Power system state estimation has been playing a core part in the energy management system (EMS) utilised by power system operators since its establishment in the 1970s. The state estimator is responsible for providing accurate information (e.g. voltage magnitudes and angles of all buses in the network) for the EMS so that its security assessment functions can be deployed reliably. Recently, the power system is experiencing unprecedented evolution of complexity due to the increasing injection of renewable energy, increasing usage of power electronic devices and the increasing number of HVDC links in the network. One of the solutions to such challenges is to deploy Wide Area Monitoring System (WAMS) supported by the Synchronised Measurement Technology (SMT). Prior to state estimation, an observability analysis must be performed to make sure the measurements (e.g. power injection and flow measurements) received can support the normal functioning of the state estimator. If the measurements cannot provide full observability of the network, the observability analysis function identifies the observable islands where state estimation can still be performed within the observable islands. In this thesis it is shown that the existing method may not correctly identify the observable islands in the so called pathological cases; the thesis proposes a new method for observability analysis that overcomes this problem. Furthermore the execution time of the proposed method is shorter than existing methods. To support the deployment of the SMT in state estimation, the thesis also proposes a new method for including the synchronised measurements in the observability analysis function. The synchronised measurements provided by phasor measurement units (PMUs) have significantly higher accuracy and sampling rate than conventional measurements. However, the widespread installation of PMUs is limited by its high costs. A more feasible method that takes advantage of SMT is to use a hybrid state estimator (HSE). It uses a combination of PMU measurements and the existing conventional methods. To support the observability of the HSE, the thesis first proposes a new method for optimal PMU placement in the presence of conventional measurements. Then, the thesis performs simulations in the IEEE 14 and 118 Bus Test Systems comparing the performance of five different HSEs. It is found that even a small number of PMUs in a large network can significantly improve the estimation accuracy of the HSE compared to the conventional state estimator. Furthermore, the rectangular current type HSE has the best performance in terms of estimation accuracy, execution time and convergence. These conclusions are rigorously validated by mathematical analysis. The final work presented in this thesis is the development of a new algorithm for a dynamic state estimator (DSE) supported by SMT. The new method applies the Cubature Kalman Filter which is demonstrated to be more efficient but more sensitive to the anomalies compared to the DSEs using other nonlinear filters. Thus, the new algorithm also involves new methods that can accurately detect and identify three different types of anomaly, including bad data, sudden change of load, and sudden change of topology due to fault, to mitigate the impact of this sensitivity.