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Constrained Markov decision processes with uncertain costs

OPERATIONS RESEARCH LETTERS 2022年第2期50卷 218-223页

作者： Varagapriya, V. Singh, Vikas Vikram Lisser, Abdel Indian Inst Technol Delhi Dept Math New Delhi 110016 India Univ Paris Saclay CNRS Cent Supelec Lab Signaux & Syst F-91190 Gif Sur Yvette France

We consider a finite state-action discounted constrained Markov decision process with uncertain running costs and known transition probabilities. We propose equivalent linear programming, second-order cone programming and semidefinite programming problems for the robust constrained Markov decision processes when the uncertain running cost vectors belong to polytopic, ellipsoidal, and semidefinite cone uncertainty sets, respectively. As an application, we study a variant of a machine replacement problem and perform numerical experiments on randomly generated instances of various sizes. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Constrained Markov decision processes Uncertainty sets Linear programming problem second-order cone programming problem Semidefinite programming problem Machine replacement problem

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Optimal Power Flow Based on Branch Flow Model for Bipolar DC Distribution Networks

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CSEE Journal of Power and Energy Systems 2025年第2期11卷 944-948页

作者： Yiyao Zhou Qianggang Wang Xiaolong Xu Tao Huang Jianquan Liao Yuan Chi Xuefei Zhang Niancheng Zhou School of Electrical Engineering Chongqing UniversityChongqing 400044China Department of Energy Politecnico di TorinoTorino 10129Italy

Optimal Power Flow (OPF) plays a crucial role in optimization and operation of the bipolar DC distribution network (Bi-DCDN). However, existing OPF models encounter difficulties in the power optimization of Bi-DCDNs due to the optimal power expressed as a product form, i.e., the product of voltage and current. Hence, this brief formulates the OPF problem of Bi-DCDNs using the branch flow model (BFM). The BFM employs power, instead of current, to account for the unique structure of Bi-DCDNs. Convex relaxation and linear approximation are sequentially applied to reformulate the BFM-based OPF, presenting it as a second-order cone programming (SOCP) problem. Further, the effectiveness of the proposed OPF model is verified in case studies. The numerical results demonstrate that the BFM-based OPF is a feasible and promising approach for Bi-DCDNs.

关键词： Bipolar DC distribution network branchflow model optimal powerflow second-order cone programming problem

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Data-driven distributionally robust joint planning of distributed energy resources in active distribution network

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第9期14卷 1653-1662页

作者： Gao, Hongjun Wang, Renjun Liu, Youbo Wang, Lingfeng Xiang, Yingmeng Liu, Junyong Sichuan Univ Coll Elect Engn Chengdu 610065 Peoples R China Univ Wisconsin Dept Elect Engn & Comp Sci Milwaukee WI 53211 USA Global Energy Interconnect Res Inst North Amer San Jose CA 95134 USA

With the increasing penetration of distributed energy resources (DERs) in the active distribution network (ADN), how to enable joint planning of DERs under the uncertainty of distributed generations (DGs) has become a challenging problem. This study establishes a two-stage joint planning model considering doubly-fed induction generator, photovoltaics (PVs) with the ancillary services of PV inverter, distributed energy storage systems and different types of controllable loads in the ADN. To address the uncertainties of DGs, a two-stage data-driven distributionally robust planning model is constructed. The proposed model is solved in a 'master and sub-problem' framework by column-and-constraint generation algorithm, where the master problem is to minimise the total cost and find the optimal planning decision under the worst probability distributions, and the sub-problem is to find the worst probability distribution of given uncertain scenarios. Besides, the original mixed-integer non-linear planning problem is converted into a mixed-integer second-order cone programming problem through second-order cone relaxation, Big-M and piecewise linearisation method. The numerical results based on 33-bus system verify the effectiveness of the proposed model.

