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This paper proposes the FTFT for the real-time monitoring of modern power grids through dynamic harmonic estimations. The FTFT results from the DTTFT implemented with the FFT, instead of its filter bank implementation. In FTFT, the harmonic Taylor-Fourier coefficients are obtained in batch, and from these complex coefficients, estimates of frequency, amplitude, and RoCoF are obtained. The FTFT is embedded in two low-cost platforms, one consisting of a digital signal processor (DSP) coded using C programming language, and a development PMU (D-PMU); where a computationally efficient calculation of the FTFT is coded in both platforms. Both platforms process instantaneous voltage and current signals, rendering phasor and harmonic estimates as if they were extracted by the impulse response of a set of FIR filters and their first and second differentiators of the DTTFT. The phasor and harmonic estimations are accomplished using a sliding window that updates sample by sample, instantaneously providing amplitude, phase, frequency, and RoCoF estimations at the fundamental and harmonic frequencies with a high reporting rate. Experimental results confirm the proposition's performance, precision, and effectiveness under steady-state conditions, sudden changes, and harmonic analysis.