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Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem

JOURNAL OF GLOBAL OPTIMIZATION 2019年第1期75卷 143-161页

作者： Cavallo, Bice Univ Naples Federico II Dept Architecture Naples Italy

Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. The paper deals with a crucial step in multi-criteria decision analysis, that is to obtain coherent weights for alternatives/criteria that are compared by means of a PCM. Firstly, we provide a condition ensuring coherent weights. Then, we provide and solve a mixed-integer linear programming problem in order to obtain the closest PCM, to a given PCM, having coherent weights. Isomorphisms and the mixed-integer linear programming problem allow us to solve an infinity of optimization problems, among them optimization problems concerning additive, multiplicative and fuzzy PCMs.

关键词： Pairwise comparison matrix mixed-integer linear programming problem Isomorphism Coherent weights

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Optimized graph-cut approach for the screen-line traffic counting location problem: An exact and efficient solution method

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 275卷

作者： Sase, Ruri Sugiura, Satoshi Chen, Anthony Hokkaido Univ Grad Sch Engn Kita 13Nishi 8Kita ku Sapporo Hokkaido 0608628 Japan Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Peoples R China

Observed traffic data are widely recognized as an essential source of information for monitoring, evaluating, and planning transportation systems. The traffic sensor location problem is aimed at determining the optimal locations for collecting the most informative partial observations. This study focuses on the screen-line traffic counting location problem (SLTCLP). Screen lines are commonly used to validate traffic assignment results because of the ease of interpreting their positions. Therefore, addressing this problem is valuable for effective transportation management. Conventional solutions to this problem are based on path enumeration, which is computationally expensive and difficult to implement for large-scale transportation networks. Thus, we establish an exact and efficient solution method for the SLTCLP, using the concept of cut in graph theory and formulating the problem as the "cut optimization problem." The proposed method is applied to different types of network instances, including a large network, and its performance and effectiveness are evaluated.

关键词： Screen-line traffic counting location problem Graph cut mixed-integer linear programming problem

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Optimally coordinated dispatch of combined-heat-and-electrical network with demand response

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第11期13卷 2216-2225页

作者： Chen, Yumin Xu, Yan Li, Zhengmao Feng, Xue Nanyang Technol Univ Sch Elect & Elect Engn 50 Nanyang Ave Singapore 639798 Singapore Singapore Inst Technol 10 Dover Dr Singapore 13868 Singapore

A multi-energy microgrid (MEMG) aims to simultaneously supply electricity and thermal energy to customers for higher energy utilisation efficiency. In this study, a system-wide coordinated operation method for MEMGs is proposed to dispatch different components including generation resources and flexible loads. In the coordination method, the coupling constraints of electrical and heat network, dynamic characteristics of heat network as well as the power flow constraints are comprehensively modelled. Besides, the price-based demand response and indoor temperature control strategy are used as demand response for more flexible operation of the combine electrical and thermal networks. The coordination model is formulated as a mixed-integer linear programming problem and tested on 33-bus and 69-bus MEMGs. Simulation results verify the advantages of the proposed method over existing methods.

关键词： linear programming power generation dispatch load flow distributed power generation integer programming cogeneration demand side management coordinated dispatch multienergy microgrid thermal energy system-wide coordinated operation method heat network power flow constraints price-based demand response indoor temperature control strategy MEMG energy utilisation combined-heat-and-electrical network mixed-integer linear programming problem

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Available transfer capability evaluation in a deregulated electricity market considering correlated wind power

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第1期12卷 53-61页

作者： Chen, Houhe Fang, Xin Zhang, Rufeng Jiang, Tao Li, Guoqing Li, Fangxing Northeast Elect Power Univ Dept Elect Engn Jilin 132012 JL Peoples R China GE Grid Solut Market Applicat Redmond WA 98052 USA Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN 37996 USA

Evaluation of available transfer capability (ATC) is a complicated process involving the determination of the total transfer capability (TTC) and the existing transfer commitments (ETC). Considering the uncertain renewable generation such as wind power will bring more challenge to this process. Previously the uncertainty of wind power is considered either in the ED model or the following TTC calculation, but not included in two process simultaneously. Therefore, the ATC output may not be accurate since the uncertainty impact two problem simultaneously. To consider the uncertainty and correlation of wind power in both ISO's ED and ATC evaluation, this paper proposes a bi-level optimization framework in which the ATC evaluation is formulated as the upper level problem and the ED is the lower level. The bi-level model is first converted to a mathematic program with equilibrium constraints (MPEC) by recasting the lower level problem as its Karush-Kuhn-Tucker (KKT) optimality conditions, and then transformed to a mixed-integer linear programming (MILP) problem which can be solved by existing optimization tools. Case studies on the PJM 5-bus and IEEE 118-bus systems are presented to verify the proposed methodology and the impacts of correlation of wind power on ATC are analysed.

