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Price-based Demand Response Supported Three-stage Hierarchically Coordinated Voltage Control for Microgrids

Journal of Modern Power Systems and Clean Energy 2025年第1期13卷 338-350页

作者： Bo Wang Cuo Zhang Xingying Chen Yan Xu Kun Yu Haochen Hua Zhao Yang Dong School of Electrical and Power Engineering Hohai UniversityNanjing 211100China School of Electrical and Computer Engineering The University of SydneySydneyNSW2006Australia Center for Power Engineering(CPE) School of Electrical and Electronic EngineeringNanyang Technological UniversitySingapore 639798Singapore Department of Electrical Engineering City University of Hong KongHong KongChina

Photovoltaic(PV)inverter,as a promising voltage/var control(VVC)resource,can supply flexible reactive power to reduce microgrid power loss and regulate bus ***,active power plays a significant role in microgrid voltage ***-based demand response(PBDR)can shift load demand via determining time-varying prices,which can be regarded as an effective means for active power ***,due to the different characteristics,PBDR and inverter-based VVC lack systematic ***,this paper proposes a PBDR-supported three-stage hierarchically coordinated voltage control method,including day-ahead PBDR price scheduling,hour-ahead reactive power dispatch of PV inverters,and realtime local droop control of PV *** their mutual influence,a stochastic optimization method is utilized to centrally or hierarchically coordinate adjacent two *** solve the bilinear constraints of droop control function,the problem is reformulated into a second-order cone programming relaxation ***,the concave constraints are convexified,forming a penalty convex-concave model for feasible solution ***,a convex-concave procedure-based solution algorithm is proposed to iteratively solve the penalty *** proposed method is tested on 33-bus and IEEE 123-bus distribution networks and compared with other *** results verify the high efficiency of the proposed method to achieve power loss reduction and voltage regulation.

关键词： Photovoltaic inverter voltage control demand response convex-concave procedure second-order cone programming relaxation

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New phase-changing soft open point and impacts on optimising unbalanced power distribution networks

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第23期14卷 5685-5696页

作者： Lou, Chengwei Yang, Jin Li, Tianrui Vega-Fuentes, Eduardo Univ Glasgow James Watt Sch Engn Glasgow G12 8QQ Lanark Scotland State Grid Taizhou Power Supply Bur Taizhou 318000 Zhejiang Peoples R China

Three-phase unbalanced conditions in distribution networks are conventionally caused by load imbalance, asymmetrical fault conditions of transformers and impedances of three phases. The uneven integration of single-phase distributed generation (DG) worsens the imbalance situation. These unbalanced conditions result in financial losses, inefficient utilisation of assets and security risks to the network infrastructure. In this study, a phase-changing soft open point (PC-SOP) is proposed as a new way of connecting soft open points (SOPs) to balance the power flows among three phases by controlling active power and reactive power. Then an operational strategy based on PC-SOPs is presented for three-phase four-wire unbalanced systems. By optimising the regulation of SOPs, optimal energy storage systems dispatch and DG curtailment, the proposed strategy can reduce power losses and three-phase imbalance. second-order cone programming (SOCP) relaxation is utilised to convert the original non-convex and non-linear model into an SOCP model which can be solved efficiently by commercial solvers. Case studies are conducted on a modified IEEE 34-node three-phase four-wire system and the IEEE 123-node test feeder to verify the effectiveness, efficiency and scalability of the proposed PC-SOP concept and its operational strategy.

关键词： load flow power distribution control energy storage power distribution faults concave programming power system security reactive power control power distribution economics demand side management power losses three-phase imbalance second-order cone programming relaxation four-wire system PC-SOP concept operational strategy new phase-changing soft open point unbalanced power distribution networks three-phase unbalanced conditions load imbalance asymmetrical fault conditions transformers uneven integration single-phase distributed generation imbalance situation financial losses inefficient utilisation security risks network infrastructure soft open points SOPs active power reactive power four-wire unbalanced systems optimal energy storage systems dispatch DG curtailment

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Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第1期221卷 38-48页

