Two-stage Robust Optimization Research Articles

Low-carbon Economic Dispatching Strategy Based on Feasible Region of Cooperative Interaction between Wind-storage System and Carbon Capture Power Plant

The high penetration of new energy into the grid is an effective method for reducing carbon emissions. However, the randomness and uncertainty of large-scale wind power (WP) output pose challenges to the grid dispatch operation and increase the requirements for carbon emission control. This paper proposes a low-carbon economic dispatching strategy based on the feasible region (FR) of cooperative interaction between WP and flexible resources to promote the consumption of WP and reduce carbon emissions. In particular, energy storage (ES) and carbon capture power plant (CCPP) are used as a set of adjustable flexible resources, and the power FR of WP, ES and CCPP is constructed to provide a visualization reference for grid scheduling. Then, a two-stage robust optimization (RO) dispatching FR-based model considering WP consumption capacity is proposed to cope with the operational risk of WP output stochasticity for power grid. Finally, the column constraint generation algorithm (C&CG) is used to solve the problem and evaluate low carbon level in the system according to the carbon flow theory. The simulation results verified the effectiveness of the suggested approach demonstrated by the modified IEEE 39-bus and IEEE 118-bus test cases.

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.

Robust two-stage optimization consensus models with uncertain costs

In the consensus-reaching process (CRP), decision-makers (DMs) frequently encounter the dilemma of too much uncertain information, which can lead the actual decision to deviate from the optimal solution obtained by the currently used consensus models. To do this, we construct two robust two-stage optimization consensus models with uncertain costs and obtain their robust two-stage counterparts. We then apply a Benders decomposition algorithm to solve the resulting models. Finally, the experimental results show that the new models are better suited for uncertain contexts and could help DMs produce more reliable choices.

Evaluating the reliability of microgrids consisting of renewable energy sources using stochastic scheduling based on the data-driven uncertainty set

The paper addresses challenges arising from the unpredictable and probabilistic nature of wind speed and solar irradiance, leading to variable power production in renewable sources. Power imbalance issues in grids result from the difficulty in accurately estimating these variables. The study introduces an improved data-driven uncertainty set, utilizing a neural network trained with extensive historical data from a multi-microgrid system. This set efficiently identifies strong coupling and extracts characteristic scenarios, ensuring high reliability with a minimal number of scenes. The proposed probabilistic model, implemented in the coordination of pumped storage, wind, and solar power plants, incorporates energy limits and storage characteristics. A four-mode IEEE model for storage units allows quick response to system needs. Simulating storage unit states every hour, considering system load, output power, and energy limitations, optimizes power dispatch based on battery capacity. Additionally, the paper addresses the uncertainty in electric power demand in microgrids, proposing an improved data-driven uncertainty set obtained from a neural network. By eliminating unrealistic worst-case scenarios, the approach accurately captures system characteristics, maintaining high reliability while significantly reducing convergence time. The proposed uncertainty set is applied in a novel two-stage robust optimization dispatch model, transforming the optimization problem into a mixed-integer linear programming problem, and solving it using a column and constraint generation algorithm. Numerical case studies verify the feasibility and superiority of the proposed approach in terms of economy and convergence performance compared to existing robust optimization methods.

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.

Coordinated planning of soft open point and energy store system in active Distribution networks under source-load imbalance

With the increasing penetration rate of renewable energy, the uncertainty of its output has exacerbated power imbalances among different distribution networks. In this paper, we propose collaborative planning of soft open points and energy storage systems to balance a distribution network with source-load imbalance, aiming to improve the economy and reliability of the distribution network. Firstly, considering that distributed generation has uncertainty, the K-means is used to construct a typical day scenario, on the basis of which a collaborative planning model is established with the objective function of minimizing the annual integrated cost. Then, the original nonlinear nonconvex model is transformed into a mixed-integer second-order conical planning model by Big-M and second-order conical relaxation, and a two-stage robust optimization is used to seek the planning solution with the lowest operational cost under the worst-case scenarios, aiming to enhance the robustness of the planning model. Finally, the feasibility of the proposed planning model is verified on two source-load unbalanced IEEE 33-node active distribution network arithmetic cases.

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.

