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bi-level stochastic optimization Model for Coordination of Transmission and Distribution Networks Considering Generic Resources

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2024年第2期19卷 961-976页

作者： Tamizkar, Roozbeh Moghaddam, Mahmoud Samiei Azarfar, Azita Abardeh, Mohamad Hoseini Vahedi, Mojtaba Islamic Azad Univ Dept Elect Engn Shahrood Branch Shahrood Iran Islamic Azad Univ Dept Elect Engn Damghan Branch Damghan Iran

In this paper, an optimization model for transmission and distribution network integration is proposed. The proposed model is a bi-level optimization model formulated as an upper and lower-level problem. The problem of unit commitment in the transmission network as the upper level problem with the aim of reducing operating costs and load shedding as a mixed integer linear programming model and the problem of optimal operation in the distribution network by considering renewable and non-renewable resources along with electric vehicle charging stations (EVCS), it has been considered as a linear model with the aim of reducing the cost of purchasing power from the transmission network and increasing the use of renewable energy and charging power of EVCS. According to the literature, the study gap can be seen in three key points;firstly, it is of great importance to provide a convex model that can guarantee global optimal solutions. The next point is related to the problem-solving time, according to the dimensions and number of variables and parameters in the problem of optimal coordination of the transmission and distribution network, providing a method to achieve global optimal solutions in the shortest time and the last point is related to the modeling of any number of distribution networks is integrated with the transmission network. To solve the proposed bi-level optimization problem, the method of rewriting the optimization problems using Karush-Kuhn-Tucker condition equations, which can model global optimal solutions as well as fast solution time and modeling a large number of distribution networks in the transmission network has been proposed. Several different networks have been considered for the validation of the proposed model and method, which proves the results obtained from the simulation of the efficiency of the proposed model and method in considering the coordinated operation of transmission and smart distribution networks. The results showed that the p

关键词： Coordination of transmission and distribution network bi-level stochastic optimization Renewable energy Mixed integer linear programming

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bi-level stochastic optimization model of smart distribution grids considering the transmission network to reduce vulnerability

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ENERGY SYSTEMS-optimization MODELING SIMULATION AND ECONOMIC ASPECTS 2023年第2期16卷 851-884页

作者： Ghanaei, Niki Moghaddam, Mahmoud Samiei Alibeaki, Esmaeil Salehi, Nasrin Davarzani, Reza Islamic Azad Univ Dept Elect Engn Shahrood Branch Shahrood Iran Islamic Azad Univ Dept Elect Engn Damghan Branch Damghan Iran Islamic Azad Univ Dept Basic Sci Shahrood Branch Shahrood Iran

This paper presents a novel optimization framework for integrating transmission and distribution networks. The proposed framework consists of a bi-level optimization model, which comprises an upper-level problem and a lower-level problem. The upper-level problem addresses unit commitment (UC) in the transmission network, aiming to minimize operating costs and load shedding. It is formulated as a mixed-integer linear programming model (MILP). Meanwhile, the lower-level problem focuses on the optimal operation of the distribution network, considering both renewable and non-renewable resources, as well as electric vehicle charging stations (EVCS). This problem is formulated as a linear model with the objectives of reducing power purchase costs from the transmission network and maximizing the utilization of renewable energy and EVCS charging power. The literature review highlights three main research gaps. Firstly, it is crucial to develop a convex model that ensures globally optimal solutions. Secondly, considering the problem-solving time, it is important to devise a method that can achieve globally optimal solutions in the shortest possible time, accounting for the dimensions, number of variables, and parameters involved in coordinating the transmission and distribution networks. Lastly, there is a need to develop a modeling approach that allows the integration of any number of distribution networks with the transmission network. To address these research gaps, we propose a solution methodology that involves rewriting the optimization problems using reformulation and decomposition methods. This approach enables the modeling of globally optimal solutions while ensuring faster solution times and the ability to incorporate numerous distribution networks into the transmission network. We validate the proposed model and methodology using various networks, and the results demonstrate the efficiency of our approach in coordinating the operation of transmission and smart dis

关键词： Coordination of transmission and distribution network bi-level stochastic optimization Renewable energy Mixed integer linear programming

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Projection-Free stochastic bi-level optimization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 6332-6347页

