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Robust and low-order design of flexible AC transmission systems and power system stabilisers for oscillation damping

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IET GENERATION TRANSMISSION & DISTRIBUTION 2012年第5期6卷 445-452页

作者： Simfukwe, D. D. Pal, B. C. Jabr, R. A. Martins, N. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon Electrobras CEPEL BR-21941911 Rio De Janeiro RJ Brazil

The study presents a method for the coordinated design of low-order robust controllers for stabilising power system oscillations. The design uses conic programming to shift under-damped or unstable modes into a region of sufficient damping of the complex plane and involves two stages. The first stage is a phase compensation design that accounts for multiple operating conditions with flexible AC transmission systems (FACTS) and power system stabilisers (PSS), unlike our earlier approach involving PSS only. The second stage is gain tuning. This is done effectively in a coordinated way using conic programming. An example demonstrates the method's ability to design coordinated FACTS and PSS controllers resulting in damping oscillations over all given operating conditions of the power system with very simple and low-order control structure.

关键词： FACTS conic programming flexible AC transmission systems power system stabilisers gain tuning Robust and low-order design of low-order robust controllers a.c. transmission Power system control Control of electric power systems Power supply quality and harmonics power system stability power system harmonics Power transmission lines and cables oscillation damping

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A 3D upper bound limit analysis using radial point interpolation meshless method and second-order cone programming

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2016年第13期108卷 1686-1704页

作者： Yu, Shengbing Zhang, Xue Sloan, S. W. Univ Newcastle ARC Ctr Excellence Geotechn Sci & Engn Callaghan NSW Australia

This paper presents a 3D formulation for quasi-kinematic limit analysis, which is based on a radial point interpolation meshless method and numerical optimization. The velocity field is interpolated using radial point interpolation shape functions, and the resulting optimization problem is cast as a standard second-order cone programming problem. Because the essential boundary conditions can be only guaranteed at the position of the nodes when using radial point interpolation, the results obtained with the proposed approach are not rigorous upper bound solutions. This paper aims to improve the computing efficiency of 3D upper bound limit analysis and large problems, with tens of thousands of nodes, can be solved efficiently. Five numerical examples are given to confirm the effectiveness of the proposed approach with the von Mises yield criterion: an internally pressurized cylinder;a cantilever beam;a double-notched tensile specimen;and strip, square and rectangular footings. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： limit analysis upper bound meshless method conic programming

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A Robust State Estimation Method Based on SOCP for Integrated Electricity-Heat System

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IEEE TRANSACTIONS ON SMART GRID 2021年第1期12卷 810-820页

作者： Chen, Yanbo Yao, Yuan Zhang, Ying North China Elect Power Univ Sch Elect & Elect Engn Beijing 102206 Peoples R China Southern Methodist Univ Dept Elect & Comp Engn Dallas TX 75205 USA

With the application and development of combined heat and power (CHP) techniques, the coupling of electrical and heat energy is gradually increasing. State estimation (SE) is essential to achieve the comprehensive and accurate operating status in an integrated electricity-heat system (IEHS). This article proposes a robust SE method based on second-order conic programming (SOCP) for IEHS. Firstly, auxiliary state variables and measurements are introduced to obtain the exact linear measurement equations for IEHS. Then, a robust SE model based on weighted least absolute values (WLAV) for IEHS is proposed. To further improve the estimation performance, the constraint conditions satisfied by auxiliary state variables are relaxed into second-order cone constraints and added to the proposed WLAV model, leading a SOCP-based robust SE method. Simulations demonstrate that the proposed method ensures a global optimal solution and has good robustness and high estimation accuracy.

