A long-term power system state calculation method using sequential power and holomorphic embedding

•After making the requested revisions to the manuscript, the highlights are as follows:.•We propose a power sequential analysis model that shifts power system analysis from a traditional time-series perspective to an energy-based approach;.•The incremental properties of the power series in the HE method are analyzed, and an incremental holomorphic embedding load flow method is established;.•By combining the power sequential analysis model with the incremental holomorphic embedding load flow Method, a power sequential flow method from the energy perspective is developed to rapidly and accurately calculate the distribution of power system state variables over long time scales. Traditional Power Flow (PF) calculations struggle to support the data analysis requirements as the power system develops. Therefore, this paper introduces a non-sequential and non-iterative PF calculation method to enhance the computational speed and analytical efficiency of power system state variables over long time scales. Firstly, a Power Sequential Division (PSD) method is proposed, representing the power curve using hierarchical energy with temporal characteristics. Next, based on the Fast and Flexible Holomorphic Embedding (FFHE) method, the paper explores the incremental properties of Voltage Power Series Coefficients (VPSC) and proposes an Incremental Holomorphic Embedding (IHE) method. Finally, by combining PSD and IHE, this study introduces a Power Sequential Flow (PSPF) method for rapid computation of power system state variables over long time scales. Unlike traditional PF methods, PSPF method shifts away from time-series calculations and instead analyzes the distribution of power system state variables over long time scales from an energy perspective. Various test cases are set up to analyze the performance characteristics of IHE and PSPF from multiple perspectives. The results indicate that the proposed methods significantly outperform traditional PF methods in terms of computational speed, adaptability to test cases, and analytical efficiency.