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Constrained NLP via gradient flow penalty continuation: Towards self-tuning robust penalty schemes

COMPUTERS & CHEMICAL ENGINEERING 2017年 101卷 243-258页

作者： Scott, Felipe Conejeros, Raul Vassiliadis, Vassilios S. Univ Andes Fac Ingn & Ciencias Aplicadas Green Technol Res Grp Mons Alvaro del Portillo 12455 Santiago 7620001 Chile Pontificia Univ Catolica Valparaiso Sch Biochem Engn Av Brasil 2085 Valparaiso Chile Univ Cambridge Dept Chem Engn & Biotechnol Cambridge CB2 3RA England

This work presents a new numerical solution approach to nonlinear constrained optimization problems based on a gradient flow reformulation. The proposed solution schemes use self-tuning penalty parameters where the updating of the penalty parameter is directly embedded in the system of ODEs used in the reformulation, and its growth rate is linked to the violation of the constraints and variable bounds. The convergence properties of these schemes are analyzed, and it is shown that they converge to a local minimum asymptotically. Numerical experiments using a set of test problems, ranging from a few to several hundred variables, show that the proposed schemes are robust and converge to feasible points and local minima. Moreover, results suggest that the GF formulations were able to find the optimal solution to problems where conventional NLP solvers fail, and in less integration steps and time compared to a previously reported GF formulation. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Gradient flow nonlinear programming problem Convergence analysis

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Linear approximated formulation of AC optimal power flow using binary discretisation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第5期10卷 1117-1123页

作者： Akbari, Tohid Bina, Mohammad Tavakoli KN Toosi Univ Technol Fac Elect Engn Tehran Iran

This study presents a novel linear approximated methodology for full alternating current-optimal power flow (AC-OPF). The AC-OPF can provide more precise and real picture of full active and reactive power flow modelling, along with the voltage profile of buses compared to the commonly used direct current-optimal power flow. While the AC-OPF is a non-linear programming problem, this can be transformed into a mixed-integer linear programming environment by the proposed model without loss of accuracy. The global optimality of the solution for the approximated model can be guaranteed by existing algorithms and software. The numerical results and simulations which represent the effectiveness and applicability of the proposed model are given and completely discussed in this study.

关键词： load flow nonlinear programming integer programming linear programming linear approximated formulation AC optimal power flow binary discretisation linear approximated methodology full alternating current-optimal power flow AC-OPF reactive power flow modelling voltage profile direct current-optimal power flow nonlinear programming problem mixed-integer linear programming

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Hybrid battery-ultracapacitor storage system sizing for renewable energy network integration

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IET RENEWABLE POWER GENERATION 2020年第13期14卷 2367-2375页

作者： Gonzalez-Gonzalez, Jose M. Martin, Sebastian Lopez, Pablo Aguado, Jose A. Univ Malaga Dept Elect Engn C Doctor Ortiz Ramos S-N Malaga 29071 Spain

Wind and Solar photovoltaic power plants outputs are usually highly variable due to gusts of wind and sharp sun irradiance level variations caused by cloud shading effects. These effects negatively impact system security, especially in weak power networks. On the other hand, due to the recent technological progress and cost reductions, electrical energy storage systems are an attractive alternative that can be easily integrated into non-despatchable power plants to compensate for those power output fluctuations. This study proposes a methodology for optimal sizing of a hybrid (lithium-ion battery and ultracapacitor) energy storage system for renewable energy network integration. Special attention is paid to the battery cycling degradation process. It is shown that battery aging due to cycling is a major driver for optimal sizing. The resulting sizing problem is posed as a non-linear programming problem. Finally, real and illustrative case studies are presented for both, wind and photovoltaic power plants integrating a hybrid energy storage system. Results are reported by comparing different energy storage system configurations.

关键词： photovoltaic power systems supercapacitors secondary cells cost reduction energy management systems ageing wind power plants solar power wind power nonlinear programming battery storage plants battery management systems lithium compounds power generation economics power system security hybrid power systems solar photovoltaic power plants hybrid battery-ultracapacitor storage system sizing renewable energy network integration cloud shading effects system security cost reductions electrical energy storage systems nondespatchable power plants power output fluctuations lithium-ion battery battery cycling degradation process nonlinear programming problem sun irradiance level variations wind power plants battery aging

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Optimal Design of IIR Filters Using Linear Semi-Indefinite programming Method

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ELECTRONICS AND COMMUNICATIONS IN JAPAN 2011年第6期94卷 17-23页

