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Inflow Aggregation and Run-of-the-River Inflow Energy for Reducing Dimensionality in the Long-Term Generation Scheduling Problem

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IEEE ACCESS 2021年 9卷 98542-98560页

作者： Minetto Fredo, Guilherme Luiz Finardi, Erlon Cristian Larroyd, Paulo Vitor Picarelli, Lucas Borges Univ Fed Santa Catarina Dept Elect & Elect BR-88040900 Florianopolis SC Brazil INESC P&D Brasil BR-11055300 Santos SP Brazil Norus BR-88036003 Florianopolis SC Brazil Norte Energia SA BR-70390025 Brasilia DF Brazil

The long-term generation scheduling (LTGS) problem aims to build an operating policy over a multi-year planning horizon, correlating thermal generation and deficit costs with water storage. The LTGS is modeled as a linear multistage stochastic program, whose state-of-art solution is the stochastic dual dynamic programming (SDDP). One critical challenge is to represent the time-dependency of river inflows accurately. Despite recent advances, modeling simplifications are needed to allow the LTGS computational tractability via SDDP since it is necessary to increase the state space to include the time-dependent variables properly. Thus, most works simplify the hydro production function (HPF) to represent the inflows in detail to overcome this negative aspect. However, the literature lacks this trade-off, i.e., finding a balance between stochastic inflow modeling and HPF representation. Thus, this paper proposes an alternative approach to analyzing this trade-off, using the inflow aggregation and run-of-the-river energy inflow instead of individual inflow in SDDP. The proposed approach drastically reduces the number of state variables in SDDP, allowing a detailed HPF representation in the LTGS. We employ a one-sided confidence interval for expected cost estimation to show that our approach provides better performance than the individualized inflows. The analysis is performed in several large-scale computational instances using a power system with 53 geographically widespread hydro plants. The numerical results demonstrate that inflow aggregation provides, on average, a 4 % reduction on the operating cost, whereas for the run-of-the-river inflow energy, the reduction is, on average, 2 %.

关键词： Computational modeling stochastic processes Reservoirs Planning Hydroelectric power generation dynamic programming Analytical models Inflow modeling hydro production function the long-term generation scheduling problem stochastic dual dynamic programming run-of-the-river inflow energy

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stochastic Hydro-Thermal Scheduling Under CO₂ Emissions Constraints

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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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Assessing solution quality and computational performance in the long-term generation scheduling problem considering different hydro production function approaches

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RENEWABLE ENERGY 2019年 131卷 45-54页

作者： Minetto Fredo, Guilherme Luiz Finardi, Erlon Cristian de Matos, Vitor Luiz Fed Univ Santa Catarina UFSC Elect Syst Planning Res Lab LabPlan Florianopolis SC Brazil Plan4 Engn Lauro Linhares 2055 Room 201 BR-88036003 Florianopolis SC Brazil

The long-term generation scheduling (LTGS) problem aims at finding a generation policy that minimizes an objective function over a multi-year planning horizon. A crucial aspect of this problem is the Hydropower Production Function (HPF), which relates power with head, turbined outflow, and efficiency of the generating units. Given that the LTGS is a large-scale stochastic optimization problem, the HPF is modeled in a simplified manner. However, considering the high-performance computers currently available and the recent advances in stochastic optimization algorithms, it is possible to enhance the HPF modeling to use the energy resources more efficiently. This paper proposes a piecewise linear model of HPF that considers the plant generation as a function of the volume and the total outflow. Unlike previous works, the HPF also considers the (nonlinear) efficiency function of each generating unit. The paper also presents a comparison between the proposed HPF and a one-dimensional HPF known as constant productivity. The generation policy and the computational burden are analyzed using an optimization simulation process based on stochastic dual dynamic programming algorithm. The computational tests use data of a large-scale electrical power system, which corresponds to about 90% of the Brazilian system. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Hydropower production function Long-term generation scheduling problem Piecewise linear model Constant productivity model 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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