关键词： wind power plants power markets transmission networks power generation economics linear programming integer programming power generation planning transfer capability evaluation deregulated electricity market correlated wind power available transfer capability total transfer capability transmission commitments independent system operator economic dispatch continuous power flow wind power bi-level optimisation framework mathematic program with equilibrium constraints Karush-Kuhn-Tucker optimality conditions mixed-integer linear programming problem IEEE 118-bus systems wind farms planning

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Efficient linear network model for TEP based on piecewise McCormick relaxation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第23期13卷 5404-5412页

作者： Goodarzi, Shahin Gitizadeh, Mohsen Abbasi, Ali Reza Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran Fasa Univ Fac Engn Dept Elect Fasa Iran

This study presents a novel scheme for transmission expansion planning (TEP) based on piecewise McCormick relaxation. The model presented considers investment and operation cost and identifies the transmission lines to be built. Since the AC power flow equations are inherently non-convex and non-linear, the resulting TEP model will be a highly complex optimisation problem, in which the optimal global solution is not guaranteed to be found by the existing techniques. This study aims to transform the non-linear model of the power network into a novel linear one. The model proposed is much more precise compared with the DC approach, while the global solution is guaranteed to be found by the off-the-shelf solvers. This accurate transformation from a non-convex and non-linear AC-TEP formulation into a linear-TEP model enables the planner to get more insight into the power flow of the power system. The TEP problem is formulated as a mixed-integer linear programming problem and is solved using the efficient commercial solvers. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.

关键词： power transmission planning linear programming nonlinear programming integer programming investment concave programming load flow power transmission economics power transmission lines nonconvex AC-TEP formulation nonlinear AC-TEP formulation off-the-shelf solvers power network nonlinear model optimal global solution complex optimisation problem AC power flow equations transmission lines operation cost investment transmission expansion planning piecewise McCormick relaxation efficient linear network model efficient commercial solvers mixed-integer linear programming problem TEP problem power system linear-TEP model

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A bi-level transactive control model for integrating decision-making and DLMP-pricing in distribution networks

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IET GENERATION TRANSMISSION & DISTRIBUTION 2022年第19期16卷 3814-3824页

作者： Li, Biao Wan, Can Luo, Fengji Yu, Peng Sun, Mingyang Zhejiang Univ Coll Elect Engn Hangzhou Peoples R China Univ Sydney Sch Civil Engn Sydney NSW Australia Zhejiang Univ Coll Control Sci & Engn Hangzhou Peoples R China

The market-driven demand side management of distribution networks suffers from the challenge of operational security issues. This paper proposes a distribution locational marginal price (DLMP) based bi-level transactive control model for distribution networks to manage demand side resources of nodal agents, ensuring both the network security and the agents' optimal decision. The proposed model consists of a DLMP-pricing model at the upper level and DLMP-based demand response (D-DR) models at the lower level, integrating the DLMP-pricing of the distribution network and the decision-making of agents. The DLMP-pricing model is constructed as the dual form of a linearized optimal power flow problem to determine DLMP related to the decision of all agents. The D-DR model enables each nodal agent to minimize its own expenditure under the DLMP, which is established as a linear programming problem. The bi-level model is converted into single-level programming through replacing the D-DR models by Karush-Kuhn-Tucker conditions, in which the bi-linear items of the complementary slackness are further linearized by introducing integer variables. Consequently, the intractable bi-level transactive control model is equivalently reconstructed as a single-level mixed-integer linear programming problem that can be conveniently solved. Comprehensive numerical studies validate the effectiveness of the proposed model.

关键词： D-DR model network security nodal agent agents single-level programming decision-making power distribution economics linear programming integer programming operational security issues power markets mixed-integer linear programming problem DLMP-pricing model linearized optimal power flow problem pricing market-driven demand side management intractable bi-level transactive control model decision making load flow distribution locational marginal price demand side management DLMP-based demand response bi-linear items distribution network bi-level model

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Controlled islanding algorithm for AC/DC hybrid power systems utilising DC modulation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第26期14卷 6440-6449页

作者： Fan, Xinkai Crisostomi, Emanuele Thomopulos, Dimitri Zhang, Baohui Yang, Songhao Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian Peoples R China Univ Pisa Dept Energy Syst Terr & Construct Engn DESTEC Pisa Italy

The controlled islanding problem is typically considered only for pure ac power systems, with the ultimate objective of either minimising power imbalance or power-flow among islands. However, as ac/dc hybrid power systems are becoming popular worldwide, current controlled islanding schemes should be redesigned to take into account the presence of high-voltage dc (HVDC) links, possibly connecting different islands. Accordingly, in this study, the authors solve the classic islanding problem combining HVDC power modulation with the conventional ac cutset search. The flexibility of the HVDC allows the authors' strategy to jointly capture the previously mentioned objectives, and provides even lower power imbalances than the minimum imbalance strategy, at a relatively small cost of increasing power-flow impact. Then, the optimisation problem is formulated as a mixed-integer linear programming problem, which can be conveniently solved with existing commercial solvers. Finally, they validate their proposed strategy in two case studies, corresponding to a modified IEEE-118 system and to the China Southern Power Grid system. In both cases, dynamic simulations show that their proposed approach outperforms classic algorithms where the presence of HVDC power modulation is not explicitly taken into account.