关键词： energy storage power distribution planning distributed power generation asynchronous generators nonlinear programming probability distribution networks integer programming data-driven distributionally robust joint planning distributed energy resources active distribution network DERs ADN distributed generations two-stage joint planning model induction generator distributed energy storage systems two-stage data-driven distributionally robust planning model sub-problem framework -constraint generation algorithm master problem optimal planning decision worst probability distribution mixed-integer nonlinear planning problem second-order cone programming problem

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Optimal allocation of soft open points in active distribution network with high penetration of renewable energy generations

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第26期14卷 6732-6740页

作者： Cong, Pengwei Hu, Zechun Tang, Wei Lou, Chengwei Zhang, Lu Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China China Agr Univ Coll Informat & Elect Engn Beijing 100083 Peoples R China Aston Univ Sch Engn & Appl Sci Birmingham W Midlands England

With the integration of more and more renewable energy generations (REGs), the structure of traditional distribution networks is hard to accommodate the volatile power injections of REGs. As a new power electronic device, soft open point (SOP) can be installed to control both active and reactive power flow among active distribution networks (ADNs). This paper presents a comprehensive optimization method for allocating SOPs within an ADN with high penetration of REGs. In order to find proper SOP candidate locations, a selection strategy based on two technical indices is proposed. To mitigate the risk of voltage violation caused by REG forecast errors and improve the adaptiveness of allocation results, a two-stage robust optimization model for SOP allocation is formulated to minimize the total cost of SOP investment and network operation. The proposed model is converted into a mixed-integer second-order cone programming (MISCOP) problem, which is then decoupled into a master problem of planning and a subproblem of operation and solved by column and constraint generation (CCG) algorithm. Simulation results show that the proposed method can effectively find the optimal SOP allocation schemes. Comparisons with different mathematical formulation and solution methods show the advantages of the proposed method.

关键词： reactive power distributed power generation integer programming load flow power distribution planning power generation planning soft open point active distribution network renewable energy generations volatile power injections power electronic device reactive power flow ADN comprehensive optimisation method SOP candidate locations two-stage robust optimisation model network operation second-order cone programming problem constraint generation algorithm optimal SOP allocation IEEE 123 bus systems IEEE 33 bus systems PG& E 69 bus systems REG forecast errors column and constraint generation algorithm

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Convex probabilistic allocation of wind generation in smart distribution networks

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IET RENEWABLE POWER GENERATION 2017年第9期11卷 1211-1218页

作者： Akbari, Mohammad-Amin Aghaei, Jamshid Barani, Mostafa Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

This study introduces a probabilistic optimisation model for allocation of renewable distributed generations (DGs) in radial distribution networks. The methodology is based on a probabilistic generation - load model that combines all possible operating conditions of the wind-based DG units as well as load levels with their probabilities. A multiobjective performance index is extracted that is formulated as a combination of two indices, namely energy losses reduction and voltage improvement. Besides, a probabilistic AC optimal power flow is used to determine the optimal allocation of wind DG and maximise the multiobjective performance index. Two alternative control approaches of the future smart grids, i.e. area based under load tap changer control and adaptive power factor control, are assessed to maximise potential benefits and expand the penetration level of DGs. At first, this problem is formulated as a mixed-integer non-linear programming (MINLP) which leads to a computationally NP-hard problem. Accordingly, the obtained MINLP problem is relaxed and reformulated in the form of a well-suited second-order cone programming problem which is computationally efficient scheme to be solved. The implementation of the proposed framework on 4-bus and IEEE 33-bus radial distribution systems shows the performance of the proposed optimisation mechanism.

关键词： distribution networks wind power load flow smart power grids power factor nonlinear programming integer programming computational complexity optimisation distributed power generation on load tap changers smart distribution networks wind generation convex probabilistic allocation probabilistic optimisation model renewable distributed generation allocation radial distribution networks probabilistic generation wind-based DG units multiobjective performance index energy losses reduction voltage improvement probabilistic AC optimal power flow optimal allocation smart grids load tap changer control adaptive power factor control mixed-integer nonlinear programming MINLP computationally NP-hard problem second-order cone programming problem IEEE 4-bus radial distribution systems IEEE 33-bus radial distribution systems

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Cooperative security communications design with imperfect channel state information in wireless sensor networks

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IET WIRELESS SENSOR SYSTEMS 2016年第2期6卷 35-41页

作者： Gong, Xiangwu Long, Hang Dong, Feihong Yao, Qing PLA Univ Sci & Technol Coll Commun Engn Nanjing 210000 Jiangsu Peoples R China Beijing Univ Posts & Telecommun Wireless Signal Proc & Networks WSPN Lab Beijing 100876 Peoples R China China Elect Equipment Syst Engn Co Spectrum Div Beijing Peoples R China

