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Keywords = stochastic optimization

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19 pages, 1668 KiB  
Article
Optimal Weighted Markov Model and Markov Optimal Weighted Combination Model with Their Application in Hunan’s Gross Domestic Product
by Dewang Li, Chingfei Luo and Meilan Qiu
Mathematics 2025, 13(3), 533; https://doi.org/10.3390/math13030533 (registering DOI) - 5 Feb 2025
Abstract
In this paper, we mainly establish an optimal weighted Markov model to predict the GDP of Hunan Province from 2017 to 2023. The new model is composed of a fractional grey model and a quadratic function regression model weighted combination and is obtained [...] Read more.
In this paper, we mainly establish an optimal weighted Markov model to predict the GDP of Hunan Province from 2017 to 2023. The new model is composed of a fractional grey model and a quadratic function regression model weighted combination and is obtained through Markov correction. First, the optimal order r of the fractional grey model (FGM) is determined by using the particle swarm optimization (PSO) algorithm, and the FGM model is established. Second, a quadratic regression model is established based on the scatter plot of the data. Then, the optimal weighted Markov model (OWMKM) is obtained by combining the above two sub-models (i.e., the optimal weighted combination model (OWM)) and using Markov correction. Finally, the new model is applied to estimate and predict the GDP of Hunan Province from 2017 to 2023. The forecast results show that the four statistical measures of the optimal weighted Markov model, such as MAPE, RMSE, , and STD, are superior to the optimal weighted combination model (OWM), the nonlinear auto regressive model (NAR) and the autoregressive integrated moving average model (ARIMA), which indicates that our new model has strong fitting and higher accuracy. We establish the quadratic regression Markov model (QFRMKM), the fractional grey Markov model (FGMKM), and the optimal combination model of these two sub-models (MKMOWM). The effects of the MKMOWM and OWMKM are compared. This research provides a scientifically reliable reference and has significant importance for understanding the development trends of the economy in Hunan Province, enabling governments and companies to make sound and reliable decisions and plans. Full article
(This article belongs to the Special Issue Statistical Forecasting: Theories, Methods and Applications)
25 pages, 3806 KiB  
Review
Truck Appointment Scheduling: A Review of Models and Algorithms
by Maria D. Gracia, Julio Mar-Ortiz and Manuel Vargas
Mathematics 2025, 13(3), 503; https://doi.org/10.3390/math13030503 - 3 Feb 2025
Viewed by 326
Abstract
This paper provides a comprehensive review of truck appointment scheduling models and algorithms that support truck appointment systems (TASs) at container terminals. TASs have become essential tools for minimizing congestion, reducing wait times, and improving operational efficiency at the port and maritime industry. [...] Read more.
This paper provides a comprehensive review of truck appointment scheduling models and algorithms that support truck appointment systems (TASs) at container terminals. TASs have become essential tools for minimizing congestion, reducing wait times, and improving operational efficiency at the port and maritime industry. This review systematically categorizes and evaluates existing models and optimization algorithms, highlighting their strengths, limitations, and applicability in various operational contexts. We explore deterministic, stochastic, and hybrid models, as well as exact, heuristic, and metaheuristic algorithms. By synthesizing the latest advancements and identifying research gaps, this paper offers valuable insights for academics and practitioners aiming to enhance TAS efficiency and effectiveness. Future research directions and potential improvements in model formulation are also discussed. Full article
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27 pages, 621 KiB  
Article
Long-Term Energy Consumption Minimization Based on UAV Joint Content Fetching and Trajectory Design
by Elhadj Moustapha Diallo, Rong Chai, Abuzar B. M. Adam, Gezahegn Abdissa Bayessa, Chengchao Liang and Qianbin Chen
Sensors 2025, 25(3), 898; https://doi.org/10.3390/s25030898 - 2 Feb 2025
Viewed by 215
Abstract
Caching the contents of unmanned aerial vehicles (UAVs) could significantly improve the content fetching performance of request users (RUs). In this paper, we study UAV trajectory design, content fetching, power allocation, and content placement problems in multi-UAV-aided networks, where multiple UAVs can transmit [...] Read more.
