Harmonic State-Space Modelling of an HVdc Converter with Closed-Loop Control
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Frequency domain models for power electronic circuits are either based on iterative techniques such as Newton's method or linearised around an operating point. Iterative frequency domain models provide great accuracy as they are capable of calculating the exact switching instants of the device. On the other hand, the accuracy of a linearised frequency domain model relies on the magnitude of input waveform to be small so that the circuit's operating point does not vary or varies very little. However, an important advantage of a linearised model is its ability to provide insight into waveform distortion interaction, more specifically, the frequency cross-coupling around a power electronic circuit.
In general, a linearised model for harmonic analysis would not normally include the description of feedback control. Likewise a linearised model for control analysis would usually disregard frequency interactions above the fundamental (or the most significant component); that is assuming the cross-coupling between harmonic frequencies does not affect the dynamics of control. However, this thesis proposes that a linearised model for control analysis shall also include the complete description of frequency cross-coupling between harmonics to produce the correct dynamic response.
This thesis presents a harmonic state-space (HSS) model of an HVdc converter that incorporates the full effect of varying switching instants, both through control and commutation period dynamics, while remaining within the constraints of a linear time-invariant (LTI) system. An example is given using the HSS model to explain how a close to fifth harmonic resonance contributes to the dominant system response through the frequency cross-coupling of the converter and the controller feedback loop. The response of the system is validated against a time domain model built in PSCAD/EMTDC, and more importantly, the correct response cannot be produced without including the harmonic interactions beyond the fundamental frequency component.