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An interior point algorithm for Parameter Estimation of a Geared PMDC Motor Using Current and Speed Step Responses

IEEE ACCESS 2023年 11卷 121892-121901页

作者： Deraz, Said A. Alharbi, Fahd King Abdulaziz Univ Fac Engn Rabigh Elect Engn Dept Jeddah 21589 Saudi Arabia Menoufia Univ Fac Engn Elect Engn Dept El kom 32511 Egypt

In this paper, the parameters of the geared PMDC motor are estimated using the interior point algorithm (IPA). The problem of parameter estimation is converted to an optimization problem. The proposed estimation method measures the current and speed responses of the motor under a step input voltage. The objective of the IPA is to search for the parameters of the simulated PMDC motor in order to minimize the errors between the measured current and speed responses of the PMDC motor and the corresponding responses from the simulated model of the PMDC motor. Steady-state mathematical relations between the geared PMDC motor parameters are derived and used as equality and inequality constraints for constructing the proposed IPA. The proposed IPA is a gradient-based optimization algorithm. Therefore, it can efficiently and quickly minimize the objective function and obtain the solution. Moreover, the proposed estimation algorithm considers the estimation of the Coulomb friction torque of the motor. Hence, seven parameters of the geared PMDC motor are estimated: armature resistance, armature inductance, back EMF constant, torque constant, moment of inertia, viscous friction, and Coulomb friction torque. MATLAB and Arduino IDE software are utilized with the Pololu 25D motor for programming and simulation. The experimental setup is used to obtain the measured current and speed step responses. MATLAB and Simulink are used for modeling the simulated PMDC motor and the implementation of the IPA. Simulation and experimental results express the effectiveness of the proposed estimation algorithm in estimating the geared PMDC motor parameters.

关键词： Geared PMDC motor interior point algorithm parameter estimation Coulomb friction torque

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An interior point algorithm for convex quadratic programming with strict equilibrium constraints

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RAIRO-OPERATIONS RESEARCH 2005年第1期39卷 13-33页

作者： Benouahboun, R Mansouri, A Fac Sci Semlalia Dept Math Marrakech Morocco

We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of O(root nL) number of iterations, where L is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.

关键词： convex quadratic programming with a strict equilibrium constraints interior point algorithm Newton's method

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Fuel cost optimization of the power system by involving all operating limits based on the developed interior point algorithm

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2020年第5期30卷 1-14页

作者： Zein, Hermagasantos Kurniasetiawati, Annisa S. Wachjoe, Conny K. POLBAN State Polytech Bandung Energy Convers Engn Dept Bandung Indonesia

Power flow control in the power system aims to supply electricity to customers efficiently and low operating costs. Based on the conventional approach, the electric power operators only emphasize the function of optimizing generating costs according to load demand and active power limits of generators. On the other hand, the adjustment of the optimization results requires manual adjustments in its implementation. The optimization of the fuel costs minimization, which involves all constraints, is very expected by the operators so that the operator can implement the results directly without making any adjustments. Furthermore, the constraints in power flow optimization that consist of generator capability curve limits, voltage limits, transmission line limits, and active power limits on generators will lead to more complicated optimization, and the application program will run slowly. This paper proposes a method that can reduce optimization constraints with less computation time. The method is to reduce the limits of the generator capability curve through a mathematical model. While the optimization method used is the predictor-correctors techniques and reduction techniques in the interior point algorithm. The method uses a simple power system using a four-bus power system that provides accurate and satisfying results. Besides, this method has been successfully implemented in a large-scale system, namely, the 500 kV Java-Bali Power System with 65 buses and 40 generating units.

