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Keywords = stochastically proportional system

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19 pages, 1035 KB  
Article
Spectral Bounds and Exit Times for a Stochastic Model of Corruption
by José Villa-Morales
Math. Comput. Appl. 2025, 30(5), 111; https://doi.org/10.3390/mca30050111 - 8 Oct 2025
Viewed by 374
Abstract
We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant [...] Read more.
We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article
(This article belongs to the Section Social Sciences)
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25 pages, 3408 KB  
Article
A Dual-Layer Optimal Operation of Multi-Energy Complementary System Considering the Minimum Inertia Constraint
by Houjian Zhan, Yiming Qin, Xiaoping Xiong, Huanxing Qi, Jiaqiu Hu, Jian Tang and Xiaokun Han
Energies 2025, 18(19), 5202; https://doi.org/10.3390/en18195202 - 30 Sep 2025
Viewed by 491
Abstract
The large-scale utilization of wind and solar energy is crucial for achieving carbon neutrality targets. However, as extensive wind and solar power generation is integrated via power electronic devices, the inertia level of power systems continues to decline. This leads to a significant [...] Read more.
The large-scale utilization of wind and solar energy is crucial for achieving carbon neutrality targets. However, as extensive wind and solar power generation is integrated via power electronic devices, the inertia level of power systems continues to decline. This leads to a significant reduction in the system’s frequency regulation capability, posing a serious threat to frequency stability. Optimizing the system is an essential measure to ensure its safe and stable operation. Traditional optimization approaches, which separately optimize transmission and distribution systems, may fail to adequately account for the variability and uncertainty of renewable energy sources, as well as the impact of inertia changes on system stability. Therefore, this paper proposes a two-layer optimization method aimed at simultaneously optimizing the operation of transmission and distribution systems while satisfying minimum inertia constraints. The upper-layer model comprehensively optimizes the operational costs of wind, solar, and thermal power systems under the minimum inertia requirement constraint. It considers the operational costs of energy storage, virtual inertia costs, and renewable energy curtailment costs to determine the total thermal power generation, energy storage charge/discharge power, and the proportion of renewable energy grid connection. The lower-layer model optimizes the spatiotemporal distribution of energy storage units within the distribution network, aiming to minimize total network losses and further reduce system operational costs. Through simulation analysis and computational verification using typical daily scenarios, this model enhances the disturbance resilience of the transmission network layer while reducing power losses in the distribution network layer. Building upon this optimization strategy, the model employs multi-scenario stochastic optimization to simulate the variability of wind, solar, and load, addressing uncertainties and correlations within the system. Case studies demonstrate that the proposed model not only effectively increases the integration rate of new energy sources but also enables timely responses to real-time system demands and fluctuations. Full article
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23 pages, 1924 KB  
Article
Metaheuristic-Based PID Controller Design with MOOD Decision Support Applied to Benchmark Industrial Systems
by Wilson Pavon
Electronics 2025, 14(18), 3630; https://doi.org/10.3390/electronics14183630 - 13 Sep 2025
Viewed by 1068
Abstract
This paper presents a comprehensive methodology for the multiobjective tuning of MIMO proportional integral derivative (PID) controllers using advanced metaheuristic strategies. The proposed approach formulates a cost function based on two conflicting performance criteria—the integral of absolute error (IAE) and the integral of [...] Read more.
This paper presents a comprehensive methodology for the multiobjective tuning of MIMO proportional integral derivative (PID) controllers using advanced metaheuristic strategies. The proposed approach formulates a cost function based on two conflicting performance criteria—the integral of absolute error (IAE) and the integral of absolute derivative of control (IADU)—to explore the trade-off between tracking performance and control effort systematically. Three metaheuristic techniques are employed: stochastic hill climbing, a Voronoi-based heuristic, and the Nondominated Sorting Genetic Algorithm (NSGA-II). A novel Multiobjective Optimization Design (MOOD)-based classification framework is incorporated to facilitate decision making across the Pareto front. The methodology is validated on three benchmark MIMO plants, demonstrating its robustness and generalizability. The results highlight that the NSGA-II controller achieves the lowest IADU value of 0.3694 in the mass damper system while maintaining acceptable performance metrics. The inclusion of a PID-split strategy further enhances system flexibility. This study emphasizes the value of metaheuristics in navigating complex design spaces and delivering tailored control solutions for multiobjective scenarios. Full article
(This article belongs to the Section Systems & Control Engineering)
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27 pages, 4022 KB  
Article
Performance Analysis of Multivariable Control Structures Applied to a Neutral Point Clamped Converter in PV Systems
by Renato Santana Ribeiro Junior, Eubis Pereira Machado, Damásio Fernandes Júnior, Tárcio André dos Santos Barros and Flavio Bezerra Costa
Energies 2025, 18(16), 4394; https://doi.org/10.3390/en18164394 - 18 Aug 2025
Cited by 1 | Viewed by 548
Abstract
This paper addresses the challenges encountered by grid-connected photovoltaic (PV) systems, including the stochastic behavior of the system, harmonic distortion, and variations in grid impedance. To this end, an in-depth technical and pedagogical analysis of three linear multivariable current control strategies is performed: [...] Read more.
