Transmission lines are indispensable part of power transmission system, which are highly exposed to fault risk factors of environmental and anthropogenic nature. Therefore, protection and control have to be robust and reliable as possible. Distance protection and some of fault location methods, used today for transmission lines, operate within a limited scope of available information that can result in errors and incorrect operation, especially when faults have high transient resistance. In order to overcome these drawbacks of one-terminal-based distance protection and fault locations methods it is proposed to use a technique of estimation of unknown power system model parameters, solving these problems as an optimisation tasks. The scope of available information is extended by incorporation of all measurements, available from the controlled substation, thus eliminating necessity of long-distance communication networks, and by a separate stage of parameter estimation during the pre-fault regime, which is similar to estimation of fault parameters but operates with a nonlinear model reflecting the influence of governors. The Thesis provides modelling tools for both pre-fault and different fault regimes based on symmetrical component and topological modelling methods to accommodate the increased measurement scope. The proposed method was extensively tested considering two different strategies for selection of measured parameters used by the optimisation. The proposed method and its results is not limited to the fault location or distance protection, as the developed technique was also used to create a new method of an adaptive single-phase automatic reclosing algorithm. The proposed method can be used as a base for creation of robust algorithms and devices for the fault location, distance protection and single-phase automatic reclosing. It can also be modified or directly implemented for different transmission line automation and protection problems. The modelling tools described in the Thesis can be used for a further analysis and development of relay protection and automation. The Doctoral Thesis consists of an Introduction; 8 chapters; Conclusions; appendices; the Bibliography. The total number of pages is 179 including appendices. The Doctoral Thesis contains 25 tables; 85 figures; 75 equations; 163 cited sources of information; 3 appendices.