Dynamic synchrophasor estimation by Taylor–Prony method in harmonic and non‐harmonic conditions

Abstract

Dynamic phasor is suitable for analysis of non-stationary signals (such as power swings) in phasor measurement unit. In this study, dynamic phasor of the generated signals during power swing is analysed by a classical signal processing technique known as Prony. The Prony analysis is a useful technique to model a linear sum of damped complex exponential signals. In this study, a combination of the least square-based Prony analysis and Taylor expansion called as Taylor-Prony is proposed to estimate the dynamic phasor. Zeroth-order Taylor-Prony, i.e. static phasor is compared with the second-order Taylor-Prony, i.e. dynamic phasor for illustrating the dynamic phasor capability. Sinusoidal and step changes of amplitude and phase, harmonic condition, frequency tracking tests, noise infiltration and computation time are different tests which are used to validate the proposed method. First, the method is explained theoretically, and then its potential is demonstrated by simulating various numerical signals in MATLAB and measured signals during power swing from three-machine power system simulated in PSCAD. Simulation results show that the proposed method can estimate the dynamic phasor during power swing accurately. Ultimately, the proposed method is compared with six methods which have already presented to verify the capability of the proposed method.

Dynamic Phasors Estimation Based on Taylor-Fourier Expansion and Gram Matrix Representation

“…where and are real and estimated values. Figure 2 shows the total vector error of the proposed method in the first ten cycles; one cycle time delay of estimated phasor is compensated as in [27]. It can be concluded that the error occurring is above all the results of the introduced delay, similar to that of [15,21].…”

“…Figures 1(a) and 1(b) show the size of the estimated amplitude and phase of the fundamental dynamic phasor, using the proposed estimation method. It is clear that the main difference between the proposed method and some other methods based on the application of the least square methods [15,21,27], and the methods based on the application of Kalman filters [16,17,23,31] is in the occurrence of the delay in the estimation due to the use of the data window.…”

“…Now, by (27) we obtain the elements of Gram's matrix ⋅ . Namely, for all , = 1, 2, 3 and = + − 2, the elements are given by…”

“…This method uses a kth Taylor polynomial to linearize the complex exponential of the signal model and estimates the dynamic phasor using DSTKF. In [27], a combination of the least square-based Prony analysis and Taylor expansion called Taylor-Prony is proposed to estimate the dynamic phasor.…”

Application of a Hybrid Method for Power System Frequency Estimation with a 0.2-second Sampled Period

“…In the past, several researches have successfully shown that the frequency assessment technology was able to detect the PQs of defects in power system. These technologies include Zero-crossing Algorithm [5][6][7], Discrete Fourier Transform (DFT) [8][9][10][11][12][13], Kalman Filter (KF) [14,15], Phase-Locked Loops (PLL) [16,17], Newton Algorithm [18,19], Least squares Algorithm (LMS) [20,21], Prony Algorithm [4,22], Taylor Algorithm [23,24], and Artificial-intelligence Algorithm [25,26].…”