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Stochastic Look-Ahead Economic Dispatch With Variable Generation Resources

IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第1期32卷 17-29页

作者： Gu, Yingzhong Xie, Le GE Energy Consulting Schenectady NY 12345 USA Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

With the continuing growth of renewable penetration in power systems, it becomes increasingly challenging to manage the operational uncertainty at near-real-time stage via deterministic scheduling approaches. This paper explores the necessity, benefits and implementability of applying stochastic programming to security constrained economic dispatch (SCED). We formulate a stochastic look-ahead economic dispatch (LAED-S) model for near-real-time power system operation. A concept of uncertainty responses is introduced to assess the power system economic risk with respect to net load uncertainties. This concept offers the system operator a simple yet effective gauge to decide whether a stochastic approach is more desirable than a deterministic one. For an efficient stochastic dispatch algorithm, an innovative hybrid computing architecture is proposed. It leverages the progressive hedging algorithm and the L-shaped method. Numerical experiments are conducted on a practical 5889-bus system to illustrate the effectiveness of the proposed approach.

关键词： L-shaped method optimal size reduction parallel computing power system economic risk progressive hedging algorithm renewable integration stochastic look-ahead dispatch uncertainty response

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Solving Lagrangian variational inequalities with applications to stochastic programming

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MATHEMATICAL PROGRAMMING 2020年第2期181卷 435-451页

作者： Rockafellar, R. Tyrrell Sun, Jie Univ Washington Dept Math Box 354350 Seattle WA 98195 USA Curtin Univ Dept Math & Stat Bentley WA 6102 Australia

Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where "multipliers" in a very general sense need to be brought in. Their stochastic version relates to problems of stochastic programming and covers not only classical formats with inequality constraints but also composite models with nonsmooth objectives. The progressive hedging algorithm, as a means of solving stochastic programming problems, has however focused so far only on optimality conditions that correspond to variational inequalities in primal variables alone. Here that limitation is removed by appealing to a recent extension of progressive hedging to multistage stochastic variational inequalities in general.

关键词： Stochastic variational inequality problems Stochastic programming problems Lagrangian variational inequalities Lagrange multipliers progressive hedging algorithm Proximal point algorithm Composite optimization

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Hybrid Stochastic-Robust Service Restoration for Wind Power Penetrated Distribution Systems Considering Subsequent Random Contingencies

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IEEE TRANSACTIONS ON SMART GRID 2022年第4期13卷 2859-2872页

作者： Cai, Sheng Zhang, Menglin Xie, Yunyun Wu, Qiuwei Jin, Xiaolong Xiang, Zhengrong Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China China Univ Geosci Sch Automat Wuhan 430074 Peoples R China Tsinghua Univ Tsinghua Shenzhen Int Grad Sch Tsinghua Berkeley Shenzhen Inst Shenzhen Peoples R China Tianjin Univ Key Lab Smart Grid Minist Educ Tianjin 30072 Peoples R China

Service restoration (SR) is essential to recovering distribution systems with outages when extreme weather conditions occur. However, the occurrence of long-duration extreme weather events may cause a restored system to become susceptible to subsequent random contingencies. To address this challenge, this paper proposes a microgrid-based SR approach for recovering critical loads in wind power penetrated distribution systems incorporating the impacts from subsequent random contingencies. A hybrid stochastic-robust optimization model is developed considering both the subsequent random contingencies that may occur and the uncertainty of wind power generation. The expected load shedding is minimized by locating mobile emergency generators, dynamically adjusting microgrid (MG) topologies, and dispatching power sources. To ensure the tractability of the optimization, the original problem is reformulated and decomposed into a master problem and several robust optimization subproblems based on the column-and- constraint generation approach. In addition, the master problem, which is in the format of stochastic optimization is solved by an improved progressive hedging algorithm to accelerate optimization. The proposed method is validated on the modified IEEE distribution systems and the simulation results show the effectiveness of the proposed SR method in reducing security violation risk and reducing the computational complexity.

