CPLEX Solver Research Articles

A three-level model for integration of hydrogen refuelling stations in interconnected power-gas networks considering vehicle-to-infrastructure (V2I) technology

The coupling with natural gas networks creates an excellent opportunity for renewable-rich power systems to facilitate the utilisation of renewable energy resources; on the other hand, with the increase in employment of fuel cell vehicles (FCVs), the number of hydrogen refuelling stations (HRSs) is increasing. The integration of HRSs in electric distribution systems may impact the operation of electric distribution systems. Through vehicle-to-infrastructure (V2I) technology, vehicles may exchange information with HRSs and know hydrogen prices. The operation of the coupled power and natural gas networks with integration of green HRSs, considering the model of FCVs has not been investigated in the literature, so, it has been set as the goal of this paper. To avoid the challenges of nonlinear gas flow model, they are linearized through piecewise linearisation. The case study is a 33-bus electric distribution system, coupled with a 14-node gas distribution network; each HRS includes a battery, a hydrogen tank, an electrolyzer, a PV and a wind turbine. MILP models have been used for FCVs, HRSs and power-gas networks. CPLEX solver is used for solving the developed MILP models. The results show that the total cost of the coupled electricity-gas network is $760.37 and the refuelling cost of each FCV is $17.30. The results indicate that both electric and hydrogen storage systems enhance the flexibility of HRSs, enabling efficient utilisation of PV modules and wind turbines, so, only in few hours, HRSs need to purchase electricity from electric distribution system; that is why each HRS makes a considerable profit of $519 per day. The achieved results also indicate that the pressure of all gas nodes and gas flow of all pipelines fall within their prespecified range.

Hub production scheduling problem with mold availability constraints

This research delves into a scheduling challenge inherent in the wheel hub casting process, a critical stage in automotive wheel manufacturing. The process involves shaping molten metal into specific wheel hub designs using dedicated molds. Diverse customer demands necessitate a unique mold for each wheel hub design, posing a scheduling challenge due to the limited availability of these expensive and long-lasting molds. There are 2 machines available for casting. Each wheel hub design requires a specific mold. These molds are expensive, long-lasting, and need periodic maintenance. The objective function is to minimize the total time (makespan) to complete all casting jobs. Only one job requiring a specific mold can be processed at a time (due to mold limitations). Molds are unavailable during maintenance periods. The challenge lies in scheduling jobs considering both machine availability and mold constraints to minimize the overall production time. We formulate a mathematical model using mixed integer programming to precisely represent the problem and its constraints. Inspired by the Longest Processing Time (LPT) rule, we propose a heuristic named LRTPT to efficiently schedule jobs on the two machines. For large-scale problems, we employ a novel SIAIS algorithm to find near-optimal solutions effectively. We also present a dedicated branch and bound algorithm specifically tailored to solve smaller-sized instances of the problem. This algorithm leverages two lower bounds and several dominance properties to expedite the search for the optimal solution. To evaluate the effectiveness of our proposed approaches, we conduct a series of comprehensive experiments. The results demonstrate that the branch and bound algorithm significantly outperforms the widely used optimization solver CPLEX for smaller problems. Furthermore, the SIAIS algorithm proves to be more efficient than existing scheduling heuristics.

A learning-driven multi-objective cooperative artificial bee colony algorithm for distributed flexible job shop scheduling problems with preventive maintenance and transportation operations

In recent years, distributed production scheduling problems receive much attention from both scholars and practicers. Nevertheless, existing research on such problems commonly ignores machine maintenance and job transportation operations. This work proposes a distributed flexible job shop scheduling problem with preventative maintenance and transportation operations in consideration of sequence-dependent setup time. First, a mixed integer programming model is formulated to minimize maximum completion time of jobs and maximum workload of factories. Second, a learning-driven multi-objective cooperative artificial bee colony algorithm is developed to deal with the model. A Q-learning-based cooperation strategy between population and obtained non-dominated individuals is devised to strengthen the exploration and exploitation performance. Furthermore, heuristic-based population initialization, crossover operations in employed bee phase and iterated local search methods in onlooker bee phase are specially developed considering the problem characteristics. Finally, the proposed method is compared against three well-known meta-heuristics from existing literature and an exact solver CPLEX by using a set of benchmark instances. The results confirm the competitive performance of the developed model and algorithm for addressing the studied problems.

