Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads
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 incorpora...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/9/1439 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850032143508439040 |
|---|---|
| author | Keyong Hu Qingqing Yang Lei Lu Yu Zhang Shuifa Sun Ben Wang |
| author_facet | Keyong Hu Qingqing Yang Lei Lu Yu Zhang Shuifa Sun Ben Wang |
| author_sort | Keyong Hu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e293ff4448fc42929e9cb2927a872377 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e293ff4448fc42929e9cb2927a8723772025-08-20T02:58:44ZengMDPI AGMathematics2227-73902025-04-01139143910.3390/math13091439Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and LoadsKeyong Hu0Qingqing Yang1Lei Lu2Yu Zhang3Shuifa Sun4Ben Wang5School of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, ChinaSchool of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, ChinaSchool of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, ChinaSchool of Engineering, Hangzhou Normal University, Hangzhou 311121, ChinaSchool of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, ChinaSchool of Information Science and Technology, Hangzhou Normal University, Hangzhou 311121, ChinaTo 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.https://www.mdpi.com/2227-7390/13/9/1439integrated energy systemtwo-stage distributionally robust optimizationdemand responseuncertainties analysis |
| spellingShingle | Keyong Hu Qingqing Yang Lei Lu Yu Zhang Shuifa Sun Ben Wang Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads Mathematics integrated energy system two-stage distributionally robust optimization demand response uncertainties analysis |
| title | Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads |
| title_full | Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads |
| title_fullStr | Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads |
| title_full_unstemmed | Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads |
| title_short | Two-Stage Distributionally Robust Optimal Scheduling for Integrated Energy Systems Considering Uncertainties in Renewable Generation and Loads |
| title_sort | two stage distributionally robust optimal scheduling for integrated energy systems considering uncertainties in renewable generation and loads |
| topic | integrated energy system two-stage distributionally robust optimization demand response uncertainties analysis |
| url | https://www.mdpi.com/2227-7390/13/9/1439 |
| work_keys_str_mv | AT keyonghu twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads AT qingqingyang twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads AT leilu twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads AT yuzhang twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads AT shuifasun twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads AT benwang twostagedistributionallyrobustoptimalschedulingforintegratedenergysystemsconsideringuncertaintiesinrenewablegenerationandloads |