Some Properties of Impulse Response of Distribution Networks With Periodic Tree-Type Topology

The main motivation for this paper was to investigate certain asymptotic properties of impulse response in periodic tree-type distribution networks owed to the network topology alone, regardless of ohmic losses or material dispersion normally present in practical situations. The research was performed using theoretical analysis of Dirac impulse propagation through a model network, with a focus on topology-related features. Several numerical examples were designed to illustrate the meaning of the main conclusion, namely that the very topology of any tree-type network leads to an impulse response in which amplitudes of individual pulses decay rapidly with their respective delays after the leading impulse. On the other hand, it was not a goal of this research to design any practical tool for network-response calculation. The very fact that impulse response decays rather quickly after the train of the first few impulses does not mean that the calculation of these first few is by any means simple. The frequency-domain network-analysis methods in case of a complex distribution network with a tree-like topology seem to have practical advantages over the impulse-response calculation techniques, especially because the effects of ohmic losses and material dispersion would have to be included in any model constructed for realistic simulations, and in the authors' experience, this can be done more easily in frequency-domain-based models.