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Dealing with the stochastic prosumager problem with controllable loads

SOFT COMPUTING 2023年第18期27卷 12913-12924页

作者： Violi, Antonio Beraldi, Patrizia Carrozzino, Gianluca Univ Sannio Dept Law Econ Management & Quantitat Methods Benevento BN Italy Univ Calabria Dept Mech Energy & Management Engn Arcavacata Di Rende CS Italy

This paper focuses on the home energy management for a residential prosumager with flexible loads. In particular, three different types of controllable appliances (shiftable, interruptible, thermostatically controllable) have been considered, each one with a specific representation of energy consumption profile and a potential discomfort rate for the user. The inherent uncertainty affecting the main model parameters (i.e., non- controllable loads, solar production, external temperature) is explicitly accounted for by adopting the two-stage stochastic programming modeling paradigm. The model solution provides the prosumager with the optimal scheduling of the controllable loads and the operation of the storage system that guarantee the minimum expected energy procurement cost, taking into account the overall discomfort. A preliminary computational experience has shown the effectiveness of the proposed approach in terms of cost savings and the advantage related to the use of a stochastic programming approach over a deterministic formulation.

关键词： Home energy management stochastic programming Controllable appliances User discomfort modeling

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Coordinated Planning of Wind Power Generation and Energy Storage With Decision-Dependent Uncertainty Induced by Spatial Correlation

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IEEE SYSTEMS JOURNAL 2023年第2期17卷 2247-2258页

作者： Yin, Wenqian Li, Yujia Hou, Jiazuo Miao, Miao Hou, Yunhe Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China HKU Shenzhen Inst Res & Innovat Shenzhen 518053 Peoples R China

The global experience on wind farm development reveals that due to the spatial correlation, the prediction error of wind power is related to the scale of wind farms. This evidence indicates that the uncertainty features of wind power output from large-scale wind farms are not fixed but dependent on expansion decisions. The decision-dependent uncertainty (DDU) will alter the traditional optimization process and pose solution challenges. This article proposes a coordinated planning model for large-scale wind farms and energy storage considering DDU. First, a DDU model, which quantifies the relationship between wind power prediction errors and the wind farm size, is established based on historical data. The proposed DDU model for a single wind farm is extended to multiple wind farms with their spatial correlation captured by a Gaussian Mixture Model. Then, tackling the coupling relationship between decisions and uncertainty, an affine function-based solution method for the stochastic model with decision-dependent probability distributions is proposed. The constructed affine function maps planning decisions to decision-dependent wind power scenario sets via linear transformation. The difference between the planning model with and without the DDU in wind power is compared and discussed. Case studies verify the proposed model and solution method.

关键词： Wind power generation Uncertainty Wind farms Correlation Planning Renewable energy sources Generators Decision-dependent uncertainty (DDU) energy storage Gaussian mixture model (GMM) spatial correlation stochastic programming wind power generation planning

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Non-anticipative risk-averse analysis with effective scenarios applied to long-term hydrothermal scheduling

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第3期42卷 1-12页

作者： Arsie, Karla Cristiane Gonzaga, Clovis Caesar Karas, Elizabeth Wegner Pericaro, Gislaine Aparecida Pontificia Univ Catolica Parana Curitiba Parana Brazil Inst Lactec Curitiba Parana Brazil Univ Fed Parana Curitiba Parana Brazil Univ Estadual Parana Campo Mourao Brazil

We deal with long-term operation planning problems of hydrothermal power systems by considering scenario analysis and risk aversion. This is a stochastic sequential decision problem whose solution must be non-anticipative, in the sense that a decision at a stage cannot use knowledge of the future. We propose strategies to reduce the number of scenarios in such way that the decision obtained by solving the non-anticipative risk-averse problem considering the subset of effective scenarios is as reliable as the decision from the whole set of scenarios. Numerical experiments are presented for validation of the strategies proposed by solving the problem for two test systems with real data extracted of the Brazilian interconnected system.

关键词： Non-anticipative scenario analysis stochastic programming Nonlinear optimization Hydrothermal power systems

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An Overview of Uncertain Control Co-Design Formulations

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JOURNAL OF MECHANICAL DESIGN 2023年第9期145卷 091709-091709页

作者： Azad, Saeed Herber, Daniel R. Colorado State Univ Dept Syst Engn Ft Collins CO 80523 USA

This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified.

