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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Cycles-L: A Coupled, 3-D, Land Surface, Hydrologic, and Agroecosystem Landscape Model

Managing landscapes to increase agricultural productivity and environmental stewardship can be informed by spatially-distributed models that operate at spatial and temporal scales that are intervention-relevant. This paper presents Cycles-L, a landscape-scale agroecosystem and hydrologic modeling system, using as a test case a watershed in Pennsylvania. Cycles-L emerges from melding the landscape and hydrology structure of Flux-PIHM, a 3-D land surface hydrologic model, with the agroecosystem processes in the Cycles model. Consequently, Cycles-L can simulate processes affected by topography, soil heterogeneity, and management practices, owing to its physically-based hydrology that can simulate horizontal and vertical transport of solutes with water. The model was tested at a 730-ha experimental watershed within the Mahantango Creek watershed. Cycles-L simulated well stream water and mineral nitrogen discharge (Nash-Sutcliffe coefficient 0.55 and 0.60, respectively) and grain yield (root mean square error 1.2 Mg ha -1 ). Cycles-L outputs are as good or better than those obtained with the uncoupled Flux-PIHM (water discharge) and Cycles (grain yield) models. Modeled spatial patterns of nitrogen fluxes like denitrification illustrate the combined control of crop management and topography. For example, denitrification is almost twice as high when simulated with Cycles-L than when simulated with Cycles 1-D. Due to its spatial and temporal resolution, Cycles-L fills a gap in the availability of models that operate at a scale relevant to evaluate interventions in the landscape. Cycles-L can become a central component in tools for climate change scenario analysis, precision agriculture, precision conservation, and artificial intelligence-based decision support systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Propulsion Electrification Architecture Selection Process and Cost of Carbon Abatement Analysis for Heavy-Duty Off-Road Material Handler

The heavy-duty off-road industry continues to expand efforts to reduce fuel consumption and CO 2 e (carbon dioxide equivalent) emissions. Many manufacturers are pursuing electrification to decrease fuel consumption and emissions. Future policies will likely require electrification for CO2e savings, as seen in light-duty on-road vehicles. Electrified architectures vary widely in the heavy-duty off-road space, with parallel hybrids in some applications and series hybrids in others. The diverse applications for different types of equipment mean different electrified configurations are required. Companies must also determine the value in pursuing electrified architectures; this work analyzes a range of electrified architectures, from micro hybrids to parallel hybrids to series hybrids to a BEV, looking at the total cost, total CO 2 e, and cost per CO 2 e (cost of carbon abatement, or cost of carbon reduction) using data for the year 2021. This study is focused on a heavy-duty off-road material handler, the Pettibone Cary-Lift 204i. This machine’s specialty application, including events like unloading large oil pipes from a railcar, requires a unique electrified architecture that suits its specific needs. However, the results from this study may be extrapolated to similar machinery to inform fuel savings options across the heavy-duty off-road industry. In this study, a unique electrified architecture is determined for the Cary-Lift. This architecture is informed by multiple rounds of a Pugh matrix decision analysis to select a shortened list of desirable electrified architectures. The shortened list is modeled and simulated to determine CO 2 e, cost, and cost per CO 2 e. A final architecture is determined as a plug-in series hybrid that reduces fuel consumption by 65%, targeting the large fuel and CO 2 e savings that are likely to be required for the future of the heavy-duty off-road industry.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Engineering↗
DOE OSTI2024

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

Markov decision process↗
DOE OSTI2021

Modeling and Optimization Methods for Controlling and Sizing Grid-connected Energy Storage: A Review

Purpose of Review Energy storage is capable of providing a variety of services and solving a multitude of issues in today's rapidly evolving electric power grid. This paper reviews recent research on modeling and optimization methods for optimally controlling and sizing grid-connected battery energy storage systems (BESSs). Open issues and promising research directions are discussed. Recent Findings Recent studies on BESS dispatch, evaluation, and sizing focus on advanced modeling and optimization methods to maximize stacked value streams from multiple services. BESS models have been improved to better represent operational characteristics or capture degradation effects. Different solution methods and optimization techniques have been proposed to improve the benefits and cost-effectiveness of BESSs, using deterministic approaches prevalently but with impressive progress in capturing and addressing uncertainties. Summary Recent progress in BESS scheduling and sizing better supports planning and operational decision-making in different use cases, which is highly important to advance the deployment of BESSs. Additional research is required to properly model the trade-off between short-term benefits and service life with multiple degradation effects explicitly considered in the decision-making process. Advanced methods are to be developed for effectively determining optimal BESS sizes that maximize overall benefits within a varying lifetime considering diversified system, conditions as well as uncertainties at planning and operational stages.

