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Resilient-enhancing critical load restoration using mobile power sources with incomplete information

SUSTAINABLE ENERGY GRIDS & NEtwoRKS 2021年 26卷

作者： Sedgh, Seyed Amin Doostizadeh, Meysam Aminifar, Farrokh Shahidehpour, Mohammad Univ Tehran Coll Engn Sch Elect & Comp Engn Tehran *** Iran Lorestan Univ Fac Engn Khorramabad *** Iran IIT Elect & Comp Engn Dept Chicago IL 60616 USA

Mobile power sources (MPSs) have great potentials to enhance the resilience of distribution system due to mobility and flexibility. However, because of incomplete and asynchronous data after a natural disaster, decisions may lead to under-utilization of MPS and weak recovery performance. This paper proposes a robust receding horizon recovery strategy that dispatches MPSs and forms multiple micro-grids (MGs) to maximize the restored critical loads (CLs). The receding horizon framework is utilized to update the system information dynamically and re-optimize the problem until accomplishment of the recovery process. A two-stage robust optimization formulation is adopted to take into account the problem uncertainty, i.e. unknown status of branches in damaged areas. Due to long-lasting duration of the recovery process, charging capability for re-chargeable MPSs is added to the proposed approach. Several case studies are carried out on IEEE 33-node distribution test system and IEEE 123-node test feeder to verify the effectiveness of proposed framework. The benefits of the new model are remarkable when there is a significant level of incomplete information, which is a likely case after high impact natural disasters. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Microgrid Mobile power sources Resilience two-stage robust optimization

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robust transmission network expansion planning considering non-convex operational constraints

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ENERGY ECONOMICS 2021年 98卷 105246-105246页

作者： Garcia-Cerezo, Alvaro Baringo, Luis Garcia-Bertrand, Raquel Univ Castilla La Mancha Escuela Tecn Super Ingn Ind Power & Energy Anal & Res Lab Campus Univ S-N Ciudad Real 13071 Spain

This paper proposes a two-stage robust optimization model for the transmission network expansion planning problem. Long-term uncertainties in the peak demand and generation capacity are modeled using confidence bounds, while the short-term variability of demand and renewable production is modeled using a set of representative days. As a distinctive feature, this work takes into account the non-convex operation of conventional generating units and storage facilities, which results in a two-stage robust optimization model with a discrete recourse problem. The resulting problem is solved using a nested column-and-constraint generation algorithm that guarantees convergence to the global optimum in a finite number of iterations. An illustrative example and a case study are used to show the performance of the proposed approach. Numerical results show that neglecting the non-convex operation of conventional generating units and storage facilities leads to suboptimal expansion decisions. (c) 2021 Elsevier B.V. All rights reserved.

关键词： two-stage robust optimization Transmission network expansion planning Commitment status Storage units Uncertainty Nested column-and-constraint generation algorithm

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two-stage robust economic dispatch of distribution networks considering electric vehicles charging demand-price uncertainty correlations

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Electric Power Systems Research 2025年 248卷

作者： Xinghua Liu Zhonghe Li Xiang Yang Zhengmao Li Zhongbao Wei Peng Wang School of Electrical Engineering Xi’an University of Technology Xi’an 710048 China School of Electrical Engineering Aalto University Espoo 02150 Finland National Engineering Research Center for Electric Vehicles and the School of Mechanical Engineering Beijing Institute of Technology Beijing 100081 China School of Electrical and Electronic Engineering Nanyang Technological University Singapore 639798 Singapore

With a large number of electric vehicles (EV) connected to the distribution networks (DN), the uncertainty of the charging load of EV brings challenges to the economic operation of DN. In this paper, the economic dispatch strategy of planning and operation is proposed to optimize the economy of DN. To better describe the correlation between EV charging demand and price uncertainty, a data-driven uncertainty set based on adjacent days is incorporated into two-stage robust optimization (TSRO) model. The proposed uncertainty set abandons the extreme scenario and is closer to the real-world scenarios. In the planning stage, charging piles are upgraded to devices with vehicle-to-grid (V2G) service capability, minimizing the planning cost. In the operational stage, the recourse method is adopted to quantify the worst output scenarios for wind, photovoltaic, and EV charging demands, which are reflected as the operating costs of the DN. The numerical simulations are carried out under the modified IEEE-33 bus system, and the nested column and constraint generation (N-C&CG) algorithm is adopted to solve the TSRO model under data-driven uncertainty sets. The results indicate that our proposed model decreases the total cost by 14% to 32% compared to other uncertainty models, which guarantees the economy of the decisions made by the model. The analysis demonstrates that the model possesses low conservatism while ensuring robustness and economy, and is suitable for long-term planning.

