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At least 541 records · Page 30

Streamline integration as a method for two-dimensional elliptic grid generation

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.

97 MATHEMATICS AND COMPUTING↗

A treatment planning approach to spatially fractionated megavoltage grid therapy for bulky lung cancer

The purpose of this study was to explore the treatment planning methods of spatially fractionated megavoltage grid therapy for treating bulky lung tumors using multileaf collimator (MLC). A total of 5 patients with lung cancer who had gross tumor volumes ranging from 277 to 635 cm{sup 3} were retrospectively chosen for this study. The tumors were from 6.5 to 9.6 cm at shortest dimension. Several techniques using either electronic compensation or intensity-modulated radiation therapy (IMRT) were used to create a variety of grid therapy plans on the Eclipse treatment planning system. The dose prescription point was calculated to the volume, and a dose of 20 Gy with 6-MV/15-MV beams was used in each plan. The dose-volume histogram (DVH) curves were obtained to evaluate dosimetric characteristics. In addition, DVH curves from a commercially available cerrobend grid collimator were also used for comparison. The linear-quadratic radiobiological response model was used to assess therapeutic ratios (TRs) and equivalent uniform doses (EUD) for all generated plans. A total of 6 different grid therapy plans were created for each patient. Overall, 4 plans had different electronic compensation techniques: Ecomps-Tubes, Ecomps-Circles, Ecomps-Squares, and Ecomps-Weave; the other 2 plans used IMRT and IMRT-Weave techniques. The DVH curves and TRs demonstrated that these MLC-based grid therapy plans can achieve dosimetric properties very similar to those of the cerrobend grid collimator. However, the MLC-based plans have larger EUDs than those with the cerrobend grid collimator. In addition, the field shaping can be performed for targets of any shape in MLC-based plans. Thus, they can deliver a more conformal dose to the targets and spare normal structures better than the cerrobend grid collimator can. The plans generated by the MLC technique demonstrated the advantage over the standard cerrobend grid collimator on accommodating targets and sparing normal structures. Overall, 6 different plans showed 6 different dosimetric parameters. However, an optimal grid therapy plan selection from among these 6 types requires more information from clinical trials and radiobiological studies.

61 RADIATION PROTECTION AND DOSIMETRY↗

A Framework for Counterfeit Smart Grid Device Detection

The core vision of the smart grid concept is the realization of reliable two-­way communications between smart devices (e.g., IEDs, PLCs, PMUs). The benefits of the smart grid also come with tremendous security risks and new challenges in protecting the smart grid systems from cyber threats. Particularly, the use of untrusted counterfeit smart grid devices represents a real problem. Consequences of propagating false or malicious data, as well as stealing valuable user or smart grid state information from counterfeit devices are costly. Hence, early detection of counterfeit devices is critical for protecting smart grid’s components and users. To address these concerns, in this poster, we introduce our initial design of a configurable framework that utilize system call tracing, library interposition, and statistical techniques for monitoring and detection of counterfeit smart grid devices. In our framework, we consider six different counterfeit device scenarios with different smart grid devices and adversarial seZings. Our initial results on a realistic testbed utilizing actual smart-­grid GOOSE messages with IEC-­61850 communication protocol are very promising. Our framework is showing excellent rates on detection of smart grid counterfeit devices from impostors.

97 MATHEMATICS AND COMPUTING↗

A Stabilizer based Predictive Control Scheme for Smart Inverters in Weak Grid

This paper presents a self-stabilization mechanism based on finite-set model predictive control (FCS-MPC) framework for smart inverters operating in weak grid conditions. As weak grid’s large parasitic impedance and low short-circuitratio (SCR) challenge the stable operation of grid-connected inverters. Specifically, the inverter may experience frequencies that might excite the LCL filter resonance phenomenon. The inverter stability collapses if this LCL resonance is triggered. To address this issue, a robust predictive controller is proposed that features a self-stabilization mechanism for smart inverters interacting with a weak grid. The proposed methodology utilizes the idea that in stiff grid conditions the grid current feedback (GCF) is stable and in weak grid conditions the inverter current feedback (ICF) is stable. Therefore, the proposed FCS-MPC toggles between GCF and ICF to achieve inherent LCL filter resonance damping. The toggling action between GCF and ICF is leveraged by comparing the moving RMS grid current with threshold current as a constrained in the proposed FCS-MPC cost function. The theoretical analyses are verified by several case studies for a single-phase grid-connected inverter. The analysis and results demonstrated that the proposed FCS-MPC operates well under weak, ultra-weak and stiff grid conditions.

