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At least 73 records · Page 4

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗

OPTOM: Optimization of Parabolic Trough - Operations & Maintenance

The US Department of Energy’s SunShot goals look to reduce the cost of Concentrating Solar Power (CSP) technology to 5¢/kWh for baseload plants. This is about a 50% reduction from current costs. To achieve this cost target, a significant reduction in operation and maintenance (O&M) costs of 40 to 50% is likely needed. Advances are needed in the O&M practices of CSP plants if the technology is to achieve the SunShot cost goals. Digitization of plant performance and O&M data has become a new best practice in the world of renewable energy asset management. Owners and operators of large photovoltaic and wind power plants are working to digitize performance and O&M data at their existing assets, to improve their management of the facilities, to increase performance, reduce O&M costs, and lower the overall life cycle cost of ownership. CSP power plants are behind the curve of other technologies on the digitization of plant information to aid in the plant asset management. This project directly addresses the objective of digitizing the O&M data of the solar field, focusing on three areas: 1) creating a framework for sharing data and information, 2) creating a system for monitoring and managing the maintenance of the solar field collectors, and 3) developing analytic tools to identify issues in the solar field. According to the NREL CSP Best Practices Study, the current practice at many CSP plants is to rely on paper lists, spreadsheets, and email for monitoring and managing problems and maintenance in the solar field. The key element to digitize solar field O&M is the creation of a centralized data archive that all users and systems can interface with. This project developed a centralized relational database framework that allows users and applications to access and share data. Conventional power plants utilize Computerized Maintenance Management Systems (CMMSs) to track the corrective, preventive (scheduled), and predictive maintenance of equipment and subsystems in the power plant. CSP plants use these systems in the power block, but while these systems specialize at tracking maintenance on up to thousands of pieces of equipment, they are not well suited for tracking the tens or hundreds of thousands of components in large commercial CSP or photovoltaic solar fields. In this project we developed a new software application referred to as FieldStatus (TM). This is a specialized database program that is used to track the status of each collector and its components. This application is designed to complement the existing CMMS to enable improved tracking and management of maintenance activities in the solar field. One of the major maintenance tasks for solar fields is maintaining the cleanliness of the mirrors. Although seemingly a relatively straight forward task, it has often proven challenging to maintain high levels of cleanliness in an efficient and cost-effective manner. This project developed new tools and metrics for monitoring and optimizing solar field cleaning resources and overall solar field cleanliness.

14 SOLAR ENERGY↗

The Parabolic Wave Equation Generalized to a Spatially Varying Plasma in a Vertical Magnetic Field

This report walks through the process of deriving the wave equation for a vertical wave being propagated through a spatially varying plasma in a vertical magnetic field. Additionally, this report shows how to derive the index of refraction of the plasma corresponding to three different modes of the vertical magnetic field. Finally, this paper briefly explores the next steps planned to successfully simulate and test the equations in a pre-existing phase screen scintillation code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SMART: Simplified Melting And Rotation-joint Technology

Oil based parabolic trough solar power plants are the most commercially mature CSP technology. However, the upper limit of about 400°C of the current organic heat transfer fluid(HTF)significantly limits the future potential of the technology. Advances in parabolic trough receiver and collector technology have enabled higher operating temperatures of potentially 500°C or above. The search for an improved higher temperature HTF has identified inorganic molten salts, specifically the mix referred to as Solar Salt, a 60:40 mix of sodium nitrate and potassium nitrate salt. However, Solar Salt starts to freeze at about 240°C. This poses a significant challenge for large parabolic trough plants that could have many kilometers of header piping and hundreds of kilometers of receiver piping all filled with molten salt. Plants using molten salt need to be designed to minimize the risk of freezing and to be able to recover from freeze events. Studies and field experiments have shown that this appears to be feasible and the approach appears to have strong economic advantages over conventional trough plants. However, some technical challenges remain related to the use of molten salt in trough solar fields, the cost of the freeze recovery system is significant, and many still question whether the risk of using molten salt is worth the economic upside. In our view, the potential economic upside justifies the continued look at molten salt HTF in parabolic trough plants. The objective of this project was to address the key technical issue remaining, look for opportunities to reduce the cost of the freeze recovery system, and improve the general information and tools available for assessing the design, performance and economics of trough plants using molten salt HTF.

14 SOLAR ENERGY↗