Bi-level Optimization Model Research Articles

Low-carbon economy configuration strategy of electro-thermal hybrid shared energy storage in multiple multi-energy microgrids considering power to gas and carbon capture system

Hybrid shared energy storage based on electro-thermal coupling is an economical and effective way to solve the mismatch between the demand and supply of multiple multi-energy microgrids (MEMGs). However, its impact on the environment is often ignored. How to take into account economic development and environmental protection by optimizing its capacity configuration has become a key challenge. From the perspective of economy and environment, this paper explores the comprehensive benefits and capacity configuration of electro-thermal hybrid shared energy storage (ET-HSES) while considering the carbon trading mechanism and the coupling system of power to gas (P2G) and carbon capture system (CCS). Firstly, an energy sharing framework between the ET-HSES and the MEMGs is built. Secondly, a bi-level optimization model is constructed for the optimal scheduling problem of different stakeholders. Thirdly, Karush-Kuhn-Tucker (KKT) optimality conditions and Big-M method are used to transform the bi-level model into a single-level model. The results show that ET-HSES can effectively save the capacity of energy storage equipment, significantly reduce the operating costs and carbon emissions of MEMGs, and improve the income of ET-HSES operator (ET-HSESO). The combination of carbon trading mechanism and coupling system of P2G and CCS can effectively reduce the operating costs and carbon emissions of MEMGs. Meanwhile, it will also reduce the benefits of ET-HSESO.

Network-constrained flexible ramping product provision of prosumer aggregator: a data-driven stochastic bi-level optimization

Prosumers are expected to provide the flexible ramping product (FRP) in the power system. However, voltage violations and line congestion may arise in the distribution network, when FRP delivered by prosumers. Hence, this paper proposes a data-driven stochastic bi-level optimization model to coordinate the prosumer aggregator to decide FRP-offering while ensuring distribution network security under FRP delivery. In the proposed bi-level model, the upper-level is a min-max problem, representing the minimum expected cost under the worst-case scenario probability distribution for the prosumer aggregator. The lower-level is the operation cost minimization within the distribution network security for distribution network operator. The proposed model is converted into a single-level model using the Karush-Kuhn-Tucker condition and strong duality theory, and applied to the modified IEEE 33-bus network with three prosumers. The results demonstrate the effectiveness of the proposed model.

Bi-level stochastic optimization model of smart distribution grids considering the transmission network to reduce vulnerability

Bi-level stochastic optimization model of smart distribution grids considering the transmission network to reduce vulnerability

Capacity-Operation Collaborative Optimization for Wind-Solar-Hydrogen Multi-Energy Supply System

In pursuit of widespread adoption of renewable energy and the realization of decarbonization objectives, this study investigates an innovative system known as a wind-solar-hydrogen multi-energy supply (WSH-MES) system. This system seamlessly integrates a wind farm, photovoltaic power station, solar thermal power station, and hydrogen energy network at the power grid level. Central to the study is the introduction of a bi-level collaborative optimization model—an innovative algorithmic framework specifically tailored for complex multi-energy systems. This model co-optimizes both the capacity planning of essential system components and their annual load distribution, adeptly navigating the complexities of optimizing capacity and annual load distribution under uncertain energy sources and load conditions. A layered methodology synergistically combines linear programming with an advanced version of non-dominated sorting genetic algorithm-II. When applied to a real-world case study in Zhangbei, China, this approach identifies an optimal system capacity, leading to annual green power generation of 201.56 GW and a substantial reduction of over 173,703 tons of CO2 emissions. An economic analysis further reveals that each 1% reduction in CO2 emissions corresponds to a modest 1.7% increase in the system’s levelized cost of energy. Moreover, a comprehensive exploration of the impacts of various capacity parameters on the WSH-MES system’s performance is conducted. These insights offer invaluable guidance for the large-scale advancement of efficient renewable energy utilization and the attainment of decarbonization targets.

Optimum cooperation strategy for different cooperative motivations: a case study of the Kobe and Osaka ports

ABSTRACT Developing cooperative relationships between neighboring ports has emerged as an effective strategy for enhancing overall productivity. Two key factors to consider in such collaborations are: cooperative motivation (which drives the decision to cooperate between ports) and cooperation type (which defines the business scope of collaborative activities). Cooperative motivation can be categorized into regional welfare and competition, while cooperation type encompasses activities related to hinterland access and terminal management. This study aims to determine the most optimal types of cooperation based on different motivations. To achieve this, a bi-level optimization model was developed to analyze the relationship between shippers and ports, specifically focusing on the cooperation between the Kobe and Osaka ports. Competition with the Busan port was examined as a case study to provide a comprehensive understanding of the dynamics involved. The findings revealed that cooperation plays a crucial role in enhancing regional welfare for both North American and Southeast Asian cargo, particularly when cooperation levels are relatively low. Furthermore, it was observed that an effective cooperative strategy for competition in the Kobe and Osaka ports is contingent upon specific conditions. Hence, for successful competition-based cooperation, careful consideration of market dynamics and prevailing circumstances is essential.

