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Single- and three-phase synchronisation methods based on optimum filtering theory are proposed. These methods are based mainly on the Kalman filter and are therefore termed Kalman filter-phase locked loop. they explicitly include in the problem formulation the presence of harmonics, voltage unbalance, measurement noise, transients and frequency deviation. such perturbations degrade the performance of many synchronisation structures presented in literature. the formulation presented here makes the synchronisation signals less sensitive to these perturbations. it is also shown that the proposed methods can be helpful by also providing the amplitude, instantaneous phase and frequency of grid voltages that can be useful for the analysis of power quality. furthermore, the Kalman filter provides a way of obtaining the best compromise between transient response and measurement noise rejection for the synchronisation signals. The paper sets out the development of the proposed methods together with the choice of tuning parameters and their physical meaning. simulations and experimental results using a DSP TMS320F2812 are presented to show the effectiveness of the proposed schemes.