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stochastic Hydro-Thermal Scheduling Under CO₂ Emissions Constraints

IEEE TRANSACTIONS ON POWER SYSTEMS 2012年第1期27卷 58-68页

作者： Rebennack, Steffen Flach, Bruno Pereira, Mario V. F. Pardalos, Panos M. Colorado Sch Mines Div Econ & Business Golden CO 80401 USA PSR Rio De Janeiro Brazil Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

Despite the uncertainty surrounding the design of a mechanism which is ultimately accepted by nations worldwide, the necessity to implement regulations to curb emissions of greenhouse gases on a global scale is consensual. The electricity sector plays a fundamental role in this puzzle and countries may soon have to revise their operating policy directives in order to make them compatible with additional constraints imposed by such regulations. We present a modeling approach for greenhouse gas emissions quotas which can be incorporated into a stochastic dual dynamic programming algorithm, commonly used to solve the hydro-thermal scheduling problem. Our approach is flexible and capable of accommodating a detailed representation of emissions and related constraints. A case study based on the Guatemalan power system exemplifies the potential effects of considering these restrictions.

关键词： CO2 emissions hydro-thermal scheduling stochastic dual dynamic programming stochastic programming

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stochastic inflow modeling for hydropower scheduling problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期246卷 496-504页

作者： Pritchard, Geoffrey Univ Auckland Stat Auckland 1 New Zealand

We introduce a new stochastic model for inflow time series that is designed with the requirements of hydropower scheduling problems in mind. The model is an "iterated function system": it models inflow as continuous, but the random innovation at each time step has a discrete distribution. With this inflow model, hydro-scheduling problems can be solved by the stochastic dual dynamic programming (SDDP) algorithm exactly as posed, without the additional sampling error introduced by sample average approximations. The model is fitted to univariate inflow time series by quantile regression. We consider various goodness-of-fit metrics for the new model and some alternatives to it, including performance in an actual hydro-scheduling problem. The numerical data used are for inflows to New Zealand hydropower reservoirs. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： OR in energy Hydro-thermal scheduling stochastic dual dynamic programming Time series Quantile regression

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Hydropower scheduling and financial risk management

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OPTIMAL CONTROL APPLICATIONS & METHODS 2006年第1期27卷 1-18页

作者： Kristiansen, T KEMA Consulting GmbH D-53113 Bonn Germany

This paper describes a risk management tool for hydropower generators and its application to Norway's second-largest generation company and largest electricity consumer, Norsk Hydro ASA. The tool considers both operations scheduling and the utilization of financial contracts for risk management. Financial risks are accounted for by penalizing incomes below a reference income. The risk management problem is solved by a combination of stochastic dual dynamic programming and stochastic dynamic programming. Simulations demonstrate that lower income scenarios improve when risk aversion is introduced. Copyright (C) 2005 John Wiley & Sons, Ltd.

关键词： risk management generation planning stochastic dual dynamic programming

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Identifying Key Water Resource Vulnerabilities in Data-Scarce Transboundary River Basins

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WATER RESOURCES RESEARCH 2018年第8期54卷 5264-5281页

作者： Rouge, Charles Tilmant, Amaury Zaitchik, Ben Dezfuli, Amin Salman, Maher Univ Laval Dept Civil Engn & Water Engn Quebec City PQ Canada Cornell Univ Dept Civil & Environm Engn Ithaca NY 14853 USA Johns Hopkins Univ Dept Earth & Planetary Sci Baltimore MD 21218 USA NASA Global Modeling & Assimilat Off Goddard Space Flight Ctr Greenbelt MD USA Sci Syst & Applicat Inc Lanham MD USA United Nations Food & Agr Org Land & Water Div Rome Italy

This paper presents a two-step framework to identify key water resource vulnerabilities in transboundary river basins where data availability on both hydrological fluxes and the operation of man-made facilities is either limited or nonexistent. In a first step, it combines two state-of-the-art modeling tools to overcome data limitations and build a model that provides a lower bound on risks estimated in that basin. Land data assimilation (process-based hydrological modeling taking remote-sensed products as inputs) is needed to evaluate hydrological fluxes, that is, streamflow data and consumptive use in irrigated agriculture-a lower-end estimate of demand. Hydroeconomic modeling provides cooperative water allocation policies that reflect the best-case management of storage capacity under hydrological uncertainty at a monthly time step for competing uses-hydropower, irrigation. In a second step, the framework uses additional scenarios to proceed with the in-depth analysis of the vulnerabilities identified despite the use of what is by definition a best-case model. We implement this approach to the Tigris-Euphrates river basin, a politically unstable region where water scarcity has been hypothesized to serve as a trigger for the Syrian revolution and ensuing war. Results suggest that even under the framework's best-case assumptions, the Euphrates part of the basin is close to a threshold where it becomes reliant on transfers of saline water from other parts of the basin to ensure irrigation demands are met. This Tigris-Euphrates river basin application demonstrates how the proposed framework quantifies vulnerabilities that have been hitherto discussed in a mostly qualitative, speculative way.

