Yu, Yun Bai
Cable trees are primarily employed in industrial products to facilitate energy transfer and information exchange among various components. When utilizing machines for assembly, it is essential to convert the wiring plan into a sequence of cable insertion operations executed by the machine under various constraints. This poses a combinatorial optimization problem. In this domain, constraint programming (CP) solvers often exhibit outstanding performance by leveraging their robust problem‐modelling capabilities, excellent scalability, and precise solving capabilities. However, CP solvers may achieve various performances for different problem instances. Selecting the most suitable CP solver for each problem instance is crucial. This paper introduces an automatic selection algorithm for CP solvers to solve the cable tree wiring problem (CTW). Firstly, a scoring system is used to conduct an in‐depth analysis and compare four well‐known CP solvers: CPLEX, Chuffed, OR‐Tools, and Gurobi. The results indicate that OR‐Tools and CPLEX outperform other solvers in performance. Moreover, these two solvers exhibit complementary advantages in quickly finding optimal and feasible solutions within specified time limits. Therefore, CP and machine learning are ingeniously integrated, harnessing their complementary advantages. 4240 instances covering various scenarios are randomly generated to form the problem space. This method incorporates decision trees, random forests, K‐nearest neighbours, and naive Bayes, utilizing these four machine learning techniques. The proposed method can achieve better results than traditional single CP solvers. Among all the evaluated machining learning techniques, the automatic solver selection methods based on decision trees and random forests can achieve accuracy rates of 91.29% and 84.15%, respectively.
电缆树主要应用于工业产品,以促进各部件之间的能量传输和信息交换。利用机器进行装配时,必须将布线计划转换为机器在各种约束条件下执行的电缆插入操作序列。这就提出了一个组合优化问题。在这一领域,约束编程(CP)求解器通常利用其强大的问题建模能力、出色的可扩展性和精确的求解能力,表现出卓越的性能。然而,对于不同的问题实例,CP 求解器可能会实现不同的性能。为每个问题实例选择最合适的 CP 求解器至关重要。本文介绍了一种解决电缆树布线问题(CTW)的 CP 求解器自动选择算法。首先,本文使用评分系统对四种著名的 CP 求解器进行了深入分析和比较:CPLEX、Chuffed、OR-Tools 和 Gurobi。结果表明,OR-Tools 和 CPLEX 的性能优于其他求解器。此外,这两种求解器在指定时间内快速找到最优可行解方面表现出互补优势。因此,CPLEX 与机器学习巧妙地结合在一起,发挥了互补优势。4240 个涵盖各种情况的实例随机生成,形成问题空间。该方法结合了决策树、随机森林、K-近邻和天真贝叶斯这四种机器学习技术。与传统的单一 CP 求解器相比,所提出的方法能取得更好的结果。在所有经过评估的机器学习技术中,基于决策树和随机森林的自动求解器选择方法的准确率分别达到 91.29% 和 84.15%。
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引用次数: 0
Reactive power capacity allocation technology of shore‐based power supply system of offshore oil production platform under different network topology reliability measures 不同网络拓扑可靠性措施下海上采油平台岸基供电系统的无功功率容量分配技术
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12365
Wenle Song, Lei Wang, Xiangyu Hao, Le Wan, Chenyang Li
To improve the economy of offshore oil production platform shore‐based power transmission mode, the reactive power capacity allocation technology of offshore oil production platform shore‐based power supply system based on different network topology reliability measures was proposed. The optimization model of power supply system network topology and the structure model of voltage source converter high voltage direct current transmission system were established, the start and stop control scheme of flexible direct current (DC) transmission system was designed, and the operation parameters of converter station and DC line were monitored in real time. The topological structure of offshore oil production platform shore‐based power supply system is constructed, the mathematical model of flexible DC transmission system is established when the alternating current side voltage is balanced, the reactive power capacity configuration of offshore oil production platform shore‐based power supply system is optimized, and the life cycle cost results are calculated. The experimental results show that the algorithm proposed in this paper can obtain the optimal solution only after 26 calculations, with high optimization efficiency and good convergence effect. Reactive capacity configuration of shore‐based power supply system for offshore production platform can reduce failure rate and life cycle cost.
