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Economic dispatch of generation load aggregators based on two-stage robust optimization

FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Zhang, Haonan Tian, Youwen Zhao, Yi Liu, Qingyu Zhang, Nannan Shenyang Agr Univ Sch Informat & Elect Engn Shenyang Liaoning Peoples R China Shenyang Inst Engn Coll Elect Power Shenyang Liaoning Peoples R China

Introduction: In recent years, with the rapid development of renewable energy generation, the stability of the power grid has been greatly reduced. In response to this problem, integrating the user side transferable load into the power market has become the key to the development of future power grid. At present, large transferable loads have entered the electricity market in some pilot areas of China, but the relevant research on small and medium-sized transferable users entering the electricity market is still ***: This paper proposes the concept of generation load aggregators. A two-stage generation load aggregator robust optimization model is developed to obtain the scheduling scheme with the lowest operating cost under the worst scenario. The model consists of distributed renewable power, transferable load, self-provided power, energy storage, etc. Uncertainties of renewable energy and load are introduced in the model. By using the column constraint generation algorithm and strong pairwise theory, the original problem is decomposed into the main problem and sub-problems to be solved alternately, so as to obtain the scheduling scheme with the lowest operating cost in the worst scenario under different ***: The solved results are compared with those without the generation load aggregator, illustrating the role of the generation load aggregator in relieving peak and valley pressure on the grid from the load side, reducing the cost of electricity for loads, and promoting the consumption of renewable energy. The comparison with the deterministic optimization algorithm shows a significant decrease in the total cost and validates the performance of the selected solution algorithm. The boundary conditions for the use of energy storage by generation load aggregators for peak and valley reduction under the time-sharing tariff mechanism are also ***: This study can provide reference for the investors of generation load aggregators w

关键词： generation load aggregator two-stage robust optimization uncertainty optimization economic dispatch column constraint generation algorithm

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A two-stage robust optimization model for a virtual power plant considering responsiveness-based electric vehicle aggregation

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JOURNAL OF CLEANER PRODUCTION 2023年 405卷

作者： Chen, Yue Niu, Yuguang Du, Ming Wang, Jiahui North China Elect Power Univ Sch Control & Comp Engn State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China

With the goal of pursuing carbon neutrality, this study is aimed to investigate effectively managing distributed renewable energy. Considering the uncertainty of wind power (WP), photovoltaic power (PV), and load, a two-stage robust optimization model for virtual power plant (VPP) is proposed, with a focus on calculating the available capacity of electric vehicle (EV) aggregated virtual energy storage (VES). Time-space distribution characteristics of EVs and the responsiveness of EV users are analyzed and the available capacity calculation model is constructed. In the first stage, the bidding strategy and unit combination of the VPP are determined based on the predicted values of WP, PV, and load. Combining with the pre-decided decision from the first stage, the output of each unit is determined by considering an uncertainty set in the second stage, for achieving the best operational benefit under worst-case scenarios. robust control parameters are introduced into the model and used to adjust conservativeness. The model is solved by applying the C&CG algorithm. Additionally, a carbon trading mechanism is leveraged to balance the system economy and environmental friendliness. The results show that the optimal scheduling solution helps to reduce fluctuations caused by uncertainties, balancing the economic benefits and operational risks of the VPP. Besides, guidance is provided for VPP operators to formulate reasonable incentives for EV users and the construction of energy storage systems. When the carbon trading price of the VPP proposed in the paper is set at 160 yen /ton, economic and environmental sustainability can be effectively balanced.

关键词： Virtual power plant Electric vehicle virtual energy storage Available capacity two-stage robust optimization Carbon trading mechanism

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A multi-ship power sharing strategy: Using two-stage robust optimization and Shapley value approach

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RENEWABLE ENERGY 2024年 232卷

作者： Yang, Jie Zhang, Zhengxu Ma, Kai Yang, Kun Guo, Shiliang Li, Haibin Yanshan Univ Sch Elect Engn 438 West Hebei Ave Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Key Lab Power Elect Energy Conservat & Dr Control 438 West Hebei Ave Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Key Lab Intelligent Control & Neural Informat Proc Minist Educ 438 West Hebei Ave Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Sch Civil Engn & Mech 438 West Hebei Ave Qinhuangdao 066004 Hebei Peoples R China

In recent years, the use of cold ironing (CI) has effectively reduced the carbon emissions of ships in port areas. However, due to the limitation of port CI quantity and power supply capacity, the power demand of some ships cannot be met. To solve this problem, this paper proposes a multi-ship power sharing strategy based on two-stage robust optimization and improved Shapley value method. Firstly, considering the uncertainty of ship photovoltaic power generation, a multi-ship power sharing model based on two-stage robust optimization is established. This model is a three-level optimization model with mixed integer variables, which is a NP-hard problem. In this paper, the nested column-and-constraint generation algorithm combined with duality theory and big-M method is used to obtain the optimal scheduling strategy of ship shared power, CI power and load demand response power. Secondly, an improved Shapley value method considering berth and remaining berthing time is proposed to realize the cost allocation in the process of ship power sharing. Finally, the effectiveness of the multi-ship power sharing strategy in reducing berthing costs and carbon emissions is verified by simulation. This method is expected to provide a new idea for the development of green ports.

