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A regional integrated energy system is an important carrier of the energy Internet. It is a major challenge for the operation of a regional integrated energy system to deal with the uncertainty of distributed energy and multiple loads by using the coupling characteristics of equipment in a regional integrated energy system. In this paper, a two-stage robust economic dispatch model of a regional integrated energy system is proposed considering the source-load uncertainty. Firstly, the basic architecture of the regional integrated energy system is introduced. Based on the extreme scenario of uncertain power supply and load, the uncertainty set was established, the two-stage robust optimization model of regional integrated energy system was constructed and the column-and-constraint generation algorithm was used to solve the model. The effectiveness of the two-stage robust optimization model in improving the economy and robustness of the system was analyzed.

This paper addresses the limitations of existing research that focuses on single-sided resources and two-timescale optimization, overlooking the coordinated response of various energy storage resources across different timescales in comprehensive energy systems. To tackle these shortcomings, the study integrates flexible demand-side resources, such as electric vehicles (EVs), hydrogen storage, and air conditioning clusters, as generalized energy storage. It explores their impact on the operation cost of the comprehensive energy system across three stages: day-ahead, intraday, and real-time. The paper establishes an optimization scheduling model for mobile energy storage, hydrogen storage, and virtual energy storage of air conditioning clusters, considering the physical and temporal constraints of different storage devices, aiming to minimize the operational cost. The day-ahead stage employs C&CG to address the uncertainty of wind and photovoltaic power generations, while the intraday stage synergizes hydrogen storage, gas turbines, and demand-side substitutable and transferable loads to mitigate renewable energy fluctuations. The real-time stage leverages the virtual energy storage model of air conditioning clusters for rapid response to renewable energy deviations. Case studies validate the effectiveness of the model, demonstrating that multi-timescale optimization of generalized energy storage in comprehensive energy systems can significantly reduce operational costs and enhance system reliability.

High intermittence of renewable energy resources (RESs) and restriction for greenhouse gas (GHG) emissions have significantly challenged the operations of traditional diesel generator (DG) based microgirds. This paper considers an emission-free microgid with hybrid hydrogen-battery energy storage (HHBES) and proposes a coordinated operational strategy to minimize its daily operation costs. In addition to the electricity purchase costs in the day-ahead market and the operational costs of RESs, the total degradation cost of HHBES is also included in the cost calculation. The proposed operational strategy consists of two coordinated stages. At the day-ahead stage, the schedule for the tie-line power is exchanged with the main grid, the output power of the fuel cell (FC) and the input power of the electrolysis device (ED) are optimized under the worst case of uncertain power output from RESs and power demand from electricity loads (ELs). At the intra-day stage, the battery power is determined according to the short-term prediction for the power of RESs and ELs. The problem is formulated as a robust optimization model and solved by a two-level column-and-constraint-generation (C&CG) algorithm. Numerical simulations using Australian energy market operator (AEMO) data are carried out to validate the effectiveness of the proposed strategy.

This work presents two solution methods for the m-machine robust permutation flow shop problem with processing time uncertainty. The goal is to minimize the makespan of the worst-case scenario by utilizing an approach based on budgeted uncertainty, in which only a subset of operations will reach their worst-case processing time values. To obtain efficient solutions to this problem, we first extend an existing two-machine worst-case procedure, based on dynamic programming, generalizing it to m machines. The worst-case calculation is then incorporated into two proposed solution methods: an exact column-and-constraint generation algorithm and a GRASP metaheuristic. Based on experiments with four sets of literature-based instances, empirical results demonstrate the ability of the GRASP to efficiently produce an optimal or near-optimal solution in most cases.

Hydrogen energy is developing rapidly, and the hydrogen-based integrated energy system (HIES) offers improved economic performance, flexibility, and environmental benefits compared with conventional power systems. However, the increasing frequency of natural disasters caused by climate change introduces significant vulnerabilities that threaten system security. Preventive scheduling provides a proactive and economical means to enhance system resilience against such uncertainties. This paper proposes a preventive scheduling model for HIES based on adaptive robust optimization (ARO) to address the uncertain impacts of natural disasters on transmission lines, pipelines, and roads. The model incorporates the operational constraints and interdependencies among multiple energy subsystems and integrates flexible scheduling strategies such as power-to-hydrogen-and-heat (P2HH) and hydrogen transportation (HT). A hybrid algorithm is developed to efficiently solve the large-scale ARO problem with numerous integer variables. Case studies performed on two test systems demonstrate that the proposed preventive scheduling model effectively reduces operational costs and load curtailments. Simulation results show that coordinating P2HH and HT reduces power, heat, hydrogen, and gas load curtailments by 14.35%, 43.39%, 49.97%, and 40.32%, respectively, as well as operational costs by 14.60%. Moreover, the proposed hybrid algorithm enhances computational efficiency, reducing solution time by 21% with only a 2% deviation from the solution obtained by the conventional C&CG–AOP algorithm.