为提高海上采油平台岸基输电模式的经济性,提出了基于不同网络拓扑可靠性措施的海上采油平台岸基供电系统无功容量分配技术。建立了供电系统网络拓扑优化模型和电压源换流高压直流输电系统结构模型,设计了柔性直流输电系统启停控制方案,实时监测了换流站和直流线路的运行参数。构建了海上采油平台岸基供电系统的拓扑结构,建立了交流侧电压平衡时柔性直流输电系统的数学模型,优化了海上采油平台岸基供电系统的无功容量配置,并计算了生命周期成本结果。实验结果表明,本文提出的算法只需经过 26 次计算即可得到最优解,优化效率高,收敛效果好。海上生产平台岸基供电系统的无功容量配置可降低故障率和寿命周期成本。
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引用次数: 0
Distribution system resilience improvement against hurricanes: optimal line hardening according to reconfiguration potentials 提高配电系统抵御飓风的能力:根据重新配置潜力优化线路加固
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12364
Navid Talaei Pashiri, Sasan Azad, M. Ameli
In recent years, there has been a notable increase in the frequency and intensity of natural disasters related to global warming. Large‐scale blackouts caused by natural disasters demonstrate the extreme vulnerability of power systems to these devastations. Resilience planning is the key to preparing power systems for natural disasters by enhancing the vital infrastructure's robustness. This paper proposes a new resilience improvement framework based on resiliency assessment and optimal hardening to improve the distribution system's resiliency against hurricanes. The main goal is to find the optimal distribution system line hardening solution according to reconfiguration potentials after the hurricane to minimize the distribution system cost of energy not supplied. Fragility curves and Monte Carlo simulations are used for the distribution system resilience assessment. Poles and conductors are vulnerable components of distribution system lines; therefore, two hardening strategies have been outlined using measures like replacing old poles with new poles, upgrading pole classes, and vegetation management. This method is modelled as an optimization program considering budget limitations and load priorities and implemented by a genetic algorithm on the IEEE 33‐bus standard network. The results show that optimal line hardening according to network reconfiguration potentials significantly increased the distribution system's resilience.
近年来,与全球变暖有关的自然灾害的频率和强度明显增加。自然灾害造成的大规模停电表明,电力系统极易受到这些破坏的影响。通过增强重要基础设施的稳健性,制定抗灾规划是电力系统应对自然灾害的关键。本文提出了一个基于恢复力评估和优化加固的新恢复力改进框架,以提高配电系统抵御飓风的能力。其主要目标是根据飓风过后的重新配置潜力,找到最优的配电系统线路加固方案,从而最大限度地降低配电系统未供应能源的成本。配电系统抗灾能力评估采用易损性曲线和蒙特卡罗模拟。电线杆和导线是配电系统线路的易损部件;因此,利用新电线杆替换旧电线杆、提升电线杆等级和植被管理等措施,概述了两种加固策略。考虑到预算限制和负载优先级,该方法被模拟为优化程序,并通过遗传算法在 IEEE 33 总线标准网络上实施。结果表明,根据网络重新配置潜力进行的最优线路加固大大提高了配电系统的恢复能力。
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引用次数: 0
Research on SSVEP‐EEG feature enhancement algorithm based on fractional differentiation 基于分数微分的 SSVEP-EEG 特征增强算法研究
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12363
Zenghui Li, Wei Wang, Saijie Yuan, Junpeng Pei, Qianqian Yang, Yousong Wang
Steady‐state visual evoked potentials (SSVEP), significant in brain‐computer interfaces (BCI) and medical diagnostics, benefit from enhanced signal processing for improved analysis and interpretation. This study introduces a novel enhancement algorithm for SSVEP electroencephalogram (EEG) signals, employing fractional‐order differentiation operators combined with image processing techniques. Utilizing fractional‐order differentiation within a Laplace pyramid framework, the algorithm achieves hierarchical signal enhancement, facilitating detailed feature extraction and emphasizing SSVEP signal characteristics. This innovative approach merges the precision of fractional calculus with the structural benefits of the Laplace pyramid, leading to enhanced signal clarity and feature discrimination. The efficacy of this method was validated using canonical correlation analysis (CCA), filter bank CCA (FBCCA), and task‐related component analysis (TRCA) on a public dataset. Compared to conventional methods, our algorithm not only mitigates trend components in SSVEP signals but also significantly boosts the recognition accuracy of CCA, FBCCA, and TRCA algorithms. Experimental results indicate a marked improvement in recognition precision, underscoring the algorithm's potential to advance SSVEP‐based BCI research.
