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作者： Golari, Mehdi The University of Arizona

学位级别：Ph.D.

Electric energy constitutes one of the most crucial elements to almost every aspect of life of people. The modern electric power systems face several challenges such as efficiency, economics, sustainability, and reliability. Increase in electrical energy demand, distributed generations, integration of uncertain renewable energy resources, and demand side management are among the main underlying reasons of such growing complexity. Additionally, the elements of power systems are often vulnerable to failures because of many reasons, such as system limits, weak conditions, unexpected events, hidden failures, human errors, terrorist attacks, and natural disasters. One common factor complicating the operation of electrical power systems is the underlying uncertainties from the demands, supplies and failures of system components. stochastic programming provides a mathematical framework for decision making under uncertainty. It enables a decision maker to incorporate some knowledge of the intrinsic uncertainty into the decision making process. In this dissertation, we focus on application of two-stage and multistage stochastic programming approaches to electric energy systems modeling and optimization. Particularly, we develop models and algorithms addressing the sustainability and reliability issues in power systems. First, we consider how to improve the reliability of power systems under severe failures or contingencies prone to cascading blackouts by so called islanding operations. We present a two-stage stochastic mixed-integer model to find optimal islanding operations as a powerful preventive action against cascading failures in case of extreme contingencies. Further, we study the properties of this problem and propose efficient solution methods to solve this problem for large-scale power systems. We present the numerical results showing the effectiveness of the model and investigate the performance of the solution methods. Next, we address the sustainability issue co

关键词： multistage stochastic programming Renewable Energy Integration Systems & Industrial Engineering Energy systems optimization

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Limited multistage stochastic programming for Water Distribution Systems Optimal Operation

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2016年第10期142卷 1-6页

作者： Schwartz, Rafael Housh, Mashor Ostfeld, Avi Technion Israel Inst Technol Fac Civil & Environm Engn IL-32000 Haifa Israel Univ Haifa Dept Nat Resources & Environm Management IL-31905 Haifa Israel

Least-cost operation of water distribution systems (WDS) is a well-known problem in water distribution systems optimization. The formulation of the problem started with deterministic modeling, and the problem was subsequently handled with more sophisticated stochastic models that incorporate uncertainties related to the problem's parameters. This work applied a recently developed algorithm entitled limited multistage stochastic programming (LMSP) to deal with the stochastic formulation of the least-cost operation of WDS and serves merely as a proof of concept on an illustrative network. The demand is considered as the uncertain parameter in the problem formulation. This algorithm reduces the complexity of the classical multistage stochastic programming (MSP) by adding constraints which result in a linear growth of the problem, as opposed to an exponential growth in the MSP problem. This is accomplished by clustering decision variables based on a postanalysis of the implicit stochastic program of the problem. The clusters allow reduction of the number of decision variables, thus reducing the complexity of the optimization problem. The LMSP is expected to increase the cost because of the additional constraints imposed on the problem;however, a trade-off exists between the computational complexity and the optimality of the objective value to the number of clusters considered. An illustrative example application is provided for demonstrating the suggested methodology abilities.

关键词： multistage stochastic programming Limited multistage stochastic programming Water distribution system Operation Optimization

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FiWi Network Planning for Smart Metering Based on multistage stochastic programming

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IEEE LATIN AMERICA TRANSACTIONS 2015年第12期13卷 3838-3843页

作者： Peralta, A. Inga, E. Hincapie, R. Univ Politecn Salesiana Cuenca Ecuador Univ Politecn Salesiana Engn Quito Ecuador Univ Pontificia Bolivariana Telecommun Engn Medellin Colombia

This article presents a novel model of mixed integer linear programming (MILP) to conduct network planning (Fiber-Wireless-FiWi) that along a timeline space facilitates growth, expansion and scalability of resources involved in communications network, traditionally used in cellular telephony, and is possible that extends as a multiservice network to provide smart metering, as is the case in Advanced Metering Infrastructure (AMI) in Smart Grid, thus optimizing their infrastructure and minimizing investment costs. This paper proposes a hybrid architecture (fiber optic-wireless networks) with realistic approaches to planning and scalability considerations under scenarios that present uncertainty in the evolution of consumer demand, both for primary users of cell phone and smart metering as a secondary user. We propose a model for network planning based on multistage stochastic programming (MSP) with a growth in demand for stochastic users and FiWi networks scalability through expected maximum benefit for their investment. The approach of this article shows that it is possible to design real FiWi large-scale networks under a cost-effective evolution considering a scheme appropriate growth in the timeline.

