Search Results (271)

The widespread adoption of renewable energy generation and diversified end-user equipment has significantly enhanced user benefits, attracting sustained attention from the research community. As energy systems become increasingly decentralized, traditional centralized optimization methods struggle to effectively capture the interactions among multiple agents. Achieving efficient interaction between diversified energy devices and load demands has emerged as a key challenge in current research. This study first outlines the system operation architecture and the involved game-theoretic agents, clarifying the roles of all participating entities. Subsequently, optimization models are established for the Virtual Power Plant (VPP) and the user aggregator, respectively, incorporating an integrated electro-thermal demand response mechanism under multi-device scenarios. By analyzing the Stackelberg game between the VPP and end-users, the existence of a unique equilibrium solution for this game is demonstrated. Simulations are conducted on the MATLAB R2021b platform using the YALMIP 20210331 toolbox and the CPLEX solver, with heuristic algorithms applied to further optimize the results. The proposed model effectively balances the interests of both parties while maintaining robust privacy protection for critical data. Full article

Addressing the high investment costs and market revenue uncertainties faced by hydrogen energy storage projects, this study examines the economic implications of green bond financing on their participation in electricity market transactions. A two-level optimization decision model is constructed: the upper level aims to minimize the total cost over the project’s lifetime by optimizing the proportion of green bond financing, while the lower level aims to minimize daily operational costs by optimizing the hydrogen storage system’s charging and discharging strategy. The model comprehensively accounts for factors including medium-to-long-term contracted electricity volumes, tiered carbon pricing, and forecasting errors for wind and solar generation, utilizing the CPLEX solver for optimization. Case study analysis demonstrates that green bonds can substantially reduce financing costs, achieving optimal net present value within a financing share range of 60–80% and a storage capacity range of 1000–2000 MWh. This enhances the full lifecycle economics of hydrogen storage projects, providing theoretical support for integrated ‘financing–investment–operation’ decision-making. Full article

To address the significant scheduling challenges arising from high-penetration renewable integration and coupled multi-energy loads, this study examines the operational scheduling of an integrated energy system (IES) that incorporates system operators, user aggregators, electric vehicles, and other stakeholders. First, the flexibility demand and supply resources in the IES were analyzed, and flexibility indicators were quantified. Subsequently, a multi-objective bi-level optimization model considering flexibility and multi-entity participation was established for the IES’s low-carbon economic dispatch. The upper-level model considered the IES operator’s revenue and system flexibility, incorporating a green certificate carbon trading mechanism, while the lower-level model accounted for user aggregator costs and electric vehicle self-benefits, with interactions between the two levels through energy prices and purchase quantities. Finally, an improved Particle Swarm Optimization (PSO) algorithm was employed to solve the proposed upper-level model, and CPLEX 12.10 software was used for the lower-level model. A typical scenario in northern China was selected to validate the proposed model. The results demonstrated that the proposed model balanced system economy and flexibility compared to the traditional single-objective economic dispatch. Compared with only considering the benefits of operators, the proposed model can balance the interests of multiple parties. Additionally, compared to the traditional PSO algorithm, the improved PSO algorithm reduced the number of iterations at convergence by 52.0%, improved the closeness of the obtained optimal solution to the ideal solution by 7.5%, and had better convergence and optimization performance. Full article

As the composition of energy markets becomes increasingly diverse and distributed in character, it is difficult for traditional vertically integrated energy system (IES) structures and centralized optimization methods to stimulate coupled interactions and interactive synergies among multiple subjects. Consequently, a collaborative low-carbon scheduling strategy utilizing a leader–follower game framework is introduced for the distributed IES. Making the integrated energy system operator (IESO) a leader, distributed integrated energy supply system (DIESS) and smart user terminal (SUT) as followers, the optimal interaction operation strategy of each subject in the game process can be solved. Firstly, the overall energy interaction process of the system and the game objectives of each participant are introduced to construct a distributed collaborative optimization model with one leader and multiple followers. Secondly, the integrated demand response (IDR) and the ladder-type carbon trading scheme are considered, the two-stage operation process of the electrical gas technology (P₂G) equipment is analyzed in detail, and the genetic algorithm nested CPLEX solver is used to solve the model. Finally, the results show that this paper can provide guarantee and theoretical support for the optimal operation of the integrated energy market in terms of trading model and algorithm. Full article

