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Coordinated Planning With Predetermined Renewable Energy Generation Targets Using Extended two-stage robust optimization

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IEEE ACCESS 2020年 8卷 2395-2407页

作者： Tian, Kunpeng Sun, Weiqing Han, Dong Yang, Ce Univ Shanghai Sci & Technol Dept Control Sci & Engn Shanghai 200093 Peoples R China Univ Shanghai Sci & Technol Dept Elect Engn Shanghai 200093 Peoples R China

Coordinated planning is an effective method to balance investment costs and benefits in achieving high renewable target under the renewable-driven power system expansion wave. This paper proposes a coordinated planning model to support the efficient achievement of renewable target considering economy of the system by accounting for the interaction among source, grid, and energy storage system. An adaptive two-stage min-max-min robust optimization model is formulated to take into account renewable target as well as the uncertainty associated with renewable production and load demand. To reduce the conservatism of robust optimization, uncertain budget, multiple uncertain sets, and data-driven method are used to design uncertain sets. The resulting model is transformed into a tractable bi-level programming through strong duality theory and big-M method. A customized column-and-constraint generation algorithm is used to solve the bi-level programming. Simulation results presented for the modified IEEE 30-bus test system corroborates the effectiveness of the methodology, which finds siting and sizing of renewable energy sources and energy storage systems as well as transmission expansion schemes. It is capable to provide a fiexible planning tool driven by renewable target under a reasonable computational burden.

关键词： Coordinated planning renewable target two-stage robust optimization multiple uncertain sets data-driven column-and-constraint generation algorithm

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Oracle-based algorithms for binary two-stage robust optimization

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COMPUTATIONAL optimization AND APPLICATIONS 2020年第2期77卷 539-569页

作者： Kaemmerling, Nicolas Kurtz, Jannis TU Dortmund Univ Inst Transport Logist Leonhard Euler Str 2 D-44227 Dortmund Germany Rhein Westfal TH Aachen Chair Math Informat Proc Pontdriesch 12-14 D-52062 Aachen Germany

In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

关键词： two-stage robust optimization Non-linear binary optimization Branch and bound algorithm

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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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Saddle point approximation approaches for two-stage robust optimization problems

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JOURNAL OF GLOBAL optimization 2020年第4期78卷 651-670页

作者： Zhang, Ning Fang, Chang Dongguan Univ Technol Sch Comp Sci & Technol Dongguan 523808 Guangdong Peoples R China Anhui Normal Univ Sch Econ & Management 189 Jiuhua South Rd Wuhu City 241002 Anhui Peoples R China

This paper aims to present improvable and computable approximation approaches for solving the two-stage robust optimization problem, which arises from various applications such as optimal energy management and production planning. Based on sampling finite number scenarios of uncertainty, we can obtain a lower bound approximation and show that the corresponding solution is at least -level feasible. Moreover, piecewise linear decision rules (PLDRs) are also introduced to improve the upper bound that obtained by the widely-used linear decision rule. Furthermore, we show that both the lower bound and upper bound approximation problems can be reformulated into solvable saddle point problems and consequently be solved by the mirror descent method.

关键词： two-stage robust optimization Randomized approach Piecewise linear decision rule Saddle point problem Mirror descent algorithm

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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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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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Designing networks with resiliency to edge failures using two-stage robust optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期279卷 704-720页

作者： Matthews, Logan R. Gounaris, Chrysanthos E. Kevrekidis, Ioannis G. Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Johns Hopkins Univ Dept Chem & Biomol Engn Baltimore MD USA

We study the design of resilient single-commodity flow networks that can remain robust against multiple concurrent edge failures. We model these failures as binary random variables, allowing us to formally formulate the network design problem as a two-stage robust optimization problem. With an objective of minimizing the overall cost of building and operating the network, the capacities of the edges are decided in the first stage, while the optimal flows are determined in the second stage once the uncertainty has been realized. We first examine the standard affine decision rules approach and show that it is not a viable approach when two or more edges are allowed to fail at the same time. We then propose a column and constraint generation algorithm that we tailor to this application. Since the problem does not satisfy the relatively complete recourse assumption, we employ an oracle with two subproblems: one to determine edge failure scenarios that render the required demand satisfaction infeasible, and if no such scenario exists, a second one to determine the flow rerouting plan of highest cost. Our column and constraint generation algorithm is applied to networks adapted from the Survivable Network Design Library. For each instance, we determine sequences of fully adaptive, robust optimal solutions for various levels of resiliency, identifying also the maximum number of concurrent edge failures that can be sustained by these networks. Finally, we demonstrate how our algorithm can be applied to a defender versus attacker context, via the use of a decision-dependent uncertainty set. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Networks Network design Network resiliency two-stage robust optimization Column and constraint generation

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Staffing and scheduling flexible call centers by two-stage robust optimization

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2017年 72卷 25-37页

作者： Mattia, Sara Rossi, Fabrizio Servilio, Mara Smriglio, Stefano CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy Univ Aquila Dipartimento Ingn Sci & Informaz & Matemat Via Vetoio I-67010 Coppito AQ Italy

We study the shift scheduling problem in a multi-shift, flexible call center. Differently from previous approaches, the staffing levels ensuring the desired quality of service are considered uncertain, leading to a two-stage robust integer program with right-hand-side uncertainty. We show that, in our setting, modeling the correlation of the demands in consecutive time slots is easier than in other staffing approaches. The complexity issues of a Benders type reformulation are investigated and a branch-and-cut algorithm is devised. The approach can efficiently solve real-world problems from an Italian call center and effectively support managers decisions. In fact, we show that robust shifts have very similar costs to those evaluated by the traditional (deterministic) method while ensuring a higher level of protection against uncertainty. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Call center optimization Shift scheduling two-stage robust optimization Benders decomposition

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A two-stage robust optimization for Centralized-Optimal Dispatch of Photovoltaic Inverters in Active Distribution Networks

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2017年第2期8卷 744-754页

作者： Ding, Tao Li, Cheng Yang, Yongheng Jiang, Jiangfeng Bie, Zhaohong Blaabjerg, Frede Xi An Jiao Tong Univ Dept Elect Engn State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China Aalborg Univ Dept Energy Technol DK-9220 Aalborg Denmark

Optimally dispatching photovoltaic (PV) inverters is an efficient way to avoid overvoltage in active distribution networks, which may occur in the case of the PV generation surplus load demand. Typically, the dispatching optimization objective is to identify critical PV inverters that have the most significant impact on the network voltage level. Following, it ensures the optimal set-points of both active power and reactive power for the selected inverters, guaranteeing the entire system operating constraints (e.g., the network voltage magnitude) within reasonable ranges. However, the intermittent nature of solar PV energy may affect the selection of the critical PV inverters and also the final optimal objective value. In order to address this issue, a two-stage robust centralized-optimal dispatch model is proposed in this paper to achieve a robust PV inverter dispatch solution considering the PV output uncertainties. In addition, the conic relaxation-based branch flow formulation and the column-and-constraint generation algorithm are employed to deal with the proposed robust optimization model. Case studies on a 33-bus distribution network and comparisons with the deterministic optimization approach have demonstrated the effectiveness of the proposed method.

关键词： Active distribution network column-and-constraint generation algorithm optimal inverter dispatch (OID) photovoltaic generation two-stage robust optimization

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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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