Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling

Benxi Liu,Chuntian Cheng,Shengli Liao,Josué Medellín-Azuara,Zhiyu Yan

doi:10.3390/su13094706

Abstract

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.

Highlights

Technique and standard proximal bundle method (PBM) within the Lagrangian relaxation (LR) framework is presented in this paper
In improved proximal bundle method (IPBM), the expert system (ES) consists of two parts: a knowledge base and inference engine
The knowledge base is built by extracting knowledge expressions from historical generation scenarios

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. According to the International Energy Agency, thermal power and hydropower are basic sources of electricity production in many countries [1]. Short-term hydrothermal scheduling (STHS) is necessary in power system operations. The significance of STHS is to improve water use efficiency, reduce carbon emissions, and increase economic benefits by optimizing the commitment and generation level of hydro and thermal generating units together [2]. Limited by complex hydraulic and electrical constraints, the nature of STHS is a large-scale nonconvex, nonlinear problem with integer variables, posing great challenges in modeling for operators [3]

Methods

Results

Conclusion