关键词： control co-design dynamics uncertainty stochastic programming fuzzy programming robust optimization

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Optimized Scenario Reduction: Solving Large-Scale stochastic Programs with Quality Guarantees

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INFORMS JOURNAL ON COMPUTING 2023年第4期35卷 886-908页

作者： Zhang, Wei Wang, Kai Jacquillat, Alexandre Wang, Shuaian Tsinghua Univ Sch Vehicle & Mobil Beijing 100084 Peoples R China Hong Kong Polytech Univ Dept Logist & Maritime Studies Hong Kong Peoples R China MIT Sloan Sch Management Cambridge MA 02142 USA

stochastic programming involves large-scale optimization with exponentially many scenarios. This paper proposes an optimization-based scenario reduction approach to generate high-quality solutions and tight lower bounds by only solving small-scale instances, with a limited number of scenarios. First, we formulate a scenario subset selection model that optimizes the recourse approximation over a pool of solutions. We provide a theoretical justification of our formulation, and a tailored heuristic to solve it. Second, we propose a scenario assortment optimization approach to compute a lower bound-hence, an optimality gap-by relaxing nonanticipativity constraints across scenario "bundles." To solve it, we design a new column-evaluation-and-generation algorithm, which provides a generalizable method for optimization problems featuring many decision variables and hard-to-estimate objective parameters. We test our approach on stochastic programs with continuous and mixed-integer recourse. Results show that (i) our scenario reduction method dominates scenario reduction benchmarks, (ii) our scenario assortment optimization, combined with column-evaluation-and-generation, yields tight lower bounds, and (iii) our overall approach results in stronger solutions, tighter lower bounds, and faster computational times than state-of-the-art stochastic programming algorithms.

关键词： Massachusetts 02142 stochastic programming scenario reduction column evaluation and generation

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Dynamic optimization with side information

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第2期304卷 634-651页

作者： Bertsimas, Dimitris McCord, Christopher Sturt, Bradley MIT Operat Res Ctr Cambridge MA USA Univ Illinois Dept Informat & Decis Sci Chicago IL 60607 USA

We develop a tractable and flexible data-driven approach for incorporating side information into multi-stage stochastic programming. The proposed framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of vari-ous data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concen-tration result for a class of supervised machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information. We also describe a general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of multi-stage and single-stage examples in inventory management, finance, and shipment planning, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.(c) 2022 Elsevier B.V. All rights reserved.

关键词： stochastic programming Distributionally robust optimization Machine learning Dynamic optimization

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The integrated lot-sizing and cutting stock problem under demand uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第20期61卷 6691-6717页

作者： Curcio, Eduardo de Lima, Vinicius L. Miyazawa, Flavio K. Silva, Elsa Amorim, Pedro INESC TEC Campus FEUP Porto Portugal Univ Estadual Campinas Inst Comp Campinas SP Brazil Univ Porto Fac Engn Porto Portugal INESC TEC Campus FEUP Rua Dr Roberto FriasS-N P-4200465 Porto Portugal

Interest in integrating lot-sizing and cutting stock problems has been increasing over the years. This integrated problem has been applied in many industries, such as paper, textile and furniture. Yet, there are only a few studies that acknowledge the importance of uncertainty to optimise these integrated decisions. This work aims to address this gap by incorporating demand uncertainty through stochastic programming and robust optimisation approaches. Both robust and stochastic models were specifically conceived to be solved by a column generation method. In addition, both models are embedded in a rolling-horizon procedure in order to incorporate dynamic reaction to demand realisation and adapt the models to a multistage stochastic setting. Computational experiments are proposed to test the efficiency of the column generation method and include a Monte Carlo simulation to assess both stochastic programming and robust optimisation for the integrated problem. Results suggest that acknowledging uncertainty can cut costs by up to 39.7%, while maintaining or reducing variability at the same time.

