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Synchrophasors and frequency estimations play an increasingly important role in power systems. Discrete Fourier transform (DFT) may introduce errors into phasor and frequency estimations under dynamic conditions, such as power oscillation. A dynamic phasor and frequency estimator for phasor measurement units (PMUs) is proposed to improve accuracy by considering dynamic characteristics of power systems expressed as Taylor derivatives. Firstly, phasor estimations of sequence components of diffident data windows are attained via DFT. Secondly Taylor derivatives, expressed by adjacent phasors at different data windows, are employed to improve accuracy of estimations by reassigning estimations with the knowledge of dynamic characteristics. Finally, dynamic characteristics of positive sequence components are applied to estimate the fundamental frequency with less delay compared to a state-of-the-art algorithm, phasor-based synchronised frequency measurement (PSFM). To verify the performance, a set of digital dynamic tests and a power oscillation model using PSCAD/EMTDC are presented. The simulation results show that proposed algorithm can achieve highly accurate estimations of phasor and frequency over a wide range of dynamic conditions. Even though a minor increase in calculation burden is required, this technique provides accurate phasor and frequency estimations without changing the legacy structure of PMU devices. Additionally, it has been found that proposed algorithm really meets the needs of online applications.