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Hybrid simplicial-randomized approximate stochastic dynamic programming for multireservoir optimization

COMPUTATIONAL MANAGEMENT SCIENCE 2024年第1期21卷 31-31页

作者： Zephyr, Luckny Lamond, Bernard F. Lang, Pascal Laurentian Univ Sch Business Adm Barthi Sch Engn & Comp Sci Cross Appointment Sudbury ON P3E 2C6 Canada Univ Laval Dept Operat & Syst Decis Quebec City PQ G1V 0A6 Canada

We revisit an approximate stochastic dynamic programming method that we proposed earlier for the optimization of multireservoir problems. The method exploited the convexity properties of the value function to sample the reservoir level space based on the local curvature of the value function, which is estimated by the difference between a lower and an upper bounds (error bound). Unlike the previous approach in which the state space is exhaustively partitioned into full dimensional simplices whose vertices formed a discrete grid over which the value function was approximated, here we propose instead a new randomized approach for selecting the grid points from a small number of randomly sampled simplices from which an error bound is estimated. Results of numerical experiments on three literature test problems and simulated midterm reservoir optimization problems illustrate the advantages of the randomized approach which can solve models of higher dimensions than with the exhaustive approach.

关键词： Reservoir optimization stochastic dynamic programming Simplicial-randomized approximation Piecewise linear approximation

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Evaluation of photovoltaic storage systems on energy markets under uncertainty using stochastic dynamic programming

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ENERGY ECONOMICS 2022年 106卷 1页

作者： Keles, Dogan Dehler-Holland, Joris Tech Univ Denmark Dept Technol Management & Econ Akademivej 358 DK-2800 Kgy Lyngby Denmark Karlsruhe Inst Technol Chair Energy Econ Hertzstr 16 D-76187 Karlsruhe Germany

The rising share of intermittent renewable energy production in energy systems increasingly poses a threat to system stability and the price level in energy markets. However, the effects of renewable energy production onto electricity markets also give rise to new business opportunities. The expected increase in price differences increases the market potential for storage applications and combinations with renewable energy production. The value of storage depends critically on the operation of the storage system. In this study, we evaluate large-scale photovoltaic (PV) storage systems under uncertainty, as renewable energy production and electricity prices are fundamentally uncertain. In comparison to households who largely consume the stored energy themselves, the major business case for large-scale PV and storage systems is arbitrage trading on the electricity markets. The operation problem is formulated as a Markov decision process (MDP). Uncertainties of renewable energy production are integrated into an electricity price model using ARIMA-type approaches and regime switching. Due to non-stationarity and heteroskedasticity of the underlying processes, an appropriate stochastic modeling procedure is developed. The MDP is solved using stochastic dynamic programming (SDP) and recombining trees (RT) to reduce complexity taking into account the different time scales in which decisions have to be taken. We evaluate the solution of the SDP problem against Monte Carlo simulations with perfect foresight and against a storage dispatch heuristic. The program is applied to the German electricity and reserve power market to show the potential increase in storage value with higher price spreads, and evaluate a possible imposition of the feed-in levy onto energy directly stored from the common grid.

关键词： PV storage Energy markets Markov decision process ARMA process stochastic dynamic programming

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COMPARISON OF stochastic AND DETERMINISTIC dynamic programming FOR RESERVOIR OPERATING RULE GENERATION

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JAWRA Journal of the American Water Resources Association 1987年第1期23卷 1-9页

作者： Karamouz, Mohammad Houck, Mark H. Department of Civil and Enviromnental Engineering Polytechnic University Brooklyn New York 11201 333 Jay St United States School of Civil Engineering Purdue University West Lafayette Indiana 47907 United States

ABSTRACT: Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag‐one Markov process. To test the usefulness of both models in generating reservoir operating rules, real‐time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs. Copyright © 1987, Wiley Blackwell. All rights reserved

关键词： deterministic dynamic programming optimization reservoir operation stochastic dynamic programming water resources management

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stochastic Dual dynamic programming to Schedule Energy Storage Units Providing Multiple Services

Stochastic Dual Dynamic Programming to Schedule Energy Stora...

