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Voltage Stability Constrained Optimal Power Flow for Unbalanced Distribution System Based on semidefinite programming

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Journal of Modern Power Systems and Clean Energy 2022年第6期10卷 1614-1624页

作者： Yanling Lin Xiaohu Zhang Jianhui Wang Di Shi Desong Bian GEIRI North America San JoseUSA Southern Methodist University DallasUSA

This paper proposes a voltage stability constrained optimal power flow(VSC-OPF)for an unbalanced distribution system with distributed generators(DGs)based on semidefinite programming(SDP).The AC optimal power flow(ACOPF)for unbalanced distribution systems is formulated as a chordal relaxation-based SDP *** minimal singular value(MSV)of the power flow Jacobian matrix is adopted to indicate the voltage stability *** Jacobian matrix can be explicitly expressed by ACOPF state *** nonlinear constraint on the Jacobian MSV is then replaced with its maximal convex subset using linear matrix inequality(LMI),which can be incorporated in the SDP-based ACOPF formulation.A penalty technique is leveraged to improve the exactness of the SDP *** studies performed on several IEEE test systems validate the effectiveness of the proposed method.

关键词： Voltage stability semidefinite programming Jacobian matrix optimal power flow

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Economic dispatch of energy storage systems in dc microgrids employing a semidefinite programming model

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JOURNAL OF ENERGY STORAGE 2019年 21卷 1-8页

作者： Gil-Gonzalez, Walter Danilo Montoya, Oscar Holguin, Erika Garces, Alejandro Fernando Grisales-Norena, Luis Univ Tecnol Pereira AA 97 Pereira 660003 Colombia Univ Tecnol Bolivar Programa Ingn Elect & Ingn Elect Km 1 Via Turbaco Cartagena Colombia Inst Tecnol Metropolitano Dept Mecatron & Electromecan Medellin Colombia

A mathematical optimization approach for the optimal operation focused on the economic dispatch for dc microgrid with high penetration of distributed generators and energy storage systems (ESS) via semidefinite programming (SDP) is proposed in this paper. The SDP allows transforming the nonlinear and non-convex characteristics of the economic dispatch problem into a convex approximation which is easy for implementation in specialized software, i.e., CVX. The proposed mathematical approach contemplates the efficient operation of a dc microgrid over a period of time with variable energy purchase prices, which makes it a practical methodology to apply in real-time operating conditions. A nonlinear autoregressive exogenous (NARX) model is employed for training an artificial neural network (ANN) for forecasting solar radiation and wind speed for renewable generation integration and dispatch considering periods of prediction of 0.5 h. Four scenarios are proposed to analyze the inclusion of ESS in a dc microgrid for economic dispatch studies. Additionally, the results are compared with GAMS commercial optimization package, which allows validating the accuracy and quality of the proposed optimizing methodology.

关键词： Economic dispatch Dc microgrids Energy storage systems semidefinite programming Convex reformulation

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Linear, Quadratic, and semidefinite programming Massive MIMO Detectors: Reliability and Complexity

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IEEE ACCESS 2019年 7卷 29506-29519页

作者： Fukuda, Rafael Masashi Abrao, Taufik Univ Estadual Londrina Elect Engn Dept BR-86057970 Londrina Brazil

One of the downsides of the massive multiple-input-multiple-output (M-MIMO) system is its computational complexity. Considering that techniques and different algorithms proposed in the literature applied to conventional MIMO may not be well suited or readily applicable to M-MIMO systems, in this paper, the application of different formulations inside the convex optimization framework is investigated. This paper is divided into two parts. In the first part, linear programming, quadratic programming (QP), and semidefinite programming are explored in an M-MIMO environment with high-order modulation and under realistic channel conditions, i.e., considering spatial correlation, error in the channel estimation, as well as different system loading. The bit error rate is evaluated numerically through Monte Carlo simulations. In the second part, algorithms to solve the QP formulation are explored, and computational complexity in terms of floating-point operations (flops) is compared with linear detectors. Those algorithms have interesting aspects when applied to our specific problem (M-MIMO detection formulated as QP), such as the exploitation of the structure of the problem (simple constraints) and the improvement of the rate of convergence due to the well-conditioned Gram matrix (channel hardening). The number of iterations is higher when the number of users K becomes similar to the number of base station antennas M (i.e., K approximate to M) than the case K << M;the number of iterations increases slowly as the number of users K and base station antennas M increases while keeping a low system loading. The QP with projected algorithms presented better performance than minimum mean square error detector when K approximate to M and promising computational complexity for scenarios with increasing K and low system loading.

