A universal coefficient theorem for twisted K-theory

In this paper, we recall the definition of twisted K-theory in various settings. We prove that for a twist $\tau$ corresponding to a three dimensional integral cohomology class of a space X, there exist a "universal coefficient" isomorphism K_{*}^{\tau}(X)\cong K_{*}(P_{\tau})\otimes_{K_{*}(\mathbb{C}P^{\infty})} \hat{K}_{*} where $P_\tau$ is the total space of the principal $\mathbb{C}P^{\infty}$-bundle induced over X by $\tau$ and $\hat K_*$ is obtained form the action of $\mathbb{C}P^{\infty}$ on K-theory

Application fields and control principles of variable shunt reactors with tap-changer. Investigation of possible control strategies of variable shunt reactors through simulation of a power system under different operating conditions.

The market interest in Variable Shunt Reactors (VSR) is steadily increasing and from a manufacturer’s perspective, tender requests for VSRs become more frequent. Although a few VSRs have been in service for several years and such application is not new, it is within the last years that utilities and network planners have become more interested in this option. With increasing market interest in the application of VSRs, the control strategy of VSRs has become an important issue. Since ABB is the leading company in design and manufacturing of large High Voltage VSRs, the investigation of VSR control strategy is of great interest and importance for ABB. The purpose of this project is to investigate the control strategy of tap-change Variable Shunt Reactors (VSR) to control the voltage level during different load conditions. As an approach, operation of a VSR under various network conditions has been simulated and changes in different parameters of the network have been observed. The work starts with investigating the voltage behaviour after running load flow simulation and studies in DIgSILENT, and continues with extracting a control strategy of the VSR through modelling and simulation using MATLAB. One of the very challenging parts of the work is to design a proper and accurate model for VSR with tap-change control system, since there is no available model for such a VSR in MATLAB. For this reason, all the required data from Statnett (Norway’s Transmission Grid Owner and Operator) and also Test Report Sheets of ABB Transformers AB, Ludvika have been collected. In order to have an intelligent, wise, and accurate tap changing process, various practical issues are taken into account and several simulations have been done. Finally, a robust and reliable control signal has been introduced in this thesis