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mixed integer Optimization of the Flow Pattern for Stochastic Feeder Reconfiguration

IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第1期39卷 1896-1904页

作者： Jabr, Rabih A. Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

mixed-integer conic programming provides an approach to solving the Optimal Feeder Reconfiguration (OFR) problem with guarantees on the quality of the solution. Integrating renewable generation into the distribution network and its associated variability renders stochastic OFR, which simultaneously considers several snapshots of the network, a more viable approach. While the established mixed-integer conic program for deterministic OFR can be extended to the stochastic case, the resulting optimization problem that still uses the bus injection relaxation is challenging to solve. This paper proposes a new mixed integer conic optimization of the flow pattern for solving the stochastic OFR. The new optimization framework exploits the perspective reformulation to obtain a tighter relaxation for stochastic OFR, which improves computational performance, and a feasibility pump heuristic to give a feasible solution. The mixed integer optimization of the flow pattern can also provide an initial solution to the mixed integer conic program employing the bus injection relaxation, giving rise to a hierarchical solution approach. Numerical results on stochastic OFR show that the hierarchical approach provides much-improved system performance compared to solutions considering a single snapshot. In addition, the proposed feasibility pump heuristic gives rise to network configurations close to global optimality in several test instances.

关键词： Feasibility pump mixed-integer conic programming network reconfiguration perspective reformulation power distribution stochastic optimization

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Perspective Reformulations of the Two-Level Service Restoration Problem

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第2期39卷 4714-4722页

作者： Jabr, Rabih A. Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

This article presents the two-level service restoration problem, which involves finding a reconfigured network suitable for serving the loads while a fault affecting some components is attended to. The first stage minimizes the actual branch overload in the reconfigured network. In contrast, the second stage chooses the network structure that maintains an acceptable voltage profile while preserving the overload level of the first stage. The two-level solution paradigm differs from some real-life implementations of service restoration programs based on the secure flow pattern concept, which employs successive branch openings to minimize a load balancing index. The proposed two-level service restoration problem is solved using a sequence of two mixed-integer conic programs, for which solvers that guarantee global optimality are available. The presented perspective reformulation combines tight relaxations in mixed-integer conic programming with the poly-hedral representation to expedite the search for the reconfigured network. Numerical results are reported on networks that have over 900 switchable branches. The results demonstrate that while the secure flow pattern implementation relying on branch opening provides results close to the globally optimal load balancing, much improvement to the actual branch overloads and voltage profile is attained from the proposed two-level service restoration problem.

关键词： mixed-integer conic programming network reconfiguration perspective reformulation power distribution service restoration two-level optimization

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Optimal Reconfiguration of Power Distribution Grids to Maintain Line Thermal Efficiency During Progressive Wildfires

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IEEE SYSTEMS JOURNAL 2024年第1期18卷 632-643页

作者： Rostamzadeh, Mehdi Kapourchali, Mohammad Heidari Zhao, Long Aravinthan, Visvakumar Wichita State Univ Dept Elect & Comp Engn Wichita KS 67260 USA Univ Alaska Anchorage Dept Elect Engn Anchorage AK 99508 USA Alaska Ctr Energy & Power Fairbanks AK 99775 USA South Dakota Sch Mines & Technol Dept Elect Engn & Comp Sci Rapid City SD 57701 USA

The worsening wildfires due to intensified climate variability increases the risk of both unplanned power outages as well as planned power line de-energizations. It is because wildfires cause thermal stress on overhead conductors, which harms the mechanical properties of overhead distribution lines. This article proposes a proactive strategy for improving the operational efficiency and decision-making capabilities of power distribution networks under progressive wildfire conditions. Dynamic heat balance equations are used to characterize the effect of wildfire on the overhead line conductors. The optimal dynamic reconfiguration of the distribution system and the operation of backup generators are considered as tools to minimize the curtailed loads while maintaining the maximum flow of current through the lines within the thermal rating of the line conductors. A mixed-integer conic programming model is adopted to minimize the operation and load curtailment costs. A higher value of lost load is applied to enhance the continuity of the electricity supply to critical loads. The proposed framework is tested under various environmental conditions and wildfire paths using both a modified 33-node network and the practical 83-node Taiwan Power Company's distribution grid. Results show that the proposed approach enhances proactive decision-making for power distribution system operations and increases the resilience of critical loads to wildfire threats.