Umar, Muhammad Farooq↗

Feasibility study of a synchronized-moving-grid (SMOG) system to improve image quality in cone-beam computed tomography (CBCT)

Purpose: To evaluate the feasibility of a synchronized moving grid (SMOG) system to remove scatter artifacts, improve the contrast-to-noise ratio (CNR), and reduce image lag artifacts in cone-beam CT (CBCT). Methods: The SMOG system proposed here uses a rapidly oscillating, synchronized moving grid attached to the kV source. Multiple partial projections are taken at different grid positions to form a complete projection in each gantry position, before the gantry moves to the next position during a scan. The grid has a low transmission factor, and it is used for both scatter reduction and scatter measurement for postscan scatter correction. Experimental studies using a static grid and an enlarged CATphan phantom were performed to evaluate the potential CNR enhancement for different SMOG exposure numbers (1, 2, and 4). Simulation studies were performed to evaluate the image lag correction for different exposure numbers (2, 3, and 4) and grid interspace widths in SMOG using the data from an anthropomorphic pelvis phantom scan. Imaging dose of SMOG was also estimated by measuring the imaging dose in a CIRS CT dose phantom using a static grid. Results: SMOG can enhance the CNR by 16% and 13% when increasing exposure number from 1 to 2 and from 2 to 4, respectively. This enhancement was more dramatic for larger phantoms and smaller initial exposure numbers. Simulation results indicated that SMOG could reduce the lag to less than 4.3% for 2-exposure mode and to less than 0.8% for 3-exposure mode when the grid interspace width was 1.4 cm. Increasing the number of exposures in SMOG dramatically reduced the residual lag in the image. Reducing the grid interspace width somewhat reduced the residual lag. Skin line artifacts were removed entirely in SMOG. Point dose measurement showed that imaging dose of SMOG at isocenter was similar as that of a conventional CBCT. Conclusions: Compared to our previously developed static-grid dual-rotation method, the proposed SMOG technique has the advantages of enhancing the CNR, correcting the image lag, and reducing the delivery time. Once implemented, SMOG has the potential to remove scatter and image lag artifacts, and significantly enhance CNR for CBCT using the same scanning time as conventional CBCT.

60 APPLIED LIFE SCIENCES↗

SU-E-T-374: Evaluation and Verification of Dose Calculation Accuracy with Different Dose Grid Sizes for Intracranial Stereotactic Radiosurgery

Purpose: In this study, we aim to evaluate the effect of dose grid size on the accuracy of calculated dose for small lesions in intracranial stereotactic radiosurgery (SRS), and to verify dose calculation accuracy with radiochromic film dosimetry. Methods: 15 intracranial lesions from previous SRS patients were retrospectively selected for this study. The planning target volume (PTV) ranged from 0.17 to 2.3 cm{sup 3}. A commercial treatment planning system was used to generate SRS plans using the volumetric modulated arc therapy (VMAT) technique using two arc fields. Two convolution-superposition-based dose calculation algorithms (Anisotropic Analytical Algorithm and Acuros XB algorithm) were used to calculate volume dose distribution with dose grid size ranging from 1 mm to 3 mm with 0.5 mm step size. First, while the plan monitor units (MU) were kept constant, PTV dose variations were analyzed. Second, with 95% of the PTV covered by the prescription dose, variations of the plan MUs as a function of dose grid size were analyzed. Radiochomic films were used to compare the delivered dose and profile with the calculated dose distribution with different dose grid sizes. Results: The dose to the PTV, in terms of the mean dose, maximum, and minimum dose, showed steady decrease with increasing dose grid size using both algorithms. With 95% of the PTV covered by the prescription dose, the total MU increased with increasing dose grid size in most of the plans. Radiochromic film measurements showed better agreement with dose distributions calculated with 1-mm dose grid size. Conclusion: Dose grid size has significant impact on calculated dose distribution in intracranial SRS treatment planning with small target volumes. Using the default dose grid size could lead to under-estimation of delivered dose. A small dose grid size should be used to ensure calculation accuracy and agreement with QA measurements.

