This thesis considers how an assessment method for reinvestments in the distribution grid can be designed and implemented. The assessment method was created to give long-term estimations of the amount overhead lines that could be substituted with underground cables and how to prioritize between different areas. The regulation of power grid companies was reviewed to highlight important factors for profitable reinvestments. The assessment method was implemented for overhead lines in Ellevio´s distribution grid using the database program FME and validated against real reinvestment decisions in a case study area called Sinntorp. The resulting reinvestment proposals mainly consist of replacing older grid sections and sections where expensive maintenance is planned in the future. The script show similar results as real reinvestment decisions but small differences are noticed related to the script’s hard focus on older grid sections. The script has potential to be used on Ellevio´s entire overhead line network but this requires work to complete essential data. Further validation on new areas are also desired to see if results are reasonable and if the script can be developed to consider more reinvestment factors.

In this thesis, having in mind applications to the fault-detection/diagnosis of electrical networks, we consider some inverse scattering problems for the Zakharov-Shabat equations and time-independent Schrödinger operators over star-shaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the star-shaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless case and for Zakharov-Shabat system for the lossy transmission network. In chapter 2 we introduce some elements of the inverse scattering theory for 1 d Schrödinger equations and the Zakharov-Shabat system. We recall the basic results for these two systems and we present the state of art of scattering theory on network. The third chapter deals with some inverse scattering for the Schrödinger operators. We prove the identifiability of the geometry of the star-shaped graph: the number of the edges and their lengths. Next, we study the potential identification problem by inverse scattering. In the last chapter we focus on the inverse scattering problems for lossy transmission star-shaped network. We prove the identifiability of some geometric informations by inverse scattering and we present a result toward the identification of the heterogeneities, showing the identifiability of the loss line factor.

Uncertainty is a quantitative attribute that represents the difference between reality and representation of reality. Uncertainty analysis and error propagation modeling reveals the propagation of input error through output. Main objective of this thesis is to model the uncertainty and its propagation for dependent line segments considering positional correlation. The model is implemented as a plug-in, called Propagated Band Model (PBM) Plug-in, to a commercial desktop application, GeoKIT Explorer. Implementation of the model is divided into two parts. In the first one, model is applied to each line segment of the selected network, separately. In the second one, error in each segment is transmitted through the line segments from the start node to the end node of the network. Outcomes are then compared with the results of the G-Band model which is the latest uncertainty model for vector features. To comment on similarities and differences of the outcomes, implementation is handled for two different cases. In the first case, users digitize the selected road network. In the second case recently developed software called Interactive Drawer (ID) is used to allow user to define a new network and simulate this network through Monte Carlo Simulation Method. PBM Plug-in is designed to accept the outputs of these implementation cases as an input, as well as generating and visualizing the uncertainty bands of the given line network. Developed implementations and functionality are basically for expressing the importance and effectiveness of uncertainty handling in vector based geometric features, especially for line segments which construct a network.