关键词： fuel costs generator capability curves interior point algorithm optimization model reduction technique

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Shape optimization using the boundary element method and a SAND interior point algorithm for constrained optimization

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COMPUTERS & STRUCTURES 2008年第13-14期86卷 1517-1526页

作者： Canelas, A. Herskovits, J. Telles, J. C. F. Univ Fed Rio de Janeiro COPPE Mech Engn Program BR-21945970 Rio De Janeiro Brazil Univ Fed Rio de Janeiro COPPE Civil Engn Program BR-21945970 Rio De Janeiro Brazil

The shape optimization problem consists in looking for the geometry that minimizes an objective function, like mass or compliance, subject to mechanical constraints. The boundary element method (BEM) is used for the structural analysis. For linear elasticity problems, it needs only a mesh on the boundary of the structure. This characteristic makes the BEM a natural method for shape optimization, since only the boundary is needed to define the optimization problem and to carry out the structural analysis. The simultaneous analysis and design formulation (SAND) for structural optimization considers the state variables as unknowns of the optimization problem and includes the equilibrium equations as equality constraints. In this way, it is not necessary to solve the equilibrium equation per iteration;the equilibrium is only obtained at the end of the optimization process. In this paper, the shape optimization problem is dealt with using the BEM formulation to define a SAND optimization problem that is solved using an interior point algorithm. Numerical results for two-dimensional linear elasticity problems are presented to illustrate the efficacy of the proposed technique. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： shape optimization boundary element method interior point algorithm structural design SAND formulation sensitivity analysis

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A self-adjusting interior point algorithm for linear complementarity problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2005年第1-2期50卷 33-40页

作者： He, SY Li, XS Pan, SH Dalian Univ Foreign Languages Ctr Comp Dalian 116002 Peoples R China Dalian Univ Technol Dept Mech Engn State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China S China Univ Technol Dept Appl Math Guangzhou 510641 Peoples R China

Based on the min-max principle, the standard centering equation in the interior point method is replaced by the optimality condition of a new proximity measure function. Thus, a self-adjusting mechanism is constructed in the new perturbed system. The Newton direction can be adjusted self-adaptively according to the information of last iterates. A self-adjusting interior point method is given based on the new perturbed system. Numerical comparison is made between this algorithm and a primal-dual interior point algorithm using "standard" perturbed system. Results demonstrate the efficiency and some advantages of the proposed algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： linear complementarity problems central path proximity measure interior point algorithm self-adjusting

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Bid-based dynamic economic dispatch with an efficient interior point algorithm

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2002年第1期24卷 51-57页

作者： Lin, WM Chen, SJ Natl Sun Yat Sen Univ Inst Elect Engn Kaohsiung 80424 Taiwan

An efficient interior point algorithm for solving the bid-based dynamic economic dispatch (BBDED) problem is proposed in this paper. This algorithm is an extension of interior point quadratic programming (IPQP), and is called the predictor-corrector interior point quadratic programming (PCIPQP) algorithm. In a competitive electricity market, the dynamic economic dispatch has evolved to become bid-based framework to maximize the profits and achieve the resource scheduling. To generate a physically feasible dispatch and market spot prices, we form BBDED problem of dealing with various constraints such as ramp rates, transmission line capacity and emission constraints. In this paper, BBDED allows both supply-side and demand-side bids in the spot market, which includes multi-player, multi-period and a large number of constraints. Compared with the pure IPQP algorithm, PCIPQP is more attractive in performance, robustness, and the property of convergence. Many numerical tests reconfirmed the advantages of the predictor-corrector method. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： competitive electricity market bid-based operation dynamic economic dispatch interior point algorithm predictor-corrector method

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Electricity market equilibrium analysis based on nonlinear interior point algorithm with complementarity constraints

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IET GENERATION TRANSMISSION & DISTRIBUTION 2007年第4期1卷 603-612页

作者： Petoussis, S. G. Zhang, X. P. Godfrey, K. R. Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England Elect Author Cyprus CY-1399 Nicosia Cyprus Univ Birmingham Inst Energy Res & Policy Birmingham B15 2TT W Midlands England

