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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Grid Optimization Competition on Synthetic and Industrial Power Systems

This paper summarizes a grid optimization (GO) competition effort in the United States to find the best solution strategies for up to interconnect-scale power system networks with around 32,000 buses. The optimization problem is a mixedinteger, non-convex non-linear problem, (MINLP) and includes discrete variables such as unit commitment and line switching, control settings (transformer taps and phase shifters with impedance correction tables), and bus shunts. The case study includes six actual industry grids as well as 16 realistic synthetic grids created by three different dataset teams. The winners are selected and ranked based on scoring criteria, which consider the solution quality (such as objective functions) within time limits. Nine winner teams are selected from 26 competitor teams. The results achieved by different teams are described and the performance of different algorithms on synthetic grids and actual industry grids are compared and analyzed.

mixed-integer non-linear programming↗
NASA NTRS1975

Experiments on solar photovoltaic power generation using concentrator and liquid cooling

Calculations and experimental data are presented leading to the development of a practical, economical solar photovoltaic power supply. The concept involves concentration of sunlight up to about 100 times normal solar intensity in a solar tracking collector and directing this to an array of solar cells. The cells are immersed in water circulated from a thermal reservoir which limits cell temperature rise to about 20 C above ambient during the day and which cools to ambient temperature during the night. Experiments were conducted on solar cells using a Fresnel lens for magnification, a telescope equatorial mount with clock drive, and tap water circulated through the solar cell holder cavity. Test results show that cells operate satisfactorily under these conditions. Power outputs achieved experimentally with cell optimized for 25 suns were linear with concentration to about 15 suns. Cells optimized for 100 suns were not available, but a corresponding linear relation of power output with concentration is anticipated. Test results have been used in a design analysis of the cost of systems utilizing this technique.

Beam, B. H.↗
DOE OSTI2025

Optimization for Bioenergy Systems

The Sustainable Aviation Fuel (SAF) Grand Challenge (Langholtz, 2024 ) seeks to generate 35 billion gallons of SAF each year by 2050, with corn stover, an agricultural byproduct, playing a key role as a feedstock. This study develops an optimization framework to enhance the quality and quantity of corn stover while ensuring economic and environmental viability. Using the Decision Support System for Agrotechnology Transfer (DSSAT) crop model, we simulate the effects of cover crops on rotation yield, soil moisture balance, and nitrogen cycling across diverse climates and soils. The model outputs, including yield data and soil quality changes, inform a Mixed-Integer Linear Programming (MILP) optimization model. This model aims to maximize economic and environmental returns by incorporating production costs, direct and indirect income, and environmental incentives. The optimization model evaluates 280 agriculture management plans composed of various crop management strategies, including corn stover removal rates, cover crop adoption, and fertilization practices. It seeks to identify the optimal combination of crop and tillage decisions for each subfield, maximizing profits while enhancing soil carbon sequestration and reducing greenhouse gas emissions. Outputs include detailed subfield locations, optimal management plans, and profits per hectare and per acre, allowing for comparison with literature values on farm profits. This study provides a robust optimization framework supporting the SAF Grand Challenge by proposing economically viable and environmentally sustainable strategies for corn stover utilization. The findings highlight corn stover's potential as a sustainable feedstock for SAF production, offering practical solutions to enhance its quality and quantity while maintaining soil health. Idaho is used as a case study to demonstrate the framework's applicability and effectiveness in real-world scenarios. Langholtz, M. H., Davis, M., Hellwinckel, C., De La Torre Ugarte, D., Efroymson, R., Jacobson, R., Milbrandt, A., Coleman, A., Davis, R., Kline, K. L., Badgett, A., Curran, S., Schmidt, E., Theiss, T., Fried, J., English, B., Lambert, L., Cook, H., Field, J., ... Walker, L. (2024). 2023 Billion-Ton Report: An Assessment of U.S. Renewable Carbon Resources. https://doi.org/10.2172/2441098 DSSAT Foundation. (2025). Decision Support System for Agrotechnology Transfer (DSSAT). Retrieved from https://dssat.net/

09 - BIOMASS FUELS↗
DOE OSTI2015

Scalable Heuristics for Planning, Placement and Sizing of Flexible AC Transmission System Devices

