Mathematical Optimization Model Research Articles

Startup optimization of gas foil bearings-rotor system in proton exchange membrane fuel cells

The startup performance is crucial to the high-efficient operation of the sustainable power generation system. Current literature usually focuses on catalysts and startup strategy to improve startup performance of the proton exchange membrane fuel cell, which ignores the gas foil bearings-rotor system that directly affects startup response. Therefore, in this paper, the effects of bump foil structure, coating, and nominal clearance on the startup response of the bearings-rotor system are first investigated experimentally. Multi-objectives optimization mathematical model considering simultaneously lower power consumption, takeoff speed, and vibration is presented based on grey relational analysis. The optimal bearings-rotor system with radial trisection bump foil, coating MoS2, and nominal clearance of 50 μm is identified. Compared to average values, the power consumption of the optimal system is diminished by 27.2% while the takeoff speed and nonlinear vibration are reduced by 16.2% and 47.3%, respectively. These findings can be used to improve energy efficiency and startup performance for fuel cells. The systematic methodology proposed in this study can be extended to other investigations about the startup.

Designing and Solving two Mathematical Models for the Optimal Distribution of Urban Water Resources

The lack of optimal distribution of water resources in cities with a lack of quality water resources can be a threat to the sustainability of these cities.
 The present study seeks to design a method for urban water distribution among urban districts using two optimization mathematical models applied in Qom Responding to the water needs of the consumption districts was to be carried out with the least distribution costs, towards which end the first mathematical model was designed. Thus, by solving the first model, it will be clear how much water is needed to be transferred from each surface and ground resources that, while considering resources’ limitation of allocation to consumption districts, the needs of the districts are satisfied and the costs of the water company kept at the minimum.
 The scarcity of high-quality water resources in Qom has rendered water allocation from these resources to all consumption districts in the city impossible. On the other hand, urban consumption districts demand the highest-quality water given their predominant fabric (residential, commercial, or industrial). Thus, distribution management must take measures to allocate high-quality water to each district depending on its fabric, to which end the second mathematical model has been designed. Hence, solving the second model would answer the question of whether, by using the mathematical model of water distribution from various resources with different qualities, it would be possible to satisfy citizens’ needs in terms of water quality (so that the quality of the allocated water is higher than the quality demanded by the district) and ensure that optimized resource allocation would take place at minimum costs for the company.

A survey on optimization-based approaches to Dynamic Centralized Group Key management

Abstract—In secure multicast communication, only authorized group members are able to receive the transmitted data. Key generation, distribution, and management are all carried out by a single entity (called the Key Server) in the centralized system. The main challenges of a dynamic centralized group key management scheme include scalability overhead, rekeying overhead, storage overhead, maintaining forward and backward secrecy, etc. Logical Key Hierarchy (LKH), one of the key management methods, uses a tree structure to manage keys to share with participants. Due to the fact that members may join or exit the group at any time during communication, a crucial problem in centralized group key management (CGKM) is minimizing rekeying costs while maintaining a balanced tree. The majority of CGKM methods effectively update the group key by modifying cryptographic techniques or based on logical/heuristic arguments. One of the efficient approaches is based on an optimization model with the two mentioned important objectives. In this paper, we conduct a survey on optimization-based approaches to dynamic CGKM, which can be divided into two categories based on logical/heuristic arguments and a rigorous mathematical optimization model.

Mathematical model for optimization in air traffic scheduling management during the COVID-19 pandemic

In this paper, the object of the study is determining air traffic scheduling management by optimizing mathematical models. The problem in this study is that the COVID-19 pandemic has significantly disrupted air traffic, resulting in changes to regulations, travel restrictions and a decrease in passenger demand. One of the problems that must be resolved is how to organize and adapt flight schedules to current conditions by focusing on mathematical models that are used to optimize or increase the efficiency of managing flight schedules or air traffic. Mathematical models can help find ways to optimize the use of available resources, such as airport capacity, flight routes and flight frequency. The results obtained in this research are a mathematical model that specifically takes into account the variables involved in setting air traffic schedules during the COVID-19 pandemic so that capacity limits at airports and airspace are always normal. An optimization model was developed from previous research, namely the model that takes into account ground and air delays as well as the use of alternative paths and avoids deviations from the initial more accurate flight plan, which overall indicates that the maximum time and maximum distance values for each item have been optimized to achieve better values. This research has the novelty of producing a mathematical model using variables, objective functions, capacity limits, flight structure limits and variable domains, which then produces an algorithm with data input processes, determining optimization models, determining variables, determining objective functions, determining problems. The results of this model can be recommended to airlines in scheduling flights during the pandemic

