1,212 research outputs found
A Generalized Framework for Chance-constrained Optimal Power Flow
Deregulated energy markets, demand forecasting, and the continuously
increasing share of renewable energy sources call---among others---for a
structured consideration of uncertainties in optimal power flow problems. The
main challenge is to guarantee power balance while maintaining economic and
secure operation. In the presence of Gaussian uncertainties affine feedback
policies are known to be viable options for this task. The present paper
advocates a general framework for chance-constrained OPF problems in terms of
continuous random variables. It is shown that, irrespective of the type of
distribution, the random-variable minimizers lead to affine feedback policies.
Introducing a three-step methodology that exploits polynomial chaos expansion,
the present paper provides a constructive approach to chance-constrained
optimal power flow problems that does not assume a specific distribution, e.g.
Gaussian, for the uncertainties. We illustrate our findings by means of a
tutorial example and a 300-bus test case
Surrogate modelling for stochastic dynamical systems by combining NARX models and polynomial chaos expansions
The application of polynomial chaos expansions (PCEs) to the propagation of
uncertainties in stochastic dynamical models is well-known to face challenging
issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a
sufficient level of long term accuracy requires the use of high-order
polynomials. In numerous cases, it is even infeasible to obtain accurate
metamodels with regular PCEs due to the fact that PCEs cannot represent the
dynamics. To overcome the problem, an original numerical approach was recently
proposed that combines PCEs and non-linear autoregressive with exogenous input
(NARX) models, which are a universal tool in the field of system
identification. The approach relies on using NARX models to mimic the dynamical
behaviour of the system and dealing with the uncertainties using PCEs. The
PC-NARX model was built by means of heuristic genetic algorithms. This paper
aims at introducing the least angle regression (LAR) technique for computing
PC-NARX models, which consists in solving two linear regression problems. The
proposed approach is validated with structural mechanics case studies, in which
uncertainties arising from both structures and excitations are taken into
account. Comparison with Monte Carlo simulation and regular PCEs is also
carried out to demonstrate the effectiveness of the proposed approach
Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos
Uncertainties have become a major concern in integrated circuit design. In
order to avoid the huge number of repeated simulations in conventional Monte
Carlo flows, this paper presents an intrusive spectral simulator for
statistical circuit analysis. Our simulator employs the recently developed
generalized polynomial chaos expansion to perform uncertainty quantification of
nonlinear transistor circuits with both Gaussian and non-Gaussian random
parameters. We modify the nonintrusive stochastic collocation (SC) method and
develop an intrusive variant called stochastic testing (ST) method to
accelerate the numerical simulation. Compared with the stochastic Galerkin (SG)
method, the resulting coupled deterministic equations from our proposed ST
method can be solved in a decoupled manner at each time point. At the same
time, ST uses fewer samples and allows more flexible time step size controls
than directly using a nonintrusive SC solver. These two properties make ST more
efficient than SG and than existing SC methods, and more suitable for
time-domain circuit simulation. Simulation results of several digital, analog
and RF circuits are reported. Since our algorithm is based on generic
mathematical models, the proposed ST algorithm can be applied to many other
engineering problems.Comment: published by IEEE Trans CAD in Oct 201
On Uncertainty Quantification in Particle Accelerators Modelling
Using a cyclotron based model problem, we demonstrate for the first time the
applicability and usefulness of a uncertainty quantification (UQ) approach in
order to construct surrogate models for quantities such as emittance, energy
spread but also the halo parameter, and construct a global sensitivity analysis
together with error propagation and error analysis. The model problem
is selected in a way that it represents a template for general high intensity
particle accelerator modelling tasks. The presented physics problem has to be
seen as hypothetical, with the aim to demonstrate the usefulness and
applicability of the presented UQ approach and not solving a particulate
problem.
The proposed UQ approach is based on sparse polynomial chaos expansions and
relies on a small number of high fidelity particle accelerator simulations.
Within this UQ framework, the identification of most important uncertainty
sources is achieved by performing a global sensitivity analysis via computing
the so-called Sobols' indices.Comment: submitted to Journal of Uncertainty Quantification. arXiv admin note:
text overlap with arXiv:1505.07776, arXiv:1307.0065 by other author
Optimal Power Flow: An Introduction to Predictive, Distributed and Stochastic Control Challenges
The Energiewende is a paradigm change that can be witnessed at latest since
the political decision to step out of nuclear energy. Moreover, despite common
roots in Electrical Engineering, the control community and the power systems
community face a lack of common vocabulary. In this context, this paper aims at
providing a systems-and-control specific introduction to optimal power flow
problems which are pivotal in the operation of energy systems. Based on a
concise problem statement, we introduce a common description of optimal power
flow variants including multi-stage-problems and predictive control, stochastic
uncertainties, and issues of distributed optimization. Moreover, we sketch open
questions that might be of interest for the systems and control community
Stochastic Galerkin Framework with Locally Reduced Bases for Nonlinear Two-Phase Transport in Heterogeneous Formations
The generalized polynomial chaos method is applied to the Buckley-Leverett
equation. We consider a spatially homogeneous domain modeled as a random field.