关键词： Data-driven uncertainty set Distribution network dispatch Electric vehicles two-stage robust optimization

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Adaptive data driven multi period power supply recovery method for distribution networks

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Scientific reports 2025年第1期15卷 19002页

作者： Xi Ye Meng Yang Zhihong Yang Qing Xiang Yazhuo Li Institute of Intelligent Manufacturing Jianghan University Wuhan Hubei China. ***@***. Hubei Engineering Research Center for Intelligent Detection and Control of Specialized Equipment Wuhan China. ***@***. Economics and Technology Research Institute State Grid Hubei Electric Power Company Wuhan 430077 China. Institute of Intelligent Manufacturing Jianghan University Wuhan Hubei China.

In the process of distribution network fault recovery, in order to better address the issues caused by the uncertainty of new energy power output, this paper proposes a multi period power supply recovery method for distribution networks based on adaptive data driven approach. Firstly, this method uses the historical data of new energy power output to construct an ellipsoidal uncertainty set, and forms a data driven convex hull polyhedral set by connecting the vertices of the high-dimensional ellipsoid. Then, aiming at the problem of large conservatism during the reduction process of the convex hull polyhedral set, based on the range of the box set, cutting planes are made starting from the vertices, and a data driven hyperplane polyhedral set model is constructed. Furthermore, considering the constraints of cyber-physical integration, an adaptive data driven power supply recovery model for distribution networks is established, and the column and constraint generation (C&CG) algorithm is adopted to solve the robust scheduling model. Finally, simulations on the improved IEEE-33 bus system and actual example systems verify that the adaptive data driven power supply recovery model for distribution networks can reduce conservatism and improve the robustness of the optimization results. This power supply recovery model can reduce conservatism and enhance the robustness of the optimization results. In the actual distribution network fault recovery scenarios, it can make more efficient use of new energy and ensure the stability of power supply, which strongly demonstrates the effectiveness and application value of the proposed method.

关键词： Convex hull polyhedron set Hyperplane polyhedron set Power supply recovery two-stage robust optimization

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robust Coordinated optimization of Active and Reactive Power in Active Distribution Systems

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IEEE TRANSACTIONS ON SMART GRID 2018年第5期9卷 4436-4447页

作者： Gao, Hongjun Liu, Junyong Wang, Lingfeng Sichuan Univ Sch Elect Engn & Informat Chengdu 610065 Sichuan Peoples R China Univ Wisconsin Dept Elect Engn & Comp Sci Milwaukee WI 53211 USA

Active power dispatch and reactive power optimization problems are usually handled separately in active distribution systems, aiming at minimizing the total generation cost or transmission losses. However, the separate optimization cannot achieve a global optimum scheme in distribution system operations. Moreover, the significant relationship between the active power and reactive power may pose great challenges to distribution system operations due to the uncertain nature of load demands and intermittent renewable energy resources. In this paper, using the branch flow model-based relaxed optimal power flow, we formulate a robust coordinated optimization problem for active and reactive powers as a mixed integer second-order cone (SOC) programming problem. Furthermore, in order to address the uncertainties, a two-stage robust optimization model is proposed to coordinate the on load tap changer ratios, reactive power compensators, and charge discharge power of energy storage system to find a robust optimal solution. Then the column-and-constraint generation algorithm is applied to solve the proposed robust two-stage optimization model. In the relaxed optimal power flow, a stricter cut is added to speed up the computation process of the SOC relaxation in order to guarantee the exactness for representative cases, such as those with high penetration of distributed energy resources. Numerical results based on the 33-bus and 69-bus systems verify the effectiveness of the proposed method.

关键词： Active distribution system coordinated optimization second order cone (SOC) branch flow model (BFM) two-stage robust optimization column-and-constraint generation (CCG) algorithm

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robust Energy and Reserve Scheduling Under Wind Uncertainty Considering Fast-Acting Generators

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2019年第4期10卷 2142-2151页

作者： Cobos, Noemi G. Arroyo, Jose M. Alguacil, Natalia Street, Alexandre Univ Castilla La Mancha ETSI Ind Dept Ingn Elect Elect Automat & Comunicac E-13071 Ciudad Real Spain Pontifical Catholic Univ Rio de Janeiro Elect Engn Dept BR-22451045 Rio De Janeiro Brazil

The large-scale integration of wind power generation has significantly boosted the role played by conventional fast-acting generating units in power system operation. Due to their short response time, these relatively expensive devices are particularly suited to cope with the intermittency and volatility featured by uncertain wind-based generation. Within the context of network-constrained generation scheduling underwind-related uncertainty, this paper presents a new robust approach wherein the operation of both slow-and fast-acting generating units is precisely characterized in a day-ahead co-optimized energy and reserve market. As salient modeling features, the ramping-related effect of dispatch nonanticipativity and nonspinning reserve offers are both accounted for. The resulting robust counterpart is formulated as a challenging trilevel program with lower-level binary variables that is effectively solved by an exact nested column-and-constraint generation algorithm. Numerical results including a practical out-of-sample validation procedure demonstrate the operational advantages and the computational effectiveness of the proposed approach.