The Development and Adaptation of a Predictive Model of Full-Factor Optimisation of the Basic Probiotic Fermented Dairy Product Technological Process

Introduction: In the conditions of rapidly developing markets and the increasing needs of the population for new types of products with long shelf life, there is a need to expand their range, further improve their quality and biological value, and modernize traditional technologies. The main means of achieving these goals is to increase the efficiency and quality of scientific research and accelerate the introduction of scientific achievements in industry. The latter will make adjustments to accelerate the development of effective technologies of whole-milk products. The use of new methods of experiment planning in order to optimize technological processes will reduce the duration of research on the creation of new types of products.Purpose: The article is devoted to the research related to the development and adaptation of a predictive (mathematical) model for optimization of the technological process of probiotic fermented dairy product production. This approach will allow to ensure the design of a certain set of formulations for probiotic fermented dairy product, in which the relative biological value (RBV) will correspond to the maximum value at satisfactory given process parameters.Materials and Methods: The objects of research were: probiotic fermented dairy product manufactured in accordance with the developed mathematical model of the process. The search of specialized literature was carried out using electronic databases: E-library, Scopus, MDPI, Science Direct. Mathematical processing of experimental data for the development of the probiotic fermented dairy product model was carried out using Microsoft Excel 2010 (Microsoft Corporation, Ink.) with the "Solution Search" add-in, as well as specialized software packages TableCurve 2D v.5.01 (SYSTAT Software, Ink.) and Wolfram Mathematica 10.2 (Wolfram Research, Ink.).Results: A mathematical model for optimization of the technological process of probiotic fermented dairy product production was developed. A full-factor experiment (FFE) was conducted, in which the mass fraction of sucrose ( , %) and fat-protein index (r) - the ratio of the mass fraction of fat to the mass fraction of protein in the normalized mixture in the intervals from 0 to 10 and from 0 to 1.5%, respectively, were taken as independent factors. RBV was taken as the resultant factor. Based on the results of the research, a refined mathematical description of the dependence of RBV indicator on the mass fraction of sucrose and fat-protein index was obtained. The set of data on the influence of the mass fraction of sucrose on the dynamics of local maximum of RBV and the dynamics of the corresponding values of the mass fraction of fat showed that the maximum of RBV equal to 244.866% corresponded to the mass fraction of sucrose equal to 7.31%. The latter corresponded to the optimum fat-protein index of 1.241. In order to ensure maximum RBV, the lower limit of the mass fraction of fat had to correspond to 3.475%. The analysis of the FFE data showed the presence of additional corrective factors of RBV indicator dependence on fat and protein mass fraction indices. To refine the developed model taking into account additional factors, a correction factor (Q) was introduced into it.Conclusion: Approbation of the optimization model of the technological process of probiotic fermented dairy product production and the obtained mathematical dependencies can serve as a criterion for the formation of a set of formulations for the production of sugar-containing fermented dairy products with a high potential of relative biological value. It should be taken into account that the definition area of this approach is limited in terms of mass fraction of fat in the range from 0.06 to 4.84% and mass fraction of protein - from 2.8 to 3.9%. With this approach (model development) it is possible to analyze promising modes for the studied process, which in real conditions at the experimental stage are not always possible to obtain. The development of this model will significantly reduce the duration of research on the optimization of the technological process.

Multi-Objective Optimization of a Long-Stroke Moving-Iron Proportional Solenoid Actuator.

