A grid search optimization subroutine for use with the GOSPEL optimization software package
Grid search optimization subroutine for analyses on distributed lumped activity networks
Allgaier, G. R.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Least-cost Optimal Distribution Grid Expansion (LODGE): Utility Pilots
The Least-cost Optimal Distribution Grid Expansion (LODGE) model provides the optimal portfolio of distribution system upgrades—e.g., voltage regulators, feeder reconductoring, transformer upgrades and non-wires alternatives (NWA), such as strategic siting of storage and distributed generation—to interconnect distributed energy resources (DERs) and enable load growth. It can be used to assess grid infrastructure costs and explore policy and regulatory solutions for distribution planning and DER valuation.In 2025, Berkeley Lab conducted three pilot analyses to validate LODGE results with empirical utility data before the model’s first release in 2026. The pilots, done with utilities in Washington, Colorado, and New Mexico, provide examples that illustrate how the model works, what it can do, and the value of the analysis.
Heleno, Miguel↗
Grid Expansion Optimal Planning Tools (GridEO): Manual for Users and Developers
This report describes Grid Expansion Optimal Planning Tools (GridEO). GridEO is a Python package for electric power grid capacity expansion modeling. With GridEO, the user can build and solve instances of the Capacity Expansion Planning (CEP) problem to determine an optimal plan of investment in capacity of various types of power grid equipment.
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Optimal moving grids for time-dependent partial differential equations
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.
Wathen, A. J.↗
Optimal moving grids for time-dependent partial differential equations
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.
Wathen, A. J.↗
Evaluation of truncation error and adaptive grid generation for the transonic full potential flow calculations
The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.
Nakamura, S.↗
Is a Generator the Only Solution When the Grid Fails? Optimizing Systems for Resiliency and Carbon Reduction: Preprint
Traditionally, buildings are dependent on utility infrastructure, and when a grid failure happens, end users rely on the closest source of energy storage to sustain operation until power is restored. For buildings, that typically means using an electric generator. This electric generator either uses on-site energy storage such as fossil fuels in a tank or a gas connection which is, in turn, tied to gas wells—also a form of energy storage. Generators are popular for their ease of implementation and low capital costs; however, they have limited value outside of disruptions, and they are a source of scope 1 emissions, or direct greenhouse gas emissions from sources controlled by the building owner. In contrast, some power generation and storage systems, such as photovoltaic (PV) panels and battery energy storage systems (BESS), can serve the same purpose during grid disruptions while presenting advantages outside of power failure. This paper explores methods for storing and converting energy on-site to increase building resiliency, focusing on solutions that minimize scope 1 emissions. We analyze the cost and carbon impacts of energy efficiency measures, PV arrays, and BESS, with and without generators, in a simulation test case. We find significant benefits can be achieved both during and outside of power failure events when designing systems that integrate the on-demand capability of generators, the low carbon energy supplied by PV, and the storage capabilities of BESS. Specifically, adding even minimal BESS and PV can result in downsizing the generator, increasing generator efficiency and requiring less fuel.
ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗
An optimized top contact design for solar cell concentrators
A new grid optimization scheme is developed for point focus solar cell concentrators which employs a separated grid and busbar concept. Ideally, grid lines act as the primary current collectors and receive all of the current from the semiconductor region. Busbars are the secondary collectors which pick up current from the grids and carry it out of the active region of the solar cell. This separation of functions leads to a multithickness metallization design, where the busbars are made larger in cross section than the grids. This enables the busbars to carry more current per unit area of shading, which is advantageous under high solar concentration where large current densities are generated. Optimized grid patterns using this multilayer concept can provide a 1.6 to 20 percent increase in output power efficiency over optimized single thickness grids.
