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Modelling Cyber Attacks on Electricity Market Using mathematical programming with equilibrium constraints

IEEE ACCESS 2019年 7卷 27376-27388页

作者： Ahmadian, Saeed Tang, Xiao Malki, Heidar A. Han, Zhu Univ Houston Dept Elect & Comp Engn Houston TX 77004 USA Northwestern Polytech Univ Dept Commun Engn Xian 710065 Shaanxi Peoples R China Univ Houston Dept Engn Technol Houston TX 77004 USA

With the development of communication infrastructure in smart grids, cyber security reinforcement has become one of the most challenging issues for power system operators. In this paper, an attacker is considered a participant in the virtual bidding procedure in the day-ahead (DA) and real-time (RT) electricity markets to maximize its profit. The cyber attacker attempts to identify the optimal power system measurements to attack along with the false data injected into measurement devices. Towards the maximum profit, the attacker needs to specify the relation between manipulated meters, virtual power traded in the markets, and electricity prices. Meanwhile, to avoid being detected by the system operator, the attacker considers the physical power system constraints existing in the DA and RT markets. Then, a bi-level optimization model is presented which combines the real electricity market state variables with the attacker decision-variables. Using the mathematical problem with equilibrium constraints, the presented bi-level model is converted into a single level optimization problem and the optimal decision variables for the attacker are obtained. Finally, simulation results are provided to demonstrate the performance of the attacker, which also provides insights for security improvement.

关键词： Cyber-security electricity market false data injection mathematical programming with equilibrium constraints

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On the solution of mathematical programming problems with equilibrium constraints

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mathematical METHODS OF OPERATIONS RESEARCH 2001年第3期54卷 345-358页

作者： Andreani, R Martínez, JM UNESP Dept Comp Sci & Stat BR-15054000 Sao Jose do Rio Preto SP Brazil Univ Estadual Campinas UNICAMP IMECC Dept Appl Math BR-13081970 Campinas SP Brazil

mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

关键词： mathematical programming with equilibrium constraints optimality conditions minimization algorithms reformulation

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Optimality Conditions and Duality for Semi-Infinite mathematical programming Problem with equilibrium constraints

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2015年第4期36卷 460-480页

作者： Mishra, S. K. Jaiswal, M. Banaras Hindu Univ Dept Math Fac Sci Varanasi 221005 Uttar Pradesh India Indian Inst Sci Dept Elect Engn Bangalore 560012 Karnataka India

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

关键词： 90C34 90C46 90C33 Optimality conditions Duality mathematical programming with equilibrium constraints Semi-infinite programming

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Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints

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OPTIMIZATION 2003年第3期52卷 333-359页

作者： Dempe, S TU Bergakad Freiberg Fak Math & Informat Inst Angew Math 2 D-09596 Freiberg Germany

In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized. Focus is also on the diffi... 详细信息

关键词： bilevel programming mathematical programming with equilibrium constraints set-valued optimization applications optimality conditions

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Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2012年第1期21卷 134-147页

作者： Meng, Qiang Liu, Zhiyuan Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Cordon-based congestion pricing Mode-split Probit-based stochastic user equilibrium Continuously distributed value-of-time mathematical programming with equilibrium constraints

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OPTIMAL CONTROL OF A SEMIDISCRETE CAHN-HILLIARD-NAVIER-STOKES SYSTEM WITH NONMATCHED FLUID DENSITIES

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2017年第3期55卷 1954-1989页

作者： Hintermueller, Michael Keil, Tobias Wegner, Donat Humboldt Univ Inst Math Unter Linden 6 D-10099 Berlin Germany Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany

This paper is concerned with the distributed optimal control of a time-discrete Cahn-Hilliard-Navier-Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier-Stokes equation. By proposing a suitable time-discretization, energy estimates are proved, and the existence of solutions to the primal system and of optimal controls is established for the original problem as well as for a family of regularized problems. The latter correspond to Moreau-Yosida-type approximations of the double-obstacle potential. The consistency of these approximations is shown, and first-order optimality conditions for the regularized problems are derived. Through a limit process with respect to the regularization parameter, a stationarity system for the original problem is established. The resulting system corresponds to a function space version of C-stationarity which is a special notion of stationarity for mathematical programs with equilibrium constraints.