E-Commerce Delivery Optimization with Bicycle Deliveryman and Dual Autonomous Robots

The rapid growth of e-commerce has led to a surge in package deliveries, particularly during promotional events, resulting in increased workload for deliveryman. To address this challenge, this paper explores traveling salesman problem with bike and two autonomous delivery robots-referred to as 2TSPBR. The robots, each with three different-sized cargo compartments, are responsible for delivering packages of varying sizes. When their inventory is low, they restock from the bicycle’s service points. The Variable Neighborhood Search (VNS) algorithm is employed to generate and optimize delivery routes for the bicycle and robots. The results indicate that the VNS algorithm significantly outperforms the CPLEX solver in terms of computational time, providing rapid convergence to near-optimal solutions. This study demonstrates the efficiency and effectiveness of the proposed VNS algorithm in delivering accurate solutions for the integrated delivery system.

Developing an incentive‐based model for efficient product recovery and reverse logistics

AbstractThis study presents an inventive model aligning with sustainable development goals (SDGs) 11, 12, and 9. SDG 11 emphasizes sustainable urban aspects, SDG 12 centers on responsible consumption, and SDG 9 highlights resilient infrastructure. Focused on enhancing operational profits, the model integrates a robust reverse logistics network and policy framework to ensure safe disposal and environmental preservation. Employing the CPLEX solver software, we evaluated various methodologies, including proximity‐based allocation, set covering problems, p‐median allocation, and capacity‐relaxed models, to maximize profitability and efficiency in battery return systems. Our findings underscored the limitations of conventional proximity‐based methods, emphasizing the necessity of advanced optimization. Scenario 3, utilizing the p‐median problem, emerged as the most profitable, optimizing customer allocation and reducing distance‐related costs. Additionally, our sensitivity analysis highlighted the collection rate parameter's pivotal role in influencing customer behavior and overall system profitability. The study also emphasizes the significance of accessible collection centers, revealing disparities in accessibility across customer zones. These findings call for nuanced analyses to ensure equitable access. Implications include advocating for strategic policies to enhance collection rates, optimize center accessibility, and promote responsible disposal, benefiting policymakers, industry professionals, and environmental stakeholders. Ultimately, this research contributes to sustainable practices, fostering eco‐conscious societies, and accelerating progress toward SDGs.

Global supply chain network design for shelf-life products under uncertainty: a case study of pistachios

PurposeSupply chain management has become critical in today’s globalized environment, with growingly intense competition on the international level. The particular characteristics of modern trade have led companies to globalize and devise increasingly sophisticated supply chains to meet customer demand worldwide. Motivated by the need to address these challenges, we have developed a new model for a global supply chain that incorporates uncertainties in exchange rates, demand fluctuations, and the quantity of produce.Design/methodology/approachThe objective of the proposed model is to maximize supply chain profitability. Our model optimizes several critical decisions in the proposed global supply chain, including the location of domestic and foreign distribution centers, allocating the centers to customers, transportation mode selection, storage temperature, optimal farm purchase quantities, product flows across the network, and the shelf-life of products. Scenario-based stochastic programming approach is employed to account for the inherent uncertainties within the model. A pistachio supply chain is examined as a case study in this article, and the efficiency of the proposed model is demonstrated through computational results.FindingsThe model was solved using the CPLEX solver in GAMS and the results, the Sirjan DDC and Turkey FDC have been selected. In general, 40% of demand for customers from FDC (turkey) and 60% of demand from DDC (sirjan) is provided. Changes in the demand of foreign customers make the net profit more effective than changes in the demand for domestic customers. The decrease in exchange rate decreases the network profit with a higher slope and the increase in exchange rate will increase network profit with a relatively stable slope.Originality/valueWhile research on GSCs for perishable products has been ongoing for several years, the importance of the subject necessitates continued investigation in this area. This paper aimed to address this gap by presenting an optimization model for designing GSCs for perishable products under uncertainty and with various transportation modes. The proposed model was designed with the aim of improving supply chain performance and real-world applicability.