Crowd Evacuation With Multi-Modal Cooperative Guidance in Subway Stations: Computational Experiments and Optimization

Setting up guidance equipment and leaders is widely used as an effective measure to improve the operation and evacuation efficiency of subway stations for the safety of passengers. Cooperation among different kinds of guidance modals can benefit the passenger evacuation process and reduce the operating and management costs as well as the risk of injury to people in subway stations. This article proposes a framework of multimodal cooperative guidance (MMCG) systems for commanding the crowd evacuation in case of emergency, where three types of guidance modes are considered. The bi-level MMCG optimization models are constructed to determine the optimal quantities and initial locations of multimodal guidance. The MMCG schemes are designed by minimizing cost functions taking into account the constraints of the number of guidance, valid coverage, and guiding expectation. An extended social force (SF) model is proposed to study crowd evacuation dynamics with multimodal guidance. The computational experiments are conducted to evaluate the performance of the proposed cooperative guidance schemes at the subway platform scenario. Three unimodal guidance schemes and a contrasted scheme without guidance are also proposed as comparison schemes. The results show that the crowd evacuation efficiency and the utilization ratio of exits are improved by taking into account the cooperation among different guidance modals.

Game analysis of product specifications for design optimisation using big sales data

Product specifications that precisely describe customers’ preference for product comparison and purchase decision-making are critical to product competitiveness. Competitive specifications’ determination requires a better understanding of the comparison-oriented product competition mechanism. Big sales data that consist of comprehensive and multi-dimensional datasets of products are valuable sources for the investigation of the specification competition mechanism. In this work, the relative satisfaction hypothesis and rational comparison hypothesis are proposed on the basis of product competition analysis. A framework is proposed to support rational design decisions in the context of competitiveness-oriented design optimisation. This framework is based on game analysis of product specifications using big sales data. Initially, competing products in the market are collected and modelled for game analysis. To monitor the competition mechanism of specifications amongst competing products, the relative satisfaction is then defined to evaluate the comparison results of product specifications. By comparing different specifications and their combinations, four design scenarios (i.e. dominant, dominated, equivalent and mixed design) are identified for design evaluation. Similarities amongst specifications are considered for supporting both homogeneous and differentiated competition. Ultimately, a bi-level optimisation model is proposed for enhancing product competitiveness. A case study illustrates the implementation of the proposed method.

Robust Bi-Level Optimization for Maritime Emergency Materials Distribution in Uncertain Decision-Making Environments

Maritime emergency materials distribution is a key aspect of maritime emergency responses. To effectively deal with the challenges brought by the uncertainty of the maritime transport environment, the multi-agent joint decision-making location-routing problem of maritime emergency materials distribution (MEMD-LRP) under an uncertain decision-making environment is studied. First, two robust bi-level optimization models of MEMD-LRP are constructed based on the effect of the uncertainty of the ship’s sailing time and demand of emergency materials at the accident point, respectively, on the premise of considering the rescue time window and priority of emergency materials distribution. Secondly, with the help of robust optimization theory and duality theory, the robust optimization models are transformed into robust equivalent models that are easy to solve. Finally, a hybrid algorithm based on the ant colony and tabu search (ACO-TS) algorithm solves multiple sets of numerical cases based on the case design of the Bohai Sea area, and analyzes the influence of uncertain parameters on the decision making of MEMD-LRP. The study of MEMD-LRP under uncertain decision-making environments using bi-level programming and robust optimization methods can help decision makers at different levels of the maritime emergency logistics system formulate emergency material reserve locations and emergency material distribution schemes that can effectively deal with the uncertainty in maritime emergencies.

