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A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its Pareto Frontier

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2017年 88卷 13-20页

作者： Ding, Tao Li, Cheng Li, Fangxing Chen, Tianen Liu, Ruifeng Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN USA Northwest China Grid Co Ltd NWG 50 Middle Segment East Huancheng Rd Xian 710048 Shaanxi Peoples R China

The DC optimal power flow (DC-OPF) plays an important role in the operation and planning of modern power systems. In this paper, a bi-objective DC-OPF model minimizing both network losses and generation costs is introduced, which can further be converted into a single objective model via the weighted sum method. Furthermore, the Pareto Frontier is employed to solve this problem. In the mathematical view, the model is a special non-convex quadratic constraints quadratic programming problem. In order to obtain a continuous Pareto Frontier, the original non-convex feasible region is relaxed to its convex hull using a linear relaxation-based second order cone programming method. Compared with the semi-definite relaxation method, the proposed method can greatly reduce the number of dummy variables and the complexity of solutions. Finally, simulations on eight small systems and four practical, large systems are performed, in addition to the comparison of a Monte Carlo simulation. The results verify the effectiveness of the proposed algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Optimal power flow second order cone programming Pareto Frontier Multi-objective optimization Linear relaxation

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A note on second order cone programming approach to two-stage network data envelopment analysis

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期263卷 733-735页

作者： Guo, Chuanyin Wei, Fajie Chen, Yao Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Nanjing Audit Univ Coll Auditing & Evaluat Nanjing 211815 Jiangsu Peoples R China Univ Massachusetts Manning Sch Business Lowell MA 01845 USA

In network data envelopment analysis (DEA) literature, the general multiplicative two-stage network model, where the objective function is the product of the two stage efficiency ratios, is highly non-linear and is impossible to be directly transformed into linear programming problems. Chen and Zhu (2017) discovered that this model corresponds to a cone-type structure and can be transformed into a second order cone programming (SOCP) problem with a parameter. The transformed parametric SOCP problem is solved by computing a series of SOCP models when the parameter is varied. We show that Chen and Zhu's (2017) model can be directly transformed into a single SOCP problem, without the need for solving parametric SOCP problems. This greatly reduces the computational burden. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis Two-stage Multiplicative second order cone programming

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Weak infeasibility in second order cone programming

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OPTIMIZATION LETTERS 2016年第8期10卷 1743-1755页

作者： Lourenco, Bruno F. Muramatsu, Masakazu Tsuchiya, Takashi Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku 2-12-1-W8-41 Ookayama Tokyo 1528552 Japan Univ Electrocommun Dept Comp Sci 1-5-1 Chofugaoka Chofu Tokyo 1828585 Japan Natl Grad Inst Policy Studies Minato Ku 7-22-1 Roppongi Tokyo 1068677 Japan

The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a sequence of feasibility problems which mostly preserve the feasibility status of the original problem. This is used to show that for a given weakly infeasible problem at most m directions are needed to get arbitrarily close to the cone, where m is the number of Lorentz cones. We also tackle a closely related question and show that given a bounded optimization problem satisfying Slater's condition, we may transform it into another problem that has the same optimal value but it is ensured to attain it. From solutions to the new problem, we discuss how to obtain solution to the original problem which are arbitrarily close to optimality. Finally, we discuss how to obtain finite certificate of weak infeasibility by combining our own techniques with facial reduction. The analysis is similar in spirit to previous work by the authors on SDPs, but a different approach is required to obtain tighter bounds on the number of directions needed to approach the cone.

关键词： Weak infeasibility second order cone programming Feasibility problem

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A second order cone programming approach for semi-supervised learning

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PATTERN RECOGNITION 2013年第12期46卷 3548-3558页

作者： Huang, Gao Song, Shiji Gupta, Jatinder N. D. Wu, Cheng Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Univ Alabama Coll Business Adm Huntsville AL 35899 USA

Semi-supervised learning (SSL) involves the training of a decision rule from both labeled and unlabeled data. In this paper, we propose a novel SSL algorithm based on the multiple clusters per class assumption. The proposed algorithm consists of two stages. In the first stage, we aim to capture the local cluster structure of the training data by using the k-nearest-neighbor (kNN) algorithm to split the data into a number of disjoint subsets. In the second stage, a maximal margin classifier based on the second order cone programming (SOCP) is introduced to learn an inductive decision function from the obtained subsets globally. For linear classification problems, once the kNN algorithm has been performed, the proposed algorithm trains a classifier using only the first and second order moments of the subsets without considering individual data points. Since the number of subsets is usually much smaller than the number of training points, the proposed algorithm is efficient for handling big data sets with a large amount of unlabeled data. Despite its simplicity, the classification performance of the proposed algorithm is guaranteed by the maximal margin classifier. We demonstrate the efficiency and effectiveness of the proposed algorithm on both synthetic and real-world data sets. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Semi-supervised learning K-nearest-neighbor Support vector machine second order cone programming

