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Cheap Conic OPF Models for Low-Voltage Active Distribution Networks

IEEE ACCESS 2020年 8卷 99691-99708页

作者： Usman, Muhammad Cervi, Andrea Coppo, Massimilano Bignucolo, Fabio Turri, Roberto Univ Padua Dept Ind Engn I-35131 Padua Italy Univ Padua Interdept Ctr Giorgio Levi Cases Energy Econ & Te I-35131 Padua Italy

The increasing focus on the active participation of low-voltage (LV) active distribution networks (DNs) in electricity markets requires the real-time optimal control of these DNs. To achieve this goal, a cheap semi-definite programming (SDP)-based optimal power flow (OPF) model for active neutral-equipped DNs, hosting both wye- and delta-connected loads, is proposed in this paper, aiming at overcoming the high computational requirement of the primal SDP-based OPF model. The coupled power injections between conductors are explicitly represented for each conductor by utilizing the network admittance matrix-based approach. Furthermore, three novel propositions (P1, P2 and P3) are proposed for the modelling of the constant current component of ZIP end-users in the context of the proposed OPF model. Moreover, the impact of the voltage-angle deviation on the exactness of the P1- and P2-based models is discussed. Simulations are carried out on several LV active DNs for various parameters of ZIP end-users, and the quality of the proposed OPF model is verified through the % optimality gap, power mismatch, voltage violation and root-mean-square error criteria. It is successfully shown that the proposed OPF model provides an optimal and feasible solution for all load types (wye, delta, mixed wye-delta) under a large range of ZIP load parameters. Furthermore, among the three propositions, the P3-based OPF model appears to be the most accurate in terms of determining an optimal and feasible solution. Finally, the reduced computational time of the cheap conic model allows its real-time implementation for medium- and large-sized DNs for which the primal multi-phase SDP-based model is practically difficulty to realize.

关键词： Load modeling Computational modeling Conductors Biological system modeling Solid modeling Real-time systems programming Active distribution networks branch flow methodology conic models neutral conductor optimal power flow semi-definite programming wye- and delta-connected ZIP loads

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A distributionally robust optimization approach for two-stage facility location problems

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2020年第2期8卷 141-172页

作者： Gourtani, Arash Nguyen Tri-Dung Xu, Huifu Univ Southampton Sch Math Southampton SO17 1BJ Hants England Univ Southampton Sch Management Southampton SO17 1BJ Hants England Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

In this paper, we consider a facility location problem where customer demand constitutes considerable uncertainty, and where complete information on the distribution of the uncertainty is unavailable. We formulate the optimal decision problem as a two-stage stochastic mixed integer programming problem: an optimal selection of facility locations in the first stage and an optimal decision on the operation of each facility in the second stage. A distributionally robust optimization framework is proposed to hedge risks arising from incomplete information on the distribution of the uncertainty. Specifically, by exploiting the moment information, we construct a set of distributions which contains the true distribution and where the optimal decision is based on the worst distribution from the set. We then develop two numerical schemes for solving the distributionally robust facility location problem: a semi-infinite programming approach which exploits moments of certain reference random variables and a semi-definite programming approach which utilizes the mean and correlation of the underlying random variables describing the demand uncertainty. In the semi-infinite programming approach, we apply the well-known linear decision rule approach to the robust dual problem and then approximate the semi-infinite constraints through the conditional value at risk measure. We provide numerical tests to demonstrate the computation and properties of the robust solutions.

关键词： Distributionally robust optimization Facility location problem semi-definite programming semi-infinite programming

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A Quantum Interior Point Method for LPs and SDPs

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ACM TRANSACTIONS ON QUANTUM COMPUTING 2020年第1期1卷 1–32页

作者： Kerenidis, Iordanis Prakash, Anupam Univ Paris Diderot CNRS IRIF Inst Rech Informat Fondamentale Batiment Sophie Germain 8 Pl Aurelie Nemours F-75013 Paris France QCWare Corp 550 Hamilton AveSuite 226 Palo Alto CA 94301 USA

We present a quantum interior point method (IPM) for semi-definite programs that has a worst-case running time of (O) over tilde (n(2.5)/xi(2) mu kappa(3) log(1/c)). The algorithm outputs a pair of matrices (S, Y) that have objective value within epsilon of the optimal and satisfy the constraintsv approximately to error xi. The parameter mu is at most root 2n while kappa is an upper bound on the condition number of the intermediate solution matrices arising in the classical IPM. For the case where kappa << n(5/6), our method provides a significant polynomial speedup over the best-known classical semi-definite program solvers that have a worst-case running time of O(n(6)). For linear programs, our algorithm has a running time of (O) over tilde (n(1.5)/xi(2) mu kappa(3) log(1/epsilon)) with the same guarantees and with parameter mu < root 2n. Our technical contributions include an efficient quantum procedure for solving the Newton linear systems arising in the classical IPMs, an efficient pure state tomography algorithm, and an analysis of the IPM where the linear systems are solved approximately. Our results pave the way for the development of quantum algorithms with significant polynomial speedups for applications in optimization and machine learning.