作者： Akhtar, Zeeshan Bedi, Amrit Singh Thomdapu, Srujan Teja Rajawat, Ketan Indian Inst Technol Kanpur Dept Elect Engn Kanpur 208016 India Univ Maryland Inst Syst Res College Pk MD 20742 USA

bi-level optimization, where the objective function depends on the solution of an inner optimization problem, provides a flexible framework for solving a rich class of problems such as hyper-parameter optimization and model-agnostic meta-learning. This work puts forth the first stochastic bi-level Frank-Wolfe (SBFW) algorithm to solve the stochastic bi-level optimization problems in a projection-free manner. We utilize a momentum based gradient tracker that results in a sample complexity of O(epsilon(-3)) for convex outer objectives and O(epsilon(-4)) for non-convex outer objectives with strongly convex inner objectives. The stochastic compositional optimization problems (a special case of bi-level optimization problems entailing the minimization of a composition of two expected-value functions) are also considered within the same rubric. The proposed stochastic Compositional Frank-Wolfe (SCFW) algorithm is shown to achieve a sample complexity of O (epsilon(-2)) for convex objectives and O(epsilon(-3)) for non-convex objectives, at par with the state-of-the-art rates of projection-free algorithms for single-level problems. The usefulness and flexibility of SBFW and SCFW algorithms are demonstrated via extensive numerical tests. We show that SBFW outperforms the state-of-the-art methods for the problem of matrix completion with denoising, and achieve improvements of up to 82% in terms of the wall-clock time required to achieve a particular level of accuracy. Furthermore, we demonstrate the improved performance of SCFW over the competing projection-free variants on the policy evaluation problem in reinforcement learning.

关键词： optimization Signal processing algorithms stochastic processes Noise reduction Complexity theory Noise measurement Data models bi-level stochastic optimization frank-wolfe algorithm projection free algorithm

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bi-level stochastic modeling of multi-microgrid transactive energy system via coalition formation considering battery storage and demand response programs

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JOURNAL OF ENERGY STORAGE 2025年 111卷

作者： Norouzi, Fahimeh Jadid, Shahram Iran Univ Sci & Technol Dept Elect Engn Tehran Iran

To enhance energy management efficiency in multi-microgrid (MMG) systems, we propose creating a multimicrogrid transactive energy system (MMG-TES). This paper models MMG-TES with distribution system operators (DSO) using a bi-level optimization structure based on Stackelberg game theory. To increase model realism, we use probabilistic approaches to incorporate uncertainties in load, market price, and renewable energy. In the upper level, the DSO optimizes operational costs and emissions by implementing AC power flow calculations and price design. Microgrids act as followers, responding to DSO prices. To enhance MMG-TES bargaining power, microgrids form coalitions, determined by the Bell numbers representing various groupings. Considering minimum MMG cost, the optimal strategy is selected, sharing profit according to a defined index, more use of internal resources, and reduction of emissions for each microgrid. The IEEE 33-bus network simulation demonstrates significant improvements in operational efficiency, including a 34.5 % decrease in operational cost (from 23,527 $ to15,417 $), a 34.6 % reduction in emissions (from 9742 kg to 6369 kg), and an 18.9 % decrease in ENS (from 461 kWh to 374 kWh). Additionally, the total active and reactive power losses in MMG-TES were reduced by about 59 kWh (11 %) and 52 kVarh (12 %), respectively. These results have practical implications for real-world energy management, including improved operational efficiency, enhanced resource utilization within microgrids, and better alignment of economic incentives with environmental goals. This study contributes to the development of dynamic and stochastic modeling in MMG-TES by emphasizing cooperative approach and coalition formation, uncertainty management, emission reduction, and system optimization.