关键词： All-electric ships Power sharing Cold-ironing two-stage robust optimization Improved Shapley value method

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A two-stage robust optimization method based on the expected scenario for island microgrid energy management

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Procedia Computer Science 2022年 203卷 388-394页

作者： Wei Ruizeng Wang Lei Liu Qi Wang Tong Zhou Enze Liu Shuqin He Huan Guangdong Key Laboratory of Electric Power Equipment Reliability Electric Power Research Ititute of Guangdong Power Grid Co. Ltd. Shuijungang 8th DongFengDong Road YueXiu District GuangZhou 510080 China Guangdong Power Grid Co. Ltd. Guangzhou Shuijungang 8th DongFengDong Road YueXiu District GuangZhou 510080 China

One of the main challenges in microgrid system energy management is dealing with uncertainties such as the power output from renewable energy sources. The classic two-stage robust optimization (C-TSRO) method was proposed to cope with these uncertainties. However, this method is oriented to the worst-case scenario and is therefore somewhat conservative. In this study, focusing on the energy management of a typical island microgrid and considering uncertainties such as the power output of renewable energy sources and the power demand of loads, an expected-scenario-oriented two-stage robust optimization (E-TSRO) method is proposed to alleviate the conservative tendency of the C-TSRO method, because the E-TSRO method chooses to optimize the system cost according to the expected scenario instead, while ensuring the feasibility of the first-stage variables for all possible scenarios, including the worst case. According to the structural characteristics of the proposed model based on the E-TSRO method, a column-and-constraint generation (C&CG) algorithm is utilized to solve the proposed model. Finally, the effectiveness of the E-TSRO model and the solution algorithm are analyzed and validated through a series of experiments, and thus obtaining some important conclusions, i.e., the economic efficiency of system operation can be improved at about 6.7% in comparison with the C-TSRO.

关键词： two-stage robust optimization island microgrid energy management column-and-constraint generation

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LP-based approximations for disjoint bilinear and two-stage adjustable robust optimization

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MATHEMATICAL PROGRAMMING 2024年第1-2期206卷 239-281页

作者： El Housni, Omar Foussoul, Ayoub Goyal, Vineet Cornell Univ Operat Res & Informat Engn New York NY USA Columbia Univ Ind Engn & Operat Res New York NY 10027 USA

We consider the class of disjoint bilinear programs max {x(T) y | x is an element of X, y is an element of Y} where X and Y are packing polytopes. We present an O( log logm1 /logm1 log logm2/ logm2)-approximation algorithm for this problem where m1 and m2 are the number of packing constraints in X and Y respectively. In particular, we show that there exists a near-optimal solution ( (x) over tilde, (y) over tilde) such that (x) over tilde and (y) over tilde are "near-integral". We give an LP relaxation of the problem from which we obtain the near-optimal near-integral solution via randomized rounding. We show that our relaxation is tightly related to the widely used reformulation linearization technique. As an application of our techniques, we present a tight approximation for the two-stage adjustable robust optimization problem with covering constraints and right-hand side uncertainty where the separation problem is a bilinear optimization problem. In particular, based on the ideas above, we give an LP restriction of the two-stage problem that is an O( log n /log log n log L/ log log L)-approximation where L is the number of constraints in the uncertainty set. This significantly improves over state-of-the-art approximation bounds known for this problem. Furthermore, we show that our LP restriction gives a feasible affine policy for the two-stage robust problem with the same (or better) objective value. As a consequence, affine policies give an O( log n log log n/ log L log log L)-approximation of the two-stage problem, significantly generalizing the previously known bounds on their performance.

关键词： Disjoint bilinear programming two-stage robust optimization Approximation algorithms RLT Affine policies

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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

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APPLIED ENERGY 2024年 362卷

作者： Ju, Liwei Bai, Xiping Li, Gen Gan, Wei Qi, Xin Ye, Fan North China Elect Power Univ Sch Econ & Management Changping 102206 Beijing Peoples R China North China Elect Power Univ Beijing Key Lab New Energy & Low Carbon Dev Beijing 102206 Peoples R China Tech Univ Denmark DTU Dept Engn Technol & Didact DK-2750 Ballerup Denmark Cardiff Univ Sch Engn Cardiff CF24 3AA Wales State Grid Jiangxi Extra High Voltage Co Nanchang 330096 Peoples R China

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.

