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Coordination of wind generation and demand response to minimise operation cost in day-ahead electricity markets using bi-level optimisation framework

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第16期12卷 3793-3802页

作者： Mohammad, Nur Mishra, Yateendra Queensland Univ Technol Sch Elect Engn & Comp Sci George St Brisbane Qld 4000 Australia

Demand response (DR) can play an important role when dealing with the increasing variability of renewables in power system. This study proposes a bi-level market model for wind-integrated electricity market, where the DR requirement is paired with the wind profile to deal with wind variability. At the upper level, an electricity market operator aims to minimise the day-ahead operation cost considering plausible wind generation scenarios. At the lower level, the DR exchange operator aims to maximise social welfare by trading aggregated DR among several aggregators. The solution at this level determines the optimal DR amount and price setting for each aggregator. The DR from the flexible loads is modelled from the end-users' perspective considering their willingness parameter. The market model is formulated as a bi-level optimisation problem using Lagrangian relaxation with Karush-Kuhn-Tucker optimality conditions. The effectiveness of the proposed scheme is demonstrated on sample 4-bus and IEEE 24-bus systems. Different scenarios such as high, medium and low levels of wind and DR are investigated. The high-wind low-DR scenario leads to minimum operation cost and is least inconvenient for end users as it sets the DR at a minimum level while keeping the higher levels of wind generation.

关键词： power generation economics power generation scheduling wind power plants power markets demand side management mathematical programming minimisation associated Karush-Kuhn-Tucker optimality conditions Lagrangian relaxation complementarity constraints mathematical programming problem monetary benefit maximisation DR-capable loads social welfare maximisation DR exchange operator electricity market operator plausible wind generation scenarios wind variability wind profile DR requirement wind-integrated electricity market bilevel market model power system bilevel optimisation framework day-ahead electricity markets day-ahead operation cost minimisation demand response wind generation

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Optimal wind energy bidding strategies in real-time electricity market with multi-energy sources

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IET RENEWABLE POWER GENERATION 2019年第13期13卷 2383-2390页

作者： Zhang, Zijing Chen, Zhi Washington State Univ Sch Engn & Comp Sci Vancouver WA 98686 USA

This study investigates optimal wind power generator bidding strategies in the real-time electricity market. The goal is to maximise its operating profit by determining the optimal amount of wind power to bid in the real-time market. A bi-level stochastic optimisation model is proposed in which the upper-level problem is minimising the negative profit of wind power producers, while the low-level problem clears the real-time market. The uncertainties in the wind power production, thermal power, hydro power, demand, and energy storage are considered in the stochastic model. This study utilises a mathematical programming problem with equilibrium constraints (MPEC) and Karush-Kuhn-Tucker (KKT) conditions to transform the bi-level problem into an equivalent single-level mixed-integer linear problem (MILP). Case studies obtained with the IEEE RTS-24 Bus system demonstrate the effectiveness of the proposed model and the effect of scenarios on the wind power producer's profit.

关键词： stochastic processes profitability power markets integer programming wind power plants power generation economics optimisation stochastic programming mathematical programming linear programming case studies wind power producer optimal wind energy bidding strategies real-time electricity market multienergy sources optimal wind power generator bidding strategies operating profit real-time market bi-level stochastic optimisation model upper-level problem negative profit wind power producers low-level problem wind power production thermal power hydro power energy storage stochastic model mathematical programming problem bi-level problem equivalent single-level mixed-integer linear problem

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Shape-Dependent Velocity Based Droplet Routing on MEDA Biochips

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IEEE ACCESS 2022年 10卷 122423-122430页

作者： Shiro, Chiharu Nishikawa, Hiroki Kong, Xiangbo Tomiyama, Hiroyuki Yamashita, Shigeru Roy, Sudip Ritsumeikan Univ Grad Sch Sci & Engn Kusatsu Shiga 5258577 Japan Osaka Univ Grad Sch Informat Sci & Technol Dept Informat Syst Engn Informat Syst Synth Grp Suita Osaka 5650871 Japan Ritsumeikan Univ Coll Sci & Engn Kusatsu Shiga 5258577 Japan Ritsumeikan Univ Coll Informat Sci & Engn Kusatsu Shiga 5258577 Japan Indian Inst Technol IIT Roorkee Dept Comp Sci & Engn Roorkee 247667 Uttaranchal India

