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Iterative LP-Based Methods for the Multiperiod Optimal Electricity and Gas Flow Problem

IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第1期37卷 153-166页

作者： Mhanna, Sleiman Saedi, Isam Mancarella, Pierluigi Univ Melbourne Dept Elect & Elect Engn Melbourne Vic 3010 Australia

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned, parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles.

关键词： Manganese Pipelines programming Computational modeling Mathematical model Iterative methods Regulators sequential linear programming polyhedral envelopes integrated electricity and gas systems piecewise linear approximations mixed-integer nonlinear programming mixed-integer second-order cone programming branch-and-bound

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Response surface approximations: Noise, error repair, and modeling errors

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AIAA JOURNAL 2000年第12期38卷 2336-2343页

作者： Papila, M Haftka, RT Univ Florida Dept Aerosp Engn Mech & Engn Sci Gainesville FL 32611 USA

In the past few Sears there has been interest in using response surface techniques to create surrogates to computer simulations. Response surface techniques allow detection and correction of errors as well as filtering out numerical noise, but these techniques introduce additional modeling errors. Methods of reducing both noise and modeling errors are explored. It is also demonstrated that repairing designs with large errors is preferable to eliminating these designs from consideration. Response surface approximations for a high-speed civil transport wing weight equation created from the results of a large number of structural optimizations are used for demonstration. It is shown that the statistical tools available for response surface techniques are effective for error detection and for filtering out noise. Once the noise is reduced, modeling errors can also be reduced by increasing the order of the approximation.

关键词： High Speed Civil Transport Structural Optimization Structural Response Fuselages Aerodynamic Simulation sequential Quadratic programming sequential linear programming Shape Functions Sweep Angle Central Composite Designs

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OPTIMIZATION OF PIPE NETWORKS

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MATHEMATICAL programming 1991年第1期52卷 45-58页

作者： HANSEN, CT MADSEN, K NIELSEN, HB 1. Institute for Numerical Analysis Technical University of Denmark DK 2800 Lyngby Denmark

The paper treats a piping system, where the layout of the network is given but the diameters of the pipes should be chosen among a small number of different values. The cost of realizing the system should be minimized while keeping the energy heads at the nodes above some lower limits. A new algorithm using successive linear programming is presented. The performance of the algorithm is illustrated by optimizing a network with 201 pipes and 172 nodes. It is concluded that the new algorithm seems to be very efficient and stable, and that it always finds a solution with a cost near the best possible.

关键词： GAS AND WATER DISTRIBUTION NETWORKS sequential linear programming TRUST REGIONS SPARSE MATRIX TECHNIQUES

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Buckling optimization of unsymmetrically laminated plates under transverse loads

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STRUCTURAL ENGINEERING AND MECHANICS 1999年第1期7卷 19-33页

作者： Hu, HT Chen, ZZ Natl Cheng Kung Univ Dept Civil Engn Tainan 701 Taiwan

The critical buckling loads of unsymmetrically laminated rectangular plates with a given material system and subjected to combined lateral and inplane loads are maximized with respect to fiber orientations by using a sequential linear programming method together with a simple move-limit strategy. Significant influence of plate aspect ratios, central circular cutouts, lateral loads and end conditions on the optimal fiber orientations and the associated optimal buckling loads of unsymmetrically laminated plates has been shown through this investigation.

关键词： buckling optimization unsymmetrically laminated plates end conditions sequential linear programming

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NEW SUCCESSIVE APPROXIMATION METHOD FOR OPTIMUM STRUCTURAL DESIGN

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AIAA JOURNAL 1994年第6期32卷 1310-1315页

作者： SNYMAN, JA STANDER, N University of Pretoria Pretoria 0002 South Africa

A new procedure for solving structural optimization problems, using only first-order explicit information and consisting of the successive solution of approximate subproblems, is proposed. The method differs from established sequential quadratic programming methods by not utilizing the Lagrangian form and not attempting to store full and explicit Hessian information. Instead each constraint is individually approximated by a quadratic function involving only one coefficient in the quadratic term. This coefficient is determined from a two-point collocation. A novel feature of the method is that each quadratic subproblem is solved by a recently proposed interior feasible direction method. An auxiliary problem which is easily integrated into the code is formulated to generate a feasible starting point for each subproblem. Four truss sizing problems were analyzed and results point to competitiveness of the proposed method with regard to robustness, efficiency, accuracy, and generality.

关键词： Structural Optimization sequential Quadratic programming Trusses Lagrange Multipliers sequential linear programming Taylor Series Shape Optimization Computing

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Buckling optimization of symmetrically laminated plates with various geometries and end conditions

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COMPOSITES SCIENCE AND TECHNOLOGY 1995年第3期55卷 277-285页

作者： Hu, HT Lin, BH Department of Civil Engineering National Cheng Kung University 1 University Road Tainan 701 Taiwan

The buckling resistance of symmetrically laminated plates with a given material system and subjected to uniaxial compression is maximized with respect to fiber orientations by using a sequential linear programming method together with a simple move-limit strategy. Significant influence of plate thicknesses, aspect ratios, central circular cutouts and end conditions on the optimal fiber orientations and the associated optimal buckling loads of symmetrically laminated plates are shown.

