Abstract:With increasing use of photovoltaic (PV) power generation by utilities and their residential customers, the need for accurate intra-hour and day-ahead solar irradiance forecasting has become critical. This paper details the development of a low cost all-sky imaging system and an intra-hour cloud motion prediction methodology that produces minutes-ahead irradiance forecasts. The SkyImager is designed around a Raspberry Pi single board computer (SBC) with a fully programmable, high resolution Pi Camera, housed in a durable all-weather enclosure. Our software is written in Python 2.7 and utilizes the open source computer vision package OpenCV. The SkyImager can be configured for different operational environments and network designs, from a standalone edge computing model to a fully integrated node in a distributed, cloud-computing based micro-grid. Preliminary results are presented using the imager on site at the National Renewable Energy Laboratory (NREL) in Golden, CO, USA during the fall of 2015 under a variety of cloud conditions.

SUMMARYThe article explores the relationship between Sobolev gradients and H −1 mixed methods for a variety of partial differential equations (PDEs) from image processing. A first-order system least-squares problem is used to introduce the method and compare the Euclidean with the Sobolev gradient. The standard two-term decomposition of an image as f = u + v with u ∈ H 1 and v ∈ L 2 = H 0 yields a second-order linear PDE, while minimizing other L p norms give nonlinear PDEs. Finally, a three-term decomposition f = u + v + w with u ∈ H 1 , v ∈ H −1 , w ∈ H 0 requires the solution of a fourth-order system with the biharmonic operator.

A new model for impurity diffusion in silicon by a point defect-impurity pair mechanism is described. A pair of coupled, nonlinear, partial differential equations for the silicon self-interstitial and the impurity is derived and solved numerically. The familiar kink and tail of phosphorus and, to a lesser extent, boron diffused profiles arise naturally from the solution. The coupling between defect and impurity becomes smaller at high temperatures and at low impurity concentrations, in agreement with experimental observations. The transient buildup of the defect concentration may have implications for models of rapid thermal processes.

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SUMMARYInadequate spatial mesh resolution for simulation of the time-dependent Ginzburg-Landau equations is shown to give rise to spurious solutions. Phenomenological studies to examine the effect of the physical parameters and boundary conditions in 2D and 3D are presented to illustrate the solution structure and to highlight non-linear effects related to evolving vortex patterns. We illustrate and explore this issue further by considering a related simplified model in which the number of vortices is equal to the 'winding number' that is associated with the applied boundary conditions. Using this model we demonstrate that the solution structure is non-unique for several values of winding number.