Holomorphic embedding method based Three-Phase power flow algorithm considering the sensitivity of the initial value

The transmission network is generally considered as three-phase balanced, while the consideration of three-phase unbalance is mainly on distribution networks. However, with the increasingly interconnection of renewable energy, such as wind energy, onto transmission networks, non-adoption of commutation long transmission lines usually results in unbalanced line parameters. Therefore, developing reliable three-phase power flow algorithms for transmission and distribution (T&D) systems becomes more and more important for the reliable and safe operation of emerging power systems. Among the many three-phase power flow algorithms, Newton Raphson method (NRM) and its variants occupy a large share, due to their ability in dealing with multiple sources and looped sub-networks. However, they are sensitive to the initial value, and can hardly ensure convergence to a physically meaningful solution with improper initial values, especially for three-phase unbalanced system. To this end, a general three-phase power flow method for T&D systems is proposed based on the holomorphic embedding method (HEM), and the advantages of the proposed method compared with traditional NRM in solving the power flow problem to a physically meaningful solution are theoretically analyzed. Based on the IEEE 33 system, the modified IEEE 123 system, and a regional power grid in China, it is verified that the proposed method has the advantages of high computational efficiency, reliable converging ability, and independence to the initial value. © 2024 The Author(s)