Search Results (811)

With the widespread adoption of renewable energy, distribution grids face increasing challenges in efficiency, safety, and economic performance due to stochastic generation and fluctuating load demand. Traditional operational models often exhibit limited adaptability, weak coordination, and insufficient holistic optimization, particularly in early-/mid-stage distribution planning where feeder-level network information may be incomplete. Accordingly, this study adopts a planning-oriented formulation and proposes a distributed energy storage system (DESS) planning strategy to enhance distribution network resilience under high uncertainty. First, representative wind and photovoltaic (PV) scenarios are generated using an improved Gaussian Mixture Model (GMM) to characterize source-side uncertainty. Based on a grid-based network partition, a priority index model is developed to quantify regional storage demand using quality- and efficiency-oriented indicators, enabling the screening and ranking of candidate DESS locations. A mixed-integer linear multi-objective optimization model is then formulated to coordinate lifecycle economics, operational benefits, and technical constraints, and a sequential connection strategy is employed to align storage deployment with load-balancing requirements. Furthermore, a node–block–grid multi-dimensional evaluation framework is introduced to assess resilience enhancement from node-, block-, and grid-level perspectives. A case study on a Zhejiang Province distribution grid—selected for its diversified load characteristics and the availability of detailed historical wind/PV and load-category data—validates the proposed method. The planning and optimization process is implemented in Python and solved using the Gurobi optimizer. Results demonstrate that, with only a 4% increase in investment cost, the proposed strategy improves critical-node stability by 27%, enhances block-level matching by 88%, increases quality-demand satisfaction by 68%, and improves grid-wide coordination uniformity by 324%. The proposed framework provides a practical and systematic approach to strengthening resilient operation in distribution networks. Full article

The construction cost of offshore wind farms (OWFs) is heavily influenced by vessel scheduling and meteorological uncertainties. To address these challenges, this paper proposes a constraint-driven hierarchical optimization framework for the coordinated scheduling of installation vessels (IVs) and transport vessels (TVs). First, a Mixed-Integer Linear Programming (MILP) model is established to describe the operational constraints, which is then decomposed into two interrelated sub-problems: vessel path planning and scheduling optimization. For path planning, the problem is modeled as a Multiple Traveling Salesman Problem (MTSP) to ensure balanced fleet workloads. This stage is solved via a tailored three-stage heuristic combining balanced sweep clustering and penalized local search. For scheduling optimization, a hybrid Earliest Deadline First (EDF)-Simulated Annealing (SA) strategy is employed, where EDF generates a strictly feasible baseline to warm-start the SA optimization. Furthermore, a stochastic optimization approach integrates historical meteorological data to ensure schedule robustness against weather uncertainty. The validity of the framework is supported by two real-world OWF cases, which demonstrate total cost reductions of 15.44% and 13.20%, respectively, under stochastic weather conditions. These results demonstrate its effectiveness in solving high-constraint offshore engineering problems. Full article

Uncertainty in optimization models often causes awkward properties in their deterministic equivalent formulations (DEFs), even for simple linear models. Chance-constrained programming is a reasonable tool for handling optimization problems with random parameters in objective functions and constraints, but it assumes that the distribution of these random parameters is known, and its DEF is often associated with the complicated computation of multiple integrals, hence impeding its extensive applications. In this paper, for optimization models with chance constraints, the historical data of random model parameters are first exploited to construct an adaptive approximate density function by incorporating piecewise linear interpolation into the well-known histogram method, so as to remove the assumption of a known distribution. Then, in view of this estimation, a novel confidence set only involving finitely many variables is constructed to depict all the potential distributions for the random parameters, and a computable reformulation of data-driven distributionally robust chance constraints is proposed. By virtue of such a confidence set, it is proven that the deterministic equivalent constraints are reformulated as several ordinary constraints in line with the principles of the distributionally robust optimization approach, without the need to solve complicated semi-definite programming problems, compute multiple integrals, or solve additional auxiliary optimization problems, as done in existing works. The proposed method is further validated by the solution of the stochastic multiperiod capacitated lot-sizing problem, and the numerical results demonstrate that: (1) The proposed method can significantly reduce the computational time needed to find a robust optimal production strategy compared with similar ones in the literature; (2) The optimal production strategy provided by our method can maintain moderate conservatism, i.e., it has the ability to achieve a better trade-off between cost-effectiveness and robustness than existing methods. Full article

