Search Results (75)

The decarbonization of multi-energy coupled ports necessitates addressing the complex interplay between renewable energy fluctuations and flexible load management. However, existing research has clear limitations in describing multi-source uncertainties and clarifying the synergistic mechanism of electro-hydrogen energy storage systems. To fill this gap, this study addresses the core problem of the coordinated operation of port microgrids under multiple uncertainties. A comprehensive physical model is established for wind–solar–tidal–hydrogen systems, capturing the intricate dynamics of the “generation–consumption–storage–conversion” chain. A novel two-stage stochastic optimization framework, integrating day-ahead pre-decision with real-time compensation, is proposed. To overcome computational bottlenecks, an adaptive progressive hedging algorithm is introduced. Comparative analyses show that the proposed strategy reduces the total port operational costs by 60.8% and grid transaction costs by 74.4%, compared with the single-stage deterministic mode. The adaptive PH algorithm also achieves 4–6 times higher computational efficiency than quadratic integer Benders decomposition, while maintaining an optimality gap below 2%. These findings elucidate the critical synergy between electro-hydrogen storage and stochastic optimization, offering a theoretical basis for sustainable port operations. Full article

As UAVs are increasingly used in emergency rescue, task allocation under uncertainty still faces tail delay risk. Existing studies mainly optimize expected cost and pay insufficient attention to task temporal relations and delay losses under extreme scenarios. To address this issue, this study develops a risk-averse two-stage stochastic programming model that incorporates the precedence relation between reconnaissance and delivery tasks, UAV routes, and task execution sequences into a unified decision process. The first stage determines task assignment, route selection, and visit order, while the second stage evaluates waiting, delay, and recourse costs under stochastic scenarios. A Mean-CVaR risk measure is adopted to characterize both average performance and tail risk. To solve the resulting multi-scenario risk-averse model, this study develops a problem-tailored Enhanced BD framework based on the classical Benders decomposition structure. The proposed framework integrates partial scenario embedding, heuristic warm start, and dynamic cut-pool management to strengthen early master problem information, improve feasible-route search, and control the growth of scenario-wise cuts. Numerical experiments based on a Nanjing emergency rescue instance evaluate the model and algorithm in terms of solution performance, acceleration ablation, optimized scheduling results, and parameter sensitivity. The results show that the proposed model can identify tail delay risk concentrated at a small number of demand points and downstream nodes in task chains. Across ten independent replications, Enhanced BD achieves a higher convergence success rate and lower final BD Gap than Basic BD in the medium-sized and largest tested instances. Parameter analysis shows that moderate risk aversion improves out-of-sample performance, whereas excessive risk aversion or resource allocation may reduce overall scheduling efficiency. The proposed method improves tail risk identification and solution capability for emergency UAV task allocation under time uncertainty and provides a methodological reference for risk-aware UAV emergency scheduling. Full article

In modern power systems, the rapid growth of renewable energy capacity, such as wind and solar photovoltaic (PV) power, has led to a decline in system equivalent inertia and primary frequency regulation margin. At the same time, net load fluctuations have intensified across multiple time scales, making it more likely for the RoCoF, frequency nadir, and quasi-steady-state frequency deviation to approach safety limits following disturbances. To achieve a balance between frequency security and economic operation, this paper proposes a two-stage stochastic frequency-security-constrained unit commitment (FSC-SUC) model tailored for scenarios with high renewable energy penetration. The day-ahead hourly dispatch stage jointly determines the on/off status and reference output of synchronous units and the reservation of slow frequency regulation capacity, as well as energy storage charging and discharging plans, SoC trajectories, and the reservation of fast frequency regulation capacity. The intraday minute-level real-time dispatch stage accommodates prediction errors through scenario-based rescheduling and ensures the deliverability of both slow and fast frequency regulation capabilities via commitment consistency constraints. To address the challenge of directly embedding frequency nadir constraints into mixed-integer optimization, this paper employs a modeling approach that combines analytical criteria with linear surrogate constraints. The RoCoF and quasi-steady-state frequency deviation are specified via aggregated analytical constraints, while the nadir is embedded into the main problem after generating samples offline using a simplified frequency response model and training a polyhedral linear surrogate for external approximation. The safety margin is then calibrated using high-quantile residuals from the validation set to ensure conservativeness. Case studies on the IEEE 33-bus system under different renewable penetration levels demonstrate that the proposed method significantly reduces the probability of frequency nadir violations and load-loss risk with only a modest cost increase while also improving coordination between fast and slow frequency regulation. Full article