Wu, Di↗
DOE OSTI2025

CMIP7 data request: impacts and adaptation priorities and opportunities

The Coupled Model Intercomparison Project Phase 7 (CMIP7) undertook an extensive process to gather community input and refine data requests related to impacts and adaptation applications of Earth System Model (ESM) outputs. The Impacts and Adaptation (I&A) Data Request Team worked with CMIP7 leadership to distribute an open solicitation across many communities that use climate model outputs requesting inputs for new and existing variables, the most applicable temporal characteristics, and groupings of variables that together allow for specific application opportunities. This input was then collated and translated into CMIP7 standard templates for inclusion in the broader data request, leading to 13 I&A data request opportunities, 60 variable groups and 539 unique variables sought by vulnerability, impacts, adaptation, and climate services user communities. Here, we describe these opportunities and variable groups, as well as new insights into how ESM groups can prioritize outputs that set off a chain of further analyses, ultimately informing decisions impacting society and natural systems. These include an emphasis on high-resolution outputs to allow further modeling of climate impacts at regional and local scales, improved representation of extreme weather events, enhanced accuracy of downscaling and bias-adjustment techniques, and support for more detailed assessments for decision-making in adaptation and mitigation strategies. There is also broad interest in more extensive provisioning of two-dimensional variables at the Earth's surface, prioritizing experiments that enhance our understanding of both the recent past and future scenarios, and providing outputs that allow further downscaling and bias adjustment. We emphasize that variable groups are the fundamental level at which to engage with the I&A data request, matching the scale of input and the way output provision enables specific I&A applications. Given resource constraints, we applaud CMIP7 efforts to foster strong engagement and communication between ESM groups and the I&A team to build consensus around prudent compromises in priority variables, temporal resolutions, simulation experiments, time subsets, and ensemble members.

Ruane, Alex C. [NASA Goddard Inst. for Space Studi↗
DOE OSTI2021

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoitaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

A Multi-objective Microgrid Assessment and Sizing Framework for Economic and Resilience Benefits

This paper presents an innovative multi-objective assessment and sizing framework for battery energy storage system paired with photovoltaics for a cost-effective and resilient microgrid. In the proposed framework, we simultaneously consider i) economic benefits from bundling grid services in grid-connected mode and ii) enhanced resilience by operating the microgrid in island mode upon outages of the main grid. Instead of simply treating resilience as another monetary value stream, this paper models resilience and economic benefits as two separate objectives. Multi-objective optimization is developed to explore different sizing and dispatch options and generate the Pareto front to assist decision-making in system design. Case studies on a real-world microgrid project in Puget Sound Energy system are presented to illustrate the proposed modeling and sizing methods.

Battery energy storage, Microgrid, Optimal Sizingp↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery through Logic-based Superstructure Optimization

In this work, we extend the superstructure model proposed by Wamble et al. (2022) that considers feed input locations, recycling strategies, split fractions, stage numbers, and membrane area. We include the total number of stages as a decision variable, which might be particularly useful when there is cost as- sociated with adding additional stages. We propose a Generalized Disjunctive Programming (GDP) superstructure model that integrates all the design variables of the system. We also investigate the scalability of the model by varying the number of stages and the number of finite elements per stage to determine the impact on recovery and solution time.

Tran, Norman↗
DOE OSTI2022

Development and assessment of a model predictive controller enabling anticipatory control strategies for a heat-pipe system

To support the reliable and resilient operation of modular reactors and microreactors, anticipatory control strategies have been proposed for achieving faster-than-real-time predictions and decision-making capabilities in anticipation of potential anomalies, including setpoint changes and cyber incidents. Here this work presents how anticipatory control strategies can be implemented via model predictive control (MPC) of a single heat pipe’s temperature. Considering the uncertainty in developing and applying MPC, this work evaluates MPC performance given three different model forms: a linear response surface model, an artificial neural network (ANN), and an autoregressive model with exogenous input (ARX). This work also evaluates the impacts of different input biases and variance on MPC performance in order to account for potential sensor reading variations due to cyber incidents. We observe that nonparametric models such as the ANN and ARX result in more fluctuated control actions compared to the MPC applied to the linear response surface model. However, when the cyber incidents are of a large magnitude, the linear response surface model produces smaller feasible regions than the nonparametric models under identical constraints.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy: Preprint

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Prognostic model and failure mechanisms of steam generators in Sodium-Cooled fast reactors