关键词： Quantum algorithms semi-definite programming linear programming interior point methods

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A new approximation algorithm for unrelated parallel machine scheduling with release dates

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ANNALS OF OPERATIONS RESEARCH 2020年第1-2期285卷 397-425页

作者： Pei, Zhi Wan, Mingzhong Wang, Ziteng Zhejiang Univ Technol Dept Ind Engn Hangzhou Peoples R China Northern Illinois Univ Dept Ind & Syst Engn De Kalb IL 60115 USA

In the current study, an unrelated parallel machine scheduling problem with release dates is considered, which is to obtain a job assignment with minimal sum of weighted completion times. Although this problem is NP-hard in the strong sense, which renders the optimality seeking a formidable task within polynomial time, a 4-approximation algorithm based on the constant worst-case bound is devised and proved in comparison with the existing 16/3-approximation (Hall et al. in Math Oper Res 22(3):513-544, 1997). In the newly proposed algorithm, the original scheduling problem is divided into several sub-problems based on release dates. For each sub-problem, a convex quadratic integer programming model is constructed in accordance with the specific problem structure. Then a semi-definite programming approach is implemented to produce a lower bound via the semi-definite relaxation of each sub-problem. Furthermore, by considering the binary constraint, a branch and bound based method and a local search strategy are applied separately to locate the optimal solution of each sub-problem. Then the solution of the original scheduling problem is derived by integrating the outcomes of the sub-problems via the proposed approximation algorithm. In the numerical analysis, it is discovered that the proposed methods could always obtain a scheduling result within 1% of the optimal solution. And an asymptotic trend could be observed where the quality of solutions improves even further as the scale of the scheduling problem increases.

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Decimations of intrinsic mode functions via semi-infinite programming based optimal adaptive nonuniform filter bank design approach

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SIGNAL PROCESSING 2019年 159卷 53-71页

作者： Yang, Chuqi Ling, Bingo Wing-Kuen Kuang, Weichao Gu, Jialiang Guangdong Univ Technol Fac Informat Engn Guangzhou 510006 Guangdong Peoples R China

A signal can be represented as the sum of the intrinsic mode functions via performing the empirical mode decomposition. For the discrete time signals, the lengths of the intrinsic mode functions are equal to the lengths of the input signals. As there is usually more than one intrinsic mode function, the total numbers of discrete points of all the intrinsic mode functions are usually more than the lengths of the input signals. In other words, the empirical mode decomposition is an oversampled representation. For some applications such as the compression application, the oversampled representation is not preferred. Therefore, this paper proposes an optimal adaptive nonuniform filter bank design approach for performing the decimations on the intrinsic mode functions. In particular, the passbands of the intrinsic mode functions are estimated based on an adaptive gradient algorithm. Then, the intrinsic mode functions are nonuniformly downsampled and upsampled with the sampling integers derived based on their estimated passbands. Next, a bank of filters is employed to reconstruct the original signal. Here, the passbands of the filters are also derived based on those of the intrinsic mode functions. After that, the nonuniform filter bank design problem is formulated as a semi-infinite programming problem such that the total ripple energies of all the filters are minimized subject to the specifications on the absolute maximum values of both the real part and the imaginary part of the reconstruction error. The semi-infinite programming problem is approximated by a semi-definite programming problem. Computer numerical simulation results show that our proposed system could achieve a very small reconstruction error at a very small oversampling ratio. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Decimation Empirical mode decomposition Decimated intrinsic mode functions Optimal adaptive nonuniform filter bank design semi-infinite programming semi-definite programming

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Minimal mass design of active tensegrity structures

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ENGINEERING STRUCTURES 2021年 234卷 111965-111965页

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

Tensegrity structures have been widely utilized as lightweight structures due to their high stiffness-to-mass and strength-to-mass ratios. Minimal mass design of tensegrity structures subject to external loads and specific constraints (e.g., member yielding and buckling) has been intensively studied. However, all the existing studies focus on passive tensegrity structures, i.e., the structural members cannot change their lengths actively and the structure has to passively resist external loads. An active tensegrity structure equipped with actuators can actively adapt its internal forces and nodal positions and thus can actively resist external loads. Therefore, it is expected that active tensegrity structures use less material compared to passive tensegrity structures thus leading to a smaller mass. Due to the integration of the active control system, the design of active tensegrity structures is different from passive tensegrity structures. This study proposes a general approach for the design of minimal mass active tensegrity structures based on a mixed integer programming scheme, in which the member crosssectional areas, prestress, actuator layout and control strategies (i.e., actuator length changes) are designed simultaneously. The member cross-sectional areas, prestress level, and actuator control strategies are treated as continuous variables and the actuator layout is treated as a binary variable. The equilibrium condition, member yielding, cable slackness, strut buckling, and the limitations on the nodal displacements as well as other practical requirements are formulated as constraints. Three typical active tensegrity structures are designed through the proposed approach and the results are benchmarked with the equivalent minimal mass passive designs. It is illustrated that the active designs can significantly decrease the material consumption compared with the equivalent passive designs thus leading to more lightweight tensegrity structures.

