Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling
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Institute of Hydropower System & Hydroinformatics, Dalian University of Technology, Dalian 116024, China
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Department of Civil and Environmental Engineering, University of California, Merced, CA 95340, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Tomonobu Senjyu
Sustainability 2021, 13(9), 4706; https://doi.org/10.3390/su13094706
Received: 26 March 2021
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Revised: 17 April 2021
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Accepted: 21 April 2021
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Published: 22 April 2021
(This article belongs to the Special Issue Multi-Utility Energy System Optimization)
Short-term hydrothermal scheduling (STHS) can improve water use efficiency, reduce carbon emissions, and increase economic benefits by optimizing the commitment and dispatch of hydro and thermal generating units together. However, limited by the large system scale and complex hydraulic and electrical constraints, STHS poses great challenges in modeling for operators. This paper presents an improved proximal bundle method (IPBM) within the framework of Lagrangian relaxation for STHS, which incorporates the expert system (ES) technique into the proximal bundle method (PBM). In IPBM, initial values of Lagrange multipliers are firstly determined using the linear combination of optimal solutions in the ES. Then, each time PBM declares a null step in the iterations, the solution space is inferred from the ES, and an orthogonal design is performed in the solution space to derive new updates of the Lagrange multipliers. A case study in a large-scale hydrothermal system in China is implemented to demonstrate the effectiveness of the proposed method. Results in different cases indicate that IPBM is superior to standard PBM in global search ability and computational efficiency, providing an alternative for STHS.
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Keywords:
Lagrangian relaxation; expert system; proximal bundle method; orthogonal design; hydrothermal scheduling
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MDPI and ACS Style
Yan, Z.; Liao, S.; Cheng, C.; Medellín-Azuara, J.; Liu, B. Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling. Sustainability 2021, 13, 4706. https://doi.org/10.3390/su13094706
AMA Style
Yan Z, Liao S, Cheng C, Medellín-Azuara J, Liu B. Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling. Sustainability. 2021; 13(9):4706. https://doi.org/10.3390/su13094706
Chicago/Turabian StyleYan, Zhiyu, Shengli Liao, Chuntian Cheng, Josué Medellín-Azuara, and Benxi Liu. 2021. "Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling" Sustainability 13, no. 9: 4706. https://doi.org/10.3390/su13094706
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