Discharge characteristics and discharge simulation model of long air gaps containing a floating conductor

Long air gaps containing a floating conductor are common insulation types in power grids. During the transmission line live-line work, the process of lineman entering the transmission line air gap constitutes a live-line work combined air gap, which is a typical long air gap containing a floating conductor. This thesis investigates the discharge characteristics, the discharge mechanism and a discharge simulation model of long air gaps containing a floating conductor in order to address the engineering issues in live-line work. The innovative achievements of the thesis are as follows: (1) The effect of the gap distance, the floating electrode structure, the switching impulse wavefront time, the altitude, and the deviation of the floating conductor from the axis on the breakdown voltage was determined. (2) The physical process of the discharges in long air gaps containing a floating conductor was determined. The reason why the discharge characteristics of long air gaps containing a floating electrode with complex geometrics and sharp protrusions and long air gaps with a rod-shaped floating electrode are similar has been studied. The formation mechanism of the lowest breakdown voltage area of a long air gap containing a floating conductor is explained. (3) A simulation discharge model of long air gaps containing a floating conductor was established, which can describe the physical process and predict the breakdown voltage. The model can realize the accurate prediction of the breakdown voltage of typical long air gaps containing a floating conductor and live-line work combined air gaps in transmission lines. The findings of the study can provide theoretical reference and technical support for improving the safety of live-line work.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.