20,933 research outputs found
Geometry-based Estimation of Stability Region for A Class of Structure Preserving Power Grids
The increasing development of the electric power grid, the largest engineered
system ever, to an even more complicated and larger system requires a new
generation of stability assessment methods that are computationally tractable
and feasible in real-time. In this paper we first extend the recently
introduced Lyapunov Functions Family (LFF) transient stability assessment
approach, that has potential to reduce the computational cost on large scale
power grids, to structure-preserving power grids. Then, we introduce a new
geometry-based method to construct the stability region estimate of power
systems. Our conceptual demonstration shows that this new method can certify
stability of a broader set of initial conditions compared to the
minimization-based LFF method and the energy methods (closest UEP and
controlling UEP methods)
Lyapunov Functions Family Approach to Transient Stability Assessment
Analysis of transient stability of strongly nonlinear post-fault dynamics is
one of the most computationally challenging parts of Dynamic Security
Assessment. This paper proposes a novel approach for assessment of transient
stability of the system. The approach generalizes the idea of energy methods,
and extends the concept of energy function to a more general Lyapunov Functions
Family (LFF) constructed via Semi-Definite-Programming techniques. Unlike the
traditional energy function and its variations, the constructed Lyapunov
functions are proven to be decreasing only in a finite neighborhood of the
equilibrium point. However, we show that they can still certify stability of a
broader set of initial conditions in comparison to the traditional energy
function in the closest-UEP method. Moreover, the certificates of stability can
be constructed via a sequence of convex optimization problems that are
tractable even for large scale systems. We also propose specific algorithms for
adaptation of the Lyapunov functions to specific initial conditions and
demonstrate the effectiveness of the approach on a number of IEEE test cases
A Framework for Robust Assessment of Power Grid Stability and Resiliency
Security assessment of large-scale, strongly nonlinear power grids containing
thousands to millions of interacting components is a computationally expensive
task. Targeting at reducing the computational cost, this paper introduces a
framework for constructing a robust assessment toolbox that can provide
mathematically rigorous certificates for the grids' stability in the presence
of variations in power injections, and for the grids' ability to withstand a
bunch sources of faults. By this toolbox we can "off-line" screen a wide range
of contingencies or power injection profiles, without reassessing the system
stability on a regular basis. In particular, we formulate and solve two novel
robust stability and resiliency assessment problems of power grids subject to
the uncertainty in equilibrium points and uncertainty in fault-on dynamics.
Furthermore, we bring in the quadratic Lyapunov functions approach to transient
stability assessment, offering real-time construction of stability/resiliency
certificates and real-time stability assessment. The effectiveness of the
proposed techniques is numerically illustrated on a number of IEEE test cases
Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods
Recently sum-of-squares (SOS) based methods have been used for the stability
analysis and control synthesis of polynomial dynamical systems. This analysis
framework was also extended to non-polynomial dynamical systems, including
power systems, using an algebraic reformulation technique that recasts the
system's dynamics into a set of polynomial differential algebraic equations.
Nevertheless, for large scale dynamical systems this method becomes
inapplicable due to its computational complexity. For this reason we develop a
subsystem based stability analysis approach using vector Lyapunov functions and
introduce a parallel and scalable algorithm to infer the stability of the
interconnected system with the help of the subsystem Lyapunov functions.
Furthermore, we design adaptive and distributed control laws that guarantee
asymptotic stability under a given external disturbance. Finally, we apply this
algorithm for the stability analysis and control synthesis of a network
preserving power system.Comment: to appear at the 14th annual European Control Conferenc
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Chaos and the continuum limit in nonneutral plasmas and charged particle beams
This paper examines discreteness effects in nearly collisionless N-body
systems of charged particles interacting via an unscreened r^-2 force, allowing
for bulk potentials admitting both regular and chaotic orbits. Both for
ensembles and individual orbits, as N increases there is a smooth convergence
towards a continuum limit. Discreteness effects are well modeled by Gaussian
white noise with relaxation time t_R = const * (N/log L)t_D, with L the Coulomb
logarithm and t_D the dynamical time scale. Discreteness effects accelerate
emittance growth for initially localised clumps. However, even allowing for
discreteness effects one can distinguish between orbits which, in the continuum
limit, feel a regular potential, so that emittance grows as a power law in
time, and chaotic orbits, where emittance grows exponentially. For sufficiently
large N, one can distinguish two different `kinds' of chaos. Short range
microchaos, associated with close encounters between charges, is a generic
feature, yielding large positive Lyapunov exponents X_N which do not decrease
with increasing N even if the bulk potential is integrable. Alternatively,
there is the possibility of larger scale macrochaos, characterised by smaller
Lyapunov exponents X_S, which is present only if the bulk potential is chaotic.
Conventional computations of Lyapunov exponents probe X_N, leading to the
oxymoronic conclusion that N-body orbits which look nearly regular and have
sharply peaked Fourier spectra are `very chaotic.' However, the `range' of the
microchaos, set by the typical interparticle spacing, decreases as N increases,
so that, for large N, this microchaos, albeit very strong, is largely
irrelevant macroscopically. A more careful numerical analysis allows one to
estimate both X_N and X_S.Comment: 13 pages plus 17 figure
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