Harmonic modelling in Hartley's domain with particular reference to three phase thyristor-controlled reactors

The main objectives of this paper are to present a new frame-of-reference based on the use of Hartley's transform and to present a three-phase thyristor controlled reactor (TCR) harmonic model which uses Hartley's domain. Solutions using the new frame-of-reference are between two to four times faster than solutions using an established frame-of-reference based on Fourier's transform because Hartley's transform makes use of the real plane as opposed to the complex plane. Harmonic switching vectors in Hartley's domain have been developed for maximum computer efficiency. Their use, combined with discrete convolution operations, provide cleaner and faster operations than those afforded by the fast Hartley transform. The TCR model is completely general and caters for any kind of plant imbalances, e.g. uneven firing angles and inductances. Network imbalances are accounted for via the excitation voltage. The new frame-of-reference accommodates any number of buses, phases, harmonics and cross-couplings between harmonics. It provides a reliable and efficient means for the iterative solution of power systems harmonic problems through a Newton-Raphson method which exhibits quadratic convergence.