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Retrofit Planning and Flexible Operation of Coal-Fired Units Using stochastic dual dynamic integer programming

IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第1期39卷 2154-2169页

作者： Li, Zhuangzhuang Yang, Ping Zhao, Zhuoli Lai, Loi Lei South China Univ Technol Sch Elect Power Engn Guangzhou 510641 Peoples R China Guangdong Univ Technol Sch Automat Dept Elect Engn Guangzhou 510006 Peoples R China

The continuous growth of wind power requires greater power system operational flexibility owing to the variability and uncertainty of wind power generation. Retrofitting existing coal-fired units is a demonstrated cost-effective method for improving system flexibility. This study proposes a decision support tool that provides optimal investment decisions to enhance power system operational flexibility. A novel flexibility retrofit planning (FRP) model is proposed in which the embedded operational problem is a stochastic mixed-integer nonlinear programming (SMINLP) unit commitment problem. In the operational unit commitment model, novel mixed-integer nonlinear formulations are proposed to represent the coal-fired unit attribute (minimum power output, startup and shutdown times, and maximum ramp rate) modifications after retrofitting. A new solution method based on the Benders decomposition (BD) and stochastic dual dynamic integer programming (SDDIP) algorithms is proposed to solve the proposed FRP model. The modified IEEE 39-bus, 57-bus, and 118-bus test systems were used to verify the effectiveness of the proposed model and solution method. The results demonstrate that the proposed FRP model can balance the retrofitting and operational costs to minimize the total cost and accommodate more wind generation. The proposed solution method is computationally efficient for solving FRP models.

关键词： Costs Wind power generation Planning Wind farms stochastic processes Load modeling Wind forecasting Coal-fired units flexibility retrofit flexible operation renewable energy sources stochastic dual dynamic integer programming

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Efficient power system year-round hourly operation simulation based on multi-stage stochastic dual dynamic integer programming

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 161卷

作者： Qian, Tao Wu, Qiyu Hu, Qinran Southeast Univ Sch Elect Engn Nanjing 210096 Peoples R China Jiangsu Key Lab Smart Grid Technol & Equipment Nanjing 210096 Peoples R China

In the context of power systems increasingly reliant on renewable energy sources, the consideration of uncertainty becomes paramount for year-round hourly operational simulations aimed at assessing the efficacy of power grid development strategies. While multi-stage stochastic programming has been effective in capturing multi-scale power fluctuations, its adoption faces challenges related to computational complexity and convergence performance. To address these issues, this paper presents a novel fast multi-stage stochastic unit commitment method tailored for year-round hourly operational simulation. This method strategically incorporates the expectations of a limited number of future stages to expedite the iteration process, thereby mitigating computational burdens. The annual time-series data is adaptively segmented based on the fluctuation characteristics of power and load, ensuring a balanced sub-problem scale aligned with the number of stages. Results from rigorous testing across multiple standard cases demonstrate that the proposed method consistently achieves optimal lower bounds within 6-8 iterations, resulting in significant computational time savings of up to 50%. Furthermore, the efficacy of the proposed method is showcased through its application in the annual operational simulation of a real-world provincial high-voltage power grid in China.

关键词： Year-round operation simulation stochastic dual dynamic integer programming Unit commitment Renewable energy sources Uncertainty

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Combining Polyhedral Approaches and stochastic dual dynamic integer programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty

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INFORMS JOURNAL ON COMPUTING 2022年第2期34卷 1024-1041页

作者： Quezada, Franco Gicquel, Celine Kedad-Sidhoum, Safia Sorbonne Univ Lab Informat Paris 6 LIP6 Ctr Natl Rech Sci CNRS F-75005 Paris France Univ Santiago Chile USACH Program Dev Sustainable Prod Syst PDSPS Fac Engn Santiago Chile Univ Paris Saclay Lab Interdisciplinaire Sci Numer LISN F-91190 Gif Sur Yvette France Ctr Etud & Rech Informat & Commun CEDRIC Conservatoire Natl Arts & Metiers CNAM F-75003 Paris France

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane-generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders' cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The prop

关键词： multistage stochastic programming stochastic lot sizing stochastic dual dynamic integer programming node aggregation valid inequalities partial decomposition

