Multi-Dimensional Holomorphic Embedding Three-Phase Power Flow for AC-DC Hybrid Distribution Systems

In this paper, a multi-dimensional holomorphic embedding method (MDHEM) is developed to solve three-phase unbalanced power flow in AC-DC hybrid distribution systems (DSs). According to the
${\bm{\pi }}$
-model of AC-DC converters, a proper embedding approach is first designed for the unified single-phase power flow model, which is compatible with the existing holomorphic embedding method (HEM) for AC and DC systems. Then, independent variables are embedded to represent the unbalanced power injection at each phase at each bus, and the MDHEM is proposed to solve the complete three-phase power flow. The characteristics of AC-DC hybrid DSs and the advantages of HEM (such as reliable convergence and non-iteration) are fully reserved in the proposed approach. Additionally, this approach is capable of encountering versatile unbalanced operating conditions by plugging the actual status values. Moreover, an Epsilon algorithm is implemented in Multivariate Padé approximants to get rid of redundant calculations but maintaining accuracy. Several case studies with different system scale are also conducted by MDHEM and Newton-Raphson methods in order to demonstrate the effectiveness and reliability of the proposed MDHEM.