Computational Complexity Analysis of the Holomorphic Embedding Method and Parallel Optimization Strategies for Improving Efficiency

IF 2.8 Q3 ENERGY & FUELS

IEEE Open Access Journal of Power and Energy Pub Date : 2026-01-01 Epub Date: 2026-03-26 DOI:10.1109/OAJPE.2026.3696776

Yongjian Luo;Chengxi Liu;Pengfei Tang;Zaiyu He

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Abstract

The holomorphic embedding (HE) method has gained significant attention in power flow analysis. However, there is no consensus regarding its computational efficiency compared to the traditional Newton-Raphson (NR) method. This paper presents a comprehensive analysis of the computational complexity of the HE method focusing on key steps such as matrix factorization, higher-order power series calculation, and Padé approximation. A theoretical investigation of these steps is conducted, followed by the implementation of multi-core parallel computing using Numba to enhance performance. Case studies on test systems ranging from 300 to 25,000 buses are used to evaluate the parallel strategies for accelerating computation. The results show a significant improvement in the computational efficiency of the HEM, demonstrating its scalability and practical applicability for large-scale power flow calculations. This study provides both theoretical and practical foundations for the broader adoption of the HE method in power system analysis.

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全纯嵌入方法的计算复杂度分析及提高效率的并行优化策略

全纯嵌入（HE）方法在潮流分析中得到了广泛的关注。然而，与传统的Newton-Raphson （NR）方法相比，其计算效率并没有达成共识。本文全面分析了HE方法的计算复杂度，重点介绍了矩阵分解、高阶幂级数计算和pad近似等关键步骤。对这些步骤进行了理论研究，然后使用Numba实现了多核并行计算以提高性能。在300到25000总线的测试系统上进行了案例研究，以评估加速计算的并行策略。结果表明，HEM的计算效率有了显著提高，证明了其在大规模潮流计算中的可扩展性和实用性。本研究为HE方法在电力系统分析中的广泛应用提供了理论和实践基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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