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Stochastic Operation of Multi-Terminal Soft Open Points in Distribution Networks With Distributionally Robust chance-constrained optimization

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2025年第1期16卷 81-94页

作者： Han, Changhee Rao, Ramesh R. Cho, Seokheon Gyeongsang Natl Univ Dept Elect Engn Jinju 52725 South Korea Univ Calif San Diego UCSD Qualcomm Inst La Jolla CA 92093 USA

To achieve flexible operation of modern distribution networks with increasing renewable energy sources (RESs), this study proposes a stochastic operation method for a novel energy management platform that combines energy storage with a power flow controller, which is presented as a multi-terminal soft open point (MT-SOP). A Wasserstein metric-based distributionally robust chance-constrained optimization for the operation of the MT-SOP is proposed under the assumption that there is no prior knowledge about the distribution of forecast errors for both the load and RES outputs. The proposed method stochastically relaxes the reliability constraints on the bus voltage and branch power flow to maximize the cost-benefit of the distribution system operator (DSO). The proposed problem was reformulated into a tractable convex program using the concept of conditional value-at-risk. Based on case studies using modified IEEE-33 systems, the trade-offs between operational risks and cost-benefits were analyzed using parameters on the risk level and radius of the ambiguity set. Through numerical comparisons of the simulation results, we show that the DSO can achieve economic efficiency for imported electricity by relaxing conservativeness in distribution network reliability.

关键词： Uncertainty Stochastic processes Load modeling Voltage optimization Load flow Reliability chance-constrained optimization distribution networks distributionally robust optimization loss minimization soft open point

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chance-constrained co-optimization of demand response and Volt/Var under Gaussian mixture model

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RENEWABLE ENERGY FOCUS 2025年 53卷

作者： Najafi, Soroush Livani, Hanif Univ Nevada Dept Elect & Biomed Engn Reno NV 89557 USA

Managing voltage and active load in distribution networks is an increasingly challenging task with the integration of volatile distributed energy resources (DERs) and flexible demands. This paper proposes a two-stage chance-constrained co-optimization framework using a Gaussian mixture model (GMM) to address Volt-VAR optimization (VVO) and demand response programs (DRP). The utilization of GMM in chance constrained optimization CCO (GMM-CCO) approach handles non-Gaussian forecast errors, ensuring network resilience with manageable computational demands. In the first stage, flexible demands, inverters' reactive power, capacitor bank switching, and battery states of charge are co-scheduled, focusing on minimizing energy loss, reducing grid operational costs, and managing voltage deviations over a four-hour ahead schedule with hourly intervals. The second stage involves intra-hour, near-real-time optimization for VVO to respond to real-time disturbances. Simulations on a modified unbalanced three-phase IEEE 37-node system validate the framework's effectiveness, comparing it to traditional chance-constrained optimization methods. Additionally, the proposed framework is implemented on the IEEE 69-node system to analyze its scalability and robustness under different levels of uncertainty and varying penetration levels.

关键词： chance-constrained optimization Gaussian mixture model Demand response program Volt/Var optimization

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chance-constrained optimization for Flexibility Provision From the Local Energy Communities Using Logit-Based Regression

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IEEE ACCESS 2024年 12卷 164606-164620页

作者： Nguyen, An Thien Huu Singh, Anshuman Huy, Truong Hoang Bao Tran, Trung Thai Nguyen, Hung Dinh Slootweg, J. G. Nguyen, Phuong Hong Eindhoven Univ Technol Dept Elect Engn NL-5612 AZ Eindhoven Netherlands Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Soonchunhyang Univ Dept Future Convergence Technol Asan 31538 South Korea Enexis Netbeheer NL-5232 BX Shertogenbosch Netherlands

Local energy communities (LECs) represent a paradigm shift toward decentralized power management, facilitating self-consumption and efficient resource sharing. In addition, battery energy storage systems can empower LECs for flexibility provision (FP). However, the FP performance of LECs relies on the prediction capability, which unfortunately suffers from the uncertain nature of distributed energy resources, and electric vehicle's charging demand. While (profile-based) stochastic optimization (SO) can partly handle forecast errors, integrating it with the network-aware model is computationally demanding in a rolling horizon optimization framework. To overcome this computational burden, this paper proposes a novel method based on chance-constrained optimization (CCO) in convex form by leveraging logit-based regression. By deriving a closed-form expression for probabilistic constraints, this approach correlates forecast errors with network issues, such as congestion and voltage violations. Numerical simulations are conducted on the modified IEEE 33-bus network connected to two LECs in the Bunnik campus, the Netherlands to demonstrate the method's effectiveness. The proposed CCO method outperforms profile-based SO and network-aware SO by factors of 8 and 165, respectively, in terms of reducing computational time. Additionally, it limits voltage violation risks to below 5% compared to 20% in profile-based SO along with a 2% reduction in operations cost.