关键词： Energy and reserve scheduling fast-acting generating units nonanticipativity nonspinning reserve offers ramping capability two-stage robust optimization wind uncertainty

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A robust operation-based scheduling optimization for smart distribution networks with multi-microgrids

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APPLIED ENERGY 2018年 228卷 130-140页

作者： Liu, Yixin Guo, Li Wang, Chengshan Tianjin Univ Minist Educ Key Lab Smart Grid Tianjin Peoples R China

This paper proposes a two-level interactive mechanism to address the day-ahead scheduling optimization of smart distribution networks with multi-microgrids. Each microgrid realizes the economic dispatch in the lower level interactive model, where the uncertainties caused by renewable energy integration and loads as well as the coordination of controllable distributed generator, energy storage and demand response are handled through a two-stage robust model. In the upper level interactive model, the distribution network operator (DNO) guarantees the operational quality by considering the power flow constraints and decides the transaction price and quantity with each microgrid based on the solutions of the lower level problem, to minimize the operation cost. The interaction process is formulated as a Stackelberg game, in which the trading strategies of coupled micro grids, acted as followers, are influenced by price incentive mechanism of DNO and affect the decision of DNO in turn. A collaborative strategy promoting the internal power trading among microgrids is also presented to deal with the market power of DNO, such that the participating microgrids can benefit from the internal trading and further reduce the cost. Numerical cases on an improved IEEE 33-bus system show the effectiveness of the proposed model and solution strategy.

关键词： Smart distribution networks Multi-microgrids Interactive mechanism two-stage robust optimization Price incentive

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robust Transmission Network Expansion Planning Under Correlated Uncertainty

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第3期34卷 2071-2082页

作者： Roldan, Cristina Minguez, Roberto Garcia-Bertrand, Raquel Arroyo, Jose M. Univ Castilla La Mancha Dept Ingn Elect Elect Automat & Comunicac ETSI Ind E-13071 Ciudad Real Spain

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This paper differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results fromstructural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach.

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robust planning-operation co-optimization of energy hub considering precise model of batteries’ economic efficiency

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Energy Procedia 2019年 158卷 6496-6501页

作者： Cong Chen Xinwei Shen Qinglai Guo Hongbin Sun Tsinghua-Berkeley Shenzhen Institute Tsinghua University Shenzhen People’s Republic of China The Department of Electrical Engineering State Key Laboratory of Power System Tsinghua University Beijing People’s Republic of China

The increasing penetration of renewable energy in integrated energy system (IES) makes it necessary to consider the uncertainty and an appropriate investment and operation for energy storage systems (ESS). In this paper, we propose a robust planning-operation co-optimization method for Energy Hub (EH) considering the sizing problem and precise model of batteries’ economic efficiency, in which batteries’ total cost and the lifetime loss cost is mainly considered. The problem is formulated as a two-stage robust optimization model, in which the second-stage problem has integer variables. To solve the problem, dual norms are used to transform the uncertain constraints into robust counterparts, then the problem is rearranged and can be solved by Benders Decomposition. Through case studies, the benefits on the flexibility and economy of EH brought by precise ESS model is analyzed. And the consideration of lifetime factor and robust optimization strengthen the economy and reliability of EH, respectively.

关键词： Energy hubs energy storage systems two-stage robust optimization lifetime of batteries planning-operation co-optimization

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robust transmission expansion planning with uncertain generations and loads using full probabilistic information

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ELECTRIC POWER SYSTEMS RESEARCH 2020年 189卷 106793-106793页

作者： Roldan, Cristina Garcia-Bertrand, Raquel Minguez, Roberto Univ Castilla La Mancha Dept Elect Engn Ciudad Real Spain ESCISSION Co Madrid Spain

Recent advances in Transmission Network Expansion Planning (TNEP) have demonstrated that two-stage adaptive robust optimization (ARO) renders the expansion planning problem tractable for real systems and, at the same time, constitutes a relevant approach to deal with uncertain demand and generation capacity in the TNEP problem. However, the use of cardinality and polyhedral uncertainty sets does not consider the correlation of uncertain parameters and makes the interpretation of final results difficult from a probabilistic view-point. The recent use of level II structural-reliability and decomposition techniques allows the incorporation of ellipsoidal uncertainty sets, which permits the use of expected values and the variance-covariance matrix of uncertain parameters (First-Order Second-Moment, FOSM). However, it also constitutes an approximation. This paper presents an iterative method which, using FOSM and appropriately modifying the reliability index associated with the desired objective function quantile, transforms the model into a level III structural-reliability method that allows the consideration of the complete probabilistic structure of the uncertain parameters. Numerical results from a realistic case study are presented and discussed.

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