关键词： Tigris-Euphrates hydroeconomic modeling land data assimilation data-scarce transboundary river basins stochastic dual dynamic programming vulnerability analysis

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The PAR(p) Interconfigurations model used by the Brazilian Electric Sector

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2015年第Dec.期73卷 45-55页

作者： Costa Ferreira, Pedro Guilherme Souza, Reinaldo Castro Marques Marcato, Andre Luis Brazilian Inst Econ FGVIBRE Rio De Janeiro Brazil Pontificia Univ Catolica Rio de Janeiro BR-22453 Rio De Janeiro Brazil Univ Fed Juiz de Fora Juiz De Fora Brazil

This study discusses the characteristics of the Periodic Autoregressive model, PAR(p), which is used to generate synthetic series of inflow energies that serve as entries for computer platforms that implement the planning and expansion of the operations of the BES - the Brazilian Electric Sector (SEB - Sistema Eletrico Brasileiro). The methodology for the design of a generating plant is presented in addition to the fundamentals of the "PAR(p) Interconfigurations" Model, which is referred to as the Inflow Energy Generation Model (IEGM) in this study. The major contribution of this study is to provide the first scientific discussion of the representation of multiple configurations using the PAR(p) model. For this purpose, several topics related to the time series are discussed, such as the definition of the model order, the matter of stationarity and the need to address possible outliers. Finally, a case study is presented, wherein the results of the estimation and generation of the described model's scenarios are demonstrated. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Operation planning Expansion planning stochastic optimisation stochastic dual dynamic programming

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A time series model for building scenarios trees applied to stochastic optimisation

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2015年 67卷 315-323页

作者： Cyrino Oliveira, Fernando Luiz Souza, Reinaldo Castro Marques Marcato, Andre Luis Pontif Catholica Univ Rio Janeiro PUC Rio Dept Ind Engn Rio De Janeiro Brazil Pontif Catholica Univ Rio Janeiro PUC Rio Dept Elect Engn Rio De Janeiro Brazil Univ Fed Juiz de Fora Dept Elect Engn Juiz De Fora Brazil

Given the dependence on hydrologic regimes, the uncertainty in energy planning in Brazil requires adequate and coherent stochastic modelling. The structure used to simulate synthetic series in the current Brazilian Electrical Sector model generates nonlinearity in the model equation via lognormal distribution adopted for the model residuals. This nonlinearity can cause non-convexity problems in calculating the Cost to Go Functions, which are formed by convex polyhedral approximation through piecewise linear functions. Given the above considerations, the stochastic model characteristics used to generate a scenarios tree and its use in optimisation models, this study proposes the development of an alternative methodology for scenario construction. Thus, a new general approach is proposed for constructing trees used in the stochastic optimisation processes. This simulation structure combines the computationally intensive Bootstrap technique and Monte Carlo simulation method. Scenario trees were generated using a time horizon consistent with the long-term hydrothermal dispatch planning. The synthetic series were compared to the historical series through statistical tests, which demonstrated that the developed model was sustainable during the stochastic portion of the experiment. Finally, the tree paths were applied to the stochastic dual dynamic programming, and various response variables were analysed. Such analysis support the conclusion that the model herein can reproduce structures that are compatible with the current model without nonlinearity in the stochastic model equation and non-convexity in the Cost to Go Functions. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Scenario trees Non-parametric techniques stochastic simulation stochastic dual dynamic programming

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dynamic Inventory Repositioning in On-Demand Rental Networks

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MANAGEMENT SCIENCE 2022年第11期68卷 7861-7878页

作者： Benjaafar, Saif Jiang, Daniel Li, Xiang Li, Xiaobo Univ Minnesota Dept Ind & Syst Engn Minneapolis MN 55455 USA Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Amazon Res & Dev R&D Seattle WA USA Natl Univ Singapore Dept Ind Syst Engn & Management Singapore 117576 Singapore

We consider a rental service with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers can decide on how long to keep a unit and where to return it. Because of the randomness in demand and in returns, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where, the system manager balances potential lost sales with repositioning costs. Although the problem is increasingly common in applications involving on-demand rental services, not much is known about the nature of the optimal policy for systems with a general network structure or about effective approaches to solving the problem. In this paper, first, we show that the optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory, whereas, outside the region, it is optimal to reposition but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We also provide a simple check for when a state is in the no-repositioning region. Second, we leverage the features of the optimal policy, along with properties of the optimal cost function, to propose a provably convergent approximate dynamic programming algorithm to tackle problems with a large number of dimensions.