Relay strategies can increase coverage range and improve reliability for power-limited sensors. In this study, cooperative jamming schemes are investigated for security communications in two-hop multi-sensors relay networks where a passive eavesdropper can wiretap the relay channels in both hops. The normally inactive nodes can be used as cooperative jamming sources to confuse the eavesdropper. Artificial noise (AN) is maximised to degrade the signal-to-interference-plus-noise ratio (SINR) level at the eavesdropper, while satisfying the individual power constraint of each relay sensor and SINR constraint at the desired receiver. Assuming that CSI is perfect, relay beamforming weights can be obtained by solving a second-order cone programming problem. However, the available CSI is impossible to be perfect in practice. Therefore, a robust beamforming scheme is also presented. The transmit power used for AN is maximised, while satisfying the power constraint of each relay sensor and worst-case SINR constraint at the desired receiver under a bounded spherical region for the norm of the CSI error vector from the relays to the destination. Robust beamforming weight vector can be obtained by using S-procedure and rank relaxation techniques. The benefits of the proposed schemes are shown in simulation results.

关键词： cooperative communication wireless sensor networks relay networks (telecommunication) amplify and forward communication array signal processing jamming cooperative security communications design imperfect channel state information wireless sensor networks cooperative jamming schemes two-hop multisensors relay networks relay channels cooperative beamforming schemes amplify-and-forward protocol artificial noise SINR constraint second-order cone programming problem robust beamforming weight vector S-procedure rank relaxation techniques

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Design of Variable Fractional Delay Filter with Fractional Delay Constraints

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IEEE SIGNAL PROCESSING LETTERS 2014年第11期21卷 1361-1364页

作者： Hai Huyen Dam Curtin Univ Dept Math & Stat Bentley WA 6102 Australia

This letter develops an efficient computational procedure for the design of an odd-order variable fractional delay (VFD) digital filter with minimum peak variable fractional delay error subject to restrictions on the peak variable frequency response error. An iterative algorithm is developed to solve the formulated non-linear optimization problem where a first order linear approximation is employed for the variable fractional delay error. This results in a second-order cone programming (SOCP) problem with linear constraints. Design examples show that the peak fractional delay error can be reduced significantly from the minimax solution while maintaining approximately the same peak frequency response error. In addition, for a fixed level of peak variable frequency response error, approximately 1.61-2.09 dB improvement for the peak variable delay error can be obtained over existing methods.

关键词： Fractional delay constraints second-order cone programming problem variable fractional delay filter

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Support vector machines maximizing geometric margins for multi-class classification

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TOP 2014年第3期22卷 815-840页

作者： Tatsumi, Keiji Tanino, Tetsuzo Osaka Univ Grad Sch Engn Suita Osaka 5650871 Japan

Machine learning is a very interesting and important branch of artificial intelligence. Among many learning models, the support vector machine is a popular model with high classification ability which can be trained by mathematical programming methods. Since the model was originally formulated for binary classification, various kinds of extensions have been investigated for multi-class classification. In this paper, we review some existing models, and introduce new models which we recently proposed. The models are derived from the viewpoint of multi-objective maximization of geometric margins for a discriminant function, and each model can be trained by solving a second-order cone programming problem. We show that discriminant functions with high generalization ability can be obtained by these models through some numerical experiments.

关键词： Multi-class classification Support vector machine Machine learning Multiobjective optimization second-order cone programming problem

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Efficient Beamforming in Cognitive Radio Multicast Transmission

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2012年第11期11卷 4108-4117页

作者： Beko, Marko Univ Lusofona Humanidades & Tecnol P-1749024 Lisbon Portugal Univ Nova Lisboa P-2829516 Monte De Caparica Caparica Portugal

The optimal beamforming problems for cognitive multicast transmission are quadratic nonconvex optimization problems. The standard approach is to convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation and later employ randomization techniques for solution search. However, in many cases, this approach brings solutions that are far from the optimal ones. We consider the problem of minimizing the total power transmitted by the antenna array subject to quality-of-service (QoS) at the secondary receivers and interference constraints at the primary receivers. It is shown that this problem, which is known to be nonconvex NP-hard, can be approximated by a convex second-order cone programming (SOCP) problem. Then, an iterative algorithm in which the SOCP approximation is successively improved is presented. Simulation results demonstrate the superior performance of the proposed approach in terms of total transmitted power and feasibility, together with a reduced computational complexity, as compared to the existing ones, for both the perfect and imperfect channel state information (CSI) cases. It is further shown that the proposed approach can be used to address the max-min fairness (MMF) based beamforming problem.

关键词： Cognitive radio beamforming second-order cone programming problem MIMO convex-concave procedure

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