19,786 research outputs found
Theoretical basis of the community effect in development
Peer reviewedPublisher PD
Voltage Stabilization in Microgrids via Quadratic Droop Control
We consider the problem of voltage stability and reactive power balancing in
islanded small-scale electrical networks outfitted with DC/AC inverters
("microgrids"). A droop-like voltage feedback controller is proposed which is
quadratic in the local voltage magnitude, allowing for the application of
circuit-theoretic analysis techniques to the closed-loop system. The operating
points of the closed-loop microgrid are in exact correspondence with the
solutions of a reduced power flow equation, and we provide explicit solutions
and small-signal stability analyses under several static and dynamic load
models. Controller optimality is characterized as follows: we show a one-to-one
correspondence between the high-voltage equilibrium of the microgrid under
quadratic droop control, and the solution of an optimization problem which
minimizes a trade-off between reactive power dissipation and voltage
deviations. Power sharing performance of the controller is characterized as a
function of the controller gains, network topology, and parameters. Perhaps
surprisingly, proportional sharing of the total load between inverters is
achieved in the low-gain limit, independent of the circuit topology or
reactances. All results hold for arbitrary grid topologies, with arbitrary
numbers of inverters and loads. Numerical results confirm the robustness of the
controller to unmodeled dynamics.Comment: 14 pages, 8 figure
Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation
We study the statistical physics of a surprising phenomenon arising in large
networks of excitable elements in response to noise: while at low noise,
solutions remain in the vicinity of the resting state and large-noise solutions
show asynchronous activity, the network displays orderly, perfectly
synchronized periodic responses at intermediate level of noise. We show that
this phenomenon is fundamentally stochastic and collective in nature. Indeed,
for noise and coupling within specific ranges, an asymmetry in the transition
rates between a resting and an excited regime progressively builds up, leading
to an increase in the fraction of excited neurons eventually triggering a chain
reaction associated with a macroscopic synchronized excursion and a collective
return to rest where this process starts afresh, thus yielding the observed
periodic synchronized oscillations. We further uncover a novel anti-resonance
phenomenon: noise-induced synchronized oscillations disappear when the system
is driven by periodic stimulation with frequency within a specific range. In
that anti-resonance regime, the system is optimal for measures of information
capacity. This observation provides a new hypothesis accounting for the
efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a
neurodegenerative disease characterized by an increased synchronization of
brain motor circuits. We further discuss the universality of these phenomena in
the class of stochastic networks of excitable elements with confining coupling,
and illustrate this universality by analyzing various classical models of
neuronal networks. Altogether, these results uncover some universal mechanisms
supporting a regularizing impact of noise in excitable systems, reveal a novel
anti-resonance phenomenon in these systems, and propose a new hypothesis for
the efficiency of high-frequency stimulation in Parkinson's disease
Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition
The process of desertification in the semi-arid climatic zone is considered
by many as a catastrophic regime shift, since the positive feedback of
vegetation density on growth rates yields a system that admits alternative
steady states. Some support to this idea comes from the analysis of static
patterns, where peaks of the vegetation density histogram were associated with
these alternative states. Here we present a large-scale empirical study of
vegetation dynamics, aimed at identifying and quantifying directly the effects
of positive feedback. To do that, we have analyzed vegetation density across
of the African Sahel region, with spatial
resolution of meters, using three consecutive snapshots. The
results are mixed. The local vegetation density (measured at a single pixel)
moves towards the average of the corresponding rainfall line, indicating a
purely negative feedback. On the other hand, the chance of spatial clusters (of
many "green" pixels) to expand in the next census is growing with their size,
suggesting some positive feedback. We show that these apparently contradicting
results emerge naturally in a model with positive feedback and strong
demographic stochasticity, a model that allows for a catastrophic shift only in
a certain range of parameters. Static patterns, like the double peak in the
histogram of vegetation density, are shown to vary between censuses, with no
apparent correlation with the actual dynamical features
On the importance of including vegetation dynamics in Budyko's hydrological model
The Budyko curve describes the patterns observed between between climate, evapotranspiration and run-off and has proven to be a useful model for predicting catchment energy and water balances. In this paper we review the Budyko curve's underlying framework and, based on the literature, present an argument for why it is important to include vegetation dynamics into the framework for some purposes. The Budyko framework assumes catchments are at steady-state and are driven by the macro-climate, two conditions dependent on the scales of application, such that the framework's reliability is greatest when applied using long-term averages (≫1 year) and to large catchments (> 10 000 km2). At these scales previous experience has shown that the hydrological role of vegetation does not need to be explicitly considered within the framework. By demonstrating how dynamics in the leaf area, photosynthetic capacity and rooting depth of vegetation affect not only annual and seasonal vegetation water use, but also steady-state conditions, we argue that it is necessary to explicitly include vegetation dynamics into the Budyko framework before it is applied at small scales. Such adaptations would extend the framework not only to applications at small timescales and/or small catchments but to operational activities relating to vegetation and water management
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