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NASA NTRS1994

Unstructured-grid large-eddy simulation of flow over an airfoil

Historically, large-eddy simulations (LES) have been restricted to simple geometries where spectral or finite difference methods have dominated due to their efficient use of structured grids. Structured grids, however, not only difficulty representing complex domains and adapting to complicated flow features, but also are rather inefficient for simulating flows at high Reynolds numbers. The lack of efficiency stems from the need to resolve the viscous sublayer, which requires very fine resolution in all three directions near the wall. Structured grids make use of a stretching to reduce the normal grid spacing but must carry the fine resolution in the streamwise and spanwise directions throughout the domain. The unnecessarily fine grid for much of the domain leads to disturbingly high grid estimates. Chapman (1979), and later Moin & Jimenez (1993), pointed out that, in order to advance the technology to airfoils at flight Reynolds numbers, structured grids must be abandoned in lieu of what are known as nested or unstructured grids. The finite element method can efficiently solve the Navier-Stokes equations on unstructured grids. Although the CPU cost per time step per element is somewhat higher than structured grid methods, this effect is more than offset by the reduction in the number of elements. The use of unstructured grids, coupled with the advances in dynamic subgrid-scale modeling such as those made by Germano et al. (1991) and Ghosal et al. (1994), make LES of an airfoil tractable. We have chosen the NACA 4412 airfoil at maximum lift as the first simulation since this flow has not been successfully simulated with the Reynolds-averaged Navier-Stokes equations.

Jansen, Kenneth↗

NASA NTRS1995

Evaluation of grid generation technologies from an applied perspective

An analysis of the grid generation process from the point of view of an applied CFD engineer is given. Issues addressed include geometric modeling, structured grid generation, unstructured grid generation, hybrid grid generation and use of virtual parts libraries in large parametric analysis projects. The analysis is geared towards comparing the effective turn around time for specific grid generation and CFD projects. The conclusion was made that a single grid generation methodology is not universally suited for all CFD applications due to both limitations in grid generation and flow solver technology. A new geometric modeling and grid generation tool, CFD-GEOM, is introduced to effectively integrate the geometric modeling process to the various grid generation methodologies including structured, unstructured, and hybrid procedures. The full integration of the geometric modeling and grid generation allows implementation of extremely efficient updating procedures, a necessary requirement for large parametric analysis projects. The concept of using virtual parts libraries in conjunction with hybrid grids for large parametric analysis projects is also introduced to improve the efficiency of the applied CFD engineer.

Hufford, Gary S.↗

NASA NTRS1997

Surface Modeling and Grid Generation of Orbital Sciences X34 Vehicle

The surface modeling and grid generation requirements, motivations, and methods used to develop Computational Fluid Dynamic volume grids for the X34-Phase 1 are presented. The requirements set forth by the Aerothermodynamics Branch at the NASA Langley Research Center serve as the basis for the final techniques used in the construction of all volume grids, including grids for parametric studies of the X34. The Integrated Computer Engineering and Manufacturing code for Computational Fluid Dynamics (ICEM/CFD), the Grid Generation code (GRIDGEN), the Three-Dimensional Multi-block Advanced Grid Generation System (3DMAGGS) code, and Volume Grid Manipulator (VGM) code are used to enable the necessary surface modeling, surface grid generation, volume grid generation, and grid alterations, respectively. All volume grids generated for the X34, as outlined in this paper, were used for CFD simulations within the Aerothermodynamics Branch.

Alter, Stephen J.↗

NASA NTRS1995

Blocked Grid Technologies as Applied to Aerodynamic Configurations

The advantages and disadvantages of the blocked grid methodology are discussed using results from ENSAERO, CNS, and CNS-FV. The first two codes are based on finite differences and the last on cell-centered finite volume formulation. Techniques that enhance the utility of the blocked (or patched) grid methodology are described. These techniques include mesh discontinuous zonal interfaces, sliding zonal interfaces, fast search procedures, and virtual zones. All of these methods are designed with two goals; namely extend the use of patched grids to unsteady aerodynamics, e.g. oscillating control flaps, and provide the user more flexibility in the grid topologies available for gridding complex aerodynamic configurations. For example, the use of virtual zones allows the user the choice of using one grid topology for surface grids, and another for the volume grids. This additional flexibility has a large impact in the amount of calendar time required to block and grid a complex aerodynamic configuration. Several examples are shown demonstrating the new features. Other issues involving grid generation are also discussed. In particular the existing problems of defining grid quality measures which are relevant are also described.

