The sequential power flow in complex plane for solving the VSC-MTDC hybrid AC/DC transmission grids

Abstract

This paper presents new methodologies and modeling aimed at studying interwoven AC and DC subsystems of a power system in the complex plane. It is well known that the development of any former power flow application in real domain addressed to embedding FACTS devices is preceded by an arduous algebra task. To overcome this difficulty, a novel power flow solution method is proposed in this work. Thanks to the Wirtinger calculus, a Newton–Raphson method based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates is developed. Thus, the voltage-source-converter multi-terminal direct current is formulated in complex plane without any loss of accurateness and is termed as VSC-MTDC. Its performance is assessed through IEEE-test systems interconnected across a DC network prone to several scenarios, e.g., topology, loading magnitude and interchanging of active power.