This paper presents a prognostic model for sodium-cooled fast reactor (SFR) steam generators (SGs). Here, the purpose of the model is to estimate the remaining useful life of SFR SGs and thus to support the decision-making of autonomous control. SFR SGs are of great interest for plant integrity due to their harsh operation environment. They operate at higher temperatures and higher coolant-to-steam pressure differences than those of current light water reactors (LWR). The severity of the SFR SG failure consequences, which include water-sodium contact, is another reason. Understanding its failure mechanisms is important for the development of its prognostic model. Based on our literature review and physics-based analysis, we concluded that creep would be a dominant degradation mode of SFR SGs due to SFR’s high-temperature and high-pressure environment. Thus, creep is the focus of the prognostic model. Various other failure modes were also investigated in this study. The mechanical fatigue due to flow-induced vibration is usually observed in early developmental phases and would not be an important issue during normal operation. The thermal fatigue due to thermal stripping is occasionally observed in other components in SFRs but does not affect SG integrity. Pure water stress corrosive crack, fretting, and so on are commonly observed in LWR SGs but are significantly less important in SFR SGs because of the high temperatures, high pressure differences, and chemical properties of liquid sodium. Based on these investigations, a prognostic model focusing on creep failures was developed. It estimates the failure probability profile by sampling the Larson-Miller parameter (LMP) and temperature and associated uncertainties through Monte Carlo methods. Two case studies were presented. The first one demonstrated the model’s capability to calculate the failure probability for a new specimen within a given time. If the tube is working under temperatures of 500C ± 3 and pressures of 15.2 MPa, which leads to LMP of 20,100 ± 50, the failure probabilities within 50, 70, and 90 years are approximately 0.1 %, 3.2 %, and 17.5 %. The second demonstrated how adjusting the workload can help to protect the integrity of the component. For an old tube reaching 99 % of its lifespan, continuing to run at temperatures of 500C ± 3 and LMP of 20,100 ± 50 leads to a failure probability of about 29.0 % within a year. If the temperature is reduced by 5C, the failure probability can be reduced to 2.5 %, and, if the pressure is also reduced such that the LMP is increased by 100, the failure probability can further be reduced to 0.12 %.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Feature review of photovoltaic modeling software utilizing blind performance assessment

While confidence in photovoltaic (PV) modeling software has always been essential, the rapid pace of new PV plant developments makes accuracy and credibility more critical than ever. Independent assessments, particularly through blind modeling comparisons, are therefore necessary to ensure unbiased benchmarking across PV modeling software. Previous studies have been limited by a narrow range of models compared, anonymized results, or system size. This study presents results from the first-ever onymous blind modeling comparison, evaluated using both lab- and utility-scale fixed-tilt, monofacial, south-facing systems at sub-hourly time intervals. Seven commercially used PV software tools were compared: 3E SynaptiQ, PlantPredict, PVsyst, RatedPower, SAM, SolarFarmer, and Solargis Evaluate. Predictions were submitted directly by software representatives, providing unique insights into each software’s implementation and resulting prediction behavior. Notable features, including plane-of-array (POA) transposition model, module temperature model, shading model, and performance model were analyzed and compared. Four summary tables compile these features of the software, serving as a resource to help users understand the methodological differences and select the most suitable software for their applications. The software tools show deviations from mean error in annual yield up to 2.5 % in the lab-scale system, increasing to 6.0 % for the utility-scale system. These differences arise from a combination of user decisions and the inherent behavior of the software, indicating the need for continuous and rigorous validation of modeling methods using these software tools against complex, real-world systems.

14 SOLAR ENERGY↗
DOE OSTI2022

Optimal Coordination of Distributed Energy Resources Using Deep Deterministic Policy Gradient

Recent studies showed that reinforcement learning (RL) is a promising approach for coordination and control of distributed energy resources (DER) under uncertainties. Many existing RL approaches, including Q-learning and approximate dynamic programming, are based on lookup table methods, which become inefficient when the problem size is large and infeasible when continuous states and actions are involved. In addition, when modeling battery energy storage system (BESS), the loss of life is not reasonably considered into the decision-making process. This paper proposes an innovative deep RL method for DER coordination considering BESS degradation. The proposed deep RL is designed based on an adaptive actor-critic architecture and employs an off-policy deterministic policy gradient method for determining the dispatch operation that minimizes the operation cost and BESS life loss. Case studies were performed to validate the proposed method and demonstrate the effects of incorporating degradation models into control design.

Das, Avijit↗
DOE OSTI2020

Survey of Technologies to Meet PAG limits for Detection of Cesium-137 in Water

The goal of this report is to evaluate the process of adding a sorbent to the sampling process to preconcentrate Cs-137 and then analyze the sorbent to provide a rapid assessment of results to guide decisions on drinking water sources and the protection of the public. Multiple unit design variables were considered: sample configuration/geometry, sorbent efficiency, sample volume. Model simulations demonstrated through these unit design efficiencies that 10 L of sample volume processed through a sorbent provides nearly two orders of magnitude improvement in sample counting time to provide results to a decision maker than the current process. Over 60 publications and reports concerning Cs-137 and sorbents were evaluated. The key attributes were readiness of sorbent to be deployed in a mobile laboratory environment, and minimum sample preparation and conditioning. Examples of sorbents not considered further included nanomaterials, which have not been evaluated at a commercial scale and are limited in availability. The recommended sorbents for further consideration include: ferrocyanide salts, zeolite, and chemically modified granular activated carbon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