Cosine Similarity Based Directional Comparison Scheme for Subcycle Transmission Line Protection

Data-Driven Coordinated Voltage Control Method of Distribution Networks With High DG Penetration

“…To quantify the similarities between nodes, the modified cosine similarity is utilized, which is widely used to measure the difference between two vectors [31]. Taking node 𝑖 in area 𝑚 as an example, by using the modified cosine similarity, the similarity between node 𝑖 with other nodes in area 𝑚 can be quantified as follows.…”

Waveform Similarity-Based Robust Pilot Protection for Transmission Lines

“…where In is the rated current. The threshold of 0.2 In is a predetermined value from experience [16], which has a good sensitivity to distinguish normal and faulty conditions under various conditions with an appropriate speed of action of about 1 ms. Once the above condition is satisfied for any three successive samples starting from the instant k, the algorithm proceeds to the following step.…”

“…Figs. 12 (a For comparison, CS-based [16]- [19] and PCC-based methods [20]- [23] are chosen. As shown in Fig.…”

“…Digital Object Identifier Currently, many new schemes have been proposed for pilot protection in power systems. Protection schemes based on the waveform similarity principle have been one of the most used in AC transmission line [8]- [10], [16], [17], [22]- [24], DC transmission lines [11], [18]- [21], and transformers [12]- [15], because of their explicit and straightforward principle, and rapid and reliable fault detection. For instance, the authors of [10] utilized fault-induced traveling waves to design ultra-high-speed directional protection criteria based on the correlation between incremental quantities; with this, internal and external faults of an AC transmission line could be discriminated.…”

“…A suitable threshold should be set to normalize the sampling data utilized in these methods. The Cosine Similarity (CS) [16]- [19] and Pearson Correlation Coefficient (PCC) [20]- [23] are widely used measure indices to calculate the similarity between two time-series signals. The effectiveness of these waveform similarity-based methods has been validated through extensive testing under different fault types, fault distances, fault resistances, noise, and CT saturation.…”