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Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme

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OPTIMIZATION AND ENGINEERING 2020年第4期21卷 1243-1281页

作者： Lara, Cristiana L. Siirola, John D. Grossmann, Ignacio E. Carnegie Mellon Univ 5000 Forbes Ave Pittsburgh PA 15213 USA Sandia Natl Labs Ctr Comp Res POB 5800 Albuquerque NM 87185 USA

We address the long-term planning of electric power infrastructure under uncertainty. We propose a Multistage stochastic Mixed-integer programming formulation that optimizes the generation expansion to meet the projected electricity demand over multiple years while considering detailed operational constraints, intermittency of renewable generation, power flow between regions, storage options, and multiscale representation of uncertainty (strategic and operational). To be able to solve this large-scale model, which grows exponentially with the number of stages in the scenario tree, we decompose the problem using stochastic dual dynamic integer programming (SDDiP). The SDDiP algorithm is computationally expensive but we take advantage of parallel processing to solve it more efficiently. The proposed formulation and algorithm are applied to a case study in the region managed by the Electric Reliability Council of Texas for scenario trees considering natural gas price and carbon tax uncertainty for the reference case, and a hypothetical case without nuclear power. We show that the parallelized SDDiP algorithm allows in reasonable amounts of time the solution of multistage stochastic programming models of which the extensive form has quadrillions of variables and constraints.

关键词： Generation expansion planning Multistage stochastic programming stochastic dual dynamic integer programming

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Multistage stochastic Unit Commitment Using stochastic dual dynamic integer programming

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第3期34卷 1814-1823页

作者： Zou, Jikai Aluned, Shabbir Sun, Xu Andy Georgia Inst Technol Dept Ind & Syst Engn Atlanta GA 30332 USA

Unit commitment (UC) is a key operational problem in power systems for the optimal schedule of daily generation commitment. Incorporating uncertainty in this already difficult mixedinteger optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning horizon is decided before the uncertainty is realized, or a multistage stochastic programming model with relatively small scenario trees to ensure tractability. We propose a new type of decomposition algorithm, based on the recently proposed framework of stochastic dual dynamic integer programming (SDDiP), to solve the multistage stochastic unit commitment (MSUC) problem. We propose a variety of computational enhancements to SDDiP, and conduct systematic and extensive computational experiments to demonstrate that the proposed method is able to handle elaborate stochastic processes and can solve MSUCs with a huge number of scenarios that are impossible to handle by existing methods.

关键词： Unit commitment multistage stochastic integer programming stochastic dual dynamic integer programming

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Goal-based investing with goal postponement: multistage stochastic mixed-integer programming approach

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ANNALS OF OPERATIONS RESEARCH 2024年 1-25页

作者： Bae, Sanghyeon Lee, Yongjae Kim, Woo Chang Kim, Jang Ho Fabozzi, Frank J. Korea Adv Inst Sci & Technol KAIST Dept Ind & Syst Engn Daejeon 34141 South Korea Ulsan Natl Inst Sci & Technol UNIST Artificial Intelligence Grad Sch Dept Ind Engn Ulsan South Korea Korea Univ Grad Sch Management Technol Seoul South Korea Johns Hopkins Univ Carey Business Sch Baltimore MD USA

This paper introduces a multistage stochastic mixed-integer programming model designed for a goal-based investing (GBI) problem, incorporating the option of goal postponement. Our model allows individuals to defer the fulfillment of their goals within a predefined timeframe. We emphasize the advantages of incorporating goal postponement into the GBI framework, including its ability to accommodate stage-preference ambiguity, address mistiming issues, and enhance utility for individuals. Theoretical results of a GBI problem with goal postponement are presented, and to tackle large-scale multistage GBI problems, we employ a decomposition algorithm known as stochastic dual dynamic integer programming (SDDiP). Numerical results demonstrate that the option to postpone a goal proves especially advantageous when goals are exposed to high inflation rates, and SDDiP emerges as a computationally efficient approach for handling large-scale GBI problems.