Caching the contents of unmanned aerial vehicles (UAVs) could significantly improve the content fetching performance of request users (RUs). In this paper, we study UAV trajectory design, content fetching, power allocation, and content placement problems in multi-UAV-aided networks, where multiple UAVs can transmit contents to the assigned RUs. To minimize the energy consumption of the system, we develop a constrained optimization problem that simultaneously designs UAV trajectory, power allocation, content fetching, and content placement. Since the original minimization problem is a mixed-integer nonlinear programming (MINLP) problem that is difficult to solve, the optimization problem was first transformed into a semi-Markov decision process (SMDP). Next, we developed a new technique to solve the joint optimization problem: option-based hierarchical deep reinforcement learning (OHDRL). We define UAV trajectory planning and power allocation as the low-level action space and content placement and content fetching as the high-level option space. Stochastic optimization can be handled using this strategy, where the agent makes high-level option selections, and the action is carried out at a low level based on the chosen option’s policy. When comparing the proposed approach to the current technique, the numerical results show that it can produce more consistent learning performance and reduced energy consumption. Full article
(This article belongs to the Section Communications)
34 pages, 7041 KiB  
Article
Research on Mobile Robot Path Planning Based on MSIAR-GWO Algorithm
by Danfeng Chen, Junlang Liu, Tengyun Li, Jun He, Yong Chen and Wenbo Zhu
Sensors 2025, 25(3), 892; https://doi.org/10.3390/s25030892 - 1 Feb 2025
Viewed by 199
Abstract
Path planning is of great research significance as it is key to affecting the efficiency and safety of mobile robot autonomous navigation task execution. The traditional gray wolf optimization algorithm is widely used in the field of path planning due to its simple [...] Read more.
Path planning is of great research significance as it is key to affecting the efficiency and safety of mobile robot autonomous navigation task execution. The traditional gray wolf optimization algorithm is widely used in the field of path planning due to its simple structure, few parameters, and easy implementation, but the algorithm still suffers from the disadvantages of slow convergence, ease of falling into the local optimum, and difficulty in effectively balancing exploration and exploitation in practical applications. For this reason, this paper proposes a multi-strategy improved gray wolf optimization algorithm (MSIAR-GWO) based on reinforcement learning. First, a nonlinear convergence factor is introduced, and intelligent parameter configuration is performed based on reinforcement learning to solve the problem of high randomness and over-reliance on empirical values in the parameter selection process to more effectively coordinate the balance between local and global search capabilities. Secondly, an adaptive position-update strategy based on detour foraging and dynamic weights is introduced to adjust the weights according to changes in the adaptability of the leadership roles, increasing the guiding role of the dominant individual and accelerating the overall convergence speed of the algorithm. Furthermore, an artificial rabbit optimization algorithm bypass foraging strategy, by adding Brownian motion and Levy flight perturbation, improves the convergence accuracy and global optimization-seeking ability of the algorithm when dealing with complex problems. Finally, the elimination and relocation strategy based on stochastic center-of-gravity dynamic reverse learning is introduced for the inferior individuals in the population, which effectively maintains the diversity of the population and improves the convergence speed of the algorithm while avoiding falling into the local optimal solution effectively. In order to verify the effectiveness of the MSIAR-GWO algorithm, it is compared with a variety of commonly used swarm intelligence optimization algorithms in benchmark test functions and raster maps of different complexities in comparison experiments, and the results show that the MSIAR-GWO shows excellent stability, higher solution accuracy, and faster convergence speed in the majority of the benchmark-test-function solving. In the path planning experiments, the MSIAR-GWO algorithm is able to plan shorter and smoother paths, which further proves that the algorithm has excellent optimization-seeking ability and robustness. Full article
(This article belongs to the Section Sensors and Robotics)
37 pages, 401 KiB  
Article
Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach
by Paramahansa Pramanik
Mathematics 2025, 13(3), 475; https://doi.org/10.3390/math13030475 - 31 Jan 2025
Viewed by 309
Abstract
This paper defines stubbornness as an optimal feedback Nash equilibrium within a dynamic setting. Stubbornness is treated as a player-specific parameter, with the team’s coach initially selecting players based on their stubbornness and making substitutions during the game according to this trait. The [...] Read more.
