Two-stage Robust Optimization Model Research Articles

Cooperative game robust optimization control for wind-solar-shared energy storage integrated system based on dual-settlement mode and multiple uncertainties

Aiming at the problems of renewable energy output uncertainties and single scenario operation mode of energy storage systems, a cooperative game robust optimization control method for wind-solar-shared energy storage system based on dual-settlement mode of power market is proposed in this paper. A cooperative game-based energy management framework under dual settlement mode of electricity market is constructed, the profit relationship between shared energy storage under multiple application scenarios and renewable energy are extracted and the corresponding profit models are established. Considering the multiple uncertainties of renewable energy and electricity prices, combined with robust optimization theory, a multi-level two-stage robust optimization model is established to make optimal electricity trading decisions for renewable energy and shared energy storage. Additionally, the cooperative game robust optimization model is solved by i-C&CG algorithm. The effectiveness of proposed control method is verified through actual operating data of a certain power grid in China. The simulation results show that the cooperative game robust optimization model achieves the optimal operation of the wind-solar-shared energy storage system considering multiple uncertainties, which can improve the ability of the system to cope with the uncertainty risk and the reliability of the system.

Robust cooperative hub location optimization considering demand uncertainty and hub disruptions

Amidst the rise of economic globalization and increased commodity trading, the logistics industry is experiencing rapid growth, encountering intricate transportation demands and fierce market competition. Simultaneously, it faces challenges related to infrastructure development and resource allocation efficiency. To enhance the adaptability and robustness of transportation networks when facing uncertain demands and potential hub disruptions, this paper proposes a two-stage robust optimization model for cooperative hub location problem. The model utilizes a hybrid algorithm that effectively combines the global search capability of genetic algorithms with the step-by-step optimization efficiency of Benders decomposition. Case study analyses demonstrate that, irrespective of the uncertainty environment, the cooperative model maintains lower total costs. Particularly in the case of large demand fluctuations, its cost advantages over non-cooperative models become notably prominent, showcasing remarkable performance in meeting service demands and enhancing resource utilization. Additionally, in cooperative networks, hub disruptions have a more significant impact on hub location decisions, with penalty and supplementary costs further exacerbating this influence. These research findings offer crucial insights for management practices: in uncertain market environments, adopting cooperative and robust planning strategies is pivotal for mitigating operational risks. When making decisions on cooperative hub location selection, carriers should comprehensively consider the interaction between uncertainty and economic benefits to achieve an optimal balance between risk and cost, ensuring the sustained economic feasibility of cooperative ventures.

A Two-Stage Robust Optimization for Reliable Logistics Network Design via Evolutionary Computation

This paper presents a novel two-stage robust optimization model for designing a dependable logistics network that integrates evolutionary computation techniques. The proposed model considers both the normal and disrupted states of the logistics network and seeks to reduce the overall network cost and operating time in different disruption situations. The challenge is a multi-objective optimization problem addressed using a hybrid evolutionary method that combines the advantages of the non-dominated sorting genetic algorithm with the large neighborhood search heuristic. Numerical experiments are conducted on various test instances to demonstrate the effectiveness and efficiency of the proposed model and algorithm. The results show that the proposed algorithm can generate robust and reliable logistics network designs resilient to disruptions and uncertainties, leading to significant improvements in logistics performance and cost savings compared to traditional methods.

Robust optimization of community energy sharing considering source-load uncertainty and demand response

Community energy consumption is a crucial aspect of the overall societal energy consumption landscape. The allocation rate of distributed photovoltaic (PV) systems within communities is steadily increasing. However, managing and optimizing the consumption of PV resources while mitigating the impact of their inherent randomness and volatility, along with minimizing electricity costs, presents a significant challenge. This paper proposes a mechanism for community energy sharing that utilizes rooftop PV systems, energy storage systems, and bi-directional electric vehicles. To achieve the goal of finding the minimum cost of electricity in the worst scheduling scenarios, a two-stage robust optimization model is established. This model considers the two-sided uncertainty of source and load as well as flexible load demand response. The simulation outcomes prove the proposed method's efficacy in substantially mitigating residential electricity costs and enhancing PV utilization. Notably, during peak summer demand, a substantial 24.78% reduction in electricity costs was achieved, while PV utilization witnessed a significant 16.52% increase.

