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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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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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Strong Stationarity Conditions for the Optimal Control of a Cahn-Hilliard-Navier-Stokes System

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APPLIED MATHEMATICS AND OPTIMIZATION 2024年第1期89卷 12-12页

作者： Hintermueller, Michael Keil, Tobias Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany Humboldt Univ Inst Math Unter Linden 6 D-10099 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 variational inequality of fourth order and the Navier-Stokes equation. The existence of solutions to the primal system and of optimal controls is established. The Lipschitz continuity of the constraint mapping is derived and used to characterize the directional derivative of the constraint mapping via a system of variational inequalities and partial differential equations. Finally, strong stationarity conditions are presented following an approach from Mignot and Puel.

关键词： Cahn-Hilliard Strong stationarity mathematical programming with equilibrium constraints Navier-Stokes Non-matched densities Non-smooth potentials Optimal control Semidiscretization in time Directional differentiability

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Data Driven Solution to Market equilibrium via Deep Reinforcement Learning 2

Data Driven Solution to Market Equilibrium via Deep Reinforc...

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IEEE 2nd International Conference on Power Science and Technology (ICPST)

作者： Wen, Lin Wang, Jianxiao Lin, Li Zou, Yang Gao, Feng Hong, Qiteng North China Elect Power Univ Sch Elect & Elect Engn Beijing Peoples R China Peking Univ Natl Engn Lab Big Data Anal & Applicat Beijing Peoples R China Peking Univ Coll Engn Dept Ind Engn & Management Beijing Peoples R China Univ Strathclyde Dept Elect & Elect Engn Glasgow Lanark Scotland

ISBN: (纸本)9798350349047;9798350349030

equilibrium analysis is an effective tool to analyze the operation efficiency of the electricity market, but how to efficiently solve the power market equilibrium model with multiagent participation remains to be further studied. The traditional model transformation method has low computational efficiency and poor ability to deal with strong uncertainty. The optimality and convergence of the solution are not fully guaranteed. Therefore, this paper intends to use a multi-agent deep reinforcement learning algorithm to reach a fast solution to the market equilibrium model. Here we take the interaction between multiple virtual power plants (VPPs) and the upstream power grid as an example. A bi-level mathematical programming with equilibrium constraints (MPEC) is constructed. The upper level aims to minimize the cost of running the VPPs, the lower level aims to minimize the cost of running the power grid. A multi-agent reinforcement learning algorithm is employed to solve the MPEC based on deep deterministic policy gradient (DDPG), which is a data-driven, selflearning and model-free approach without the modeling and computational complexity caused by existing methods. Finally, an example of iteration between an IEEE-30 node power grid system and a VPP is given to verify the rationality and effectiveness of the proposed algorithm.

关键词： Market equilibrium mathematical programming with equilibrium constraints reinforcement learning virtual power plant

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Strategic Generation Investment in Energy Markets: A Multiparametric programming Approach

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第4期37卷 2590-2600页

作者： Taheri, Sina Kekatos, Vassilis Veeramachaneni, Sriharsha Virginia Tech Bradley Dept ECE Blacksburg VA 24061 USA NextEra Analyt St Paul MN 55107 USA

An investor has to carefully select the location and size of new generation units it intends to build, since adding capacity in a market affects the profit from units this investor may already own. To capture this closed-loop characteristic, strategic investment (SI) of generation can be posed as a bilevel optimization. By analytically studying a small market, we first show that its objective function can be non-convex and discontinuous. Realizing that existing mixed-integer problem formulations become impractical for larger markets and number of instances, this work put forth two SI solvers: a grid search to handle setups where the candidate investment locations are few, and a stochastic gradient descent approach for otherwise. Both solvers leverage powerful results of multiparametric programming (MPP), each in a unique way. The grid search entails finding the primal/dual solutions for a large number of optimal power flow (OPF) problems, which nonetheless can be efficiently computed several at once thanks to the properties of MPP. The same properties facilitate the rapid calculation of gradients in a mini-batch fashion, thus accelerating the implementation of a stochastic (sub)-gradient descent search. Tests on the IEEE 30- and 118-bus systems using real-world data corroborate the advantages of the novel solvers.

