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Performance analysis of linear and nonlinear techniques for automatic scaling of discretized control problems

OPERATIONS RESEARCH LETTERS 2014年第3期42卷 213-216页

作者： Sagliano, Marco Deutsch Zentrum Luft & Raumfahrt Guidance Nav & Control Dept D-28359 Bremen Germany

This paper introduces three (one linear and two nonlinear) automatic scaling techniques for NLPs with states and constraints spread over several orders of magnitude, without requiring complex off-the-shelf external tools. All of these methods have been compared to standard techniques and applied to three problems using SNOPT and IPOPT. The results confirm that the proposed techniques significantly improve the NLP conditioning, yielding more reliable and in some cases, faster NLP solutions. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Automatic scaling Optimal control problem nonlinear programming problem

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An optimal modeling of multidimensional wave digital filtering network for free vibration analysis of symmetrically laminated composite FSDT plates

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2015年第1期52-53卷 465-494页

作者： Tseng, Chien-Hsun Kun Shan Univ Dept Informat Engn Tainan 71013 Taiwan

The technique of multidimensional wave digital filtering (MDWDF) that builds on traveling wave formulation of lumped electrical elements, is successfully implemented on the study of dynamic responses of symmetrically laminated composite plate based on the first order shear deformation theory. The philosophy applied for the first time in this laminate mechanics relies on integration of certain principles involving modeling and simulation, circuit theory, and MD digital signal processing to provide a great variety of outstanding features. Especially benefited by the conservation of passivity gives rise to a nonlinear programming problem (NLP) for the issue of numerical stability of a MD discrete system. Adopting the augmented Lagrangian genetic algorithm, an effective optimization technique for rapidly achieving solution spaces of NLP models, numerical stability of the MDWDF network is well received at all time by the satisfaction of the Courant-Friedrichs-Levy stability criterion with the least restriction. In particular, optimum of the NLP has led to the optimality of the network in terms of effectively and accurately predicting the desired fundamental frequency, and thus to give an insight into the robustness of the network by looking at the distribution of system energies. To further explore the application of the optimum network, more numerical examples are engaged in efforts to achieve a qualitative understanding of the behavior of the laminar system. These are carried out by investigating various effects based on different stacking sequences, stiffness and span-to-thickness ratios, mode shapes and boundary conditions. Results are scrupulously validated by cross referencing with early published works, which show that the present method is in excellent agreement with other numerical and analytical methods. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Laminated composite plate MDWDF network Courant-Friedrichs-Levy stability Free vibration analysis Augmented Lagrangian genetic algorithm nonlinear programming problem

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A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices

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ENGINEERING WITH COMPUTERS 2019年第2期35卷 423-449页

作者： Takahashi, Toru Yamamoto, Tatsuro Shimba, Yuta Isakari, Hiroshi Matsumoto, Toshiro Nagoya Univ Grad Sch Engn Dept Mech Syst Engn Furo Cho Nagoya Aichi 4648603 Japan Nagoya Univ Grad Sch Engn Dept Micronano Syst Engn Furo Cho Nagoya Aichi 4648603 Japan

We propose a gradient-based optimisation framework to design the shape of the interfaces in periodic layered structures, which can model photovoltaic devices, optical gratings, etc., according to a desired electromagnetic property. To this end, we first develop an isogeometric boundary element method (IGBEM) to analyse singly periodic boundary value problems for 2D Helmholtz equation in layered media. By nature, the IGBEM is not only numerically accurate but also suitable for the shape optimisation in comparison with the conventional boundary- and domain-type solvers. Next, we derive the shape derivative (or shape sensitivity) of the objective function in terms of the magnetic field strength or energy absorption rate on the basis of the adjoint variable method. The shape derivative can be computed by solving the primal and adjoint problems with the IGBEM. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a general-purpose software for the latter problems. After verifying our optimisation framework rigorously by comparing with the exact solutions, we demonstrate a shape optimisation of the silicon-metal interface in a model of thin-silicon photovoltaic devices: it is crucial to determine the interface so that the energy of the incident light can be confined in the silicon layer as much as possible when the thickness of the layer is unconventionally small;one micrometre in our model. The optimal shape achieved 8.6 times higher absorption rate than the reference (flat) shape. This simulation shows that the proposed framework is capable of making a fundamental contribution to analysing and designing photovoltaic devices as well as photonic and plasmonic devices that consist of singly periodic layers.

关键词： Boundary element method Isogeometric analysis Periodic structure Shape optimisation Adjoint variable method nonlinear programming problem Quasi-Newton method Photovoltaic device Surface plasmon Plasmonics

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Network expansion planning with microgrid aggregators under uncertainty

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第9期12卷 2105-2114页

作者： Sardou, Iman Goroohi Azad-Farsani, Ehsan Univ Jiroft Dept Elect Engn Jiroft Iran Golpayegan Univ Technol Dept Elect Engn Golpayegan Iran

In this paper, a bi-objective robust model is proposed for network expansion planning (NEP) considering the integration of the microgrid aggregators. The objectives include minimization of both the expansion cost and transmission lines loading index. Forced outages of system components are taken into account as the system uncertainties. A hybrid method as the combination of gravitational search algorithm (GSA) and primal-dual interior point (PDIP) method is employed to solve the nonlinear programming (NLP) problem of the NEP. In the proposed hybrid method, the operation sub-problems are solved by the PDIP method under the worst-case single component contingencies, while the expansion plan is defined as scenario independent variables obtained by the GSA algorithm. To detect the worst-case single component contingencies with the severest effects on the system security, a subsidiary optimization problem is solved for each load level of the system. A realistic network of Qom as a part of Tehran Regional Electric Company, Iran, as well as IEEE 118-bus test system are analysed to evaluate the efficiency of the proposed method. A key conclusion is that the stochastic model may not provide sufficient security level, and a robust model is required to ensure the system security against the severe contingencies.

关键词： distributed power generation power distribution planning substations search problems nonlinear programming power system security network expansion planning microgrid aggregators NEP problem power system planner substations effective biobjective robust model expansion cost transmission lines loading index system components system uncertainties hybrid method gravitational search algorithm GSA primal-dual interior point method nonlinear programming problem NLP operation subproblems PDIP method worst-case single component contingencies scenario independent variables first stage decision variables subsidiary optimisation problem Qom Tehran Regional Electric Company IEEE 118-bus test system Iran stochastic model security level economical solution

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

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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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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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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： reactive power flow modelling mixed-integer linear programming integer programming Power transmission, distribution and supply load flow linear approximated formulation AC optimal power flow voltage profile AC-OPF linear approximated methodology full alternating current-optimal power flow binary discretisation Optimisation techniques direct current-optimal power flow linear programming nonlinear programming problem nonlinear programming

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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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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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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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