A two‐stage adaptive robust model for designing a reliable blood supply chain network with disruption considerations in disaster situations

AbstractWe consider multi‐period blood supply chain network design in disaster situations that involve blood donor groups, permanent and temporary blood collection facilities, blood banks, and hospitals. We use a discrete scenario set to model the uncertain blood supply and demand, and the unforeseeable disruptions in permanent blood collection facilities, blood banks, and road links arising from a disaster, where instead of complete failure, disrupted permanent blood collection facilities and blood blanks may only lose part of their capacities. To design a reliable blood supply network to mitigate the possible disruptions, we present a two‐stage adaptive robust model that integrates the location, inventory, and allocation decisions incorporating a blood sharing strategy, where blood can be delivered from a disrupted/non‐disrupted blood bank to disrupted blood banks to enhance the flexibility of the relief network. For this novel problem, we devise an exact algorithm that integrates column‐and‐constraint generation and Benders decomposition and introduce several non‐trivial acceleration techniques to speed up the solution generation process. We conduct extensive numerical studies on random data sets to evaluate the algorithmic performance. We also conduct a case study in Tehran to demonstrate its real‐life applicability and examine the impacts of key model parameters on the solutions. The numerical results verify the benefits of our model over typical benchmarks, that is, deterministic and stochastic models, and the superiority of our solution algorithm over the CPLEX solver and two well‐known solution approaches, that is, column‐and‐constraint generation and Benders decomposition. Finally, based on the numerical results, we derive managerial insights from the analytical findings.

Mixed-integer programming models for a multi-period integrated reverse logistics network with multiple recovery options and different quality levels of returns

This paper addresses an integrated reverse logistics (RL) model with a production route and multiple recovery options, including repair, refurbishing, remanufacturing, recycling, and selling spare components. We aim to use the quality grading system method to analyse returns comprehensively. In this regard, quality levels are used to classify returns and quality thresholds are utilised to categorise them into certain quality groups. The proposed model deals with different activities such as locating, purchasing, transporting, processing, inventory holding, recovering, and production in a planning horizon with multiple periods. A two-stage optimisation model is proposed to facilitate the decision-making process. In Stage 1, a mixed integer linear programming (MILP) model is proposed to minimise the costs and determine the number of returned products directed into different recovery routes. In Stage 2, another MILP is proposed to maximise the network’s profit. Furthermore, 350 scenarios are defined to examine the network’s performance and decide the optimal quality thresholds. Finally, the proposed models are applied to a real dataset and solved by the CPLEX solver through Pyhton. According to the results, scenarios that use multiple recovery options earn higher profits and lower costs as most demands are satisfied and the stock level of inventories decreases.

Global Optimization and Quantitative Assessment of Large-Scale Renewables-Based Hydrogen System Considering Various Transportation Modes and Multi-Field Hydrogen Loads