关键词： Massive MIMO communication low-complexity detectors convex optimization linear programming quadratic programming semidefinite programming

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Exploiting sparsity in semidefinite programming via matrix completion II: implementation and numerical results

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MATHEMATICAL programming 2003年第2期95卷 303-327页

作者： Nakata, K Fujisawa, K Fukuda, M Kojima, M Murota, K Tokyo Inst Technol Dept Ind Engn & Management Meguro Ku Tokyo 1528552 Japan Kyoto Univ Dept Architecture & Architectural Syst Kyoto 6068501 Japan Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku Tokyo 1528552 Japan Univ Tokyo Dept Math Informat Tokyo 1138656 Japan

In Part I of this series of articles, we introduced a general framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefinite programs (SDPs) when solving them by primal-dual interior-point methods. This framework is based on some results about positive semidefinite matrix completion, and it can be embodied in two different ways. One is by a conversion of a given sparse SDP having a large scale positive semidefinite matrix variable into an SDP having multiple but smaller positive semidefinite matrix variables. The other is by incorporating a positive definite matrix completion itself in a primal-dual interior-point method. The current article presents the details of their implementations. We introduce new techniques to deal with the sparsity through a clique tree in the former method and through new computational formulae in the latter one. Numerical results over different classes of SDPs show that these methods can be very efficient for some problems.

关键词： semidefinite programming primal-dual interior-point method matrix completion problem clique tree numerical results

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Non-Iterative Rigid 2D/3D Point-Set Registration Using semidefinite programming

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2016年第7期25卷 2956-2970页

作者： Khoo, Yuehaw Kapoor, Ankur Siemens Corp Corp Technol Imaging & Comp Vision Team Princeton NJ 08540 USA Princeton Univ Dept Phys Princeton NJ 08540 USA

We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINLP) formulations of the 2D/3D registration problem when there are multiple 2D images, and propose convex relaxations for both the MINLPs to semidefinite programs that can be solved efficiently by interior point methods. Our approach to the 2D/3D registration problem is non-iterative in nature as we jointly solve for pose and correspondence. Furthermore, these convex programs can readily incorporate feature descriptors of points to enhance registration results. We prove that the convex programs exactly recover the solution to the MINLPs under certain noiseless condition. We apply these formulations to the registration of 3D models of coronary vessels to their 2D projections obtained from multiple intra-operative fluoroscopic images. For this application, we experimentally corroborate the exact recovery property in the absence of noise and further demonstrate robustness of the convex programs in the presence of noise.

关键词： Rigid registration 2D/3D registration iterative-closest-point convex relaxation semidefinite programming

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Eigenvalue multiplicity estimate in semidefinite programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第1期94卷 55-72页

作者： Fan, MKH Gong, Y Associate Professor School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta Georgia Graduate Student School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta Georgia

A semidefinite programming problem is a mathematical program in which the objective function is linear in the unknowns and the constraint set is defined by a linear matrix inequality. This problem is nonlinear, nondifferentiable, but convex. It covers several standard problems (such as linear and quadratic programming) and has many applications in engineering. Typically, the optimal eigenvalue multiplicity associated with a linear matrix inequality is larger than one. Algorithms based on prior knowledge of the optimal eigenvalue multiplicity for solving the underlying problem have been shown to be efficient. In this paper, we propose a scheme to estimate the optimal eigenvalue multiplicity from points close to the solution. With some mild assumptions, it is shown that there exists an open neighborhood around the minimizer so that our scheme applied to any point in the neighborhood will always give the correct optimal eigenvalue multiplicity. We then show how to incorporate this result into a generalization of an existing local method for solving the semidefinite programming problem. Finally, a numerical example is included to illustrate the results.