关键词： Mathematical model Robustness Resistance heating Electric variables measurement Loss measurement Cogeneration Integrated electricity-heat system robust state estimation conic programming multiple conforming gross errors convex optimization

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A Joint Risk- and Security-Constrained Control Framework for Real-Time Energy Scheduling of Islanded Microgrids

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IEEE TRANSACTIONS ON SMART GRID 2022年第5期13卷 3354-3368页

作者： Nikkhah, Saman Sarantakos, Ilias Zografou-Barredo, Natalia-Maria Rabiee, Abbas Allahham, Adib Giaouris, Damian Newcastle Univ Sch Engn Newcastle Upon Tyne NE1 7RU Tyne & Wear England Univ Zanjan Dept Elect Engn Zanjan *** Iran

High penetration of intermittent renewable energy sources (RES) and unexpected disruptions (e.g., natural disasters) are fundamental challenges which can threaten the secure operation of microgrids, especially during the islanded condition, with no support from the upstream grid. This paper introduces a hierarchical tri-layer min-max-min joint risk- and security-constrained model predictive control (RSC-MPC) framework for real-time energy scheduling of islanded microgrids (IMGs) under the influence of uncertainty and real-time time-varying contingency conditions. While the first layer processes a pre-scheduling day-ahead optimisation, the second layer detects the worst-case contingency conditions by maximising the load curtailment and the mismatch between pre-scheduling (i.e., first layer) and real-time operation. The third layer implements the corrective security measures to minimise the negative effect of contingency conditions while accounting to the cost associated with the risk of uncertainty in the forecasted inputs. The third layer also explores the economic effects of the RES' uncertainty on the proposed RSC-MPC, considering the risk and energy procurement cost as conflicting objectives. The computational efficiency of the proposed hierarchical control system in terms of accuracy and processing time is guaranteed through a mixed integer conic programming model. The proposed RSC-MPC is tested in different case studies and its efficiency is validated by numerical results.

关键词： Security Real-time systems Uncertainty Costs Microgrids Renewable energy sources Optimization Islanded microgrid (IMG) security risk conic programming

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POLYNOMIAL APPROXIMATIONS FOR CONTINUOUS LINEAR PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2012年第2期22卷 628-648页

作者： Bampou, Dimitra Kuhn, Daniel Univ London Imperial Coll Sci Technol & Med Dept Comp London SW7 2BZ England

Continuous linear programs have attracted considerable interest due to their potential for modeling manufacturing, scheduling, and routing problems. While efficient simplex-type algorithms have been developed for separated continuous linear programs, crude time discretization remains the method of choice for solving general (nonseparated) problem instances. In this paper we propose a more generic approximation scheme for nonseparated continuous linear programs, where we approximate the functional decision variables (policies) by polynomial and piecewise polynomial decision rules. This restriction results in an upper bound on the original problem, which can be computed efficiently by solving a tractable semidefinite program. To estimate the approximation error, we also compute a lower bound by solving a dual continuous linear program in (piecewise) polynomial decision rules. We establish the convergence of the primal and dual approximations under Slater-type constraint qualifications. We also highlight the potential of our method for optimizing large-scale multiclass queueing systems and dynamic Leontief models.

关键词： continuous linear programming polynomial decision rules conic programming

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OPTIMAL SELF-CONCORDANT BARRIERS FOR QUANTUM RELATIVE ENTROPIES

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SIAM JOURNAL ON OPTIMIZATION 2023年第4期33卷 2858-2884页

作者： Fawzi, Hamza Saunderson, James Univ Cambridge Dept Appl Math & Theoret Phys Cambridge CB3 0WA England Monash Univ Dept Elect & Comp Syst Engn Clayton Vic 3800 Australia

Quantum relative entropies are jointly convex functions of two positive definite matrices that generalize the Kullback-Leibler divergence and arise naturally in quantum information theory. In this paper, we prove self-concordance of natural barrier functions for the epigraphs of various quantum relative entropies and divergences. Furthermore we show that these barriers have optimal barrier parameters. These barriers allow convex optimization problems involving quantum relative entropies to be directly solved using interior point methods for nonsymmetric cones, avoiding the approximations and lifting techniques used in previous approaches. More generally, we establish the self-concordance of natural barriers for various closed convex cones related to the noncommutative perspectives of operator concave functions and show that the resulting barrier parameters are optimal.

