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Service Restoration Model With mixed-integer second-order cone programming for Distribution Network With Distributed Generations

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IEEE TRANSACTIONS ON SMART GRID 2019年第4期10卷 4138-4150页

作者： Li, Yong Xiao, Juanxia Chen, Chun Tan, Yi Cao, Yijia Hunan Univ Coll Elect & Informat Engn Changsha 410082 Hunan Peoples R China

Fast and reliable service restoration strategy is necessary to restore as many out-of-service loads as possible in a short time. In this paper, a mixed-integer second-order cone programming formulation is proposed for service restoration of a distribution network with distributed generations (DGs). This formulation relaxes the original non-convex power flow equations into a conic quadratic format. The employment of conic relaxation is of great importance because it ensures the quality of the obtained solution. The service restoration is formulated as a multi-objective optimization problem considering the minimization of de-energized loads and total number of switching operations. Moreover, PQ and PV model of DGs are considered in this formulation. The proposed method is tested on the 33-bus system and the Taiwan Power Company 84-bus system to show its effectiveness.

关键词： Convex optimization problem distribution network distributed generations mixed-integer second-order cone programming service restoration

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A mixed-integer second-order cone programming Algorithm for the Optimal Power Distribution of AC-DC Parallel Transmission Channels

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ENERGIES 2019年第19期12卷 3605页

作者： Lin, Shunjiang Yang, Zhibin Fan, Guansheng Liu, Mingbo He, Sen Tang, Zhiqiang Song, Yunong South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Guangdong Peoples R China

For the controllability of the transmission power of DC transmission channels, the optimal power distribution (OPD) of AC-DC parallel transmission channels is an effective measure for improving the economic operation of an AC-DC interconnected power grid. A dynamic optimal power flow model for day-ahead OPD of AC-DC parallel transmission channels is established in this paper. The power flow equation constraints of an AC-DC interconnected power grid and the constraints of the discrete regulation requirement of the transmission power of DC channels are considered, which make the OPD model of the AC-DC parallel transmission channels a mixed-integer nonlinear non-convex programming (MINNP) model. Through a cone relaxation transformation and a big M method equivalent transformation, the non-convex terms in the objective function and constraints are executed with the convex relaxation, and the MINNP model is transformed into a mixed-integer second-order cone programming model that can be solved reliably and efficiently using the mature optimization solver GUROBI. Taking an actual large-scale AC-DC interconnected power grid as an example, the results show that the OPD scheme of the AC-DC parallel transmission channels obtained by the proposed algorithm can effectively improve the economical operation of an AC-DC interconnected power grid.

关键词： AC-DC interconnected power grid optimal power distribution of transmission channels dynamic optimal power flow cone relaxation big M method mixed-integer second-order cone programming

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mixed-integer second-order cone programming taking appropriate approximation for the unit commitment in hybrid AC–DC grid

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The Journal of Engineering 2017年第13期2017卷 1462-1467页

作者： Bo Zhou Xiaomeng Ai Jiakun Fang Jingyu Wen Jianhua Yang State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology Wuhan People's Republic of China Department of Energy Technology Aalborg University Aalborg Denmark Central China Branch of State Grid Corporation of China Wuhan People's Republic of China

With the rapid development and deployment of voltage source converter based high-voltage direct current, the traditional power system is evolving to the hybrid AC–DC grid. New optimisation methods are urgently needed for these hybrid AC–DC power systems. In this study, mixed-integer second-order cone programming (MISOCP) for the hybrid AC–DC power systems is proposed. The second-order cone relaxation is adopted to transform the AC and DC power flow constraints to MISOCP. Several IEEE test systems are used to validate the proposed MISCOP formulation of the optimal power flow and unit commitment in the hybrid AC–DC power systems.