关键词： Heat gain heat loss mixed-integer conic programming power distribution grid reconfiguration thermal rating wildfire

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Sizing and Siting of Energy Storage Systems in a Military-Based Vehicle-to-Grid Microgrid

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2021年第3期57卷 1909-1919页

作者： Lai, Kexing Zhang, Lin Kansas State Univ Dept Elect & Comp Engn Manhattan KS 66506 USA Amer Elect Power Co New Albany OH 43054 USA

Due to the absence of utility power grid infrastructure in remote military bases, on-site diesel generators serve as the primary sources for power demands. Increasing efficiency and preventing frequent startup/shutdown operations of on-site diesel generators are therefore becoming a critical issue for reducing fuel cost. Application of vehicle-to-grid technology in a military-based microgrid embodies potential for significant fuel economy benefits since on-board vehicle generators and energy storage units can serve as mobile power sources that provide higher flexibility for supplying power demands. In addition, energy storage system integration is considered as an alternative solution for increasing on-site diesel generators efficiency and lessening their startup/shutdown operations. This article proposes a three-stage planning procedure for identifying the optimal locations and capacities of energy storage systems, considering multiple operating scenarios via stochastic programming. Note that on-site diesel generators and on-board vehicle generators support plug-and-play functionality, meaning their startup/shutdown operations can be decided in real time. Furthermore, network-constrained ac unit commitment model is used to optimize operation of microgrids. It is assumed that in the tested microgrid systems, several tactical military vehicles with on-board generators and energy storage units are deployed as alternative power sources. The economic merits of vehicle-to-grid implementation and energy storage system integration in a military-based microgrid are validated in the numerical studies.

关键词： Generators Energy storage Microgrids Fuels Indexes Vehicle-to-grid Real-time systems Energy storage system (ESS) microgrid military vehicle-to-grid (V2G) mixed-integer conic programming unit commitment

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Consistent Second-Order conic integer programming for Learning Bayesian Networks

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年 24卷

作者： Kucukyavuz, Simge Shojaie, Ali Manzour, Hasan Wei, Linchuan Wu, Hao-Hsiang Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Washington Dept Biostat Seattle WA USA Univ Washington Dept Ind & Syst Engn Seattle WA USA Natl Yang Ming Chiao Tung Univ Dept Management Sci Hsinchu Taiwan

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as a mixed-integer program with an objective function composed of a convex quadratic loss function and a regularization penalty subject to linear constraints. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. However, the state-of-the-art optimization solvers are not able to obtain provably optimal solutions to the existing mathematical formulations for medium -size problems within reasonable computational times. To address this difficulty, we tackle the problem from both computational and statistical perspectives. On the one hand, we propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution to the mixed-integer program, and establish the consistency of this approximate solution. On the other hand, we improve the existing formulations by replacing the linear "big -M" constraints that represent the relationship between the continuous and binary indicator variables with second-order conic constraints. Our numerical results demonstrate the effectiveness of the proposed approaches.

关键词： mixed-integer conic programming Bayesian networks directed acyclic graphs early stopping criterion consistency

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Consistent second-order conic integer programming for learning Bayesian networks

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 15299-15336页

作者： Simge Küçükyavuz Ali Shojaie Hasan Manzour Linchuan Wei Hao-Hsiang Wu Department of Industrial Engineering and Management Sciences Northwestern University Department of Biostatistics University of Washington Department of Industrial and Systems Engineering University of Washington Department of Management Science National Yang Ming Chiao Tung University

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as a mixed-integer program with an objective function composed of a convex quadratic loss function and a regularization penalty subject to linear constraints. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. However, the state-of-the-art optimization solvers are not able to obtain provably optimal solutions to the existing mathematical formulations for mediumsize problems within reasonable computational times. To address this difficulty, we tackle the problem from both computational and statistical perspectives. On the one hand, we propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution to the mixed-integer program, and establish the consistency of this approximate solution. On the other hand, we improve the existing formulations by replacing the linear "big-M" constraints that represent the relationship between the continuous and binary indicator variables with second-order conic constraints. Our numerical results demonstrate the effectiveness of the proposed approaches.