Rural freight mobility and logistics face persistent challenges, including inadequate road infrastructure, high transportation costs, safety risks, tolls at link access points, and dispersed demand. Traditional inventory routing models often fail to address these complexities, especially in rural contexts where alternative routing options and integrated in-haul/back-haul operations are essential for improving efficiency and reducing empty miles. This study proposes a bi-objective mathematical model for the inventory routing problem in rural logistics, incorporating multiple routing attributes (transportation costs, risks, link-access tolls, and distances) and inventory dynamics (integrated in-haul and back-haul visits). The model aims to minimize total logistics costs and accident risk while balancing operational expenses and safety considerations. Risk estimation is derived from crash data along rural road links connecting distribution nodes. A real-world case study involving Walmart distribution centers in Macclenny, Baker County, Florida, and several rural Supercenters is conducted to validate the model. A modified Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is developed and compared with CPLEX for solution efficiency across small and large-scale problem instances. Results indicate that the proposed approach outperforms classical methods, improves routing decisions in rural logistics systems, and achieves cost savings of up to 17% for the evaluated objectives, emphasizing the importance of using multi-attribute, multi-route network structures in rural logistics optimization. Full article

To address the limitation of traditional microgrid operator-led optimization models that compromise user-side benefits, this paper proposes a novel method for the collaborative optimal operation strategy of community-based integrated energy microgrids and diversified flexible resources. The method deeply integrates user-side flexibility resources into the decision-making process. Unlike existing research that only considers electro-heat coupling, our model integrates shared energy storage services into an integrated energy system, reflecting a more realistic future application. A Stackelberg game framework is then established with the microgrid operator (MGO) as the leader and the user aggregator as the follower. The user aggregator optimizes its energy strategy by coordinating user demand response, thereby increasing the profits of both itself and the shared energy storage operator. Meanwhile, this model guides the MGO’s pricing decisions for electricity and heat, balancing interests of all stakeholders. To solve the model, a hierarchical approach that merges the Harris Hawks Optimization algorithm with the CPLEX solver is employed. Finally, simulation results demonstrate that the proposed model and strategy significantly enhance user-side revenue and flexibility, achieve a win-win outcome for the user aggregator and MGO, and lay the foundation for future shared energy storage service providers to participate in market pricing as key game entities. 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

Electric vehicles (EVs) and renewable energy generation are widely regarded as key drivers of low-carbon transformation in the transportation and energy sectors due to their emission reduction potential and environmental benefits. However, the inherent intermittency and volatility of photovoltaic (PV) power, coupled with increasingly stochastic and disorderly EV charging demand, pose significant challenges to grid stability and local renewable energy utilization. To address these issues, this paper proposes a dynamic pricing optimization approach based on a Stackelberg game framework, in which the PV charging station operator acts as the leader and EV users as followers. Unlike conventional models, the proposed framework explicitly incorporates user psychological expectations and response deviations through a three-stage “dead-zone-linear-saturation” responsiveness structure, thereby capturing the uncertainty and partial rationality of EV charging behavior. The upper-level objective seeks to maximize operator profit and enhance PV self-consumption, while the lower-level objective minimizes user energy cost under price-responsive charging decisions. The bilevel optimization problem is solved via a differential evolution (DE) algorithm combined with YALMIP + CPLEX. Simulation results for a regional PV-EV charging station show that the proposed strategy increases PV self-consumption to about 90.5% and shifts the load peak from 18:00–20:00 to 10:00–15:00, effectively aligning charging demand with PV output. Compared with both flat and standard time-of-use (TOU) tariffs, the dynamic pricing scheme yields higher operator profit (about 7% improvement over flat pricing) while keeping total user energy expenditure essentially unchanged. In addition, the cumulative carbon reduction cost over the operating cycle is reduced by approximately 4.1% relative to flat pricing and 1.9% relative to TOU pricing, demonstrating simultaneous economic and environmental benefits of the proposed game-based dynamic pricing framework. Full article

To address the challenges associated with energy decarbonization and economic operation in integrated energy systems (IESs), this paper proposes a collaborative optimal dispatch strategy for IES that considers multiple flexible loads under a carbon trading mechanism. First, a mathematical model of user-side loads is constructed according to the characteristics of flexible loads. Second, a comprehensive optimization framework is constructed by embedding the carbon trading mechanism into the IES operational model. The objective function minimizes the total operating costs, including energy purchase costs, fuel costs, carbon trading costs, operation and maintenance costs, compensation costs, and green certificate revenues. The CPLEX solver is then employed to solve the model. Finally, a case study is conducted to validate the proposed method. Simulation results demonstrate that the carbon trading mechanism effectively leverages the demand response capabilities and coordinates multiple resources, including electricity, heat, and storage, thereby achieving low-carbon economic operation of the system. Full article

