Three-phase three-limb transformer models in the harmonic domain
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis describes a new three-limb three-phase electromagnetic transformer model in the Harmonic Domain. It is a composite model, with the linear circuit represented by the short-circuit impedances, and the non-linear magnetic circuit represented in a linearised form by means of Norton equivalents. The proposed Norton equivalents accurately represent the magnetic circuit, as they are derived from the linearisation (in the Harmonic Domain) of individual magnetising characteristics for the magnetic branches and the magnetic circuit laws. A Newton-Raphson iterative procedure is also developed to accurately determine the non-linear distribution of the magnetic fluxes. The influence of the magnetising characteristic approximation upon the harmonic solution is investigated. The adequacy of several approximations, including cubic splines, are assessed and Singular Value Decomposition have been explored to determine the equation parameters. The widely accepted assumption of equally distributing the magnetising currents between the primary and secondary terminals is also investigated. For single-phase transformer models this assumption is shown to be inaccurate, at harmonic frequencies, and inadequate, for star-connected three-phase transformer models and improved harmonic distribution factors for the magnetising currents are proposed. Three-phase three-limb electromagnetic transformer models for the most commonly used winding electrical configurations are derived, and the simulations results analysed by means of sensitivity analysis and comparisons with the practical and theoretical knowledge reported in the literature.