Harmonic state-space modelling of a controlled HVdc converter

In this paper a harmonic state-space (HSS) model of a 6-pulse HVdc converter with constant current control is presented. The HSS provides a linear time-invariant (LTI) environment for modelling system harmonics under both steady-state and transient conditions. Although nonlinear and time-variant in nature, the HVdc converter can be linearised around an operating point described by fixed thyristor switching instants. The effect of varying switching instants, both through control and commutation period dynamics, is modelled. The HSS model is implemented in MATLAB and it is validated against a purely time domain model built in PSCAD/EMTDC. It is shown that the combination of frequency coupling through the converter and closing the current control loop can result in high frequency resonances dominating low frequency transient performance. The approach can be generalised to many switching converters, and the HVdc converter example shows how the mechanism behind problems involving non-characteristic frequencies can be identified.