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arXiv 2021年

作者： De Mel, Ishanki Klymenko, Oleksiy V. Short, Michael Department of Chemical and Process Engineering University of Surrey GuildfordGU2 7XH United Kingdom

Distributed energy systems (DES) have the potential to minimise costly network upgrades while increasing the proportion of renewable energy generation in the electrical grid, when properly designed. In contrast, poorly designed DES can accelerate the degeneration of existing network infrastructure. Most optimisation models used to design grid-connected DES have oversimplified or excluded constraints associated with alternating current (AC) power flow, as the latter has been studied in a standalone class of models known as Optimal Power Flow (OPF). A small subset of models, labelled DES-OPF models, have attempted to combine these independent frameworks. However, the impacts of using a DES-OPF framework on the resulting designs, as opposed to a conventional DES framework without AC power flow, have not been studied in previous work. This study aims to shed light on these impacts by proposing a bi-level method to solve the computationally-expensive DES-OPF framework, and simultaneously comparing results to a baseline MILP model that utilises direct current (DC) approximations in place of AC OPF, as found abundantly in literature. Two test cases of varying scale are employed to test the frameworks and compare resulting designs. The practical feasibility of the designs is assessed, based on whether the designs can mitigate network violations and energy wastage during standard operation. Results demonstrate that the baseline MILP underestimates total costs due to its inability to detect current and voltage violations, resulting in a 37% increase for one case study when tested with the DES-OPF framework. Major implications on battery capacity are also observed, primarily to manage higher levels of renewable energy curtailment, which emphasise the need to use DES-OPF frameworks when designing grid-connected DES. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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nonlinear optimized Schwarz preconditioner for elliptic optimal control problems

arXiv

引用

arXiv 2021年

作者： Ciaramella, Gabriele Kwok, Felix Müller, Georg Politecnico di Milano Italy Université Laval Canada Universität Konstanz Germany

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A novel augmented Lagrangian method of multipliers for optimization with general inequality constraints

arXiv

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arXiv 2021年

作者： Liu, Xin-Wei Dai, Yu-Hong Huang, Ya-Kui Sun, Jie Institute of Mathematics Hebei University of Technology Tianjin300401 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Business National University of Singapore Singapore119245 Singapore

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented Lagrangian. A novel augmented Lagrangian method of multipliers (ALM) is then presented. Our method is originated from a generalization of the Hetenes-Powell augmented Lagrangian, and is a combination of the augmented Lagrangian and the interior-point technique. It shares a similar algorithmic framework with existing ALMs for optimization with inequality constraints, but it can use the second derivatives and does not depend on projections on the set of inequality constraints. In each iteration, our method solves a twice continuously differentiable unconstrained optimization subproblem on primal variables. The dual iterates, penalty and smoothing parameters are updated adaptively. The global and local convergence are analyzed. Without assuming any constraint qualification, it is proved that the proposed method has strong global convergence. The method may converge to either a Kurash-Kuhn-Tucker (KKT) point or a singular stationary point when the converging point is a minimizer. It may also converge to an infeasible stationary point of nonlinear program when the problem is infeasible. Furthermore, our method is capable of rapidly detecting the possible infeasibility of the solved problem. Under suitable conditions, it is locally linearly convergent to the KKT point, which is consistent with ALMs for optimization with equality constraints. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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D-LIO: 6DoF Direct LiDAR-Inertial Odometry based on Simultaneous Truncated Distance Field Mapping

arXiv

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arXiv 2025年

作者： Coto-Elena, L. Maese, J.E. Merino, L. Caballero, F. Service Robotics Laboratory Universidad Pablo de Olavide Seville Spain

This paper presents a new approach for 6DoF Direct LiDAR-Inertial Odometry (D-LIO) based on the simultaneous mapping of truncated distance fields on CPU. Such continuous representation (in the vicinity of the points) enables working with raw 3D LiDAR data online, avoiding the need of LiDAR feature selection and tracking, simplifying the odometry pipeline and easily generalizing to many scenarios. The method is based on the proposed Fast Truncated Distance Field (FastTDF) method as a convenient tool to represent the environment. Such representation enables i) solving the LiDAR point-cloud registration as a nonlinear optimization process without the need of selecting/tracking LiDAR features in the input data, ii) simultaneously producing an accurate truncated distance field map of the environment, and iii) updating such map at constant time independently of its size. The approach is tested using open datasets, aerial and ground. It is also benchmarked against other state-of-the-art odometry approaches, demonstrating the same or better level of accuracy with the added value of an online-generated TDF representation of the environment, that can be used for other robotics tasks as planning or collision avoidance. The source code is publicly available at https://***/r/D-LIO © 2025, CC BY-SA.