This study establishes a comprehensive structural isomorphism between Conway’s Game of Life and the entrepreneurial process, analysing the latter as a complex adaptive system governed by non-linear dynamics rather than linear predictability. Through a rigorous qualitative approach based on a systematic literature review and abductive inference, the research identifies and correlates four fundamental dimensions: uncertainty, adaptability, growth, and sustainability. Transcending traditional metaphorical comparisons, this paper introduces a novel mathematical model that modifies Conway’s deterministic logic by incorporating an «Agency» variable (A). This critical addition quantifies how an entrepreneur’s internal capabilities can counterbalance environmental pressures (neighbourhood density) to determine survival thresholds, effectively transforming the simulation into a «Game of Life with Agency» where participants actively influence their viability potential (Ψ). The analysis explicitly correlates specific algorithmic configurations with real-world business phenomena: high-entropy initial states («The Soup») mirror early-stage market uncertainty where outcomes are probabilistic; «gliders» represent the necessity of strategic pivoting and continuous displacement for survival; and «oscillators» symbolise dynamic sustainability through rhythmic equilibrium rather than static permanence. Furthermore, the study validates the «Gosper Glider Gun» pattern as a model for scalable, generative growth. By bridging abstract systems theory with managerial practice, the research positions these simulations as «mental laboratories» for decision-making. The findings theoretically validate iterative methodologies like the Lean Startup and conclude that successful entrepreneurship operates on the «Edge of Chaos», providing a rigorous framework for navigating high stochastic uncertainty. Full article

This paper presents a robust data-driven methodology for estimating transmission loss coefficients (B-coefficients) in power systems using linear and quadratic programming (LP and QP), both of which belong to the family of convex optimization models. The first model employs a linear objective function with linear constraints, ensuring computational efficiency for simpler scenarios. The second model utilizes a quadratic objective function, also under linear constraints, to better capture more complex nonlinear relationships. By framing the estimation problem as a parameter identification task, both methodologies minimize the cost functions that quantify the mismatch between measured and modeled power losses. By considering a broad range of operational scenarios, our approach effectively captures the stochastic behavior inherent in power system operations. The effectiveness of both the LP and QP models is validated in terms of their ability to accurately extract physically meaningful B-coefficients from diverse simulation datasets. This study underscores the potential of integrating linear and quadratic programming as powerful and scalable tools for data-driven parameter estimation in modern power systems, especially in environments characterized by uncertainty or incomplete information. Full article

This work presents the design of passivity based non-fragile retarded sampled data control (NFRSDC) for the wind energy system using permanent magnet synchronous generator. At first, the proposed system is characterized in terms of non-linear dynamical equations, which is later expressed in terms of linear sub-systems via fuzzy membership functions using the Takagi–Sugeno fuzzy approach. After that, a more applicative NFRSDC is proposed along with the delay involved during signal transmission as well as randomly occurring controller gain perturbations (ROCGPs). Here, the ROCGPs are modeled accordingly using stochastic variable which obeys the certain Bernoulli distribution sequences. Folowing that, an appropriate Lyapunov–Krasovskii functionals are constructed to obtain the sufficient conditions in the form of linear matrix inequalities. These obtained conditions are then used to ensure the global asymptotic stability of the given system with the exogenous disturbances. Finally, numerical simulations are performed using MATLAB/Simulink and the obtained results have clearly demonstrated the efficacy of the proposed controller. Full article