This paper defines stubbornness as an optimal feedback Nash equilibrium within a dynamic setting. Stubbornness is treated as a player-specific parameter, with the team’s coach initially selecting players based on their stubbornness and making substitutions during the game according to this trait. The payoff function of a soccer player is evaluated based on factors such as injury risk, assist rate, pass accuracy, and dribbling ability. Each player aims to maximize their payoff by selecting an optimal level of stubbornness that ensures their selection by the coach. The goal dynamics are modeled using a backward parabolic partial stochastic differential equation (BPPSDE), leveraging its theoretical connection to the Feynman–Kac formula, which links stochastic differential equations (SDEs) to partial differential equations (PDEs). A stochastic Lagrangian framework is developed, and a path integral control method is employed to derive the optimal measure of stubbornness. The paper further applies a variant of the Ornstein–Uhlenbeck BPPSDE to obtain an explicit solution for the player’s optimal stubbornness. Full article
30 pages, 4023 KiB  
Article
Forecasts Plus Assessments of Renewable Generation Performance, the Effect of Earth’s Geographic Location on Solar and Wind Generation
by César Berna-Escriche, Lucas Álvarez-Piñeiro and David Blanco
Appl. Sci. 2025, 15(3), 1450; https://doi.org/10.3390/app15031450 - 31 Jan 2025
Viewed by 319
Abstract
Solar and wind resources are critical for the global transition to net-zero emission energy systems. However, their variability and unpredictability pose challenges for system reliability, often requiring fossil fuel-based backups or energy storage solutions. The mismatch between renewable energy generation and electricity demand [...] Read more.
Solar and wind resources are critical for the global transition to net-zero emission energy systems. However, their variability and unpredictability pose challenges for system reliability, often requiring fossil fuel-based backups or energy storage solutions. The mismatch between renewable energy generation and electricity demand necessitates analytical methods to ensure a reliable transition. Sole reliance on single-year data is insufficient, as it does not account for interannual variability or extreme conditions. This paper explores probabilistic modeling as a solution to more accurately assess renewable energy availability. A 22-year dataset is used to generate synthetic data for solar irradiance, wind speed, and temperature, modeled using statistical probability distributions. Monte Carlo simulations, run 93 times, achieve 95% confidence and confidence levels, providing reliable assessments of renewable energy potential. The analysis finds that during Dunkelflaute periods, in high-solar and high-wind areas, DF events average 20 h in the worst case, while low-resource regions may experience DF periods lasting up to 48 h. Optimal energy mixes for these regions should include 15–20% storage and interconnections to neighboring areas. Therefore, stochastic consideration and geographic differentiation are essential analyses to address these differences and ensure a reliable and resilient renewable energy system. Full article
(This article belongs to the Special Issue Energy and Power Systems: Control and Management)
26 pages, 6834 KiB  
Article
Stochastic Potential Game-Based Target Tracking and Encirclement Approach for Multiple Unmanned Aerial Vehicles System
by Kejie Yang, Ming Zhu, Xiao Guo, Yifei Zhang and Yuting Zhou
Viewed by 499
Abstract
Utilizing fully distributed intelligent control algorithms has enabled the gradual adoption of the multiple unmanned aerial vehicles system for executing Target Tracking and Encirclement missions in industrial and civil applications. Restricted by the evasion behavior of the target, current studies focus on constructing [...] Read more.