关键词： Active tensegrity structure Minimal mass Lightweight structure semi-definite programming Mixed integer nonlinear programming

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Form-finding of tensegrity structures via rank minimization of force density matrix

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ENGINEERING STRUCTURES 2021年 227卷 111419-111419页

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

This study proposes a general computational framework for the form-finding of tensegrity structures. The procedure is divided into two stages in which the member force densities and nodal coordinates are obtained respectively. In the first stage, the determination of force densities is transformed into a rank minimization problem regarding the force density matrix and then formulated into a semi-definite programming. The unilaterality condition of member forces and the positive semi-definiteness condition of force density matrix are incorporated as constraints. In the second stage, the determination of nodal coordinates is formulated into a constrained nonlinear programming model. The nodal positions and member lengths are assigned as constraints and auxiliary variables are introduced to homogenize the member lengths. The proposed formulation bypasses the number of self-stress states in a tensegrity structure thus applies to both tensegrity structures with single and multiple self-stress states. Different from existing studies that are based on the minimum required rank deficiency condition of force density matrix, the proposed method can handle tensegrity structures that have a force density matrix with rank deficiency greater than the required minimum number. Several examples are presented to verify the effectiveness of the proposed method on different types of tensegrity structures.

关键词： Tensegrity structure Form-finding Force density method Rank minimization semi-definite programming Constrained nonlinear programming

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Data-Driven Quadratic Stabilization of Continuous LTI Systems 21st

Data-Driven Quadratic Stabilization of Continuous LTI System...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Dai, Tianyu Sznaier, Mario Solvas, Biel Roig Northeastern Univ ECE Dept Boston MA 02115 USA

This paper introduces a simple data-driven quadratic stabilization control (DDQSC) method to design a state feedback controller based solely on experimental measurements while avoiding explicitly identifying the plant. Rather, we seek a controller guaranteed to quadratically stabilize all plants that could have possibly generated the observed data. While in principle this leads to a very challenging non-convex robust optimization problem, our main result provides a convex, albeit infinite-dimensional, necessary and sufficient condition for the existence of such a controller and its associated Lyapunov function. In the second part of the paper, we provide a tractable finite-dimensional convex relaxation of this condition and illustrate its effectiveness with several examples. Copyright (C) 2020 The Authors.

关键词： Data-Driven Control Robust Control Quadratic Stability semi-definite programming

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EXPLOITING SPARSITY FOR ROBUST SENSOR NETWORK LOCALIZATION IN MIXED LOS/NLOS ENVIRONMENTS

EXPLOITING SPARSITY FOR ROBUST SENSOR NETWORK LOCALIZATION I...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Fin, Di Yin, Feng Fauss, Michael Muma, Michael Zoubir, Abdelhak M. Tech Univ Darmstadt Signal Proc Grp Darmstadt Germany Chinese Univ Hong Kong Sch Sci & Engn Shenzhen Peoples R China Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

ISBN: (纸本)9781509066315

We address the problem of robust network localization in realistic mixed LOS/NLOS environments. We make use of the fact that the bias of range measurement errors is not only non-negative but also sparse when LOS dominates, which has been long overlooked in the existing literature. To exploit these two properties, we introduce a sparsity-promoting regularization term and relax the resulting optimization problem to a semi-definite programming (SDP) problem. The proposed method admits a neat mathematical formulation and is computationally cheap. Moreover, its global convergence is guaranteed and it achieves good robustness against NLOS measurements. In numerical results, the proposed method outperforms representative state-of-the-art SDP approaches, in terms of both localization accuracy and computational efficiency.

关键词： Cooperative localization non-line-of-sight sparsity semi-definite programming

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semi-definite programming Based Pulse Shaping Algorithm in IEEE 802.15.4a

Semi-Definite Programming Based Pulse Shaping Algorithm in I...

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2nd International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

作者： Wu Xuan-li Sun Lu-kuan Feng Wei Luo Ming-xin Harbin Inst Technol Sch Elect & Informat Engn Harbin 150006 Peoples R China ZTE Corp Shenzhen Peoples R China

ISBN: (纸本)9780769549354

In order to increase the peak transmission data rate of Zigbee and expand its application scenario, IEEE 802.15.4a standard has been proposed in 2007, and ultra-wideband (UWB) technique has been selected as one of its physical layer standard. The performance of wireless sensor networks (WSN) will be affected by the pulse waveform transmitted in the channel, hence, in this paper, the Chinese regulation for UWB devices is firstly given, and then, a semi-definite programming based pulse shaping algorithm to comply with such regulation is proposed. Simulation results show that the proposed algorithm can comply with the given regulation with high power efficiency, which can increase the signal to noise ratio (SNR) in the receiver end.

关键词： ultra-wideband wireless sensor network pulse shaping Chinese regulation semi-definite programming

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