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A Least-squares-based Iterative Method with Better Convergence for PF/OPF in Integrated Transmission and Distribution Networks

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CSEE Journal of Power and Energy Systems 2024年第3期10卷 953-962页

作者： Kunjie Tang Shufeng Dong Yonghua Song College of Electrical Engineering Zhejiang UniversityHangzhou 310027China State Key Laboratory of Internet of Things for Smart City and Department of Electrical and Computer Engineering University of MacaoMacao SARChina IEEE

The limitations of the conventional master-slavesplitting(MSS)method,which is commonly applied to power flow and optimal power flow in integrated transmission and distribution(I-T&D)networks,are first *** that the MSS method suffers from a slow convergence rate or even divergence under some circumstances,a least-squares-based iterative(LSI)method is *** with the MSS method,the LSI method modifies the iterative variables in each iteration by solving a least-squares problem with the information in previous iterations.A practical implementation and a parameter tuning strategy for the LSI method are ***,a LSI-PF method is proposed to solve I-T&D power flow and a LSIheterogeneous decomposition(LSI-HGD)method is proposed to solve optimal power *** experiments demonstrate that the proposed LSI-PF and LSI-HGD methods can achieve the same accuracy as the benchmark ***,these LSI methods,with appropriate settings,significantly enhance the convergence and efficiency of conventional ***,in some cases,where conventional methods diverge,these LSI methods can still converge.

关键词： fixed-point theory integrated transmission and distribution networks least-squares-based iterative method master-slave-splitting method optimal power flow power flow

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A Novel Modeling Method for Both Steady-State and Transient Analyses of Serial Bernoulli Production Systems

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2015年第1期45卷 97-108页

作者： Wang, Yong Li, Lin Univ Illinois Dept Mech & Ind Engn Chicago IL 60607 USA

Conventionally, production system modeling (PSM) has been conducted for the purpose of steady-state analysis, which only facilitates characterizing the long-term performance of production systems. More recently, there has been a rising concern regarding analyzing production system transients, which depict the system behavior before reaching the steady state. Transients are generally undesirable because the performance measures can be quite different from those of the steady state, and such differences will cause substantial production loss. Compared to the rich knowledge on steady-state analysis of production systems, PSM for transient performance analysis is much less studied. In this paper, a novel analytical method has been established to model the production system for both steady-state and transient analyses. This research has overcome the restrictions of existing methods on the number of machines and the capacity of buffers. That is, it has greatly advanced PSM for both steady-state and transient analyses by directly dealing with general serial production systems with multiple unreliable Bernoulli machines and finite buffer capacities. The proposed PSM is a method derived based on probability theory and fixed-point theory. The solvability of the method is proved theoretically. The transient performance metrics, such as second largest eigenvalue modulus, duration of the transients (t(ITER)), settling time of work-in-process (t(WIP)) and production rate (t(PR)), and percent loss of production (L-PR) have been investigated numerically based on the proposed PSM method. This research can serve as an atomic model for more complex optimization problems in production system design and operation.

关键词： Bernoulli reliability model fixed-point theory production system modeling steady-state analysis transient analysis

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Model-Free λ-Policy Iteration for Discrete-Time Linear Quadratic Regulation

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第2期34卷 635-649页

作者： Yang, Yongliang Kiumarsi, Bahare Modares, Hamidreza Xu, Chengzhong Univ Macau State Key Lab IoTSC Taipa 999078 Macao Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Michigan State Univ Dept Elect & Comp Engn E Lansing MI 48824 USA Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA

This article presents a model-free lambda-policy iteration (lambda-PI) for the discrete-time linear quadratic regulation (LQR) problem. To solve the algebraic Riccati equation arising from solving the LQR in an iterative manner, we define two novel matrix operators, named the weighted Bellman operator and the composite Bellman operator. Then, the lambda-PI algorithm is first designed as a recursion with the weighted Bellman operator, and its equivalent formulation as a fixed-point iteration with the composite Bellman operator is shown. The contraction and monotonic properties of the composite Bellman operator guarantee the convergence of the lambda-PI algorithm. In contrast to the PI algorithm, the lambda-PI does not require an admissible initial policy, and the convergence rate outperforms the value iteration (VI) algorithm. Model-free extension of the lambda-PI algorithm is developed using the off-policy reinforcement learning technique. It is also shown that the off-policy variants of the lambda-PI algorithm are robust against the probing noise. Finally, simulation examples are conducted to validate the efficacy of the lambda-PI algorithm.