Data-driven two-stage robust optimization dispatching model and benefit allocation strategy for a novel virtual power plant considering carbon-green certificate equivalence conversion mechanism

Aiming at a large number of decentralized resources such as rural biomass, rooftop photovoltaic, and decentralized wind power, a novel rural virtual power plant (VPP) has been conceptualized. The VPP is integrated by biomass waste conversion system (BWC), carbon to energy (C2P), demand response aggregator (DRA), and distributed renewable energy (DRE), namely, BDCD-VPP. Then, this paper proposes a data-driven two-stage robust optimization dispatching model for BDCD-VPP considering carbon-green certificates equivalent conversion mechanism. This model aims to address the uncertainty of wind power plants (WPP) and photovoltaic (PV) power generation. Strong duality theorem (SDT) and C&CG algorithm are applied to construct this model. Thirdly, the Aumann-Shapley method (A-S) was enhanced by incorporating risk factor, cost factor, and carbon reduction factor. This refinement results in the development of a synergistic scheduling revenue allocation method for electricity‑carbon-green certificates. Finally, the Lankao rural energy revolution pilot program in China is selected as the case study, the results showed: (1) The BDCD-VPP aggregates distributed energy sources such as the rural WPP and the PV to realize electricity‑carbon-electricity cycle effect. The BDCD-VPP generates a green certificate revenue of 47.17¥/MWh and exhibited carbon emissions of 0.37 t/MWh. The proposed Carbon-Green Certificates Equivalent Conversion Mechanism increases BDCD-VPP benefit ratio by 3.52%. (2) The proposed two-stage robust optimization dispatching model enhances the ability of BDCD-VPP to adapt to uncertainty. Compared to the day-ahead stage, biomass power generation (BPG) and waste power generation (WPG) increase upward peaking power by 24.05% and 9.99% in intra-day stage. Flue gas treatment system (FG-TS), gas-power plant carbon capture (GPPCC) and power to gas (P2G) increase downward peaking power by 65.15%, 70.99% and 25.94%. (3) Utilizing the proposed benefit allocation methodology, BPG and WPG need to concede 38.25¥/MWh and 65.02¥/MWh for carbon emissions associated with electricity. WPP and PV need to concede 64.25¥/MWh and 33.71¥/MWh for power generation uncertainty. GPPCC, P2G, DRA, and small hydropower station (SHS) obtain revenues of 24.48 ¥/MWh, 55.07 ¥/MWh, 70.38 ¥/MWh, and 51.30 ¥/MWh. Compared to the A-S, the proposed benefit allocation methodology exhibits 6.92% improvement in satisfaction. Overall, the proposed data-driven two-stage robust optimization dispatching model and benefit allocation strategy facilitates the optimal aggregation and utilization of rural distributed energy resources, considering the interests of various stakeholders. This is conducive to achieving a clean and low-carbon transformation of the overall energy structure.

A new shared energy storage business model for data center clusters considering energy storage degradation

In recent years, the energy consumption of data centers (DCs) has shown a sharp upward trend. Given the high investment cost of energy storage, this study introduces the concept of energy sharing within a data center cluster (DCC) and proposes a novel shared energy storage (SES) business model. The model realizes the co-optimization for DCC and SES and is divided into three main layers. Firstly, considering the SES's economy and the DCC's cleanliness, the upper layer establishes a novel multi-objective optimization configuration scheme for SES with lifetime degradation. In addition, a two-stage robust optimization technique for DCC is proposed in the middle layer, considering the demand response mechanism for data loads. Subsequently, the concept of contribution degree (CD) is defined, and a novel benefit distribution mechanism based on cooperative game and CD is presented in the lower layer. The simulation results demonstrate that the proposed business model positively enhances the economic benefits of the SES and DCC. The constructed uncertainty optimization model exhibits strong robustness, and the proposed benefit allocation scheme is fairer and more reasonable.

Robust optimal operation scheduling method for integrated energy system considering flexible energy storage and mixed hydrogen natural gas

ABSTRACT At present, the number of electric vehicles is increasing day by day. The full integration of electric vehicles and multi-energy coupled integrated energy systems is the future development trend. This paper introduces a novel form of flexible energy storage in the integrated energy system ;(IES): electric vehicle (EV). And It proposes that mixed natural gas hydrogen be used as the primary energy source for IES, which replaces traditional natural gas. Combined with the above, the IES is scheduled to meet the system’s multi-load for heating, cooling, and electricity demands. Based on the integrated energy system’s structure and energy conversion principles, a robust two-stage optimization model for the IES is proposed to minimize the daily operation scheduling costs. The proposed model considers the uncertainty of distributed renewable generation and flexible energy storage. Uncertain adjustment parameters are introduced into the model, which can flexibly adjust the conservatism of the scheme. Using the column and constraint generation algorithm (C&CG) and the strong duality theory, the model presented in this paper is solved and the optimal scheduling scheme is obtained. The final simulation results validate the effectiveness of the model and algorithm. The addition of flexible energy storage and mixed natural gas hydrogen effectively improves the economy and flexibility of the system while reducing carbon emissions costs. Consideration of uncertainty improves system robustness and safety. In addition, sensitivity analyses of the influence of the proportion of hydrogen mixed with natural gas, the setting of uncertain adjustment parameters, electricity prices, weather, and load fluctuations on system operation. The results show that compared to existing research, electric vehicles as a flexible energy storage device and mixed natural gas hydrogen supply, increase the economic benefits of IES by 19.8% and 23%, respectively.