关键词： Multi-microgrid system Transactive energy system AC optimal power flow Cooperative approach Stackelberg game theory bi-level stochastic optimization Demand response programs

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stochastic Energy Scheduling for Urban Railway Smart Grids Considering Distributed EVs Charging and PV Output Uncertainty

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2025年

作者： Chen, Minwu Deng, Hao Chen, Yinyu Peng, Gaoqiang Liang, Zongyou Southwest Jiaotong Univ Sch Elect Engn Chengdu 611756 Sichuan Peoples R China

In order to improve the utilization rate of regenerative braking energy (RBE) and reduce the operation cost of railway system, this paper proposed an urban railway smart grids (URSG) with efficient and flexible energy management strategy is proposed, which integrates a traction power supply system (TPSS), electric vehicle charging station (EVCS), PV and battery storage. In this study, a bi-level stochastic optimization (BLSO) model is employed to determine the sizing of battery storage and the energy scheduling of URSG. The upper level aims to determine the optimal size of battery storage and minimize the comprehensive cost, considering the degradation of the battery capacity. In the lower level, based on piecewise linearization method, the power transmission loss of catenary is formulated as a linear mathematical model, and a stochastic mixed-integer linear programming model of URSG is established to schedule the power flow to minimize the electrical cost. Furthermore, regarding to the stochastic nature of EV charging behavior and PV output, the constraints with uncertain parameters are posed as chance constraints, for which Sample Average Approximation (SAA) method is introduced to transform chance constraints into deterministic constraints. Based on the actual urban rail transit line and traction load data, the simulation results show that the above system can reduce the cost by 18.16 %.

关键词： Costs Rail transportation Batteries stochastic processes Electric vehicle charging Propagation losses Energy storage Uncertainty Transformers Rails Urban railway smart grids electric vehicles battery storage bi-level stochastic optimization chance constraints

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A stochastic optimization Model to Reduce Expected Post-Disaster Response Time Through Pre-Disaster Investment Decisions

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NETWORKS & SPATIAL ECONOMICS 2014年第2期14卷 271-295页

作者： Du, Lili Peeta, Srinivas IIT Dept Civil Architectural & Environm Engn Chicago IL 60616 USA Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA

This paper seeks to enhance network survivability under a disaster and reduce the expected post-disaster response time for transportation networks through pre-disaster investment decisions. The planning focuses on determining the links of the network to strengthen through investment under two types of uncertainties: the disaster characteristics, and the surviving network under each disaster. A bi-level stochastic optimization model is proposed for this problem, in which link investment decisions are made at the upper level to enhance the network survivability subject to a budget constraint such that the expected post-disaster response time is minimized at the lower level. A two-stage heuristic algorithm is proposed to obtain effective solutions efficiently. The numerical experiments indicate that the proposed heuristic algorithm converges to a fixed point representing a feasible solution, within an acceptable tolerance level, of the bi-level stochastic optimization model which is an effective solution under disasters of moderate severity. Parametric and sensitivity analyses reinforce the need for a holistic approach that integrates multiple relevant considerations to determine the link investment decisions.

关键词： Pre-disaster investment decisions Network survivability Post-disaster response times bi-level stochastic optimization

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Participation of a Combined Wind and Storage Unit in the Day-ahead and Local Balancing Markets 15

Participation of a Combined Wind and Storage Unit in the Day...

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15th International Conference on the European Energy Market (EEM)

作者： Farrokhseresht, Mana Paterakis, Nikolaos G. Gibescu, Madeleine Slootweg, J. G. Eindhoven Univ Technol Elect Energy Syst Eindhoven Netherlands

ISBN: (纸本)9781538614884

In this paper, the market participation of an independent energy producer owning a combined wind generator energy storage system (WG-ESS) connected to the distribution network is considered. A mathematical model for the profit maximization of the WG-ESS participating strategically in wholesale day-ahead and local balancing markets (LBMs) is proposed. We assume that in a future dominated by uncertainty and variability from distributed renewable energy sources, such a LBM, to be operated by a new entity called distribution market operator (DMO) will evolve. A stochastic bi-level optimization algorithm is adopted, where the WG-ESS maximizes its profit in the day ahead market and the DMO-operated LBM. The results show that the strategic decisions of the WG-ESS in multiple markets significantly change compared to a single DA energy-only market.