In the past, hydrogen was mostly produced from fossil fuels, causing a certain degree of energy and environmental problems. With the development of low-carbon energy systems, renewable energy hydrogen production technology has developed rapidly and become one of the focuses of research in recent years. However, the existing work is still limited by small-scale hydrogen production systems, and there is a lack of comprehensive research on the whole production-storage-transportation-utilization hydrogen system (PSTUH2S), especially on the modeling of different hydrogen transportation modes and various hydrogen loads in different fields. To make up for these deficiencies, the specific physical and mathematical models of the PSTUH2S are firstly described in this paper, with a full account of large-scale water-electrolytic hydrogen production from renewable power curtailment and grid power, various hydrogen storage and transportation modes, and multi-field hydrogen consumption paths. Furthermore, to achieve the maximum economic, energy, and environmental benefits from the PSTUH2S, a multi-objective nonlinear optimization model is also presented herein and then solved by the hybrid method combining the nonlinear processing method, the CPLEX solver and the piecewise time series production simulation method. Lastly, case studies are conducted against the background of a region in northwest China, where hydrogen consumption capacity in various years is accurately assessed and the potential advantages of the PSTUH2S are demonstrated. As the simulation results show, the power curtailment of renewable energy generation can be reduced by 3.61/11.87/14.72 billion kW·h in 2025/2030/2035, respectively, thus contributing to a 4.98%~10.09% increase in the renewable energy consumption rate and millions of tons of carbon emission reduction in these years. In terms of the total equivalent economic benefits, the proposed method is able to bring about a cost saving of USD 190.44 million, USD 634.66 million, and USD 865.87 million for 2025, 2030, and 2035, respectively.

Integrated scheduling of multi-constraint open shop and vehicle routing: Mathematical model and learning-driven brain storm optimization algorithm

Recent years have witnessed a surge of interest in integrated production and distribution scheduling problems which can achieve an overall optimization of the production and distribution activities. However, integrated scheduling of open shop and distribution receives rare attention in existing studies. This work proposes an integrated scheduling problem of multi-constraint open shop and vehicle routing to minimize maximum completion time, where group and transportation operations are considered together in the production process. All jobs are divided into multiple groups, and then handled in an open shop with multiple machines. Subsequently, the jobs are delivered to their corresponding customers. First, a mixed integer programming model is formulated to define the problem. Second, a Q-learning-driven brain storm optimization algorithm is developed to address the formulated model. A Q-learning method is employed to choose search strategies for generating new individuals rather than using fixed probability parameters straightforwardly as basic brain storm optimizers. In addition, the solution encoding, heuristic decoding, population initialization, clustering, new individual generation and selection methods are specially devised in consideration of problem-specific knowledge. At last, the developed model and algorithm are verified by addressing a set of benchmark instances, and comparison experiments are conducted with an exact solver CPLEX and four meta-heuristics from existing literature. The results validate the competitive advantages of the formulated model and algorithm in solving the considered problems.

A location-production-routing problem for distributed manufacturing platforms: A neural genetic algorithm solution methodology

Additive Manufacturing (AM) enhances the flexibility of manufacturing networks. In this paper, we present a Location-Production-Routing (LPR) problem designed for a distributed manufacturing platform, where the manufacturing facilities are distributed in different locations with the support of AM technologies. The proposed LPR problem encompasses three different types of decisions: location-allocation, production planning, and product delivery routing decisions. This is one of the first studies that analyzes integrated logistics and manufacturing optimization under distributed and resilient manufacturing platforms. To efficiently solve the complex problem, we design a novel solution method called the Neural Genetic Algorithm (NGA). The numerical experiments show that the proposed method can attain near-optimal solutions, achieving an average gap of 3% with a standard deviation of 1.4% and a 99% improvement in computational time compared to the CPLEX solver. The sensitivity analysis illustrates the high impact of the unit shortage cost on the customer service level and on the distribution of the AM facilities. Moreover, our results for a given instance show that through the periodic reconfiguration of AM supply chains using the proposed LPR model, we can achieve an average cost reduction of up to 25% in the supply network.

