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stochastic dual dynamic programming for optimal power flow problems under uncertainty

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第3期321卷 814-836页

作者： Kiszka, Adriana Wozabal, David Tech Univ Munich TUM Sch Management Arcisstr 21 D-80333 Munich Germany Vrije Univ Amsterdam Sch Business & Econ Boelelaan 1105 NL-1081 HV Amsterdam Netherlands

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

关键词： stochastic programming Optimal power flow Semi-definite programming stochastic dual dynamic programming Electricity storage

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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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stochastic dual dynamic programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2019年第1期10卷 459-469页

作者： Fatouros, Panagiotis Konstantelos, Ioannis Papadaskalopoulos, Dimitrios Strbac, Goran Imperial Coll London Dept Elect & Elect Engn London SW7 2BT England

The operation of aggregators of distributed energy resources (DER) is highly complex, since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. The large number of possible stochastic realizations that arise can lead to complex operational models that become problematic in real-time market environments. Previous stochastic programming approaches resort to two-stage uncertainty models and scenario reduction techniques to preserve the tractability of the problem. However, two-stage models cannot fully capture the evolution of uncertain processes and the a priori scenario selection can lead to suboptimal decisions. In this context, this paper develops a novel stochastic dual dynamic programming approach which does not require discretization of either the state space or the uncertain variables and can be efficiently applied to a multi-stage uncertainty model. Temporal dependencies of the uncertain variables as well as dependencies among different uncertain variables can be captured through the integration of any linear multidimensional stochastic model, and it is showcased for a p-order vector autoregressive model. The proposed approach is compared against a traditional scenario-tree-based approach through a Monte-Carlo validation process, and is demonstrated to achieve a better trade-off between solution efficiency and computational effort.

关键词： Aggregator distributed energy resources multi-dimensional uncertainty stochastic dual dynamic programming vector autoregressive modeling

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stochastic dual dynamic programming applied to nonconvex hydrothermal models

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第3期218卷 687-697页

作者： Cerisola, Santiago Latorre, Jesus M. Ramos, Andres Univ Pontificia Comillas ICAI Inst Invest Tecnol Madrid 28015 Spain

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented. (C) 2011 Elsevier B.V. All rights reserved.

关键词： programming: stochastic Integer Benders decomposition Lagrangean relaxation stochastic dual dynamic programming Production/scheduling: planning

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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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Combining sampling-based and scenario-based nested Benders decomposition methods: application to stochastic dual dynamic programming

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MATHEMATICAL programming 2016年第1-2期156卷 343-389页

作者： Rebennack, Steffen Colorado Sch Mines Div Econ & Business Golden CO 80401 USA

Nested Benders decomposition is a widely used and accepted solution methodology for multi-stage stochastic linear programming problems. Motivated by large-scale applications in the context of hydro-thermal scheduling, in 1991, Pereira and Pinto introduced a sampling-based variant of the Benders decomposition method, known as stochastic dual dynamic programming (SDDP). In this paper, we embed the SDDP algorithm into the scenario tree framework, essentially combining the nested Benders decomposition method on trees with the sampling procedure of SDDP. This allows for the incorporation of different types of uncertainties in multi-stage stochastic optimization while still maintaining an efficient solution algorithm. We provide an illustration of the applicability of our method towards a least-cost hydro-thermal scheduling problem by examining an illustrative example combining both fuel cost with inflow uncertainty and by studying the Panama power system incorporating both electricity demand and inflow uncertainties.

关键词： stochastic dual dynamic programming Hydro-thermal power system Nested Benders decomposition Sampling Scenario tree Electricity demand and inflow uncertainty

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Multi-Stage Distributionally Robust stochastic dual dynamic programming to Multi-Period Economic Dispatch With Virtual Energy Storage

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2022年第1期13卷 146-158页

作者： Ding, Tao Zhang, Xiaosheng Lu, Runzhao Qu, Ming Shahidehpour, Mohammad He, Yuankang Chen, Tianen Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Shaanxi Peoples R China China Elect Power Res Inst Power Syst Res Dept Beijing 100085 Peoples R China IIT ECE Dept Chicago IL 60616 USA State Grid Corp China Northwest Branch Xian 710048 Shaanxi Peoples R China

A virtual energy storage (VES) model is proposed in this paper to accommodate renewable energy under a special market regulation. Such VESs can provide or consume electricity to the main power grid under the premise that the daily net electricity energy is balanced. Furthermore, a multi-stage distributionally robust optimization (MSDRO) model is set up in this paper to address the temporal uncertainties in the day-ahead economic dispatch model. Compared with the traditional two-stage distributionally robust optimization, the proposed multi-stage approach provides more flexibilities so that the decision variables can be adjusted at each time period, leading to a complex nested formulation. To efficiently solve the MSDRO model, a stochastic dual dynamic programming method is employed to decompose the original large-scale optimization model into several sub-problems in the stages, as two steps: forward pass and backward pass. In the forward pass, the expected cost-to-go function is approximated by piecewise-linear functions and then several samples are used to generate a lower bound;the backward pass will generate Benders' cuts at each stage from the solution of the forward pass. The forward and backward passes are performed iteratively until the convergence is reached. Numerical results on an IEEE 118-bus system and a practical power system in China verify the proposed method.