作者： Zheng, Xiaojin Sun, Xiaoling Li, Duan Cui, Xueting Fudan Univ Sch Management Dept Management Sci Shanghai 200433 Peoples R China Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Probabilistically constrained quadratic programming (PCQP) problems arise naturally from many real-world applications and have posed a great challenge in front of the optimization society for years due to the nonconvex and discrete nature of its feasible set. We consider in this paper a special case of PCQP where the random vector has a finite discrete distribution. We first derive second-order cone programming (SOCP) relaxation and semidefinite programming (SDP) relaxation for the problem via a new Lagrangian decomposition scheme. We then give a mixed integer quadratic programming (MIQP) reformulation of the PCQP and show that the continuous relaxation of the MIQP is exactly the SOCP relaxation. This new MIQP reformulation is more efficient than the standard MIQP reformulation in the sense that its continuous relaxation is tighter than or at least as tight as that of the standard MIQP. We report preliminary computational results to demonstrate the tightness of the new convex relaxations and the effectiveness of the new MIQP reformulation. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Quadratic programming Probabilistic constraint second-order cone programming relaxation Semidefinite program relaxation Mixed-integer quadratic program reformulation

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Linear inequalities convex transformation for optimal reactive power flow model based on MISOCP relaxations

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第7期12卷 1589-1594页

作者： Lin, Chunmei Wei, Hua Hou, Wenting Tan, Jiancheng Guangxi Univ Guangxi Key Lab Power Syst Optimizat & Energy Tec Nanning 530004 Peoples R China

A convex optimisation model for global optimum solution of optimal reactive power flow (ORPF) problem is proposed in this study, to solve the challenge of discrete variables of transformer taps involved in traditional ORPF models. Based on the second-order cone programming relaxation, a set of inequalities with 0-1 variables are introduced, to convexify the non-convex items that are products of discrete variables (or squares of discrete variables) and linear functions. After convexification, items containing second order of transformer ratio variables are dropped to the first order, and the non-convex non-linear nodal power equalities are equivalently transformed into linear equalities, thus formulating a mix-integer second-order cone programming (MISOCP) model of ORPF problem over feasible convex domain, which guarantees the global optimum theoretically. The results of IEEE-14, 30, 57, 118 bus systems show that, with stable numerical property and good optimum effect, the proposed model can give consideration to not only the quality of solution, but also the efficiency of calculation.

关键词： reactive power load flow convex programming concave programming power supply quality integer programming power transformers linear inequalities convex transformation optimal reactive power flow model MISOCP relaxations convex optimisation model global optimum solution discrete variables transformer taps second-order cone programming relaxation 0-1 variables nonconvex items linear functions convexification second order-of-transformer ratio variables nonconvex nonlinear nodal power equalities mix-integer second-order cone programming model convex domain numerical property

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CONVEX relaxationS OF THE WEIGHTED MAXMIN DISPERSION PROBLEM

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SIAM JOURNAL ON OPTIMIZATION 2013年第4期23卷 2264-2294页

作者： Haines, Sheena Loeppky, Jason Tseng, Paul Wang, Xianfu UBC Okanagan Irving K Barber Sch Kelowna BC V1V 1V7 Canada Univ Washington Dept Math Seattle WA 98195 USA

Consider the weighted maxmin dispersion problem of locating point(s) in a given region chi subset of R-n that is/are furthest from a given set of m points. The region is assumed to be convex under componentwise squaring. We show that this problem is NP-hard even when chi is a box and the weights are equal. We then propose a convex relaxation of this problem for finding an approximate solution and derive an approximation bound of 1-O(root ln(m)gamma*)/2, where gamma* depends on chi. When chi is a box or a product of low-dimensional spheres, gamma* = O(1/n) and the convex relaxation reduces to a semidefinite program and a second-order cone program.