Desalvo, Gregory C.↗
Optimizing Grid-interactive Efficient Building Designs with Stacked Value Streams
Grid-interactive efficient buildings (GEBs) are those characterized by the combination of energy efficiency and demand flexibility with smart technologies and communications to not only deliver greater affordability and comfort to buildings, but also help utilities manage grid operations and lower system costs. This paper presents an innovative techno-economic assessment framework to effectively examine different GEB design options, explore various use cases, define technically achievable benefits, and thereby assist in informed decision-making. In particular, building load flexibility, thermal storage, and battery energy storage are considered. Advanced optimal dispatch problem is formulated to maximize the stacked value streams from multiple, competing use cases, subject to the physical capabilities and operational flexibility associated with different designs and configurations. Comprehensive case studies were performed for a real-world building to evaluate the cost-effectiveness of different GEB designs and offer in-depth insights. It was found that the proposed assessment method could effectively capture the costs and benefits linked to each GEB design option. Furthermore, the study revealed that outage mitigation and demand response are the two most significant sources of benefits for GEBs.
Ma, Xu↗
CRADA Number NFE-24-10110 with Qubit Engineering Inc. (CRADA Final Report)
Over the past year, the Qubit Engineering team has pushed the frontiers of power‑grid optimization, working in close collaboration with Oak Ridge National Laboratory (ORNL) and the Tennessee Valley Authority (TVA). Their progress is reflected in three newly submitted conference papers, “Unified Relational GNN Architecture for AC Optimal Power Flow Calculations in Electric Grids,” “Graph‑Based Attention Mechanisms for Solving the AC Optimal Power Flow Problem in Electrical‑Power Networks,” and “Enhanced Power‑Grid Maintenance Planning and Quantum‑Inspired Combinatorial Prospects.” These publications showcase state‑of‑the‑art graph‑neural‑network methods for AC‑OPF and novel quantum‑inspired heuristics for maintenance scheduling. Beyond the academic results, the Qubit team has converted the research into two production‑grade tools built on TVA data: Neuro‑Grid, an AI‑driven power‑flow simulator that provides instant, interactive full‑grid load‑flow visualizations, and Quanta‑Grid, a quantum‑inspired maintenance‑scheduling engine to support logistics optimization for power utilities. Together, these advances demonstrate how Qubit’s partnership with ORNL and TVA is delivering practical, physics‑grounded analytics for next‑generation grid management.
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Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances
Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.
Liu, Gao-Lian↗
Recent progress in unstructured grid generation
A number of recent developments and improvements in unstructured grid generation are discussed. Emphasis is given to the enhancement of capabilities of unstructured grid generation code based on the advancing front technique for generating triangular and tetrahedral grids. Two new methods have been devised to facilitate the process of grid generation: (1) structured background grids and their application to 3D unstructured grid generation and (2) grid restart capability. New postprocessing tools to manipulate generated grids include grid optimization, local remeshing, and interpolation for unstructured grids. Examples and references are given to show the applications of these developments.
Pirzadeh, Shahyar↗
Structured adaptive grid generation using algebraic methods
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.
Yang, Jiann-Cherng↗
High-Fidelity, Large-Scale, Realistic Dataset Development
The final report summarizes the work performed for supporting the ARPA-E Grid Optimization Competition (Challenge 2 and Challenge 3) within the stated period. Challenge 2 For the challenge period, the main responsibility of the team is to investigate, gen- erate, and deliver parts of the data sets for the competition, based on the competition model for Challenge 2, existing data sets from Challenge 1, and data source supplied by other data set teams. Challenge 3 For the challenge period, the main responsibility of the team is to propose, create, deliver, and maintain the data format during the competition period. The data format will specify how the benchmark data will be represented and communicated to competitors. It will also specify how competitors should report back the solutions. The data format will be closely aligned with the problem formulation (maintained by the formulation team) and the solution validation process (maintained by the validation team). Our team is also responsible in investigating, generating, and delivering parts of the data sets for the competition. The data sets will be created based on the competition model for Challenge 3, existing data sets from Challenge 1 and Challenge 2, and data source supplied by other data set teams.
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RNS Applications for Interacting Sub- and Supersonic Flows
A solution based grid adaptation method that combines elements of the multigrid method for solution acceleration and the domain decomposition philosophy for grid optimization is described. Unlike other solution based adaptive gridding schemes, wherein the overhead of recomputing the grid and re-evaluating the solution on the adapted grid leads to higher computational costs compared to a non-adapted calculation, the present methodology reduces the computational time required to obtain the solution. The computational effort involved in the present calculation is significantly lower than a non-adapted calculation that utilizes the multigrid method purely as a convergence acceleration tool. In addition to convergence acceleration, the multigrid framework provides a mechanism of information transfer from regions wherein grid refinement is specified to unrefined coarse grid regions. The basis for domain decomposition in the current procedure is the variation in grid refinement requirements for each coordinate direction in different portions of the flow field. The method is demonstrated herein on an efficient set of governing equations termed the reduced Navier Stokes equations, applied in conjunction with a set of physical boundary conditions. The governing equations are discretized through a pressure based flux splitting procedure that is uniformly applicable from incompressible to supersonic Mach numbers.
