Phase-domain power flows in the rectangular co-ordinates frame of reference including VSC-based FACTS controllers

This paper presents a method for systematic modelling of VSC-based FACTS controllers within three-phase power flows in rectangular co-ordinates. Among the FACTS controllers modelled are the STATCOM, SSSC, UPFC and HVDC-VSC. The approach taken is to represent the fundamental frequency operation of each power converter as a three-phase voltage source behind a leakage reactance, where one or two of them may be connected in either series or parallel depending on the FACTS controller being modelled. Active and reactive power flow equations are developed for each voltage source circuit together with constraint equations to account for co-ordinated operation of two converters, such as in modelling of UPFC and HVDC-VSC. The power flow equations representing the VSC-based FACTS controllers are combined with the nodal power equations of the power network for a combined iterative solution using a Newton–Raphson three-phase power flow algorithm in rectangular co-ordinates enabling robust and efficient solutions of three-phase power networks with any number and kind of VSC-based controllers.