In this study, the performance of a long-stroke moving-iron proportional solenoid actuator (MPSA) was improved by combining numerical simulations and experiments. A finite element model of the MPSA was developed; its maximum and mean relative absolute errors of electromagnetic force were 4.3% and 2.3%, respectively, under typical work conditions. Seven design parameters including the cone angle, cone length, depth of the inner hole of the coil skeleton, cone width of the armature, inner cone diameter, and initial position of the moving-iron core were selected for developing the model, and the coefficient of the variation in electromagnetic force, nominal acceleration, 95% of the maximum stable output electromagnetic force, and corresponding response time were used as the performance indicators. The constraint relation between each performance indicator and the influence of each design parameter on the performance indicators were revealed using the uniform Latin hypercube experiment design, correlation analysis, and the main effect analysis method. A multi-objective optimization mathematical model of the MPSA was developed by combining traditional surrogate and machine learning models. The Pareto solution set was obtained using the nondominated sorting genetic algorithm II (NSGA-II), and three decision schemes with different attitudes were determined using the Hurwicz multi-criteria decision-making method. The results showed that a strong contradiction exists among the 95% of the maximum stable output electromagnetic force and its corresponding response time and the coefficient of the variation in electromagnetic force. The cone angle considerably influenced the performance indicators. Compared with the initial design, the coefficient of the variation in electromagnetic force was reduced by 54.08% for the positive decision, the corresponding response time was shortened by 15.65% for the critical decision, and the corresponding acceleration was enhanced by 10.32% for the passive decision. Thus, the overall performance of the long-stroke MPSA effectively improved.

Efficient computational strategies for a mathematical programming model for multi-echelon inventory optimization based on the guaranteed-service approach

This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time.

Peculiarities of truck transportation in wartime conditions

Purpose. To identify the peculiarities and problems of automobile transport (AT) in the war conditions (WC) in Ukraine. To propose ways to solve the mentioned problems, to eliminate reasons that lead to an increase in the risks for AT. To develop a mathematical model for optimization of transportation by AT under unclear military risks. Methodology. The method of abstract-logical analysis made it possible to establish peculiarities and problems of AT in WC and propose ways to solve these problems, to eliminate the causes that lead to increase in risks of AT. The method of analysis and synthesis is used to determine the circumstances of the narrowing of the influence of institutional approaches on the optimization of AT and to propose a combination of direct and indirect institutional influence. The method of comparative analysis finds that the unevenness of risks on transport routes leads to the imbalance of transportation and proposes measures to reduce the level of imbalance, to approach optimal results as well as proposes the formation of multi-stage transportation, which will ensure the variability of transport chains due to fragmentation and an increase in the level of organization of transport networks. Mathematical methods were applied to develop a model for optimization of AT in WC. Findings. The key tasks of building a strategy of a highly adaptive transport system were formulated and its peculiarities were indicated. Circumstances of narrowing the influence of institutional approaches to AT in WC were established and a combination of direct and indirect institutional influence was proposed, which will be based on the developed mathematical model. It is established that unevenness of risks on transport routes leads to imbalance of transportation and measures to reduce the imbalance are proposed. The formation of multi-stage transportation is proposed for variability of transport chains, organization of transport networks and ensuring the reliability of AT. Originality. To take into account risks with a significant level of uncertainty, a strategy for building a highly adaptive transport system was proposed, and a mathematical model for optimization of AT in the presence of uncertain military risks was developed. Practical values. The peculiarities and problems of AT in the conditions of the war in Ukraine are given. Ways to solve the mentioned problems, to eliminate the causes that lead to increase in risks for AT are proposed.

Mathematical optimization of the sustainable gasoline supply chain: systematic literature review

Purpose The purpose of this paper is to review studies on mathematical optimization of the sustainable gasoline supply chain to help decision-makers understand the current situation, the exact dimensions of the problem and the models provided in the literature. So, a more realistic mathematical optimization model can be achieved by fully covering all dimensions of the supply chain of this product. Design/methodology/approach To evaluate and comprehend the mathematical optimization of the sustainable gasoline supply chain research area, a systematic literature review is undertaken that covers material collection, descriptive analysis, content analysis and material evaluation steps. Finally, based on this process, 69 related articles were carefully investigated. Findings The results of the systematic literature review show the main areas of the published papers on mathematical optimization of sustainable gasoline supply chain problems and the gaps for future research in this field presented based on them. Research limitations/implications This approach is subject to limitations because the protocol of the systematic review of the research literature only included searching for the considered combination of keywords in the Scopus and ProQuest databases. Furthermore, the protocol used in this paper restricts documents to English. Practical implications The results have significant implications for both academicians and practitioners in this field. It can be useful for academics to comprehend the gaps and future trends in this field. Also, for practitioners, it can be useful to identify and understand the parts of the mathematical optimization model, which can help them model this problem effectively and efficiently. Originality/value No systematic literature review has been done in this field by considering gasoline to the best of the authors’ knowledge and delivers new facts for the future development of this field.

Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model

Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and the maintenance workshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon. We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.

Design optimization for pressurized water reactor using improved quantum fish swarm algorithm and intuitionistic linguistic decision-making

Nuclear power has garnered significant attention as a clean energy resource in expediting carbon peaking and achieving carbon neutrality. It contributes to sustainable economic growth while addressing national energy security concerns. As one of the most crucial components, pressurized water reactors require improvements in several key aspects, including strengthening the natural circulation capacity, increasing the reactor power, and reducing the reactor volume. However, the volume of pressurized water reactors is usually positively correlated with their power. Increasing the reactor power results in an expansion of its volume, which poses challenges for the reactor layout and also requires additional investment. Hence, in order to reduce the reactor volume while meeting its performance requirements, this study introduces a novel design optimization approach utilizing an improved quantum fish swarm algorithm and intuitionistic linguistic decision-making. Firstly, a nonlinear mathematical model for volume optimization of the steam generator (SG) and pressurizer (PR) is constructed. Then, the improved quantum fish swarm algorithm is proposed to obtain volume optimization alternatives for the SG and PR. Quantum computation strategies are introduced to enhance the global optimization ability and population diversity. Additionally, the vision range and step size of the quantum fish swarm are adjusted adaptively to improve the optimization precision. To further accelerate the algorithm convergence, the prospect-elimination strategy is built. Last but not least, the intuitionistic linguistic decision-making is presented to gain the optimal design alternative by taking four characteristics into account, namely, the fuzziness and hesitancy of evaluation information, the consensus reaching process, the bounded rationality of decision-making behaviors, and the complementarity, independence and redundancy among nuclear evaluation criteria. A case study on the SG and PR design optimization is implemented to demonstrate the reliability and reasonability of the proposed approach.

Setting Optimization of Distribution Network Current Protection Based on Constrained Multi‐Objectives Backbone Particle Swarm Optimization

With the increase in residential electricity consumption, the number of branch lines connected to the 10 kV main line and the load all increase. When the main line is segmented into several shorter lines, the current protections of these lines are difficult to coordinate with each other. This condition may cause the number of protection mal‐operation increases, the power outage scope expands, and the reliability of the power supply decreases. Therefore, this paper studies the setting optimization method of distribution network current protections. First, a mathematical model of protection setting optimization is established with three objective functions keeping the fault clearing time minimal, the protection sensitivity highest, and the outage load minimal. Some constraints are considered, such as the cooperation between the protections of the adjacent lines. Second, the multi‐objective backbone particle swarm optimization algorithm is used. The problems of the traditional particle swarm optimization algorithm that lacks population diversity and easily falls into local optimization are solved by adopting the time‐varying variation and linear decreasing dynamic allocation strategy. Finally, the K‐means clustering algorithm is used to get the most representative optimal solution providing a variety of feasible solutions for the practical application. This paper takes a 10 kV line as an example to test the setting optimization method and compares the optimized settings with the traditional ones. The results show that the setting optimization method based on the constrained multi‐objective backbone particle swarm can effectively reduce the protection mal‐operations and improve the overall performance of distribution network protections. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Towards Sustainable Integration: Techno-Economic Analysis and Future Perspectives of Co-Located Wind and Hydrogen Energy Systems

