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Regularized stochastic dual dynamic programming for convex nonlinear optimization problems

OPTIMIZATION AND ENGINEERING 2020年第3期21卷 1133-1165页

作者： Guigues, Vincent Lejeune, Miguel A. Tekaya, Wajdi FGV Praia Botafogo Sch Appl Math Rio De Janeiro Brazil George Washington Univ Washington DC 20052 USA Quant Dev Hammam Chatt 1164 Tunisia

We define a regularized variant of the dual dynamic programming algorithm called DDP-REG to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the stochastic dual dynamic programming (SDDP) algorithm recently introduced which was studied for linear problems only and with less general prox-centers. We show the convergence of DDP-REG and SDDP-REG. We assess the performance of DDP-REG and SDDP-REG on portfolio models with direct transaction and market impact costs. In particular, we propose a risk-neutral portfolio selection model which can be cast as a multistage stochastic second-order cone program. The formulation is motivated by the impact of market impact costs on large portfolio rebalancing operations. Numerical simulations show that DDP-REG is much quicker than DDP on all problem instances considered (up to 184 times quicker than DDP) and that SDDP-REG is quicker on the instances of portfolio selection problems with market impact costs tested and much faster on the instance of risk-neutral multistage stochastic linear program implemented (8.2 times faster).

关键词： stochastic optimization stochastic dual dynamic programming Regularization Portfolio selection Market impact costs

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On the solution variability reduction of stochastic dual dynamic programming applied to energy planning

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期258卷 743-760页

作者： Soares, Murilo Pereira Street, Alexandre Valladao, Davi Michel Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Elect Engn Rua Marques de Sao Vicente 225 BR-22451900 Gavea Rio De Janeiro RJ Brazil Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Ind Engn Rua Marques de Sao Vicente 225 BR-22451900 Gavea Rio De Janeiro RJ Brazil

In the hydrothermal energy operation planning of Brazil and other hydro-dependent countries, stochastic dual dynamic programming (SDDP) computes a risk-averse optimal policy that often considers river inflow autoregressive models. In practical applications, these models induce an undesirable variability of primal (thermal generation) and dual (marginal cost and spot price) solutions that are highly sensitive to changes in current inflow conditions. This work proposes two differing approaches to stabilize SDDP solutions to the energy operation planning problem: the first approach regularizes primal variables by considering an additional penalty on thermal dispatch revisions over time, and the second approach indirectly reduces thermal generation and marginal cost variability by disregarding past inflow information in the cost-to-go function and compensates with an increase in risk aversion. For comparison purposes, we assess solution quality with a set of proposed indexes summarizing each important aspect of a hydrothermal operation planning policy. In conclusion, we show that it is possible to obtain high-quality solutions in comparison to current benchmarks with significantly reduced variability. (C) 2016 Elsevier B.V. All rights reserved.

关键词： stochastic programming stochastic dual dynamic programming Risk aversion OR in energy

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Strategic bidding for a price-maker hydroelectric producer: stochastic dual dynamic programming and Lagrangian relaxation

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IISE TRANSACTIONS 2018年第11期50卷 929-942页

作者： Steeger, Gregory Lohmann, Timo Rebennack, Steffen US Air Force Hurlburt Field FL USA Uniper Global Commod SE Dusseldorf Germany KIT Inst Operat Res Karlsruhe Germany

In bid-basedmarkets, energy producers seek bidding strategies that maximize their revenue. In this article, we seek the maximum-revenue bidding schedule for a single price-maker hydroelectric producer. We assume the producer sells energy in the day-ahead electricity market and has the ability to impact the market-clearing price with its bids. To obtain the price-maker hydroelectric producer's bidding schedule, we use a combination of stochastic dual dynamic programming and Lagrangian relaxation. In this framework, we dualize the water balance equations, allowing an exact representation of the non-concave immediate revenue function, while preserving the concave shape of the future revenue function. We model inflow uncertainty and its stagewise dependence by a periodic autoregressive model. To demonstrate our approaches' utility, we model Honduras' electricity market assuming that the thermal producers act as price-takers and that one price-maker hydro producer operates all of the hydroelectric plants.