Collaborative Service Network Design for Multiple Logistics Carriers Considering Demand Uncertainty

Collaborative designing of service networks using multiple logistics carriers can bring advantages in both economic and environmental terms, and these carriers have symmetry in their service areas. To enable such a collaborative service network and the corresponding benefits, this study proposes a problem of collaborative service network design (CSND) considering demand uncertainty. This problem is formulated as a two-stage robust optimization model using a budget uncertainty set to handle the uncertain demand. A column-and-constraint generation algorithm is developed to accurately solve the robust model. Numerical experiments show that the proposed algorithm outperforms the Benders decomposition algorithm in terms of solving efficiency and quality. Through comparative experiments, this research validates the advantages of collaborative designing and the robustness of model solutions. In addition, three allocation mechanisms are tested to investigate the importance of allocation in CSND.

Optimized scheduling study of integrated energy system considering user response characteristics

ABSTRACT Integrated Energy Systems (IES) can effectively promote the utilization of renewable energy. Reducing the impact of uncertainties and achieving energy supply-demand balance has always been a key issue in energy scheduling. However, existing research often focuses only on energy prices when designing demand response strategies, neglecting user response characteristics, particularly the influence of environmental temperature and user consumption levels. Therefore, this paper proposes an IES optimization scheduling model that considers user load response characteristics, analyzing changes in user response loads under different environmental and consumption levels. Additionally, consumption levels and environmental parameters are introduced to build an interactive response model. Different incentive measures are designed based on load types to guide users in adjusting their electricity usage behavior, optimizing the supply-demand curve. Furthermore, to address source-load uncertainties, a two-stage robust optimization model is constructed and solved iteratively using the column-and-constraint generation (C&CG) algorithm. The results indicate that considering user response characteristics reduces the peak-to-valley differences in electrical, thermal, and cooling loads by 18.6%, 7.0%, and 13.3% respectively, and reduces total costs by 8.9%. This model can ensure reliable operation while improving the economic efficiency of the system.

Bi-level robust planning of hydrogen energy system for integrated electricity–heat–hydrogen energy system considering multimode utilization of hydrogen

This paper proposes a bi-level robust planning model to address the rational configuration of a hydrogen energy system, accounting for the impact of wind power uncertainty in an integrated electricity–heat–hydrogen energy system (IEHHES) with the increasing wind power penetration. The upper-level problem aims to determine the capacity of the hydrogen energy system in this system, whereas the lower-level problem is formulated as a two-stage robust optimization model to simulate the typical daily operational scheme of the system, considering uncertain wind turbine output and the on/off switching of devices. This model considers multiple hydrogen utilization modes and the physical characteristics of various hydrogen storage tanks. The complex bi-level robust model is intractable directly. Therefore, this bi-level robust planning model is initially decomposed into planning and operation subproblems. These subproblems are then can be solved in parallel using the alternating direction method of multipliers (ADMM) algorithm; the planning subproblem, a quadratic programming model, is solved using a commercial solver; the operating subproblem, a two-stage robust optimization model, is solved using the column and constraint generation algorithm. Finally, case studies validate the advantages and effectiveness of the developed model and algorithm.

A data-driven robust optimization method based on scenario clustering for PVC production scheduling under uncertainty

In this paper, a data-driven robust optimization method based on scenario clustering is proposed for addressing energy consumption uncertainty characterized by correlation and multi-peaked distribution within the PVC production process. Firstly, principal component analysis (PCA) and kernel density estimation (KDE) methods are used to capture the correlation and distribution information effectively across multidimensional uncertain parameters; then a modified K-means clustering method based on density peaks is applied to cluster energy consumption scenarios and the flexible uncertainty subsets is established. A two-stage robust optimization model for the vinyl chloride production section is then proposed, and the column and constraint generation algorithm is applied to solved. Finally, the effectiveness of the proposed method is validated through a PVC production case study. Comparative results demonstrate that the proposed model reduces energy consumption under uncertainty and improves the robustness of PVC production scheduling.

Decomposition algorithms for the robust unidirectional quay crane scheduling problems

Our study focuses on a two-stage robust optimization model for the unidirectional quay crane scheduling problem with uncertain handling times at container terminals. We first implement two classical algorithms adopted in Li and Zhang (2021), the Benders decomposition algorithm and the column-and-constraint generation algorithm, to solve the robust model. Based on analytical and numerical comparisons of them, we design an exact hybrid algorithm to leverage capabilities of both algorithms by alternatively adding cuts of both kinds. Extensive experiments validate the effectiveness of this mechanism. Numerical experiments also reveal that the benefit and the cost of robustness fade away as the uncertainty budget increases and highlight the advantage of our robust approach to deal with uncertainty over a two-stage stochastic program under extreme situations.