Digital microfluidic biochip (DMFB) has attracted attention in the biochemical and medical industries. In particular, a microelectrode dot array (MEDA) biochip, which is composed of a two-dimensional microelectrode array, enables to realize fine-grained manipulation such as dilution, mixing, sensing, and so on in real-time. Unlike existing DMFB biochips, a MEDA architecture allows microelectrodes to control a certain volume of droplet in a fine-grained manner and can vary droplet volume and shape in such a way that it efficiently conducts synthesis and manipulation of droplets. There have been many works in order to improve the efficiency of synthesis of MEDA biochips;however, the synthesis, especially droplet routing, has never considered the shape-dependent velocity of droplets. In this paper, we propose the droplet routing techniques for MEDA biochips with shape-dependent velocity of droplets. The proposed techniques take the advantage of variant velocities of droplets dependent on the shapes and aim to reduce the overall routing time of a droplet from a source to a destination. Simulation results confirm that the proposed techniques can shorten the routing time by 80% compared to the state-of-the-art techniques.

关键词： Digital microfluidics MEDA droplet routing mathematical programming problem

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Transformed Legendre spectral method for solving infinite horizon optimal control problems

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IMA JOURNAL OF mathematical CONTROL AND INFORMATION 2018年第2期35卷 341-356页

作者： Shahini, M. Mehrpouya, M. A. Gonbad Kavous Univ Fac Basic Sci Dept Math & Stat 163 Basirat BlvdShahid Fallahi St Gonbad Kavous Iran Tafresh Univ Dept Math POB 39518-79611 Tafresh Iran

In this paper, an efficient computational method for numerical solution of infinite horizon optimal control problems is presented. In the proposed method, transformed Legendre spectral scheme is utilized to transcribe the problem to a mathematical programming problem which can be solved by the well-developed optimization algorithms. The main advantages of the present method are obtaining good results and high rate of convergence, while the infinite horizon problem is solved on the original time interval of the problem without transforming it to a finite one. Numerical results of three examples are presented and efficiency of the method is reported.

关键词： optimal control infinite horizon problems spectral methods mathematical programming problem

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Optimal stratification in stratified designs using weibull-distributed auxiliary information

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2019年第12期48卷 3136-3152页

作者： Reddy, Karuna G. Khan, M. G. M. Univ South Pacific Off Deputy Vice Chancellor Res Int & Innovat Suva Fiji Univ South Pacific Sch Comp Informat & Math Sci Suva Fiji Australian Natl Univ ANU Ctr Social Res & Methods Canberra ACT Australia

Sampling has evolved into a universally accepted approach for gathering information and data mining as it is widely accepted that a reasonably modest- sized sample can sufficiently characterize a much larger population. In stratified sampling designs, the whole population is divided into homogeneous strata in order to achieve higher precision in the estimation. This paper proposes an efficient method of constructing optimum stratum boundaries (OSB) and determining optimum sample size (OSS) for the survey variable. The survey variable may not be available in practice since the variable of interest is unavailable prior to conducting the survey. Thus, themethod is based on the auxiliary variable which is usually readily available from past surveys. To illustrate the application as an example using a real data, the auxiliary variable considered for this problem follows Weibull distribution. The stratification problem is formulated as a mathematical programming problem (MPP) that seeks minimization of the variance of the estimated population parameter under Neyman allocation. The solution procedure employs the dynamic programming technique, which results in substantial gains in the precision of the estimates of the population characteristics.

关键词： Optimal stratification mathematical programming problem dynamic programming technique stratified random sampling Weibull distribution

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Generalized invariant monotonicity and invexity of non-differentiable functions

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第4期36卷 537-564页

作者： Jabarootian, T. Zafarani, J. Univ Isfahan Dept Math Esfahan 81745163 Iran

This paper is devoted to the study of relationships between several kinds of generalized invexity of locally Lipschitz functions and generalized monotonicity of corresponding Clarke's subdifferentials. In particular, some necessary and sufficient conditions of being a locally Lipschitz function invex, quasiinvex or pseudoinvex are given in terms of momotonicity, quasimonotonicity and pseudomonotonicity of its Clarke's subdifferential, respectively. As an application of our results, the existence of the solutions of the variational-like inequality problems as well as the mathematical programming problems (MP) is given. Our results extend and unify the well known earlier works of many authors.