关键词： Investment Task analysis Costs Schedules Generators programming Optimization mathematical programming with equilibrium constraints bilevel programming locational marginal prices stochastic gradient descent strategic investment multiparametric programming

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Implementing Maximum Likelihood Estimation of Empirical Matching Models MPEC versus NFXP

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COMPUTATIONAL ECONOMICS 2022年第1期59卷 71-102页

作者： Dong, Baiyu Hsieh, Yu-Wei Zhang, Xing Univ Southern Calif Dept Econ Los Angeles CA 90007 USA Microsoft Corp Redmond WA 98052 USA

We propose two mathematical programming with equilibrium constraints (MPEC) formulations: the MPEC-Sparse and the MPEC-Dense to estimate a class of separable matching models. We compare MPEC with the Nested Fixed-Point (NFXP) algorithm-a well-received method in the literature of structural estimation. Using both simulated and actual data, we find that MPEC is more robust than NFXP in terms of convergence and solution quality. In terms of computing time, MPEC-Dense is 9 to 20 times faster than NFXP in simulations. For practitioners, MPEC is considerably simpler to program.

关键词： Aggregate matching Two-sided matching Separable matching models mathematical programming with equilibrium constraints Nested fixed-point algorithm Constrained optimization

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Tri-Level Adaptive Robust Optimization for the Optimal Charging Coordination of EVs Considering Grid Impact

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IEEE ACCESS 2024年 12卷 169755-169767页

作者： Silva, Jessica Alice A. Lopez, Juan Camilo Arias, Nataly Banol Terada, Lucas Zenichi Rider, Marcos J. Univ Estadual Campinas UNICAMP Sch Elect & Comp Engn FEEC Dept Syst & Energy DSE BR-13083852 Campinas SP Brazil Univ Twente Dept Elect Engn Math & Comp Sci EEMCS NL-7522 NB Enschede Netherlands

The rapid integration of electric vehicles (EVs) into power grids introduces substantial operational challenges, particularly in managing the grid and ensuring efficient energy distribution. Addressing these issues, this paper presents a novel tri-level adaptive robust optimization model for EV charging coordination, explicitly considering active and reactive power control (RPC) and its impact on the distribution network. The first level optimizes the operation of unbalanced three-phase AC distribution systems through economic dispatch of distributed generation (DG) units, modeled using mathematical programming with equilibrium constraints (MPEC). The second level minimizes the energy non-supplied (ENS) to EVs during charging, considering both grid constraints and DG dispatches. The third level introduces an adaptive robust approach to handle uncertainties related to demand, renewable energy generation, and EV initial states of charge. This tri-level model, formulated as a min-max-min optimization, is solved using the column-and-constraint generation (C&CG) method. Validation on 25-node and 123-node systems equipped with dispatchable DG units, photovoltaic systems, and an EV fleet managed by a charging point operator (CPO) demonstrates the model's ability to mitigate uncertainties and balance conflicting interests between the CPO/aggregator and the distribution system operator (DSO). The results show that incorporating RPC reduces grid impact and ENS by up to 17.26% in the 25-node system and 30.68% in the 123-node system, highlighting the effectiveness of the proposed approach in enhancing grid resilience amidst increasing EV penetration. This work offers a comprehensive and scalable solution for private charging infrastructures, providing critical insights into improving grid resilience, optimizing EV charging operations, and effectively balancing the interests of both the CPO/aggregator and the DSO.

关键词： Adaptation models Renewable energy sources Reactive power control Uncertainty Adaptive systems Linear programming Electric vehicle charging Voltage control Resilience mathematical programming Electric vehicle fleets mathematical programming with equilibrium constraints optimal charging coordination tri-level adaptive robust optimization

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Adaptive grids for the estimation of dynamic models

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QME-QUANTITATIVE MARKETING AND ECONOMICS 2022年第2期20卷 179-238页

作者： Lanz, Andreas Reich, Gregor Wilms, Ole HEC Paris Jouy En Josas France Tsumcor Res AG Schwerzenbach Switzerland Univ Hamburg Hamburg Germany Tilburg Univ Tilburg Netherlands

