A practical, precise method for frequency tracking and phasor estimation

Comprehensive analysis of discrete Fourier transform (DFT) error is given in this paper, including why it is accurate when used in the case of synchronous sampling and how error rises when sampling frequency does not synchronized to signal frequency. Simple but precise expressions of phase angle error and amplitude error are given. Practical formulas to calculate the true phase angle and amplitude are presented. The formulas are very simple and precise. Based on the formula to calculate true phase angle, a new frequency tracking method is developed. The proposed method can be calculated recursively. And, with notable accuracy improvement, the calculation burden is little more than the traditional DFT method. Also, an adaptive method to suppress the effect of harmonics is presented, which adds very little calculation burden with satisfying performance. The most distinguished feature of the proposed method is that it is not only precise, but also simple. Some examples are given to demonstrate the feasibility, precision, simpleness and robustness of the proposed method.