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The classical two-parameter Fourier algorithm for computing synchrophasors is appropriate when the underlying voltage and current waveforms are sinusoids with constant amplitude and phase angle and with a frequency equal to the assumed value. Synchrophasor measurements, however, are applied in power systems to track dynamic conditions where, by definition, currents and voltages, though resembling sine-waves, exhibit changes in their magnitudes and vectorial positions. This paper presents a novel algorithm for estimating synchrophasors under such dynamic conditions. In contrast to the classical Fourier algorithm, our model is a complex Taylor expansion, yielding several parameters in the model to be estimated. Four- and six-parameter models are presented corresponding to first and second order Taylor expansions. This paper derives a compensation method for canceling the error in the classical Fourier algorithm that arises under dynamic conditions, shows comparative simulation and test results and describes an efficient implementation. Application of the error cancellation method to other phasor algorithms and extending the technique to higher order Taylor expansions, are discussed. Implementation of synchrophasor measurements on protection and control intelligent electronic devices (IEDs) is discussed, and solutions are presented that allow for secure integration.