This paper develops a method to flexibly adapt interpolation grids of value function approximations in the estimation of dynamic models using either NFXP (Rust, Econometrica: Journal of the Econometric Society, 55, 999-1033, 1987) or MPEC (Su & Judd, Econometrica: Journal of the Econometric Society, 80, 2213-2230, 2012). Since MPEC requires the grid structure for the value function approximation to be hard-coded into the constraints, one cannot apply iterative node insertion for grid refinement;for NFXP, grid adaption by (iteratively) inserting new grid nodes will generally lead to discontinuous likelihood functions. Therefore, we show how to continuously adapt the grid by moving the nodes, a technique referred to as r-adaption. We demonstrate how to obtain optimal grids based on the balanced error principle, and implement this approach by including additional constraints to the likelihood maximization problem. The method is applied to two models: (i) the bus engine replacement model (Rust, 1987), modified to feature a continuous mileage state, and (ii) to a dynamic model of content consumption using original data from one of the world's leading user-generated content networks in the domain of music.

关键词： Numerical dynamic programming mathematical programming with equilibrium constraints r-adaptive grid refinement Equi-oscillation

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Distribution LMP-Based Demand Management in Industrial Park via a Bi-Level programming Approach

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2021年第3期12卷 1695-1706页

作者： Wei, Jingdong Zhang, Yao Wang, Jianxue Wu, Lei Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Peoples R China Stevens Inst Technol Elect & Comp Engn Dept Hoboken NJ 07030 USA

To enhance industrial park's economic gains and effectively allocate its electricity bill among industrial users with combined heat and power (CHP) units and photovoltaic (PV) panels, this paper proposes a distribution locational marginal price (DLMP)-based bi-level demand management approach. The upper level optimizes dispatching decisions of industrial users with the objective of minimizing their energy bills, and the lower level is a DLMP-based market clearing problem to minimize the two-part tariff cost of the industrial park operator. In order to solve the proposed bi-level model efficiently, it is first equivalently converted into a single-level mathematical programming with equilibrium constraints (MPEC), and then reformulated as a mixed-integer second-order conic programming (MISOCP) model by linearizing bilinear terms. Numerical results demonstrate the effectiveness of our proposed bi-level method in lowering industrial park's electricity bill and achieving effective allocation among users.

关键词： Cogeneration Reactive power Tariffs programming Energy consumption Resistance heating Natural gas Bi-level optimization combined heat and power distribution locational marginal price mathematical programming with equilibrium constraints mixed-integer second-order conic programming solar photovoltaics

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Global Product Design Platforming: A Comparison of Two equilibrium Solution Methods

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JOURNAL OF MECHANICAL DESIGN 2023年第6期145卷 061702-061702页

作者： Case, Sarah Michalek, Jeremy J. Whitefoot, Kate S. Carnegie Mellon Univ Mech Engn Pittsburgh PA 15213 USA Carnegie Mellon Univ Mech Engn Engn & Publ Policy Civil & Environm Engn by Courtesy Pittsburgh PA 15213 USA Carnegie Mellon Univ Mech Engn Engn & Publ Policy Pittsburgh PA 15213 USA

Global product platforms can reduce production costs through economies of scale and learning but may decrease revenues by restricting the ability to customize for each market. We model the global platforming problem as a Nash equilibrium among oligopolistic competing firms, each maximizing its profit across markets with respect to its pricing, design, and platforming decisions. We develop and compare two methods to identify Nash equilibria: (1) a sequential iterative optimization (SIO) algorithm, in which each firm solves a mixed-integer nonlinear programming problem globally, with firms iterating until convergence;and (2) a mathematical program with equilibrium constraints (MPEC) that solves the Karush Kuhn Tucker conditions for all firms simultaneously. The algorithms' performance and results are compared in a case study of plug-in hybrid electric vehicles where firms choose optimal battery capacity and whether to platform or differentiate battery capacity across the US and Chinese markets. We examine a variety of scenarios for (1) learning rate and (2) consumer willingness to pay (WTP) for range in each market. For the case of two firms, both approaches find the Nash equilibrium in all scenarios. On average, the SIO approach solves 200 times faster than the MPEC approach, and the MPEC approach is more sensitive to the starting point. Results show that the optimum for each firm is to platform when learning rates are high or the difference between consumer willingness to pay for range in each market is relatively small. Otherwise, the PHEVs are differentiated with low-range for China and high-range for the US.

关键词： product platform learning by doing design for market systems designoptimization mixed-integer nonlinear programing global optimization mathematical programming with equilibrium constraints mathematical programming with complementarity constraints Nash equilibrium oligopoly product design product familydesign product platform design

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