关键词： Optimal control Heuristic algorithms Convergence Regulation Performance analysis Mathematical model Approximation algorithms Algebraic Riccati equation (ARE) fixed-point theory off-policy reinforcement learning (RL) optimal control

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Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

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ASIAN JOURNAL OF CONTROL 2023年第5期25卷 4039-4057页

作者： Kumar, Surendra Yadav, Shobha Univ Delhi Fac Math Sci Dept Math Delhi India Univ Delhi Fac Math Sci Dept Math Delhi 110007 India

Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.

关键词： approximate controllability fixed-point theory instantaneous impulses noninstantaneous impulses Poisson jumps stochastic delay differential systems

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A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport

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IMA JOURNAL OF NUMERICAL ANALYSIS 2021年第1期41卷 381-411页

作者： Alvarez, Mario Gatica, Gabriel N. Ruiz-Baier, Ricardo Univ Costa Rica Sect Matemat Sede Occidente San Ramon De Alajuela 1114250 Costa Rica Univ Concepcion CI2MA Casilla 160-C Concepcion Chile Univ Concepcion Dept Ingn Matemat Casilla 160-C Concepcion Chile Univ Oxford Math Inst Woodstock Rd Oxford OX2 6GG England Univ Adventista Chile Casilla 7-D Chillan Chile Monash Univ Sch Math Sci Clayton Vic 3800 Australia

This paper is devoted to the mathematical and numerical analysis of a model describing the interfacial flow-transport interaction in a porous-fluidic domain. The medium consists of a highly permeable material, where the flow of an incompressible viscous fluid is governed by Brinkman equations (written in terms of vorticity, velocity and pressure), and a porous medium where Darcy's law describes fluid motion using filtration velocity and pressure. Gravity and the local fluctuations of a scalar field (representing for instance, the solids volume fraction or the concentration of a contaminant) are the main drivers of the fluid patterns on the whole domain, and the Brinkman-Darcy equations are coupled to a nonlinear transport equation accounting for mass balance of the scalar concentration. We introduce a mixed-primal variational formulation of the problem and establish existence and uniqueness of solution using fixed-point arguments and small-data assumptions. A family of Galerkin discretizations that produce divergence-free discrete velocities is also presented and analysed using similar tools to those employed in the continuous problem. Convergence of the resulting mixed-primal finite element method is proven, and some numerical examples confirming the theoretical error bounds and illustrating the performance of the proposed discrete scheme are reported.

关键词： nonlinear transport Brinkman-Darcy coupling vorticity-based formulation fixed-point theory mixed finite elements error analysis

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A Well-Posedness Framework for Inpainting Based on Coherence Transport

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2015年第4期15卷 973-1033页

作者： Maerz, Thomas Univ Oxford Oxford Ctr Collaborat Appl Math Radcliffe Observ Quarter Oxford OX2 6GG England

Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and Marz (J Math Imaging Vision, 28:259-278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.

关键词： Functional PDEs Method of characteristics Lyapunov functions Functions of bounded variation fixed-point theory Image inpainting

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Analysis and Optimization of the Novel Inerter-Based Dynamic Vibration Absorbers

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IEEE ACCESS 2018年 6卷 33169-33182页

作者： Wang, Xiaoran Liu, Xiandong Shan, Yingchun Shen, Yongjun He, Tian Beihang Univ Sch Transportat Sci & Engn Beijing 100191 Peoples R China Shijiazhuang Tiedao Univ Dept Mech Engn Shijiazhuang 050043 Hebei Peoples R China

Passive dynamic vibration absorber (DVA) is widely used in structural vibration reduction, and the higher efficient DVA is always required for some special situations. This paper aims to propose the novel inerter-based dynamic vibration absorbers (IDVAs) to enhance the performance of the passive DVA. First, several novel IDVAs are presented by matching the inerter with DVA in different places. Then, the closed-form optimal parameters of six kinds of IDVAs are obtained based on the classical fixed-point theory. The obtained parameters demonstrates that all the inerters connected between the primary system and absorber system do not provide improvement for the performance of DVAs, while all the inerters connected to the earth can improve the performance of DVAs. Moreover, the comparisons among the IDVAs show that the inerter connected to the earth in the grounded DVA (IR2 in this paper) performs the best performance in vibration absorption. More than 30 % improvement can be obtained from IR2 as compared with other IDVAs. Finally, the further comparison among the IDVAs under white noise excitation also shows that IR2 is superior to other IDVAs. The results may provide theoretical basis for design of the optimal IDVA in engineering practice.