Abstract This article presents a comprehensive study that focuses on the techno-economic analysis of co-located wind and hydrogen energy integration within an integrated energy system (IES). The research investigates four distinct cases, each exploring various configurations of wind farms, electrolyzers, batteries, hydrogen storage tanks, and fuel cells. To obtain optimal results, the study employs a sophisticated mathematical optimization model formulated as a mixed-integer linear program. This model helps determine the most suitable component sizes and hourly energy scheduling patterns. The research utilizes historical meteorological data and wholesale market prices from diverse regions as inputs, enhancing the study’s applicability and relevance across different geographical locations. Moreover, sensitivity analyses are conducted to assess the impact of hydrogen prices, regional wind profiles, and potential future fluctuations in component prices. These analyses provide valuable insights into the robustness and flexibility of the proposed IES configurations under varying market conditions and uncertainties. The findings reveal cost-effective system configurations, strategic component selections, and implications of future energy scenarios. Specifically comparing to configurations that only have wind and battery combinations, we find that incorporating an electrolyzer results in a 7% reduction in the total cost of the IES, and utilizing hydrogen as the storage medium for fuel cells leads to a 26% cost reduction. Additionally, the IES with hybrid hydrogen and battery energy storage achieves even higher and stable power output. This research facilitates decision-making, risk mitigation, and optimized investment strategies, fostering sustainable planning for a resilient and environmentally friendly energy future.

A mathematical optimization model for determining safety integrity levels in process facilities

In process industries, Safety Instrumented Functions (SIFs) are implemented to meet government-mandated risk tolerance criteria, which aim to ensure the safety of both individuals and society. The level of risk reduction achieved by a SIF is quantified by its Safety Integrity Level (SIL). Determining the target SILs is a challenging task for facility owners as they must balance the costs and benefits of risk reduction while complying with regulatory requirements. Furthermore, governments define risk tolerance criteria for an overall facility rather than for single scenarios. Therefore, determining a set of SILs for all SIFs becomes imperative to collectively reduce both individual and societal risks to tolerable levels intended for the overall facility. In this paper, we propose a mathematical optimization model to determine the most beneficial collection of SILs that guarantees meeting the risk tolerance criteria. Our model considers both individual and societal risk perspectives and effectively models an overall facility. The proposed model is applied to a process facility and the results are compared with the results from the existing methods for SIL determination. The results demonstrate the model's superior effectiveness in helping owners to select the most beneficial target SILs while ensuring compliance with government requirements.

Optimization of engineering for the salt cavern oil storage (SCOS) during construction in China

Salt cavern oil storage (SCOS) is a mature underground energy storage method which is widely used in the EU and US. The construction of SCOS is a complex system that involves all kinds of engineering. In this paper, four typical problems of SCOS engineering are analyzed: economical evaluation, pipeline laying, stability analysis, and operation method. To solve these four typical problems, five mathematical optimization models (fuzzy comprehensive evaluation model, analytic hierarchy process model, grey prediction model, simulated annealing model, and systematic clustering model) are implemented. The key findings show that the investment weight of SCOS is 0.5834, which is the best investment storage method, an improved stability evaluation criterion of the SCOS is adopted based on evaluation score: 0.72–1.0 is stable; 0.54–0.72 is more stable; 0.23–0.54 is a little unstable; 0.01–0.23 is very unstable, and a new salt cavern sediment void oil storage (SVOS) operation method is proposed. The research has a significance for the implementation of large-scale SCOS in China.

Towards an interpretable data-driven switch placement model in electric power distribution systems: An explainable artificial intelligence-based approach

The fault management process is facilitated by equipping power distribution systems with automated devices, especially remote-controlled switches (RCSs). Although RCS plays a key role in improving the system's reliability, it imposes significant investment, installation, and maintenance costs. Hence, RCSs should be optimally located in distribution feeders for the highest profit. In previous works, reliability-oriented mathematical optimization models have been formulated to reach this goal. However, the number of test solutions exponentially grows with the problem size to find the globally optimal solution. This paper uses machine learning to propose a scalable and easy-to-implement model for optimal switch placement in real power distribution systems. At first, the features of candidate points for installing RCSs are introduced. Then, a learning model is applied to deeply explore the relationship between these features and optimal locations for installing RCSs. After training, the learning-based surrogate model directly determines the optimal RCS placement strategy in real power distribution systems by leveraging knowledge gained from past experiences. Simulation results demonstrate that the proposed surrogate model is approximately 29 times faster than the integer programming-based mathematical model, without a significant loss of accuracy, when implemented on a modified 11 kV network connected to Bus 4 of the Roy Billiton test system. This paper also employs explainable artificial intelligence (XAI) tools to select the most important features, where the Hamming loss is decreased by approximately 5%.