稳态视觉诱发电位(SSVEP)在脑机接口(BCI)和医疗诊断中非常重要,可通过增强信号处理来改进分析和解释。本研究采用分数阶微分算子与图像处理技术相结合,为 SSVEP 脑电图(EEG)信号引入了一种新型增强算法。该算法在拉普拉斯金字塔框架内利用分数阶微分,实现了分层信号增强,促进了详细特征提取并突出了 SSVEP 信号特征。这种创新方法融合了分数微积分的精确性和拉普拉斯金字塔的结构优势,从而提高了信号的清晰度和特征识别能力。在一个公开数据集上,使用典型相关分析(CCA)、滤波器组CCA(FBCCA)和任务相关成分分析(TRCA)验证了这种方法的有效性。与传统方法相比,我们的算法不仅能减轻 SSVEP 信号中的趋势成分,还能显著提高 CCA、FBCCA 和 TRCA 算法的识别准确率。实验结果表明,该算法显著提高了识别精确度,凸显了该算法在推进基于 SSVEP 的生物识别研究方面的潜力。
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引用次数: 0
Equivalent converter method for analyzing complex DC–DC converting systems 用于分析复杂直流-直流转换系统的等效转换器方法
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12359
Sagi Orel Moshe, Yefim Berkovich
This paper introduces a new approach for analyzing the dynamics of DC–DC converters. Currently, the primary widely accepted method for examining dynamic processes is the Small Signal Analysis technique. However, when applied to modern complex converters, this method poses additional challenges in formulating and solving systems of differential equations. The method proposed in this paper is based on its application to the analysis of dynamic modes of energy functions—Lagrangians. These functions make it possible to define simple criteria to describe the course of dynamic processes, and in the end define an equivalent (approximating) conventional converter identical to the original one with respect to the course of dynamics. If the magnetic and electrical energies in the Lagrangians of both the converters are equal, the outcome is practically identical transient processes. These findings were confirmed by both theoretical analysis and experimentally modelling the dynamics of the initial converter and an equivalent to it in the Matlab–Simscape program. An additional possibility of using the transfer functions of a conventional boost converter for the theoretical analysis of the converters of much greater orders is also discussed. The authors’ experiments confirm the correctness of their theoretical conclusions.
本文介绍了一种分析直流-直流转换器动态的新方法。目前,被广泛接受的主要动态过程分析方法是小信号分析技术。然而,当应用于现代复杂的转换器时,这种方法在制定和求解微分方程系统方面带来了额外的挑战。本文提出的方法基于其在能量函数-拉格朗日动态模式分析中的应用。通过这些函数,可以定义简单的标准来描述动态过程,并最终定义出一个在动态过程方面与原始转换器相同的等效(近似)常规转换器。如果两个变流器的拉格朗日中的磁能和电能相等,那么结果就是几乎相同的瞬态过程。这些发现通过理论分析和实验模拟初始转换器的动态以及 Matlab-Simscape 程序中的等效转换器得到了证实。此外,还讨论了使用传统升压转换器的传递函数对阶数更高的转换器进行理论分析的可能性。作者的实验证实了其理论结论的正确性。
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引用次数: 0
Analysis and optimization of the automated TIG welding process parameters on SS304 incorporating Taguchi optimization technique 采用田口优化技术分析和优化 SS304 的自动 TIG 焊接工艺参数
Pub Date : 2024-03-01 DOI: 10.1049/tje2.12373
Subramaniam Thangavel, C. Maheswari, E. Bhaskaran Priyanka, Albert Alexander Stonier, Geno Peter, Vivekananda Ganji
The present research work focused on optimizing the input parameters of the automated TIG welding process of SS304 metal. Since SS304 possesses high inter‐granular toughness and corrosion resistance with increased lifespan in the pressure vessel and automobile sector, SS304 is mainly referred for gas arc welding compared with SS 202. The SS304 workpieces of 60 mm × 40 mm × 4 mm with dimension are utilized in the experiment and the same metal has been used as the filler material. The TIG welding experimental lab‐scale setup utilizes a 2‐axis servo workbench programmed with PLC to perform an automatic trajectory path using Taguchi design of