关键词： Flexible printed circuits optimization Real-time systems Mathematical models Costs Photovoltaic systems Correlation Voltage control Uncertainty Stakeholders chance-constrained optimization flexibility provision logit-based regression second-order cone programming rolling horizon

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chance-constrained optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks

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IEEE TRANSACTIONS ON POWER DELIVERY 2013年第3期28卷 1855-1864页

作者： Cao, Yijia Tan, Yi Li, Canbing Rehtanz, Christian Hunan Univ Coll Elect & Informat Engn Changsha 410082 Hunan Peoples R China TU Dortmund Univ Inst Energy Syst Energy Efficiency & Energy Econ D-44227 Dortmund Germany

Optimal power flow (OPF) is an important tool for active management of distribution networks with renewable energy generation (REG). It is better to treat REG as stochastic variables in the distribution network OPF. In addition, distribution networks are unbalanced in nature. Thus, in this paper, a chance constrained optimization-based multiobjective OPF model is formulated to consider the forecast errors of REG in the short-term operation of radial unbalanced distribution networks. In the model, expected total active power losses of distribution lines, expected overload risk and voltage violation risk with respect to contingencies are minimized, and inequality constraints in the normal state are satisfied with a predefined probability level. Thus, the profitability and security can be balanced in the presence of stochastic REG. The proposed multiobjective OPF problem is solved by the multiobjective group search optimization and the two-point estimate method. Simulation results show that distribution network economy and postcontingency performance deteriorate with increased penetration level of REG, and the penetration level has a greater impact than the forecast errors of REG.

关键词： chance-constrained optimization distributed generation (DG) unbalanced distribution networks multiobjective optimal power flow

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The robust binomial approach to chance-constrained optimization problems with application to stochastic partitioning of large process networks

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JOURNAL OF HEURISTICS 2014年第3期20卷 261-290页

作者： Stan, Oana Sirdey, Renaud Carlier, Jacques Nace, Dritan CEA LIST Embedded Real Time Syst Lab F-91191 Gif Sur Yvette France Univ Technol Compiegne UMR CNRS Heudiasyc 6599 F-60205 Compiegne France

In this paper, we study an interpretation of the sample-based approach to chance-constrained programming problems grounded in statistical testing theory. On top of being simple and pragmatic, this approach is theoretically well founded, non parametric and leads to a general method for leveraging existing heuristic algorithms for the deterministic case to their chance-constrained counterparts. Throughout this paper, this algorithm design approach is illustrated on a real world graph partitioning problem which crops up in the field of compilation for parallel systems. Extensive computational results illustrate the practical relevance of the approach, as well as the robustness of the obtained solutions.

关键词： chance-constrained optimization Heuristic design Graph partitioning

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Air traffic flow management under uncertainty using chance-constrained optimization

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2017年 102卷 124-141页

作者： Chen, J. Chen, L. Sun, D. Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA Univ Dayton Dept MIS Operat Management & Decis Sci Dayton OH 45469 USA

In order to efficiently balance traffic demand and capacity, optimization of Air Traffic Flow Management (ATFM) relies on accurate predictions of future capacity states. However, these predictions are inherently uncertain due to factors, such as weather. This paper presents a novel computationally efficient algorithm to address uncertainty in ATFM by using a chance-constrained optimization method. First, a chance-constrained model is developed based on a previous deterministic Integer Programming optimization model of ATFM to include probabilistic sector capacity constraints. Then, to efficiently solve such a large-scale chance-constrained optimization problem, a polynomial approximation-based approach is applied. The approximation is based on the numerical properties of the Bernstein polynomial, which is capable of effectively controlling the approximation error for both the function value and gradient. Thus, a first-order algorithm is adopted to obtain a satisfactory solution, which is expected to be optimal. Numerical results are reported in order to evaluate the polynomial approximation-based approach by comparing it with the brute-force method. Moreover, since there are massive independent approximation processes in the polynomial approximation-based approach, a distributed computing framework is designed to carry out the computation for this method. This chance-constrained optimization method and its computation platform are potentially helpful in their application to several other domains in air transportation, such as airport surface operations and airline management under uncertainties. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Air traffic flow management chance-constrained optimization Bernstein polynomial

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Data-driven decision making in power systems with probabilistic guarantees: Theory and applications of chance-constrained optimization

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ANNUAL REVIEWS IN CONTROL 2019年 47卷 341-363页

作者： Geng, Xinbo Xie, Le Texas A&M Univ College Stn TX 77843 USA

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. We first review three categories of existing methods to chance-constrained optimization: (1) scenario approach;(2) sample average approximation;and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Key results of the analytical reformulation approach for specific distributions are briefly discussed. We then provide a comprehensive review on the applications of chance-constrained optimization in power systems. Finally, this paper provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases. (C) 2019 Published by Elsevier Ltd.

