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Identification of the Worst-case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

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CSEE Journal of Power and Energy Systems 2024年第3期10卷 974-987页

作者： Wanbin Liu Shunjiang Lin Yuerong Yang Mingbo Liu Qifeng Li School of Electric Power Engineering South China University of TechnologyGuangzhou 510640China Guangdong Key Laboratory of Clean Energy Technology South China University of TechnologyGuangzhou 511458China Department of Electrical and Computer Engineering University of Central FloridaOrlandoFL 32816USA CSEE IEEE

Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation *** paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission *** of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF ***,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case *** two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain ***,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct *** results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

关键词： AC/DC power system control mode switching convex relaxation dual programming multi-level optimization optimal power flow static voltage stability margin

convexification of Hybrid AC-DC Optimal Power Flow with Line-Commutated Converters

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CSEE Journal of Power and Energy Systems 2024年第2期10卷 617-628页

作者： Hongyuan Liang Zhigang Li J.H.Zheng Q.H.Wu School of Electric Power Engineering South China University of TechnologyGuangzhou 510641China

Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.

关键词： AC-DC power system convex relaxation linecommutated converter optimal power flow second-order cone programming

Optimization in Machine Learning:a Distribution-Space Approach

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1217-1240页

作者： Yongqiang Cai Qianxiao Li Zuowei Shen School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsMOEBeijing Normal UniversityBeijing 100875China Department of Mathematics National University of Singapore21 Lower Kent Ridge RoadSingapore119077Singapore

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space,but with a non-convex constraint set introduced by model *** observation allows us to repose such problems via a suitable relaxation as convex optimization problems in the space of distributions over the training *** derive some simple relationships between the distribution-space problem and the original problem,e.g.,a distribution-space solution is at least as good as a solution in the original ***,we develop a numerical algorithm based on mixture distributions to perform approximate optimization directly in the distribution *** of this approximation is established and the numerical efficacy of the proposed algorithm is illustrated in simple *** both theory and practice,this formulation provides an alternative approach to large-scale optimization in machine learning.

关键词： Machine learning convex relaxation Optimization Distribution space

Survey of convex optimization for aerospace applications

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Astrodynamics 2017年第1期1卷 23-40页

作者： Xinfu Liu Ping Lu Binfeng Pan Beijing Institute of Technology Beijing 100081China San Diego State University San DiegoCalifornia 92182-1308USA Northwestern Polytechnical University Xi'an 710072China

convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

关键词： convex optimization optimal control convexification convex relaxation

Transmission capacity maximization for LED array-assisted multiuser VLC systems

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Science China(Information Sciences) 2015年第8期58卷 117-130页

作者： KONG Lei SHEN Hong XU Wei ZHANG Hua ZHAO ChunMing YOU XiaoHu National Mobile Communications Research Laboratory Southeast University

In this paper, we present a light-emitting diode(LED) array-assisted visible light communication(VLC) system. Considering the requirements of illumination, the human eye safety, and the energy saving,we optimize the optical power allocation(PA) to maximize the transmission capacity of the overall ***, we discuss two typical scenarios where the LED array in each room serves multiple users either simultaneously or in a round-robin manner. The problem corresponding to the first case turns out to be nonconvex whose globally optimal solution is hard to obtain. To address this difficult problem, we first adopt the famous gradient projection algorithm to obtain a locally optimal solution, then we employ powerful convex relaxation techniques, and achieve a high-quality solution. While for the round-robin case, we are able to derive an optimal solution in closed form by virtue of Karush-Kuhn-Tucker conditions. Interestingly, the derived closedform solution follows a water-filling pattern with both square root and two-side clipping operations, which differs from the conventional water-filling-like PA in radiofrequency channels. Numerical results depict the performance advantage provided by the proposed PA strategies under various settings.

关键词： light-emitting diodes visible light communication power allocation multiuser transmission convex relaxation

Optimal Operation of Integrated Heat and Electricity Systems:A Tightening McCormick Approach

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Engineering 2021年第8期7卷 1076-1086页

作者： Lirong Deng Hongbin Sun Baoju Li Yong Sun Tianshu Yang Xuan Zhang Tsinghua–Berkeley Shenzhen Institute Tsinghua UniversityShenzhen 518055China State Key Laboratory of Power Systems Department of Electrical EngineeringTsinghua UniversityBeijing 100084China State Grid Jilin Electric Power Supply Co. Ltd.Changchun 130000China Electrical College Harbin Institute of TechnologyHarbin 150006China

Combined heat and electricity operation with variable mass flow rates promotes flexibility,economy,and sustainability through synergies between electric power systems(EPSs)and district heating systems(DHSs).Such combined operation presents a highly nonlinear and nonconvex optimization problem,mainly due to the bilinear terms in the heat flow model—that is,the product of the mass flow rate and the nodal *** methods,such as nonlinear optimization,generalized Benders decomposition,and convex relaxation,still present challenges in achieving a satisfactory performance in terms of solution quality and computational *** resolve this problem,we herein first reformulate the district heating network model through an equivalent transformation and variable *** reformulated model has only one set of nonconvex constraints with reduced bilinear terms,and the remaining constraints are *** a reformulation not only ensures optimality,but also accelerates the solving *** relax the remaining bilinear constraints,we then apply McCormick envelopes and obtain an objective lower bound of the reformulated *** improve the quality of the McCormick relaxation,we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned *** propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible *** studies show that,compared with the interior point method and the method implemented in a global bilinear solver,the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.

关键词： Integrated heat and electricity system convex relaxation Operation McCormick envelopes

The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor

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Journal of the Operations Research Society of China 2023年第4期11卷 735-758页

作者： Amina Sabir Peng-Fei Huang Qing-Zhi Yang School of Mathematics and Statistics Kashi UniversityKashi844008XinjiangChina School of Mathematical Sciences and LPMC Nankai UniversityTianjin300071China

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric(CPS)tensor and show that the greedy successive rank-one approximation(SROA)algorithm can recover this decomposition *** on this matrix decomposition,the CP rank of CPS tensor can be bounded by the matrix rank,which can be applied to low-rank tensor ***,we give the rank-one equivalence property for the CPS tensor based on the SVD of matrix,which can be applied to the rank-one approximation for CPS tensors.

关键词： Conjugate partial-symmetric tensor Approximation algorithm Rank-one equivalence property convex relaxation

A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem

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Journal of the Operations Research Society of China 2023年第1期11卷 1-28页

作者： Ruo-Tian Gao Shu-Cherng Fang Cheng Lu Wen-Xun Xing Big Data Center of State Grid Corporation of China Beijing 100053China Department of Industrial and System Engineering North Carolina State UniversityRaleigh 27695-7906USA School of Economics and Management North China Electric Power UniversityBeijing 102206China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be *** theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are *** results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.

关键词： Nonlinear programming Lagrangian dual Unit commitment problem Mixed-integer quadratic programming convex relaxation