992 research outputs found
Low-Resolution Fault Localization Using Phasor Measurement Units with Community Detection
A significant portion of the literature on fault localization assumes (more
or less explicitly) that there are sufficient reliable measurements to
guarantee that the system is observable. While several heuristics exist to
break the observability barrier, they mostly rely on recognizing
spatio-temporal patterns, without giving insights on how the performance are
tied with the system features and the sensor deployment. In this paper, we try
to fill this gap and investigate the limitations and performance limits of
fault localization using Phasor Measurement Units (PMUs), in the low
measurements regime, i.e., when the system is unobservable with the
measurements available. Our main contribution is to show how one can leverage
the scarce measurements to localize different type of distribution line faults
(three-phase, single-phase to ground, ...) at the level of sub-graph, rather
than with the resolution of a line. We show that the resolution we obtain is
strongly tied with the graph clustering notion in network science.Comment: Accepted in IEEE SmartGridComm 2018 Conferenc
The Intermodulation Coefficient of an Inhomogeneous Superconductor
The high-T_c cuprate superconductors are now believed to be intrinsically
inhomogeneous. We develop a theory to describe how this inhomogeneity affects
the intermodulation coefficient of such a material. We show that the continuum
equations describing intermodulation in a superconducting layer with spatially
varying properties are formally equivalent to those describing an inhomogeneous
dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we
calculate the effect of inhomogeneity on the intermodulation coefficient in a
high-T_c material, using several assumptions about the topology of the layer,
and some simple analytical approximations to treat the nonlinearity. For some
topologies, we find that the intermodulation critical supercurrent density
J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly
leading to more desirable material properties. We discuss this result in light
of recent spatial mappings of the superconducting energy gap in BSCCO-2212.Comment: 26 pages, 9 figures, accepted for publication in the Journal of
Applied Physic
Least p-Variances Theory
As a result of a rather long-time research started in 2016, this theory whose
structure is based on a fixed variable and an algebraic inequality, improves
and somehow generalizes the well-known least squares theory. In fact, the fixed
variable has a fundamental role in constituting the least p-variances theory.
In this sense, some new concepts such as p-covariances with respect to a fixed
variable, p-correlation coefficient with respect to a fixed variable and
p-uncorrelatedness with respect to a fixed variable are first defined in order
to establish least p-variance approximations. Then, we obtain a specific system
called p-covariances linear system and apply the p-uncorrelatedness condition
on its elements to find a general representation for p-uncorrelated variables.
Afterwards, we apply the concept of p-uncorrelatedness for continuous functions
particularly for polynomial sequences and find some new sequences such as a
generic two-parameter hypergeometric polynomial of 4F3 type that satisfy such a
p-uncorrelatedness property. In the sequel, we obtain an upper bound for
1-covariances, an approximation for p-variances, an improvement for the
approximate solutions of over-determined systems and an improvement for the
Bessel inequality and Parseval identity. Finally, we generalize the notion of
least p-variance approximations based on several fixed orthogonal variables.Comment: 85 pages, 1 figure and 1 tabl
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