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Neural Risk Limiting Dispatch in Power Networks: Formulation and Generalization Guarantees

IEEE Transactions on Power Systems 2025年

作者： Chen, Ge Qin, Junjie Great Bay University School of Engineering Dongguan China Purdue University Elmore Family School of Electrical and Computer Engineering West LafayetteIN United States

Risk limiting dispatch (RLD) has been proposed as an approach that effectively trades off economic costs with operational risks for power dispatch under uncertainty. However, how to solve the RLD problem with provably near-optimal performance still remains an open problem. This paper presents a learning-based solution to this challenge. We first design a data-driven formulation for the RLD problem, which aims to construct a decision rule that directly maps day-ahead observable information to cost-effective dispatch decisions for the future delivery interval. Unlike most existing works that follow a predict-then-optimize paradigm, this end-to-end rule bypasses the additional suboptimality introduced by separately handling prediction and optimization. We then propose neural RLD, a novel solution method to the data-driven formulation. This method leverages an L2-regularized neural network (NN) to learn the decision rule, thereby transforming the data-driven formulation into a training task that can be efficiently completed by stochastic gradient descent. A theoretical performance guarantee is further established to characterize the suboptimality of our method, which implies that its suboptimality approaches to zero with high probability as more samples are utilized. Simulation tests across various systems demonstrate our method's superior performance in convergence, suboptimality, and computational efficiency compared with benchmarks. © 1969-2012 IEEE.

关键词： stochastic programming

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The stochastic multi-modal hub location problem with direct link strategy and multiple capacity levels for cargo delivery systems

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2021年第4期17卷 380-410页

作者： Shang, Xiaoting Yang, Kai Jia, Bin Gao, Ziyou Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ State Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

This paper introduces the stochastic multi-modal hub location problem with direct link strategy and multiple capacity levels for cargo delivery systems under demand uncertainty. For capturing the uncertain nature of demand, we present a stochastic optimization model to formulate this problem formally via the expected value and the chance-constrained programming techniques. Under some mild assumptions, we propose a computationally tractable approach to turn the original model into a crisp equivalent integer second-order cone programming model, which can be efficiently solved by CPLEX for only small instances. Hence, we design a memetic algorithm incorporating genetic search and local intensification for realistic size instances. Furthermore, we provide extended analyses of the original model by considering the mode-specific hub and incorporating the fixed transportation cost. To demonstrate the superiority of the proposed model and the effectiveness of the solution approach, we conduct a series of computational experiments based on Turkish network data set.

关键词： Hub location problem cargo delivery systems hybrid hub-and-spoke topology stochastic programming memetic algorithm

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Decomposition methods for solving Markov decision processes with multiple models of the parameters

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IISE TRANSACTIONS 2021年第12期53卷 1295-1310页

作者： Steimle, Lauren N. Ahluwalia, Vinayak S. Kamdar, Charmee Denton, Brian T. Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We study an approach in which the decision maker considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the performance with respect to each model, such as maximizing the expected performance or maximizing worst-case performance. Existing solution methods rely on mixed-integer program (MIP) formulations, but have previously been limited to small instances, due to the computational complexity. In this article, we present branch-and-cut and policy-based branch-and-bound (PB-B&B) solution methods that leverage the decomposable structure of the problem and allow for the solution of MDPs that consider many models of the parameters. Numerical experiments show that a customized implementation of PB-B&B significantly outperforms the MIP-based solution methods and that the variance among model parameters can be an important factor in the value of solving these problems.

关键词： Markov decision processes dynamic programming parameter ambiguity decomposition stochastic programming

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Generalized Sequential Differential Calculus for Expected-Integral Functionals

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SET-VALUED AND VARIATIONAL ANALYSIS 2021年第3期29卷 621-644页

作者： Mordukhovich, Boris S. Perez-Aros, Pedro Wayne State Univ Dept Math Detroit MI 48202 USA Univ OHiggins Inst Ciencias Ingn Rancagua Chile

Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the second one an integrable function. The main goal of this paper is to establish sequential versions of Leibniz's rule for regular subgradients by employing and developing appropriate tools of variational analysis.

关键词： Variational analysis Generalized differentiation stochastic programming Expected-integral functionals Sequential calculus

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A Secured Social-Economic Framework Based on PEM-Blockchain for Optimal Scheduling of Reconfigurable Interconnected Microgrids

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IEEE ACCESS 2021年 9卷 40797-40810页

作者： Yin, Fengyuan Hajjiah, Ali Jermsittiparsert, Kittisak Al-Sumaiti, Ameena Saad Elsayed, Salah K. Ghoneim, Sherif S. M. Mohamed, Mohamed A. Wuhan Qingchuan Univ Dept Mech & Elect Engn Wuhan 430204 Peoples R China Kuwait Univ Elect Engn Dept Coll Engn & Petr Safat 13060 Kuwait Univ City Isl Fac Adm Econ & Social Sci TR-99450 Gazimagusa Northern Cyprus Turkey Univ Muhammadiyah Sinjai Fac Social & Polit Sci Sulawesi Selatan 92615 Indonesia Khalifa Univ Elect Engn & Comp Sci Dept Adv Power & Energy Ctr Abu Dhabi U Arab Emirates Taif Univ Coll Engn Dept Elect Engn At Taif 21944 Saudi Arabia Minia Univ Elect Engn Dept Fac Engn Al Minya 61519 Egypt Fuzhou Univ Dept Elect Engn Fuzhou 350116 Peoples R China