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Robust second order cone conditions and duality for multiobjective problems under uncertainty data

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JOURNAL OF GLOBAL OPTIMIZATION 2024年第4期88卷 901-926页

作者： Tinh, Cao Thanh Chuong, Thai Doan Vietnam Natl Univ Ho Chi Minh City Vietnam Univ Informat Technol Dept Math & Phys Ho Chi Minh City Vietnam Brunel Univ London Dept Math London England Saigon Univ Dept Math & Applicat 273 Duong Vuong StDist 5 Ho Chi Minh City Vietnam

This paper studies a class of multiobjective convex polynomial problems, where both the constraint and objective functions involve uncertain parameters that reside in ellipsoidal uncertainty sets. Employing the robust deterministic approach, we provide necessary conditions and sufficient conditions, which are exhibited in relation to second order cone conditions, for robust (weak) Pareto solutions of the uncertain multiobjective optimization problem. A dual multiobjective problem is proposed to examine robust converse, robust weak and robust strong duality relations between the primal and dual problems. Moreover, we establish robust solution relationships between the uncertain multiobjective optimization program and a (scalar) second order cone programming relaxation problem of a corresponding weighted-sum optimization problem. This in particular shows that we can find a robust (weak) Pareto solution of the uncertain multiobjective optimization problem by solving a second order cone programming relaxation.

关键词： Multiobjective optimization second order cone programming Robust optimization Convex polynomial Optimality condition

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Collaborative optimization control of hybrid distribution transformers integrated with photovoltaics in unbalanced distribution networks

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 159卷

作者： Zhang, Lishi Kong, Zihan Liu, Yibin Liang, Deliang Fan, Libo Jin, Minhao Huang, Jiabin Xi An Jiao Tong Univ Sch Elect Engn State Key Lab Elect Insulat & Power Equipment Shaanxi Key Lab Smart Grid Xian 710049 Peoples R China State Grid Hangzhou Power Supply Co Hangzhou 310000 Peoples R China

This paper proposes a novel hybrid distribution transformer integrated with photovoltaic (HDT-PV) including a three-phase four-leg inverter, as a promising electrical device applied in the unbalanced active distribution network (ADN). The HDT-PV has the ability to access distributed PV system, balance three-phase power and provide reactive power compensation. In order to take advantage of these capabilities of the HDT-PV, collaborative optimization control strategy of HDT-PVs in the unbalanced ADN is presented. The optimization aims at minimizing network power losses and improving voltage profiles of the entire ADN. To do so, the HDT-PV's model in the case of unequal three-phase loads is established, and the corresponding simulation is conducted to verify the correctness of the model. Finally, case studies of collaborative optimization control of HDT-PVs are carried out in various scenarios using the modified unbalanced IEEE 33 -bus system. The results verify the effectiveness of the proposed collaborative control scheme on reducing network power losses and suppressing three-phase voltage unbalance.

关键词： Unbalanced active distribution network Hybrid distribution transformer second order cone programming Collaborative optimization control

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Robust distribution networks reconfiguration considering the improvement of network resilience considering renewable energy resources

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SCIENTIFIC REPORTS 2024年第1期14卷 1-27页

作者： Choobdari, Mahsa Moghaddam, Mahmoud Samiei Davarzani, Reza Azarfar, Azita Hoseinpour, Hesamodin Islamic Azad Univ Dept Elect Engn Shahrood Branch Shahrood Iran Islamic Azad Univ Dept Elect Engn Damghan Branch Damghan Iran

The integration of renewable energy sources into smart distribution grids poses substantial challenges in maintaining grid stability, efficiency, and reliability due to their inherent variability and intermittency. This study addresses these challenges by proposing a novel two-level optimization model aimed at enhancing operational efficiency and robustness in smart distribution grids. The model synergistically integrates renewable energy sources, energy storage systems, electric vehicles, and demand-side management through a dynamic reconfiguration approach. It employs a robust optimization framework combined with a two-stage second-order cone optimization model to manage real-time operations and strategic grid reconfiguration. Key findings from simulations on the IEEE 33 and 69-bus networks underscore the model's effectiveness. In the 33-bus system, implementing the demand response program led to a significant reduction in power losses, from 0.64 MW to 0.52 MW, and improved voltage stability, with the minimum voltage increasing from 0.970 to 0.980 p.u. Similarly, in the 69-bus system, power losses decreased from 0.85 MW to 0.79 MW, and voltage stability improved, with the minimum voltage rising from 0.962 to 0.972 p.u. The model also demonstrated reduced energy procurement needs, showcasing its impact on enhancing grid efficiency and reliability. These results highlight the model's potential for advancing smart grid management strategies, offering significant improvements in operational performance and stability under varying demand conditions.