Klopfer, Goetz↗

NASA NTRS1997

Grid Generation Issues and CFD Simulation Accuracy for the X33 Aerothermal Simulations

Grid generation issues relating to the simulation of the X33 aerothermal environment using the GASP code are explored. Required grid densities and normal grid stretching are discussed with regards to predicting the fluid dynamic and heating environments with the desired accuracy. The generation of volume grids is explored and includes discussions of structured grid generation packages such as GRIDGEN, GRIDPRO and HYPGEN. Volume grid manipulation techniques for obtaining desired outer boundary and grid clustering using the OUTBOUND code are examined. The generation of the surface grid with the required surface grid with the required surface grid topology is also discussed. Utilizing grids without singular axes is explored as a method of avoiding numerical difficulties at the singular line.

Polsky, Susan↗

NASA NTRS2002

Implementing Production Grids

We have presented the essence of experience gained in building two production Grids, and provided some of the global context for this work. As the reader might imagine, there were a lot of false starts, refinements to the approaches and to the software, and several substantial integration projects (SRB and Condor integrated with Globus) to get where we are today. However, the point of this paper is to try and make it substantially easier for others to get to the point where Information Power Grids (IPG) and the DOE Science Grids are today. This is what is needed in order to move us toward the vision of a common cyber infrastructure for science. The author would also like to remind the readers that this paper primarily represents the actual experiences that resulted from specific architectural and software choices during the design and implementation of these two Grids. The choices made were dictated by the criteria laid out in section 1. There is a lot more Grid software available today that there was four years ago, and various of these packages are being integrated into IPG and the DOE Grids. However, the foundation choices of Globus, SRB, and Condor would not be significantly different today than they were four years ago. Nonetheless, if the GGF is successful in its work - and we have every reason to believe that it will be - then in a few years we will see that the 28 functions provided by these packages will be defined in terms of protocols and MIS, and there will be several robust implementations available for each of the basic components, especially the Grid Common Services. The impact of the emerging Web Grid Services work is not yet clear. It will likely have a substantial impact on building higher level services, however it is the opinion of the author that this will in no way obviate the need for the Grid Common Services. These are the foundation of Grids, and the focus of almost all of the operational and persistent infrastructure aspects of Grids.

Johnston, William E.↗

NASA NTRS2006

Fibonacci Grids

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.

Swinbank, Richard↗

NASA NTRS2007

Modeling and Grid Generation of Iced Airfoils

SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.

Vickerman, Mary B.↗

NASA NTRS2010

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.

Pirzadeh, Shahyar↗

NASA NTRS2011

Grid Fin Stabilization of the Orion Launch Abort Vehicle

Wind tunnel tests were conducted by Nielsen Engineering & Research (NEAR) and Rose Engineering & Research (REAR) in conjunction with the NASA Engineering & Safety Center (NESC) on a 6%-scale model of the Orion launch abort vehicle (LAV) configured with four grid fins mounted near the base of the vehicle. The objectives of these tests were to 1) quantify LAV stability augmentation provided by the grid fins from subsonic through supersonic Mach numbers, 2) assess the benefits of swept grid fins versus unswept grid fins on the LAV, 3) determine the effects of the LAV abort motors on grid fin aerodynamics, and 4) generate an aerodynamic database for use in the future application of grid fins to small length-to-diameter ratio vehicles similar to the LAV. The tests were conducted in NASA Ames Research Center's 11x11-foot transonic wind tunnel from Mach 0.5 through Mach 1.3 and in their 9x7-foot supersonic wind tunnel from Mach 1.6 through Mach 2.5. Force- and moment-coefficient data were collected for the complete vehicle and for each individual grid fin as a function of angle of attack and sideslip angle. Tests were conducted with both swept and unswept grid fins with the simulated abort motors (cold jets) off and on. The swept grid fins were designed with a 22.5deg aft sweep angle for both the frame and the internal lattice so that the frontal projection of the swept fins was the same as for the unswept fins. Data from these tests indicate that both unswept and swept grid fins provide significant improvements in pitch stability as compared to the baseline vehicle over the Mach number range investigated. The swept fins typically provide improved stability as compared to the unswept fins, but the performance gap diminished as Mach number was increased. The aerodynamic performance of the fins was not observed to degrade when the abort motors were turned on. Results from these tests indicate that grid fins can be a robust solution for stabilizing the Orion LAV over a wide range of operating conditions.