Utilizing fully distributed intelligent control algorithms has enabled the gradual adoption of the multiple unmanned aerial vehicles system for executing Target Tracking and Encirclement missions in industrial and civil applications. Restricted by the evasion behavior of the target, current studies focus on constructing zero-sum game settings, and existing strategy solvers that accommodate continuous state-action spaces have exhibited only modest performance. To tackle the challenges mentioned above, we devise a Stochastic Potential Game framework to model the mission scenario while considering the environment’s limited observability. Furthermore, a multi-agent reinforcement learning method is proposed to estimate the near Nash Equilibrium strategy in the above game scenario, which utilizes time-serial relative kinematic information and obstacle observation. In addition, considering collision avoidance and cooperative tracking, several techniques, such as novel reward functions and recurrent network structures, are presented to optimize the training process. The results of numerical simulations demonstrate that the proposed method exhibits superior search capability for Nash strategies. Moreover, through dynamic virtual experiments conducted with speed and attitude controllers, it has been shown that well-trained actors can effectively act as practical navigators for the real-time swarm control. Full article
15 pages, 1170 KiB  
Review
CyberKnife in Pediatric Oncology: A Narrative Review of Treatment Approaches and Outcomes
by Costanza M. Donati, Federica Medici, Arina A. Zamfir, Erika Galietta, Silvia Cammelli, Milly Buwenge, Riccardo Masetti, Arcangelo Prete, Lidia Strigari, Ludovica Forlani, Elisa D’Angelo and Alessio G. Morganti
Curr. Oncol. 2025, 32(2), 76; https://doi.org/10.3390/curroncol32020076 - 29 Jan 2025
Viewed by 377
Abstract
Pediatric cancers, while rare, pose unique challenges due to the heightened sensitivity of developing tissues and the increased risk of long-term radiation-induced effects. Radiotherapy (RT) is a cornerstone in pediatric oncology, but its application is limited by concerns about toxicity, particularly secondary malignancies, [...] Read more.
Pediatric cancers, while rare, pose unique challenges due to the heightened sensitivity of developing tissues and the increased risk of long-term radiation-induced effects. Radiotherapy (RT) is a cornerstone in pediatric oncology, but its application is limited by concerns about toxicity, particularly secondary malignancies, growth abnormalities, and cognitive deficits. CyberKnife (CK), an advanced robotic radiosurgery system, has emerged as a promising alternative due to its precision, non-invasiveness, and ability to deliver hypofractionated, high-dose RT while sparing healthy tissues. This narrative review explores the existing evidence on CK application in pediatric patients, synthesizing data from case reports, small series, and larger cohort studies. All the studies analyzed reported cases of tumors located in the skull or in the head and neck region. Findings suggest CK’s potential for effective tumor control with favorable toxicity profiles, especially for complex or inoperable tumors. However, the evidence remains limited, with the majority of studies involving small sample sizes and short follow-up periods. Moreover, concerns about the “dose-bath” effect and limited long-term data on stochastic risks warrant cautious adoption. Compared to Linac-based RT and proton therapy, CK offers unique advantages in reducing session numbers and enhancing patient comfort, while its real-time tracking provides superior accuracy. Despite these advantages, CK is associated with significant limitations, including a higher potential for low-dose scatter (often referred to as the “dose-bath” effect), extended treatment times in some protocols, and high costs requiring specialized expertise for operation. Emerging modalities like π radiotherapy further underscore the need for comparative studies to identify the optimal technique for specific pediatric cases. Notably, proton therapy remains the benchmark for minimizing long-term toxicity, but its cost and availability limit its accessibility. This review emphasizes the need for balanced evaluations of CK and highlights the importance of planning prospective studies and long-term follow-ups to refine its role in pediatric oncology. A recent German initiative to establish a CK registry for pediatric CNS lesions holds significant promise for advancing evidence-based applications and optimizing treatment strategies in this vulnerable population. Full article
(This article belongs to the Special Issue Updates on Diagnosis and Treatment for Pediatric Solid Tumors)
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18 pages, 8574 KiB  
Article
Neural Network-Based Evaluation of Hardness in Cold-Rolled Austenitic Stainless Steel Under Various Heat Treatment Conditions
by Milan Smetana, Michal Gala, Daniela Gombarska and Peter Klco
Appl. Sci. 2025, 15(3), 1352; https://doi.org/10.3390/app15031352 - 28 Jan 2025
Viewed by 459
Abstract
This study introduces an innovative, non-contact method for classifying the hardness of austenitic stainless steels (grade AISI 304) based on their intrinsic magnetic fields. Utilizing a 3 × 3 matrix sensor system, this research captures weak magnetic fields to produce precise 2D magnetic [...] Read more.