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PowerTech, 2015 IEEE Eindhoven

作者： Megel, Olivier Mathieu, Johanna L. Andersson, Goran Swiss Fed Inst Technol Power Syst Lab Zurich Switzerland Univ Michigan Elect & Comp Engn Ann Arbor MI 48109 USA

ISBN: (纸本)9781479976959

When energy storage units, such as batteries, are installed to support photovoltaics and defer power system upgrades they are inactive or only partially used most of time. Their unused capacities could be used to provide frequency control, allowing them to generate additional revenues. However, the challenge is to decide how much of their energy and power capacities to allocate to either service. Photovoltaic generation profiles are difficult to forecast accurately, and frequency deviation is a highly stochastic process. This paper develops a stochastic Dual dynamic programming (SDDP) approach to generate decision rules for determining how much capacity to assign to each service at each time step, depending on the time of day and the storage energy level. Unlike stochastic dynamic programming (SDP), our approach does not require us to discretize the state and decision spaces. We show that, when storage efficiency is high, SDDP outperforms SDP, but when short computation times are required, SDP may be preferred. We also discuss challenges associated with using SDDP when storage efficiency is lower than unity. Finally, we show that the number of tuning parameters is lower for SDDP than for SDP, and that the relation between tuning parameters and policy quality is more intuitive for SDDP than for SDP.

关键词： Batteries stochastic dynamic programming stochastic Dual dynamic programming Frequency Control

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A stochastic Dual dynamic programming Framework for Multiscale MPC

A Stochastic Dual Dynamic Programming Framework for Multisca...

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6th International-Federation-of-Automatic-Control (IFAC) Conference on Nonlinear-Model-Predictive-Control (NMPC)

作者： Kumar, Ranjeet Wenzel, Michael J. Ellis, Matthew J. ElBsat, Mohammad N. Drees, Kirk H. Zavala, Victor M. Univ Wisconsin Madison Dept Chem & Biol Engn Madison WI 53706 USA Johnson Controls Int 507 E Michigan St Milwaukee WI 53202 USA

We derive and interpret stochastic dual dynamic programming (SDDP) from the perspective of MPC to argue that SDDP provides a scalable approach to handle complex MPC applications with uncertainties evolving over long time horizons and with fine time resolutions. Scalability is enabled by the use of a nested cutting-plane scheme, which uses forward and backward sweeps along the time horizon to adaptively construct and refine cost to -go functions. SDDP can also select random paths on-the-fly, thus avoiding the exponential complexity associated with the construction of scenario trees and enabling the construction of statistical performance bounds. Our work seeks to establish connections between SDDP and MPC that allow us to obtain performance bounds for deterministic and stochastic MPC and to propose new MPC schemes that can deal with multiple timescales. We demonstrate the developments using a stationary battery system that participates in multiscale energy markets. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： multiscale MPC stochastic dynamic programming duality energy systems

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stochastic Dual dynamic programming to Schedule Energy Storage Units Providing Multiple Services

Stochastic Dual Dynamic Programming to Schedule Energy Stora...

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IEEE Eindhoven PowerTech Conference

作者： Olivier Megel Johanna L. Mathieu Goran Andersson ETH Zurich Power Systems Laboratory Zurich Switzerland Electrical and Computer Engineering University of Michigan Ann Arbor USA

关键词： Batteries stochastic dynamic programming stochastic Dual dynamic programming Frequency Control

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Modified dynamic programming algorithms for GLOSA systems with stochastic signal switching times

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2023年 157卷

作者： Typaldos, Panagiotis Papageorgiou, Markos Tech Univ Crete Sch Prod Engn & Management Dynam Syst & Simulat Lab Khania 73100 Greece Ningbo Univ Fac Maritime & Transportat Ningbo Peoples R China

A discrete-time stochastic optimal control problem was recently proposed to address the GLOSA (Green Light Optimal Speed Advisory) problem in cases where the next signal switching time is decided in real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (stochastic dynamic programming) calls for substantial computation time, which excludes problem solution in the vehicle's on-board computer in real time. In this context, the present paper concentrates on the challenge of developing numerical algorithms to solve efficiently the stochastic GLOSA problem. As a first attempt to overcome the computation time bottleneck, a modified version of dynamic programming, known as Discrete Differential dynamic programming (DDDP) was recently employed for the numerical solution of the stochastic optimal control problem and was demonstrated to achieve results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly reduced computation times. After an outline of the DDDP approach, the present work considers a second modified version of dynamic programming, known as Differential dynamic programming (DDP). For the stochastic GLOSA problem, it is demonstrated that DDP achieves quasi-instantaneous (extremely fast) solutions in terms of CPU times, which allows for the proposed approach to be readily executable online, in an MPC (Model Predictive Control) framework, in the vehicle's on-board computer. The novel numerical approach is tested and demonstrated by use of realistic examples and is compared to the SDP and DDDP solutions. It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions.