Pruzan, Daniel A.↗

NASA NTRSDate not supplied

Micro-grid for Future Planetary Surface Needs

Under the current Artemis Program, the National Aeronautics and Space Administration (NASA) will send its next set of astronauts (first woman and next man) to the Moon by 2024 and establish a sustainable presence on the lunar surface by 2028. The challenge of creating a sustained lunar surface presence is significantly different than previous efforts. Lunar surface operations will require access to continuous and highly reliable power to support mission needs, such as to support ISRU operations. Adding to this challenge, the lunar surface operations are not going to be established over a single effort, rather the system and operations will evolve and grow over time (years). The first initial loads that arrive on the lunar surface will be integrated to their own dedicated power sources. As the lunar surface operations grow, so will the demand for power and at some point these individual loads will require more power than can be generated with any single power device. This power demand drives the need for inter-connecting the loads and power devices to share power between them, resulting in a micro-grid. One of the advantages of developing a lunar surface micro-grid is that allows lunar surface operations to resemble electrical utility operations on Earth; it allows power to be generated where it is convenient and allows power to be consumed where it is convenient, rather than negotiating between generation and consumption. The micro-grid concept also provides another benefit of affording the ability to increase overall system reliability by integrating dissimilar power generation and energy storage devices together, for example modifying the power generation strategy to include both solar arrays and nuclear. Creating a lunar surface micro-grid has its advantages, however there are significant challenges associated with an evolvable micro-grid concept. The challenges include how to efficiently transmit large amounts of power (10kW+) long distances (1kW+), how to effectively integrate dissimilar power generation and energy storage devices to maximize power consumption and minimize downtime, and how to physically connect these devices together with a connector that can survive the lunar environment (dust, extreme cold temperatures) and is capable of both astronaut and robotic operation. The basic components of the micro-grid have to be designed to ensure the system is sustainable, modular, and reconfigurable. An interface to the micro-grid has to be designed that allows for additional technologies, some of which may not yet be fully designed, to easily integrate into the micro-grid concept. This presentation discusses these lunar challenges in some more depth and offers a path forward in designing an evolvable micro-grid to meet the needs of the lunar surface operations and proposes a Universal Micro-grid Interface Converter to connect these dissimilar power sources and mission loads to the micro-grid.

Jeffrey Csank↗

NASA NTRSDate not supplied

Automatic Boundary-Layer Adaptation of Structured Grids in VULCAN-CFD

In supersonic and hypersonic flow computations, well-resolved boundary layers are essential for accurate quantification of surface heating and transition prediction, particularly via linear stability analysis. Grid design for hypersonic flows with shocks, boundary-layer separation, and/or complex mean flow features incorporating spanwise/azimuthal inhomogeneities is a difficult issue. In comparison to a manual grid adaptation procedure, an autonomous grid adaptation technique offers significant improvements in computing time and solution quality. The VULCAN-CFD solver already includes a validated procedure for automatic adaption of structured grids to the bow shock. The present focus is on implementing an automatic boundary-layer adaptation capability in VULCAN-CFD that adapts structured, multiblock grids to both the bow shock and the boundary layer at the same time. The boundary-layer adaptation algorithm allows the user to specify the number of cells within the boundary layer, along with the input parameters used for detecting the edge of the boundary layer, namely, the variable used in the edge detection criterion,the edge detection method, the detection direction, and the relaxation factor used during the morphing of the grid. The algorithm automatically distributes grid points along the wall-normal direction to achieve a smooth variation in grid spacing from the edge of the boundary layer to a"junction" location within the outer part of the grid. Illustrative results are presented for three different high-speed configurations: the two-dimensional flow over a cylinder at Mach 17.6 and unit Reynolds number of Re=0.38x10^6 m^-1, the axisymmetric flow over a cone-cylinder-flare model at Mach 6.0 and Re = 10.5×10^6 m^-1, and the three-dimensional flow over a blunt, 7-degree half-angle cone at 5-degree angle of attack in a Mach 9.79 flow with Re = 17.1×10^6 m^-1. The automated boundary-layer adaptation is shown to provide an adequate grid topology that is aligned with the bow shock in the outer part of the grid and also resolves the viscous boundary-layer region close to the surface.

