Adaptive Phasor Estimation Algorithm Based on a Least Squares Method

Abstract

This paper proposes an adaptive phasor estimation algorithm based on a least square method that can suppress the adverse effect of an exponentially decreasing DC offset component in a phasor estimation process. The proposed algorithm is composed of three stages: a basic least squares model, a time constant calculation, and an adaptive least squares model. First, we use the basic least squares model to estimate the parameter of the DC offset component in the fault current signal. This model is designed to incorporate fundamental frequency, and harmonic and constant components. Second, we use the estimated parameter to calculate the time constant of the DC offset component. Third, we redesign a least squares model that incorporates fundamental frequency, harmonic components, and exponential function of the DC offset component. Since this model incorporates the exponential function of the DC offset component contained in the fault current signal, it estimates the phasor of the correct fundamental frequency component without influence of the DC offset component. We evaluated the performance of the proposed algorithm using computer generated signals and EMTP simulation signals. The evaluation results show that the proposed algorithm can effectively suppress the adverse influence of the exponentially decaying DC offset component.

Decaying DC Offset Current Mitigation in Phasor Estimation Applications: A Review

“…An adaptive least-squares method is presented in [45], which uses a recursive approach to estimate the DDC parameter in the first stage. Then, the estimated DDC is used as a known parameter in the second LS application where primary phasor values are updated to increase the estimation accuracy.…”

“…Noise Harmonics Off-Nominal Frequency Multiple DDCs Sample Requirements [37] x x x 7 samples [38] x x 1 cycle [39] x x x 20 samples [40] x x x 1 cycle [41] x x x 1 cycle [42] 7/8 cycle [43] x x x 1 cycle [44] x x 8 samples [45] x 1 cycle…”

“…In [45], the LS method is used twice for the adaptive DDC estimation. First, the amplitude of DDC is estimated through LS, then TC is calculated through two consecutive samples, which are highly sensitive to noise.…”

A Robust Algorithm for Real-Time Phasor and Frequency Estimation under Diverse System Conditions

“…To ensure the relevance of the measurements obtained from these devices for monitoring, protection, and control applications, it is necessary that the estimation algorithms used in them are accurate, robust against stray components, computationally efficient, and have low response time [1,2]. Hence, digital signal processing techniques such as discrete Fourier transform (DFT) [3][4][5][6][7][8][9][10][11], least squares (LS) [12][13][14][15], maximum likelihood [16], space vector transform [17], artificial neural networks [18], Hilbert transform [19], Stockwell transform [20], matrix pencil method [21], Kalman filters [22,23], subspace-based methods [24,25], and filter-based methods [26,27] have been proposed recently to estimate phasor and/or frequency under different operating conditions. However, many of the techniques mentioned above suffer from long response time during switching transients [9,13,20], high computational complexity [7,21,24], susceptibility to grid disturbances [12,18,22] and noise [19], lengthy observation window [7,10,11,[25]…”

“…Hence, digital signal processing techniques such as discrete Fourier transform (DFT) [3][4][5][6][7][8][9][10][11], least squares (LS) [12][13][14][15], maximum likelihood [16], space vector transform [17], artificial neural networks [18], Hilbert transform [19], Stockwell transform [20], matrix pencil method [21], Kalman filters [22,23], subspace-based methods [24,25], and filter-based methods [26,27] have been proposed recently to estimate phasor and/or frequency under different operating conditions. However, many of the techniques mentioned above suffer from long response time during switching transients [9,13,20], high computational complexity [7,21,24], susceptibility to grid disturbances [12,18,22] and noise [19], lengthy observation window [7,10,11,[25][26][27], and performance degradation due to: (i) off-nominal frequency condition [4][5][6]…”