关键词： convex programming semidefinite programming linear matrix inequality eigenvalue multiplicity estimate quadratic rate of convergence Newton method

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Ranging Energy Optimization for Robust Sensor Positioning Based on semidefinite programming

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第12期57卷 4777-4787页

作者： Wang, Tao Leus, Geert Huang, Li Delft Univ Technol Fac Elect Engn Math & Comp Sci NL-2628 CD Delft Netherlands Holst Ctr Stichting IMEC Nederland Eindhoven Netherlands

Sensor positioning is an important task of location-aware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribed accuracy requirements. This motivates us to investigate ranging energy optimization problems. We address ranging energy optimization for an unsynchronized positioning system, which features robust sensor positioning (RSP) in the sense that a specific accuracy requirement is fulfilled within a prescribed service area. We assume a line-of-sight (LOS) channel exists between the sensor and each beacon. The positioning is implemented by time-of-arrival (TOA) based two-way ranging between a sensor and beacons, followed by a location estimation at a central processing unit. To establish a dependency between positioning accuracy and ranging energy, we assume the adopted TOA and location estimators are unbiased and attain the associated Cramer-Rao bound. The accuracy requirement has the same form as the one defined by the Federal Communication Commission (FCC), and we present two constraints with linear-matrix-inequality form for the RSP. Ranging energy optimization problems, as well as a practical algorithm based on semidefinite programming are proposed. The effectiveness of the algorithm is illustrated by numerical experiments.

关键词： Cramer-Rao bound localization semidefinite programming wireless sensor networks

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A new notion of weighted centers for semidefinite programming

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SIAM JOURNAL ON OPTIMIZATION 2006年第4期16卷 1092-1109页

作者： Chua, CB Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada

The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties -(1) each choice of weights uniquely determines a pair of primal-dual weighted centers, and ( 2) the set of all primal-dual weighted centers completely fills up the relative interior of the primal-dual feasible region. This paper presents a new notion of weighted centers for semidefinite programming that possesses both uniqueness and completeness. Furthermore, it is shown that under strict complementarity, these weighted centers converge to weighted centers of optimal faces. Finally, this convergence result is applied to homogeneous cone programming, where the central paths defined by a certain class of optimal barriers for homogeneous cones are shown to converge to analytic centers of optimal faces in the presence of strictly complementary solutions.

关键词： weighted center semidefinite programming homogeneous cone programming facial structure Cholesky decomposition

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On semidefinite programming relaxations for the satisfiability problem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2004年第3期60卷 349-367页

作者： Anjos, MF Univ Southampton Sch Math Operat Res Grp Southampton SO17 1BJ Hants England

This paper is concerned with the analysis and comparison of semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. Our presentation is focussed on the special case of 3-SAT, but the ideas presented can in principle be extended to any instance of SAT specified by a set of boolean variables and a propositional formula in conjunctive normal form. We propose a new SDP relaxation for 3-SAT and prove some of its theoretical properties. We also show that, together with two SDP relaxations previously proposed in the literature, the new relaxation completes a trio of linearly sized relaxations with increasing rank-based guarantees for proving satisfiability. A comparison of the relative practical performances of the SDP relaxations shows that, among these three relaxations, the new relaxation provides the best tradeoff between theoretical strength and practical performance within an enumerative algorithm.

关键词： satisfiability problem semidefinite programming combinatorial optimization global optimization

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Discrete transforms, semidefinite programming, and sum-of-squares representations of nonnegative polynomials

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SIAM JOURNAL ON OPTIMIZATION 2006年第4期16卷 939-964页

作者： Roh, T Vandenberghe, L Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

We present a new semidefinite programming formulation of sum-of-squares representations of nonnegative polynomials, cosine polynomials, and trigonometric polynomials of one variable. The parametrization is based on discrete transforms (specifically, the discrete Fourier, cosine, and polynomial transforms) and has a simple structure that can be exploited by straightforward modi. cations of standard interior-point algorithms.

关键词： semidefinite programming interior-point methods nonnegative polynomials

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