关键词： stochastic processes Uncertainty Renewable energy sources Optimization Power systems Load modeling Computational modeling Distributionally robust optimization economic dispatch multi-stage stochastic programming renewable energy stochastic dual dynamic programming virtual energy storage

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Multi-stage stochastic dual dynamic programming to low-carbon economic dispatch for power systems with flexible carbon capture and storage devices

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IET GENERATION TRANSMISSION & DISTRIBUTION 2023年第19期17卷 4359-4374页

作者： Zhang, Xiaosheng Liu, Zesan Ding, Tao Zhang, Hongji Siano, Pierluigi Meng, Hongmin Zhu, Chao Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China State Grid Informat & Telecommun Grp Co Ltd Beijing Peoples R China Univ Salerno Dept Management & Innovat Syst Salerno Italy State Grid Shaanxi Elect Power Res Inst Xian Peoples R China

The carbon capture and storage (CCS) technique gains much attention due to its role in reducing CO2 emissions. By introducing flexible CCS devices into conventional power plants, the low-carbon economic operation of the power system can be achieved. However, the uncertainty of renewable energy makes it hard to obtain an optimal operation policy. First, the detailed model of CCS consisting of bypass venting stacks, solvent storage tanks, absorber, and stripper is described. Then, a low-carbon economic dispatch model of the power system with CCS is proposed to minimize the total operation and renewable energy abandonment penalty costs. Next, the problem is reformulated as multi-stage stochastic programming, and the stochastic dual dynamic programming (SDDP) method is applied to relieve the computation burden. To control the probability of stopping the algorithm prematurely, a new stopping criterion based on a two-sided hypothesis test is proposed. Finally, the effectiveness of the proposed model and the new stopping criterion is demonstrated by case studies on a practical power system. A low-carbon economic dispatch model of the power system with carbon capture and storage (CCS) is proposed to minimize the total operation and renewable energy abandon penalty costs. The basic formulation of SDDP and a new stopping criterion avoiding the premature convergence of the algorithm are ***

关键词： flexible carbon capture and storage devices low-carbon economic dispatch multi-stage stochastic programming stochastic dual dynamic programming

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Risk neutral and risk averse stochastic dual dynamic programming method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期224卷 375-391页

作者： Shapiro, Alexander Tekaya, Wajdi da Costa, Joari Paulo Soares, Murilo Pereira Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA ONS Operador Nacl Sistema Eletr BR-20091005 Ctr Rio De Janeiro RJ Brazil

In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the stochastic dual dynamic programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Multistage stochastic programming dynamic equations stochastic dual dynamic programming Sample average approximation Risk averse Average Value-at-Risk

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Using stochastic dual dynamic programming in problems with multiple near-optimal solutions

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WATER RESOURCES RESEARCH 2016年第5期52卷 4151-4163页

作者： Rouge, Charles Tilmant, Amaury Univ Laval Dept Civil Engn & Water Engn Quebec City PQ Canada Univ Manchester Dept Mech Civil & Aerosp Engn Manchester Lancs England

stochastic dual dynamic programming (SDDP) is one of the few algorithmic solutions available to optimize large-scale water resources systems while explicitly considering uncertainty. This paper explores the consequences of, and proposes a solution to, the existence of multiple near-optimal solutions (MNOS) when using SDDP for mid or long-term river basin management. These issues arise when the optimization problem cannot be properly parametrized due to poorly defined and/or unavailable data sets. This work shows that when MNOS exists, (1) SDDP explores more than one solution trajectory in the same run, suggesting different decisions in distinct simulation years even for the same point in the state-space, and (2) SDDP is shown to be very sensitive to even minimal variations of the problem setting, e.g., initial conditionswe call this algorithmic chaos. Results that exhibit such sensitivity are difficult to interpret. This work proposes a reoptimization method, which simulates system decisions by periodically applying cuts from one given year from the SDDP run. Simulation results obtained through this reoptimization approach are steady state solutions, meaning that their probability distributions are stable from year to year.

关键词： stochastic dual dynamic programming year-periodic reoptimization limited data availability multiple near-optimal solutions Zambezi River Basin chaos

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