关键词： self-concordant barrier conic programming quantum relative entropies interior-point methods

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AN EXACT PENALTY METHOD FOR NONCONVEX PROBLEMS COVERING, IN PARTICULAR, NONLINEAR programming, SEMIDEFINITE programming, AND SECOND-ORDER CONE programming

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SIAM JOURNAL ON OPTIMIZATION 2015年第3期25卷 1732-1759页

作者： Auslender, Alfred Univ Lyon 1 Inst Camille Jordan F-69365 Lyon France

This paper presents an exact penalty method for solving optimization problems with very general constraints covering, in particular, nonlinear programming (NLP), semidefinite programming (SDP), and second-order cone programming (SOCP). The algorithm is called the sequential linear cone method (SLCM) because for SDP and SOCP the main cost of computation amounts to solving at each iteration a linear cone program for which efficient solvers are available. Restricted to NLP, SLCM is exactly a sequential quadratic program method. Under two basic conditions which concern only the data, it is proved that the sequence of iterates is bounded. Furthermore, in particular, when the feasible set is nonempty, under two additional constraint qualification conditions, it is proved that the cluster points are stationary points. In that case, it is established also that the sequence of penalty parameters eventually stays constant, and for a particular class of data it is proved that a unit step length can be obtained.

关键词： sequential quadratic programming sequential quadratically constrained quadratic programming nonlinear programming semidefinite programming second-order cone programming conic programming global convergence

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Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第2期183卷 490-519页

作者： Banjac, Goran Goulart, Paul Stellato, Bartolomeo Boyd, Stephen Swiss Fed Inst Technol Automat Control Lab Zurich Switzerland Univ Oxford Dept Engn Sci Oxford England MIT Operat Res Ctr Cambridge MA 02139 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive information regarding problem infeasibility for optimization problems with linear or quadratic objective functions and conic constraints, which includes quadratic, second-order cone, and semidefinite programs. In particular, we show that in the limit the iterates either satisfy a set of first-order optimality conditions or produce a certificate of either primal or dual infeasibility. Based on these results, we propose termination criteria for detecting primal and dual infeasibility.

关键词： Convex optimization Infeasibility detection Alternating direction method of multipliers conic programming

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Min-sup-type zero duality gap properties for DC composite optimization problem

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2019年第1期2019卷 1-13页

作者： Tian, Li Ping Fang, Dong Hui Jishou Univ Coll Math & Stat Jishou Peoples R China

In this paper, we present min-sup-type zero duality gap properties for DC composite optimization problem with conic constraints. Using properties of the subdifferentials of involved functions, we introduce some new constraint qualifications. Under these new constraint qualifications, we provide necessary and/or sufficient conditions for the min-sup-type stable zero duality to hold.

关键词： Zero duality gap property DC function Composite function Constraint qualification conic programming

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Warmstarting the homogeneous and self-dual interior point method for linear and conic quadratic problems

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MATHEMATICAL programming COMPUTATION 2013年第1期5卷 1-25页

作者： Skajaa, Anders Andersen, Erling D. Ye, Yinyu Tech Univ Denmark Dept Informat & Math Modelling 2800 Kgs Lyngby Denmark MOSEK ApS DK-2100 Copenhagen Denmark Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems. Common to both strategies is their use of only the final (optimal) iterate of the initial problem and their negligible computational cost. This is a major advantage when compared to previously suggested strategies that require a pool of iterates from the solution process of the initial problem. Consequently our strategies are better suited for users who use optimization algorithms as black-box routines which usually only output the final solution. Our two strategies differ in that one assumes knowledge only of the final primal solution while the other assumes the availability of both primal and dual solutions. We analyze the strategies and deduce conditions under which they result in improved theoretical worst-case complexity. We present extensive computational results showing work reductions when warmstarting compared to coldstarting in the range 30-75% depending on the problem class and magnitude of the problem perturbation. The computational experiments thus substantiate that the warmstarting strategies are useful in practice.

关键词： Warmstart Interior point method Homogeneous model conic programming

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