Switching Instant Variation in Harmonic State-Space modelling of power electronic devices

In classical harmonic domain (HD) modelling, a frequency transfer matrix is used to describe the frequency coupling across a power electronics device. This is normally based on switching functions using pre-defined switching instants. These are usually arrived at via an iterative process. In extending HD to Harmonic State-Space (HSS) where transient harmonic variation can be modelled, it is imperative to have a linear model for Switching Instant Variation (SIV) which is either produced autonomously due to input variation or introduced from the control algorithm. Control contributes significantly to system stability and must be modelled for correct system representation. This paper presents these types of SIV in the context of developing an HSS model for a three-phase Thyristor Controlled Reactor (TCR) and a High Voltage Direct Current (HVDC) Converter.