Local Phasors Research Articles

A Fault Location Algorithm for Two-End Series-Compensated Double-Circuit Transmission Lines Using the Distributed Parameter Line Model

A new fault location algorithm for two-end series-compensated double-circuit transmission lines utilizing unsynchronized two-terminal current phasors and local voltage phasors is presented in this paper. The distributed parameter line model is adopted to take into account the shunt capacitance of the lines. The mutual coupling between the parallel lines in the zero-sequence network is also considered. The boundary conditions under different fault types are used to derive the fault location formulation. The developed algorithm directly uses the local voltage phasors on the line side of series compensation (SC) and metal oxide varistor (MOV). However, when potential transformers are not installed on the line side of SC and MOVs for the local terminal, these measurements can be calculated from the local terminal bus voltage and currents by estimating the voltages across the SC and MOVs. MATLAB SimPowerSystems is used to generate cases under diverse fault conditions to evaluating accuracy. The simulation results show that the proposed algorithm is qualified for practical implementation.

Efficient acquisition algorithm for long pseudorandom sequence

In this paper, a novel method termed the phase coherence acquisition (PCA) is proposed for pseudorandom (PN) sequence acquisition. By employing complex phasors, the PCA requires only complex additions in the order of N, the length of the sequence, whereas the conventional method using fast Fourier transform (FFT) requires complex multiplications and additions both in the order of N log2N. To combat noise, the input and local sequences are partitioned and mapped into complex phasors in PCA. The phase differences between pairs of input and local phasors are used for acquisition; thus, complex multiplications are avoided. For more noise-robustness capability, the multilayer PCA is developed to extract the code phase step-by-step. The significant reduction of computational loads makes the PCA an attractive method, especially when the sequence length of N is extremely large, which becomes intractable for the FFT-based acquisition.

An improved voltage-collapse protection algorithm based on local phasors

An improved algorithm to protect against voltage collapse based on two consecutive voltage- and current-phasor measurements to evaluate the voltage stability at a bus is proposed. The change in the apparent-power bus injection during a time interval is exploited for computing the voltage-collapse criterion. The criterion is based on the fact that in the vicinity of the voltage collapse no extra apparent power can be delivered to the affected bus. The one-step algorithm needs no additional checking, irrespective of whether the lines are generating or consuming reactive power. The new algorithm was rigorously tested on different test systems. The results were obtained on a static IEEE 30-bus test system and on the dynamic Belgian–French 32-bus test system that includes full dynamic models of all the power-system components crucial to a voltage-instability analysis. The results show the advantages of the proposed algorithm: it is simple, computationally very fast and easy to implement in a numerical relay.

A New Concept of Voltage-Collapse Protection Based on Local Phasors

A new algorithm for protection against voltage collapse is proposed. The algorithm makes use of the magnitudes and angles of the local phasors (i.e., bus voltages and load currents). The change in an apparent power-line flow during a time interval is exploited for computing the voltage-collapse criterion. The criterion is based on the fact that the line losses in the vicinity of the voltage collapse increase faster than the delivery of the apparent power and, at the voltage-collapse point, the losses consume all of the increased power. The selected criterion equals 0 when a voltage collapse occurs. The proposed algorithm could be easily implemented in a numerical relay. The information obtained by the relay can be used at two levels-for the coordinated system-wide control action or for automatic action on the local level. The algorithm is simple and computationally very fast. It was tested on the IEEE 118-bus test system.

A novel scheme of local protection against voltage collapse based on the apparent-power losses

A new algorithm for protection against voltage collapse is proposed using local phasors' magnitudes and angles. A change in apparent power line flow in a time interval is exploited for computation of the voltage collapse criterion. The criterion is based on the fact that the line losses in the vicinity of voltage collapse increase faster than delivery of the apparent power and at the voltage collapse point the losses take all the increase. The selected criterion equals zero when a voltage collapse occurs, which gives the relay an opportunity to react earlier with an appropriate setting. The proposed algorithm could be easily implemented in a numerical relay. The algorithm is simple and computationally very fast. An on-line protection scheme could be applied at the end of an endangered line. The algorithm was tested on various test systems including New England 39-bus test system.

Fast voltage-collapse line-protection algorithm based on local phasors

An algorithm for protection against voltage collapse is proposed. The algorithm makes use of the magnitudes and angles of the local phasors. The change in an apparent-power line flow during a time interval is exploited for computing the voltage-collapse criterion. The criterion is based on the fact that the line losses in the vicinity of the voltage collapse increase faster than the delivery of the apparent power, and, at the voltage-collapse point, the losses consume all the increased power. The selected criterion equals 0 when a voltage collapse occurs, which gives the protection relay with an appropriate setting an opportunity to react earlier. The proposed algorithm could be easily implemented in a numerical relay. The algorithm is simple and computationally very fast. An online protection scheme can be applied at the relay point of an endangered line. The algorithm was tested on various test systems including the Slovenian 275-busbar test system.

Demodulation, predictive coding, and spatial vision.

We argue that some aspects of human spatial vision, particularly for textured patterns and scenes, can be described in terms of demodulation and predictive coding. Such nonlinear processes encode a pattern into local phasors that represent it completely as a modulation, in phase and amplitude, of a prediction associated with the image structure in some region by its predominant undulation(s). The demodulation representation of a pattern is an anisotropic, second-order form of predictive coding, and it offers a particularly efficient way to analyze and encode textures, as it identifies and exploits their underlying redundancies. In addition, self-consistent domains of redundancy in image structure provide a basis for image segmentation. We first provide an algorithm for computing the three elements of a complete demodulation transform of any image, and we illustrate such decompositions for both natural and synthetic images. We then present psychophysical evidence from spatial masking experiments, as well as illustrations of perceptual organization, that suggest a possible role for such underlying representations in human vision. In psychophysical experiments employing masks with more than two oriented Fourier components, we find that peaks of threshold elevation occur at locations in the Fourier plane remote from the orientations and frequencies of the actual mask components. Rather, as would occur from demodulation, these peaks in the frequency plane are related to the vector difference frequencies between the actual masking components and their spectral centers of mass. We offer a neural interpretation of demodulation coding, and finally we demonstrate a practical application of this process in a system for automatic visual recognition of personal identity by demodulation of a facial feature.