Dynamic aggregation strategy for a virtual power plant to improve flexible regulation ability

The virtual power plant (VPP) provides an effective way for the coordinated and optimized operation of distributed energy resources (DERs). To solve the aggregation problem of a VPP containing scattered layouts and heterogeneous performance DERs, this study proposes a dynamic aggregation strategy to improve the flexible regulation ability of the VPP. A VPP aggregation model considering network constraints and temporal coupling constraints of DERs is constructed, while some VPP performance parameters are proposed to characterize and quantify the regulation ability. An uncertainty set considering time-series coupling properties of variables is constructed, and an aggregation method under uncertainty scenarios is proposed based on a two-stage robust optimization model. In addition, a dynamic aggregation strategy is proposed for the application of VPPs in electricity markets. Finally, case studies demonstrates that the proposed method provides a more extensive feasible region compared to other methods, and the deviation power remains within a reasonable range. The dynamic aggregation strategy facilitates the synergistic and correlative operation of DERs, exploits the regulation ability of the VPP in frequency regulation and spinning reserve, and improves the feasibility of practical applications. Simultaneously, the income of the VPP increased by 29.5 %.

A two-stage robust configuration optimization model and solution algorithm for new flexibility resources considering uncertainty response characterization

As the proportion of new energy continues to increase, the safety and stability of the new power system are challenged, urgently requiring the allocation of new flexible resources. This paper proposes a two-stage robust capacity optimization model considering flexibility demand constraints. Firstly, the uncertain characteristics of new energy are described, and a model of flexible resource adjustment capacity is established. Then, uncertain parameters are introduced to construct a robust capacity optimization model considering supply-demand balance, solved by column constraint generation algorithm and KKT theorem. Finally, a power system in a certain region of China is selected as the simulation object for empirical analysis to verify the effectiveness of the constructed model. The results show that the two-stage robust configuration optimization model constructed in this paper can address the uncertainty of power system and the flexibility demand brought by new energy, and the planning results can achieve a balance between the safety and economy of the new power system.

Uncertain parameters adjustable two-stage robust optimization of a rural housing integrated energy system considering biomass on-site utilization

Rural areas will be an important component to achieve carbon neutrality. However, there are currently issues such as an unreasonable energy consumption structure and low efficiency in renewable energy utilization. It is urgent to propose an energy optimization solution to address these problems. Therefore, considering the advantages of renewable energy in rural areas and the diversified and decentralized energy consumption patterns of rural households, a rural housing integrated energy system (RHIES) is proposed, which includes photovoltaics and a biomass utilization chain through self-production and local consumption. Subsequently, considering the economic and low-carbon aspects of the system's operational process, an uncertain parameters adjustable two-stage robust optimization model (UPATSRO) is developed to achieve a balance between robustness and economic efficiency during the scheduling optimization process. The results of case study indicate that the proposed RHIES reduces costs and carbon emissions by 28.15% and 93.83%, respectively, compared to conventional approaches. The biomass utilization mode satisfies 52.31% of the gas load and 39.71% of the thermal load for households. Additionally, it is shown that the proposed UPATSRO optimization model can achieve a flexible adjustment of scheduling schemes during the scheduling optimization process.

Two-stage robust transaction optimization model and benefit allocation strategy for new energy power stations with shared energy storage considering green certificate and virtual energy storage mode

In the context of the large-scale participation of renewable energy in market trading, this paper designs a cooperation mode of new energy power stations (NEPSs) and shared energy storage (SES) to participate in the power-green certificate market, which divides SES into physical energy storage and virtual energy storage. Secondly, combining the advantages of scenario generation and robust optimization (RO), a two-stage RO model with improved uncertainty interval is proposed to determine the optimal trading strategy. Then, to better align the distribution results of cooperative benefits with the actual contributions of NEPSs and SES, an entropy weight modified Shapley value benefit allocation strategy is constructed. Finally, the new energy base in Qinghai Province, China is chosen for simulation. The results show: (1) Adding energy storage and using two-stage RO are able to effectively improve the ability of NEPSs to resist uncertainty, which increases the revenue of the alliance by 22.8%. (2) The application of SES has better economic benefits than each member equipped with energy storage separately. Compared with the latter, the deviation penalty cost of the former is reduced by 66.4%, and the revenue is increased by 3.4%. (3) The proposed entropy weight modified Shapley value method embodies the important auxiliary role of SES more obviously. Based on this method, the overall satisfaction of the alliance increases by 12.6%. Generally speaking, the optimization model and benefit allocation strategy proposed in this paper can provide guidance for NEPSs and SES participating in power trading, and promote the low-carbon transformation of the power sector.