关键词： Goal-based investing Multistage stochastic mixed-integer programming stochastic dual dynamic integer programming Goal postponement

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Multistage dynamic Planning of Integrated Hydrogen-Electrical Microgrids Under Multiscale Uncertainties

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IEEE TRANSACTIONS ON SMART GRID 2023年第5期14卷 3482-3498页

作者： Sun, Xunhang Cao, Xiaoyu Zeng, Bo Zhai, Qiaozhu Guan, Xiaohong Xi An Jiao Tong Univ Sch Automat Sci & Engn Xian 710049 Shaanxi Peoples R China Xi An Jiao Tong Univ Minist Educ Key Lab Intelligent Networks & Network Secur Xian 710049 Shaanxi Peoples R China Sichuan Digital Econ Ind Dev Res Inst Smart Integrated Energy Dept Chengdu 610037 Sichuan Peoples R China Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15106 USA Univ Pittsburgh Dept Elect & Comp Engn Pittsburgh PA 15106 USA Tsinghua Univ Dept Automat Ctr Intelligent & Networked Syst Beijing 100084 Peoples R China

Integrated Hydrogen-Electrical (IHE) microgrids are desirable testbeds for the practice of carbon-neutral energy supply. This paper studies the IHE microgrids planning (IHEMP) under a dynamic perspective. To keep track with the fast development of hydrogen industry, we propose a multistage stochastic mixed-integer program (MS-MIP) formulation. It comprehensively considers the siting and sizing decisions of IHE microgrids, the dynamic expansion of distributed energy facilities, and the detailed operational model to derive a robust, flexible and profitable investment policy. Moreover, a scenario-tree based sampling strategy is leveraged to capture both the large-scale strategic uncertainties (e.g., the long-term growth of electric loads and hydrogen refueling demands, as well as the cost changes of system components) and fine-scale operating uncertainties (e.g., random variation of renewable energy outputs and loads) under different time scales. As the resulting formulation could be computationally very challenging, we develop a nested decomposition algorithm based on stochastic dual dynamic integer programming (SDDiP). Case studies on exemplary IHE microgrids validate the effectiveness of our dynamic planning approach. Also, the customized SDDiP algorithm shows a superior solution capacity to handle large-scale MS-MIPs than the state-of-the-art solver (i.e., Gurobi) and a popular scenario-oriented decomposition method (i.e., progressive hedging algorithm).

关键词： Hydrogen Microgrids Planning Investment Renewable energy sources Vehicle dynamics stochastic processes Hydrogen-electricity synergy multistage microgrids planning multiscale uncertainties stochastic dual dynamic integer programming

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Medium-term multi-stage distributionally robust scheduling of hydro-wind-solar complementary systems in electricity markets considering multiple time-scale uncertainties

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APPLIED ENERGY 2023年第1期347卷

作者： Li, Zhuangzhuang Yang, Ping Guo, Yi Lu, Guanpeng South China Univ Technol Sch Elect Power Engn Guangzhou Peoples R China Xian Univ Technol State Key Lab Ecohydraul Northwest Arid Reg China Xian Peoples R China

Joint trading of hydro-wind-solar complementary systems (HWSCSs) in the electricity market (EM) helps to reduce the imbalance cost and increase profits. However, multiple energy resources and market price uncertainties affect the trading strategies. Existing medium-term (MT) scheduling approaches assume that the probability distribution of the random variable is perfectly known. Short-term variations were also ignored, which led to revenue loss and trading risk. To address the above issues, this paper proposes an MT multi-stage distributionally robust optimization (MDRO) scheduling approach for a price-taking HWSCS in the EM. Firstly, hourly unit commitment (HUC) constraints are incorporated into the MT scheduling model to accurately capture short-term variations. A novel ambiguity set is designed based on the modified chi-square distance to address probability distribution uncertainties at two different time scales. Subsequently, an MDRO scheduling model is proposed to optimize the trading strategy. Finally, the proposed MDRO model is converted to a large-scale multistage integer programming problem based on linearization and reformation. The stochastic dual dynamic integer programming algorithm is modified to ensure computational tractability. Xiluodu-Xiangjiaba HWSCS, located in the Jinsha River in China, was selected as a case study. The results show that: 1) the MDRO model is more robust to distributional uncertainties than the multi-stage stochastic programming (MSSP) model. When the probability distribution of the random variable changes, the MDRO model yields a higher expected revenue (+2.43%) and a lower standard deviation (-60.8%) of revenue, which illustrates lower trading risk. 2) Compared with MSSP, deterministic, two-stage stochastic programming, and distributionally robust optimization models, the MDRO model exhibits the best out-of-sample performance in terms of the highest expected revenue and lowest trading risk. 3) Incorporating HUC constraints in