This paper addresses the challenges encountered by grid-connected photovoltaic (PV) systems, including the stochastic behavior of the system, harmonic distortion, and variations in grid impedance. To this end, an in-depth technical and pedagogical analysis of three linear multivariable current control strategies is performed: proportional-integral (PI), proportional-resonant (PR), and deadbeat (DB). The study contributes to theoretical formulations, detailed system modeling, and controller tuning procedures, promoting a comprehensive understanding of their structures and performance. The strategies are investigated and compared in both the rotating (dq) and stationary (αβ) reference frames, offering a broad perspective on system behavior under various operating conditions. Additionally, an in-depth analysis of the PR controller is presented, highlighting its potential to regulate both positive- and negative-sequence components. This enables the development of more effective and robust tuning methodologies for steady-state and dynamic scenarios. The evaluation is conducted under three main conditions: steady-state operation, transient response to input power variations, and robustness analysis in the presence of grid parameter changes. The study examines the impact of each controller on the total harmonic distortion (THD) of the injected current, as well as on system stability margins and dynamic performance. Practical aspects that are often overlooked are also addressed, such as the modeling of the inverter and photovoltaic generator, the implementation of space vector pulse-width modulation (SVPWM), and the influence of the output LC filter capacitor. The control structures under analysis are validated through numerical simulations performed in MatLab® software (R2021b) using dedicated computational routines, enabling the identification of strategies that enhance performance and ensure compliance of grid-connected photovoltaic systems. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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17 pages, 2694 KB  
Article
Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services
by Wei Chen, Liang Chen, Xiaoxiao Shen, Yutao Zhang and Xiulai Wang
Mathematics 2025, 13(16), 2591; https://doi.org/10.3390/math13162591 - 13 Aug 2025
Cited by 1 | Viewed by 1321
Abstract
Patient unpunctuality substantially complicates appointment scheduling in integrated telemedicine–traditional outpatient systems. The current research frequently ignores behavioral distinctions between telemedicine patients and outpatients, while neglecting to measure the intangible burden on physicians from service mode switches. To address these gaps, this study incorporates [...] Read more.
Patient unpunctuality substantially complicates appointment scheduling in integrated telemedicine–traditional outpatient systems. The current research frequently ignores behavioral distinctions between telemedicine patients and outpatients, while neglecting to measure the intangible burden on physicians from service mode switches. To address these gaps, this study incorporates patient heterogeneity and introduces two novel cost metrics. Specifically, we implement penalties for service-mode switching and penalties for consecutive telemedicine sessions. We develop a Stochastic Mixed-Integer Programming (SMIP) model. This stochastic model is transformed into a deterministic Mixed-Integer Linear Programming (MILP) formulation via Sample Average Approximation (SAA). Linearization techniques enhance computational efficiency. In numerical experiments, the dual-penalty model yields balanced schedules with moderate patient mix, reducing physician overtime by 62.5% and service mode switches by 55% compared to baseline approaches. Sensitivity analysis confirms that narrowing outpatient unpunctuality ranges significantly reduces patient waiting and overtime, while raising telemedicine patient proportions bolsters system stability at the cost of increased physician idle time. These insights offer actionable guidance for healthcare institutions managing integrated online–offline services. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization in Operational Research)
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23 pages, 1146 KB  
Review
A Review of Optimization Scheduling for Active Distribution Networks with High-Penetration Distributed Generation Access
by Kewei Wang, Yonghong Huang, Yanbo Liu, Tao Huang and Shijia Zang
Energies 2025, 18(15), 4119; https://doi.org/10.3390/en18154119 - 3 Aug 2025
Cited by 3 | Viewed by 1427
Abstract
The high-proportion integration of renewable energy sources, represented by wind power and photovoltaics, into active distribution networks (ADNs) can effectively alleviate the pressure associated with advancing China’s dual-carbon goals. However, the high uncertainty in renewable energy output leads to increased system voltage fluctuations [...] Read more.