Active distribution networks (ADNs) with high DER penetration require coordinated decisions to ensure voltage security, limit losses, and support low-carbon targets. However, most reconfiguration-centric studies prioritize loss/cost and rarely integrate carbon pricing and emission accounting into a unified framework with verifiable optimality. This study develops a DistFlow-based mixed-integer second-order cone programming (MISOCP) model that co-optimizes feeder reconfiguration and resource active/reactive dispatch under a price-calibrated loss–emission objective. The framework coordinates PV/WT generation, MTs, aggregated PHEVs (V2G), and reactive-support devices (SVCs and switched capacitor banks (CBs)) and is solved by commercial CPLEX to global optimality for the SOCP-relaxed problem. On the IEEE 33-bus feeder, device coordination reduces losses from 0.203 MW to 0.0382 MW (81.18%) and CO₂ emissions from 2.3872 to 0.3433 tCO₂ (85.62%), while reducing operating cost from CNY 354.9357 to CNY 56.6271 (84.05%). Enabling reconfiguration further reduces losses to 0.0205 MW (89.90%), emissions to 0.2580 tCO₂ (89.19%), and operating cost to CNY 37.4677 (89.44%), while keeping voltages within 0.99–1.01 p.u. Relative to device-only operation, reconfiguration yields 46.34% loss reduction, 24.85% emission reduction, and 33.83% operating-cost reduction. The mixed-integer optimality gap is ~10⁻⁷, and the solution quality for the original non-convex model depends on the tightness of the SOCP relaxation, which is numerically tight in the cases we studied. These results show interpretable technical and environmental gains via coordinated dispatch and topology control in radial ADNs at scale. Full article

With the increasing penetration of distributed energy resources (DERs) and the rapid development of active distribution networks, the traditional centrally controlled operation mode can no longer meet the flexibility and autonomy requirements under the multi-dimensional coupling of sources, networks, loads, and storage. To achieve regional energy self-balancing and autonomous operation, this paper proposes a partitioned configuration method for energy storage systems (ESSs) in energy-autonomous distribution networks based on autonomous unit division. First, the concept and hierarchical structure of the energy-autonomous distribution network and its autonomous units are clarified, identifying autonomous units as the fundamental carriers of the network’s autonomy. Then, following the principle of “tight coupling within units and loose coupling between units,” a comprehensive indicator system for autonomous unit division is constructed from three aspects: electrical modularity, active power balance, and reactive power balance. An improved genetic algorithm is applied to optimize the division results. Furthermore, based on the obtained division, an ESS partitioned configuration model is developed with the objective of minimizing the total cost, considering the investment and operation costs of ESSs, power purchase cost from the main grid, PV curtailment losses, and network loss cost. The model is solved using the CPLEX solver. Finally, a case study on a typical multi-substation, multi-feeder distribution network verifies the effectiveness of the proposed approach. The results demonstrate that the proposed model effectively improves voltage quality while reducing the total cost by 20.89%, ensuring optimal economic performance of storage configuration and enhancing the autonomy of EADNs. Full article

The increasing popularity of electric vehicles (EVs) as green alternatives to traditional internal combustion engine cars has highlighted the need for sustainable and environmentally friendly supply chain models. In particular, the handling of EV batteries, which are environmentally unfriendly and logistically critical due to their hazardous nature and short life cycle, requires a well-designed closed-loop supply chain (CLSC). This study proposes a new multi-objective optimization model of the CLSC, explicitly tailored to EV batteries under demand and return rate uncertainty. The proposed model incorporates three primary objectives that are typically in conflict with one another: minimizing the total cost, reducing carbon emissions throughout the entire supply chain network, and maximizing the recycling and reuse of batteries. The model employs a neutrosophic goal programming (NGP) methodology to address the uncertainties associated with demand and battery return quantities. The NGP model translates multiple objectives into non-monolithic goals with crisp aspiration levels (i.e., prescribed ideal levels for achieving the best of each goal) and thresholds that capture tolerances, thereby accounting for uncertainty. The efficiency of the proposed method is illustrated by a numerical example, solved using a IBM ILOG CPLEX Optimization Studio 22.1.2 solver. The findings demonstrate that the NGP can offer cost-effective, low-impact, and environmentally friendly solutions, thereby enhancing system robustness and flexibility to adapt to uncertainties. This study contributes to the emerging literature on sustainable operations research by developing a decision-making tool for EV-HV battery supply chain management. It also offers relevant suggestions for policymakers and industrialists who seek to co-optimize economic benefits, ecological sustainability, and logical feasibility in the emerging green society. Full article