Optimal scheduling of reconfigurable interconnected microgrids is a precious and critical task for the residential consumers especially with the integration of renewable energy sources, dispatchable units and energy storage systems. In this regard, not only the optimal scheduling of the microgrids in a realistic and correlated environment is a necessity, but also the guarantied security and the prevention of cyber-attacks are mandatory tasks for the operators. This article first addresses these issues by developing a novel framework based on blockchain for secured data transaction from the individual microgrids' components to the central control unit and then tries to find the optimal scheduling plan using stochastic programming based on point estimate method (PEM). Through such a hybrid PEM-blockchain based framework, the interconnected microgrids can supply the residential loads in a fully reliable, economic and secured structure. We also consider a social-economic framework to not only minimize the total operating cost of the microgrids, but also benefit the customers by enhancing the social factors through the optimal switching. Considering the complex and nonlinear nature of the problem, an effective corrected crow search (CCS) algorithm is deployed to find the most optimal operating point for the microgrids. The quality and capabilities of the proposed model are investigated using a practical residential interconnected microgrid. The results show that the optimal switching could reduce the total operation cost from $22,716 to $21,935 (3.56% reduction). Also, the average energy not supplied (AENS) has reduced from 1.4115 to 1.352 kWh/*** (4.40% reduction), which are notable values. The results advocate the quality and functionality of the proposed framework.

关键词： Microgrids Optimal scheduling Economics Renewable energy sources Electrical engineering Blockchain Manganese Reconfigurable interconnected microgrid social-economic analysis blockchain point estimate method corrected crow search stochastic programming

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Autonomous and conventional bus fleet optimization for fixed-route operations considering demand uncertainty

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TRANSPORTATION 2021年第5期48卷 2735-2763页

作者： Tian, Qingyun Lin, Yun Hui Wang, David Z. W. Nanyang Technol Univ Sch Civil & Environm Engn 50 Nanyang Ave Singapore 639798 Singapore Natl Univ Singapore Dept Ind Syst Engn & Management 1 Engn Dr 2Blk E1A 06-25 Singapore 117576 Singapore

The emerging technology of autonomous vehicles has been widely recognized as a promising urban mobility solution in the future. This paper considers the integration of autonomous vehicles into bus transit systems and proposes a modeling framework to determine the optimal bus fleet size and its assignment onto multiple bus lines in a bus service network considering uncertain demand. The mixed-integer stochastic programming approach is applied to formulate the problem. We apply the sample average approximation (SAA) method to solve the formulated stochastic programming problem. To tackle the nonconvexity of the SAA problem, we first present a reformulation method that transforms the problem into a mixed-integer conic quadratic program (MICQP), which can be solved to its global optimal solution by using some existing solution methods. However, this MICQP based approach can only handle the small-size problems. For the cases with large problem size, we apply the approach of quadratic transform with linear alternating algorithm, which allows for efficient solution to large-scale instances with up to thousands of scenarios in a reasonable computational time. Numerical results demonstrate the benefits of introducing autonomous buses as they are flexible to be assigned across different bus service lines, especially when demand uncertainty is more significant. The introduction of autonomous buses would enable further reduction of the required fleets and total cost. The model formulation and solution methods proposed in this study can be used to provide bus transit operators with operational guidance on including autonomous buses into bus services, especially on the autonomous and conventional bus fleets composition and allocation.

关键词： Autonomous bus service Demand uncertainty stochastic programming Conic programming Quadratic transform

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LOCAL CONVERGENCE OF A SEQUENTIAL QUADRATIC programming METHOD FOR A CLASS OF NONSMOOTH NONCONVEX OBJECTIVES ∗

arXiv

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arXiv 2023年

作者： Wang, Jingyi Petra, Cosmin G. Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States

A sequential quadratic programming (SQP) algorithm is designed for nonsmooth optimization problems with upper-C2 objective functions. Upper-C2 functions are locally equivalent to difference-of-convex (DC) functions with smooth convex parts. They arise naturally in many applications such as certain classes of solutions to parametric optimization problems, e.g., recourse of stochastic programming, and projection onto closed sets. The proposed algorithm conducts line search and adopts an exact penalty merit function. The potential inconsistency due to the linearization of constraints are addressed through relaxation, similar to that of S1QP. We show that the algorithm is globally convergent under reasonable assumptions. Moreover, we study the local convergence behavior of the algorithm under additional assumptions of Kurdyka- Lojasiewicz (KL) properties, which have been applied to many nonsmooth optimization problems. Due to the nonconvex nature of the problems, a special potential function is used to analyze local convergence. We show that under acceptable assumptions, upper bounds on local convergence can be proven. Additionally, we show that for a large number of optimization problems with upper-C2 objectives, their corresponding potential functions are indeed KL functions. Numerical experiment is performed with a power grid optimization problem that is consistent with the assumptions and analysis in this paper. © 2023, CC BY.

