A Novel Fast and Flexible Holomorphic Embedding Power Flow Method

A novel, fast, and flexible holomorphic embedding (FFHE) method is proposed for solving power flow problems with Q-limits. New embedded systems are developed for power flow equations at the PV and PQ buses for flexibility that allows us taking any state, instead of accepting only some certain point (e.g., a flat start and a zero-current injection point), as the initial guess. This flexibility allows us a warm start, a dc power flow solution, or other starts, leading to the reduced runtime and a decreased number of needed steps, as compared with existing embedded systems that only accept several particular points as the initial guess. However, the proposed method may not be globally convergent in the sense that such flexibility and flexible embedded systems do not ensure convergence or a superior rate of convergence for an arbitrary start. To implement the proposed FFHE, a new numerical scheme is devised to compute the numerical solution without explicitly calculating the rational approximant. To evaluate its effectiveness and practicability, the proposed novel FFHE method is applied to a series of power flow test cases ranging from 3 to 13659 buses. It is found that the proposed FFHE method requires less runtime than Newton's method for most test cases. By using Newton's method as a reference, FFHE is shown to be more effective than the holomorphic embedding methods that had been documented in the literature; partly due to its flexibility and the new scheme for computing numerical solutions.