Integrating renewable energy into modern grids while reducing carbon emissions represents a critical challenge for achieving “dual carbon” objectives. This paper proposes a two-stage stochastic optimization scheduling model for integrated energy systems (IES) that accounts for dynamic carbon emission factors and spatiotemporal uncertainty in wind power. First, a dynamic carbon emission factor model is developed to reflect real-time grid operational status and marginal power generation characteristics, replacing the conventional fixed-factor approach and enabling precise guidance for low-carbon electricity procurement strategies. Second, a Copula-based joint probability distribution model is established to capture complex temporal and spatial correlations in multi-wind-farm clusters, from which representative scenarios are generated and reduced through advanced pruning techniques. The scheduling model minimizes total operating costs and tiered carbon trading costs via mixed-integer quadratic programming (MIQP) and Benders decomposition. Case studies demonstrate that the proposed approach reduces daily operating costs by 6.4% (from 2.069 to 1.936 million yuan) and total carbon emissions by 8.4% (from 1051.8 to 963.2 tonnes) compared to conventional static-factor methods. Further, by accurately characterizing wind power uncertainty, the model achieves wind power absorption rates exceeding 90%, reducing curtailment from 272 kWh to 75 kWh and improving renewable energy utilization from 57.5% to 92%. The results validate that dynamic carbon factors and spatiotemporal correlation modelling effectively enhance both low-carbon performance and economic efficiency in IES dispatch, offering theoretical and practical guidance for achieving carbon-neutral energy system operations. Full article

This paper studies capacity planning for a wind–hydrogen integrated energy system under scenario-based uncertainty in wind generation, hydrogen demand, and electricity prices. The model is formulated as a two-stage stochastic program in which first-stage investment decisions are selected before uncertainty is realized and second-stage hourly operation is optimized for each representative scenario. The main methodological difficulty is that part of the first-stage hydrogen-storage investment cost may be available only through a non-analytical evaluator, such as supplier quotation logic, simulation software, or a data-driven estimator, while the operational recourse model remains linear. To address this setting, a hybrid heuristic–Benders framework, denoted as GSOA-Benders, is developed by coupling the General-Soldiers Optimization Algorithm for derivative-free first-stage search with Benders cuts generated from linear programming subproblems. The framework is not presented as a replacement for commercial solvers on explicit convex or mixed-integer models; rather, it is intended for cases where exact algebraic reformulation of the first-stage cost is unreliable or unavailable. In the black-box case study with 500 scenarios, the method converges in 35.86 s and obtains an investment plan expressed as $\mathbf{x}=[1,0.53,23.23,0]$, corresponding to wind-farm construction, a 0.53 MW electrolyzer, a 23.23 MWh hydrogen tank, and no fuel-cell investment. Additional discussion is provided on stability-gap interpretation, benchmark limitations, component lifetime assumptions, hydrogen losses, and environmental extensions. Full article

Given the energy-intensive operations and considerable carbon emissions of offshore oil and gas platforms (OOGPs) in deep-sea regions, adopting floating offshore wind farms (FOWFs) as power sources offers substantial benefits. However, the expenses associated with dynamic submarine cables constitute a substantial portion of the capital expenditure (CAPEX) for this hybrid system, highlighting the crucial need for optimization in the power collection system design. In this study, we present a mixed-integer quadratic programming (MIQP) model designed to reduce both the costs of investment and power losses associated with dynamic submarine cables, taking into account the influence of the wake effect in local wind conditions. Due to the complexity of this problem, we employ the Benders’ decomposition method to reformulate it into a master problem and a slave problem. Additionally, two valid inequalities are specifically incorporated into the master problem to accelerate the solution process. These constraints are derived from a heuristic combination of various cable connection configurations and a greedy-based spanning tree structure. Through multiple case studies, we first demonstrate the accuracy and rapid convergence of our method. Furthermore, we reveal that as the wind farm grows in size, the influence of the wake effect becomes increasingly pronounced. Full article