optimization to obtain the optimal welding parameters for the SS304 welding process. To analyze the influence of welding current, welding speed, gas flow rate, and welding arc length on the tensile strength and hardness based on predicted R‐squared, p‐value and co‐efficient of the sum of squares from are verified. From the regression analysis, the predicted model R‐squared value holds 95.78% and 94.83% for the hardness and tensile strength respectively associating with the actual coefficient confirming the model which has maximum precision. Further, it is inferred that on increasing welding current and welding speed, the hardness of the welded joints seems to increase whereas when the minimum gas flow rate is maintained, the tensile strength of the SS304 decreases drastically. Overall, among the four input factors, the welding current is a major influencing parameter on the SS304 which is directly proportional to tensile strength and hardness.
本研究工作的重点是优化 SS304 金属自动氩弧焊工艺的输入参数。由于 SS304 具有较高的晶间韧性和耐腐蚀性,在压力容器和汽车领域的使用寿命较长,因此与 SS 202 相比,SS304 主要用于气弧焊。实验中使用了尺寸为 60 mm × 40 mm × 4 mm 的 SS304 工件,并使用相同的金属作为填充材料。实验室规模的氩弧焊实验装置使用了一个由 PLC 编程的双轴伺服工作台,利用田口优化设计执行自动轨迹路径,以获得 SS304 焊接工艺的最佳焊接参数。根据预测的 R 方、P 值和平方和系数,分析焊接电流、焊接速度、气体流量和焊接电弧长度对拉伸强度和硬度的影响。通过回归分析,硬度和拉伸强度的预测模型 R 平方值分别为 95.78% 和 94.83%,与实际系数相关联,证实该模型具有最高精度。此外,还可以推断出,随着焊接电流和焊接速度的增加,焊点的硬度似乎会增加,而当保持最小气体流量时,SS304 的抗拉强度会急剧下降。总之,在四个输入因素中,焊接电流是影响 SS304 的主要参数,它与抗拉强度和硬度成正比。
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引用次数: 0
Design and implementation of a cost‐effective practical single‐phase power quality analyzer using pyboard microcontroller and python‐to‐python interface 使用 pyboard 微控制器和 python-to-python 接口设计并实现经济实用的单相电能质量分析仪
Pub Date : 2024-02-01 DOI: 10.1049/tje2.12360
Mehran Sabahi, Ashkan Safari, Morteza Nazari‐Heris
This work presents the design, development, and performance evaluation of a cost‐effective and practical single‐phase power quality analyzer (SPPQA) using Pyboard microcontroller and Python‐to‐Python interface. The SPPQA offers comprehensive measurements, including voltage/current harmonics up to the seventh order, frequency, voltage and current root mean square values, total power, active/reactive power, power factor, voltage and current crest factor, as well as voltage/current total harmonic distortion. To ensure the accuracy of the SPPQA, a testing procedure was conducted using a test bench equipped with a non‐linear load and a 220‐V power source operating at a frequency of 50 Hz. The obtained results, such as and , are compared with measurements obtained from classical approaches and devices, validating the authenticity and reliability of the SPPQA's performance. The SPPQA demonstrates considerable accuracy and reliability in its measurements, establishing it as an efficient and practical tool for power quality assessment. The ability to measure the seven harmonics of voltage and current, alongside other critical parameters, positions the SPPQA as a practical asset in the academic, industrial, and commercial sectors. The affordability and practicality of the SPPQA make it practical in both academic research and practical scenarios. Utilizers can gain deeper information into power quality through its measurements and harmonics analysis, while also enhancing industrial processes and ensuring a reliable power supply in commercial settings.