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.

Planning model for rural distribution networks with integrated energy stations via robust optimization method

With the modernization and intelligent development of agriculture, the energy demand in rural areas continues to increase, which leads to an increased operational burden on the existing rural distribution network. Integrated energy stations (IESs), in rural areas, use renewable energy sources such as biogas, wind power, and photovoltaic as energy inputs, which can fully improve energy efficiency and help reduce the operating load and peak valley difference of rural distribution networks. In this paper, a multistage planning model is proposed for rural distribution networks with IESs based on the robust optimization method. Firstly, a rural distribution network operation framework with IESs is proposed, and a mathematical model of rural IESs is built based on the energy hub (EH). Then, the multistage robust planning model of rural distribution net-works with IESs is developed and typical scenarios of stochastic source and load are generated based on improved k-means. An iterative solution method for a two-stage robust optimization method is proposed based on the nested column constraint generation (NC&CG) algorithm. Finally, the effectiveness of the presented model and solution approach is assessed through case studies on a modified IEEE 33-node distribution network and a real 152-node distribution network.

Robust Wind Power Ramp Control Strategy Considering Wind Power Uncertainty

Recent climate change has worsened the risk of extreme weather events, among which extreme offshore wind storms threaten secure operation by inducing offshore wind power ramps. Offshore wind power ramps cause the instantaneous power fluctuation of interconnected onshore grids and may lead to unexpected load shedding or generator tripping. In this paper, considering offshore wind power uncertainties, we propose a novel robust coordinated offshore wind power ramp control strategy by dispatching thermal units, energy storage systems, and hydrogen storage systems cooperatively. First, the impact of extreme wind storms on an offshore wind farm output power ramp is analyzed, and the general framework of offshore wind power ramp control is presented based on the two-stage robust optimization considering the dual uncertainties of load demand and wind power. Second, a coordinated wind power ramp control model is established considering the operational characteristics of different ramp control sources such as thermal units, energy storage systems, and offshore wind farms. Third, a robust ramp control strategy is developed using the column-and-constraint generation (CC&G) algorithm. Simulation results show the effectiveness of the proposed ramp control strategy.

Probabilistic Forecasting-Based Reserve Determination Considering Multi-Temporal Uncertainty of Renewable Energy Generation

Operating reserve, among the most important ancillary services, is a powerful prescription for mitigating increasing uncertainty of renewable generation. Traditional reserve determination neglects uncertainty of renewable generation variations within the dispatch interval, which cannot gurantee sufficient reserve deliverability in real-time operation. This paper proposes a probabilistic forecasting-based reserve determination method to efficiently deal with multi-temporal uncertainty of renewable energy in power systems. A novel probabilistic forecasting approach is proposed by integrating Dirichlet process Gaussian mixture model into bootstrap-based extreme learning machine. A unified uncertainty model is constructed for depicting both interval-averaged uncertainty and intra-interval uncertainty by combing the probabilistic forecasts and linearized Itô-process model. In current business practices of many independent system operators, the coordinated determination of two well-designed reserve products, including regulating reserve and ramp capability reserve, is formulated in a two-stage robust optimization framework. A Bernstein polynomial-based model reformulation approach is then employed to handle the existing heterogeneity in the sub-models of each stage. Consequently, the integrated reserve determination is embedded in a generic two-stage robust optimization problem, which can be efficiently solved by the adopted modified column-and-constraint generation method. Finally, numerical simulations are implemented to validate the effectiveness and profitability of the proposed approach.

A Sequential Follower Refinement Algorithm for Robust Surgery Scheduling

An algorithm for the two-stage robust optimization surgery-to-operating room allocation problem is presented. The second-stage problem is an integer linear program whose convex hull is approximated using three types of specialized valid inequalities and Chvátal-Gomory cuts. The resulting linear relaxation of the second-stage problem is then dualized and integrated into the first-stage problem. The resulting mixed integer linear program, which is an approximation of the original problem, is then solved using a commercial solver. If the solution of this model is not optimal for the second-stage problem, valid inequalities for the second-stage problem are generated, yielding a type of column-generation based approach that we refer to as the sequential follower refinement (SFR) algorithm. Data from an academic medical center are used to compare the computational performance of SFR with the constraint and column generation (C&CG) algorithm, which is the only exact approach that has been specifically applied for this problem in the literature. An extensive numerical study of SFR and its computational characteristics is presented that shows that SFR yields better-quality solutions compared with C&CG, even as the termination criterion of SFR is met much sooner, especially for problems involving higher number of surgeries. History: Accepted by Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0191 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0191 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

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.