关键词： smart grid advanced metering infrastructure scalability network planning fiwi network multistage stochastic programming optimization

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multistage stochastic programming approach for offshore oilfield infrastructure planning under production sharing agreements and endogenous uncertainties

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2014年 124卷 180-197页

作者： Gupta, Vijay Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

The paper presents a new optimization model and solution approach for the investment and operations planning of offshore oil and gas field infrastructure. As compared to the conventional models where either fiscal rules or uncertainty in the field parameters is considered, the proposed model is the first one in the literature that includes both of these complexities in an efficient manner. In particular, a tighter formulation for the production sharing agreements based on our recent work, and a perfect positive or negative correlation among the endogenous uncertain parameters (field size, oil deliverability, water-oil ratio and gas-oil ratio) is considered to reduce the total number of scenarios in the resulting multistage stochastic formulation. To solve the large instances of the problem, a Lagrangean decomposition approach allowing parallel solution of the scenario subproblems is implemented in the GAMS grid computing environment. Computational results on a variety of oilfield development planning examples are presented to illustrate the efficiency of the model and the proposed solution approach. (c) 2014 Elsevier B.V. All rights reserved.

关键词： multistage stochastic programming endogenous uncertainties non-anticipativity constraints Lagrangean decomposition oil & gas exploration production sharing agreements

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stochastic dual dynamic programming for multistage stochastic mixed-integer nonlinear optimization

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MATHEMATICAL programming 2022年第1-2期196卷 935-985页

作者： Zhang, Shixuan Sun, Xu Andy Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA MIT Sloan Sch Management Operat Res Ctr 77 Massachusetts Ave Cambridge MA 02139 USA

In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient is a new type of cuts based on generalized conjugacy. Several interesting classes of MS-MINLP are identified, where the new algorithms are guaranteed to obtain the global optimum without the assumption of complete recourse. This significantly generalizes the classic SDDP algorithms. We also characterize the iteration complexity of the proposed algorithms. In particular, for a (T + 1)-stage stochastic MINLP satisfying L-exact Lipschitz regularization with d-dimensional state spaces, to obtain an e-optimal root node solution, we prove that the number of iterations of the proposed deterministic sampling algorithm is upper bounded by O((2LT/epsilon)(d)), and is lower bounded by O((LT/4 epsilon)(d)) for the general case or by O((LT/8 epsilon)(d/2-1)) for the convex case. This shows that the obtained complexity bounds are rather sharp. It also reveals that the iteration complexity depends polynomially on the number of stages. We further show that the iteration complexity depends linearly on T, if all the state spaces are finite sets, or if we seek a (T epsilon)-optimal solution when the state spaces are infinite sets, i.e. allowing the optimality gap to scale with T. To the best of our knowledge, this is the first work that reports global optimization algorithms as well as iteration complexity results for solving such a large class of multistage stochastic programs. The iteration complexity study resolves a conjecture by the late Prof. Shabbir Ahmed in the general setting of multistage stochastic mixed-integer o

关键词： multistage stochastic programming MINLP SDDP Complexity analysis

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Data-Driven multistage Distribuionally Robust programming to Hydrothermal Economic Dispatch With Renewable Energy Sources

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2024年第4期15卷 2322-2335页

作者： Zhang, Xiaosheng Ding, Tao Xiao, Yang Zhang, Hongji Liu, Jinbo Wang, Yishen Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Peoples R China Natl Power Dispatching & Control Ctr Beijing 100032 Peoples R China State Grid Smart Grid Res Inst Co Ltd Beijing 102209 Peoples R China

The multistage solution is very important to achieve optimal hydrothermal economic dispatch considering the uncertainty of renewable energy sources. In data-driven settings, only some historical trajectories are available and the probability distribution is unknown. A data-driven scheme for multistage stochastic hydrothermal economic dispatch with Markovian uncertainties is proposed in this paper. Then a data-driven distributionally robust stochastic dual dynamic programming (DDR-SDDP) is proposed to tackle the corresponding computational intractability, where the conditional probability distributions are estimated by using kernel regression. The out-of-sample performances are improved by distributionally robust optimization on a Wasserstein distance-based ambiguity set. Furthermore, a scenario aggregation method is designed to reduce the computational burden. Numerical results for a practical regional power system in China are presented and analyzed to verify the effectiveness of the proposed method.