本研究利用 Pyboard 微控制器和 Python-to-Python 接口设计、开发了一款经济实用的单相电能质量分析仪 (SPPQA),并对其进行了性能评估。SPPQA 提供全面的测量,包括电压/电流七阶以下谐波、频率、电压和电流均方根值、总功率、有功/无功功率、功率因数、电压和电流波峰因数以及电压/电流总谐波失真。为确保 SPPQA 的准确性,使用配备了非线性负载和频率为 50 Hz 的 220 V 电源的测试台进行了测试。获得的结果,如 和 ,与传统方法和设备获得的测量结果进行了比较,从而验证了 SPPQA 性能的真实性和可靠性。SPPQA 在测量中表现出相当高的准确性和可靠性,使其成为一种高效实用的电能质量评估工具。SPPQA 能够测量电压和电流的七次谐波以及其他关键参数,是学术、工业和商业领域的实用工具。SPPQA 的经济性和实用性使其在学术研究和实际应用中都非常实用。用户可以通过测量和谐波分析获得更深入的电能质量信息,同时还能改进工业流程,确保商业环境中的可靠供电。
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引用次数: 0
Net saving improvement of capacitor banks in power distribution systems by increasing daily size switching number: A comparative result analysis by artificial intelligence 通过增加日开关次数提高配电系统中电容器组的净节电率:人工智能比较结果分析
Pub Date : 2024-02-01 DOI: 10.1049/tje2.12357
Omid Sadeghian, Ashkan Safari
This paper studies the effect of the number of switching (NOS) per day of capacitor banks on loss reduction in radial distribution systems. To this aim, the daytime (more precisely, 24 h) is divided into different numbers of time segments (equal to the same NOS) for capacitors’ size switching. The resulting non‐linear programming with discontinuous derivatives (called DNLP) model is solved subject to related constraints. The results reveal the impact of hourly switching of capacitor banks on further loss reduction (namely 118.4435, 83.7856, and 101.738 MWh for three IEEE systems) and higher net savings (i.e. k$5.6067, k$4.2772, and k$5.3542 for the same systems) of radial distribution systems compared to daily switching. Then, the hyper‐tuned Random Forest model is trained based on the IEEE 69‐bus network, fine‐tuned by the IEEE 10‐bus network, and fitted by the IEEE 33‐bus network to have an intelligent multi‐classification task with the highest accuracy. Numerical simulation, in both classic and intelligent parts, is presented to demonstrate the performance of DeepOptaCap. For the final step, DeepOptaCast is compared to other intelligent models of Light Gradient Boosting Method (LGBM), Decision Tree, and XGBoost, regarding KPIs of mean absolute percentage error, root mean squared percentage error, mean absolute error, root mean squared error, and coefficient of determination to demonstrate the model's superiority.
本文研究了电容器组每日投切次数(NOS)对径向配电系统损耗降低的影响。为此,将白天(更准确地说是 24 小时)划分为不同的时间段(等于相同的 NOS)来进行电容器的大小投切。由此产生的非线性编程与不连续导数(称为 DNLP)模型根据相关约束条件进行求解。结果表明,与每日切换相比,每小时切换电容器组可进一步减少径向配电系统的损耗(三个 IEEE 系统分别为 118.4435、83.7856 和 101.738 兆瓦时)和更高的净节约(相同系统分别为 k$5.6067、k$4.2772 和 k$5.3542)。然后,基于 IEEE 69 总线网络训练超调随机森林模型,通过 IEEE 10 总线网络进行微调,并通过 IEEE 33 总线网络进行拟合,从而以最高精度完成智能多分类任务。为了展示 DeepOptaCap 的性能,我们对传统和智能部分进行了数值模拟。最后,DeepOptaCast 与光梯度提升法 (LGBM)、决策树和 XGBoost 等其他智能模型在平均绝对百分比误差、平均平方根百分比误差、平均绝对误差、平均平方根误差和判定系数等 KPI 方面进行了比较,以证明该模型的优越性。
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引用次数: 0
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