60 APPLIED LIFE SCIENCES↗

SU-E-T-429: Feasibility Study On Three-Dimensional GRID Therapy in Conventional Linacs

Purpose: Two-dimensional GRID therapy, traditionally planned and delivered using a dedicated GRID block or MLC modulation, has shown clinical efficacy in treating bulky tumors. However, the large dose to normal tissues outside target can be limiting. We hypothesize that modulation in the third dimension will improve dose sparing of normal tissues, maximize the bystander effect within the target, and ultimately improve the therapy effectiveness. This study aims to investigate the feasibility of a three-dimensional GRID technique using conventional LINACs to achieve a 3D lattice of high dose volumes within a target. Methods: Datasets of patient’s having large tumor sizes were used to investigate the planning and delivering of 3D GRID using a Varian TrueBeam linac. Original patient contours of PTV are exported from a TPS to DICOManTX where 3D GRID targets are generated in programmable configurations. A structure of avoidance (SOA), i.e., PTV minus GRID targets, is also generated to facilitate inverse planning to achieve the desired pattern. The artificial structures were sent back to the TPS where an IMRT or VMAT plan is designed to deliver a desired high dose to GRID targets while minimizing the dose to the SOA as much as possible. Results: The programmable GRID target generator enables us to modify the target geometry to maximize the peak-to-valley ratio. Preliminary results show that plans based on spherical GRID targets achieve a higher peak-to-valley dose ratio compared with cylindrical targets. High dose spillage outside the target was eliminated. IMRT planning requires the number of beams to be larger than 16, while for VMAT the number of arcs should be at least 4 in order to achieve dosimetric goals. Conclusion: Planning and delivering 3D GRID therapy using conventional LINACs was shown to be feasible. More research and development are required before this new modality can be implemented clinically.

60 APPLIED LIFE SCIENCES↗

Caldera_Grid

Caldera Grid is part of Caldera software platform, a suite of collective, open-source tools that was developed to improve the state of the art in modeling the impacts of Electric Vehicle (EV) charging on the grid. Caldera Grid is a co-simulation framework implemented using Hierarchical Engine for Large scale Infrastructure Co-Simulation (HELICS). The framework facilitates the co-simulation of EV charging and Smart Charge Management (SCM) strategies in Caldera Infrastructure Charge Model (ICM) with distribution level grid models in OpenDSS. Vehicle energy needs and charge session requirements generated using Caldera Charge Decision Module (CDM) are fed in as input to Caldera Grid. The EV charging models in Caldera ICM simulates both the uncontrolled charging loads as well as loads modified by the SCM strategies to develop distributed load profiles for each grid node hosting an Electric Vehicle Supply Equipment (EVSE) – also known as chargers. These loads were simulated in OpenDSS alongside existing distribution feeder loads. Each of these models are co-simulated in a HELICS federate. The HELICS co-simulation framework facilitates communication and synchronization between the federates. By co-simulating EV loads and distribution feeder loads, Caldera Grid can assess the potential grid impacts of EV charging on distribution feeders under various grid conditions. A control strategy federate is implemented with an interface where control strategies based on feedback from EV charging status and grid conditions can be developed and implemented. The platform can also support multiple control strategies in a single co-simulation.