Finding the right one: Decision support for selecting cost-efficient order picking solutions

Enabled via recent technological advances coupled with the advent of new systems providers and decreased price points, automated and robotized order-picking solutions (e.g., pick-assisting autonomous mobile robots) have evolved as a surging market. Such innovative picking technologies aim to reduce labor costs, use available space more efficiently, and increase throughput rates. As implementation projects and the variety of solutions rise, managers decide which ones to select for their specific warehouse and products. However, comprehensive decision models for this strategic problem are lacking in the pertinent literature. We propose a mathematical optimization model for the novel problem that selects and sizes order-picking solutions and assigns them products and warehouse spaces. Expert interviews are used to identify the comprehensive decision-relevant costs and constraints. Specifically, we minimize setup, module, labor, and error costs while adhering to characteristics related to the area (e.g., available space), technology (e.g., throughput, handling capabilities of certain products), and product (e.g., physical dimensions). We conduct a case study and complement our findings with numerical experiments. We find significant cost reduction potential of up to 57% by selecting a mix of different order-picking solutions. Further analyses highlight the need to retain human workers and to account for maximum labor capacity.

Multicriteria Optimization of Lower Limb Exoskeleton Mechanism

Typical leg exoskeletons employ open-loop kinematic chains with motors placed directly on movable joints; while this design offers flexibility, it leads to increased costs and heightened control complexity due to the high number of degrees of freedom. The use of heavy servo-motors to handle torque in active joints results in complex and bulky designs, as highlighted in the existing literature. In this analytical study, we introduced a novel synthesis method with analytical solutions provided for synthesizing the lower-limb exoskeleton. Furthermore, we proposed a mathematical model of multicriteria optimization; as a result, we obtained several lower-limb exoskeleton mechanisms comprising only six links, well-suited to the human anatomical structure, exhibit superior trajectory accuracy, efficient force transmission, satisfactory step height, and having internal transfer segment of the foot.

Impacts of different hydrogen demand levels and climate policy scenarios on the Chilean integrated hydrogen–electricity network

As countries continue to update their climate ambitions, they are seeking cost-effective solutions for decarbonizing energy use. In this context, low-carbon hydrogen production and use presents relevant opportunities for emissions reductions and economic development, and recent studies show important potential benefits from integrating electricity and hydrogen networks. Based on a novel mathematical optimization model, we conduct a case study for Chile in 2020–2050 to assess the least-cost evolution of the integrated hydrogen–electricity system, testing different carbon prices, 100% renewable mandates, and incorporating domestic and international hydrogen demand. By optimizing over various scenarios, we find that, due to the country’s significant renewable potential and the flexibility that electrolyzers can provide, adding hydrogen exports to domestic hydrogen use may enhance renewable integration, while not necessarily increasing average wholesale electricity prices for typical end-users (relative to our baseline scenario), but also make battery deployment unattractive. Further, we conclude that climate policies such as a high carbon price or a 100% renewable mandate may be crucial to achieve a fully renewable system by 2050 and reduce cumulative emissions, resulting in 3%–14% higher net present system costs. Finally, we discuss that various concerns such as water and land use must be addressed by policymakers.

A Deep Neural Network-Based Optimal Scheduling Decision-Making Method for Microgrids

With the rapid growth in the proportion of renewable energy access and the structural complexity of distributed energy systems, traditional microgrid (MG) scheduling methods that rely on mathematical optimization models and expert experience are facing significant challenges. Therefore, it is essential to present a novel scheduling technique with high intelligence and fast decision-making capacity to realize MGs’ automatic operation and regulation. This paper proposes an optimal scheduling decision-making method for MGs based on deep neural networks (DNN). Firstly, a typical mathematical scheduling model used for MG operation is introduced, and the limitations of current methods are analyzed. Then, a two-stage optimal scheduling framework comprising day-ahead and intra-day stages is presented. The day-ahead part is solved by mixed integer linear programming (MILP), and the intra-day part uses a convolutional neural network (CNN)—bidirectional long short-term memory (Bi LSTM) for high-speed rolling decision making, with the outputs adjusted by a power correction balance algorithm. Finally, the validity of the model and algorithm of this paper are verified by arithmetic case analysis.