This paper proposes Phasor Measurement Unit (PMU) based adaptive zone settings of distance relays (PAZSD) methodology for protection of multi-terminal transmission lines (MTL). The PAZSD methodology employs current coefficients to adjust the zone settings of the relays during infeed situation. These coefficients are calculated in phasor data concentrator (PDC) at system protection center (SPC) using the current phasors obtained from PMUs. The functioning of the distance relays during infeed condition with and without the proposed methodology has been illustrated through a four-bus model implemented in PSCAD/EMTDC environment. Further, the performance of the proposed methodology has been validated in real-time, on a laboratory prototype of Extra High Voltage multi-terminal transmission lines (EHV MTL). The phasors are estimated in PMUs using NI cRIO-9063 chassis embedded with data acquisition sensors in conjunction with LabVIEW software. The simulation and hardware results prove the efficacy of the proposed methodology in enhancing the performance and reliability of conventional distance protection system in real-time EHV MTLs.

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In statistical inference, the information-theoretic performance limits can often be expressed in terms of a statistical divergence between the underlying statistical models (e.g., in binary hypothesis testing, the error probability is related to the total variation distance between the statistical models). As the data dimension grows, computing the statistics involved in decision-making and the attendant performance limits (divergence measures) face complexity and stability challenges. Dimensionality reduction addresses these challenges at the expense of compromising the performance (the divergence reduces by the data-processing inequality). This paper considers linear dimensionality reduction such that the divergence between the models is maximally preserved. Specifically, this paper focuses on Gaussian models where we investigate discriminant analysis under five f-divergence measures (Kullback–Leibler, symmetrized Kullback–Leibler, Hellinger, total variation, and χ2). We characterize the optimal design of the linear transformation of the data onto a lower-dimensional subspace for zero-mean Gaussian models and employ numerical algorithms to find the design for general Gaussian models with non-zero means. There are two key observations for zero-mean Gaussian models. First, projections are not necessarily along the largest modes of the covariance matrix of the data, and, in some situations, they can even be along the smallest modes. Secondly, under specific regimes, the optimal design of subspace projection is identical under all the f-divergence measures considered, rendering a degree of universality to the design, independent of the inference problem of interest.

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