关键词： integer programming hybrid power systems power generation dispatch power generation scheduling voltage-source convertors HVDC power convertors load flow optimal power flow IEEE test systems AC power flow constraints DC power flow constraints second-order cone relaxation MISOCP hybrid AC–DC power systems optimisation methods high-voltage direct current converter voltage source converter hybrid AC-DC grid unit commitment mixed-integer second-order cone programming

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MISOCP Model for Reactive Power Optimization With Nonuniform Voltage Regulators in Unbalanced Three-Phase Active Distribution Networks

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 10118-10129页

作者： Mu, Chenggang Ding, Tao Wang, Shunqi Jia, Wenhao Shahidehpour, Mohammad Luo, Zhao Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Shaanxi Peoples R China IIT Dept Elect & Comp Engn Chicago IL 60616 USA Kunming Univ Sci & Technol Sch Elect Engn Kunming 650500 Yunnan Peoples R China

Reactive power optimization (RPO) is a key task in the operation and control of active distribution networks (ADNs). The nonlinear power flow constraints and the integers introduced by voltage regulator (VR) constraints make the nonconvex RPO model difficult to solve. In this paper, a RPO model is proposed considering the nonuniform tap ratios of VRs. The three phases in VRs are independently controlled and the phase coupling effects are strictly considered. Moreover, to deal with the bilinear relationship among continuous complex voltage phasors and discrete tap ratios, the voltage phasor matrix is decoupled into real and imaginary parts, and a status variable method is proposed to exactly linearize the bilinear terms. Further, the nonlinear power flow constraints are relaxed to a set of second-order cone constraints without neglecting the coupling effect among the three phases and are proved to be equivalent to the semi-definite constraints, which does not require the rank-1 verification and is more efficient and scalable. Thus, the original nonconvex RPO for three-phase unbalanced ADNs is simplified to a mixed-integer second-order cone programming (MISOCP) model. Case studies validate the model's effectiveness, and the computational efficiency meets practical requirements. Note to Practitioners-This paper simplifies the complex problem of reactive power optimization for active distribution networks with unbalanced three-phase power flows. We offer a novel RPO model improving the typically nonconvex and nonlinear optimal power flow problem, and addressing the particular challenges imposed by voltage regulators optimization with nonuniform tap ratios. Independent control of the VR phases and accurate incorporation of phase coupling effects have been realized, greatly simplifying the optimization process. The transformation of nonlinear power flow constraints into a computationally efficient set of second-order cone constraints eliminates the need for cumbersome ran

关键词： Reactive power programming Vectors Voltage control Optimization Load flow Computational modeling Static VAr compensators Regulators MISO Reactive power optimization active distribution network three-phase unbalance nonuniform voltage regulator mixed-integer second-order cone programming

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A congested facility location problem with strategic customers

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期318卷 442-456页

作者： Marand, Ata Jalili Hoseinpour, Pooya Aarhus Univ Sch Business & Social Sci Dept Econ & Business Econ Aarhus Denmark Amirkabir Univ Technol Tehran Polytech Dept Ind Engn & Management Syst Tehran Iran

This study addresses a user -equilibrium congested facility location problem with delay-, accessibility-, and price -sensitive customers. A profit -maximizing service provider first makes location, service rate, and pricing decisions, and then strategic customers decide which facilities to patronize (if any). By incorporating the customers' choice behavior as a set of equilibrium constraints into the service provider's decision problem, the problem is modeled as a mixed integer non-linear program which is then reformulated as a mixed integer second -order cone program. The proposed model, tested on several standard instances, is shown to be efficiently solvable using commercial software packages.

关键词： OR in service industries Pricing Queueing Mathematical programming with equilibrium constraints mixed-integer second-order cone programming

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Look-Ahead Rolling Economic Dispatch Approach for Wind-Thermal-Bundled Power System Considering Dynamic Ramping and Flexible Load Transfer Strategy

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第1期39卷 186-202页

作者： Lei, Chao Bu, Siqi Wang, Qianggang Chen, Qifan Yang, Longjie Chi, Yuan Hong Kong Polytech Univ Dept Elect Engn Hong Kong Peoples R China Ctr Adv Reliabil & Safety Hong Kong Peoples R China Hong Kong Polytech Univ Shenzhen Res Inst Res Inst Smart Energy Ctr Adv Reliabil & Safety Hong Kong Peoples R China Hong Kong Polytech Univ Policy Res Ctr Innovat & Technol Hong Kong Peoples R China Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Se Chongqing 400044 Peoples R China