The economic dispatch (ED) problem is a major challenge in power system optimization. In this article, an Enhanced Social Group Optimization (ESGO) algorithm is presented for solving the economic dispatch problem with or without wind units, considering various characteristics related to valve-point effects, ramp-rate constraints, prohibited operating zones, and transmission power losses. The Social Group Optimization (SGO) algorithm models the social dynamics of individuals within a group—through mechanisms of collective learning, behavioral adaptation, and information exchange—and leverages these interactions to guide the population efficiently towards optimal solutions. ESGO extends SGO along three complementary directions: redefining the update relations of the original SGO, introducing stochastic operators into the heuristic mechanisms, and dynamically updating the generated solutions. These modifications aim to achieve a more robust balance between exploration and exploitation, enable flexible adaptation of search steps, and rapidly integrate improved-fitness solutions into the evolutionary process. ESGO is evaluated in six distinct cases, covering systems with 6, 40, 110, and 220 units, to demonstrate its ability to produce competitive solutions as well as its performance in terms of stability, convergence, and computational efficiency. The numerical results show that, in the vast majority of the analyzed cases, ESGO outperforms SGO and other known or improved metaheuristic algorithms in terms of cost and stability. It incorporates wind generation results at an operating cost reduction of approximately 10% compared to the thermal-only system, under the adopted linear wind power model. Moreover, relative to the size of the analyzed systems, ESGO exhibits a reduced average execution time and requires a small number of function evaluations to obtain competitive solutions. Full article

Background: The vehicle routing problem (VRP) is of great importance in the Industry 4.0 era because enabling technologies such as the internet of things (IoT), artificial intelligence (AI), big data, and geographic information systems (GISs) allows for real-time solutions to versions of the problem, adapting to changing conditions such as traffic or fluctuating demand. Methods: In this paper, we model and optimize a classic multi-link distribution network topology, including randomness in travel times, vehicle availability times, and product demands, using a hybrid approach of nested linear stochastic programming and Monte Carlo simulation under a time-window scheme. The proposed solution is compared with cutting-edge metaheuristics such as Ant Colony Optimization (ACO), Tabu Search (TS), and Simulated Annealing (SA). Results: The results suggest that the proposed method is computationally efficient and scalable to large models, although convergence and accuracy are strongly influenced by the probability distributions used. Conclusions: The developed proposal constitutes a viable alternative for solving real-world, large-scale modeling cases for transportation management in the supply chain. Full article

To address active power fluctuations in power grids induced by high renewable energy penetration and overcome the limitations of existing probabilistic power flow (PPF) methods that ignore generator frequency regulation constraints, this paper proposes a segmented stochastic power flow modeling method and an efficient analytical framework that incorporates the actions and capacity constraints of regulation units. Firstly, a dual dynamic piecewise linear power injection model is established based on “frequency deviation interval stratification and unit limit-reaching sequence ordering,” clarifying the hierarchical activation sequence of “loads first, followed by conventional units, and finally automatic generation control (AGC) units” along with the coupled adjustment logic upon reaching limits, thereby accurately reflecting the actual frequency regulation process. Subsequently, this model is integrated with the State-Independent Linearized Power Flow (DLPF) model to develop a segmented stochastic power flow framework. For the first time, a deep integration of unscented transformation (UT) and regulation-aware power allocation is achieved, coupled with the Nataf transformation to handle correlations among random variables, forming an analytical framework that balances accuracy and computational efficiency. Case studies on the New England 39-bus system demonstrate that the proposed method yields results highly consistent with those of Monte Carlo simulations while significantly enhancing computational efficiency. The DLPF model is validated to be applicable under scenarios where voltage remains within 0.95–1.05 p.u., and line transmission power does not exceed 85% of rated capacity, exhibiting strong robustness against parameter fluctuations and capacity variations. Furthermore, the method reveals voltage distribution patterns in wind-integrated power systems, providing reliable support for operational risk assessment in grids with high shares of renewable energy. Full article