关键词： rental networks inventory repositioning optimal policies approximate dynamic programming algorithms stochastic dual dynamic programming

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Medium-term stochastic hydrothermal scheduling with short-term operational effects for large-scale power and water networks

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APPLIED ENERGY 2024年 358卷

作者： Navarro, Andres Favereau, Marcel Lorca, Alvaro Olivares, Daniel Negrete-Pincetic, Matias Pontificia Univ Catolica Chile Dept Elect Engn Santiago 7820436 Chile Univ Andres Bello Dept Engn Sci Santiago 7500971 Chile Pontificia Univ Catolica Chile Dept Ind & Syst Engn Santiago 7820436 Chile Pontificia Univ Catolica Chile UC Energy Res Ctr Santiago 7820436 Chile Univ Adolfo Ibanez Fac Engn & Sci Santiago 7941169 Chile

The high integration of variable renewable sources in electric power systems entails a series of challenges inherent to their intrinsic variability. A critical challenge is to correctly value the water available in reservoirs in hydrothermal systems, considering the flexibility that it provides. In this context, this paper proposes a medium -term multistage stochastic optimization model for the hydrothermal scheduling problem solved with the stochastic dual dynamic programming algorithm. The proposed model includes operational constraints and simplified mathematical expressions of relevant operational effects that allow more informed assessment of the water value by considering, among others, the flexibility necessary for the operation of the system. In addition, the hydrological uncertainty in the model is represented by a vector autoregressive process, which allows capturing spatio-temporal correlations between the different hydro inflows. A calibration method for the simplified mathematical expressions of operational effects is also proposed, which allows a detailed shortterm operational model to be correctly linked to the proposed medium -term linear model. Through extensive experiments for the Chilean power system, the results show that the difference between the expected operating costs of the proposed medium -term model, and the costs obtained through a detailed short-term operational model was only 0.1%, in contrast to the 9.3% difference obtained when a simpler base model is employed. This shows the effectiveness of the proposed approach. Further, this difference is also reflected in the estimation of the water value, which is critical in water shortage situations.

关键词： OR in energy Hydrothermal scheduling Optimization under uncertainty Renewable energy stochastic dual dynamic programming

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Managing Energy Storage in Microgrids: A Multistage stochastic programming Approach

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IEEE TRANSACTIONS ON SMART GRID 2018年第1期9卷 483-496页

作者： Bhattacharya, Arnab Kharoufeh, Jeffrey P. Zeng, Bo Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA

A microgrid is a small-scale version of a centralized power grid that generates, distributes and regulates electricity flow to local entities using distributed generation and the main grid. Distributed energy storage systems can be used to mitigate adverse effects of intermittent renewable sources in a microgrid in which operators dynamically adjust electricity procurement and storage decisions in response to randomlyevolving demand, renewable supply and pricing information. We formulate a multistage stochastic programming (SP) model whose objective is to minimize the expected total energy costs incurred within a microgrid over a finite planning horizon. The model prescribes the amount of energy to procure, store and discharge in each decision stage of the horizon. However, for even a moderate number of stages, the model is computationally intractable;therefore, we customize the stochastic dual dynamic programming (SDDP) algorithm to obtain high-quality approximate solutions. Computation times and optimization gaps are significantly reduced by implementing a dynamic cut selection procedure and a lower bound improvement scheme within the SDDP framework. An extensive computational study reveals significant cost savings as compared to myopic and non-storage policies, as well as policies obtained using a two-stage SP model. The study also demonstrates the scalability of our solution procedure.

关键词： Microgrid energy storage stochastic programming stochastic dual dynamic programming

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Envelope Theorems for Multistage Linear stochastic Optimization

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OPERATIONS RESEARCH 2021年第5期69卷 1608-1629页

作者： Terca, Goncalo Wozabal, David Tech Univ Munich Sch Management Ctr Energy Markets D-80333 Munich Germany

We propose a method to compute derivatives of multistage linear stochastic optimization problems with respect to parameters that influence the problem's data. Our results are based on classical envelope theorems and can be used in problems directly solved via their deterministic equivalents as well as in stochastic dual dynamic programming for which the derivatives of the optimal value are sampled. We derive smoothness properties for optimal values of linear optimization problems, which we use to show that the computed derivatives are valid almost everywhere under mild assumptions. We discuss two numerical case studies, demonstrating that our approach is superior, both in terms of accuracy and computationally, to naive methods of computing derivatives that are based on difference quotients.

关键词： Markov decision processes sensitivity analysis stochastic dual dynamic programming semi-algebraic sets

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