The problem is projected onto stochastic basis functions which yields an
extended system of partial differential equations. Analysis and numerical
methods leading to reduced computational cost are presented for the extended
system of equations.
The accurate representation of the evolution of a discontinuous stochastic
solution over time requires a large number of stochastic basis functions.
Adaptivity of the stochastic basis to reduce computational cost is challenging
in the stochastic Galerkin setting since the change of basis affects the system
matrix itself. To achieve adaptivity without adding overhead by rewriting the
entire system of equations for every grid cell, we devise a basis reduction
method that distinguishes between locally significant and insignificant modes
without changing the actual system matrices.
Results are presented for problems in one and two spatial dimensions, with
varying number of stochastic dimensions. We show how to obtain stochastic
velocity fields from realistic permeability fields and demonstrate the
performance of the stochastic Galerkin method with local basis reduction. The
system of conservation laws is discretized with a finite volume method and we
demonstrate numerical convergence to the reference solution obtained through
Monte Carlo sampling
Uncertainty Quantification in Three Dimensional Natural Convection using Polynomial Chaos Expansion and Deep Neural Networks
This paper analyzes the effects of input uncertainties on the outputs of a
three dimensional natural convection problem in a differentially heated cubical
enclosure. Two different cases are considered for parameter uncertainty
propagation and global sensitivity analysis. In case A, stochastic variation is
introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers)
with an assumption that the boundary temperature is uniform. Being a two
dimensional stochastic problem, the polynomial chaos expansion (PCE) method is
used as a surrogate model. Case B deals with non-uniform stochasticity in the
boundary temperature. Instead of the traditional Gaussian process model with
the Karhunen-Love expansion, a novel approach is successfully
implemented to model uncertainty in the boundary condition. The boundary is
divided into multiple domains and the temperature imposed on each domain is
assumed to be an independent and identically distributed (i.i.d) random
variable. Deep neural networks are trained with the boundary temperatures as
inputs and Nusselt number, internal temperature or velocities as outputs. The
number of domains which is essentially the stochastic dimension is 4, 8, 16 or
32. Rigorous training and testing process shows that the neural network is able
to approximate the outputs to a reasonable accuracy. For a high stochastic
dimension such as 32, it is computationally expensive to fit the PCE. This
paper demonstrates a novel way of using the deep neural network as a surrogate
modeling method for uncertainty quantification with the number of simulations
much fewer than that required for fitting the PCE, thus, saving the
computational cost
Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems
Growing uncertainty from renewable energy integration and distributed energy
resources motivate the need for advanced tools to quantify the effect of
uncertainty and assess the risks it poses to secure system operation.
Polynomial chaos expansion (PCE) has been recently proposed as a tool for
uncertainty quantification in power systems. The method produces results that
are highly accurate, but has proved to be computationally challenging to scale
to large systems. We propose a modified algorithm based on PCE with
significantly improved computational efficiency that retains the desired high
level of accuracy of the standard PCE. Our method uses computational
enhancements by exploiting the sparsity structure and algebraic properties of
the power flow equations. We show the scalability of the method on the 1354
pegase test system, assess the quality of the uncertainty quantification in
terms of accuracy and robustness, and demonstrate an example application to
solving the chance constrained optimal power flow problem
Efficient Representation of Uncertainty for Stochastic Economic Dispatch
Stochastic economic dispatch models address uncertainties in forecasts of
renewable generation output by considering a finite number of realizations
drawn from a stochastic process model, typically via Monte Carlo sampling.
Accurate evaluations of expectations or higher-order moments for quantities of
interest, e.g., generating cost, can require a prohibitively large number of
samples. We propose an alternative to Monte Carlo sampling based on Polynomial
Chaos expansions. These representations are based on sparse quadrature methods,
and enable accurate propagation of uncertainties in model parameters. We also
investigate a method based on Karhunen-Loeve expansions that enables us to
efficiently represent uncertainties in renewable energy generation. Considering
expected production cost, we demonstrate that the proposed approach can yield
several orders of magnitude reduction in computational cost for solving
stochastic economic dispatch relative to Monte Carlo sampling, for a given
target error threshold.Comment: arXiv admin note: text overlap with arXiv:1407.223
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