The high-proportion integration of renewable energy sources, represented by wind power and photovoltaics, into active distribution networks (ADNs) can effectively alleviate the pressure associated with advancing China’s dual-carbon goals. However, the high uncertainty in renewable energy output leads to increased system voltage fluctuations and localized voltage violations, posing safety challenges. Consequently, research on optimal dispatch for ADNs with a high penetration of renewable energy has become a current focal point. This paper provides a comprehensive review of research in this domain over the past decade. Initially, it analyzes the voltage impact patterns and control principles in distribution networks under varying levels of renewable energy penetration. Subsequently, it introduces optimization dispatch models for ADNs that focus on three key objectives: safety, economy, and low carbon emissions. Furthermore, addressing the challenge of solving non-convex and nonlinear models, the paper highlights model reformulation strategies such as semidefinite relaxation, second-order cone relaxation, and convex inner approximation methods, along with summarizing relevant intelligent solution algorithms. Additionally, in response to the high uncertainty of renewable energy output, it reviews stochastic optimization dispatch strategies for ADNs, encompassing single-stage, two-stage, and multi-stage approaches. Meanwhile, given the promising prospects of large-scale deep reinforcement learning models in the power sector, their applications in ADN optimization dispatch are also reviewed. Finally, the paper outlines potential future research directions for ADN optimization dispatch. Full article
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21 pages, 1275 KB  
Article
Stochastic Distributionally Robust Optimization Scheduling of High-Proportion New Energy Distribution Network Considering Detailed Modeling of Energy Storage
by Bin Lin, Yan Huang, Dingwen Yu, Chenjie Fu and Changming Chen
Processes 2025, 13(7), 2230; https://doi.org/10.3390/pr13072230 - 12 Jul 2025
Cited by 2 | Viewed by 1325
Abstract
In the context of building a new type of power system, the optimal operation of high-proportion new-energy distribution networks (HNEDNs) is a current hot topic. In this paper, a stochastic distribution robust optimization method for HNEDNs that considers energy-storage refinement modeling is proposed. [...] Read more.
In the context of building a new type of power system, the optimal operation of high-proportion new-energy distribution networks (HNEDNs) is a current hot topic. In this paper, a stochastic distribution robust optimization method for HNEDNs that considers energy-storage refinement modeling is proposed. First, an energy-storage lifetime loss model based on the rainfall-counting method is constructed, and then an optimal operation model of an HNEDN considering energy storage refinement modeling is constructed, aiming to minimize the total operation cost while taking into account the energy cost and the penalty cost of abandoning wind and solar power. Then, a source-load uncertainty model of HNEDN is constructed based on the Wasserstein distance and conditional value at risk (CvaR) theory, and the HNEDN optimization model is reconstructed based on the stochastic distribution robust optimization method; based on this, the multiple linearization technique is introduced to approximate the reconstructed model, which aims to both reduce the difficulty in solving the model and ensure the quality of the solution. Finally, the modified IEEE 33-bus power distribution system is used as an example for case analysis, and the simulation results show that the method presented in this paper, through reducing the loss of life in the battery storage device, can reduce the average daily energy storage depreciation cost compared to an HNEDN optimization method that does not take the energy storage life loss into account; this, in turn, reduces the total operating cost of the system. In addition, the stochastic distribution robust optimization method used in this paper can adaptively adjust the economy and robustness of the HNEDN operation strategy according to the confidence level and the available historical sample data on new energy-output prediction errors to obtain the optimal HNEDN operation strategy when compared with other uncertainty treatment methods. Full article
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15 pages, 795 KB  
Article
Optimal Dispatch of Power Grids Considering Carbon Trading and Green Certificate Trading
by Xin Shen, Xuncheng Zhu, Yuan Yuan, Zhao Luo, Xiaoshun Zhang and Yuqin Liu
Technologies 2025, 13(7), 294; https://doi.org/10.3390/technologies13070294 - 9 Jul 2025
Cited by 1 | Viewed by 865
Abstract
In the context of the intensifying global climate crisis, the power industry, as a significant carbon emitter, urgently needs to promote low-carbon transformation using market mechanisms. In this paper, a multi-objective stochastic optimization scheduling framework for regional power grids integrating carbon trading (CET) [...] Read more.
