This thesis describes the algorithms and techniques developed for harmonic state estimation and transient state estimation, which can be used to identify the location of disturbance sources in an electrical power system. The previous harmonic state estimation algorithm is extended to include the estimation of time-varying harmonics using an adaptive Kalman filter. The proposed method utilises two covariance noise models to overcome the divergence problem in traditional Kalman filters. Moreover, it does not require an optimal covariance noise matrix of the Kalman filter to be used. The common problems faced in harmonic state estimation applications due to the influence of measurement bad data associated with measurements and the lack of measurement points, hence the system being partially observable, are investigated with reference to the Lower South Island of the New Zealand system. The state estimation technique is also extended to transient state estimation. Two formulation methods are outlined and the development of the proposed methodology is presented. Fault scenarios with reference to the Lower South Island of the New Zealand system are simulated to demonstrate the ability of transient state estimation in estimating the voltages and currents of the unmeasured locations, and applying the estimated results to search for the fault location. The estimation results are compared with PSCAD/EMTDC simulations to justify their accuracy.