关键词： Variable renewable energy Shared energy storage two-stage robust optimization Benefit allocation

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two-stage robust QUADRATIC optimization WITH EQUALITIES AND ITS APPLICATION TO OPTIMAL POWER FLOW

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SIAM JOURNAL ON optimization 2023年第4期33卷 2830-2857页

作者： Kuryatnikova, Olga Ghaddar, Bissan Molzahn, Daniel K. Erasmus Univ Econometr Inst NL-3062 PA Rotterdam Netherlands Western Univ Ivey Business Sch London ON NG6 0N1 Canada Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30313 USA

In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed, and the rest of the optimization variables (state variables) are set up as a solution to a known system of possibly nonlinear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems as well as gas and water networks. We propose a convergent iterative algorithm to build a sequence of approximately robustly feasible solutions with an improving objective value. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the nonlinearity of other constraints. We implement our approach and demonstrate its performance on Matpower instances of AC optimal power flow. Although this paper focuses on quadratic problems, the approach is suitable for more general setups.

关键词： nonconvex quadratic optimization two-stage robust optimization AC optimal power flow uncertainty in energy systems

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LP-Based Approximations for Disjoint Bilinear and two-stage Adjustable robust optimization 1

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23rd International Conference on Integer Programming and Combinatorial optimization (IPCO)

作者： El Housni, Omar Foussoul, Ayoub Goyal, Vineet Cornell Tech ORIE New York NY USA Columbia Univ IEOR New York NY 10027 USA

ISBN: (数字)9783031069017

ISBN: (纸本)9783031069017;9783031069000

We consider the class of disjoint bilinear programs max {x(T) y vertical bar x is an element of X, y is an element of Y} where X and Y are packing polytopes. We present an O(log log m(1)/log m(1) log log m(2)/log m(2))-approximation algorithm for this problem where m(1) and m(2) are the number of packing constraints in X and Y respectively. In particular, we show that there exists a near-optimal solution (x, y) such that x and y are "near-integral". We give an LP relaxation of this problem from which we obtain the nearoptimal near-integral solution via randomized rounding. As an application of our techniques, we present a tight approximation for the two-stage adjustable robust optimization problem with covering constraints and right-hand side uncertainty where the separation problem is a bilinear optimization problem. In particular, based on the ideas above, we give an LP restriction of the two-stage problem that is an O(log n/log log n log L/log log L)-approximation where L is the number of constraints in the uncertainty set. This significantly improves over state-of-the-art approximation bounds known for this problem.

关键词： Disjoint bilinear programming two-stage robust optimization Approximation algorithms

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

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FRONTIERS IN ENERGY RESEARCH 2024年 12卷

作者： Yang, Hailin Liu, Fei Yang, Hui Zhang, Xiangcheng Liu, Liantao State Grid Qinghai Elect Power Co Econ & Technol Res Inst Xining Qinghai Peoples R China North China Elect Power Univ Sch Econ & Management Beijing Peoples R China

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.

关键词： new flexibility resource configuration model uncertainty two-stage robust optimization flexibility characterization

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Data-driven prediction of relevant scenarios for robust combinatorial optimization

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COMPUTERS & OPERATIONS RESEARCH 2025年 174卷

作者： Goerigk, Marc Kurtz, Jannis Univ Passau Business Decis & Data Sci Dr Hans Kapfinger Str 30 D-94032 Passau Germany Univ Amsterdam Amsterdam Business Sch Plantage Muidergracht 12 NL-1018 TV Amsterdam Netherlands

We study iterative constraint and variable generation methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. The goal of this work is to find a set of starting scenarios that provides strong lower bounds early in the process. To this end we define the Relevant Scenario Recognition Problem (RSRP) which finds the optimal choice of scenarios which maximizes the corresponding objective value. We show for classical and two-stage robust optimization that this problem can be solved in polynomial time if the number of selected scenarios is constant and NP-hard if it is part of the input. Furthermore, we derive a linear mixed-integer programming formulation for the problem in both cases. Since solving the RSRP is not possible in reasonable time, we propose a machine-learning-based heuristic to determine a good set of starting scenarios. To this end, we design a set of dimension-independent features, and train a Random Forest Classifier on already solved small-dimensional instances of the problem. Our experiments show that our method is able to improve the solution process even for larger instances than contained in the training set, and that predicting even a small number of good starting scenarios can considerably reduce the optimality gap. Additionally, our method provides a feature importance score which can give new insights into the role of scenario properties in robust optimization.

关键词： robust optimization two-stage robust optimization Data-driven optimization Machine learning for optimization

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