关键词： Dynamic vibration absorber fixed-point theory inerter optimization vibration absorption

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Analytically optimal parameters of dynamic vibration absorber with negative stiffness

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2017年 85卷 193-203页

作者： Shen, Yongjun Peng, Haibo Li, Xianghong Yang, Shaopu Shijiazhuang Tiedao Univ Dept Mech Engn Shijiazhuang Shi 050043 Hebei Sheng Peoples R China Shijiazhuang Tiedao Univ Dept Engn Mech Shijiazhuang Shi 050043 Hebei Sheng Peoples R China Shijiazhuang Tiedao Univ Dept Math & Phys Shijiazhuang Shi 050043 Hebei Sheng Peoples R China

In this paper the optimal parameters of a dynamic vibration absorber (DVA) with negative stiffness is analytically studied. The analytical solution is obtained by Laplace transform method when the primary system is subjected to harmonic excitation. The research shows there are still two fixed points independent of the absorber damping in the amplitude frequency curve of the primary system when the system contains negative stiffness. Then the optimum frequency ratio and optimum damping ratio are respectively obtained based on the fixed-point theory. A new strategy is proposed to obtain the optimum negative stiffness ratio and make the system remain stable at the same time. At last the control performance of the presented DVA is compared with those of three existing typical DVAs, which were presented by Den Hartog, Ren and Sims respectively. The comparison results in harmonic and random excitation show that the presented DVA in this paper could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Dynamic vibration absorber Negative stiffness fixed-point theory Parameters optimization

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Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem

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NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2016年第2期32卷 445-478页

作者： Colmenares, Eligio Gatica, Gabriel N. Oyarzua, Ricardo Univ Concepcion CI2MA Casilla 160-C Concepcion Chile Univ Concepcion Dept Ingn Matemat Casilla 160-C Concepcion Chile Univ Bio Bio GIMNAP Dept Matemat Casilla 5-C Concepcion Chile

In this article, we propose and analyze a new mixed variational formulation for the stationary Boussinesq problem. Our method, which uses a technique previously applied to the Navier-Stokes equations, is based first on the introduction of a modified pseudostress tensor depending nonlinearly on the velocity through the respective convective term. Next, the pressure is eliminated, and an augmented approach for the fluid flow, which incorporates Galerkin-type terms arising from the constitutive and equilibrium equations, and from the Dirichlet boundary condition, is coupled with a primal-mixed scheme for the main equation modeling the temperature. In this way, the only unknowns of the resulting formulation are given by the aforementioned nonlinear pseudostress, the velocity, the temperature, and the normal derivative of the latter on the boundary. An equivalent fixed-point setting is then introduced and the corresponding classical Banach Theorem, combined with the Lax-Milgram Theorem and the Babuka-Brezzi theory, are applied to prove the unique solvability of the continuous problem. In turn, the Brouwer and the Banach fixed-point theorems are used to establish existence and uniqueness of solution, respectively, of the associated Galerkin scheme. In particular, Raviart-Thomas spaces of order k for the pseudostress, continuous piecewise polynomials of degree k+1 for the velocity and the temperature, and piecewise polynomials of degree k for the boundary unknown become feasible choices. Finally, we derive optimal a priori error estimates, and provide several numerical results illustrating the good performance of the augmented mixed-primal finite element method and confirming the theoretical rates of convergence. (c) 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 445-478, 2016

关键词： a priori error analysis augmented mixed-primal formulation Boussinesq equations finite element methods fixed-point theory

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Optimization design for multiple dynamic vibration absorbers on damped structures using equivalent linearization method

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART K-JOURNAL OF MULTI-BODY DYNAMICS 2022年第1期236卷 41-50页

作者： Duc Phuc, Vu Tran, Van-The Hung Yen Univ Technol & Educ Dept Mech Engn Hung Yen Vietnam

The dynamic vibration absorber and tuned mass damper are widely used to suppress harmful vibration of the damped structures under external excitation. The multiple dynamic vibration absorbers have more benefit than the single dynamic vibration absorber. The multiple dynamic vibration absorbers are portability and easy to install because its size is significantly reduced compared to an individual damper. This paper proposes a design method to obtain optimal parameters of multiple dynamic vibration absorbers attached on damped primary structures by using the least squares estimation of equivalent linearization method. An explicit expression of damping ratio and tuning parameters of multiple dynamic vibration absorbers are determined for minimizing the maximum displacement of the primary structures based on the fixed-point theory. The new contribution is provided a reliable theoretical basis for optimizing parameters of the multiple dynamic vibration absorbers that are attached on the damped primary structures. The numerical results reveal the effectiveness of the proposed optimal parameters of multiple dynamic vibration absorbers in reduce vibration of damped primary structures. In the practical applications, this research results allow to divide a large dynamic vibration absorber into many equivalent small dynamic vibration absorbers, which are convenient for manufacturing and installing on the damped primary structures such as high buildings and cable-stayed bridges.

关键词： Multiple dynamic vibration absorbers damped primary structures fixed-point theory equivalent linearization method vibration response amplitude magnification function

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