In the context of the intensifying global climate crisis, the power industry, as a significant carbon emitter, urgently needs to promote low-carbon transformation using market mechanisms. In this paper, a multi-objective stochastic optimization scheduling framework for regional power grids integrating carbon trading (CET) and green certificate trading (GCT) is proposed to coordinate the conflict between economic benefits and environmental objectives. By building a deterministic optimization model, the goal of maximizing power generation profit and minimizing carbon emissions is combined in a weighted form, and the power balance, carbon quota constraint, and the proportion of renewable energy are introduced. To deal with the uncertainty of power demand, carbon baseline, and the green certificate ratio, Monte Carlo simulation was further used to generate random parameter scenarios, and the CPLEX solver was used to optimize scheduling schemes iteratively. The simulation results show that when the proportion of green certificates increases from 0.35 to 0.45, the proportion of renewable energy generation increases by 4%, the output of coal power decreases by 12–15%, and the carbon emission decreases by 3–4.5%. At the same time, the tightening of carbon quotas (coefficient increased from 0.78 to 0.84) promoted the output of gas units to increase by 70 MWh, verifying the synergistic emission reduction effect of the “total control + market incentive” policy. Economic–environmental tradeoff analysis shows that high-cost inputs are positively correlated with the proportion of renewable energy, and carbon emissions are significantly negatively correlated with the proportion of green certificates (correlation coefficient −0.79). This study emphasizes that dynamic adjustments of carbon quota and green certificate targets can avoid diminishing marginal emission reduction efficiency, while the independent carbon price mechanism needs to enhance its linkage with economic targets through policy design. This framework provides theoretical support and a practical path for decision-makers to design a flexible market mechanism and build a multi-energy complementary system of “coal power base load protection, gas peak regulation, and renewable energy supplement”. Full article
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19 pages, 5884 KB  
Article
Partitioned Recirculating Renovation for Traditional Rice–Fish Farming Induced Substantial Alterations in Bacterial Communities Within Paddy Soil
by Yiran Hou, Hongwei Li, Rui Jia, Linjun Zhou, Bing Li and Jian Zhu
Agronomy 2025, 15(7), 1636; https://doi.org/10.3390/agronomy15071636 - 4 Jul 2025
Viewed by 894
Abstract
Integrated agriculture–aquaculture (IAA), represented by integrated rice–fish farming, offers a sustainable production method that addresses global food issues and ensures food security. Partitioned recirculating renovation based on traditional integrated rice–fish farming is an effective way to facilitate the convenient harvesting of aquatic products [...] Read more.
Integrated agriculture–aquaculture (IAA), represented by integrated rice–fish farming, offers a sustainable production method that addresses global food issues and ensures food security. Partitioned recirculating renovation based on traditional integrated rice–fish farming is an effective way to facilitate the convenient harvesting of aquatic products and avoid difficulties associated with mechanical operations. To elucidate the impact of partitioned recirculating renovation on the bacterial communities within paddy field ecosystems, we investigated the soil environmental conditions and soil bacterial communities within integrated rice–fish farming, comparing those with and without partitioned recirculating renovations. The findings indicated a significant reduction in the bacterial community richness within paddy soil in the ditch (fish farming area), along with noticeable changes in the relative proportions of the predominant bacterial phyla in both the ditch and the rice cultivation area following the implementation of partitioned recirculating renovation. In both the ditch and the rice cultivation area, partitioned recirculating renovation diminished the edges and nodes in the co-occurrence networks for soil bacterial communities and considerably lowered the robustness index, negatively impacting the stability of bacterial communities in paddy soil. Simultaneously, the partitioned recirculating renovation substantially influenced the bacterial community assembly process, enhancing the relative contributions of stochastic processes such as dispersal limitation, drift, and homogenizing dispersal. In addition, partitioned recirculating renovation significantly altered the soil environmental conditions in both the ditch and the rice cultivation area, with environmental factors being markedly correlated with the soil bacterial community, especially the total nitrogen (TN) and total phosphorus (TP), which emerged as the primary environmental drivers influencing the soil bacterial community. Overall, these results elucidated the ecological impacts of partitioned recirculating renovation on the paddy soil from a microbiomic perspective, providing a microbial basis for optimizing partitioned rice–fish systems. Full article
(This article belongs to the Special Issue Microbial Interactions and Functions in Agricultural Ecosystems)
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23 pages, 1557 KB  
Article
The Effect of Agricultural Mechanization Services on the Technical Efficiency of Cotton Production
by Yaxue Zhu, Guangyao Wang, Huijuan Du, Jiajia Liu and Qingshan Yang
Agriculture 2025, 15(11), 1233; https://doi.org/10.3390/agriculture15111233 - 5 Jun 2025
Cited by 7 | Viewed by 2973
Abstract
As the process of agricultural modernization accelerates, exploring the impact of agricultural mechanization services on production technology efficiency has become a key issue for enhancing agricultural productivity and promoting sustainable agricultural development. The study focuses on cotton growers in the Tarim River Basin [...] Read more.
