Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads

Keyong Hu (), Qingqing Yang, Lei Lu, Yu Zhang, Shuifa Sun and Ben Wang ()
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Keyong Hu: School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, China
Qingqing Yang: School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, China
Lei Lu: School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, China
Yu Zhang: School of Engineering, Hangzhou Normal University, Hangzhou 311121, China
Shuifa Sun: School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, China
Ben Wang: School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, China

Mathematics, 2025, vol. 13, issue 9, 1-30

Abstract: To effectively account for the impact of fluctuations in the power generation efficiency of renewable energy sources such as photovoltaics (PVs) and wind turbines (WTs), as well as the uncertainties in load demand within an integrated energy system (IES), this article develops an IES model incorporating power generation units such as PV, WT, microturbines (MTs), Electrolyzer (EL), and Hydrogen Fuel Cell (HFC), along with energy storage components including batteries and heating storage systems. Furthermore, a demand response (DR) mechanism is introduced to dynamically regulate the energy supply–demand balance. In modeling uncertainties, this article utilizes historical data on PV, WT, and loads, combined with the adjustability of decision variables, to generate a large set of initial scenarios through the Monte Carlo (MC) sampling algorithm. These scenarios are subsequently reduced using a combination of the K-means clustering algorithm and the Simultaneous Backward Reduction (SBR) technique to obtain representative scenarios. To further manage uncertainties, a distributionally robust optimization (DRO) approach is introduced. This method uses 1-norm and ∞-norm constraints to define an ambiguity set of probability distributions, thereby restricting the fluctuation range of probability distributions, mitigating the impact of deviations on optimization results, and achieving a balance between robustness and economic efficiency in the optimization process. Finally, the model is solved using the column and constraint generation algorithm, and its robustness and effectiveness are validated through case studies. The MC sampling method adopted in this article, compared to Latin hypercube sampling followed by clustering-based scenario reduction, achieves a maximum reduction of approximately 17.81% in total system cost. Additionally, the results confirm that as the number of generated scenarios increases, the optimized cost decreases, with a maximum reduction of 1.14%. Furthermore, a comprehensive cost analysis of different uncertainties modeling approaches is conducted, demonstrating that the optimization results lie between those obtained from stochastic optimization (SO) and robust optimization (RO), effectively balancing conservatism and economic efficiency.

Keywords: integrated energy system; two-stage distributionally robust optimization; demand response; uncertainties analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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