关键词： Lot-sizing cutting stock stochastic programming robust optimisation column generation rolling-horizon

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Drones for relief logistics under uncertainty after an earthquake

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期310卷 117-132页

作者： Dukkanci, Okan Koberstein, Achim Kara, Bahar Y. European Univ Viadrina Fac Business Adm & Econ D-15230 Frankfurt oder Germany Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkiye

This study presents a post-disaster delivery problem called the relief distribution problem using drones under uncertainty, in which critical relief items are distributed to disaster victims gathered at assembly points after a disaster, particularly an earthquake. Because roads may be obstructed by debris after an earthquake, drones can be used as the primary transportation mode. As the impact of an earthquake cannot be easily predicted, the demand and road network uncertainties are considered. Additionally, the objective is to minimize the total unsatisfied demand subject to a time-bound constraint on the deliv-eries, as well as the range and capacity limitations of drones. A two-stage stochastic programming and its deterministic equivalent problem formulations are presented. The scenario decomposition algorithm is implemented as an exact solution approach. To apply this study to real-life applications, a case study is conducted based on the western (European) side of Istanbul, Turkey. The computational results are used to evaluate the performance of the scenario decomposition algorithm and analyze the value of stochas-ticity and the expected value of perfect information under different parametric settings. We additionally conduct sensitivity analyses by varying the key parameters of the problem, such as the time-bound and capacities of the drones. (c) 2023 Elsevier B.V. All rights reserved.

关键词： Humanitarian logistics Relief distribution Drone delivery Uncertainty stochastic programming

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A contract-based trading of power flexibility between a variable renewable energy producer and an electricity retailer

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2023年 34卷

作者： Mousavi, Milad Alvarez, Manuel Lulea Univ Technol Dept Engn Sci & Math Forskargatan 1 S-93187 Skelleftea Sweden

Variable renewable energy producers and electricity retailers encounter several uncertainties in their decision-making problems, such as intermittency of renewable energy sources, variability of consumption, and market price volatility. To cope with these uncertainties, this paper presents a new contract-based trading mechanism of power flexibility (FlexCon) between two parties, a variable renewable energy producer and an electricity retailer. The proposed mechanism is managed by a new entity, named FlexCon operator, to oversee the energy and financial trades through the contract and coordinate the transactions with the system operator. Through the FlexCon, the parties are able to exchange their energy imbalances as a source of power flexibility to alleviate the negative impacts of uncertainties in their decision-making problems. To this end, two two-stage stochastic linear problems are introduced from each party's point of view. In the first stage, the variable renewable energy producer and the electricity retailer submit their bids to sell and purchase in the day-ahead market, respectively. Following the day-ahead market clearing, closer to the delivery time, the parties submit their decisions on the contract to the introduced FlexCon operator. The operator allocates possible power flexibility transactions based on the surpluses or shortages of the parties. Assuming that the imbalances are not completely resolved with the FlexCon, the remaining deviations are settled in the balancing market. The parties' decisions related to the balancing market and the FlexCon are modeled in the second stage of the stochastic problem. The uncertainties associated with prices, renewable generation, electricity consumption, and the maximum exchangeable power flexibility through the FlexCon are considered via scenarios. Meanwhile, the profit risk is considered by the Conditional Value at Risk measure. The numerical results show that FlexCon effectively diminishes the impacts of unce

关键词： Contract-based trading Electricity retailer Power flexibility stochastic programming Variable renewable energy producer

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An optimization scheme for designing power rationing schedules in a long-term power shortage

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ELECTRIC POWER SYSTEMS RESEARCH 2023年 225卷

作者： Mou, Yuting Wang, Beibei Shen, Zhan Southeast Univ Sch Elect Engn Nanjing 210018 Jiangsu Peoples R China

Power rationing is the last resort to prevent large-scale blackouts after demand response resources are exhausted during power shortages. However, the traditional rolling blackout method has been criticized for causing significant losses. To address this issue, this paper proposes a novel optimization scheme for designing power rationing schedules in a long-term power shortage, which considers different types of consumers at multiple time scales. The proposed scheme takes into account economic losses due to limited power supply, disruptions in industrial chains, and the social costs caused by excessive activation of the same consumers. First, consumers are categorized as maintenance consumers, work-shift consumers, and fast-response consumers based on their consumption characteristics. Then, a two-stage stochastic programming model is presented to account for long-term uncertainties in power shortage, which yields the maintenance and work-shifting schedules. Given these predetermined schedules, once the demand-supply gap is better revealed in real-time, a dispatch model for fast-response consumers is solved to generate the activation schedules. The case study demonstrates that the proposed scheme can effectively reduce costs when compared to the rolling blackout approach, as well as respecting industrial chain coupling and fairness.

关键词： Power rationing Orderly power utilization stochastic programming Demand side management Multiple time scales Maintenance tasks scheduling Industrial chain Fairness

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