关键词： generalized invariant monotone generalized invex functions Clarke's subdifferential variational-like problem mathematical programming problem

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A novel approach for the numerical investigation of optimal control problems containing multiple delays

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OPTIMAL CONTROL APPLICATIONS & METHODS 2018年第1期39卷 302-325页

作者： Marzban, Hamid Reza Pirmoradian, Hoda Isfahan Univ Technol Dept Math Sci Esfahan Iran

This paper deals with the numerical solution of optimal control problems with multiple delays in both state and control variables. A direct approach based on a hybrid of block-pulse functions and Lagrange interpolating polynomials is used to convert the original problem into a mathematical programming one. The resulting optimizaion problem is then solved numerically by the Lagrange multipliers method. The operational matrix of delay for the presented framework is derived. This matrix plays an imperative role to transfer information between 2 consecutive switching points Furthermore, 2 upper bounds on the error with respect to the L-2-norm and infinity norm are established. Several optimal control problems containing multiple delays are carried out to illustrate the various aspects of the proposed approach. The simulation results are compared with either analytical or numerical solutions available in the literature.

关键词： block-pulse functions hybrid functions Lagrange interpolating polynomials mathematical programming problem multidelay systems optimal control

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A novel method for solving constrained matrix games with fuzzy payoffs

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第1期40卷 191-204页

作者： Verma, Tina Indian Inst Technol Ropar Dept Math Rupnagar Punjab India

In last few years, lots of researchers have proposed different methods to solve the constrained matrix games with fuzzy payoffs. In this paper, it has been shown that the mathematical programming problem of constrained matrix games with fuzzy payoffs, considered by researchers, is mathematically invalid and hence the method, proposed by researchers to obtain the complete solution (minimum expected gain of Player I, maximum expected loss of Player II and their corresponding optimal strategies) of constrained matrix games with fuzzy payoffs by solving the mathematical programming problem with fuzzy payoffs, are also invalid. Further, in the present paper, a new method has been proposed to find the complete solution of matrix games with fuzzy payoffs. To illustrate the proposed method, some existing numerical problems of constrained matrix games with fuzzy payoffs have been solved by the proposed method.

关键词： Matrix games fuzzy payoffs mathematical programming problem

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Coordination between a supplier and a retailer in terms of profit concession for a two-stage supply chain

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2014年第7期52卷 2122-2133页

作者： Xu, Xinsheng Meng, Zhiqing Zhejiang Univ Technol Coll Econ & Management Hangzhou Zhejiang Peoples R China Binzhou Univ Dept Math & Informat Sci Binzhou Peoples R China

This paper introduces a coordination model that copes with the conflicts between a supplier and a retailer in a two-stage supply chain. In this model, the supplier aims to maximise his/her profit, while the retailer aims to maximise his/her expected profit under a stochastic demand. To solve this model, an -coordination solution to this model is introduced, which implies the supplier and the retailer both will make a same concession in their profits to cooperate with each other. Further, we show that each feasible solution to this model is an -coordination solution for a sufficiently large value , while the -optimum coordination solution gives the minimum concession for the supplier and the retailer. Besides, it is proved that the -optimum coordination solution can be obtained by solving a mathematical programming problem. At last, a numerical example and sensitivity analysis are given to show the performance of the proposed method.

关键词： supply chain coordination coordination solution mathematical programming problem

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On the Limiting Properties of Dual Trajectories in the Lagrange Multipliers Method

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COMPUTATIONAL MATHEMATICS AND mathematical PHYSICS 2011年第1期51卷 1-20页

作者： Izmailov, A. F. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119991 Russia

For the method of Lagrange multipliers (i.e., augmented Lagrangians), possible and typical scenarios for the asymptotic behavior of dual trajectories are examined in the case where the Lagrange multiplier is nonunique... 详细信息

关键词： mathematical programming problem augmented Lagrangian method of multipliers superlinear convergence critical Lagrange multiplier

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