Aiming to relieve transmission grid congestion and improve or extend feasibility domain of the operations, we build optimization heuristics, generalizing standard AC Optimal Power Flow (OPF), for placement and sizing of Flexible Alternating Current Transmission System (FACTS) devices of the Series Compensation (SC) and Static VAR Compensation (SVC) type. One use of these devices is in resolving the case when the AC OPF solution does not exist because of congestion. Another application is developing a long-term investment strategy for placement and sizing of the SC and SVC devices to reduce operational cost and improve power system operation. SC and SVC devices are represented by modification of the transmission line inductances and reactive power nodal corrections respectively. We find one placement and sizing of FACTs devices for multiple scenarios and optimal settings for each scenario simultaneously. Our solution of the nonlinear and nonconvex generalized AC-OPF consists of building a convergent sequence of convex optimizations containing only linear constraints and shows good computational scaling to larger systems. The approach is illustrated on single- and multi-scenario examples of the Matpower case-30 model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

MO-AB-BRA-08: Rapid Treatment Field Uniformity Optimization for Total Skin Electron Beam Therapy Using Cherenkov Imaging

Purpose: To evaluate treatment field heterogeneity resulting from gantry angle choice in total skin electron beam therapy (TSEBT) following a modified Stanford dual-field technique, and determine a relationship between source to surface distance (SSD) and optimized gantry angle spread. Methods: Cherenkov imaging was used to image 62 treatment fields on a sheet of 1.2m x 2.2m x 1.2cm polyethylene following standard TSEBT setup at our institution (6 MeV, 888 MU/min, no spoiler, SSD=441cm), where gantry angles spanned from 239.5° to 300.5° at 1° increments. Average Cherenkov intensity and coefficient of variation in the region of interest were compared for the set of composite Cherenkov images created by summing all unique combinations of angle pairs to simulate dual-field treatment. The angle pair which produced the lowest coefficient of variation was further studied using an ionization chamber. The experiment was repeated at SSD=300cm, and SSD=370.5cm. Cherenkov imaging was also implemented during TSEBT of three patients. Results: The most uniform treatment region from a symmetric angle spread was achieved using gantry angles +/−17.5° about the horizontal axis at SSD=441cm, +/−18.5° at SSD=370.5cm, and +/−19.5° at SSD=300cm. Ionization chamber measurements comparing the original treatment spread (+/−14.5°) and the optimized angle pair (+/−17.5°) at SSD=441cm showed no significant deviation (r=0.999) in percent depth dose curves, and chamber measurements from nine locations within the field showed an improvement in dose uniformity from 24.41% to 9.75%. Ionization chamber measurements correlated strongly (r=0.981) with Cherenkov intensity measured concurrently on the flat Plastic Water phantom. Patient images and TLD results also showed modest uniformity improvements. Conclusion: A decreasing linear relationship between optimal angle spread and SSD was observed. Cherenkov imaging offers a new method of rapidly analyzing and optimizing TSEBT setup geometry by providing a 2D image of the treatment plane as a sum of the two fields. This study has been funded by NIH grants R21EB17559 and R01CA109558 as well as Norris Cotton Cancer Center Pilot funding.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Environmental and economic optima of solar home systems design: A combined LCA and LCC approach

Here, we compare the economic and environmental optimal design of Solar Home Systems (SHSs) and explore the role of economic incentives (such as tariffs and technology costs) in approximating the two optima. To achieve that, we present a methodology for the environmental and economic evaluation of grid-connected SHSs: user-scale electric systems involving a photovoltaic (PV) power system and a battery energy storage system. The proposed methodology is based on a mixed integer linear programming (MILP) optimization, life cycle assessment and life cycle costing. This methodological framework is applied to a case study involving a typical SHS installation in Italy. The results of the environmental optimal design brought to the evaluation of a 3.25 kW PV assisted by 8.66 kWh of nickel cobalt manganese batteries, whereas the costs of the SHS are minimized by a small PV system (less than 1 kW). Results underline that the environmental optimal configurations rely on battery technologies, which entails a significant cost compared to the grid connection. In contrast, the economic optimal design solutions is less impactful than the grid mix both from an environmental and economic points of view. Thanks to a reduction of batteries and PV costs, the environmental impact of the economic optimal design is expected to decrease in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Automated Dynamic Demand Response Implementation on a Micro-grid

