Open Access

ARTICLE

Harnessing Trend Theory to Enhance Distributed Proximal Point Algorithm Approaches for Multi-Area Economic Dispatch Optimization

Yaming Ren^1,*, Xing Deng²

1 College of Mechanical and Control Engineering, Guilin University of Technology, Guilin, 541006, China
2 School of Computer, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

* Corresponding Author: Yaming Ren. Email:

Computers, Materials & Continua 2025, 82(3), 4503-4533. https://doi.org/10.32604/cmc.2024.059864

Received 18 October 2024; Accepted 12 December 2024; Issue published 06 March 2025

Abstract

The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution, particularly within multi-area interconnected power grids. This complexity necessitates the employment of distributed solution methodologies, which are not only essential but also highly desirable. In the realm of computational modelling, the multi-area economic dispatch problem (MAED) can be formulated as a linearly constrained separable convex optimization problem. The proximal point algorithm (PPA) is particularly adept at addressing such mathematical constructs effectively. This study introduces parallel (PPPA) and serial (SPPA) variants of the PPA as distributed algorithms, specifically designed for the computational modelling of the MAED. The PPA introduces a quadratic term into the objective function, which, while potentially complicating the iterative updates of the algorithm, serves to dampen oscillations near the optimal solution, thereby enhancing the convergence characteristics. Furthermore, the convergence efficiency of the PPA is significantly influenced by the parameter c. To address this parameter sensitivity, this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA, thereby enhancing the robustness of the computational models. The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour, stability, and robustness with respect to parameter selection, potentially outperforming existing methods such as the alternating direction method of multipliers (ADMM) and Auxiliary Problem Principle (APP) in the computational simulation of power system dispatch problems. The simulation results demonstrate that the trend theory-based PPPA, SPPA, ADMM and APP exhibit significant robustness to the initial value of parameter c, and show superior convergence characteristics compared to the residual balancing ADMM.

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Keywords

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