关键词： mixed-integer conic programming Bayesian networks directed acyclic graphs early stopping criterion consistency

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Joint Beam-Hopping Scheduling and Power Allocation in NOMA-Assisted Satellite Systems

Joint Beam-Hopping Scheduling and Power Allocation in NOMA-A...

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IEEE Wireless Communications and Networking Conference (WCNC)

作者： Wang, Anyue Lei, Lei Lagunas, Eva Chatzinotas, Symeon Perez Neira, Ana Isabel Ottersten, Bjorn Univ Luxembourg Interdisciplinary Ctr Secur Reliabil & Trust SnT Luxembourg Luxembourg Ctr Tecnol Telecomunicac Catalunya CTTC CERCA Castelldefels Spain

ISBN: (纸本)9781728195056

In this paper, we investigate potential synergies of non-orthogonal multiple access (NOMA) and beam hopping (BH) for multi-beam satellite systems. The coexistence of BH and NOMA provides time-power-domain flexibilities in mitigating a practical mismatch effect between offered capacity and requested traffic per beam. We formulate the joint BH scheduling and NOMA-based power allocation problem as mixed-integer non-convex programming. We reveal the exponential-conic structure for the original problem, and reformulate the problem to the format of mixed-integer conic programming (MICP), where the optimum can be obtained by exponential-complexity algorithms. A greedy scheme is proposed to solve the problem on a timeslot-by-timeslot basis with polynomial-time complexity. Numerical results show the effectiveness of the proposed efficient suboptimal algorithm in reducing the matching error by 62.57% in average over the OMA scheme and achieving a good trade-off between computational complexity and performance compared to the optimal solution.

关键词： NOMA beam hopping multi-beam satellite systems resource allocation mixed-integer conic programming

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conic relaxation approaches for equal deployment problems

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DISCRETE APPLIED MATHEMATICS 2020年 275卷 111-125页

作者： Safarina, Sena Moriguchi, Satoko Mullin, Tim J. Yamashita, Makoto Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku 2-12-1-W8-29 Ookayama Tokyo 1528552 Japan Tokyo Metropolitan Univ Fac Econ & Business Adm 1-1 Minami Osawa Hachioji Tokyo 1920397 Japan Swedish Forestry Res Inst Skogforsk Box 3 S-91821 Savar Sweden 224 Rue Grand Royal Est Shefford PQ J2M 1R5 Canada

An important problem in the breeding of livestock, crops, and forest trees is the optimum selection of genotypes that maximize genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures genetic diversity, so that optimal selection can be cast as a second-order cone programming (SOCP) problem. Yamashita et al. (2015) exploit the structural sparsity of the quadratic constraints and reduce the computation time drastically while attaining the same optimal solution. This paper is concerned with a special case of equal deployment (ED), in which we solve the optimal selection problem with the constraint that contribution of genotypes must either be a fixed size or zero. This involves a form of combinatorial optimization, and the ED problem can be described as a mixed-integer SOCP problem. In this paper, we discuss conic relaxation approaches for the ED problem based on LP (linear programming), SOCP, and SDP (semidefinite programming). We then propose a steepest-ascent method that combines the solution obtained from the conic relaxation with a concept from discrete convex optimization, in order to acquire an approximate solution for the ED problem in a practical time. From numerical tests, we observed that among the LP, SOCP, and SDP relaxation problems, SOCP gave a suitable solution from the viewpoint of the optimality and computation time. The steepest-ascent method starting from the SOCP solution provides high-quality solutions much faster than other existing methods that have been widely used for optimal selection. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Semidefinite programming Second-order cone programming mixed-integer conic programming conic relaxation Tree breeding Equal deployment problem

