Mathematical analysis of FACTS devices based on a voltage source converter Part 1: mathematical models

摘要

This paper systematically presents mathematical models of a voltage source converter in different modes of operation and with different connections to a networks. These models are very useful in examining the operation of FACTS devices based on this voltage source converter. The derivations and mathematical descriptions re based on the transformation of a three-phase system into an orthogonal stationary or synchronously rotating coordinate system. Mathematical models are necessary for the analysis of the operation of FACTS devices, especially when deriving a control algorithm. A description of a series and shunt voltage source converter is given by state space equations. The steady-state operational characteristics of various static compensators can be determined using the rotating orthogonal coordinate system, in which, under steady-state conditions, all quantities are constant values. Thus, at given parameters, it is generally possible to determine the dimensions of devices.