To further investigate the complementary characteristics among subsystems of the combined electricity–gas–heat system (CEGHS) and to enhance the renewable energy accommodation capability, this study proposes a comprehensive optimization scheduling framework. First, an optimization model is developed with the objective of minimizing the total system cost, incorporating key coupling components such as combined heat and power units, gas turbines, and power-to-gas (P2G) facilities. Second, to address the limitations of traditional robust optimization in managing wind power uncertainty, a distributionally robust optimization scheduling model based on Hausdorff distance is constructed, employing a data-driven uncertainty set to accurately characterize wind power fluctuations. Furthermore, to tackle the computational challenges posed by complex nonlinear equations within the model, various linearization techniques are applied, and a two-stage distributionally robust optimization approach is introduced to enhance solution efficiency. Simulation studies on an improved CEGHS system validate the feasibility and effectiveness of the proposed model, demonstrating significant improvements in both economic performance and system robustness compared to conventional methods.

Aiming at the uncertainty in load demand and wind-solar power output during multi-energy virtual power plant (VPP) scheduling, this paper proposes a robust optimal scheduling method incorporating incentive-based demand response (IDR). By integrating robust optimization theory, a ladder-type carbon trading mechanism, and IDR compensation strategies, a comprehensive scheduling model is established with the objective of minimizing the operational cost of the VPP. To enhance computational efficiency and adaptability, we propose a hybrid approach that combines the Column-and-Constraint Generation (C&CG) algorithm with Karush–Kuhn–Tucker (KKT) condition linearization to transform the robust optimization model into a tractable form. A robustness coefficient is introduced to ensure the adaptability of the scheduling scheme under various uncertain scenarios. The proposed framework enables the VPP to select the most economically and environmentally optimal dispatching strategy across different energy vectors. Extensive multi-scenario simulations are conducted to evaluate the performance of the model, demonstrating its significant advantages in enhancing system robustness, reducing carbon trading costs, and improving coordination among distributed energy resources. The results indicate that the proposed method effectively improves the risk resistance capability of multi-energy virtual power plants.

Rolling stock needs regular maintenance in a maintenance facility. Rolling stock from different fleets are routed to maintenance facilities by interchanging the destinations of trains at common stations and by using empty drives. We consider the problem of locating maintenance facilities in a railway network under uncertain or changing line planning, fleet planning, and other uncertain factors. These uncertainties and changes are modeled by a discrete set of scenarios. We show that this new problem is NP-hard and provide a two-stage stochastic programming and a two-stage robust optimization formulation. The second-stage decision is a maintenance routing problem with similarity to a minimum cost-flow problem. We prove that the facility location decisions remain unchanged under a simplified routing problem, and this gives rise to an efficient mixed-integer programming (MIP) formulation. This result also allows us to find an efficient decomposition algorithm for the robust formulation based on scenario addition (SA). Computational work shows that our improved MIP formulation can efficiently solve instances of industrial size. SA improves the computational time for the robust formulation even further and can handle larger instances due to more efficient memory usage. Finally, we apply our algorithms on practical instances of the Netherlands Railways and give managerial insights.

Due to the properties of zero emission and high energy density, hydrogen plays a significant role in future power system, especially in extreme scenarios. This paper focuses on scheduling hydrogen tube trailers (HTTs) before contingencies so that they can enhance resilience of distribution systems after contingencies by emergency power supply. The whole process is modeled as a two-stage robust optimization problem. At stage 1, the locations of hydrogen tube trailers and their capacities of hydrogen are scheduled before the contingencies of distribution line failures are realized. After the line failures are observed, hydrogen is utilized to generate power by hydrogen fuel cells at stage 2. To solve the two-stage robust optimization problem, we apply a column and constraint generation (C&CG) algorithm, which divided the problem into a stage-1 scheduling master problem and a stage-2 operation subproblem. Finally, experimental results show the effectiveness of enhancing resilience of hydrogen and the efficiency of the C&CG algorithm in scheduling hydrogen tube trailers.

The increasing interdependency of electricity and natural gas systems promotes coordination of the two systems for ensuring operational security and economics. This paper proposes a robust day-ahead scheduling model for the optimal coordinated operation of integrated energy systems while considering key uncertainties of the power system and natural gas system operation cost. Energy hub, with collocated gas-fired units, power-to-gas (PtG) facilities, and natural gas storages, is considered to store or convert one type of energy (i.e., electricity or natural gas) into the other form, which could analogously function as large-scale electrical energy storages. The column-and-constraint generation (C&CG) is adopted to solve the proposed integrated robust model, in which nonlinear natural gas network constraints are reformulated via a set of linear constraints. Numerical experiments signify the effectiveness of the proposed model for handling volatile electrical loads and renewable generations via the coordinated scheduling of electricity and natural gas systems.