As the process of agricultural modernization accelerates, exploring the impact of agricultural mechanization services on production technology efficiency has become a key issue for enhancing agricultural productivity and promoting sustainable agricultural development. The study focuses on cotton growers in the Tarim River Basin and systematically explores the impact and driving mechanisms of agricultural mechanization services (AMSs) on cotton production’s technical efficiency within the framework of the social–ecological system (SES). By employing a combination of stochastic frontier analysis (SFA) and propensity score matching (PSM), the research indicates that the adoption of AMSs significantly enhances the production technical efficiency of cotton farmers. Among the sample that adopted this service, as much as 53.04% of the farmers have their production efficiency within the range of [0.8, 0.9], demonstrating a high production capability. In contrast, the production efficiency values of the farmers who did not adopt such services are more dispersed, with inefficient samples accounting for 11.48%. Furthermore, while the technical efficiency levels across different regions are similar, there are significant efficiency differences within regions. A further analysis indicates that the age of the household head, their education level, the number of agricultural laborers in the family, the proportion of income from planting, and irrigation convenience have a positive impact on farmers’ adoption of AMSs, while the degree of land fragmentation has a negative impact. Therefore, AMSs are not only a core pathway to enhance cotton production’s technical efficiency but also an important support for promoting agricultural modernization in arid areas and strengthening farmers’ risk-resistance capabilities. Future policies should focus on optimizing service delivery, enhancing technical adaptability, and promoting regional collaboration to drive the high-quality development of the cotton industry and support sustainable rural revitalization. Full article
(This article belongs to the Section Agricultural Economics, Policies and Rural Management)
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21 pages, 1611 KB  
Article
Coordinated Reactive Power–Voltage Control in Distribution Networks with High-Penetration Photovoltaic Systems Using Adaptive Feature Mode Decomposition
by Yutian Fan, Yiqiang Yang, Fan Wu, Han Qiu, Peng Ye, Wan Xu, Yu Zhong, Lingxiong Zhang and Yang Chen
Energies 2025, 18(11), 2866; https://doi.org/10.3390/en18112866 - 30 May 2025
Viewed by 965
Abstract
As the proportion of renewable energy continues to increase, the large-scale grid integration of photovoltaic (PV) generation presents new technical challenges for reactive power balance in power systems. This paper proposes a coordinated reactive power and voltage optimization method based on Filtered Multiband [...] Read more.
As the proportion of renewable energy continues to increase, the large-scale grid integration of photovoltaic (PV) generation presents new technical challenges for reactive power balance in power systems. This paper proposes a coordinated reactive power and voltage optimization method based on Filtered Multiband Decomposition (FMD). First, to address the stochastic fluctuations of PV power, an improved FMD-based prediction model is developed. The model employs an adaptive finite impulse response (FIR) filter to decompose signals and captures periodicity and uncertainty through kurtosis-based feature extraction. By utilizing adaptive function windows for multiband signal decomposition, combined with kernel principal component analysis (KPCA) for dimensionality reduction and a long short-term memory (LSTM) network for prediction, the model significantly enhances forecasting accuracy. Second, to tackle the challenges of integrating high-penetration distributed PV while maintaining reactive power balance, a multi-head attention-based velocity update strategy is introduced within a multi-objective particle swarm optimization (MOPSO) framework. This strategy quantifies the spatial distance and fitness differences of historical best solutions, constructing a dynamic weight allocation mechanism to adaptively adjust particle search direction and step size. Finally, the effectiveness of the proposed method is validated through an improved IEEE 33-bus test case. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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18 pages, 3131 KB  
Article
Enhancing Load Frequency Control in Power Systems Using Hybrid PIDA Controllers Optimized with TLBO-TS and TLBO-EDO Techniques
by Ahmed M. Shawqran, Mahmoud A. Attia, Said F. Mekhamer, Hossam Kotb, Moustafa Ahmed Ibrahim and Ahmed Mordi
Processes 2025, 13(5), 1532; https://doi.org/10.3390/pr13051532 - 16 May 2025
Cited by 4 | Viewed by 1545
Abstract
Load frequency control (LFC) is essential for maintaining the stability of power systems subjected to load variations and renewable energy disturbances. This paper presents two advanced Proportional–Integral–Derivative–Acceleration (PIDA) controllers optimized using hybrid techniques: Teaching–Learning-Based Optimization combined with transit search (PIDA-TLBO-TS) and with Exponential [...] Read more.