Modeling and assessing load redistribution attacks considering cyber vulnerabilities in power systems

Introduction: Load Redistribution (LR) attacks, as a common form of false data injection attack, have emerged as a significant cybersecurity threat to power system operations by manipulating load buses’ measurements at substations. Existing LR attack methods typically assume that any substation can be equally attacked, contributing to the analysis of LR attacks in power systems. However, the diversity of cyber vulnerabilities in substation communication links implies varying costs associated with falsifying load buses’ measurements. Thus, quantitatively evaluating these costs and analyzing the impact of LR attacks on power systems within cost constraints holds practical significance.Methods: In this paper, we employ a Bayesian attack graph model to characterize the intrusion process through cyber vulnerabilities. The costs of falsifying load buses’ measurements at substations are quantitatively evaluated using the mean time-to-compromise model. Subsequently, from the attacker’s perspective, we propose a bi-level optimization model for LR attacks, considering the mean time to compromise in conjunction with limited attack resources and power flow constraints.Results: Simulations conducted on the IEEE 14-bus system illustrate the influence of cyber vulnerabilities on LR attacks within power systems. Furthermore, we verify that the attack scenario of the existing LR attack model aligns with a case of the proposed bi-level LR attack model when there is sufficient attack time to compromise all communication links.Discussion: The findings of this research demonstrate that the impact of cyber vulnerabilities on LR attacks can be quantified by assessing the attack costs. Effective management of LR attacks can be achieved under cost constraints through optimization methods. These insights contribute to enhancing network security strategies for power systems, mitigating potential threats posed by LR attacks in power system operations.

A classified retail pricing and production scheduling model for industrial customers

In the electricity retail market, it’s an important operation way for a retailer to provide diversified services and design appropriate retail pricing strategies that stimulate demand side responses in order to increase profit and maintain customer welfare. This paper proposes a novel retail contract design that a retailer can adopt to provide different time-of-use (TOU) prices for the various types of industrial customers based on their adjustabilities and a part of rewards from the demand response (DR) market to those who respond to the urgent electricity requirements. A bi-level optimization model of retail pricing for classified industrial customers is set up based on their adjustable capacities of production process operations. At the upper level, the retailer’s benefit is maximized considering the stochastic risks of load fluctuation and the spot market. This is achieved based on the electricity consumption strategies of classified industrial consumers, which are obtained from the lower level. Decisions are then made concerning purchases from the spot market and retail pricing strategies for industrial customers. Based on the retail prices from the upper level and industrial production processes modeling, the model at the lower level takes the maximum industrial user’s benefit as the objective to obtain the electricity consumption scheme of each type of industrial user. The model optimizes both the time division and price level of retail TOU prices, resulting in detailed electricity consumption strategies for all types of industrial customers. The results of the cases show that the proposed retail pricing can improve adjustable capacities of industrial production process operations, effectively smooth the load curve of the retailer by making full use of the peak-load-staggered among industrial customers, and boost profits of both the retailer and industrial customers. Thus, a mutually beneficial situation between the retailer and industrial customers is realized.

Joint energy-frequency regulation electricity market design for the transition towards a renewable-rich power system

Striving to develop renewable energy generation (REG) has become a global trend. Due to high carbon emissions, fossil-fueled generation units (FFGUs) in an electrical energy market such as the day-ahead and real-time electricity markets are facing unprecedented constraints. From the perspective of FFGUs, an effective way is to change their market roles from energy suppliers with high environmental costs to secure and reliable frequency regulation service providers. To help FFGUs successfully complete the transition, a bi-level optimization model for the joint energy and regulation service market is proposed in this paper. Different from existing joint markets, both the environmental cost of FFGUs and the frequency regulation service (FRS) cost of REG units are considered in this research for market operators to determine the scheduling priorities of submitted bids from generation units. In the frequency regulation service market model, a dynamic approach to determining the FRS demand is applied, which not only incentivizes REG units to initiatively manage their outputs, but also derives the price signals through the equilibrium of the FRS demand and supply to ensure the revenue of FFGUs in the FRS market. Meanwhile, the decision-making model of the FFGUs under the proposed market mechanism is also presented. Finally, extensive numerical experiments demonstrate the feasibility and efficiency of the mechanism. Simulation results show that the proposed mechanism can stimulate a smooth transition of FFGUs by adapting to actual situations and policy changes.

