3,515 research outputs found
Solving Stochastic AC Power Flow via Polynomial Chaos Expansion
The present contribution demonstrates the applicability of polynomial chaos expansion to stochastic (optimal) AC power flow problems that arise in the operation of power grids. For rectangular power flow, polynomial chaos expansion together with Galerkin projection yields a deterministic reformulation of the stochastic power flow problem that is solved numerically in a single run. From its solution, approximations of the true posterior probability density functions are obtained. The presented approach does not require linearization. Furthermore, the IEEE 14 bus serves as an example to demonstrate that the proposed approach yields accurate approximations to the probability density functions for low orders of polynomial bases, and that it is computationally more efficient than Monte Carlo sampling
Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario
A variety of methods is available to quantify uncertainties arising with\-in
the modeling of flow and transport in carbon dioxide storage, but there is a
lack of thorough comparisons. Usually, raw data from such storage sites can
hardly be described by theoretical statistical distributions since only very
limited data is available. Hence, exact information on distribution shapes for
all uncertain parameters is very rare in realistic applications. We discuss and
compare four different methods tested for data-driven uncertainty
quantification based on a benchmark scenario of carbon dioxide storage. In the
benchmark, for which we provide data and code, carbon dioxide is injected into
a saline aquifer modeled by the nonlinear capillarity-free fractional flow
formulation for two incompressible fluid phases, namely carbon dioxide and
brine. To cover different aspects of uncertainty quantification, we incorporate
various sources of uncertainty such as uncertainty of boundary conditions, of
conceptual model definitions and of material properties. We consider recent
versions of the following non-intrusive and intrusive uncertainty
quantification methods: arbitary polynomial chaos, spatially adaptive sparse
grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The
performance of each approach is demonstrated assessing expectation value and
standard deviation of the carbon dioxide saturation against a reference
statistic based on Monte Carlo sampling. We compare the convergence of all
methods reporting on accuracy with respect to the number of model runs and
resolution. Finally we offer suggestions about the methods' advantages and
disadvantages that can guide the modeler for uncertainty quantification in
carbon dioxide storage and beyond
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
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