An Open-Loop Fundamental and Harmonic Phasor Estimator for Single-Phase Voltage Signals

A SVD-based Dynamic Harmonic Phasor Estimator with Improved Suppression of Out-of-Band Interference

“…Namely, r h equals the sum of row elements in l h weighted by d 1,ke /(y h,ke • λ ke ). In case all multipliers y h,ke equal one, (12) gives the original FIR coefficients of the h−order DHPF in (10), otherwise the FIR coefficients and hence the filtering performance may be altered.…”

“…It depends on obtaining the optimal y h,(2a+1) to minimize the filter transition band gain by solving (13). Once the optimal y h,(2a+1) is obtained and substituted to (12), the optimized harmonic filter r h is obtained, and then employed in (11) to extract the phasor. Besides, the first restriction is to keep the computation stability.…”

“…The IEC 61000-4-7 standard employed the grouping harmonic to get the harmonic amplitude, but the phase estimation was unavailable [11]. Besides, compressive sensing algorithm is beneficial to accurate harmonic phasor estimation by enhancing the frequency resolution [12]. However, the improvement is limited, and the algorithm has the disadvantage of a considerable computation burden increase.…”

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]…”