Gate appointment design in a container terminal: A robust optimization approach

Gate congestion is a main challenge faced by container terminals worldwide. In the scenario of gate congestion, the long waiting line of container trucks can block the traffic into the terminal, leading to disrupted terminal operations and unsatisfactory operating efficiency. In this paper, we study a gate appointment design problem that aims to manage the number of trucks allowed to a container terminal over time, so as to minimize the length of the truck waiting line and alleviate gate congestion. To optimize the gate appointment strategy, the truck service plans need also be devised, which involve the decisions for assigning trucks to yard blocks for container transhipment. We develop a two-stage robust optimization model for the problem by taking into account the uncertain service capacities of the yard blocks. Our model considers two decision stages, where the first-stage decision allocates slot capacities for the appointment slots, whereas the second-stage decision designs truck service plans with observed yard service capacity. We solve the two-stage robust model using an adapted column-and-row generation algorithm. In each iteration of the adapted column-and-row generation algorithm, the second-stage decision is generated by means of a pseudo-polynomial-time dynamic programming algorithm, while the first-stage decision is generated by a tailored scenario decomposition method. We test the computational performance of the proposed solution method on instances generated from real terminal operation data, and reveal managerial insights that would inspire terminal operators in the management of truck appointment for gate congestion mitigation.

Two-stage robust optimization of unified power quality conditioner (UPQC) siting and sizing in active distribution networks considering uncertainty of loads and renewable generators

This paper proposes a robust optimization siting and sizing strategy for the unified power quality conditioner (UPQC) in the active distribution network (ADN) integrated with renewable energy generators. The optimization objectives including investment cost, line loss, and voltage deviation are integrated into an overall cost for both the planning and operating stages. A novel UPQC equivalent power injection model is proposed based on the auxiliary branch method. A set of linear and second-order conic (SOC) constraints are employed to accurately describe the steady-state operation of UPQC. An improved branch current flow model is developed to incorporate radial distribution networks with UPQCs. The UPQC siting and sizing planning is formulated as a mixed integer second-order conic programming (MISOCP) problem. Accounting for the uncertainty in loads and distributed generators, a two-stage robust optimization model is established to address worst-case operational scenarios. A solving strategy is developed based on the strong duality theory and the column-and-constraint generation (C&CG) algorithm, and then commercial solvers can solve the problem accurately and efficiently. Case studies on an IEEE 33-node distribution network demonstrate this strategy's robustness in dealing with loads and renewable energy uncertainties, making it applicable across different UPQC topologies and operation modes. The proposed method has superior performance over the representative meta-heuristic approaches in terms of global optimality as well as an over 7.5 times faster computation speed. This work has significance in enhancing the quality and efficiency of modern power systems highly integrated with renewable energy.

Robust optimal dispatch strategy of integrated energy system considering CHP-P2G-CCS

Integrated energy systems (IESs) can improve energy efficiency and reduce carbon emissions, essential for achieving peak carbon emissions and carbon neutrality. This study investigated the characteristics of the CHP model considering P2G and carbon capture systems, and a two-stage robust optimization model of the electricity-heat-gas- cold integrated energy system was developed. First, a CHP model considering the P2G and carbon capture system was established, and the electric-thermal coupling characteristics and P2G capacity constraints of the model were derived, which proved that the model could weaken the electric-thermal coupling characteristics, increase the electric power regulation range, and reduce carbon emissions. Subsequently, a two-stage robust optimal scheduling model of an IES was constructed, in which the objective function in the day-ahead scheduling stage was to minimize the start-up and shutdown costs. The objective function in the real-time scheduling stage was to minimize the equipment operating costs, carbon emission costs, wind curtailment, and solar curtailment costs, considering multiple uncertainties. Finally, after the objective function is linearized with a ψ-piecewise method, the model is solved based on the C&CG algorithm. Simulation results show that the proposed model can effectively absorb renewable energy and reduce the total cost of the system.