关键词： stochastic programming

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Optimal Self-Scheduling of a Real Energy Hub Considering Local DG Units and Demand Response Under Uncertainties

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2021年第4期57卷 3396-3405页

作者： Kermani, Mostafa Shirdare, Erfan Najafi, Arsalan Adelmanesh, Behin Carni, Domenico Luca Martirano, Luigi Chalmers Univ Technol Dept Elect Engn SE-41296 Gothenburg Sweden Sapienza Univ Rome Dept Astronaut Elect & Energy Engn I-00184 Rome Italy Wroclaw Univ Sci & Technol Fac Elect Engn Dept Elect Engn Fundamentals PL-50370 Wroclaw Poland Islamic Azad Univ Sepidan Branch Sepidan 73611 Iran Univ Calabria Dept Comp Sci Modeling Elect & Syst I-87036 Arcavacata Di Rende Italy

In this article, a cost-based mathematical optimization is used to evaluate the optimal amount of imported power from the public main grid to a private microgrid (MG), that is the "LAMBDA lab MG" testbed placed at the Sapienza University of Rome. In this regard, this article considers five tests based on using different sources, including a photovoltaic (PV) array, an emergency generator set, a fuel cell, and the main grid, for load satisfaction. The "LAMBDA lab" can be considered as a "multisource multioutput energy hub" with three optional sources and both electrical and heat demands in output. This article considers PV production and load demand as indeterministic parameters and evaluates the problem under uncertainties. As a result, a stochastic programming model is defined, and a powerful optimization function is used to reach the optimal power received from the main grid. Besides, information gap decision theory is used to model the robustness of the problem against uncertainties associated with renewable generation units (PV system) and electricity loads applied on a real case for the first time. In the result section, the contribution of each source in electrical and heat load demands is presented in addition to the cost of each test by evaluating the effect of demand response of 15%. Finally, a comparison between the stochastic programming method and IGDT has been accomplished.

关键词： Resistance heating Uncertainty SCADA systems Production Real-time systems Microgrids Protocols Demand response (DR) energy hub (EH) information gap decision theory (IGDT) microgrid (MG) photovoltaic (PV) array stochastic programming uncertainty

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Reliability-Constrained Power System Expansion Planning: A stochastic Risk-Averse Optimization Approach

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第1期36卷 97-106页

作者： da Costa, Luiz Carlos Thome, Fernanda Souza Garcia, Joaquim Dias Pereira, Mario V. F. PSR BR-22250040 Rio De Janeiro Brazil

This work presents a methodology to incorporate reliability constraints in the optimal power systems expansion planning problem. Besides Loss Of Load Probability (LOLP) and Expected Power Not Supplied (EPNS), traditionally used in power systems, this work proposes the use of the risk measures VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), widely used in financial markets. The explicit consideration of reliability constraints in the planning problem can be an extremely hard task and, to minimize computational effort, this work applies the Benders decomposition technique splitting the expansion planning problem into an investment problem and two subproblems to evaluate the system's operation cost and the reliability index. The operation subproblem is solved by stochastic Dual Dynamic programming (SDDP) and the reliability subproblem by Monte Carlo simulation. The proposed methodology is applied to the real problem of optimal expansion planning of the Bolivian power system.

关键词： Power system reliability Reliability Planning Investment Load modeling Generators System expansion planning Benders decomposition Power systems Reliability stochastic programming Risk measures Mixed Integer programming Monte Carlo stochastic Dual Dynamic programming

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Constructing Demand-Side Bidding Curves Based on a Decoupled Full-Cycle Process

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IEEE TRANSACTIONS ON SMART GRID 2021年第1期12卷 502-511页

作者： Ruan, Guangchun Zhong, Haiwang Shan, Baoguo Tan, Xiandong Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China State Grid Energy Res Inst Beijing 100084 Peoples R China

Due to heavy computational burdens, existing demand-side bidding models have to sacrifice the accuracy of uncertainty estimates in exchange for tractability, and therefore fail to derive a high bidding revenue as expected. To overcome this challenge, we analyze the entire bidding process, from scenario reduction to bidding curve construction, to find out the weak link that needs improvement. We further develop a novel process to save some computational resources by decomposing the complex bidding model, then reallocates these resources to consider more scenarios and more precise bidding curves. This process is fully decoupled, and is able to achieve both a bidding revenue growth and a significant calculation speedup. In order to reduce computational complexity, the scenario reduction and bidding steps are separated, reorganized and decoupled. The price response zone and single-period scenario reduction are specially designed for temporal decoupling, while a fine-grained bidding model is developed to meet the high-precision requirement. The proposed process and models are demonstrated through a time-shiftable-load owner who constructs piecewise linear bidding curves in a day-ahead market. Extensive case studies verify the fast computing speed and bidding revenue growth, and provide strong evidences that the proposed methodology is superior in bidding tasks.

关键词： Computational modeling Power demand Load modeling stochastic processes Linear programming Indexes Complexity theory Demand-side bidding stochastic programming fine-grained bidding model single-period scenario reduction

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