Load frequency control (LFC) is essential for maintaining the stability of power systems subjected to load variations and renewable energy disturbances. This paper presents two advanced Proportional–Integral–Derivative–Acceleration (PIDA) controllers optimized using hybrid techniques: Teaching–Learning-Based Optimization combined with transit search (PIDA-TLBO-TS) and with Exponential Distribution Optimization (PIDA-TLBO-EDO). The proposed hybrid optimization approaches integrate global exploration and local exploitation capabilities to achieve near-global optimal solutions with superior convergence performance. Three test scenarios are studied to assess controller performance: a load disturbance in area 1, a disturbance in area 2, and a disturbance introduced by stochastic wave energy input. In each case, the proposed hybrid controllers are benchmarked against the conventional TLBO-based PIDA controller available in the literature. Simulation results confirm that the hybrid PIDA-TLBO-EDO controller consistently outperforms the alternatives in terms of peak-to-peak oscillation, root mean square (RMS) error, settling time, and overshoot. Specifically, it achieves a 0.49% to 15% reduction in peak-to-peak oscillations and a 2.5% to 18% improvement in RMS error, along with a 10.27% improvement in tie-line power deviation and a 15.38% reduction in frequency oscillations under wave energy disturbances. Moreover, the PIDA structure, enhanced by its acceleration term, contributes to better dynamic response compared to traditional controller designs. The results highlight the effectiveness and robustness of the proposed hybrid controllers in damping oscillations and maintaining system stability, particularly in modern power systems with high levels of renewable energy integration. This study emphasizes the potential of combining complementary optimization techniques to enhance LFC system performance under diverse and challenging conditions. Full article
(This article belongs to the Special Issue Modeling, Operation and Control in Renewable Energy Systems)
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24 pages, 4726 KB  
Article
Soft Fuzzy Reinforcement Neural Network Proportional–Derivative Controller
by Qiang Han, Farid Boussaid and Mohammed Bennamoun
Appl. Sci. 2025, 15(9), 5071; https://doi.org/10.3390/app15095071 - 2 May 2025
Viewed by 1050
Abstract
Controlling systems with highly nonlinear or uncertain dynamics present significant challenges, particularly when using conventional Proportional–Integral–Derivative (PID) controllers, as they can be difficult to tune. While PID controllers can be adapted for such systems using advanced tuning methods, they often struggle with lag [...] Read more.