关键词： bi-level stochastic optimization Day-ahead market Energy storage systems Local balancing market Wind power

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Optimal operation of the green port system considering the multiport power electronic transformer in day-ahead markets

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FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Qing, Chen Tai, Nengling Fan, Feilong Yu, Jinming Wang, Jun Hu, Yan Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China Shanghai Jiao Tong Univ Coll Smart Energy Shanghai Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China

Increasing operation costs and carbon emissions have brought great challenges to the development of port systems, which are regarded as prosumers that comprise various renewable energy sources and diversiform electric loads. In this paper, an energy transaction framework for the green port with a multiport power electronic transformer (PET) is established to optimize the operation of the port system in day-ahead energy and reserve markets. The market behavior of the port system is formulated as a bi-level stochastic optimization model. The energy source schedule, berth allocation, and quay crane (QC) assignment are optimized to minimize the total operation cost at the upper level, whereas energy and reserve market clearing problems are settled at the lower level. The aforementioned nonlinear bi-level optimization problem is solved as a mathematical program with equilibrium constraints (MPECs). Karush-Kuhn-Tucker conditions and duality theory convert the proposed nonlinear bi-level problem into a linear single-level problem. Numerical simulations show that the proposed strategy can achieve the lowest total operation cost for the green port.

关键词： green port power electronic transformer energy transaction framework day-ahead markets bi-level stochastic optimization

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stochastic optimization framework of the energy-water-emissions nexus for regional power system planning considering multiple uncertainty

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JOURNAL OF CLEANER PRODUCTION 2021年 281卷 124470-124470页

作者： Tan, Qinliang Liu, Yuan Zhang, Xingping North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China North China Elect Power Univ Beijing Key Lab Renewable Elect Power & Low Carbo Beijing 102206 Peoples R China Res Ctr Beijing Energy Dev Beijing 102206 Peoples R China

This paper proposed a model-based framework to optimize the energy-water-emissions nexus (EWEN) for regional electric power system (EPS) planning. The framework integrated the superiority of bi-level programming (BLP), two-stage stochastic programming (TSP), mix-integer programming (MIP), interval parameter programming (IPP) models and carbon emission trading (CET) mechanism, which could effectively deal with the planning problems in the EWEN optimization process. BLP helped decision makers make leader-follower choices when they have conflicting preferences. TSP with IPP could validly address the uncertain information expressed as interval values with unknown distribution. MIP was introduced as an efficacious tool to evaluate the capacity expansion potential in EPS. CET mechanism was applied to reinforce the CO2 mitigation effect during the EWEN optimization process. Then the proposed framework was applied into a case study in Shanxi Province, a main thermal power base in China to optimize the EWEN. Results indicated that the power supply structure was inclined to show a low-carbon transition trend in the planning periods. Meanwhile, coupled with the strict water conservation policy, every 5% reduction in carbon emission density would lead to an average decreasing rate of 8% for SO2, 3% for NOx and 12% for PM. This study may help provide an effective way to deal with planning problems with conflicting and sequential goals under uncertainty and make better tradeoff strategies in EWEN optimization in EPS. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Energy-water-emissions nexus Energy planning Carbon emissions trading bi-level stochastic optimization Uncertainty

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Minimization of Distribution System Losses By Exploiting Storage and Anticipating Market-Driven Behaviour of Wind Power Producers 14

Minimization of Distribution System Losses By Exploiting Sto...

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14th International Conference on the European Energy Market (EEM)

作者： Farrokhseresht, Mana Paterakis, Nikolaos G. Gibescu, Madeleine Slootweg, J. G. Eindhoven Univ Technol Elect Energy Syst Eindhoven Netherlands

ISBN: (纸本)9781509054992

This paper presents a stochastic bi-level optimization model to determine the optimal dispatch of energy storage systems controlled directly by the distribution system operator (DSO) in order to achieve minimization of active power losses, taking into account the profit-driven participation of wind-power producers (WPPs) connected to the distribution system, in the day-ahead and imbalance markets. The upper-level optimization problem represents the optimal AC power flow problem with the objective of minimizing the active power losses from the perspective of the DSO, while the lower-level optimization problem models the profit maximization problem faced by a competitive wind producer under uncertainty associated with market prices and its own power production profile. By exploiting the convexity of the lower-level problem, the Karush-Kuhn-Tucker conditions of the latter are derived, and the bi-level problem is cast as a single level optimization problem. A simple case study of a radial distribution system, featuring one WPP and one storage device is used to illustrate the workings of the method.

关键词： Active power losses bi-level stochastic optimization distribution system energy storage wind power

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