boundary layer transition↗

DOE OSTI2021

Building Energy Codes and Grid-Interactive Efficient Buildings: How building energy codes can enable a more dynamic and energy-efficient built environment

This report considers the role of national model codes to promote grid-interactive efficient buildings (GEBs) as part of the modernization of the U.S. electricity grid. It introduces GEBs, describes their ability to support a clean, resilient grid, and considers challenges and approaches for incorporating GEB measures into national model energy codes and standards. Desirable traits of GEB include being low energy, low peaking, and responsive to grid needs, and minimizing the curtailment of renewable energy resources. In addition, the future grid incurs a time and locational value on these types of building services. Accounting for these considerations in future code development requires a continuation and expansion of code-minimum energy efficiency requirements and inclusion of demand responsive and load flexibility measures while ensuring annual use and cost reductions. Also, efforts to include GEB measures in codes will be limited until they are fully developed into an American National Standards Institute (ANSI)-approved standard. Then it would be straightforward to address GEB measures through points or packages and/or scoring requirements. Otherwise, the building code would have to describe each specific grid responsive strategy. This document reviews topics pertinent to considering codes in this context. Specifically, the study presents the status and direction of current building energy codes, the future smart grid, low-energy buildings, and grid-integrated buildings. The report concludes with recommendations for future code development activities to support low-energy, grid-interactive buildings in order to provide added value to building owners, the grid, and society.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Macroscopic Nonuniformities in Metal Grids Formed by Cracked Film Lithography Result in 19.3% Efficient Solar Cells

Cracked film lithography (CFL) is an emerging method for patterning transparent conductive metal grids. CFL can be vacuum- and Ag-free, and it forms more durable grids than nanowire approaches. In spite of CFL’s promising transmittance/grid sheet resistance/wire spacing tradeoffs, previous solar cell demonstrations have had relatively low performance. This work introduced macroscopic nonuniformities in the grids to improve the short-circuit current density/fill factor tradeoff in small area Cu(In,Ga)Se2 cells. Furthermore, the performance of optimized baseline grids was matched by CFL grids with microscopic openings and macroscopic patterns, culminating in a 19.3%-efficient cell. Simulations show that uniform CFL grids are enhanced by patterning because it leads to better balance among shadowing, grid resistance and transparent conductive oxide resistance losses. Thin-film module efficiency calculations were performed to highlight the performance gains that metal grids can enable by eliminating the transparent conductive oxide losses and widening monoliths. Adding the patterned CFL grids demonstrated in this work to CIGS modules is predicted to reach 0.7% higher efficiency (absolute) than screen-printed grids.

14 SOLAR ENERGY↗

DOE OSTI2023

LA100 Equity Strategies. Chapter 12: Distribution Grid Upgrades for Equitable Resilience and Solar, Storage, and Electric Vehicle Access