Low-carbon economic dispatch of integrated energy systems that incorporate CCPP-P2G and PDR considering dynamic carbon trading price

To address the challenge of global warming stemming from excessive fossil fuel combustion, the exploration of low-carbon technologies and improvements to carbon trading mechanisms stand out as vital strategies. An effective conduit for these strategies is the integrated energy system (IES), which has garnered increasing attention for its potential. To realize low-carbon advancements within energy systems, this study proposes a low-carbon economic scheduling framework for the IES that integrates the coupled operation of carbon-capture power plants, power-to-gas (CCPP–P2G) unit and the price-based demand response (PDR) considering dynamic carbon trading mechanisms. The proposed approach firstly concurrently considers source-side CCPP-P2G and load-side PDR to achieve coordinated low-carbon operation, elucidating the underlying mechanisms. Subsequently, a dynamic carbon trading model for the IES is formulated, flexibly capturing the ebb and flow of supply and demand in the carbon trading market. Amidst the uncertainty of the system, a bi-level optimization model is constructed to minimize the operational cost. Finally the effectiveness of the proposed method is demonstrated on an IES consisting of the IEEE-30 bus power system, 6-bus natural gas system and 6-bus district heating system. The findings indicate that the proposed dynamic carbon trading mechanism is able to effectively provide time-varying carbon trading price signals to fully reflect the supply and demand relationship of carbon emission allowance. Furthermore, the synchronized operation of CCPP-P2G and PDR yields substantial benefits, compared to the benchmark. Specifically for the test case, the proposed framework reduces system operational costs, wind power curtailment, and carbon emissions by $87,160, 1,410 MWh, and 4,849t, respectively.

Authority-enterprise equilibrium based mixed subsidy mechanism for the value-added treatment of food waste

There is a huge amount of food waste worldwide and proper disposal can provide value-added products to the society. Food waste treatment requires the authority’s financial support because of its high costs and the treatment methods need to be further explored, but there is no effective approach to help the authority determine reasonable subsidy mechanisms and help enterprises to identify the technology application strategies. Therefore, a bi-level optimization model was constructed to find decision strategies that would satisfy both parties in the interaction between the local authority’s subsidy design and the food waste treatment plant’s identification of technology applications, where a mixed subsidy mechanism and technology integrations were considered. The proposed model was applied to a case study in Shanghai, China to investigate its feasibility and applicability. The influence of total amount of food waste and the related attitude of the local authority were analysed and discussed. Some management suggestions for different decision makers were proposed. It was found that while performance subsidies are preferred over transport and treatment subsidies, mixed subsidies are more favourable. Multi-technology integration facilitates the treatment plants’s profitability, and the share of technology application needs to be determined based on the actual. Food waste treatment systems can reduce carbon emissions while achieving energy self-sufficiency.

Bi-level and multi-objective optimization of renewable energy sources and storage planning to support existing overloaded electricity grids

The paper proposes a bi-level multi-objective optimization model to optimally design and operate renewable energy sources and storage systems in an existing electrical grid with increasing demand. while respecting network constraints based. The bi-level optimization model combines particle swarm optimization (PSO) and dynamic linear AC-optimal power flow (DLOPF). The aim of the bi-objective model is to minimize costs while limiting carbon emissions. PSO sizes and identifies the placement of battery energy storage (BES) systems, and DLOPF locates and sizes RES in a spatial–temporal framework using the Levelized Cost of Energy and Storage. Different scenarios were applied to the IEEE-30 bus system to reveal the behavior of the dynamic network for the different cases, and the associated effect of integrating RES and BES. The model resulted in optimized scenarios in terms of placement and sizing of RES and BES at the lowest cost while considering cost minimization and carbon constraints. This shows how the complexity of the CO2 constraints requires more RES and BES installations and thus more funds. The maximum CO2 limit achieved is 30%, which has reached the storage limits and increased the overall cost by $15 m.

An incentivized scheme for electric vehicle charging demand management

The market share of electric vehicles (EVs) is expected to grow, necessitating infrastructure development to support this expansion. However, scientific literature predominantly focuses on charging infrastructure design, overlooking the importance of pricing strategies that can optimize their utilization. To address this gap, this study presents an integrated incentive scheme aimed at maximizing system utilization by effectively distributing the charging demand across stations. Moreover, a novel concept of Flex Accessible Charging Points (FLEX-ACP) is introduced, specifically designed to enhance accessibility and reduce waiting time for users with disabilities and seniors (UDS). The proposed framework utilizes an optimal charging network configuration, considering the number and locations of charging facilities, and then determines appropriate incentives at each station to minimize total waiting time. The problem is formulated as a bi-level optimization model, which is subsequently transformed into a single-level mixed-integer nonlinear program (MINLP). To solve this program, a combination of heuristic and branch-and-cut algorithms is employed. The developed models are tested through a realistic case study, utilizing real-world data from Salt Lake County in Utah.

Bi-level Stochastic Optimization Model for Coordination of Transmission and Distribution Networks Considering Generic Resources

Bi-level Stochastic Optimization Model for Coordination of Transmission and Distribution Networks Considering Generic Resources

Optimization of Signal Timing for Urban Expressway Exit Ramp Connecting Intersection.