关键词： Hydro -wind -solar complementary system Medium -term scheduling Electricity market Distributionally robust optimization stochastic dual dynamic integer programming

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Multistage stochastic programming for the closed-loop supply chain planning with mobile modules under uncertainty

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AICHE JOURNAL 2023年第9期69卷 e18156-e18156页

作者： Ge, Congqin Zhang, Lifeng Yang, Wenhui Yuan, Zhihong Tsinghua Univ Dept Chem Engn State Key Lab Chem Engn Beijing Peoples R China Tsinghua Univ Dept Chem Engn State Key Lab Chem Engn Beijing 100084 Peoples R China

Traditional supply chains usually follow fixed facility designs which coincide with the strategic nature of supply chain management (SCM). However, as the global market turns more volatile, the concept of mobile modularization has been adopted by increasingly more industrial practitioners. In mobile modular networks, modular units can be installed or removed at a particular site to expand or reduce the capacity of a facility, or relocated to other sites to tackle market volatility. In this work, we formulate a mixed-integer linear programming (MILP) model for the closed-loop supply chain network planning with modular distribution and collection facilities. To further deal with uncertain customer demands and recovery rates, we extend our model to a multistage stochastic programming model and efficiently solve it using a tailored stochastic dynamic dual integer programming (SDDiP) with Magnanti-Wong enhanced cuts. Computational experiments show that the added Magnanti-Wong cuts in the proposed algorithm can effectively close the gap between upper and lower bounds, and the benefit of mobile modules is evident when the temporal and spatial variability of customer demand is high.

关键词： closed-loop supply chain planning mobile modules stochastic dual dynamic integer programming stochastic programming uncertainty

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Hydropower preventive maintenance scheduling in a deregulated market: A multi-stage stochastic programming approach

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ELECTRIC POWER SYSTEMS RESEARCH 2023年第1期221卷

作者： Li, Zhuangzhuang Yang, Ping Yang, Yi Lu, Guanpeng Tang, Yufeng South China Univ Technol Sch Elect Power Engn Guangzhou Peoples R China South China Univ Technol Guangdong Key Lab Clean Energy Technol Guangzhou Peoples R China

Hydropower preventive maintenance scheduling ensures the economical and reliable operation of the plant, which is a significant and complex optimization task. The hydropower producer will schedule maintenance to pursue maximum profit in a deregulated market. The electricity price and natural inflow uncertainties have significant economic impacts and must be considered. However, the existing maintenance scheduling models were two-stage models in which the maintenance schedule for the entire planning horizon was determined before the realization of the uncertainty. This paper presents a multi-stage risk-neutral preventive maintenance scheduling model for a price-taking hydropower producer in a deregulated market. The maintenance decisions are sequentially made with the information of electricity price and inflow uncertainties being revealed gradually. To hedge against the profit risk caused by the uncertainties, a multi-stage risk-averse maintenance scheduling model is proposed based on the multi-stage Conditional Value at Risk. We reformulate the proposed multi-stage models as multi-stage mixed-integer stochastic linear programming problems and apply the stochastic dual dynamic integer programming (SDDIP) algorithm to solve them. Finally, the utility of the proposed model is verified using the data of a cascade hydropower system in Southwest China. The results show that: (1) the proposed multi-stage maintenance model outperforms two-stage model in terms of higher expected revenue (+4.95% on average) and lower risk (-10.8% on average) under both in-sample and out-of-sample scenarios. The improvements of the multi-stage model decreases with an increase in risk aversion level. (2) The risk-averse model balances the expected profit and risk according to risk preferences. More risk-averse policies lead to lower expected profits and lower risks. (3) Despite longer running time of the multi-stage model (+35% on average) than the two-stage model, it is computationally tracta

关键词： Hydropower plants Maintenance scheduling Multi -stage stochastic programming Conditional value at risk stochastic dual dynamic integer programming

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