Finding and exploring promising search space for The 0–1 Multidimensional Knapsack Problem

The 0–1, Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0–1 MKP. It maintains a set of solutions and utilizes the information from the population to extract good partial assignments. To find high-quality solutions, an exact algorithm is applied to explore the promising search space specified by the good partial assignments. The new solutions are used to update the population. Thus, the good partial assignments evolve towards a better direction with the improvement of the population. Extensive experimentation with commonly used benchmark sets shows that our algorithm outperforms the state-of-the-art heuristic algorithms, TPTEA and DQPSO, as well as the commercial solver CPlex. It finds better solutions than the existing algorithms and provides new lower bounds for 10 large and hard instances.

Operation strategy for community integrated energy system considering source–load characteristics based on Stackelberg game

Instability in supply and demand, coupled with conflicting market interests, significantly impacts the operational efficiency, reliability, cost-effectiveness, and environmental sustainability of integrated energy systems. To address this issue, an operation strategy for a community integrated energy system based on Stackelberg game theory is proposed, taking into account the characteristics of supply and load. Initially, a master–slave game model for an integrated energy system is established, with energy marketer acting as leader and energy supplier and load aggregator as followers. To manage the uncertainties of wind and photovoltaic power generation, robust optimization theory is employed to construct models for both the short-term and long-term output errors of wind and photovoltaic power generation. This approach allows for a more detailed analysis of the uncertainty associated with wind and photovoltaic power generation. Subsequently, the uniqueness of the equilibrium in the established Stackelberg game model is proven. Utilizing an improved adaptive differential evolutionary algorithm in conjunction with the CPLEX solver, not only is the optimal solution solved for, but also the efficiency of the solution scheme is significantly enhanced. The simulation results demonstrate that the strategy not only boosts the reliability of the integrated energy system but also achieves a cost saving of 1.11%, an increase in energy supplier profit of 5.16%, and a load aggregator consumer surplus of 19.68%. In scenarios considering errors in wind and photovoltaic predictions, the cost savings reach 16.95%, with energy seller and supplier profits improving by 9.34% and 32.47% respectively, and consumer surplus increasing by 18.81%.

Operation Optimization of Regional Integrated Energy Systems with Hydrogen by Considering Demand Response and Green Certificate–Carbon Emission Trading Mechanisms

Amidst the growing imperative to address carbon emissions, aiming to improve energy utilization efficiency, optimize equipment operation flexibility, and further reduce costs and carbon emissions of regional integrated energy systems (RIESs), this paper proposes a low-carbon economic operation strategy for RIESs. Firstly, on the energy supply side, energy conversion devices are utilized to enhance multi-energy complementary capabilities. Then, an integrated demand response model is established on the demand side to smooth the load curve. Finally, consideration is given to the RIES’s participation in the green certificate–carbon trading market to reduce system carbon emissions. With the objective of minimizing the sum of system operating costs and green certificate–carbon trading costs, an integrated energy system optimization model that considers electricity, gas, heat, and cold coupling is established, and the CPLEX solver toolbox is used for model solving. The results show that the coordinated optimization of supply and demand sides of regional integrated energy systems while considering multi-energy coupling and complementarity effectively reduces carbon emissions while further enhancing the economic efficiency of system operations.

A dynamic reconfiguration model and method for load balancing in the snow-shaped distribution network

The snow-shaped distribution network (SDN) is a cable distribution network composed of eight (or six) 10 kV feeders from four (or three) substations in a regular connection. Compared with the traditional 10 kV distribution network, SDN can support a wide range of load transfer among six or eight feeders. Aiming at the problem of load spatial-temporal unbalanced condition caused by the integration of distributed generators (DGs) and different load types in different feeders, this paper proposes a dynamic reconfiguration strategy for load balancing in SDN considering DGs and energy storage system (ESS). Firstly, the basic structure of SDN is analyzed and the power flow model for its dynamic reconfiguration is developed. Secondly, the dynamic reconfiguration optimization model for load balancing in SDN considering DGs and ESS is proposed to utilize the load transfer capability to mitigate the load unbalanced condition and reduce active power loss. Thirdly, the original non-convex model is converted into a mixed-integer second-order cone programming (MISOCP) model by applying the second-order cone relaxation and the big-M method, which is solved by CPLEX solver. Finally, the effectiveness of the proposed model and method are verified by an actual case in Tianjin and IEEE 33-node system. The analysis results show that the proposed method can significantly alleviate the load unbalanced spatial-temporal distribution and improve the economic efficiency by regulating the operation of SDN including ESS optimization and dynamic reconfiguration.