Controlling systems with highly nonlinear or uncertain dynamics present significant challenges, particularly when using conventional Proportional–Integral–Derivative (PID) controllers, as they can be difficult to tune. While PID controllers can be adapted for such systems using advanced tuning methods, they often struggle with lag and instability due to their integral action. In contrast, fuzzy Proportional–Derivative (PD) controllers offer a more responsive alternative by eliminating reliance on error accumulation and enabling rule-based adaptability. However, their industrial adoption remains limited due to challenges in manual rule design. To overcome this limitation, Fuzzy Neural Networks (FNNs) integrate neural networks with fuzzy logic, enabling self-learning and reducing reliance on manually crafted rules. However, most fuzzy neural network PD (FNNPD) controllers rely on mean square error (MSE)-based training, which can be inefficient and unstable in complex, dynamic systems. To address these challenges, this paper presents a Soft Fuzzy Reinforcement Neural Network PD (SFPD) controller, integrating the Soft Actor–Critic (SAC) framework into FNNPD control to improve training speed and stability. While the actor–critic framework is widely used in reinforcement learning, its application to FNNPD controllers has been unexplored. The proposed controller leverages reinforcement learning to autonomously adjust parameters, eliminating the need for manual tuning. Additionally, entropy-regularized stochastic exploration enhances learning efficiency. It can operate with or without expert knowledge, leveraging neural network-driven adaptation. While expert input is not required, its inclusion accelerates convergence and improves initial performance. Experimental results show that the proposed SFPD controller achieves fast learning, superior control performance, and strong robustness to noise, making it effective for complex control tasks. Full article
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19 pages, 4317 KB  
Article
Stochastic Programming-Based Annual Peak-Regulation Potential Assessing Method for Virtual Power Plants
by Yayun Qu, Chang Liu, Xiangrui Tong and Yiheng Xie
Symmetry 2025, 17(5), 683; https://doi.org/10.3390/sym17050683 - 29 Apr 2025
Cited by 1 | Viewed by 914
Abstract
The intervention of distributed loads, propelled by the swift advancement of distributed energy sources and the escalating demand for diverse load types encompassing electricity and cooling within virtual power plants (VPPs), has exerted an influence on the symmetry of the grid. Consequently, a [...] Read more.
The intervention of distributed loads, propelled by the swift advancement of distributed energy sources and the escalating demand for diverse load types encompassing electricity and cooling within virtual power plants (VPPs), has exerted an influence on the symmetry of the grid. Consequently, a quantitative assessment of the annual peak-shaving capability of a VPP is instrumental in mitigating the peak-to-valley difference in the grid, enhancing the operational safety of the grid, and reducing grid asymmetry. This paper presents a peak-shaving optimization method for VPPs, which takes into account renewable energy uncertainty and flexible load demand response. Firstly, wind power (WP), photovoltaic (PV) generation, and demand-side response (DR) are integrated into the VPP framework. Uncertainties related to WP and PV generation are incorporated through the scenario method within deterministic constraints. Secondly, a stochastic programming (SP) model is established for the VPP, with the objective of maximizing the peak-regulation effect and minimizing electricity loss for demand-side users. The case study results indicate that the proposed model effectively tackles peak-regulation optimization across diverse new energy output scenarios and accurately assesses the peak-regulation potential of the power system. Specifically, the proportion of load decrease during peak hours is 18.61%, while the proportion of load increase during off-peak hours is 17.92%. The electricity loss degrees for users are merely 0.209 in summer and 0.167 in winter, respectively. Full article
(This article belongs to the Special Issue Symmetry in Digitalisation of Distribution Power System)
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24 pages, 4389 KB  
Article
Trusted Web Service Discovery Based on a Swarm Intelligence Algorithm
by Zhengwang Ye, Hehe Sheng and Haiyang Zou
Mathematics 2025, 13(9), 1402; https://doi.org/10.3390/math13091402 - 25 Apr 2025
Viewed by 536
Abstract
The number of services on the internet has experienced explosive growth, and the rapid and accurate discovery of required services among a vast array of similarly functioning services with differing degrees of quality has become a critical and challenging aspect of service computing. [...] Read more.
The number of services on the internet has experienced explosive growth, and the rapid and accurate discovery of required services among a vast array of similarly functioning services with differing degrees of quality has become a critical and challenging aspect of service computing. In this paper, we propose a trusted service discovery algorithm based on an ant colony system (TSDA-ACS). The algorithm integrates a credibility-based trust model with the ant colony search algorithm to facilitate the discovery of trusted web services. During the evaluation process, the trust model employs a pseudo-stochastic proportion to select nodes, where nodes with higher reputation have a greater probability of being chosen. The ant colony uses a voting method to calculate the credibility of service nodes, factoring in both credibility and non-credibility from the query node’s perspective. The algorithm employs an information acquisition strategy, a trust information merging strategy, a routing strategy, and a random wave strategy to guide ant search. To evaluate the effectiveness of the TSDA-ACS, this paper introduces the random walk search algorithm (RW), the classic max–min ant colony algorithm (MMAS), and a trustworthy service discovery based on a modified ant colony algorithm (TSDMACS) for comparison with the TSDA-ACS algorithm. The experiments demonstrate that this method can achieve the discovery of trusted web services with high recall and precision rates. Finally, the efficacy of the proposed algorithm is validated through comparison experiments across various network environments. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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