Sundarrajan, ManojKumar Cebol↗

Smart Grid Integration Laboratory

The initial federal funding for the Colorado State University Smart Grid Integration Laboratory is through a Congressionally Directed Project (CDP), DE-OE0000070 Smart Grid Integration Laboratory. The original program requested in three one-year increments for staff acquisition, curriculum development, and instrumentation all which will benefit the Laboratory. This report focuses on the initial phase of staff acquisition which was directed and administered by DOE NETL/ West Virginia under Project Officer Tom George. Using this CDP funding, we have developed the leadership and intellectual capacity for the SGIC. This was accomplished by investing (hiring) a core team of Smart Grid Systems engineering faculty focused on education, research, and innovation of a secure and smart grid infrastructure. The Smart Grid Integration Laboratory will be housed with the separately funded Integrid Laboratory as part of CSU's overall Smart Grid Integration Center (SGIC). The period of performance of this grant was 10/1/2009 to 9/30/2011 which included one no cost extension due to time delays in faculty hiring. The Smart Grid Integration Laboratory's focus is to build foundations to help graduate and undergraduates acquire systems engineering knowledge; conduct innovative research; and team externally with grid smart organizations. Using the results of the separately funded Smart Grid Workforce Education Workshop (May 2009) sponsored by the City of Fort Collins, Northern Colorado Clean Energy Cluster, Colorado State University Continuing Education, Spirae, and Siemens has been used to guide the hiring of faculty, program curriculum and education plan. This project develops faculty leaders with the intellectual capacity to inspire its students to become leaders that substantially contribute to the development and maintenance of Smart Grid infrastructure through topics such as: (1) Distributed energy systems modeling and control; (2) Energy and power conversion; (3) Simulation of electrical power distribution system that integrates significant quantities of renewable and distributed energy resources; (4) System dynamic modeling that considers end-user behavior, economics, security and regulatory frameworks; (5) Best practices for energy management IT control solutions for effective distributed energy integration (including security with the underlying physical power systems); (6) Experimental verification of effects of various arrangements of renewable generation, distributed generation and user load types along with conventional generation and transmission. Understanding the core technologies for enabling them to be used in an integrated fashion within a distribution network remains is a benefit to the future energy paradigm and future and present energy engineers.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Software-Based Challenges of Developing the Future Distribution Grid

The software that the utility industry currently uses may be insufficient to analyze the distribution grid as it rapidly modernizes to include active resources such as distributed generation, switch and voltage control, automation, and increasingly complex loads. Although planners and operators have traditionally viewed the distribution grid as a passive load, utilities and consultants increasingly need enhanced analysis that incorporates active distribution grid loads in order to ensure grid reliability. Numerous commercial and open-source tools are available for analyzing distribution grid systems. These tools vary in complexity from providing basic load-flow and capacity analysis under steady-state conditions to time-series analysis and even geographical representations of dynamic and transient events. The need for each type of analysis is not well understood in the industry, nor are the reasons that distribution analysis requires different techniques and tools both from those now available and from those used for transmission analysis. In addition, there is limited understanding of basic capability of the tools and how they should be practically applied to the evolving distribution system. The study reviews the features and state of the art capability of current tools, including usability and visualization, basic analysis functionality, advanced analysis including inverters, and renewable generation and load modeling. We also discuss the need for each type of distribution grid system analysis. In addition to reviewing basic functionality current models, we discuss dynamics and transient simulation in detail and draw conclusions about existing software?s ability to address the needs of the future distribution grid as well as the barriers to modernization of the distribution grid that are posed by the current state of software and model development. Among our conclusions are that accuracy, data transfer, and data processing abilities are key to future distribution grid modeling, and measured data sources are a key missing element . Modeling tools need to be calibrated based on measured grid data to validate their output in varied conditions such as high renewables penetration and rapidly changing topology. In addition, establishing a standardized data modeling format would enable users to transfer data among tools to take advantage of different analysis features. ?

99 GENERAL AND MISCELLANEOUS↗

Comparison of Distributive Consensus Algorithms for AnomalyDetection on the Power-Grid

As an increasing number of devices in the power-grid rely on high-precision clocks to measure electrical properties and time stamp data, GPS receivers have become a vulnerability on the power-grid. GPS spoofing attacks, in which a fake signal is transmitted, can cause sensor measurement errors that can misinform protective equipment and grid operators for both the transmission and distribution grid. The technology being developed to secure precision clocks in the transmission grid are not appropriate for the distribution grid. Thus, there is a need to developed anomaly detection algorithms that are suitable for the hardware available on the distribution grid. Traditionally, a distributed detection framework is comprised of spatially distributed nodes which acquire observations about a quantity of interest and sends the data to the fusion center, where a global decision is made. Instead the distribution grid has low-power devices, such as smart inverters and microPMUs, that could be used to perform highly parallelized calculations. Having on node calculations is beneficial since it is more network and computation efficient, as the more calculations can be performed where the data is being captured instead of communicating across a slow network to a centralized fusion center. Instead, we could employ an alternate peer-to-peer type of information exchange on the distribution grid that can still reach a global decision. A decentralized approach to anomaly detection makes efficient use of the computational and network bandwidth that exists, and it also lacks the single point of failure of a centralized approach. Thus, a decentralized local information exchange and/or inference is preferred. Lastly, the unreliability of the distribution grid network connections and potential noise or error in the measurements must be considered. In order to produce an effective detection tool, a Byzantine-fault tolerant and asynchronous algorithm must be developed. Thus, the first phase of our project is to develop a distributed, decentralized, asynchronous, Byzantine-fault tolerant, collaborative autonomy-based anomaly detection algorithm to collectively analyze clusters of data for signs of a malicious attack.