Rubin, Stanley G.↗
An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models
Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.
CPM↗
LLGoMAX : Enhancing Industry-Standard Tools for AC Optimal Unit Commitment
In 2018, the Advanced Research Project Agency – Energy (ARPA-E) launched the Grid Optimization Competition (GOC) [1], a series of competitive challenges intended to accelerate innovation in decision support software used to schedule power grid operations, making them as efficient as possible, while respecting operational constraints of power equipment and operational security. This report covers the participation of the LLGoMAX team—a collaboration of the Lawrence Livermore National Laboratory (LLNL) and ECCO International, Inc.—in Challenge 3 of the competition.
97 MATHEMATICS AND COMPUTING↗
Synchronous Machine Governor Upgrade
Conventional generation sources play a critical role in the stability and reliability of the electrical grid, particularly as we transition towards more renewable energy sources. To understand and accurately emulate their behavior for optimizing grid operations and ensuring seamless integration with renewable technologies, it is essential to better emulate the grid- and plant-level impacts of conventional generation sources, such as natural gas (NG) driven heat recovery steam generators (HRSGs) and combustion turbines (CTs). Therefore, a governor model is developed in a programmable logic controller (PLC) to investigate the performance of the conventional generator under various dynamic operating conditions and to identify the impact on grid stability in a controlled environment. The governor model aims to enable the hardware-in-the-loop (HIL) based emulation of these conventional generation sources using the existing 2 MVA synchronous machine/generator that is driven by a flexible 2.5 MW variable speed drive. This setup will allow us to replicate the dynamic characteristics and response behaviors of NG-driven HRSGs and CTs. The controls for the emulated conventional plants follow the industry standard and are adjustable, ensuring they accurately reflect the operational capabilities and limitations of real-world systems. These controls include load-following capabilities, ramp rates, startup and shutdown sequences, and emissions characteristics. By incorporating these adjustable controls, we aim to capture the nuanced impacts of conventional generation, such as their ability to provide ancillary services like frequency regulation, voltage support, and spinning reserve. In this report, we simulate two types of dynamic operations: grid-connected and islanding. For each dynamic operation, representative starting sequences are tested, including turbine purge, ignition, speed ramping up, generator excitation and synchronizing, and breaker close. The HIL based tests provides insights for field deployment, specifically the high-fidelity governor model provides results to predict the potential stability and reliability risk and suggest possible integration measures (e.g., generation and load balancing, tuning of governor control parameters). Ultimately, this enhanced emulation capability will be integrated into our Advanced Research on Integrated Energy Systems (ARIES), enabling us to conduct comprehensive studies on the interactions between conventional and renewable energy sources. By better understanding these interactions, we can develop strategies to optimize the overall performance and reliability of the grid. This will support the deployment of advanced grid management techniques, such as demand response, grid-forming inverters, and energy storage systems. The main contributions are summarized as follows: (1) This report introduces a PLC-based governor model for gas turbines. This model accurately simulates the dynamic behavior of conventional generation sources under various operational scenarios; (2) The model is integrated with an HIL testbed that includes a 2.5 MW variable speed drive and a 2 MVA synchronous machine. This setup enables realistic, real-time emulation of conventional power plants, particularly NG driven HRSGs and CTs; (3) The developed model is adaptable to various gas turbine configurations and allows for precise control over parameters such as MW ramp rates. This flexibility makes it a valuable tool for future research and industry collaboration; and (4) By incorporating the model into the National Renewable Energy Laboratory's Advanced Research on Integrated Energy Systems, the report lays the groundwork for future studies on interactions between conventional and renewable energy sources, enhancing the ability to develop advanced grid management strategies.
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