| dc.description.abstract | Power electronics converters play a major role as interface to the AC grid as we transition towards an electric and renewable society. The converters are controlled, modelled and generally understood in time-periodic coordinate systems - for example the synchronous reference frame - where the dynamics are ostensibly time invariant. This is only true under symmetric conditions; periodically varying equations and quantities result otherwise. The last three decades have seen an ample amount of investigation into time-periodic converter dynamics, usually under the label frequency couplings. While the underlying theory is old, it is not easy to leverage in practice. This thesis targets that; to provide accessible means for efficient study of frequency coupled power electronics systems.
The first half of the thesis concerns automated model generation and parametric stability study of these, in the Harmonic State Space (HSS) framework. In absence of publicly available implementations of HSS models, the code is open sourced on GitHub. Significant stability margin differences are exposed for seemingly innocent modifications of the well-known Second Order Generalised Integrator Phase-Locked Loop. Then,HarmonicTransfer Function (HTF) impedance models illuminate the impact of synchronisation on the converter current harmonics for different current controllers – with the controversial finding that the impact is neglectable in most cases. Finally, investigation of a grid-forming, grid connected converter - operated with dispatchable Virtual Oscillator Control (dVOC) - shows strong frequency couplings and weak stability margins.
The second half concerns wideband frequency scanning of impedances with HTF representations. Such scans are generally time-consuming as a singleinput-single-output (SISO) system in time-domain becomes multiple-input-multiple-output (MIMO) in frequency domain. A time-domain interpretation of the chirp stimulus is leveraged to design a simple wideband frequency scan through only one chirp signal. Weak damping, corresponding to sharp resonances, are shown to present a particular challenge. The discrepancy between the time-domain response and the frequency response is quantified and limited through a chirp error controller. All-hardware chirp frequency scans for a dVOC operated single-phase Static Synchronous Compensator are verified against traditional single-tone scanning and a white-box HSS model. | en_US |