With a wind-thermal-bundled power system (WTBPS) under high wind penetration levels, the sharp power fluctuations of tie-lines for interconnected grids trigger a significant challenge of security-constrained power system operation. Smoothing power fluctuations with economic dispatch is widely concerned against this challenge. In this paper, an appropriate look-ahead economic dispatch framework for WTBPS considering the variable ramp rate of retrofitted coal-fired units and the flexible load transfer strategy (LTS) in high voltage distribution networks (HVDNs) is proposed. To cope with this issue, i) we derive a new family of tightened ramping constraints of retrofitted coal-fired units in the linear and second-order conic (SOC) forms, respectively. ii) Using graph characterization of typical HVDNs, the simplified voltage-constrained LTS via topological structures can be developed. This proposed look-ahead economic dispatch model is cast as a mixed-integer second-order cone programming (MISOCP) problem, which can be reformulated by Multi-cut Generalized Benders Decomposition (MGBD). This MGBD enables multiple sub-problems can be solved in parallel and accelerates the solving process. Finally, simulation results of a large-scale practical system validate the computational accuracy and efficiency of the proposed approach.

关键词： Wind power generation Biological system modeling Wind Power systems Power generation Load modeling Costs Economic dispatch wind-thermal-bundled power systems dynamic ramping load transfer strategy Benders Decomposition mixed-integer second-order cone programming

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Multi-period Two-stage Robust Optimization of Radial Distribution System with Cables Considering Time-of-use Price

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Journal of Modern Power Systems and Clean Energy 2023年第1期11卷 312-323页

作者： Jian Zhang Mingjian Cui Yigang He Fangxing Li School of Electrical Engineering and Automation Hefei University of TechnologyHefei 230009China University of Tennessee KnoxvilleTN 37996USA School of Electrical Engineering and Automation Wuhan UniversityWuhan 430072China

In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems,the capability of distributed generators(DGs)to regulate the reactive power,the operation costs of the regulation equipment,and the current of the shunt capacitor of the cables are not *** this paper,a multi-period two-stage robust scheduling strategy that aims to minimize the total cost of the power supply is *** strategy considers the time-ofuse price,the capability of the DGs to regulate the active and reactive power,the action costs of the regulation equipment,and the current of the shunt capacitors of the cables in a radial distribution ***,the numbers of variables and constraints in the first-stage model remain constant during the iteration to enhance the computation *** solve the second-stage model,only the model of each period needs to be ***,their objective values are accumulated,revealing that the computation rate using the proposed method is much higher than that of existing *** effectiveness of the proposed method is validated by actual 4-bus,IEEE 33-bus,and PG 69-bus distribution systems.

关键词： Distribution system robust optimization mixed-integer second-order cone programming cost of regulation equipment coordinated optimization of active and reactive power

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Collaborative Optimization for Active Distribution Network with Soft Open Point and Energy Storage

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RECENT ADVANCES IN ELECTRICAL & ELECTRONIC ENGINEERING 2024年

作者： Li, Kewen Yuan, Lyuzerui Ou, Shifeng Duan, Shuyin Chen, Qianyi Liu, Tong Guangxi Power Grid Co Ltd Elect Power Sci Res Inst Nanning 530023 Peoples R China Elect Power Res Inst China Southern Power Grid Guangzhou 510080 Guangdong Peoples R China

Background The increasing use of high-penetration distributed clean energy has led to voltage fluctuations in the distribution network that surpass safety limits and pose challenges to economic and low-carbon operation. Traditional voltage regulation devices are unable to meet the real-time high-precision voltage control needs when encountering frequent fluctuations due to physical limitations. The Soft Open Point (SOP) can provide continuous reactive power to achieve rapid voltage *** We propose a collaborative optimization approach that fully considers the regulatory capabilities of SOP and energy storage to eliminate voltage violations and reduce network *** This study introduces an active distribution network reactive power voltage optimization approach that incorporates intelligent SOP and energy storage, combining conventional devices (such as on-load tap changers and capacitor banks) with contemporary devices (such as SOP, distributed generators, and energy storage) to establish synergy. A coordinated optimization model was developed, considering various operational constraints to minimize network losses and regulate the voltage of distribution network nodes. By using linearization and quadratic relaxation, the original non-convex mixed-integer non-linear optimization model was transformed into a mixed-integer second-order cone programming (MISOCP) model to meet the requirements of rapid voltage *** A case study was conducted on the IEEE 33-node test system, showing that the proposed approach effectively reduces network losses and eliminates voltage *** The feasibility and effectiveness of the proposed methodology have been validated, confirming its ability to ensure the safe and economic operation of active distribution networks.

