Enhanced power flow methods in complex plane for VSC-MTDC hybrid AC/DC transmission grids

Abstract

The power flow problem is composed of phasor variables and quantities and thus can be naturally formulated in the complex domain; however, their applications are commonly developed in the real domain. The solution via the Newton-Raphson method, for example, would be restricted in the real domain once the Taylor series expansion in terms of complex variables alone does not exist. Thanks to the Wirtinger calculus, a Newton-Raphson method based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates becomes possible. As new technologies are implemented in power systems, such as the incorporation of FACTS devices, the development of power flow applications becomes increasingly intricate, and maintaining their formulations in the real domain is preceded by an arduous algebra task. To overcome this difficulty, a series of power flow solution methods are proposed in this work, specified to solve multiterminal AC/DC hybrid systems, being formulated in the complex plane without any loss of precision. Both sequential and unified approaches for solving hybrid AC/DC power flow are derived in the complex plane. In order to improve the performance of the algorithms, an exact second-order power flow algorithm in the complex domain is also proposed. Such power flow models in the complex plane are naturally developed in Cartesian coordinates; therefore, most constraint equations can be written as quadratic functions. Consequently, the Taylor series expansion stops at its second order and the exact non-linearity of complex quadratic power flow equations is maintained. Minor changes in the code structure are required to transform the Newton-Raphson method into the exact power flow approach in the complex plane. The new algorithm exhibits either a superior behavior in fully AC or hybrid AC/DC networks. In order to show the validity of its formulations, the proposed algorithms are implemented in Matlab for well-established case studies of the IEEE-14, -30, -57 and -118 bus, a modified version of the IEEE Two Area RTS-96, and the Brazilian Southern-equivalent of 1916-buses, termed as SIN-1916. The features and advantages of the proposed algorithms are illustrated through the test systems interconnected across a DC network prone to several scenarios, e.g., topology, voltage control, and interchanging of active power.