Parameter Estimation Method of Low-Frequency Oscillating Signals Using Discrete Fourier Transforms

Abstract

-This paper presents a DFT (Discrete Fourier Transform) based estimation algorithm for the parameters of a low-frequency oscillating signal. The proposed method estimates the parameters, i.e., the frequency, the damping factor, the mode amplitude, and the phase, by fitting a discrete Fourier spectrum with an exponentially damped cosine function. Parameter estimation algorithms that consider the spectrum leakage of the discrete Fourier spectrum are introduced. The multi-domain mode test functions are tested in order to verify the accuracy and efficiency of the proposed method. The results show that the proposed algorithms are highly applicable to the practical computation of low-frequency parameter estimations based on DFTs.

A method for fast estimation of slowly changing parameters of a quasi-harmonic signal

“…Usually high speed and high accuracy of the method are mutually exclusive. The resulting estimates ( 13), ( 14), (17) and (18), as well as the results of the experiments prove that the optimal values are QT ≈ π/(2ω). With a substantial changing of frequency to maintain this condition, we can apply an adaptive variation of the decimation ratio Q or sample interval T. Adaptation allows us to increase the accuracy of the method without reducing the speed of its operation.…”

“…It is also seen that the recovery is better when frequency changes are slower. It has a slight amplitude deviation from the constant value (approximately 0.4%) because the amplitude depends on the first derivative of frequency by the formula (17). Estimates obtained by these three methods are merged.…”

“…Many approaches are based on the Fourier transform [15][16][17] and a similar method wavelet transform [18], provides estimates, close to the maximum likelihood [19][20][21][22][23]. These estimates have a very high accuracy,a wide range of signal-to-noise ratios and reach the lower limit of the Cramer-Rao bound [19,24].…”

Comparison of Different Methods for Identification of Dominant Oscillation Mode

“…Prony's method is widely used in literature for identification of low frequency oscillations in power system and can be found in [5], [6]. Because Prony's method's results are strongly influenced by noise, implementation of Fast-Fourier transform (FFT) for LFO characterization can be found in [7], [8]. In [9], [10], Matrix Pencil Analysis Method for identification of oscillation modes is used.…”

Research of the Mechanism of Low Frequency Oscillation Based on Dynamic Damping Effect

“…One is the eigenvalue method [9,10], which obtains the eigenvalue from the system state matrix through the linearization of the non-linear differential equations so as to determine the stability of the system. The other one is the extraction method [11,12] based on the disturbance trajectory. It obtains the oscillation frequency, damping ration and some other information from the time series data by analyzing signals.…”