Wind-induced response poses a significant challenge to the stability of extra-large-span heavy steel box girders during synchronous lifting operations. This study adopted a method combining numerical simulation with on-site monitoring to investigate the aerodynamic characteristics the beam during the overall hoisting process of the Xiaotun Bridge. A high-fidelity finite element model was established using Midas NFX 2024 R1, and fluid–structure interaction (FSI) analysis was conducted, utilizing the RANS k-ε turbulence model to simulate stochastic wind fields. The results show that during the lifting stage from 3 m to 25 m, the maximum horizontal displacement of the steel box girder rapidly increases at wind angles of 90° and 60°, and the peak displacement is reached at 25 m. Under a strong breeze at a 90° wind angle and 25 m lifting height, the maximum lateral displacement was 42.88 mm based on FSI analysis, which is approximately 50% higher than the 28.58 mm obtained from linear static analysis. Subsequently, during the 25 m to 45 m lifting stage, the displacement gradually decreases and exhibits a linear correlation with lifting height. Concurrently, the maximum stress of the lifting lug of the steel box girder increases rapidly in the 3–25 m lifting stage, reaches the maximum at 25 m, and gradually stabilizes in the 25–45 m lifting stage. The lug stress under the same critical condition reached 190.80 MPa in FSI analysis, compared with 123.83 MPa in static analysis, highlighting a significant dynamic amplification. Furthermore, the detrimental coupling effect between mechanical vibrations from the lifting platform and wind loads was quantified; the anti-overturning stability coefficient was reduced by 10.48% under longitudinal vibration compared with lateral vibration, and a further reduction of up to 39.33% was caused by their synergy with wind excitation. Field monitoring validated the numerical model, with stress discrepancies below 9.7%. Based on these findings, a critical on-site wind speed threshold of 9.38 m/s was proposed, and integrated control methods were implemented to ensure construction safety. During on-site lifting, lifting lug stresses were monitored in real time, and if the predefined threshold was exceeded, contingency measures were immediately activated to ensure a controlled termination. Full article

The primary objective of this research is to develop a probabilistic nonlinear model predictive control structure (NMPC) that efficiently operates uncrewed surface vehicles (USVs) in an environment that has probabilistic disturbances, such as wind, waves, and currents of the water, while simultaneously maneuvering the vehicle in a way that avoids stationary or moving stochastic obstacles in its path. The proposed controller structure considers the mean and covariances of the inputs or state variables of the vehicle in the cost function to handle probabilistic disturbances, where an extended Kalman filter (EKF) is utilized to calculate the mean, and the covariances are calculated dynamically via a linear matrix equality based on this mean and obtained system matrices with successive linearization for every sampling instance. The proposed control structure deals with non-zero-mean probabilistic disturbances such as water current via an innovative approach that treats the mean of the disturbance as a deterministic part, which is estimated by a disturbance observer and eliminated by a control term in the controller in addition to the control signal obtained via MPC optimization; the effect of the remaining zero-mean part is handled over its covariance during the probabilistic MPC optimization. The probabilistic constraints are also dealt with by converting them to deterministic constraints, as in linear probabilistic MPC. However, unlike the linear MPC, these constraints updated each sampling instance with the information obtained via successive linearization. The control structure incorporates the velocity obstacle (VO) method for collision avoidance. In order to ensure stability, the proposed NMPC adopts a dual-mode strategy, and a stability analysis is presented. In the second mode, an LQG design that ensures stability in the existence of non-zero mean disturbance is also provided. The simulation results demonstrate that the proposed probabilistic NMPC framework effectively handles probabilistic disturbances as well as both stationary and moving obstacles, ensuring collision avoidance while reaching the desired position and orientation through optimal path tracking, outperforming the conventional NMPC. Full article

The increasing frequency and intensity of heat waves across Southern Europe pose growing challenges to the performance and profitability of photovoltaic (PV) systems. This study quantifies the impact of elevated ambient temperatures on three large-scale PV power plants located in distinct Portuguese climatic zones: Amareleja, Alcoutim, and Tábua. Using 15 years of hourly meteorological data from PVGIS (2009–2023), five temperature models—NOCT, Faiman, PVSyst, NOCT (SAM), and Sandia—were implemented to estimate cell temperature and corresponding PV output under reference and elevated temperature conditions (+2 °C and +5 °C). A three-fold sensitivity analysis assessed (i) the influence of module parameters (temperature coefficient and NOCT), (ii) the effect of stochastic, non-uniform temperature perturbations mimicking realistic heat waves, and (iii) the impact of the selected PV performance model by comparing the simplified linear temperature-corrected approach with the one-diode and three-parameter (1D + 3P) model. Results show that a uniform +2 °C rise reduces annual energy yield by 0.74% and a +5 °C rise by 1.85%, while stochastic perturbations slightly amplify these losses to 0.80% and 2.01%. The 1D + 3P model predicts stronger nonlinear effects, with reductions of −2.42% and −6.06%. Although modest at plant scale, such impacts could translate into annual national revenue losses exceeding 10 million EUR, considering Portugal’s 6.32 GW installed PV capacity. The findings highlight the importance of accounting for realistic temperature dynamics and model uncertainty when assessing PV performance under a warming climate. Full article