关键词： Reconfiguration Smart distribution network Demand side management Optimization Renewables second order cone programming Two stage optimization

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Performance analytics for the value chain process of international airports: a dynamic network measure with the shared and unsplittable links

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ANNALS OF OPERATIONS RESEARCH 2024年 1-31页

作者： Yu, Anyu Zhou, Fan Zheng, Zuduo Zhejiang Gongshang Univ Modern Business Res Ctr Sch Business Adm Hangzhou Peoples R China Southwestern Univ Finance & Econ Inst Western China Econ Res 555 Liutai Ave Chengdu 611130 Peoples R China Univ Queensland Sch Civil Engn St Lucia Australia

To strengthen the profitability of the international airline industry, we adopt the value chain theory to investigate airports' operational performance over periods. This study defines the runway area as a shared and unsplittable link and introduces it into a dynamic network data envelopment analysis as a special carryover link. To efficiently solve the nonlinearity issue of this dynamic operational performance evaluation problem, a second order cone programming (SOCP) approach is proposed. Local optimum obtained from different branching strategies are compared to search for the global optimum in SOCP. The proposed method is applied to study a sample of hub airports across countries, and results show that the method is able to reveal the diverse performance of transportation and profitability stages for the selected airports. Impacts of location, scale, business internationalization, and non-aeronautical profitability on the airport performance are also examined. The findings of this study assist in comprehensively evaluating the performance of international airports, pinpointing the sources of operational inefficiency, and ultimately developing strategies to enhance the profitability capability of the international airline industry.

关键词： Airport performance Data envelopment analysis (DEA) Dynamic network second order cone programming Shared and unsplittable link (SUL)

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Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

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INFORMS JOURNAL ON COMPUTING 2023年第2期35卷 458-474页

作者： Aigner, Kevin-Martin Burlacu, Robert Liers, Frauke Martin, Alexander Friedrich Alexander Univ Erlangen Nurnberg Discrete Optimizat D-91058 Erlangen Germany Energie Campus Nurnberg D-90429 Nurnberg Germany Fraunhofer Inst Integrated Circuits D-90411 Nurnberg Germany

We present a solution framework for general alternating current optimal power flow (AC OPF) problems that include discrete decisions. The latter occur, for instance, in the context of the curtailment of renewables or the switching of power-generation units and transmission lines. Our approach delivers globally optimal solutions and is provably convergent. We model AC OPF problems with discrete decisions as mixed-integer non-linear programs (MINLPs). The solution method starts from a known framework that uses piecewise linear relaxations. These relaxations are modeled as mixed-integer linear pro-grams and adaptively refined until some termination criterion is fulfilled. In this work, we extend and complement this approach by problem-specific as well as very general algorith-mic enhancements. In particular, these are mixed-integer second order cone programs as well as primal and dual cutting planes. For example, objective and no-good cuts help to compute good feasible solutions in which outer approximation constraints tighten the relaxations. We present extensive numerical results for various AC OPF problems in which discrete decisions play a major role. Even for hard instances with a large proportion of dis-crete decisions, the method is able to generate high-quality solutions efficiently. Further-more, we compare our approach with state-of-the-art MINLP solvers. Our method outperforms all other algorithms.

关键词： AC optimal power flow mixed-integer nonlinear programming discrete decisions second order cone programming piecewise linear relaxation generator switching transmission line switching curtailment of renewables

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Some comments on Russell graph efficiency measures in data envelopment analysis: The multiplicative approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期306卷 494-497页

作者： Naghavi, Mostafa Roshdi, Israfil Arjomandi, Amir Margaritis, Dimitris Tarbiat Modares Univ Fac Management & Econ Dept Ind Management Tehran Iran Islamic Azad Univ Dept Basic Sci Semnan Branch Semnan Iran Univ Wollongong Fac Business & Law Sch Business Wollongong Australia Univ Auckland Dept Accounting & Finance Auckland New Zealand

In a recently published paper, Alcaraz, J., Anton-Sanchez, L., Aparicio, J., Monge, J. F., & Ramon, N., 2021. Russell graph efficiency measures in Data Envelopment Analysis: The multiplicative approach. European Journal of Operational Research, 292(2), 663-674, propose multiplicative versions of Russell-type graph efficiency measures based on geometric aggregations of input and output efficiency measures. Within the data envelopment analysis framework, they devise an iterative algorithm to solve the multiplicative models via a second order conic programming approach. In this paper, we demonstrate that the proposed models are not convex and reformulate them as two equivalent well-known types of nonconvex optimisation problems. By providing a numerical counterexample, we illustrate that their proposed algorithm may stop at a local optimum rather than converging to a global optimal solution. Some computational remarks are further suggested in regard to solving the proposed models. (c) 2022ElsevierB.V. Allrightsreserved.

关键词： Data envelopment analysis Russell graph efficiency measure DC Optimisation Reverse convex optimisation second order cone programming

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