To alleviate the traffic problems of congestion and queue overflow on a mainline at the intersection of an urban expressway exit ramp articulation during peak hours, a bi-level programming optimization model of signal timing is proposed. The lower-level optimization objective is to maximize the capacity of the expressway exit ramp that articulates with the entrance road, while the upper-level optimization objective is to minimize the average vehicle delay and the number of stops per vehicle, taking into account the queue length in the direction of the ramp and other directions. The particle swarm optimization algorithm is selected to solve the proposed model, applied to a real case, and is validated using MATLAB and VISSIM simulation platforms. The simulation results show that the average vehicle delay and the number of stops per vehicle in the exit ramp on the expressway are reduced by 22.09% and 18.60%, while those in the intersection area are reduced by 20.96% and 17.19%, respectively. The conclusion indicates that the signal timing scheme obtained by this method can effectively improve the traffic efficiency at the intersection of the exit ramp on the expressway and alleviate the problem of congestion and the overflow of the exit ramp back to the mainline.

A Bilevel Model for Robust Network Design and Biomass Pricing Under Farmers’ Risk Attitudes and Supply Uncertainty

This paper addresses an integrated biomass pricing and logistics network design problem. A bilevel design and pricing model is proposed to capture the dynamic decision process between a biofuel producer as a Stackelberg leader and farmers as Stackelberg followers. The bilevel optimization model is transformed into a tractable single-level formulation by using optimality constraints. Other unique characteristics of our problem at hand include the incorporation of the harvesting time and frequency decisions in the biomass supply chain network design problem for the first time and consideration of the uncertainty in switchgrass yield in a robust optimization setting to take into account the risk-averse behavior of the farmers (suppliers). To efficiently solve the model, we propose a Benders decomposition algorithm enhanced by surrogate constraints, strengthened Benders cuts, and in-out cut loop stabilization. The numerical experiments show that the proposed algorithm is significantly superior to the branch-and-cut approach of CPLEX in terms of run times and gaps. We conduct a case study with data from Texas to validate the capabilities of our mathematical model and solution approach. Based on extensive experiments, the benefits of modeling are analyzed, and significant insights are explored. Funding: This research was partially supported by the National Natural Science Foundation of China [Grants 71771135, 72171129]; and the scholarship from China Scholarship Council (CSC) [Grant CSC 201906210092]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0357 .

A Bilevel Optimal Water Allocation Model Considering Water Users’ Satisfaction Degree and Water Rights Transaction: A Case Study in Qingzhang River Basin, China

The contradiction between water supply and demand in China is becoming increasingly prominent. A water allocation scheme that satisfies various water users can effectively solve it. In this paper, considering both individual rationality and collective rationality, a bilevel optimal allocation model for river basin water resources is established. Firstly, water users’ satisfaction degree was defined, to characterize their satisfaction with the water resource allocation scheme, and principles of water users’ satisfaction degree were mathematically expressed, to represent water users’ negotiation activities in the initial water rights allocation. Then, based on the initial allocation results, water users’ water intake quantity, water-saving amount, and water-trade amount were optimized by water rights trading. Finally, an algorithm based on the response surface was put forward for solving the proposed bilevel optimal allocation model. The validity and feasibility of the model and algorithm were verified by a case study in the Qingzhang River Basin in China.

Risk-based contingency analysis for power systems considering a combination of different types of cyber-attacks

Substation with various communication and control devices has become a major target of cyber-attacks. In general, two main types of cyber-attacks can be performed on substations through direct intelligent electronic device connections from remote accesses or via compromising local substation supervisory control center and data acquisition systems, thus respectively resulting in different damage to the power systems. In this paper, the combination of two types of cyber-attacks on the power systems are considered. The generalized stochastic Petri net is utilized to simulate dynamic intrusion processes of these two types of cyber-attacks. Furthermore, the successful attack probabilities of cyber-attacks are calculated based on simulation results. Then, a probabilistic bi-level optimization model is proposed to identify critical components with the maximum cyber risk and the types of cyber-attacks. The two types of cyber-attacks initiated from substation space to individual components are particularly modeled in the proposed model. Finally, a two-stage algorithm using the network flow is proposed to solve the proposed model more efficiently. Simulation results tested on the IEEE RTS 24-bus and the 118-bus systems validate the effectiveness of the proposed model. Results also show that the devised algorithm can improve the computation performance in dealing with larger-scale power systems.