In this paper, we describe a system for real-time automated Dynamic and Sustainable Demand Response with sparse data consumption prediction implemented on the University of Southern California campus microgrid. Supply side approaches to resolving energy supply-load imbalance do not work at high levels of renewable energy penetration. Dynamic Demand Response (D 2 R) is a widely used demand-side technique to dynamically adjust electricity consumption during peak load periods. Our D 2 R system consists of accurate machine learning based energy consumption forecasting models that work with sparse data coupled with fast and sustainable load curtailment optimization algorithms that provide the ability to dynamically adapt to changing supply-load imbalances in near real-time. Our Sustainable DR (SDR) algorithms attempt to distribute customer curtailment evenly across sub-intervals during a DR event and avoid expensive demand peaks during a few sub-intervals. It also ensures that each customer is penalized fairly in order to achieve the targeted curtailment. We develop near linear-time constant-factor approximation algorithms along with Polynomial Time Approximation Schemes (PTAS) for SDR curtailment that minimizes the curtailment error defined as the difference between the target and achieved curtailment values. Our SDR curtailment problem is formulated as an Integer Linear Program that optimally matches customers to curtailment strategies during a DR event while also explicitly accounting for customer strategy switching overhead as a constraint. We demonstrate the results of our D 2 R system using real data from experiments performed on the USC smartgrid and show that 1) our prediction algorithms can very accurately predict energy consumption even with noisy or missing data and 2) our curtailment algorithms deliver DR with extremely low curtailment errors in the 0.01-0.05 kWh range.

Kuppannagari, Sanmukh R.↗
DOE OSTI2016

Analysis of Modeling Assumptions used in Production Cost Models for Renewable Integration Studies

Renewable energy integration studies have been published for many different regions exploring the question of how higher penetration of renewable energy will impact the electric grid. These studies each make assumptions about the systems they are analyzing; however the effect of many of these assumptions has not been yet been examined and published. In this paper we analyze the impact of modeling assumptions in renewable integration studies, including the optimization method used (linear or mixed-integer programming) and the temporal resolution of the dispatch stage (hourly or sub-hourly). We analyze each of these assumptions on a large and a small system and determine the impact of each assumption on key metrics including the total production cost, curtailment of renewables, CO2 emissions, and generator starts and ramps. Additionally, we identified the impact on these metrics if a four-hour ahead commitment step is included before the dispatch step and the impact of retiring generators to reduce the degree to which the system is overbuilt. We find that the largest effect of these assumptions is at the unit level on starts and ramps, particularly for the temporal resolution, and saw a smaller impact at the aggregate level on system costs and emissions. For each fossil fuel generator type we measured the average capacity started, average run-time per start, and average number of ramps. Linear programming results saw up to a 20% difference in number of starts and average run time of traditional generators, and up to a 4% difference in the number of ramps, when compared to mixed-integer programming. Utilizing hourly dispatch instead of sub-hourly dispatch saw no difference in coal or gas CC units for either start metric, while gas CT units had a 5% increase in the number of starts and 2% increase in the average on-time per start. The number of ramps decreased up to 44%. The smallest effect seen was on the CO2 emissions and total production cost, with a 0.8% and 0.9% reduction respectively when using linear programming compared to mixed-integer programming and 0.07% and 0.6% reduction, respectively, in the hourly dispatch compared to sub-hourly dispatch.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

A Fast Dynamic Internal Predictive Power Scheduling Approach for Power Management in Microgrids: Preprint

This paper presents a Dynamic Internal Predictive Power Scheduling (DIPPS) approach for optimizing power management in microgrids, particularly focusing on external power exchanges among diverse prosumers. DIPPS utilizes a dynamic objective function with a time-varying binary parameter to control the timing of power transfers to the external grid, facilitated by efficient usage of energy storage for surplus renewable power. The microgrid power scheduling problem is modeled as a mixed-integer nonlinear programming (MINLP-PS) and subsequently transformed into a mixed-integer linear programming (MILPPS) optimization through McCormick's relaxation to reduce computational complexity. A predictive window window with 6 data points is solved at an average of 0.92s, a 97.6% improvement over the 38.27s required for the MINLP-PS formulation, implying the numerical feasibility of the DIPPS approach for real-time implementation. Finally, the approach is validated against a static objective using real-world load data across three case studies with different time-varying parameters, demonstrating the ability of DIPPS to optimize power exchanges and efficiently utilize distributed resources while shifting the external power transfers to specified time durations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

Digital robust control law synthesis using constrained optimization

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Mukhopadhyay, Vivekananda↗
NASA NTRS1985

The role of service areas in the optimization of FSS orbital and frequency assignments

A relationship is derived, on a single-entry interference basis, for the minimum allowable spacing between two satellites as a function of electrical parameters and service-area geometries. For circular beams, universal curves relate the topocentric satellite spacing angle to the service-area separation angle measured at the satellite. The corresponding geocentric spacing depends only weakly on the mean longitude of the two satellites, and this is true also for alliptical antenna beams. As a consequence, if frequency channels are preassigned, the orbital assignment synthesis of a satellite system can be formulated as a mixed-integer programming (MIP) problem or approximated by a linear programming (LP) problem, with the interference protection requirements enforced by constraints while some linear function is optimized. Possible objective-function choices are discussed and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed ideal location set. A test problem is posed consisting of six service areas, each served by one satellite, all using elliptical antenna beams and the same frequency channels. Numerical results are given for the three ideal location prescriptions for both the MIP and LP formulations. The resulting scenarios also satisfy reasonable aggregate interference protection requirements.