This paper presents an interior point algorithm based on a.c. network model for determining the Nash supply function equilibrium (SFE) of bid-based electricity markets. The SFE problem is considered as a bi-level game. At the first level, the problem begins with the formulation of an optimal power flow (OPF) interior point-based algorithm to handle the independent system operator (ISO) problem for maximising social welfare. This algorithm is based on the OPF with a.c. network transmission model taking into account all the operating aspects such as the generation capacity limits, bus voltage limits, transmission line constraints, network losses and especially the effect of the reactive power. The resulting Karush-Kuhn-Tucker (KKT) conditions of the problem at the first level are then reformulated using nonlinear complementarity constraints and incorporated as equality constraints in the second-level formulation for maximising the individual profit for each strategic generating firm. By employing a special nonlinear complementarity function, the complementarity constraints are then transformed into nonlinear algebraic expressions, thus the KKT conditions of the resulting combined problem can be derived. The final problem is then solved iteratively based on the solution techniques of the interior point algorithm. Numerical examples of a three-bus system, the IEEE 14-bus system and the IEEE 30-bus system, show that the algorithm can successfully determine the electricity market equilibrium with the a.c. network model.

关键词： link voltage supply balance interior point algorithm Complementarity kamikihi-to AC network PLANT CAPACITY Equilibrium analysis power markets

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Infeasible path-following interior point algorithm for Cartesian P_*() nonlinear complementarity problems over symmetric cones

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2018年第5期95卷 845-869页

作者： Zhao, Huali Liu, Hongwei Xidian Univ Sch Math & Stat Xian Shaanxi Peoples R China Xianyang Normal Univ Sch Math & Informat Sci Xianyang 712000 Peoples R China

In this paper, we establish a theoretical framework of infeasible path-following interior point algorithm for Cartesian inline-graphic> nonlinear complementarity problems over symmetric cones using a wide neighbourhood of the central path. In order to prove the convergence of the proposed algorithm, we propose a scaled Lipschitz condition which has scaling invariance. Under the condition, we estimate the iteration complexities of the proposed algorithm and provide some numerical results. The numerical results show that the algorithm is efficient and reliable.

关键词： Cartesian P*(kappa) nonlinear complementarity problem infeasible interior point algorithm symmetric cone

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A feasible BFGS interior point algorithm for solving convex minimization problems

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SIAM JOURNAL ON OPTIMIZATION 2000年第1期11卷 199-222页

作者： Armand, P Gilbert, JC Jan-Jégou, S Fac Sci LACO F-87060 Limoges France INRIA Rocquencourt F-78153 Le Chesnay France Univ Toulouse 3 UFR MIG MIP F-31062 Toulouse France

We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters mu converging to zero. We prove that it converges q-superlinearly for each fixed mu. We also show that it is globally convergent to the analytic center of the primal-dual optimal set when mu tends to 0 and strict complementarity holds.

关键词： analytic center BFGS quasi-Newton approximations constrained optimization convex programming interior point algorithm line-search primal-dual method superlinear convergence

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Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley-Torvik equation

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MATHEMATICS AND COMPUTERS IN SIMULATION 2017年 132卷 139-158页

作者： Raja, Muhammad Asif Zahoor Samar, Raza Manzar, Muhammad Anwar Shah, Syed Muslim COMSATS Inst Informat Dept Elect Engn Attock Campus Attock Pakistan Capital Univ Sci & Technol Dept Elect Engn Islamabad Pakistan Int Islamic Univ Dept Elect Engn Islamabad Pakistan

In this article, an efficient computing technique has been developed for the solution of fractional order systems governed with initial value problems (IVPs) of the Bagley-Torvik equations using fractional neural networks (FNNs) optimized with interior point algorithms (IPAs). The strength of FNNs is exploited to develop an approximate model of the equation in an unsupervised manner. The training of optimal weight of the networks is carried out using IPAs. The designed scheme is evaluated on different IVPs of the equation. Comparative studies for the results of the proposed scheme are made with an available exact solution, Podlubny numerical techniques, an analytical solver based on He's variational iteration method and a reported solution of stochastic solvers based on hybrid approaches, in order to verify the correctness of the design scheme. The results of statistical analysis based on the sufficient large number of independent runs established the consistency of the proposed scheme in terms of accuracy and convergence. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Bagley-Torvik equation Fractional differential equations interior point algorithm Neural networks Unsupervised modeling

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