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Leader-follower Optimal Selection Method for Distributed Control System in Active Distribution Networks

CSEE Journal of Power and Energy Systems 2024年第1期10卷 314-323页

作者： Jian Le Liangang Zhao Cao Wang Qian Zhou Yang Wang School of Electrical Engineering and Automation Wuhan UniversityWuhan 430072China

Aiming at the shortcomings of a traditional centralized control in an active distribution network(AND),this paper proposes a leader-follower distributed group cooperative control strategy to realize multiple operation and control tasks for an *** distributed information exchange protocols of the distributed generation(DG)group devoted to node voltage regulation or exchange power control are developed using a DG power utilization ratio as the consensus *** these bases,this study further investigates the leader optimal selection method for a DG group to improve the response speed of the distributed control ***,a single or multiple leader selection model is established to minimize the constraints of the one-step convergence factor and the number of leaders to improve the response speed of the distributed control *** simulation results of the IEEE 33 bus standard test system show the effectiveness of the proposed distributed control *** addition,the response speed of a DG control group can be improved effectively when the single or multiple leaders are selected optimally.

关键词： Active distribution1network consensus algorithm leader-follower system mixed-integer semidefinite programming optimal distributed control

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ON INTEGRALITY IN semidefinite programming FOR DISCRETE OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2024年第1期34卷 1071-1096页

作者： De Meijer, Frank Sotirov, Renata Delft Univ Technol Delft Inst Appl Math NL-2628 CD Delft Netherlands Tilburg Univ Dept Econometr & OR NL-5037 AB Tilburg Netherlands

It is well known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max -cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show similar results for a wide variety of discrete optimization problems for which SDP relaxations have been derived. Based on a comprehensive study on discrete positive semidefinite matrices, we introduce a generic approach to derive mixed -integer SDP (MISDP) formulations of binary quadratically constrained quadratic programs and binary quadratic matrix programs. Applying a problem -specific approach, we derive more compact MISDP formulations of several problems, such as the quadratic assignment problem, the graph partition problem, and the integer matrix completion problem. We also show that several structured problems allow for novel compact MISDP formulations through the notion of association schemes. Complementary to the recent advances on algorithmic aspects related to MISDP, this work opens new perspectives on solution approaches for the here considered problems.

关键词： mixed-integer semidefinite programming discrete positive semidefinite matrices binary quadratic programming quadratic matrix programming association schemes

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Flexible dynamic boundary microgrid operation considering network and load unbalances

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APPLIED ENERGY 2024年 371卷

作者： Su, Yu Li, Dingrui Wang, Fred Olama, Mohammed Ferrari, Maximiliano Ollis, Ben Liu, Yilu Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN 37996 USA ABB US Res Ctr Raleigh NC USA Oak Ridge Natl Lab Oak Ridge TN 37830 USA

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems - unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

关键词： Microgrids Dynamic boundaries Grid resilience mixed-integer linear programming mixed-integer semidefinite programming Inverter interfaced sources Unbalanced load

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Enabling Research through the SCIP Optimization Suite 8.0

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2023年第2期49卷 1-21页

作者： Bestuzheva, Ksenia Besancon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim Van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher Van Der Hulst, Rolf Koch, Thorsten Luebbecke, Marco Maher, Stephen J. Matter, Frederic Muehmer, Erik Mueller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schloesser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Inst Berlin Dept AIS2T Takustr 7 D-14195 Berlin Germany Beijing Inst Technol Sch Math & Stat 5 Zhongguancun South St Beijing 100081 Peoples R China Rhein Westfal TH Aachen Lehrstuhl Operat Res Kackertstr 7 D-52072 Aachen Germany Eindhoven Univ Technol Dept Math & Comp Sci POB 513 NL-5600 MB Eindhoven Netherlands Zuse Inst Berlin Dept ZIB AIS2T & I2DAMO GmbH Englerallee 19 D-14195 Berlin Germany Friedrich Alexander Univ Erlangen Nurnberg Dept Data Sci Cauerstr 11 D-91058 Erlangen Germany Univ Twente Dept Discrete Math & Math Programming POB 217 NL-7500 AE Enschede Netherlands Tech Univ Berlin Chair Software & Algorithms Discrete Optimizat Str 17 Juni 135 D-10623 Berlin Germany ZIB Dept A2IM Takustr 7 D-14195 Berlin Germany Univ Exeter Coll Engn Math & Phys Sci Harrison BldgStreatham CampusN Pk Rd Exeter EX4 4QF England Tech Univ Darmstadt Fachbereich Math Dolivostr 15 D-64293 Darmstadt Germany Zuse Inst Berlin Dept A2IM Takustr 7 D-14195 Berlin Germany Tech Univ Berlin Berlin Germany Zuse Inst Berlin GAMS Software GmbH Dept AIS2T Takustr 7 D-14195 Berlin Germany