With the high penetration of distributed photovoltaics (PV) in distribution areas, transformer capacity limits and source–load fluctuations have become key factors constraining PV accommodation. To accurately assess the PV hosting capacity under energy storage regulation, this paper proposes an assessment method based on operating region analysis. First, a coordinated operation model for the distribution area is established, incorporating the transformer capacity, energy storage constraints, and power balance. On this basis, the calculation boundaries for the PV hosting capacity are discussed in two scenarios: Model 1 ignores power curve uncertainty, characterizing the geometry of the conventional operating region to find the maximum deterministic hosting capacity (S₁) that keeps the region non-empty. Model 2 introduces box-type uncertainty sets for the source and load, proposes the concept of a “Self-Balanced Operating Region”, and constructs a robust feasibility determination model (f₃) based on a Min–Max–Min structure. To solve this multi-layer nested non-convex model, an iterative algorithm based on duality theory and Benders decomposition is employed to determine the robust hosting capacity under uncertainty (S₂) at the critical point where f₃ shifts from zero to non-zero. Case studies show that source–load uncertainty leads to a significant contraction of the operating region, and the robust hosting capacity under uncertainty requirements is strictly less than the deterministic hosting capacity (S₁ > S₂). This method quantifies the reduction effect of uncertainty on the accommodation capability, providing a theoretical basis for planning high-renewable penetration distribution areas and energy storage configuration. Full article

Amid the global decarbonization of urban transportation, the large-scale deployment of electric buses faces major challenges, including concentrated charging demand, increased peak electricity demand, and inefficient energy utilization at transit depots. Existing studies usually optimize depot energy system configuration and bus scheduling separately, which often leads to biased system-level decisions. To address this limitation, this study proposes a collaborative optimization framework that integrates cross-line scheduling with the configuration of photovoltaic–storage–charging systems at depots to improve overall resource utilization. Specifically, this study formulates a mixed-integer linear programming (MILP) model to minimize the total daily system cost. The proposed model comprehensively captures multiple factors, including the costs of bus investment, charging infrastructure, photovoltaic deployment, energy storage deployment, and carbon emissions. In this study, Benders decomposition is used as a solution framework to handle the coupling structure of the model. Case studies show that, compared with conventional operation modes, the combination of cross-line scheduling and fast charging technology produces a significant synergistic effect. This combination reduces the required fleet size from 17 to 14 buses and substantially lowers investment in depot infrastructure, thereby minimizing the total system cost. Sensitivity analysis further shows that the deployment scale of photovoltaic systems has a clear threshold effect on electricity costs, whereas the core economic value of energy storage systems depends on peak shaving and arbitrage under time-of-use electricity pricing. Overall, this study demonstrates the critical role of integrated planning in improving the economic efficiency and operational feasibility of electric bus systems. It provides important theoretical support and practical guidance for depot design and resource scheduling in low-carbon public transportation networks. Full article

Typhoon-induced extreme weather poses a severe threat to power systems with high offshore wind penetration. Source-side wind turbine tripping and grid-side transmission line failures are likely to occur simultaneously, which may trigger cascading outages and large-scale load shedding. A multi-level source-grid-load-storage preventive resilience dispatch strategy is proposed. A typhoon spatiotemporal evolution model is first established based on the Batts gradient wind model. Failure probability models for offshore wind turbines and overhead transmission lines are developed while considering strong wind and lightning strike effects. The most probable and severe fault scenario is identified using an entropy-based quantification method. A two-stage robust preventive dispatch model is subsequently formulated. In the day-ahead stage, unit commitment, multi-type reserve allocation, and pumped storage scheduling are optimized at a 1 h resolution. In the real-time stage, combined wind-storage systems are coordinated at a 10 min resolution to accommodate rapid wind power ramps caused by high-wind shutdown events. The model is reformulated through Lagrangian duality and solved by the Benders decomposition algorithm. Case studies on a modified IEEE-RTS 24-bus system with three offshore wind farms demonstrate that the proposed strategy reduces wind curtailment by 66.3%, load shedding by 74.6%, and total cost by 14.8% compared with the case without energy storage. The combined operation cost of storage resources accounts for only 3.1% of the total cost, confirming its favorable cost-effectiveness for resilience enhancement. The proposed strategy contributes to the sustainable integration of offshore wind energy by ensuring a reliable power supply during extreme weather events. Full article