作者： Yamazaki, Takayuki Suyama, Kenji Tokyo Denki Univ Tokyo Japan

An optimal design method for stable IIR (Infinite Impulse Response) filters under the min-max criterion is proposed. The design problem considered is the complex Chebyshev approximation of a rational function including the stability constraint. We formulate this problem as a problem of real linear semi-infinite programming problem using the real rotation theorem. The problem is solved by the three-phase method;one of the methods is used for solving semi-infinite programming problems. The three-phase method includes three operations. In the first operation, some active constraint candidates are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximate solution obtained up to the second operation is adjusted so as to satisfy the optimality condition. The filters designed by the method are found to be more precise than those designed by the conventional method. Several design examples are presented to demonstrate the effectiveness of the proposed method. (C) 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(6): 17-23, 2011;Published online in Wiley Online Library (***). DOE 10.1002/ecj.10330

关键词： digital filter linear semi-indefinite programming method nonlinear programming problem simplex method

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Pseudo-spectral method for controlling the drug dosage in cancer

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IET SYSTEMS BIOLOGY 2020年第5期14卷 261-270页

作者： Nazari, Mostafa Nazari, Morteza Noori Skandari, Mohammad Hadi Shahrood Univ Technol Fac Mech & Mechatron Engn POB *** Shahrood Iran Shahrood Univ Technol Fac Math Sci POB *** Shahrood Iran

A mixed chemotherapy-immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co-existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour-free equilibrium. Chemotherapy protocol is derived using the pseudo-spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov-based controllers. In this method, an infinite-horizon optimal control problem is proposed for a non-linear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a non-linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo-drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.

关键词： patient treatment cancer convergence linear programming optimal control nonlinear programming nonlinear control systems Lyapunov methods drugs tumours nonlinear programming problem efficient Legendre PS scheme chemo-drug dose Mamdani fuzzy system treatment strategy pseudospectral method drug dosage mixed chemotherapy-immunotherapy treatment protocol cancer treatment desired equilibrium point immunotherapy alters cancerous equilibrium point tumour-free equilibrium chemotherapy protocol pseudospectral controller high convergence rate simple implementation structure controller computational load Lyapunov-based controllers infinite-horizon optimal control problem nonlinear cancer model

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Multiobjective capacity planning of photovoltaics in smart electrical energy networks: improved normal boundary intersection method

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IET RENEWABLE POWER GENERATION 2017年第13期11卷 1679-1687页

作者： Akbari, Mohammad-Amin Aghaei, Jamshid Barani, Mostafa Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

Incentive-based regulations, toward higher performance networks, are the main driver for minimising losses in distribution systems. On the other hand, more renewable generation is needed to achieve environmental targets. Hence, a multiobjective model is introduced in this study seeking to minimise energy losses as well as maximise renewable generation in radial distribution systems (RDSs). Two alternative control strategies of future smart grids such as reactive power management using adaptive power factor control and coordinated voltage control are considered in the optimisation problem. The problem is subjected to the various technical constraints such as voltage limits, thermal limits and reactive capability limits of photovoltaic (PV) penetration, power factor regulations and underload tap changer adjustment. Also, the uncertainties of load and renewable generation are considered, too. Then, the obtained non-linear programming problem is relaxed and reformulated as a well-suited and computationally efficient second-order cone programming problems. To obtain more efficient and evenly distributed Pareto set to help decision-making process, a modified normal boundary intersection method is introduced for solution methodology. The implementation of the proposed framework on IEEE 33-bus RDSs shows the gains that the flexibility provided by innovative control strategies can have on energy loss reduction and PV capacity.

关键词： photovoltaic power systems power generation control power generation planning nonlinear programming power generation economics distribution networks smart power grids adaptive control power factor decision making multiobjective photovoltaics capacity planning smart electrical energy networks improved normal boundary intersection method incentive-based regulations performance networks energy loss minimisation radial distribution systems renewable generation environmental targets renewable generation maximisation future smart grids reactive power management adaptive power factor control coordinated voltage control optimisation problem voltage limits technical constraints thermal limits reactive capability limits photovoltaic penetration power factor regulations underload tap changer adjustment nonlinear programming problem second-order cone programming problems distributed Pareto set decision-making process modified normal boundary intersection method IEEE 33-bus RDS energy loss reduction PV capacity innovative control strategies

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A novel approach to multi-objective optimisation of the size and location of an improved hybrid flow controller

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IET GENERATION TRANSMISSION & DISTRIBUTION 2022年第18期16卷 3760-3772页