Robust energy management through aggregation of flexible resources in multi-home micro energy hub

This study introduces a novel approach to home energy management systems (HEMS) through the development of a micro energy hub. The hub proficiently aggregates flexible resources across multiple homes, underpinned by a detailed modeling of appliance characteristics for enhanced energy management accuracy. The integration of Distributed Energy Systems (DES) further enriches the micro energy hub's capabilities, while a multi-objective two-stage robust optimization (M-TSRO) model is developed to address the inherent uncertainty of DES, aiming to concurrently realize energy savings, carbon emission reduction, and load smoothing. The effectiveness of the proposed micro energy hub is evaluated using real-world REFIT data set, demonstrating improved load scheduling, smoother load profiles, and enhanced energy flexibility. The results indicate significant improvements in grid control levels, reaching 68.75% in the basic scenario and 56.25% in the prosumer scenario. The prosumer scenario exhibits a significant reduction of 13.34% in the integrated objective compared to the basic scenario. This reduction is primarily driven by a notable decrease of 31.44% in the operational cost and an 8.06% decline in carbon emissions of the micro energy hub. These findings highlight the potential of micro energy hubs in optimizing energy consumption and increasing power flexibility through collaborative load scheduling strategies.

A two-stage robust configuration optimization framework for integrated energy system considering multiple uncertainties

The optimal configuration of integrated energy system (IES) is the cornerstone of efficient investment and low-carbon operation, which is of high importance for realizing energy system sustainable transformation. Yet, the intermittency of renewable energy and uncertainty of multiple energy demands pose severe challenges to IES configuration and operation. To address the issue, this research presents a two-stage robust configuration optimization model incorporating the multiple uncertainties of supply and demand. The model takes economic benefits, environmental benefits and energy utilization efficiency as objective functions, and is executed by column and constraint generation algorithm. A case study justifies the proposed model. The findings indicate the uncertainty from renewable energy and demand raises the equipment capacity and results in an increase of investment cost. Contrasted with the deterministic scenario, the total costs in the uncertainty scenario increase from 7043795.8CNY to 7785296CNY, but the performance shows more robust and the loss of load penalty is saved up to 296888CNY. Sensitivity analysis reveals energy price fluctuations primarily impair the operating costs, whereas they cause moderate effects on the configuration results. Load fluctuations cause greater consequences on both configuration and operating costs. The research provides references for IES configuration under multiple uncertainties with renewable energy penetration.

Distribution network restoration supply method considers 5G base station energy storage participation

This paper proposes a distribution network fault emergency power supply recovery strategy based on 5G base station energy storage. This strategy introduces Theil's entropy and modified Gini coefficient to quantify the impact of power supply reliability in different regions on base station backup time, thereby establishing a more accurate base station's backup energy storage capacity model that can fully utilize the base station's energy storage resources to participate in the emergency power supply of distribution network faults. First, the optimal Copula function in each cycle is determined through the Akaike information criterion and squared Euclidean distance to establish a wind power-photovoltaic output scenario. Secondly, the traditional Gini coefficient is modified using the weighted average node degree and influence rate indicators. A comprehensive vulnerability model is established through the modified Gini coefficient and Theil's entropy indicators. Based on the comprehensive vulnerability model, a backup energy storage time model and a modified backup energy storage capacity model of the base station affected by power supply reliability are established. Thus, the callable energy storage capacity of base stations in different areas is obtained. Finally, a two-stage robust optimization model is introduced to minimize system operating costs to solve the volatility of 5G base station communications and wind-solar output, thereby establishing an emergency power supply recovery model for base station energy storage and wind-solar output. Simulated with the improved IEEE-33 node model, the results show that the proposed base station's energy storage model improves the utilization of the base station energy storage resources and, at the same time, effectively reduces the loss of load during the fault phase of the distribution network and improves the absorption of the PV output.

A robust optimization model for demand response management with source-grid-load collaboration to consume wind-power

To accommodate wind power as safely as possible and deal with the uncertainties of the output power of wind- driven generators, a min-max-min two-stage robust optimization model is presented, considering the unit commitment, source-network load collaboration, and control of the load demand response. After the constraint functions are linearized, the original problem is decomposed into the main problem and subproblem as a matrix using the strong dual method. The minimum-maximum of the original problem was continuously maximized using the iterative method, and the optimal solution was finally obtained. The constraint conditions expressed by the matrix may reduce the calculation time, and the upper and lower boundaries of the original problem may rapidly converge. The results of the example show that the injected nodes of the wind farms in the power grid should be selected appropriately; otherwise, it is easy to cause excessive accommodation of wind power at some nodes, leading to a surge in reserve costs and the load demand response is continuously optimized to reduce the inverse peak regulation characteristics of wind power. Thus, the most economical optimization scheme for the worst scenario of the output power of the generators is obtained, which proves the economy and reliability of the two-stage robust optimization method.