关键词： buckling optimization symmetrically laminated plates end conditions sequential linear programming

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Active/reactive bid based dispatch models to be used in electricity markets

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ELECTRIC POWER SYSTEMS RESEARCH 2008年第1期78卷 106-121页

作者： Gomes, M. H. R. Saraiva, J. T. [a]Departamento de Engenharia Electrotécnica Escola Superior de Tecnologia de Tomar Quinta do Contador Estrada da Serra 2300 Tomar Portugal [b]INESC Porto and Departamento de Engenharia Electrotécnica e Computadores Faculdade de Engenharia da Universidade do Porto Campus da FEUP Rua Dr. Roberto Frias 4200 - 465 Porto Portugal

This paper describes two new active/reactive dispatch models to be used by System Operators in order to assign reactive power and to validate the economic schedules prepared by Market Operators together with the injections related with Bilateral Contracts. When talking about electricity markets one usually refers to active power markets paying less attention to ancillary services, namely to reactive power/voltage control. This usually leads to a chronological sequence of activities that may lead to inefficiencies because active and reactive powers are coupled given the capability diagram of synchronous generators, the ac power flow equations and the branch thermal limits. In this paper, we propose new models to remarry active and reactive allocation procedures based on a market approach as a way to ensure operation transparency. The resulting optimization problems are solved by a sequential linear programming, SLP, approach that allows one to compute active and reactive nodal marginal prices at its final iteration. The paper includes a case study based on the IEEE 24 Bus Test System to illustrate the application of the developed models and demonstrate their interest in the scope of restructured power systems.

关键词： Integrated active/reactive dispatch Electricity markets System Operator Active/reactive nodal marginal prices sequential linear programming

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Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2010年第49-52期199卷 3101-3110页

作者： Motta Mello, Luis Augusto de Sturler, Eric Paulino, Glaucio H. Nelli Silva, Emilio Carlos Univ Sao Paulo Dept Mechatron & Mech Syst Engn Sch Engn BR-05508 Sao Paulo Brazil Virginia Tech Dept Math Blacksburg VA 24061 USA Univ Illinois Dept Civil & Environm Engn Newmark Lab Urbana IL 61801 USA

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Iterative methods Preconditioning Krylov subspace recycling Three-dimensional electrical impedance tomography sequential linear programming

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Design optimization of a controllable camber rotor airfoil

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AIAA JOURNAL 2008年第1期46卷 142-153页

作者： Gandhi, Farhan Frecker, Mary Nissly, Andrew Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA Penn State Univ Dept Mech & Nucl Engn University Pk PA 16802 USA

A conformable airfoil is proposed as an alternative to trailing-edge flaps used for active helicopter vibration reduction through high-frequency changes in camber. The design consists of several compliant mechanisms of predetermined topology that are placed serially within the airfoil along the chord, aft of the leading-edge spar. A shape optimization approach is used to design the compliant mechanisms, in which the objective is to maximize trailing-edge deflection while minimizing airfoil deflections due to aerodynamic loads. Solutions were obtained using a sequential linear programming method coupled with a finite element analysis. An optimized shape is predicted to achieve a trailing-edge deflection of +/- 6.0 mm or a +/- 4.6-deg equivalent flap deflection angle using the tip deflection objective. Results indicate that the deflection is dependent on the amount of passive material allowed and the objective function used. The aerodynamic loads are found to cause only small deformations in comparison with those caused by the actuation. Prototype fabrication and bench-top tests demonstrated that rotor airfoil camber is controllable using the proposed concept.

关键词： Airfoil Profiles Airfoil Geometry Aerodynamic Properties Lift to Drag Ratio Finite Element Analysis Trailing Edge Flap Shape Optimization sequential linear programming Helicopter Vibration Reduction Aspect Ratio

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An SLP-active set approach for feasibility restoration in power systems

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OPTIMIZATION AND ENGINEERING 2016年第2期17卷 385-419页

作者： Kim, Taedong Wright, Stephen J. Univ Wisconsin Dept Comp Sci 1210 W Dayton St Madison WI 53706 USA

We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by adjusting load at demand nodes or power production at generators, but doing so in a way that minimizes a weighted measure of the total power adjustment, and affects as few nodes as possible. Besides suggesting an optimal response to a given attack, our approach can be used to quantify disruption, thereby enabling "stress testing" to be performed and vulnerabilities to be identified. Optimization techniques including nonsmooth penalty functions, sequential linear programming, and active-set heuristics are used to solve this model. We describe an algorithmic framework and present convergence results, including a quadratic convergence result for the case in which the solution is fully determined by its constraints, a situation that arises frequently in the power systems application.

关键词： AC power flow equations Composite nonsmooth optimization sequential linear programming Active-set methods

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