An Optimized Subspace-Based Approach to Synchrophasor Estimation

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

“…where G LT is the intersection confrontation state model with the target coordinate damage probability as the intersection confrontation condition, G LT = f (ϕ mt , v r , m p ). Among them, ϕ mt is the intersection confrontation angle, v r is the intersection confrontation velocity and m p is the miss parameter [28]. G K is the damage model of the warhead fragments against the target, which is related to the flow density e(x, y, z) of the warhead fragments under the intersection confrontation, the average number of warhead fragments of the damaged target ∆N [29], the explosion point distance D, the target entry velocity v B , the damage incidence angle α, the total number of warhead fragments N W and the intersection countermeasure fragment flow density ρ(ϕ, ξ), which is determined by the inclination ϕ and the azimuth ξ.…”

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

“…ESPRIT is a well-known subspace-based technique for frequency estimation due to its strong immunity against noise [28]. However, due to its high computational complexity [25], ESPRIT is not suitable for power system applications that require fast estimation of frequency. Hence, an improved version of the ESPRIT, called iESPRIT, is proposed in this paper.…”

“…where Q S is an M × Y sub-matrix that corresponds to the Y largest magnitudes of the eigenvalues (see (25)). Since the elements of the matrix H defined in (17) completely describe the frequencies of exponential components existing in the input signal, H similar to Q S must also lie in the same subspace, called the signal subspace.…”

“…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]…”