The electrical characteristics of distribution networks (DNs) are drastically changing, which is mainly due to widespread adoption of small-scale distributed energy resources (DERs) by end-users. In these cases, conventional planning models may lead to overinvestment choices. This paper presents a planning model for utility companies that explicitly incorporates a model of end-users’ energy-related decisions, considering a neighborhood energy trading scheme (NETS). The model is formulated based on the Stackelberg game (SG) approach, which guarantees the optimality of the final solution for each user and the utility. The proposed mixed-integer second-order cone programming (MISOCP) problem finds the optimal investment plan for transformers, lines, distributed generators (DGs), and energy storage systems (ESSs) for the utility, considering the scenarios of end-users’ investments in rooftop photovoltaic (PV) and battery systems that maximize their benefits. Additionally, a dynamic network charge (NC) scheme is designed to rationalize the network use. Also, Benders decomposition (BD) is used to improve the convergence of the solution algorithm. The numerical studies on a real 23-bus low voltage (LV) network in Perth, Australia, using real-world data reveals that the proposed planning model offers the lowest total cost and the highest penetration of DERs in comparison with conventional models. Full article

Technology upgrades are a central lever for sustainability, yet many optimization models primarily account for use-phase emissions and treat embodied impacts and technological change exogenously. We propose a multi-period mixed-integer optimization framework that couples upgrade timing, technology choice, and operations with a life-cycle assessment (LCA) structure. The model (i) separates use-phase and embodied impacts at the transition level, (ii) supports time-weighted valuation of impacts through a flexible weighting sequence (time value of carbon), and (iii) incorporates endogenous learning-by-doing that can reduce both investment costs and embodied impacts of future upgrades. We derive an exact Benders (L-shaped) decomposition that separates discrete upgrade dynamics from a linear operating subproblem. Computational experiments illustrate model behavior and report runtimes under an outer-loop implementation with open-source solvers, highlighting that decomposition becomes most beneficial when extensions substantially enlarge the dispatch layer (e.g., scenario expansion). Experiments also show that ignoring embodied impacts can mis-rank upgrade schedules and even violate life-cycle caps, that stronger time-weighting pushes upgrades earlier, and that learning can make staged upgrades economically preferable. Full article

Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically modeled via a set-union operator, have been extensively studied. In the classical framework, an item becomes active once it is covered by at least one chosen meta-item. Motivated by increasing robustness requirements in applications such as automated systems, social networks, and emergency response planning, we extend this setting by introducing threshold-based activation. The resulting generalized problem can be formulated as a mixed-integer nonlinear programming problem, for which we further propose three exact algorithms. The first two methods linearize the utility function using submodular cuts (SC) and outer-approximation (OA) techniques, respectively, resulting in formulations that can be solved exactly by off-the-shelf mixed-integer linear programming solvers. The third method builds upon the OA framework and further employs Benders decomposition (BD) to project out the item-related variables, which enables superior performance on ultra-large-scale instances. Extensive computational experiments show that, compared with the SC and BD methods, the OA method exhibits a substantial speed advantage on instances with a size of around 40,000, which can be solved within 100 s. In contrast, for ultra-large-scale instances with more than 100,000 items, the BD method demonstrates superior computational efficiency. These results provide practical guidance for algorithmic strategy selection and further demonstrate the computational tractability of this broader class of utility maximization problems under threshold-based activation. Full article