关键词： Bidding problem Lagrangian relaxation price-maker stochastic dual dynamic programming periodic autoregressive model

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Risk-averse stochastic dual dynamic programming approach for the operation of a hydro-dominated power system in the presence of wind uncertainty

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2020年 115卷 105469-000页

作者： Morillo, Jose L. Zephyr, Luckny Perez, Juan F. Anderson, C. Lindsay Cadena, Angela Univ Andes Dept Elect & Elect Engn Bogota Colombia Laurentian Univ Dept Finance & Operat Sudbury ON Canada Univ Rosario Dept Appl Math & Comp Sci Bogota Colombia Cornell Univ Dept Biol & Environm Engn Ithaca NY USA

Operation planning models for hydro-dominated power systems usually use low temporal resolutions due to the excessive computational burden, thus ignoring short-term characteristics of such systems. As a result, in systems coupled with wind energy, such models may fail to accurately capture wind variability, and may not appropriately take into account potential consequences of uncertainty on the system operation. This paper addresses this drawback by (i) "controlling" the cost associated with the operation of a hydro-dominated power system equipped with wind power and batteries via a risk-measure and (ii) formulating the short-term load balance as probabilistic constraints in order to hedge against potential extreme wind power scenarios. The risk-averse scheme is embedded in the stochastic dual dynamic programming framework. Simulation results for a case study on a real industrial setting show that hedging the system against the short-term volatility of wind power contributes to mitigating the risk of excessive operations costs or load curtailments, and that the consideration of the decision maker risk profile contributes to decreasing the variability of the solutions. In addition, the results of the application also illustrate the potential of the scheme to assess the energy situation of a country or a region under the penetration of wind energy and batteries deployment.

关键词： Operation planning Hydro-dominated system stochastic dual dynamic programming Risk aversion Chance-constraint

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Improving the performance of stochastic dual dynamic programming

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年 290卷 196-208页

作者： de Matos, Vitor L. Philpott, Andy B. Finardi, Erlon C. Plan4 Engn Florianopolis SC Brazil Univ Auckland Elect Power Optimizat Ctr Auckland 1 New Zealand Univ Fed Santa Catarina Lab Planejamento Sistemas Energia Eletr BR-88040900 Florianopolis SC Brazil

This paper is concerned with tuning the stochastic dual dynamic programming algorithm to make it more computationally efficient. We report the results of some computational experiments on a large-scale hydrothermal scheduling model developed for Brazil. We find that the best improvements in computation time are obtained from an implementation that increases the number of scenarios in the forward pass with each iteration and selects cuts to be included in the stage problems in each iteration. This gives an order of magnitude decrease in computation time with little change in solution quality. (C) 2015 Elsevier B.V. All rights reserved.

关键词： stochastic programming stochastic dual dynamic programming Cut selection Hydrothermal scheduling

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Assessing the value of natural gas underground storage in the Brazilian system via stochastic dual dynamic programming

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TOP 2021年第1期29卷 106-124页

作者： Resende, Larissa de Oliveira Valladao, Davi Bezerra, Bernardo Vieira Cyrillo, Yasmin Monteiro Pontificia Univ Catolica Rio de Janeiro Ind Engn Dept Rio de Janeiro Brazil PSR Energy Consulting & Analyt PSR Rio De Janeiro Brazil Natl Elect Syst Operator ONS Rio De Janeiro Brazil

The Brazilian natural gas sector is currently characterized by low maturity and dynamism of the market. The stochastic behavior of the demand for natural gas added to its associated market price volatility motivates the usage of underground storage to provide supply flexibility and protection against price fluctuations. However, the existing literature lacks a proper analytical tool to assess the benefits of underground natural gas storage (UNGS) activity. In this work, it is proposed a stochastic dynamic programming model for long/medium-term operation planning to determine the optimal gas supply and storage policies. A markovian model characterizes the uncertainty over the thermoelectric demand and market price. The proposed model is efficiently solved using the stochastic dual dynamic programming algorithm for the Brazilian case study considering realistic data for the actual gas network and electric power system. For an exogenous but meaningful choice of underground storage location and size, it is observed the operational and economic benefits of the provided storage flexibility. Finally, our numerical simulations show that the economic benefit for the system surpasses the operational and capital expenses for the storage infrastructure in depleted fields and salt caverns.

关键词： Underground storage of natural gas Natural gas supply chain stochastic dual dynamic programming Brazilian natural gas sector

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Large-scale financial planning via a partially observable stochastic dual dynamic programming framework

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QUANTITATIVE FINANCE 2023年第9期23卷 1341-1360页

作者： Lee, Jinkyu Kwon, Do-Gyun Lee, Yongjae Kim, Jang Ho Kim, Woo Chang Korea Adv Inst Sci & Technol KAIST Dept Ind & Syst Engn 291 Daehak Ro Daejeon 34141 South Korea Ulsan Natl Inst Sci & Technol UNIST Dept Ind Engn 50 UNIST Gil Ulsan 44919 South Korea Kyung Hee Univ Dept Ind & Management Syst Engn Dept Big Data Analyt Coll EngnGrad Sch 1732 Deogyeong Daero Yongin 17104 Gyeonggi Do South Korea

The multi-stage stochastic programming (MSP) approach is widely used to solve financial planning problems owing to its flexibility. However, the size of an MSP problem grows exponentially with the number of stages, and such problem can easily become computationally intractable. Financial planning problems often consider planning horizons of several decades, and thus, the curse of dimensionality can become a critical issue. stochastic dual dynamic programming (SDDP), a sampling-based decomposition algorithm, has emerged to resolve this issue. While SDDP has been successfully implemented in the energy domain, few applications of SDDP are found in the finance domain. In this study, we identify the major obstacle in using SDDP to solve financial planning problems to be the stagewise independence assumption and propose a partially observable SDDP (PO-SDDP) framework to overcome such limitations. We argue that the PO-SDDP framework, which models uncertainties using discrete-valued partially observable Markov states and introduces feasibility cuts, can properly address large-scale financial planning problems.