关键词： Wind power generation Uncertainty Mathematical models Optimization Computational modeling Voltage Load shedding Distribution system service restoration wind power penetration potential subsequent random contingencies progressive hedging algorithm

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Solving Deterministic and Stochastic Equilibrium Problems via Augmented Walrasian

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COMPUTATIONAL ECONOMICS 2019年第1期53卷 315-342页

作者： Deride, Julio Jofre, Alejandro Wets, Roger J-B Univ Calif Davis Dept Math Davis CA 95616 USA One Shields Ave Math Sci Bldg 3125 Davis CA 95616 USA Univ Chile Ingn Matemat Santiago Chile

We described a method to solve deterministic and stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points. The numerical procedure relies on an augmentation of this bifunction. Convergence of the proposed procedure is proved by relying on the relevant lopsided convergence. In the two-stage versions of our models, deterministic and stochastic, we are mostly concerned with models that equip the agents with a mechanism to transfer goods from one time period to the next, possibly simply savings, but also allows for the transformation of goods via production.

关键词： Walras equilibrium Stochastic equilibrium Lopsided convergence Epi-convergence Augmented Walrasian progressive hedging algorithm

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Managing congestion in a multi-modal transportation network under biomass supply uncertainty

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ANNALS OF OPERATIONS RESEARCH 2019年第1-2期273卷 739-781页

作者： Poudel, Sushil R. Quddus, Md Abdul Marufuzzaman, Mohammad Bian, Linkan Burch, Reuben F., V Mississippi State Univ Dept Ind & Syst Engn Starkville MS 39759 USA

This research presents a two-stage stochastic programming model that is used to design and manage a biomass co-firing supply chain network under feedstock supply uncertainty. The model we propose extends current models by taking congestion effects into account. A non-linear cost term is added in the objective function representing the congestion factor which increases exponentially as flow of biomass approaches the capacity of multi-modal facility. We first linearize the model and then use a nested decomposition algorithm to obtain a feasible solution in a reasonable amount of time. The nested decomposition algorithm that we propose combine constraint Generation algorithm with a sample average approximation and progressive hedging (PH) algorithm. We apply some heuristics such as rolling horizon algorithm and variable fixing technique to enhance the performance of the PH algorithm. We develop a case study using data from the states of Mississippi and Alabama and use those regions to test and validate the performance of the proposed algorithm. Numerical experiments show that the proposed algorithm can solve large-scale problems with a larger number of scenarios and time periods to a near optimal solution in a reasonable amount of time. Results obtained from the experiments reveal that the delivery cost increases and less hubs with higher capacity are selected if we take congestion cost into account.

关键词： Biomass supply chain network Multi-modal facilities Constraint-generation algorithm Sample average approximation progressive hedging algorithm Rolling horizon heuristics

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RETRACTED: A mean-robustness stochastic programming model for p-hub median problem (Retracted Article)

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INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING EDUCATION 2019年第1-Sup期60卷 1622-1631页

作者： Ge, Wei Nangjing Univ Posts & Telecommun Coll Management Nanjing Jiangsu Peoples R China

A mean-robustness stochastic programming model is developed for a p-hub median problem to balance the overall system efficiency and robustness under demand and cost uncertainties. A solution algorithm based on scenario decomposition is designed to overcome computational challenges brought by the large size of the problem. The proposed modeling and computing methods are tested in the case study using a real-world China aviation dataset. The result shows the effect of our algorithm and the importance of adopting mean-robustness by the comparison over expectation model and deterministic model.

