3,118 research outputs found
Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with Battery Storage using Approximate Dynamic Programming
There is growing interest in the use of grid-level storage to smooth
variations in supply that are likely to arise with increased use of wind and
solar energy. Energy arbitrage, the process of buying, storing, and selling
electricity to exploit variations in electricity spot prices, is becoming an
important way of paying for expensive investments into grid-level storage.
Independent system operators such as the NYISO (New York Independent System
Operator) require that battery storage operators place bids into an hour-ahead
market (although settlements may occur in increments as small as 5 minutes,
which is considered near "real-time"). The operator has to place these bids
without knowing the energy level in the battery at the beginning of the hour,
while simultaneously accounting for the value of leftover energy at the end of
the hour. The problem is formulated as a dynamic program. We describe and
employ a convergent approximate dynamic programming (ADP) algorithm that
exploits monotonicity of the value function to find a revenue-generating
bidding policy; using optimal benchmarks, we empirically show the computational
benefits of the algorithm. Furthermore, we propose a distribution-free variant
of the ADP algorithm that does not require any knowledge of the distribution of
the price process (and makes no assumptions regarding a specific real-time
price model). We demonstrate that a policy trained on historical real-time
price data from the NYISO using this distribution-free approach is indeed
effective.Comment: 28 pages, 11 figure
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
In this paper we introduce a randomized version of the backward Euler method,
that is applicable to stiff ordinary differential equations and nonlinear
evolution equations with time-irregular coefficients. In the finite-dimensional
case, we consider Carath\'eodory type functions satisfying a one-sided
Lipschitz condition. After investigating the well-posedness and the stability
properties of the randomized scheme, we prove the convergence to the exact
solution with a rate of in the root-mean-square norm assuming only that
the coefficient function is square integrable with respect to the temporal
parameter.
These results are then extended to the numerical solution of
infinite-dimensional evolution equations under monotonicity and Lipschitz
conditions. Here we consider a combination of the randomized backward Euler
scheme with a Galerkin finite element method. We obtain error estimates that
correspond to the regularity of the exact solution. The practicability of the
randomized scheme is also illustrated through several numerical experiments.Comment: 37 pages, 3 figure
Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces
In this paper we present computational techniques to investigate the
solutions of two-component, nonlinear reaction-diffusion (RD) systems on
arbitrary surfaces. We build on standard techniques for linear and nonlinear
analysis of RD systems, and extend them to operate on large-scale meshes for
arbitrary surfaces. In particular, we use spectral techniques for a linear
stability analysis to characterize and directly compose patterns emerging from
homogeneities. We develop an implementation using surface finite element
methods and a numerical eigenanalysis of the Laplace-Beltrami operator on
surface meshes. In addition, we describe a technique to explore solutions of
the nonlinear RD equations using numerical continuation. Here, we present a
multiresolution approach that allows us to trace solution branches of the
nonlinear equations efficiently even for large-scale meshes. Finally, we
demonstrate the working of our framework for two RD systems with applications
in biological pattern formation: a Brusselator model that has been used to
model pattern development on growing plant tips, and a chemotactic model for
the formation of skin pigmentation patterns. While these models have been used
previously on simple geometries, our framework allows us to study the impact of
arbitrary geometries on emerging patterns.Comment: This paper was submitted at the Journal of Mathematical Biology,
Springer on 07th July 2015, in its current form (barring image references on
the last page and cosmetic changes owning to rebuild for arXiv). The complete
body of work presented here was included and defended as a part of my PhD
thesis in Nov 2015 at the University of Ber
Métodos multimalla geométricos en mallas semi-estructuradas de Vorono
En este proyecto se presenta un metodo de discretizaciĂłn de ecuaciones en derivadas parciales en mallas triangulares semi-estructuradas usando volumenes finĂtos y como punto representativo el punto de Voronoi. La posterior discretizaciĂłn se resualve usando metodos multimalla semi-estructurados y se presentan un conjunto de nuevos suavizadores asi como un algoritmo de Galerkin de tipo RAP para cuando las condiciones no son homogeneas en toda la superficie. Finalmente se muestran un conjunto de ejemplo numĂ©ricos para demostrar los resultados obtenidos
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