With the rapid growth of e-commerce, intra-city express delivery has expanded rapidly, leading to various social issues, such as traffic congestion and air pollution. To address these problems, we focus on designing a multimodal intra-city express system in which parcels are collected from clients via local tours operated by a fleet of identical trucks, temporarily stored in satellite hubs, and then sent to the center hub via underground railway for further sorting and distribution. The problem involves capacitated hub location, client-to-hub allocation, and vehicle routing. Several practical constraints are considered in the routing aspect, including vehicle capacity, time windows, and maximum path length. With these practical considerations, we first formulate a star hub location-routing problem with time windows (SHLRPTW). Second, we use a branch-and-price-and-Benders-cut (BPBC) algorithm to solve it, which combines the Benders decomposition framework and branch-and-price-and-cut (BPC) framework. The BPBC algorithm is tailored, and several acceleration techniques are applied. Third, numerical experiments show that the proposed BPBC algorithm solves more instances and achieves smaller optimality gaps (0.75%) than CPLEX (19.55%) and the pure BPC algorithm (0.83%). The computational times are also critically reduced, with average speed-ups of 74.01 and 5.97, respectively. Furthermore, sensitivity analysis indicates that the BPBC algorithm performs much better than the BPC algorithm when the unit backbone transportation cost is high. Finally, case studies show the usefulness of the proposed model and algorithm. Full article

Due to the non-convex characteristic of the power system, it may be difficult for power generators to recover costs by following the system operators. Therefore, independent system operators have introduced discriminatory supplementary payments as incentive measures. In this context, convex hull pricing serves as an integrated solution, capable of markedly reducing such additional payouts. For the convex hull pricing problem, we propose a distributed solution method. This algorithm is based on Dantzig–Wolfe decomposition and Benders decomposition. According to the characteristics of different units, the model is decomposed into a master problem and a group of independent subproblems, and the consensus ADMM method is used to solve the master problem. The convex hull pricing problem can still be solved using this method when the data is stored separately or when the independent agents responsible for each unit wish to protect their information privacy. While ensuring the confidentiality of each unit’s information, high-quality solutions can still be obtained with high efficiency. By comparing the numerical results with those of the other three convex hull pricing algorithms, it is evident that our algorithm can obtain high-quality solutions. Full article

Under the global imperative for climate action and sustainable development, accelerating the transition towards high-penetration renewable energy systems remains a universal priority, central to achieving the United Nations Sustainable Development Goals. However, the inherent uncertainty and volatility of renewables such as wind and solar PV pose fundamental challenges to power system stability and flexibility worldwide. These challenges, if unaddressed, could significantly hinder the reliable and sustainable integration of clean energy on a global scale. While pumped storage hydropower (PSH) represents a mature, large-scale solution for enhancing system regulation capabilities, existing planning methodologies frequently suffer from critical limitations. These included oversimplified scenario representations—particularly the inadequate consideration of escalating extreme weather events under climate change—and computational inefficiencies in solving large-scale stochastic optimization models. These shortcomings ultimately constrained the practical value of such approaches for advancing sustainable energy planning and building climate-resilient power infrastructures globally. To address these issues, this paper proposed a bi-level stochastic planning method integrating scenario optimization and improved Benders decomposition. Specifically, an integrated framework combining affinity propagation clustering and isolation forest algorithms was developed to generate a comprehensive scenario set that covered both typical and anomalous operating days, thereby capturing a wider range of system uncertainties. A two-layer stochastic optimization model was established, aiming to minimize total investment and operational costs while ensuring system reliability and renewable integration. The upper layer determined PSH capacity, while the lower layer simulated multi-scenario system operations. To efficiently solve the model, the Benders decomposition algorithm was enhanced through the introduction of a heuristic feasible cut generation mechanism, which strengthened subproblem feasibility and accelerated convergence. Simulation results demonstrated that the proposed method achieved a 96.7% annual renewable energy integration rate and completely avoided load shedding events with minimal investment cost, verifying its effectiveness, economic efficiency, and enhanced adaptability to diverse operational scenarios. Full article