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.

关键词： Constraint integer programming linear programming mixed-integer linear programming mixed-integer nonlinear programming optimization solver branch-and-cut branch-and-price column generation parallelization mixed-integer semidefinite programming

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Handling Symmetries in mixed-integer semidefinite Programs 1

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20th International Conference on the Integration of Constraint programming, Artificial Intelligence, and Operations Research (CPAIOR)

作者： Hojny, Christopher Pfetsch, Marc E. Eindhoven Univ Technol Dept Math & Comp Sci POB 513 NL-5600 MB Eindhoven Netherlands Tech Univ Darmstadt Dept Math Dolivostr 15 D-64293 Darmstadt Germany

ISBN: (数字)9783031332715

ISBN: (纸本)9783031332708;9783031332715

Symmetry handling is a key technique for reducing the running time of branch-and-bound methods for solving mixed-integer linear programs. In this paper, we generalize the notion of (permutation) symmetries to mixed-integer semidefinite programs (MISDPs). We first discuss how symmetries of MISDPs can be automatically detected by finding automorphisms of a suitably colored auxiliary graph. Then known symmetry handling techniques can be applied. We demonstrate the effect of symmetry handling on different types of MISDPs. To this end, our symmetry detection routine is implemented in the state-of-the-art MISDP solver SCIP-SDP. We obtain speed-ups similar to the mixed-integer linear case.

关键词： mixed-integer semidefinite programming symmetry handling branch-and-bound

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Ellipsoidal buffered area under the curve maximization model with variable selection in credit risk estimation

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COMPUTATIONAL MANAGEMENT SCIENCE 2023年第1期20卷 1-28页

作者： Tanaka, Katsuhiro Yamamoto, Rei Keio Univ Dept Ind & Syst Engn 3-14-1 HiyoshiKohoku ku Yokohama Kanagawa 2238522 Japan

In 2019, a buffered AUC (bAUC) maximization model with the linear classifier was developed to maximize the area under the curve (AUC), a popular statistic for evaluating classification performance. Previous studies have recently used the bAUC for different problems. We propose a new bAUC maximization model, including the ellipsoidal classifier and the variable selection constraint, to enhance classification performance. However, the proposed model is hard to solve because it is formulated as a mixed-integer semidefinite programming (MISDP) problem with numerous constraints. Several algorithms have been proposed to solve MISDP, but no algorithm has been proposed that can quickly solve a problem of this size. Tanaka and Yamamoto (Int J Financ Eng, 2022. https://***/10.1142/S2424786321500420 specifically suggested a heuristic algorithm for solving MISDP under hundreds of constraints, but it might not be effective for problems in this study. Therefore, we enhance the heuristic algorithm in Tanaka and Yamamoto (Int J Financ Eng, 2022. https://***/10.1142/S2424786321500420 to quickly attain solutions to our suggested MISDP and show that the proposed heuristic algorithm derives superior solutions to existing algorithms. Furthermore, we demonstrate that for a classification problem related to credit risk estimation using real-world corporate rating data, the tailored bAUC maximization model outperforms the existing bAUC maximization and standard machine learning models in terms of generalization performance.

