Harmonic state space modelling of voltage source converters

The thesis describes the development of a model of the three-phase Voltage Source Converter (VSC) in the Harmonic State Space (HSS) domain, a Linear Time Periodic (LTP) extension to the Linear Time Invariant (LTI) state space. The HSS model of the VSC directly captures harmonic coupling effects using harmonic domain modelling concepts, generalised to dynamically varying signals. Constructing the model using a reduced-order three-phase harmonic signal representation achieves conceptual simplification, reduced computational load, and direct integration with a synchronous frame vector control scheme. The numerical switching model of the VSC is linearised to gain a small-signal controlled model, which is validated against time-domain PSCAD/EMTDC simulations. The controlled model is evaluated as a STATCOM-type system, exercising closed-loop control over the reactive power flow and dc-side capacitor voltage using a simple linear control scheme. The resulting statespace model is analysed using conventional LTI techniques, giving pole-zero and root-locus analyses which predict the dynamic behaviour of the converter system. Through the ability to independently vary the highest simulated harmonic order, the dependence on the closed-loop response to dynamic harmonic coupling is demonstrated, distinguishing the HSS model from fundamental-only Dynamic Phasor models by its ability to accurately model these dynamics.

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