关键词： nonlinear programming

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Dispatch of virtual inertia and damping: Numerical method with SDP and ADMM

arXiv

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arXiv 2021年

作者： Han, Tong Hill, David J. The Department of Electrical and Electronic Engineering University of Hong Kong Hong Kong

Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual inertia and damping provided by inverters are essential to synchronism and frequency stability of future power grids. This paper numerically addresses the problem of dispatch of virtual inertia and damping (DID) among inverters in the transmission network. The DID problem is first formulated as a nonlinear program (NLP) by the Radua collocation method which is flexible to handle various types of disturbances and bounds constraints. Since the NLP of DID is highly non-convex, semi-definite programming (SDP) relaxation for the NLP is further derived to tackle the non-convexity, followed by its sparsity being exploited hierarchically based on chordality of graphs to seek enhancement of computational efficiency. Considering high dimension and inexactness of the SDP relaxation, a feasibility-embedded distributed approach is finally proposed under the framework of alternating direction method of multipliers (ADMM), which achieves parallel computing and solution feasibility regarding the original NLP. Numerical simulations carried out for five test power systems demonstrate the proposed method and necessity of DID. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators

arXiv

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arXiv 2021年

作者： Kato, Yuzuru Zlotnik, Anatoly Li, Jr-Shin Nakao, Hiroya Department of Systems and Control Engineering Tokyo Institute of Technology Tokyo152-8552 Japan Applied Mathematics and Plasma Physics Los Alamos National Laboratory Los AlamosNM87545 United States Department of Electrical and Systems Engineering Washington University in St. Louis St. LouisMO63130 United States

We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

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Numerical performance of different formulations for alternating current optimal power flow

arXiv

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arXiv 2021年

作者： Sadat, Sayed Abdullah Kim, Kibaek The Mathematics and Computer Science Division Argonne National Laboratory The U.S. Department of Energy LemontIL60439 United States

Alternating current optimal power flow (ACOPF) problems are nonconvex and nonlinear optimization problems. Utilities and independent service operators (ISO) require ACOPF to be solved in almost real time. Interior point methods (IPMs) are one of the powerful methods for solving large-scale nonlinear optimization problems and are a suitable approach for solving ACOPF with large-scale real-world transmission networks. Moreover, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. In this paper, different ACOPF formulations with various linear solvers and the impact of employing box constraints are evaluated for computational viability and best performance when using IPMs. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of sparsity. The numerical experiments suggest that the least sparse ACOPF formulations with polar voltages yield the best computational results. Additionally, nodal injected models and current-based branch flow models are improved by enforcing box constraints. A wide range of test cases, ranging from 500-bus systems to 9591-bus systems, are used to verify the test results. © 2021, CC BY.

关键词： nonlinear programming

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An Effective Method to Generate Condensation Map for Engines

An Effective Method to Generate Condensation Map for Engines

引用

2021中国汽车工程学会年会暨展览会

作者： Yan Shuchang Zhang Tianqiang Wang Yan Fu Lei Yang Fang China FAW Group Corporation

A considerable amount of desired operation points for vehicle engines can be obtained from vehicle *** desired operations points are in need to guide the design of engines with preferred *** this paper,an effective method to cluster the operating points and generate condensation maps of engines is proposed to meet this urgent ***,we divide the area where the simulation points are located according to the geometric *** operation points in one area belong to the gravity center of this *** then reallocate the simulation points to the gravity centers based on the distance between the simulation points and the gravity *** process is formulated as a mixed-integer linear programming ***,we determine representative points representing different groups of operation points by solving a nonlinear optimization *** method has been successfully utilized in our design of vehicle engines.

关键词： condensation map vehicle engine operation point mix-integer linear programming nonlinear programming

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Iterative Standard Strategy for Non-Linear Optimization in Melting Furnace Charge Calculations

Research Square

引用

Research Square 2021年

作者： Jafari-Ramiani, Amin Yousefi, Dorsa Mohajeri, Mahdiyeh No.424 Hafez St. Tehran15916-34311 Iran

This paper describes an approach to furnace charge calculation for melting processes. Some complexities of the problem, including non-homogeneous element loss, non-metal contaminations, and, melt correction have been considered in the model. The contribution of the model is that it examines a rearrangement of the non-linear complexities into an iterative standard linear programming framework. The performance of the model was evaluated and demonstrated on an industrial scale test problem. The results revealed that the non-linear phenomenological complexities can be effectively fitted in the framework of an iterative standard LP model. This feature provides a backbone for reliable and fast optimization in melting which is of significant benefit for industrial automation. © 2021, CC BY.

关键词： nonlinear programming

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Evaluating the performance of various ACOPF formulations using nonlinear interior-point method

TechRxiv

引用

TechRxiv 2021年

作者： Sadat, Sayed Abdullah Department of Electrical and Computer Engineering University of Utah United States

Alternating current optimal power flow (ACOPF) problem is a non-convex and a nonlinear optimization problem. Similar to most nonlinear optimization problems, ACOPF is an NP-hard problem. On the other hand, Utilities and independent service operators (ISO) require the problem to be solved in almost real-time. The real-world networks are often large in size and developing an efficient and tractable algorithm is critical to many decision-making processes in electricity markets. Interior-point methods (IPMs) for nonlinear programming are considered one of the most powerful algorithms for solving large-scale nonlinear optimization problems. However, the performance of these algorithms is significantly impacted by the optimization structure of the problem. Thus, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. Different ACOPF formulations are evaluated in this paper for computational viability and best performance using the interior-point line search (IPLS) algorithm. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of varying sparsity. The numerical experiments suggest that the least sparse ACOPF formulation with polar voltages yields the best computational results. A wide range of test cases, ranging from 500-bus systems to 9591-bus systems, are used to verify the test results. © 2021, CC BY.

关键词： nonlinear programming

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