Balancing Possibilist-probabilistic risk assessment for smart energy hubs: Enabling secure peer-to-peer energy sharing with CCUS technology and cyber-security

This paper introduces the Possibilistic-Probabilistic Risk-based Smart Energy Hub (PPR-SEH) scheduling model, addressing cybersecurity challenges in the transition to advanced energy systems characterized by decarbonization, decentralization, and digitalization. The model integrates cutting-edge technologies like Carbon Capture Utilization and Storage (CCUS) and demand response programs. It addresses uncertainties from renewable energy sources, demand variability, fuel supply, and energy price fluctuations using a Z-number-based approach. Covering various energy types—electricity, heat, cooling, gas, and water—the PPR-SEH model offers a comprehensive energy management solution. Employing a mixed-integer linear programming (MILP) framework optimized with the CPLEX solver in GAMS software, it uses an epsilon constraint method and a fuzzy satisfying approach for solution selection. The model also evaluates the economic and environmental impacts of peer-to-peer energy-sharing markets linked with carbon emission trading, enhancing the efficiency and sustainability of energy distribution. The findings reveal that incorporating robust cybersecurity measures and integrating demand response and CCUS significantly influence operational efficiency and sustainability, evidenced by an increase in costs and pollution by approximately 11.43 % and 1.8 %, respectively, compared to deterministic approaches. This study underscores the importance of robust planning and the beneficial impact of a carbon system on load curve management and economic returns in smart energy systems.

Blockchain-enabled framework for transactive home energy management with cloud energy storage under uncertainties

In modern paradigm of smart grid, prosumers can trade energy peer-to-peer in a transactive energy market to reduce energy costs and improve energy efficiency. In addition, cloud energy storage (CES) is a type of shared energy storage systems with high economic efficiency that can provide energy storage services for prosumers and become an active player in energy trading. However, transactive energy implementation in power systems has several challenges such as data privacy and security. In existing researches, energy trading mechanisms rely on central authorities, where security and privacy cannot be maintained. Therefore, this paper presents a decentralized stochastic optimization model of transactive energy management based on blockchain in the presence of CES. In this framework, the smart contract based on Alternating Direction Method of Multipliers technique is deployed on the Ganache and Ethereum blockchains, and the YALMIP toolbox along with CPLEX solver handle decentralized optimization in the MATLAB software. The numerical results demonstrate that not only the capacity of distributed generations is fully utilized, but also total costs of smart homes are reduced by more than 27%, and the total grid’s delivery power to smart homes is decreased by more than 24% compared to the inflexible scheduling.

Pricing Strategies for Distribution Network Electric Vehicle Operators Considering the Uncertainty of Renewable Energy

In the future, the active load of the distribution network side will be dominated by electric vehicles (EVs), showing that the charging power demand of electric vehicles will change with the change in charging electricity price. With the popularity of electric vehicles in the distribution network, their aggregation operators will play a more prominent role in pricing management and charging behavior, and setting an appropriate charging price can achieve a win–win situation for operators and electric vehicle users. At the same time, the proportion of scenery in the distribution network is relatively high, and the uncertainty of self-output has a certain impact on the pricing strategy of operators and the charging behavior of electric vehicle users, which has become an important research topic. Based on the above background, an EV operator pricing strategy considering the landscape uncertainty is proposed, a Stackelberg game model is established to maximize the respective benefits of operators and EV users, and the two-layer model is further transformed into a single-layer model through the Karush–Kuhn–Tucker (KKT) condition and duality theorem. Finally, the IEEE 33 system is simulated with the CPLEX solver, and the global optimal pricing strategy is obtained. Simulation results prove that electric vehicle operators experience a maximum profit increase of 2.6% due to the impact of maximum capacity of energy storage equipment and the uncertainty of renewable energy output can result in electric vehicle operators losing approximately 20% of their profits at most.