关键词： power grids power transmission control hybrid power systems integer programming HVDC power convertors power distribution faults linear programming HVDC power transmission distributed power generation power generation control power distribution control electric current control load flow control AC-DC power convertors controlled islanding algorithm DC modulation controlled islanding problem pure ac power systems current controlled islanding schemes high-voltage dc links islanding problem HVDC power modulation power-flow modified IEEE-118 system China Southern Power Grid system ac cutset search mixed-integer linear programming problem

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Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第11期14卷 2160-2168页

作者： Alvarez, Erik F. Paredes, Miguel Rider, Marcos J. Univ Estadual Campinas Dept Syst & Energy Av Albert Einstein 400 BR-13083852 Campinas SP Brazil IBM Res BR-04007900 Sao Paulo SP Brazil

This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed-integer non-linear programming model for the proposed planning problem is presented and rewritten with semidefinite structures. Then, the generalised Benders decomposition is used to separate the overall problem into an upper-level (master) problem and several lower-level (slaves) problems. The master problem is a mixed-integer linear programming problem that optimises the investment cost and constraints of the multistage expansion. Each slave problem minimises the operating costs associated with each stage and operating condition (normal operation or contingency), considering the AC power flow via semidefinite relaxation. With the proposed methodology, the global optimality of generalised Benders decomposition can be preserved due to the use of semidefinite relaxation in each slave problem. Garver's 6-bus system and an IEEE 118-bus system are used to show the precision and convergence to near-global optimal solutions with small relaxation gaps through the proposed approach.

关键词： load flow reactive power power transmission planning minimisation AC power flow semidefinite relaxation transmission expansion network reactive power planning problems semidefinite structures upper-level problem lower-level problems mixed-integer linear programming problem multistage expansion alternating current transmission network expansion generalised Benders decomposition investment cost Garver 6-bus system IEEE 118-bus system

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Piecewise-linear approximations for a non-linear transmission expansion planning problem

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IET GENERATION TRANSMISSION & DISTRIBUTION 2015年第12期9卷 1235-1244页

作者： Camponogara, Eduardo de Almeida, Katia Campos Hardt Junior, Rubens Univ Fed Santa Catarina Dept Automat & Syst Engn BR-88040900 Florianopolis SC Brazil Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

This study proposes a new approach to solve the transmission expansion planning (TEP) problem considering that the network is represented by a non-linear model. Non-linear constraints are approximated with piecewise-linear (PWL) functions, which renders TEP a mixed-integer linear programming (MILP) problem. This study presents MILP formulations obtained from the PWL approximation using the incremental, special ordered sets of type 2 (SOS2) and the logarithmic convex combination (Log) model. Three test systems are used to assess the effectiveness of the formulations. The computational analysis encompasses a baseline formulation, which accounts for the costs on line installation and transmission losses, and a variation of this formulation which minimises the operating costs rather than transmission losses. The results obtained by the MILP models are compared with those of a transmission planning model based on the DC representation of the network. The analysis of the results showed that expansion plans obtained from the MILP formulations are feasible, whereas the plans derived from the DC model are infeasible with respect to system constraints.

关键词： power transmission planning approximation theory piecewise linear techniques linear programming integer programming piecewise-linear approximation nonlinear transmission expansion planning problem nonlinear model nonlinear constraints mixed-integer linear programming problem MILP problem logarithmic convex combination model special ordered sets of type 2 line installation losses transmission losses

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Optimal operation of a virtual power plant in frequency constrained electricity market

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第11期13卷 2123-2133页

作者： Mousavi, Mohammad Rayati, Mohammad Ranjbar, Ali Mohammad Sharif Univ Technol Ctr Excellence Power Syst Management & Control Tehran Iran

In this study, optimal offering strategy problem of a virtual power plant (VPP) as a price-maker player in day-ahead frequency constrained electricity market is presented. The optimal offering strategy problem is modelled as a bi-level optimisation problem. In the upper-level problem, the total profit of VPP is maximised. In the lower-level problem, the clearing conditions of frequency constrained electricity market are modelled. The proposed bi-level optimisation problem is reformulated as a mathematical programming with equilibrium constraints (MPEC) problem by using Karush-Kuhn-Tucker conditions. Then, the proposed MPEC problem, which is non-linear and hard to solve by commercial solvers, is transformed into a mixed-integer linear programming problem by using strong duality theorem and big-number mathematical technique. Here, stochastic optimisation is included in the modelling to enable the VPP for optimisation in the presence of uncertainties, e.g. renewable energy source generations, demands, and offering strategies of rivals. Finally, the effectiveness of proposed model is investigated by implementing it on various case studies.

关键词： duality (mathematics) optimisation power markets integer programming linear programming pricing mathematical programming renewable energy sources price-maker player virtual power plant optimal operation big-number mathematical technique strong duality theorem mixed-integer linear programming problem MPEC problem Karush-Kuhn-Tucker conditions equilibrium constraints problem frequency constrained electricity market lower-level problem VPP upper-level problem bi-level optimisation problem optimal offering strategy problem day-ahead frequency

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