关键词： Economic dispatch renewable energy data-driven multistage stochastic programming data-driven distributionally robust dual stochastic dual dynamic programming Economic dispatch renewable energy data-driven multistage stochastic programming data-driven distributionally robust dual stochastic dual dynamic programming

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Inexact multistage Fuzzy-stochastic programming Model for Water Resources Management

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2015年第11期141卷 04015027-04015027页

作者： Chen, Fang Huang, G. H. Fan, Y. R. Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Univ Regina Inst Energy Environm & Sustainabil Res UR NCEPU Regina SK S4S 0A2 Canada North China Elect Power Univ Inst Energy Environm & Sustainabil Res UR NCEPU Beijing 102206 Peoples R China

In this study, an inexact multistage fuzzy-stochastic programming (IMFSP) model was developed for water resources management under uncertainty. In the IMFSP model, the uncertainties existing in the objective functions, and the constraints' left side and right side are expressed as fuzzy sets so that the uncertainties can be directly communicated into the optimization process and various water allocation schemes can be obtained under different a-cut levels at a plurality of periods regardless of the shapes of their membership functions. The IMFSP model can not only generate the most possible, lower and upper bound values for all possible decision schemes but it can also provide information about the degrees of membership of the decision variables between the lower and upper bound values. Meanwhile, the scenario-based multistage stochastic programming was incorporated in the IMFSP model to adequately reflect the dynamic variations and uncertain information of the water resources system. Therefore, the IMFSP model offers significant improvements over existing multistage stochastic programming models for water resources management with respect to the capacity of tackling various uncertainties and their interrelationships. Additionally, a simple hypothetical case for water resources management was provided for demonstrating applicability of the IMFSP model to support decision making within multiple scenarios during many time periods under uncertainty. In general, the proposed IMFSP has only been demonstrated and tested on a hypothetical example. Future research can be directed toward expanding/testing it on more complex real-world problems. (C) 2015 American Society of Civil Engineers.

关键词： multistage stochastic programming Water resources management Decision making Fuzzy sets Uncertainty

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Bounds in multistage Linear stochastic programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第1期163卷 200-229页

作者： Maggioni, Francesca Allevi, Elisabetta Bertocchi, Marida Bergamo Univ Dept Management Econ & Quantitat Methods I-24127 Bergamo Italy Univ Brescia Dept Econ & Management I-25122 Brescia Italy

multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.

关键词： multistage stochastic programming Expected value problem Value of stochastic solution Skeleton solution

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Capacity planning of renewable energy systems using stochastic dual dynamic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第2期322卷 573-588页

作者： Hole, J. Philpott, A. B. Dowson, O. Univ Auckland Elect Power Optimizat Ctr Auckland New Zealand Norwegian Univ Sci & Technol Trondheim Norway Norwegian Water Resources & Energy Directorate Oslo Norway

We present a capacity expansion model for deciding the new electricity generation and transmission capacity to complement an existing hydroelectric reservoir system. The objective is to meet a forecast demand at least expected cost, namely the capital cost of the investment plus the expected discounted operating cost of the system. The optimal operating policy for any level of capacity investment can be computed using stochastic dual dynamic programming. We show how to combine a multistage stochastic operational model of the hydro system with a capacity expansion model to create a single model that can be solved by existing open-source solvers for multistage stochastic programs without the need for customized decomposition algorithms. We illustrate our method by applying it to a model of the New Zealand electricity system and comparing the solutions obtained with those found in a previous study.

关键词： OR in energy stochastic dual dynamic programming Capacity expansion multistage stochastic programming Policy graph

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Column generation for multistage stochastic mixed-integer nonlinear programs with discrete state variables

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JOURNAL OF GLOBAL OPTIMIZATION 2025年 1-32页

作者： Rathi, Tushar Riley, Benjamin P. Flores-Quiroz, Angela Zhang, Qi Univ Minnesota Dept Chem Engn & Mat Sci Minneapolis MN 55455 USA Univ Chile Dept Elect Engn Santiago Chile Inst Sistemas Complejos Ingn Santiago Chile

stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty;however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the presence of discrete decisions and nonlinearities. In this work, we consider multistage stochastic mixed-integer nonlinear programs (MINLPs) with discrete state variables, which exhibit a decomposable structure that allows its solution using a column generation approach. Following a Dantzig-Wolfe reformulation, we apply column generation such that each pricing subproblem is an MINLP of much smaller size, making it more amenable to global MINLP solvers. We further propose a method for generating additional columns that satisfy the nonanticipativity constraints, leading to significantly improved convergence and optimal or near-optimal solutions for many large-scale instances in a reasonable computation time. The effectiveness of the tailored column generation algorithm is demonstrated via computational case studies on a multistage blending problem and a problem involving the routing of mobile generators in a power distribution network.

关键词： multistage stochastic programming Mixed-integer nonlinear programs (MINLPs) Column generation Stability in column generation Distributed computing

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