On the Holomorphic and Conjugate Properties for Holomorphic Embedding Methods for Solving Power Flow Equations

Holomorphic embedding (HE) methods have been proposed to solve different power flow problems using tailored embedded systems; however, a solid theoretical foundation to ensure the effectiveness of HE methods is still missing. In addition, several analytical and numerical issues associated with HE methods remain to be resolved. The present study is devoted to the theoretical foundation of HE methods and develops existence theorems and sufficient conditions to deal with two key issues: how to ensure the holomorphic and conjugate properties of solution functions for a general embedded system for the power flow problem. Useful implications and guidelines are derived from these theoretical results. Examples and simulation results are conducted to demonstrate the developed theory.