This study introduces an innovative, non-contact method for classifying the hardness of austenitic stainless steels (grade AISI 304) based on their intrinsic magnetic fields. Utilizing a 3 × 3 matrix sensor system, this research captures weak magnetic fields to produce precise 2D magnetic field maps of the samples. A key advancement is the application of a modified GoogleNet convolutional neural network, optimized with the stochastic gradient descent with momentum algorithm, which achieves exceptional classification accuracy, ranging from 95% to 100%, and median accuracies of 97.5% to 99%. This method stands out by revealing a novel correlation between annealing temperature and magnetic field strength, particularly a pronounced decline in magnetic properties at temperatures near 1000 °C. This observation underscores the sensitivity of magnetic profiles to heat treatments, offering a groundbreaking approach to material characterization. By enabling reliable, efficient, and fully automated hardness evaluation based on magnetic signatures, this work has the potential to transform materials engineering and manufacturing, setting a new benchmark for non-destructive material analysis techniques. Full article
(This article belongs to the Special Issue The Advances and Applications of Non-destructive Evaluation)
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21 pages, 7228 KiB  
Article
Reinforcement Learning Decision-Making for Autonomous Vehicles Based on Semantic Segmentation
by Jianping Gao, Ningbo Liu, Haotian Li, Zhe Li, Chengwei Xie and Yangyang Gou
Appl. Sci. 2025, 15(3), 1323; https://doi.org/10.3390/app15031323 - 27 Jan 2025
Viewed by 570
Abstract
In the complex and stochastic traffic flow, ensuring safe driving requires improvements in perception and decision-making. This paper proposed a decision-control method that leveraged the scene perception and understanding capabilities of semantic segmentation networks and the stable convergence strategies of Deep Reinforcement Learning [...] Read more.
In the complex and stochastic traffic flow, ensuring safe driving requires improvements in perception and decision-making. This paper proposed a decision-control method that leveraged the scene perception and understanding capabilities of semantic segmentation networks and the stable convergence strategies of Deep Reinforcement Learning (DRL) algorithms to achieve more accurate and effective autonomous driving decision-control. Perception features obtained from cameras and sensors equipped with a semantic segmentation model were used as input for the intelligent agent. DRL algorithms were employed to update decisions based on reward feedback. Experimental results on the CARLA simulation platform demonstrated that the semantic segmentation network effectively identified obstacles, vehicles, and drivable areas, providing high-quality perception data input for the intelligent agent’s decision-making model. Compared to the original algorithms, the proposed Double Deep Q-Network-Semantic Segmentation (DDQN-SS) and Proximal Policy Optimization-Semantic Segmentation (PPO-SS) increased the reward value by approximately 25% and enhanced driving stability by 14.2% and 28.5%, respectively, enabling more stable and precise decision-control during driving. The method proposed in this paper has better improved the decision-control performance of PPO and DDQN in complex scenarios. Full article
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18 pages, 1247 KiB  
Article
Shipping Logistics Network Optimization with Stochastic Demands for Construction Waste Recycling: A Case Study in Shanghai, China
by Ping Wu, Yue Song and Xiangdong Wang
Sustainability 2025, 17(3), 1037; https://doi.org/10.3390/su17031037 - 27 Jan 2025
Viewed by 590
Abstract
In this paper, we introduce a shipping logistics network optimization method for construction waste recycling. In our case, construction waste is transported by a relay mode integrating land transportation, shipping transportation, and land transportation. Under the influence of urban economic life, the quantity [...] Read more.