作者： Moradi, Behzad Kargar, Abbas Derakhshandeh, Sayed Yaser Niaki, Sayed Ali Nabavi Shahrekord Univ Fac Engn Shahrekord *** Iran Univ Toronto Dept Elect & Comp Engn Toronto ON Canada

Transient stability is one of the major features of power systems operation which can be also considered an objective function in the flexible AC transmission systems (FACTS) allocation problem. This paper introduces a general multi-level multi-objective optimisation framework and its application on optimising the size and location of the improved hybrid flow controller (IHFC). IHFC is a new member of the FACTS family whose ability to control power flow and improve power system stability has been investigated. The optimisation problem considers economic and stability-based objective functions simultaneously, and the allocation problem is formulated as a non-linear programming (NLP) problem. The New England 39-bus system has been used as a case study to demonstrate that the proposed framework can provide efficient and economically viable solutions to the allocation problem.

关键词： nonlinear programming problem power system stability optimisation flexible AC transmission systems IHFC power transmission control flow control objective function linear programming transient stability economic stability-based objective functions flexible AC transmission systems allocation problem FACTS family whose ability power systems operation New England 39-bus system improved hybrid flow controller optimisation problem power flow multilevel multiobjective optimisation framework load flow control

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Optimization method for solving bang-bang and singular control problems

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控制理论与应用（英文版） 2012年第4期10卷 559-564页

作者： Shurong LI Ruiyan ZHAO Qiang ZHANG College of Information and Control Engineering China University of Petroleum

In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming （NLP） problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy.

关键词： Bang-bang control Singular control Multi-stage problem nonlinear programming problem

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OPTIMAL SCALING FOR ARBITRARILY ORDERED CATEGORIES

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1979年第1期31卷 115-124页

作者： TANAKA, Y TAKEDA CHEM IND LTD OSAKA 532JAPAN

The methods of optimal scaling are usually formulated as the maximization problem of a ratio of quadratic forms, and the optimal scores are obtained by solving an eigenequation. However, there sometimes exist order relations among categories. For such cases, Bradley, Katti and Coons [2] proposed an algorithm to maximize the criterion under complete order restrictions. Nishisato and Arri [7] discussed the case of partial order and proposed an algorithm using separable programming. Their method is, however, limited to a special type of partial order. Avoiding this limitation, the present paper gives a generalized formulation applicable to arbitrary order restrictions and proposes an efficient algorithm using Wolfe's reduced gradient method. Numerical examples are provided to show the validity, the rapidness of convergence and the stability of the procedure.

关键词： Partial Order Transformation Matrix Order Restriction nonlinear programming problem Equality Restriction

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Risk-constrained offering strategies for a large-scale price-maker electric vehicle demand aggregator

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IET SMART GRID 2020年第6期3卷 860-869页

作者： Hossein Abbasi, Mohammad Taki, Mehrdad Rajabi, Amin Li, Li Zhang, Jiangfeng Univ Qom Dept Elect Engn Qom Iran Univ Technol Dept Elect & Data Engn Sydney NSW Australia Clemson Univ Dept Automot Engn Clemson SC 29631 USA

In this study, the problem of an electric vehicle (EV) aggregator participating in a three-settlement pool-based market is presented. In addition to energy procurement, it is assumed that EVs can sell electricity back to the markets. In order to obtain optimised solutions, the aggregator is considered as a price-maker agent who tries to minimise the cost of purchasing energy from the markets by offering price-energy bids in the day-ahead market and only energy bids in both adjustment and balancing markets. Since the problem is heavily constrained by equality constraints, the number of binary variables for a 24-hour market horizon is too large which leads to intractability when solved by traditional mathematical algorithms like the interior point. Therefore, an evolutionary metaheuristic algorithm based on genetic algorithms (GAs) is proposed to deal with the intractability. In this regard, first, the stochastic problem is formulated as a mixed-integer linear programming problem, and as a non-linear programming problem to be solved by CPLEX and GA, respectively. The former is used to ensure that the GA is tuned properly, and helps to avoid converging to local extremums. Furthermore, the solutions of the two formulations are compared in simulations to demonstrate GA could be faster in obtaining better results.

关键词： power generation economics genetic algorithms pricing linear programming optimisation power markets integer programming 24-hour market horizon intractability traditional mathematical algorithms evolutionary metaheuristic algorithm genetic algorithms stochastic problem mixed-integer linear programming problem nonlinear programming problem risk-constrained offering strategies large-scale price-maker electric vehicle demand aggregator electric vehicle aggregator EV three-settlement pool-based market energy procurement electricity optimised solutions price-maker agent purchasing energy price-energy bids day-ahead market balancing markets

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