Levis, C. A.↗
DOE OSTI2019

TRANSP-based closed-loop simulations of current profile optimal regulation in NSTX-Upgrade

Active control of the toroidal current density profile is critical for the upgraded National Spherical Torus eXperiment device (NSTX-U) to maintain operation at the desired high-performance, MHD-stable, plasma regime. Initial efforts towards current density profile control have led to the development of a control-oriented, physics-based, plasma-response model, which combines the magnetic diffusion equation with empirical correlations for the kinetic profiles and the non-inductive current sources. The developed control-oriented model has been successfully tailored to the NSTX-U geometry and actuators. Moreover, a series of efforts have been made towards the design of model-based controllers, including a linear-quadratic-integral optimal control strategy that can regulate the current density profile around a prescribed target profile while rejecting disturbances. In this work, the tracking performance of the proposed current-profile optimal controller is tested in numerical simulations based on the physics-oriented code TRANSP. Furthermore, these high-fidelity closed-loop simulations, which are a critical step before experimental implementation and testing, are enabled by a flexible framework recently developed to perform feedback control design and simulation in TRANSP.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

TRANSP-based closed-loop simulations of current profile optimal regulation in NSTX-Upgrade

Active control of the toroidal current density profile is critical for the upgraded National Spherical Torus eXperiment device (NSTX-U) to maintain operation at the desired high-performance, MHD-stable, plasma regime. Initial efforts towards current density profile control have led to the development of a control-oriented, physics-based, plasma-response model, which combines the magnetic diffusion equation with empirical correlations for the kinetic profiles and the non-inductive current sources. The developed control-oriented model has been successfully tailored to the NSTX-U geometry and actuators. Moreover, a series of efforts have been made towards the design of model-based controllers, including a linear-quadratic-integral optimal control strategy that can regulate the current density profile around a prescribed target profile while rejecting disturbances. In this work, the tracking performance of the proposed current-profile optimal controller is tested in numerical simulations based on the physics-oriented code TRANSP. These high-fidelity closed-loop simulations, which are a critical step before experimental implementation and testing, are enabled by a flexible framework recentlydeveloped to perform feedback control design and simulation in TRANSP.

current profile control↗
NASA NTRS1987

Singular trajectories in airplane cruise-dash optimization

Optimal cruise-dash trajectories are obtained for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. For the case of the steady-state arc being flown at full throttle, the skeletal transient trajectories are also flown at full throttle and the transients approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle, the transient trajectories follow a singular control law and exhibit a complex structure that differs from that of the full-throttle transients. With respect to optimality of the steady-state arc, it is found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large.

Bilimoria, Karl D.↗
DOE OSTI2022

Non-linear MHD modelling of edge localized modes suppression by resonant magnetic perturbations in ITER

Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. In this study, the main aim was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ~5 MW m ₋2 to ~1 MW m ₋2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Sequential design of linear quadratic state regulators with prescribed eigenvalues and specified relative stability

This paper considers the problem of optimal regulator design of linear multivariable systems with prescribed pole locations and/or poles corresponding to specified relative stability. A sequential method based on the frequency-domain optimality condition is proposed for achieving the desired pole assignment and determination of the corresponding quadratic performance index. This design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Ganesan, Sekar↗
DOE OSTI2025

Data-Driven Energy Resilience Assessment and Enhancement in Urban Communities: A Case Study in Detroit

This paper presents a data-driven framework for assessing and enhancing energy resilience in urban communities. The resilience assessment is based on two datasets: 1) annual aggregated power outage data and 2) 15-minute interval outage data. High-impact, low-probability (HILP) events are identified within these datasets to evaluate community resilience under extreme conditions. To enhance resilience, an optimization framework utilizing mixed integer linear programming is developed to determine the optimal sizing and placement of solar photovoltaic (PV) systems and battery energy storage systems (BESS). This method offers a cost-effective and practical solution for improving energy resilience in vulnerable communities. Furthermore, a case study of the City of Detroit in Michigan demonstrates the effectiveness of the framework through simulation and validation.

Energy resilience assessment↗