In supply chain management practices, supplier selection (SS) is a critical strategic planning activity that usually constitutes an ex ante decision made under uncertainty, whereas order allocation (OA) represents a subsequent operational decision determined ex post, contingent upon both the selected suppliers and actual operational conditions observed during the execution phase—specifically, the realized scenarios of uncertain circumstances. The practical performance of an SS decision inherently depends on its subsequent OA outcomes, while the OA decision itself is constrained by the preceding SS choices. Nevertheless, existing studies typically tackle the SS and OA problems separately or formulate them within a single-stage programming model, failing to adequately capture their sequential interdependence and the impact of OA on SS evaluation. To address this gap, this study develops novel two-stage bi-objective stochastic programming models in which the first-stage SS decisions are evaluated based on two key criteria—total cost and purchasing value—both of which depend on the second-stage OA decisions in response to realized operational scenarios. The stochastic performance of a given SS scheme, arising from adaptive OA decisions under uncertainty, is measured by expected value and conditional value-at-risk. An integrated approach combining weighted-satisfaction sum, linearization, Monte Carlo simulation, and genetic algorithm is developed to solve the models. Computational experiments demonstrate the effectiveness of the proposed methodology and reveal the influence of objective preferences and risk-aversion levels on the optimal supplier selection. Full article

This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the first stage, while the second stage optimizes operational decisions, including vessel assignment to routes and sailing speeds on individual voyage legs, after observing stochastic parameter realizations. The model incorporates nonlinear fuel consumption functions that are approximated using piecewise linearization techniques, with the resulting formulation being solved using the Sample Average Approximation (SAA) method. To enhance computational tractability, we employ big-M methods to linearize mixed-integer terms and introduce auxiliary variables to handle nonlinear relationships in both the objective function and constraints. The proposed model provides shipping companies with a comprehensive decision-support tool that effectively captures the complex interdependencies between long-term strategic fleet planning and short-term operational speed optimization. Numerical experiments demonstrate the model’s effectiveness in generating optimal solutions that balance economic objectives with environmental considerations under uncertain market conditions, highlighting its practical value for resilient shipping operations in volatile fuel and carbon pricing environments. Full article

The high penetration rate of renewable energy poses significant challenges to the planning and operation of power systems in regions with scarce data. In these regions, it is impossible to accurately simulate the complex nonlinear dependencies among hydro–wind–solar energy resources, which leads to huge operational risks and investment uncertainties. To bridge this gap, this study proposes a new data-driven framework that embeds the natural climate cycle (24 solar terms) into a physically consistent scenario generation process, surpassing the traditional linear approach. This framework introduces the Comprehensive Similarity Distance (CSD) indicator to quantify the curve similarity of power amplitude, pattern trend, and fluctuation position, thereby improving the K-means clustering. Compared with the K-means algorithm based on the standard Euclidean distance, the accuracy of the improved clustering pattern extraction is increased by 3.8%. By embedding the natural climate cycle and employing a two-stage dimensionality reduction architecture: time compression via improved clustering and feature fusion via Kernel PCA, the framework effectively captures cross-source dependencies and preserves climatic periodicity. Finally, combined with the simplified Vine Copula model, high-fidelity joint scenarios with a normalized root mean square error (NRMSE) of less than 3% can be generated. This study provides a reliable and computationally feasible tool for stochastic optimization and reliability analysis in the planning and operation of future power systems with high renewable energy grid integration. Full article