In this paper, we introduce a shipping logistics network optimization method for construction waste recycling. In our case, construction waste is transported by a relay mode integrating land transportation, shipping transportation, and land transportation. Under the influence of urban economic life, the quantity (demand) of construction waste is uncertain and stochastic. Considering the randomness of construction waste generation, a two-stage stochastic integer programming model for the design of a shipping logistics network for construction waste recycling is proposed, and an accurate algorithm based on Benders decomposition is presented. Based on an actual case in Shanghai, numerical experiments are carried out to evaluate the efficacy of the proposed model and algorithm. Based on an actual case study in Shanghai, numerical experiments demonstrate that the proposed model can help to reduce transportation costs of construction waste. Sensitivity analysis highlights that factors like the penalty for untransported waste and capacity constraints play a crucial role in network optimization decisions. The findings provide valuable theoretical support for developing more efficient and sustainable logistics networks for construction waste recycling. Full article
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24 pages, 1906 KiB  
Article
Deterministic and Stochastic Machine Learning Classification Models: A Comparative Study Applied to Companies’ Capital Structures
by Joseph F. Hair, Luiz Paulo Fávero, Wilson Tarantin Junior and Alexandre Duarte
Mathematics 2025, 13(3), 411; https://doi.org/10.3390/math13030411 - 26 Jan 2025
Viewed by 493
Abstract
Corporate financing decisions, particularly the choice between equity and debt, significantly impact a company’s financial health and value. This study predicts binary corporate debt levels (high or low) using supervised machine learning (ML) models and firms’ characteristics as predictive variables. Key features include [...] Read more.
Corporate financing decisions, particularly the choice between equity and debt, significantly impact a company’s financial health and value. This study predicts binary corporate debt levels (high or low) using supervised machine learning (ML) models and firms’ characteristics as predictive variables. Key features include companies’ size, tangibility, profitability, liquidity, growth opportunities, risk, and industry. Deterministic models, represented by logistic regression and multilevel logistic regression, and stochastic approaches that incorporate a certain degree of randomness or probability, including decision trees, random forests, Gradient Boosting, Support Vector Machines, and Artificial Neural Networks, were evaluated using usual metrics. The results indicate that decision trees, random forest, and XGBoost excelled in the training phase but showed higher overfitting when evaluated in the test sample. Deterministic models, in contrast, were less prone to overfitting. Notably, all models delivered statistically similar results in the test sample, emphasizing the need to balance performance, simplicity, and interpretability. These findings provide actionable insights for managers to benchmark their company’s debt level and improve financing strategies. Furthermore, this study contributes to ML applications in corporate finance by comparing deterministic and stochastic models in predicting capital structure, offering a robust tool to enhance managerial decision-making and optimize financial strategies. Full article
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38 pages, 6156 KiB  
Review
A Review of Reliability Assessment and Lifetime Prediction Methods for Electrical Machine Insulation Under Thermal Aging
by Jian Zhang, Jiajin Wang, Hongbo Li, Qin Zhang, Xiangning He, Cui Meng, Xiaoyan Huang, Youtong Fang and Jianwei Wu
Energies 2025, 18(3), 576; https://doi.org/10.3390/en18030576 - 25 Jan 2025
Viewed by 391
Abstract
The thermal aging of insulation systems in electrical machines is a critical factor influencing their reliability and lifetime, particularly in modern high-performance electrical equipment. However, evaluating and predicting insulation lifetime under thermal aging poses significant challenges due to the complex aging mechanisms. Thermal [...] Read more.