关键词： Cahn-Hilliard limiting C-stationarity mathematical programming with equilibrium constraints Navier-Stokes nonmatched densities nonsmooth potentials optimal control semidiscretization in time Yosida regularization

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Environmentally friendly facility location with market competition

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2012年第7期63卷 899-908页

作者： Ghaddar, B. Naoum-Sawaya, J. Univ Waterloo Dept Management Sci Waterloo ON N2L 3G1 Canada

Many traditional facility location models assume spatial monopoly where market competition is ignored. Since facility locations affect the firm's market exposure and subsequently its profit, accounting for the impact of the location decisions on customers while anticipating the reaction of competitor firms is essential. In this paper, we introduce a competitive facility location problem where market prices and production costs are determined through the economic equilibrium while explicitly considering competition from other firms. In order to accommodate for the growing efforts on limiting carbon emissions, the presented model includes constraints on the amount of carbon emissions that are due to transportation, while allowing carbon trading. The problem is formulated as a mixed integer non-linear model. Through numerical examples, we illustrate the effect of market competition on the location decisions and discuss the impact of emission limits and carbon trading on customers. Journal of the Operational Research Society (2012) 63, 899-908. doi: 10.1057/jors.2011.95 Published online 21 September 2011

关键词： facility location Stackelberg competition carbon emissions mathematical programming with equilibrium constraints

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OPTIMAL CONTROL OF A SEMIDISCRETE CAHN-HILLIARD-NAVIER-STOKES SYSTEM

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2014年第1期52卷 747-772页

作者： Hintermueller, M. Wegner, D. Humboldt Univ Dept Math D-10099 Berlin Germany Karl Franzens Univ Graz Dept Math & Sci Comp A-8010 Graz Austria

In this paper, the optimal boundary control of a time-discrete Cahn-Hilliard-Navier-Stokes system is studied. A general class of free energy potentials is considered which, in particular, includes the double-obstacle potential. The latter homogeneous free energy density yields an optimal control problem for a family of coupled systems, which result from a time discretization of a variational inequality of fourth order and the Navier-Stokes equation. The existence of an optimal solution to the time-discrete control problem as well as an approximate version is established. The latter approximation is obtained by mollifying the Moreau-Yosida approximation of the double-obstacle potential. First order optimality conditions for the mollified problems are given, and in addition to the convergence of optimal controls of the mollified problems to an optimal control of the original problem, first order optimality conditions for the original problem are derived through a limit process. The newly derived stationarity system is related to a function space version of C-stationarity.

关键词： Cahn-Hilliard-Navier-Stokes system double-obstacle potential mathematical programming with equilibrium constraints optimal boundary control Yosida regularization C-stationarity

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A bi-level probabilistic transmission planning with intermittent generations based on life cycle cost

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2017年第Sep.期90卷 306-314页

作者： Gan, Lei Li, Gengyin Lin, Jeremy Zhou, Ming North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China PJM Interconnect Audubon PA 19403 USA

With the growing development of intermittent renewable energy sources, such as wind and solar, transmission planners are faced with uncertainly varying generations and resultant probabilistic power flow. A bi-level programming model is proposed to coordinate the process of decision making and reliability assessment. Based on the concept of life cycle cost (LCC), its minimization can be defined as the objective function of a transmission planner. This upper level problem needs to be solved jointly with the lower probabilistic optimal power flow problem of minimizing the load shedding in the system. Hence the bi-level problem is transformed into a mathematical programming with equilibrium constraints (MPEC) with Karush-Kuhn-Tucker conditions. Due to the nonlinearity nature of MPEC, disjunctive inequalities and Generalized Benders Decomposition methods are used to solve this problem. Results of both Garver's 6-bus test system and a realistic 63-bus system are used to illustrate the rationality and validity of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Generalized Benders decomposition Life cycle cost mathematical programming with equilibrium constraints Point estimate Probabilistic optimal power flow Renewable energy Transmission planning

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Strategic offering of a flexible producer in day-ahead and intraday power markets

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期284卷 1136-1153页

作者： Rintamaki, Tuomas Siddiqui, Afzal S. Salo, Ahti Aalto Univ Sch Sci Dept Math & Syst Anal Syst Anal Lab Espoo Finland UCL Dept Stat Sci London England Stockholm Univ Dept Comp & Syst Sci Stockholm Sweden HEC Montreal Dept Decis Sci Montreal PQ Canada

The increase in intraday electricity market volumes due to intermittent renewable generation may give a strategic producer an opportunity to exert market power. We study offering strategies of a flexible producer in day-ahead and intraday markets using a bi-level model in which the upper level represents the profit-maximization problem of the producer and the lower-level problems clear the day-ahead and intraday markets sequentially. Using a three-node network, we first demonstrate that a flexible producer with perfect forecasts can increase its profit in both markets by coordinating its offer so as to cause transmission grid congestion or lack of competitive generation capacity. Moreover, we show that strategic behavior is possible even when the day-ahead and intraday markets are cleared simultaneously to lower balancing costs. We next assess these market designs in a Nordic test network and offer an explanation for high Nordic intraday prices. Finally, via an annual simulation using the Nordic market data, we verify that strategic offering in day-ahead and intraday markets under imperfect forecasts leads to increased profits vis-a-vis perfect competition but are mitigated through simultaneous market clearing. (C) 2020 Elsevier B.V. All rights reserved.

关键词： OR in energy Day-ahead market Intraday market Strategic offering mathematical programming with equilibrium constraints

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