In this paper, the generalized quadratic assignment problem (GQAP) is extended to consider multiple time periods and is called the dynamic GQAP (DGQAP). This problem considers assigning a set of facilities to a set of locations for multiple periods in the planning horizon such that the sum of the transportation, assignment, and reassignment costs is minimized. The facilities may have different space requirements (i.e., unequal areas), and the capacities of the locations may vary during a multi-period planning horizon. Also, multiple facilities may be assigned to each location during each period without violating the capacities of the locations. This research was motivated by the problem of assigning multiple facilities (e.g., equipment) to locations during outages at electric power plants. This paper presents mathematical models, construction algorithms, and two simulated annealing (SA) heuristics for solving the DGQAP problem. The first SA heuristic (SAI) is a direct adaptation of SA to the DGQAP, and the second SA heuristic (SAII) is the same as SAI with a look-ahead/look-back search strategy. In computational experiments, the proposed heuristics are first compared to an exact method on a generated data set of smaller instances (data set 1). Then the proposed heuristics are compared on a generated data set of larger instances (data set 2). For data set 1, the proposed heuristics outperformed a commercial solver (CPLEX) in terms of solution quality and computational time. SAI obtained the best solutions for all the instances, while SAII obtained the best solution for all but one instance. However, for data set 2, SAII obtained the best solution for nineteen of the twenty-four instances, while SAI obtained five of the best solutions. The results highlight the effectiveness and efficiency of the proposed heuristics, particularly SAII, for solving the DGQAP. Full article

To address the pressing challenges of low new energy utilization, high power system operating costs, and compromised power supply reliability in regional grids, we propose a multi-time-scale source–storage–load coordinated scheduling strategy that explicitly accounts for the characteristic distribution of grid-connected energy storage stations, including their state-of-charge constraints, round-trip efficiency profiles, and location-specific operational dynamics. A day-ahead scheduling framework is developed by integrating the multi-time-scale behavioral patterns of diverse load-side demand response resources with the dynamic operational characteristics of energy storage stations. By embedding intra-day rolling optimization and real-time corrective adjustments, we mitigate prediction errors and adapt to unforeseen system disturbances, ensuring enhanced operational accuracy. The objective function minimizes a weighted sum of system operation costs encompassing generation, transmission, and auxiliary services; wind power curtailment penalties for unused renewables; and load shedding penalties from unmet demand, balancing economic efficiency with supply quality. A mixed-integer programming model formalizes these tradeoffs, solved via MATLAB 2020b coupled CPLEX to guarantee optimality. Simulation results demonstrate that the strategy significantly cuts wind power curtailment, reduces system costs, and elevates new energy consumption—outperforming conventional single-time-scale methods in harmonizing renewable integration with grid reliability. This work offers a practical solution for enhancing grid flexibility in high-renewable penetration scenarios. Full article

This paper proposes a scheduling approach for multi-type spacecraft operational tasks that can be interleaved, considering constrained space–ground telemetry, tracking, and command (TT&C) resources, as well as task splitting. A mixed-integer linear programming model is formulated to maximize the total task completion reward under service time-window constraints for splittable and unsplittable routine tasks, continuous tracking requirements, coupling relationships between routine and continuous tracking tasks, temporal logic dependencies, visibility constraints, and non-overlapping scheduling conditions. To improve solution efficiency and scheduling performance, a heuristic algorithm that combines priority rules with partial backtracking is developed. Task priorities are determined based on completion rewards, due times, execution durations, and temporal relationships, and scheduling is refined to avoid conflicts with predefined constraints. A partial backtracking mechanism guided by task release times enables effective adjustment when TT&C requirements cannot be satisfied. Comparative experiments with CPLEX and four heuristic algorithms validate the effectiveness of the proposed method. Full article