97 MATHEMATICS AND COMPUTING↗

Smarter Grid Solutions | National Renewable Energy Laboratory: Active Management Integration: June 2015 - November 2016

This report presents the project results for the NREL INTEGRATE demonstration project: Active Network Management (ANM) Integration. Consistent with the INTEGRATE program's objective of increasing the grid's clean energy hosting capacity and providing grid services in a holistic manner, the project demonstrated the use of ANM to enable very high penetrations of solar PV and wind energy systems. Results obtained using a representative North American distribution system showed ANM's autonomous distributed control doubled the interconnected wind and solar systems by managing thermal and voltage constraints in real-time. These generators flexibly interconnected to the grid via ANM's end-to-end control architecture, and were managed and coordinated with other smart distributed energy resources (DER; e.g. EVs, battery ESS, controllable load) to unlock the grid's dynamic hosting capacity. As a smart grid application to standardize grid integration of diverse renewable generation sources, ANM provides the industry with a scalable, cost-effective alternative to traditional transmission and distribution (T&D) reinforcements. This project considered three use cases of the application of ANM: a Smart Home demonstration of ANM control of residential scale devices (PV, EV, and battery ESS); a Smart Campus demonstration of high penetration megawatt-scale DER (PV, EVs, battery ESS, and controllable load) behind a single point-of-common-coupling (PCC), and a Smart Distribution demonstration that combined prior use cases along with additional community/utility-scale DER at very high aggregate penetration levels. The Smart Distribution use case provided an integrated perspective of ANM across all distribution grid DER device scales (incorporating aggregated Smart Homes and the Smart Campus) in order to showcase how these devices can support smart grid services to manage DER related constraints in a safe and reliable manner; and likewise how ANM integrates with grid modernization initiatives. The ANM system was deployed in NREL's Energy Systems Integration Facility (ESIF), and project industry advisors attended an on-site demonstration and a set of workshops in order to review project outcomes and evaluate the relevance of ANM for increasing the grid hosting capacity. The outcomes of this effort include an assessment of opportunities for field deployment of ANM to address existing interconnection challenges, as well as consolidating project advisor suggestions for investment in ANM and potential future pilots for more advanced schemes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

An unstructured C-grid type variational formulation for the sea ice dynamics

Historically, B-grid formulations of sea ice dynamics have been dominant because they have matched the grid type used by ocean models. The reason for the grid match is simple – it facilitates penetration of the curl of ice-ocean stress into the deep ocean with minimal numerical diffusivity because sea ice and ocean velocity are co-located. In recent years, as ocean models have increasingly progressed to C-grids, sea ice models have followed suit on quadrilateral meshes, but the implementation of an unstructured C-grid sea ice models is new. We present an unstructured C-grid discretization of the Elastic Viscous Plastic (EVP) rheology, where the velocity unknowns are discretized at the edges of the mesh cells with n-sides, where typically n is greater than or equal to four, rather than at the vertices, as in the B-grid. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. While MPAS-Seaice is currently defined on a B-grid, MPAS-Ocean runs on a C-grid, hence interpolation operators are heavily used when coupled simulations are performed. In this work, we describe a mathematical formulation to transition the dynamics of MPAS-Seaice to a C-grid, in order to ultimately facilitate the coupling with MPAS-Ocean and reduce numerical errors associated with this communication. Numerical results are reported to highlight the features of the method.