关键词： GLOSA stochastic dynamic programming Discrete Differential dynamic programming (DDDP) Differential dynamic programming (DDP) Traffic light advisory

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stochastic dynamic resource allocation for HIV prevention and treatment: An approximate dynamic programming approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 118卷 423-439页

作者： Cosgun, Ozlem Buyuktahtakin, I. Esra Wichita State Univ Dept Ind & Mfg Engn Wichita KS 67260 USA New Jersey Inst Technol Dept Mech & Ind Engn Newark NJ 07102 USA

Human immunodeficiency virus (HIV) is a key global health concern, with 33 million people living with HIV worldwide and 2.7 million new infections occurring annually. To prevent the spread of this widely prevalent epidemic disease, prevention and treatment intervention strategies urgently need to be implemented. The goal of this study is to propose stochastic dynamic programming (SDP) and approximate dynamic programming (ADP) algorithms that will optimally allocate the limited intervention budget among the HIV disease compartments and determine the best set of interventions that should be applied to each disease compartment, while minimizing the number of HIV-infected and people diagnosed with acquired immune deficiency syndrome (AIDS) as well as related deaths over a multi-year planning horizon. A compartmental model is constructed and formulated as a nonstationary Markov decision process (MDP) in order to capture the progression of the disease among the highest risk group-African American/black men who have sex with men (BMSM). In order to alleviate the computational difficulties arising from the exponentially growing state space in the SDP, we propose ADP algorithms that determine the approximately optimal budget allocation policies over six years. Our results suggest a greater allocation of the limited budget to prevention measures rather than treatment interventions, such as antiretroviral therapy (ART). As opposed to traditional policies that allocate the budget only once at the beginning of the time horizon, the ADP model suggests using a dynamic proportional budget strategy, allocating the budget dynamically over a multi-period planning period as the uncertainty in disease transmission is revealed. Results show that our ADP approach provides significant increases in health benefits and cost savings in HIV prevention and intervention.

关键词： HIV epidemic disease Resource allocation Interventions Approximate dynamic programming stochastic dynamic programming Disease transmission uncertainty Markov decision process (MDP)

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An approximate dynamic programming approach to solving a dynamic, stochastic multiple knapsack problem

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2009年第3期16卷 347-359页

作者： Perry, Thomas C. Hartman, Joseph C. LSI Log Allentown PA USA Univ Florida Gainesville FL USA

We model a multiperiod, single resource capacity reservation problem as a dynamic, stochastic, multiple knapsack problem with stochastic dynamic programming. As the state space grows exponentially in the number of knapsacks and the decision set grows exponentially in the number of order arrivals per period, the recursion is computationally intractable for large-scale problems, including those with long horizons. Our goal is to ensure optimal, or near optimal, decisions at time zero when maximizing the net present value of returns from accepted orders, but solving problems with short horizons introduces end-of-study effects which may prohibit finding good solutions at time zero. Thus, we propose an approximation approach which utilizes simulation and deterministic dynamic programming in order to allow for the solution of longer horizon problems and ensure good time zero decisions. Our computational results illustrate the effectiveness of the approximation scheme.

关键词： stochastic dynamic programming approximate dynamic programming simulation

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dynamic programming in a heuristically confined state space: a stochastic resource-constrained project scheduling application

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 1039-1058页

作者： Choi, J Realff, MJ Lee, JH Georgia Inst Technol Sch Chem & Biomol Engn Ctr Proc Syst Engn Atlanta GA 30332 USA

The resource-constrained project scheduling problem (RCPSP) is a significant challenge in highly regulated industries, such as pharmaceuticals and agrochemicals, where a large number of candidate new products must undergo a set of tests for certification. We propose a novel way of addressing the uncertainties in the RCPSP including the uncertainties in task durations and costs, as well as uncertainties in the results of tasks (success or failure) by using a discrete time Markov chain, which enables us to model probabilistic correlation of the uncertain parameters. The resulting stochastic optimization problem can be solved by using dynamic programming, but the computational load renders this impractical. Instead, we develop a new way to combine heuristic solutions through dynamic programming in the state space that the heuristics generate. The proposed approach is tested on a simplified version of RCPSP that has a fairly complicated stochastic nature, with 1,214,693,756 possible parameter realizations (scenarios), and involves five projects and 17 tasks. As a result, an on-line policy is obtained, which can use the information states in on-line decision making and improve the heuristics rather than a fixed solution obtained by the previous mathematical programming (MILP) problem formulations. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： stochastic dynamic programming Markov chain project scheduling combinatorial optimization heuristics

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