The thermal aging of insulation systems in electrical machines is a critical factor influencing their reliability and lifetime, particularly in modern high-performance electrical equipment. However, evaluating and predicting insulation lifetime under thermal aging poses significant challenges due to the complex aging mechanisms. Thermal aging not only leads to the degradation of macroscopic properties such as dielectric strength and breakdown voltage but also causes progressive changes in the microstructure, making the correlation between aging stress and aging indicators fundamental for lifetime evaluation and prediction. This review first summarizes the performance indicators reflecting insulation thermal aging. Subsequently, it systematically reviews current methods for reliability assessment and lifetime prediction in the thermal aging process of electrical machine insulation, with a focus on the application of different modeling approaches such as physics-of-failure (PoF) models, data-driven models, and stochastic process models in insulation lifetime modeling. The theoretical foundations, modeling processes, advantages, and limitations of each method are discussed. In particular, PoF-based models provide an in-depth understanding of degradation mechanisms to predict lifetime, but the major challenge remains in dealing with complex failure mechanisms that are not well understood. Data-driven methods, such as artificial intelligence or curve-fitting techniques, offer precise predictions of complex nonlinear relationships. However, their dependence on high-quality data and the lack of interpretability remain limiting factors. Stochastic process models, based on Wiener or Gamma processes, exhibit clear advantages in addressing the randomness and uncertainty in degradation processes, but their applicability in real-world complex operating conditions requires further research and validation. Furthermore, the potential applications of thermal lifetime models, such as electrical machine design optimization, fault prognosis, health management, and standard development are reviewed. Finally, future research directions are proposed, highlighting opportunities for breakthroughs in model coupling, multi-physical field analysis, and digital twin technology. These insights aim to provide a scientific basis for insulation reliability studies and lay the groundwork for developing efficient lifetime prediction tools. Full article
(This article belongs to the Special Issue Power Electronic Converter and Its Control)
31 pages, 22638 KiB  
Review
Stochastic Scenario Generation Methods for Uncertainty in Wind and Photovoltaic Power Outputs: A Comprehensive Review
by Kun Zheng, Zhiyuan Sun, Yi Song, Chen Zhang, Chunyu Zhang, Fuhao Chang, Dechang Yang and Xueqian Fu
Energies 2025, 18(3), 503; https://doi.org/10.3390/en18030503 - 22 Jan 2025
Viewed by 594
Abstract
This paper reviews scenario generation techniques for modeling uncertainty in wind and photovoltaic (PV) power generation, a critical component as renewable energy integration into power systems grows. Scenario generation enables the simulation of variable power outputs under different weather conditions, serving as essential [...] Read more.
This paper reviews scenario generation techniques for modeling uncertainty in wind and photovoltaic (PV) power generation, a critical component as renewable energy integration into power systems grows. Scenario generation enables the simulation of variable power outputs under different weather conditions, serving as essential inputs for robust, stochastic, and distributionally robust optimization in system planning and operation. We categorize scenario generation methods into explicit and implicit approaches. Explicit methods rely on probabilistic assumptions and parameter estimation, which enable the interpretable yet parameterized modeling of power variability. Implicit methods, powered by deep learning models, offer data-driven scenario generation without predefined distributions, capturing complex temporal and spatial patterns in the renewable output. The review also addresses combined wind and PV power scenario generation, highlighting its importance for accurately reflecting correlated fluctuations in multi-site, interconnected systems. Finally, we address the limitations of scenario generation for wind and PV power integration planning and suggest future research directions. Full article
(This article belongs to the Section A: Sustainable Energy)
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16 pages, 7170 KiB  
Article
Optimizing Reactive Compensation for Enhanced Voltage Stability in Renewable-Integrated Stochastic Distribution Networks
by Yiguo Guo, Yimu Fu, Jingxuan Li and Jiajia Chen
Processes 2025, 13(2), 303; https://doi.org/10.3390/pr13020303 - 22 Jan 2025
Viewed by 490
Abstract
The rapid expansion of renewable energy sources and the increasing electrical load demand are complicating the operational dynamics of power grids, leading to significant voltage fluctuations and elevated line losses. To address these challenges, we propose an information gap decision-theory-based robust optimization method [...] Read more.
The rapid expansion of renewable energy sources and the increasing electrical load demand are complicating the operational dynamics of power grids, leading to significant voltage fluctuations and elevated line losses. To address these challenges, we propose an information gap decision-theory-based robust optimization method for the siting and operation of reactive compensation equipment, utilizing static var generators (SVGs) to mitigate voltage fluctuations and reduce losses. Our approach begins by projecting the scale of renewable energy integration and load growth, establishing scenarios with varying renewable-to-load growth ratios. We then develop a multi-objective optimization model that incorporates voltage–loss sensitivity, accounting for the uncertainties in renewable energy production. A case study demonstrates that our method reduces grid voltage fluctuations and losses by 29.53% and 7.75%, respectively, compared to non-intervention scenarios, highlighting its effectiveness in stabilizing distribution networks. Full article
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