关键词： Heuristics Buffered area under the curve mixed-integer semidefinite programming Ellipsoidal classifier Variable selection

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Towards understanding sensor and control nodes selection in nonlinear dynamic systems: Lyapunov theory meets branch-and-bound

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AUTOMATICA 2021年 134卷

作者： Nugroho, Sebastian A. Taha, Ahmad F. Univ Michigan Dept Elect Engn & Comp Sci 1301 Beal Ave Ann Arbor MI 48109 USA Vanderbilt Univ Dept Civil & Environm Engn 2201 West End Ave Nashville TN 37235 USA

Sensor and actuator selection problems (SASPs) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASPs are indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SAs) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASPs in nonlinear dynamic systems (NDSs), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDSs into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASPs. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASPs for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SAs combination for stable/unstable NDSs that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Sensor selection Actuator selection Nonlinear dynamic systems Lipschitz continuous mixed-integer semidefinite programming Branch-and-bound algorithm

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Topology-Finding of Tensegrity Structures Considering Global Stability Condition

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JOURNAL OF STRUCTURAL ENGINEERING 2020年第12期146卷

作者： Wang, Yafeng Xu, Xian Luo, Yaozhi Zhejiang Univ Dept Civil Engn 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China Swiss Fed Inst Technol Sch Architecture Civil & Environm Engn Appl Comp & Mech Lab CH-1015 Lausanne Switzerland

This study proposes a general framework for topology-finding or topology optimization of tensegrity structures. The existing topology-finding formulation of tensegrity structures based on mixed-integer linear programming (MILP) was improved and transformed into a formulation based on mixed-integer semidefinite programming (MISDP) which considers the global stability condition of tensegrity. We illustrated and analyzed two undesirable phenomena, loss of prestress stability and loss of integrity, caused by the missing global stability condition in previous MILP-based approaches. A branch-and-bound algorithm combined with a primal-dual interior-point algorithm is employed to solve the proposed MISDP model. Some numerical examples illustrated the improvements and effectiveness of the proposed approach. The proposed approach successfully can avoid the two undesirable phenomena and ensure the global stability of the found tensegrity structures. By using different stability conditions in the topology-finding process, the proposed approach can find general stable tensegrity structures and superstable tensegrity structures. DOI: 10.1061/(ASCE)ST.1943-541X.0002843. (c) 2020 American Society of Civil Engineers.

关键词： Tensegrity structures Topology-finding Global stability condition mixed-integer semidefinite programming

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A framework for solving mixed-integer semidefinite programs

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OPTIMIZATION METHODS & SOFTWARE 2018年第3期33卷 594-632页

作者： Gally, Tristan Pfetsch, Marc E. Ulbrich, Stefan Tech Univ Darmstadt Dept Math Darmstadt Germany

mixed-integer semidefinite programs (MISDPs) arise in many applications and several problem-specific solution approaches have been studied recently. In this paper, we investigate a generic branch-and-bound framework for solving such problems. We first show that strict duality of the semidefinite relaxations is inherited to the subproblems. Then solver components such as dual fixing, branching rules, and primal heuristics are presented. We show the applicability of an implementation of the proposed methods on three kinds of problems. The results show the positive computational impact of the different solver components, depending on the semidefinite programming solver used. This demonstrates that practically relevant MISDPs can successfully be solved using a general purpose solver.

关键词： mixed-integer semidefinite programming branch-and-bound strong duality dual fixing branching rules

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Allocating Sensors and Actuators via Optimal Estimation and Control

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2017年第3期25卷 1060-1067页

作者： Taylor, Joshua A. Luangsomboon, Natchanon Fooladivanda, Dariush Univ Toronto Dept Elect & Comp Engn Toronto ON M5S Canada

We consider the problem of planning the location and size of sensors and actuators to achieve optimal dynamic performance. Using basic results from control and convex optimization, we formulate mixed-integer semidefinite programs for the actuator placement and sizing to obtain the linear quadratic regulator with the lowest cost, and the sensor placement to obtain the Kalman filter with the lowest error. The two formulations are nearly identical due to the duality of optimal linear control and estimation. We also pose similar problems in terms of observability and controllability, which result in smaller mixed-integer semidefinite programs. Since the mixed-integer semidefinite programing is not yet a mature technology, we also use greedy heuristics in conjunction with continuous semidefinite programming. The approach is demonstrated on two modern applications from power systems: the placement and sizing of energy storage for regulation and the placement of phasor measurement units for estimation.

关键词： Energy storage Kalman filter (KF) linear quadratic regulator (LQR) mixed-integer semidefinite programming phasor measurement unit (PMU) sensor and actuator placement

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