Modelling of power system transformers in the complex conjugate harmonic space
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Magnetizing harmonics in power systems have received limited attention. The general belief is that they do not reach harmful levels in interconnected networks. Moreover the modelling of non-linearities is not a straightforward procedure and so there has been little motivation to develop appropriate methodologies that allow a thorough investigation to take place. In this thesis the problem of magnetizing harmonics in power systems is investigated. The results obtained show that, contrary to expectations, magnetizing currents can give rise to a considerable harmonic distortion in the voltage wave form of power networks operating under loaded conditions. The method adopted in this research linearizes each magnetic non-linearity around a base operating point. The linearization exercise takes place in the complex-conjugate harmonic space and the individual linearized equations may be interpreted as harmonic Norton equivalents. These equations combine easily with each other and with the transfer admittances representing the linear part of the network. The overall process of linearization may be seen as a linearization of the entire network and can also be interpreted as a multi-nodal, polyphase harmonic Norton equivalent. This problem is non-linear and the harmonic solution is reached by an iterative process. A re-linearization of the network takes place at each iterative step and so the solution is found through a Newton-type procedure. Several iterative strategies are tested, including unified and sequential solutions with either single or multi-evaluated Jacobians. A hitherto neglected problem which also receives attention is the harmonic modelling of non-homogenous transmission lines. A novel approach to the modelling of the frequency dependent part of the transmission line is also presented. The equations proposed are shown to be the fastest to date and yet maintain a high degree of accuracy.