关键词： Data-driven Power system chance constraint Probabilistic constraint Stochastic programming Robust optimization chance-constrained optimization

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chance-constrained optimization for active distribution networks with virtual power lines

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ELECTRIC POWER SYSTEMS RESEARCH 2023年 221卷

作者： Lee, Dongwon Han, Changhee Kang, Sungwoo Jang, Gilsoo Korea Univ Sch Elect Engn Anam Ro Seoul 02841 South Korea Univ Calif La Jolla Qualcomm Inst La Jolla CA 92093 USA

Active distribution networks (ADNs) experience uncertainties because of the high integration of distributed renewable energy resources (RESs). Stochastic analysis approaches are attracting increasing attention owing to the uncertain nature of RESs and load demands. This study proposes a chance-constrained optimal operation framework for ADNs considering virtual power lines (VPLs) solved via the second-order cone programming (SOCP) optimal power flow (OPF) problem. VPLs comprise virtual lines connected to each network's energy storage systems (ESSs). If one ESS is charged, another ESS is discharged by the same amount. We reformulate the constraints into tractable forms using a simplified Z-bus sensitivity matrix and first-order Taylor expansion to solve via SOCP OPF because the chance constraints on voltage magnitudes are generally non-convex and intractable. The efficacy of the proposed approach was verified through its application to two modified IEEE 33-bus systems, each featuring different consumer units, including commercial, residential, and industrial units. The effectiveness of the proposed methods was demonstrated by comparing three different types of constraints: conventional hard constraints, soft constraints with penalties, and chance constraints. The results showed that although the chance constraints case had a slightly higher voltage violation rate, the network power loss was reduced by 3.4% compared to the conventional hard constraints case. Furthermore, modified 85-bus and 65-bus systems are carried out to verify the algorithm's scalability. The proposed approach achieves a trade-off between voltage regulation and power loss minimization, with a voltage violation rate of 0.88% and a power loss reduction to 1.02%.

关键词： chance-constrained optimization Second-order cone programming Virtual power lines Distributed generator Stochastic analysis

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Energy Storage Planning in Active Distribution Grids: A chance-constrained optimization With Non-Parametric Probability Functions

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IEEE TRANSACTIONS ON SMART GRID 2018年第3期9卷 1972-1985页

作者： Akhavan-Hejazi, Hossein Mohsenian-Rad, Hamed Univ Calif Riverside Dept Elect & Comp Engn Riverside CA 92521 USA

By considering the specific characteristics of random variables in active distribution grids, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In particular, we develop new closed-form stochastic models for the key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. Different case studies are presented to compare the proposed approach with the conventional deterministic and parametric stochastic approaches, where the latter is based on approximating random variables with Gaussian probability distributions.

关键词： Energy storage distribution grid non-parametric probability distributions chance-constrained optimization probabilistic optimal power flow linearized branch model

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UAV Trajectory Planning With Probabilistic Geo-Fence via Iterative chance-constrained optimization

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第6期23卷 5859-5870页

作者： Du, Bin Chen, Jun Sun, Dengfeng Manyam, Satyanarayana Gupta Casbeer, David W. Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA San Diego State Univ Dept Aerosp Engn San Diego CA 92182 USA Infoscitex Corp Dayton OH 45431 USA Air Force Res Lab Autonomous Control Branch Wright Patterson AFB OH 45433 USA Air Force Res Lab Control Sci Ctr Excellence Wright Patterson AFB OH USA

chance-constrained optimization provides a promi-sing framework for solving control and planning problems with uncertainties, due to its modeling capability to capture randomness in real-world applications. In this paper, we consider a UAV trajectory planning problem with probabilistic geo-fence, building on the chance-constrained optimization approach. In the considered problem, randomness of the model, such as the uncertain boundaries of geo-fences, is incorporated in the formulation. By solving the formulated chance-constrained optimization with a novel sampling based solution method, the optimal UAV trajectory is achieved while limiting the probability of collision with geo-fences to a prefixed threshold. Furthermore, to obtain a totally collision-free trajectory, i.e., avoiding the collision not only at the discrete time-steps but also within the entire time horizon, we build on the idea of an iterative scheme. That is, to iterate the solving of the chance-constrained optimization until the collision with probabilistic geo-fence is avoided at any time within the time horizon. At last, we validate the effectiveness of our method via numerical simulations.

关键词： Trajectory optimization Trajectory planning Safety Planning Uncertainty Unmanned aerial vehicles UAV trajectory planning geo-fence chance-constrained optimization

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