关键词： Financial planning Large-scale optimization Multi-stage stochastic programming stochastic dual dynamic programming Partially observable Markov states >

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Two-Stage stochastic dual dynamic programming for Transmission Expansion Planning with Significant Renewable Generation and N-k Criterion

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CSEE Journal of Power and Energy Systems 2016年第1期2卷 3-10页

作者： Zhi Wu Pingliang Zeng Xiao-Ping Zhang School of Electronic Electrical and Systems EngineeringUniversity of BirminghamUnited Kingdom China Electric Power Research Institute BeijingChina

The large-scale integration of renewable energy sources(RES)is the global trend to deal with the energy crisis and greenhouse *** to the intermittent nature of RES together with the uncertainty of load demand,the problem of transmission expansion planning(TEP)is facing more and more challenges from *** this paper,the TEP problem is modeled as a two-stage formulation,so as to minimize the total of investment costs and generation *** ensure the utilization level of the RES generation,the expansion plan is required to provide sufficient transmission capacity for the integration of ***,N-k security criterion is considered into the model,so the expansion plan can meet the required security *** stochastic dual dynamic programming(SDDP)approach is applied to consider the uncertainties,and the whole model is solved by Benders’decomposition *** case studies are carried out to compare the performance of the SDDP approach and the deterministic *** show that the expansion plan obtained by the SDDP approach has a better performance than that of the deterministic approach.

关键词： N-k security criterion stochastic dual dynamic programming transmission expansion planning two-stage problem

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A stochastic dual dynamic programming Approach for Optimal Operation of DER Aggregators

A Stochastic Dual Dynamic Programming Approach for Optimal O...

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IEEE Manchester PowerTech

作者： Fatouros, Panagiotis Konstantelos, Ioannis Papadaskalopoulos, Dimitrios Strbac, Goran Imperial Coll London Dept Elect & Elect Engn London England

ISBN: (纸本)9781509042371

The operation of aggregators of distributed energy resources (DER) is a highly complex task that is affected by numerous factors of uncertainty such as renewables injections, load levels and market conditions. However, traditional stochastic programming approaches neglect information around temporal dependency of the uncertain variables due to computational tractability limitations. This paper proposes a novel stochastic dual dynamic programming (SDDP) approach for the optimal operation of a DER aggregator. The traditional SDDP framework is extended to capture temporal dependency of the uncertain wind power output, through the integration of an n-order autoregressive (AR) model. This method is demonstrated to achieve a better trade-off between solution efficiency and computational time requirements compared to traditional stochastic programming approaches based on the use of scenario trees.

关键词： Aggregators autoregressive modelling distributed energy resources stochastic dual dynamic programming uncertainty

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Parallel and distributed computing for stochastic dual dynamic programming

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COMPUTATIONAL MANAGEMENT SCIENCE 2022年第2期19卷 199-226页

作者： Avila, D. Papavasiliou, A. Loehndorf, N. Catholic Univ Louvain Ctr Operat Res & Econometr Louvain Belgium Univ Luxembourg Luxembourg Ctr Logist & Supply Chain Management Esch Sur Alzette Luxembourg

We study different parallelization schemes for the stochastic dual dynamic programming (SDDP) algorithm. We propose a taxonomy for these parallel algorithms, which is based on the concept of parallelizing by scenario and parallelizing by node of the underlying stochastic process. We develop a synchronous and asynchronous version for each configuration. The parallelization strategy in the parallelscenario configuration aims at parallelizing the Monte Carlo sampling procedure in the forward pass of the SDDP algorithm, and thus generates a large number of supporting hyperplanes in parallel. On the other hand, the parallel-node strategy aims at building a single hyperplane of the dynamic programming value function in parallel. The considered algorithms are implemented using Julia and JuMP on a high performance computing cluster. We study the effectiveness of the methods in terms of achieving tight optimality gaps, as well as the scalability properties of the algorithms with respect to an increasing number of CPUs. In particular, we study the effects of the different parallelization strategies on performance when increasing the number of Monte Carlo samples in the forward pass, and demonstrate through numerical experiments that such an increase may be harmful. Our results indicate that a parallel-node strategy presents certain benefits as compared to a parallel-scenario configuration.

关键词： Multistage stochastic programming stochastic dual dynamic programming High performance computing Distributed computing Parallel computing

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