Analyzing effective external interventions for optimizing energy hubs with electric and TS: A numerical study from a network topology perspective

Currently, there has been a notable surge in sabotage targeting critical infrastructures, particularly energy hub systems. External interventions on these infrastructures have significantly affected various loads, including electrical and thermal loads. Considering the significance of cybersecurity in energy hubs, there are high expectations for investigating the role of topology in their measures. The aim of this study is to investigate the impact of cyber sabotage on energy management within the demand sector, with a specific emphasis on the topology of an energy hub system. According to the structure of the desired energy hub that has been mathematically modeled, the CPLEX solver is used as a powerful optimization tool with the mixed integer linear programming (MILP) model, which serves as a framework for optimizing the operation cost of the energy hub. The findings reveal the occurrence of false data injection (FDI) into the real network loads. This inconsistency has led to disruption of energy management in the system. Utilizing considered scenarios, the first of them as the base scenario, representing the system under normal network conditions. The second scenario is modeled an attack vector aimed at the electric load, specifically utilizing FDI tactics with an understanding of the network topology. In the third scenario, attention turns to modeling a thermal load attack vector, utilizing FDI tactics with an understanding of its topology. In the final scenario, the emphasis is placed on designing an FDI-based attack vector that targets electric loads within the network, without prior knowledge of the energy hub's topology. Although in all scenarios where the attack is executed, the measuring devices during peak load indicate values lower than the actual ones, the intensity of the attack on the system is considerable in attacks conducted with knowledge of the energy hub topology. Taking into account the importance of the peak load intervals, the maximum changes in electric load during peak hours in the second scenario are compared to those in the first scenario, attributing them to interventions, representing approximately a 17.4 % difference. Similarly, assuming knowledge of the network topology during peak consumption, the impact of the attack on the thermal loads results in changes of 17.17 %. Additionally, in the fourth scenario compared to the first, the maximum changes in electric load during peak hours are approximately 2 %. In the meantime, the optimal cost has remained consistent across all scenarios, rendering the attacks undetectable to the operator and ultimately demonstrating the effectiveness of the proposed method.

Low-Carbon Economic Dispatch Model of Integrated Energy System Accounting for Concentrating Solar Power and Hydrogen-Doped Combustion

Against the background of carbon peak and carbon neutralization, in order to solve the problem of poor flexibility of integrated energy systems and wind power consumption while improving the potential of hydrogen energy emission reduction, this study proposes an integrated energy system that takes into account the coupling of concentrating solar power (CSP), hydrogen-doped combustion, and power-to-gas (P2G) conversion. Firstly, a mathematical model of a CSP-CHP unit is established by introducing a CSP power station, aiming at the defect of the “heat to power” mode in the CHP system. Secondly, the energy consumption of P2G hydrogen energy production is satisfied by surplus wind power. The utilization stage of hydrogen energy is divided into supply CHP combustion and CO2 methanation, forming a CSP-P2G-HCHP collaborative framework and establishing an IES low-carbon economic dispatch model with CSP-P2G-HCHP. At the same time, the carbon trading mechanism is introduced to constrain the carbon emissions of the system. Finally, an optimization strategy with the minimum sum of the operation and maintenance cost, the energy purchase cost, the wind curtailment cost, and the carbon emission cost as the objective function is proposed, and the CPLEX solver is used to solve and carry out multi-case analysis. The simulation results show that the carbon emissions are reduced by 6.34%, the wind curtailment cost is reduced by 52.2%, and the total cost is reduced by 1.67%. The model takes into account the carbon reduction effect and operating efficiency and effectively improves the new energy consumption capacity.