A Novel Recursive Methodology for Power Flow Analysis Based on the Holomorphic Embedding Method Using the Total Multiplication of Polynomials

This paper introduces an innovative recursive methodology for ultra-fast load flow analysis. The approach is based on the Holomorphic Embedding Load Flow Method (HELM) and employs the Total Multiplication of Polynomials (TMP) to enhance computational efficiency and accuracy. Unlike traditional HELM, the proposed procedure bypasses the need for analytical continuation, directly solving the load flow by simple polynomial multiplication. This approach provides solutions with reduced computational time compared to alternative methods. The methodology deduces general expressions for calculating higher-order terms of the Maclaurin series, eliminating the need for time-consuming matrix inversions or comparisons with Padé approximants. To demonstrate the effectiveness of the proposed method, computational simulations were performed using a wide variety of test systems, including the IEEE 118-bus transmission system and the equivalent 476-bus Brazilian distribution system. The main contribution is the TMP procedure, which accelerates the recursive solution process. Due to a significantly reduced computational time for higher-order term calculations, the proposed method is well suited for real-time applications, including ill-conditioned and overloaded power networks. This feature enables an accurate calculation of the maximum loadability point in the context of voltage stability assessment, allowing the determination of the exact solution even in cases where the traditional Newton-Raphson load flow fails to converge.