58 GEOSCIENCES↗

Emerging Trends and Systemic Issues Influencing Today’s U.S. Electric Grid

With increasing shifts from vertically integrated to horizontally structured operations and from centralized to distributed electric power delivery, today’s electric power grid (the “grid”) operators and designers face the challenge of creating an architecture that accommodates a host of diverse requirements. The grid’s modes of operation must address concerns of reliability and stability, new deployments of renewable energy sources, threats from cyber-attacks and natural disasters, and increasingly distributed system operations. Grid modernization calls for a reliable, affordable, sustainable, agile, secure, and resilient grid. However, the modernization of the U.S. power grid is hampered by mounting complexity and diverging objectives from owners and operators and is consequently risky and fraught with potential missteps. Flawed architecture, design, and implementation will lead to stranded investments and lost opportunities. A principled approach to minimize risk and develop a robust grid of the future is to begin with a sound architecture for the grid to inform the design process. Architecture development starts with the context of influencing factors that provide constraints as well as driving goals. This report provides the context of emerging trends and cross-cutting systemic issues in the U.S. electric power grid and serves as a vital input for grid architecture development.

24 POWER TRANSMISSION AND DISTRIBUTION↗

State of Common Grid Services Definitions

This document is prepared as part of the Department of Energy’s Grid Modernization Laboratory Consortium (GMLC) 2.5.2 project, whose goal is to develop and socialize a common set of grid service definitions relevant to grid-related interactions with distributed energy resources (DER: responsive generation, storage, and loads), and to advance the concept and requirements of the Energy Services Interface (ESI) to the point of launching related interface standards and guides that can be implemented in communication protocols and business process definitions. The notion of “grid services” is integral to the definition of an ESI because a key principle of the ESI is that it permits coordination between grid operators and DER facilities in a way that is service-oriented, with an understanding of performance expectations. This document reviews the current state of grid service definitions, including those actively used in the market today as well as new services that have been proposed for future implementation. The document describes grid services used in transmission as well as distribution systems. In defining grid services, this document also distinguishes between two fundamental concepts: an “operational objective” and a “grid service,” which describes a generator’s or customer’s expected physical performance in delivering power to or consuming power from the grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Common Grid Services: Terms and Definitions Report

This document is prepared as part of the Department of Energy’s Grid Modernization Laboratory Consortium (GMLC) 2.5.2 project, whose goal is to develop and socialize a common set of grid service definitions relevant to grid-related interactions with distributed energy resources (DER: responsive generation, storage, and loads) and to advance the concept and requirements of the Energy Services Interface (ESI) to the point of launching related interface standards and guides that can be implemented in communication protocols and business process definitions. The notion of grid services is associated with the definition of an ESI because a key principle of the ESI is that it permits coordination between grid operators and DER facilities in a way that is service-oriented with an understanding of performance expectations. The project investigated the current state of North American grid service definitions from various market operators and utilities, as well as the Federal Energy Regulatory Commission and the North American Electric Reliability Corporation, actively used today (Liu et al. 2022). This document builds on that work to propose terms and definitions for a set of grid service types that address operational objectives commonly found in power system operations. These grid service types derive from existing grid services used in bulk electric market operations, recognizing that each operational authority uses somewhat different names with variations on service performance parameters. Finding commonality at the wholesale or bulk system operation level will hopefully engender progress in seeking agreement on grid services for DER engagement at the distribution level in the emerging retail marketplace.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimization of electrostatic dual-grid beam-deflection system

Tests were performed to minimize accelerator grid erosion of a 5-cm diameter Kaufman ion thruster due to direct beam impingement. Several different screen hole diameters, pillow-shape-square screen holes, and dished screen grids were tried. The optimization was accomplished by copper plating the accelerator grid before testing each grid configuration on a thruster for a 2-hour run. The thruster beam sputtered copper and molybdenum from the accelerator grid where the beam impinged. The observed erosion patterns and measured accelerator currents were used to determine how to modify the accelerator system. The lowest erosion was obtained for a 50-percent open area pillow-shape-square-aperture screen grid, dished 0.043 centimeter convex toward the accelerator grid, which was positioned with the center of the screen grid 0.084 centimeter from the accelerator grid. During this investigation the accelerator current was reduced from 120 to 55 microamperes and was also more uniformly distributed over the area of the accelerator grid.

Hudson, W. R.↗

Multi-off-grid methods in multi-step integration of ordinary differential equations

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Beaudet, P. R.↗