Dynamic Analysis of Harmonics in Electrical Systems

Frequency domain analysis and design of power systems is complicated in the presence of harmonics, switching dynamics, nonlinearities, unbalances, and for systems with mixed ac/dc dynamics. The reason is that linearization of the system does not lead to a time invariant system, but a system with periodically time varying dynamics, which implies that there is coupling between different frequencies. Often one has to rely on simplifying assumptions and simulation.

The thesis uses linear time periodic (LTP) models to analyze power systems. The harmonic transfer function (HTF) for LTP systems is introduced. Using the HTF, the system can be treated as an infinitely dimensional linear time invariant system, which means that the system, under certain convergence conditions, can be analyzed using the well developed theory for LTI systems.

The thesis contains four papers with power system applications. Paper I describes the modeling and analysis of networks including components with switching dynamics, such as diodes and thyristors. An algorithm for parameter estimation from experimental data is presented. Papers II and III treats modeling and analysis of single-phase railway systems. The modeling of the locomotives is performed in collaboration with industry. Paper IV treats analysis and control aspects of a converter for grid connection of a micro-turbine used for distributed power generation. This is a three-phase application done in collaboration with the industry.