关键词： Active distribution network distributed generator mixed-integer second-order cone programming soft open point energy storage system reactive power voltage optimization

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Chance-constrained co-expansion planning for power systems under decision-dependent wind power uncertainty

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IET RENEWABLE POWER GENERATION 2023年第6期17卷 1342-1357页

作者： Yin, Wenqian Feng, Shuanglei Liu, Rong-Peng Hou, Yunhe Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China HKU Shenzhen Inst Res & Innovat Shenzhen Peoples R China China Elect Power Res Inst Renewable Energy Res Ctr Beijing Peoples R China

Variability and uncertainty in wind resources pose significant challenges to the expansion planning of wind farms and associated flexible resources. In addition, the spatial smoothing effect, indicating the impact of wind farm scale on aggregated wind power prediction errors, further aggravates the challenge. This paper proposes a chance-constrained co-expansion planning method considering the spatial smoothing effect, where the expansion of wind farm capacity, batter energy storage capacity, and power transmission lines are co-optimized. Specifically, a decision-dependent uncertainty (DDU) model is established capturing the dependency of wind power uncertainties on wind farm expansion decisions under the spatial smoothing effect. Unlike traditional optimization diagram where decisions are made under only decision-independent uncertainty (DIU) with fixe properties, properties of decision-dependent uncertain parameters would be inversely altered by decisions. To effectively tackle the coupling relation between decisions and DDU, DDU-based chance constraints are formulated in an analytical manner, where the decisions and decision-dependent uncertain parameters are expressed in a closed form. Eventually, with piecewise linearization of the DDU model and the polynomial approximation of cumulative distribution function of uncertain parameters, the proposed chance-constrained optimization model with DDU is converted into a mixed-integer second-order cone program (MISOCP). Case studies verify the effectiveness of the proposed method.

关键词： chance-constrained stochastic programming decision-dependent uncertainty expansion planning mixed-integer second-order cone programming power-generation planning power transmission planning programming stochastic wind power wind power generation

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Probabilistic wind power expansion planning of bundled wind-thermal generation system with retrofitted coal-fired plants using load transfer optimization

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期151卷

作者： Lei, Chao Wang, Qianggang Zhou, Guiping Bu, Siqi Zhou, Niancheng Lin, Tianhao Wei, Fang Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Saf Chongqing 400044 Peoples R China State Grid Liaoning Elect Power Co Shenyang Liaoning Peoples R China Hong Kong Polytech Univ Dept Elect Engn Hong Kong Peoples R China China Med Univ Sch Fundamental Sci Shenyang Liaoning Peoples R China

The bundled wind-thermal generation system (BWTGS) is an attractive option to integrate wind energy to actively participate in power systems. With the greatly enhanced penetration of wind energy in BWTGS, wind curtailment against sharp wind power fluctuations is inevitable. Thus, our study is stimulated by whether and to what extent we can maximize wind power penetration with proper provision of dispatchable loads against wind curtailment, and this is exactly the problem we aim to solve in this paper. Here, we initially focus on the flexible characteristics of retrofitted coal-fired units in BWTGS and the load transfer optimization (LTO) for high voltage distribution networks (HVDNs). Then, an appropriate probabilistic wind power capacity expansion planning method for BWTGS with retrofitted coal-fired units using LTO can be reformulated as a mixed-integer second-order cone programming problem. Moreover, since load and wind power data have inherited uncertainty, we extend this proposed model to be a probabilistic expanding model. This contributes to better decision-making for the short-term wind capacity expansion under quantified uncertainty. Numerical results of the practical HVDNs demonstrate the effectiveness of the proposed method.

关键词： Bundled wind-thermal generation system Retrofitted coal-fired units mixed-integer second-order cone programming High voltage distribution networks Load transfer optimization

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