25,396 research outputs found
Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution
With the increasing share of renewable and distributed generation in
electrical distribution systems, Active Network Management (ANM) becomes a
valuable option for a distribution system operator to operate his system in a
secure and cost-effective way without relying solely on network reinforcement.
ANM strategies are short-term policies that control the power injected by
generators and/or taken off by loads in order to avoid congestion or voltage
issues. Advanced ANM strategies imply that the system operator has to solve
large-scale optimal sequential decision-making problems under uncertainty. For
example, decisions taken at a given moment constrain the future decisions that
can be taken and uncertainty must be explicitly accounted for because neither
demand nor generation can be accurately forecasted. We first formulate the ANM
problem, which in addition to be sequential and uncertain, has a nonlinear
nature stemming from the power flow equations and a discrete nature arising
from the activation of power modulation signals. This ANM problem is then cast
as a stochastic mixed-integer nonlinear program, as well as second-order cone
and linear counterparts, for which we provide quantitative results using state
of the art solvers and perform a sensitivity analysis over the size of the
system, the amount of available flexibility, and the number of scenarios
considered in the deterministic equivalent of the stochastic program. To foster
further research on this problem, we make available at
http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution
networks of 5, 33, and 77 buses. These test beds contain a simulator of the
distribution system, with stochastic models for the generation and consumption
devices, and callbacks to implement and test various ANM strategies
The Burbea-Rao and Bhattacharyya centroids
We study the centroid with respect to the class of information-theoretic
Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence
by measuring the non-negative Jensen difference induced by a strictly convex
and differentiable function. Although those Burbea-Rao divergences are
symmetric by construction, they are not metric since they fail to satisfy the
triangle inequality. We first explain how a particular symmetrization of
Bregman divergences called Jensen-Bregman distances yields exactly those
Burbea-Rao divergences. We then proceed by defining skew Burbea-Rao
divergences, and show that skew Burbea-Rao divergences amount in limit cases to
compute Bregman divergences. We then prove that Burbea-Rao centroids are
unique, and can be arbitrarily finely approximated by a generic iterative
concave-convex optimization algorithm with guaranteed convergence property. In
the second part of the paper, we consider the Bhattacharyya distance that is
commonly used to measure overlapping degree of probability distributions. We
show that Bhattacharyya distances on members of the same statistical
exponential family amount to calculate a Burbea-Rao divergence in disguise.
Thus we get an efficient algorithm for computing the Bhattacharyya centroid of
a set of parametric distributions belonging to the same exponential families,
improving over former specialized methods found in the literature that were
limited to univariate or "diagonal" multivariate Gaussians. To illustrate the
performance of our Bhattacharyya/Burbea-Rao centroid algorithm, we present
experimental performance results for -means and hierarchical clustering
methods of Gaussian mixture models.Comment: 13 page
Online Learning of Power Transmission Dynamics
We consider the problem of reconstructing the dynamic state matrix of
transmission power grids from time-stamped PMU measurements in the regime of
ambient fluctuations. Using a maximum likelihood based approach, we construct a
family of convex estimators that adapt to the structure of the problem
depending on the available prior information. The proposed method is fully
data-driven and does not assume any knowledge of system parameters. It can be
implemented in near real-time and requires a small amount of data. Our learning
algorithms can be used for model validation and calibration, and can also be
applied to related problems of system stability, detection of forced
oscillations, generation re-dispatch, as well as to the estimation of the
system state.Comment: 7 pages, 4 figure
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