关键词： p-hub median problem mean-robustness augmented Lagrangian relaxation progressive hedging algorithm

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Multistage Stochastic Investment Planning With Multiscale Representation of Uncertainties and Decisions

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第1期33卷 781-791页

作者： Liu, Yixian Sioshansi, Ramteen Conejo, Antonio J. Ohio State Univ Dept Integrated Syst Engn Columbus OH 43210 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

We propose a multistage multiscale linear stochastic model to optimize electricity generation, storage, and transmission investments over a long planning horizon. The multiscale structure captures "large-scale" uncertainties, such as investment and fuel-cost changes and long-run demand-growth rates, and "smallscale" uncertainties, such as hour-to-hour demand and renewable-availability uncertainty. The model also includes a detailed treatment of operating periods so that the effect of dispatch decisions on long-term investments are captured. The proposed model can be large in size. The progressive hedging algorithm is applied to decompose the model by scenario, greatly reducing computation times. We also derive bounds on the optimal objective-function value, to assess solution quality. We use a case study based on the state of Texas to demonstrate the model and show the benefits of its detailed representation of the operating periods in making investment decisions.

关键词： Decomposition power system planning progressive hedging algorithm stochastic optimization

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Dynamic portfolio optimization: Time decomposition using the Maximum Principle with a scenario approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第1期163卷 217-229页

作者： Barro, D Canestrelli, E Univ Venice Dipartimento Matemat Applicata I-30123 Venice Italy

We study a dynamic portfolio management problem over a finite horizon with transaction costs and a risk averse objective function. We assume that the uncertainty faced by the investor can be modelled or approximated using discrete probability distributions via a scenario approach. To solve the resulting optimization problem we use stochastic programming techniques;in particular a scenario decomposition approach. To take advantage of the structure of the portfolio problem we propose a further decomposition obtained by means of a discrete version of the Maximum Principle. The result is a double decomposition of the original problem: The first, given by the scenario approach, focuses on the stochastic aspect of the problem while the second, using the discrete Maximum Principle, concerns the dynamics over time. Applying the double decomposition to our portfolio problem yields a simpler and more direct solution approach which we illustrate with examples. (C) 2004 Elsevier B.V. All rights reserved.

关键词： Stochastic programming scenarios dynamic portfolio progressive hedging algorithm maximum principle

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Dynamic Portfolio Optimization for Utility-Based Models

Dynamic Portfolio Optimization for Utility-Based Models

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International Conference on Information and Financial Engineering

作者： Fulga, Cristinca INCREST Bucharest Dept Math R-79622 Bucharest Romania

ISBN: (纸本)9780769536064

Portfolio management deals with the allocation of wealth among different investment opportunities, considering investor's preferences on risk. In this paper we consider a multiperiod model where the investor rebalances a portfolio at the beginning of each period facing uncertainty associated with the prices of the assets at future dates. Models of this decision problem tend to become very large because of the dynamic structure and uncertainty. We present a multiple period portfolio model over a finite horizon with transaction costs, a risk averse utility function and the uncertainty modeled using the scenario approach. We propose a new method for efficiently solving real problems;the procedure utilizes stochastic programming combined with decomposition and approximating techniques. Solving the resulting optimization problem relies on approximate dynamic programming techniques. The technique used for solving the portfolio problem provides a method whose effectiveness is proved by the experimental results.

关键词： Dynamic Portfolio Optimization progressive hedging algorithm Approximate Dynamic Programming

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Stochastická optimalizace toků v sítích

Stochastická optimalizace toků v sítích

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作者： Málek, Martin Brno University of Technology

Magisterská práce se zabývá stochastickou optimalizací síťových úloh. Teoretická část pokrývá tři témata - teorii grafů, optimalizaci a progressive hedg... 详细信息

Magisterská práce se zabývá stochastickou optimalizací síťových úloh. Teoretická část pokrývá tři témata - teorii grafů, optimalizaci a progressive hedging algoritmus. V rámci optimalizace je hlavní část věnována stochastickému programování a dvoustupňovému programování. Progressing hedging algoritmus zahrnuje také metodu přiřazování scénářů a modifikaci obecného algoritmu na dvou stupňové úlohy. Praktická část je věnována modelům na reálných datech z oblasti svozu odpadu v rámci České republiky. Data poskytl Ústav procesního inženýrství.

关键词： Teorie grafů toky v sítích stochastické programování dvoustupňová optimalizace progressive hedging algoritmus Graph theory network flows stochastic programming two-stage optimization progressive hedging algorithm Text

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