The LA100 Equity Strategies project integrates community guidance with robust research, modeling, and analysis to identify strategy options that can increase equitable outcomes in Los Angeles' clean energy transition. As Los Angeles transitions toward clean energy, existing distribution grid infrastructure will need to be updated and expanded to support reliable service during routine operations, enable interconnection with distributed energy resources and electrified loads, and provide access to energy-related services during disasters. This chapter focuses on equity in distribution grid upgrades, reliability, and resilience in Los Angeles. Specifically, NREL performed grid upgrade and resilience analyses using a detailed model of the distribution grid and income-differentiated household load profiles, electric vehicle (EV) adoption patterns, distributed solar adoption, and grid reliability to explore two key questions to inform how the City of Los Angeles can ensure a resilient and reliable distribution grid for all communities during the clean energy transition: Where can distribution system upgrades can be prioritized to enable equitable access to, and adoption of, clean energy technologies and how can Los Angeles provide equitable, resilient access to electricity-related services (e.g., health care, food) during disaster events like earthquakes and flooding? The electric distribution system is the "last mile" of the grid, linking the multistate bulk power system with customers; new loads, including EVs; and distributed energy resources, such as customer and community solar and storage. This analysis focuses on the 4.8-kilovolt (kV) system, including service transformers that represent the utility-side of the grid connection for most residential customers. Chapter 17 looks at the customer-side of the grid connection with a focus on electric panel upgrade needs. The transition toward clean energy can put additional stress on the distribution system from distributed energy resources and electrification - especially EVs and increased use of electricity for heating, cooling, cooking, and hot water. This stress, measured here as the number of equipment overloads and voltage violations, correlates strongly to grid reliability and therefore is used as a proxy for understanding additional upgrades needed and to help ensure equitable access to electrification and distributed energy resources. NREL also conducted community resilience analysis to examine customer-level access to both electricity and a larger range of services, such as hospitals and grocery stores during a disaster. This analysis explicitly considers equity to understand differences in current resilience and resilience strategies to effectively improve critical services access for all Angelenos. Research was guided by input from the community engagement process, and associated equity strategies are presented in alignment with that guidance.

14 SOLAR ENERGY↗

DOE OSTI2024

Network Security Challenges and Countermeasures for Software-Defined Smart Grids: A Survey

The rise of grid modernization has been prompted by the escalating demand for power, the deteriorating state of infrastructure, and the growing concern regarding the reliability of electric utilities. The smart grid encompasses recent advancements in electronics, technology, telecommunications, and computer capabilities. Smart grid telecommunication frameworks provide bidirectional communication to facilitate grid operations. Software-defined networking (SDN) is a proposed approach for monitoring and regulating telecommunication networks, which allows for enhanced visibility, control, and security in smart grid systems. Nevertheless, the integration of telecommunications infrastructure exposes smart grid networks to potential cyberattacks. Unauthorized individuals may exploit unauthorized access to intercept communications, introduce fabricated data into system measurements, overwhelm communication channels with false data packets, or attack centralized controllers to disable network control. An ongoing, thorough examination of cyber attacks and protection strategies for smart grid networks is essential due to the ever-changing nature of these threats. Previous surveys on smart grid security lack modern methodologies and, to the best of our knowledge, most, if not all, focus on only one sort of attack or protection. This survey examines the most recent security techniques, simultaneous multi-pronged cyber attacks, and defense utilities in order to address the challenges of future SDN smart grid research. The objective is to identify future research requirements, describe the existing security challenges, and highlight emerging threats and their potential impact on the deployment of software-defined smart grid (SD-SG).

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2018

Generating a Grid for Unstructured RANS Simulations of Jet Flows

A study has been performed to determine best practices for generating unstructured grids for Reynolds-Averaged Navier-Stokes (RANS) simulations of jet flows. The Axisymmetric Near-Sonic Jet Case from the Turbulence Modeling Resource was used for this study: a Mach 0.985 flow through the 2-in. diameter Acoustic Reference Nozzle (ARN2). Simulations were run with FUN3D and used the Menter Shear Stress Transport (SST-V), Spalart-Allmaras (S-A), and k-kL turbulence models. The axial velocity and turbulent kinetic energy fields in the jet plume of the unstructured grid solutions were compared to those of the baseline structured grid solution provided by the Turbulence Modeling Resource. Only solutions using grids with structured-like elements in the jet plume showed good agreement with the baseline structured grid solution. Using the SST-V turbulence model, the fully unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. With the S-A turbulence model, the unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. The solutions using the k-kL turbulence model seemed less sensitive to grid topology. Nozzle massflow and thrust performance were also compared for all simulations. Based on the results of this study, it is currently recommended that structured-like grid elements are used in the plumes of jet flows; unstructured grid elements can be used elsewhere.

RANS Simulations; Unstructured Grids; Jet Flows↗

DOE OSTI2020

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↗