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A mixed integer conic Model for Distribution Expansion Planning: Matheuristic Approach

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IEEE TRANSACTIONS ON SMART GRID 2020年第5期11卷 3932-3943页

作者： Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mahdi Lehtonen, Matti Mantovani, Jose Roberto Sanches Sao Paulo State Univ Dept Elect Engn BR-15385000 Ilha Solteira Brazil Aalto Univ Dept Elect Engn & Automat Espoo 02150 Finland

This paper presents a mixed-integer conic programming model (MICP) and a hybrid solution approach based on classical and heuristic optimization techniques, namely matheuristic,to handle long-term distribution systems expansion planning (DSEP) problems. The model considers conventional planning actions as well as sizing and allocation of dispatchable/renewable distributed generation (DG) and energy storage devices (ESD).The existing uncertainties in the behavior of renewable sources and demands are characterized by grouping the historical data via the k-means. Since the resulting stochastic MICPis a convex-based formulation, finding the global solution of the problem using a commercial solver is guaranteed while the computational efficiency in simulating the planning problem of medium- or large-scale systems might not be satisfactory. To tackle this issue, the subproblems of the proposed mathematical model are solved iteratively via a specialized optimization technique based on variable neighborhood descent (VND) algorithm. To show the effectiveness of the proposed model and solution technique, the 24-node distribution system is profoundly analyzed, while the applicability of the model is tested on a 182-node distribution *** results reveal the essential requirement of developing specialized solution techniques for large-scale systems where classical optimization techniques are no longer an alternative to solve such planning problems.

关键词： Distribution systems expansion planning energy storage devices VND-based matheuristic algorithm mixed-integer conic programming stochastic programming

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Sizing and Siting of Energy Storage Systems in a Military Based Vehicle-to-Grid Microgrid

Sizing and Siting of Energy Storage Systems in a Military Ba...

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IEEE-Industry-Applications-Society Annual Meeting

作者： Lai, Kexing Zhang, Lin Kansas State Univ Elect & Comp Engn Manhattan KS 66506 USA Amer Elect Power Co New Albany OH 43054 USA

ISBN: (纸本)9781728171920

Due to the absence of utility power grid infrastructure in remote military bases, on-site diesel generators serve as the primary sources for power demands. Increasing efficiency and preventing frequent startup/shutdown operations of on-site diesel generators are therefore becoming a critical issue for reducing fuel cost. Application of vehicle-to-grid technology in a military based microgrid has embodies potential for significant fuel economy benefits since vehicles can act as mobile power sources that provides higher flexibility for supplying power demands. In addition, energy storage system integration is considered as an alternative solution for increasing on-site diesel generators efficiency and lessening their start-up/shutdown operations. To further improve fuel economy in a remote military based microgrid, this paper proposes a three-stage planning procedure for identifying the optimal locations and capacities of energy storage systems, considering multiple operating scenarios via stochastic programming. In the first stage, the optimal sizing and siting strategy of storage units for each individual operating scenario is determined. In the second stage, the expected value of optimal locations and capacities of energy storage systems for all the scenarios, which are determined the first stage are obtained as the near-optimal result. In the third stage, with fixed location and capacities of energy storage systems, the optimal operation of microgrid is simulated to demonstrate their benefits. It is assumed that, in the tested microgrid systems, several tactical military vehicles with on-board generators and energy storage units are deployed as alternative power sources. Note that on-site diesel generators and on-board vehicle generators support plug-and-play functionality, meaning their start-up/shutdown operations can be decided in real time. Furthermore, network-constrained AC unit commitment model is used to optimize operation of microgrids. The economic merit

关键词： unit commitment energy storage system microgrid mixed-integer conic programming military vehicle-to-grid

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