关键词： maxmin dispersion semidefinite programming relaxation second-order cone programming relaxation approximation algorithm

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SIMULTANEOUS DIAGONALIZATION OF MATRICES AND ITS APPLICATIONS IN QUADRATICALLY CONSTRAINED QUADRATIC programming

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SIAM JOURNAL ON OPTIMIZATION 2016年第3期26卷 1649-1668页

作者： Jiang, Rujun Li, Duan Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

An equivalence between attainability of simultaneous diagonalization (SD) and hidden convexity in quadratically constrained quadratic programming (QCQP) stimulates us to investigate necessary and sufficient SD conditions, which is one of the open problems posted by Hiriart-Urruty [SIAM Rev., 49 (2007), pp. 255-273] nine years ago. In this paper we give a necessary and sufficient SD condition for any two real symmetric matrices and offer a necessary and sufficient SD condition for any finite collection of real symmetric matrices under the existence assumption of a semidefinite matrix pencil. Moreover, we apply our SD conditions to QCQP, especially with one or two quadratic constraints, to verify the exactness of its second-order cone programming relaxation and to facilitate the solution process of QCQP.

关键词： simultaneous diagonalization congruence quadratically constrained quadratic programming second-order cone programming relaxation

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A simultaneous diagonalization based SOCP relaxation for convex quadratic programs with linear complementarity constraints

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OPTIMIZATION LETTERS 2019年第7期13卷 1615-1630页

作者： Zhou, Jing Xu, Zhijun Zhejiang Univ Technol Coll Sci Hangzhou 310023 Zhejiang Peoples R China

This paper proposes a new second-order cone programming (SOCP) relaxation for convex quadratic programs with linear complementarity constraints. The new SOCP relaxation is derived by exploiting the technique that two positive semidefinite matrices can be simultaneously diagonalizable, and is proved to be at least as tight as the classical SOCP relaxation and virtually it can be tighter. We also prove that the proposed SOCP relaxation is equivalent to the semidefinite programming (SDP) relaxation when the objective function is strictly convex. Then an effective branch-and-bound algorithm is designed to find a global optimal solution. Numerical experiments indicate that the proposed SOCP relaxation based branch-and-bound algorithm spends less computing time than the SDP relaxation based branch-and-bound algorithm on condition that the rank of the quadratic objective function is large. The superiority is highlighted when solving the strictly convex quadratic program with linear complementarity constraints.

关键词： second-order cone programming relaxation Branch-and-bound algorithm Linear complementarity Simultaneous diagonalization

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Security region of inverter-interfaced power systems: Existence, expansion, and application

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2024年 192卷

作者： Hou, Jiazuo Hu, Chenxi Lei, Shunbo Liang, Liang Hou, Yunhe Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China Univ Hong Kong Shenzhen Inst Res & Innovat Shenzhen 518057 Peoples R China Chinese Univ Hong Kong Sch Sci & Engn Shenzhen 518172 Guangdong Peoples R China Harbin Inst Technol Sch Mech Engn & Automat Shenzhen 518055 Peoples R China

Since the increasing integration of inverter-based resources leads to a transition to inverter-interfaced power systems, the additional physical limits of inverters raise concerns for secure operation, which needs to be not only ensured but also enhanced. This study, therefore, investigates how to geometrically ensure and enlarge the security region of single-inverter-interfaced power systems, followed by establishing the inverter -security-constrained optimal power flow for multi-inverter-interfaced power systems. Therein, the inverter over-current and over-modulation/over-voltage limits are visualized by projecting cones into circles, ellipses, and a quadratic curve in different control variable spaces. First, for single-inverter-interfaced power systems, this study proposes a closed-form sufficient condition that guarantees the security region existence under different control modes. Then, this study quantifies and enlarges the security region size by leveraging the counter-intuitive complementary impacts of inverter parameters and the opposite impacts of system parameters. As an extension, an inverter-security-constrained optimal power flow using second-order cone programming relaxation is formulated for multi-inverter-interfaced power systems, in which this study proposes a closed-form sufficient condition to ensure a non-empty and non-decreasing security region. Numerical results of a single-inverter-interfaced power system and a modified IEEE 14 bus multi-inverter-interfaced power system verify the proposed security region properties.

关键词： Geometric perspective Inverter control Inverter-interfaced power system second-order cone programming relaxation Security region

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