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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2021

DEPRECATED AI-Batt-OS (Autonomous Identification of Battery Life Models - Open Source) [SWR 21-17]

DEPRECATED. This repository was archived by the owner on Jun 30, 2026. It is now read-only. Open source implementation of some of the methods utilized by AI-Batt, a battery lifetime modeling and analysis toolkit provided by the National Laboratory of the Rockies (NLR). This software demonstrates the use of bi-level optimization and symbolic regression techniques to semi-autonomously identify algebraic models predicting the capacity fade of lithium-ion batteries during calendar aging. Modeling the degradation of batteries is a complex task, due to the difficulty in separating the time-dependent and time-independent factors impacting cell level degradation, across multiple data series with different numbers of measurements and/or data quality. Bi-level optimization enables model parameters to be optimized to either the entire data set or to individual data series, allowing statistical disambiguation of global behaviors (data series independent) and local behaviors (data series dependent). Symbolic regression is used to automatically search for optimal low-dimesional models predicting the variation of locally optimized parameters versus time-independent experimental variables from millions of possible models, resulting in a more accurate and repeatable model identification process than is possible by a manual search. The provided tools also implement cross-validation and bootstrap resampling schemes, empowering statistical model comparison/selection and quantification of model uncertainties. An example script replicates the results from the manuscript "Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning", submitted to ECS. All code is written in MATLAB. Requires the Statistics and Machine Learning Toolbox. Contact Dr. Paul Gasper at Paul.Gasper@nlr.gov for any questions.

Gasper, Paul [National Renewable Energy Lab. (NREL↗
DOE OSTI2024

HybridSystemsSimulations.jl - Solving the Merchant Collocated Facilities with JuMP

The development of new clean-generation technologies also leads to new plant-level architectures that combine several generation and storage assets behind the point of connection. These co-located generation resources (Hybrid Systems) primarily operate as merchant assets that employ automated market bidding models and internal Energy Management Systems (EMS) to comply with the operator's signals. Formulating an optimal bidding model requires embedding the EMS control model into the bidding algorithm, resulting in a bi-level optimization problem. In this presentation, we first showcase using JuMP to formulate and solve this problem effectively for multiple merchant systems and the bidding outcomes considering different model formulations. Second, the bidding outcomes are later integrated into a PowerSimulations.jl (also built with JuMP) simulation to study the system-level effects of the various merchant bidding and the interactions between market-clearing models and the embedded EMS model. We will showcase simulations conducted in the RTS system considering different levels of merchant hybrid systems participation. The presentation provides the following specific insights on JuMP usage: 1) the Formulation of specialized bi-level problems with custom cuts to solve the merchant hybrid system bidding problem; 2) the integration of a modular model within a complex simulation workflow supported by JuMP in PowerSimulations.jl; 3) Accelerating the solution of power systems operations simulation that employ agent optimization problems using JuMP.

energy markets↗
DOE OSTI2022

Incorporate day-ahead robustness and real-time incentives for electricity market design

In this paper, we propose a two-stage electricity market framework to explore the participation of distributed energy resources (DERs) in a day-ahead (DA) market and a real-time (RT) market. The objective is to determine the optimal bidding strategies of the aggregated DERs in the DA market and generate online incentive signals for DER-owners to optimize the social-welfare taking into account network operational constraints. Distributionally robust optimization is used to explicitly incorporate data-based statistical information of renewable forecasts into the supply/demand decisions in the DA market. We evaluate the conservativeness of bidding strategies distinguished by different risk aversion settings. In the RT market, a bi-level time-varying optimization problem is proposed to design the online incentive signals to tradeoff the RT imbalance penalty for distribution system operators (DSOs) and the costs of individual DER-owners. This enables tracking their optimal dispatch to provide fast balancing services, in the presence of time-varying network states while satisfying the voltage regulation requirement. Simulation results on both DA wholesale market and RT balancing market demonstrate the necessity of this two-stage design, and its robustness to uncertainties, the performance of convergence, the tracking ability and the feasibility of the resulting network operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Multistage robust optimization for the day-ahead scheduling of hybrid thermal-hydro-wind-solar systems

The integration of large-scale uncertain and uncontrollable wind and solar power generation has brought new challenges to the operations of modern power systems. In a power system with abundant water resources, hydroelectric generation with high operational flexibility is a powerful tool to promote a higher penetration of wind and solar power generation. In this paper, we study the day-ahead scheduling of a thermal-hydro-wind-solar power system. The uncertainties of renewable energy generation, including uncertain natural water inflow and wind/solar power output, are taken into consideration. We explore how the operational flexibility of hydroelectric generation and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under a multistage robust optimization (MRO) framework. To address the computational issue, mixed decision rules are employed to reformulate the original MRO model with a multi-level structure into a bi-level one. Column-and-constraint generation (C &CG) algorithm is extended into the MRO case to solve the bi-level model. The proposed optimization approach is tested in three real-world cases. Furthermore, the computational results demonstrate the capability of hydroelectric generation to promote the accommodation of uncertain wind and solar power.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Bi-Level Adaptive Storage Expansion Strategy for Microgrids Using Deep Reinforcement Learning

Battery energy storage (BES) is a versatile resource for the secure and economic operation of microgrids (MGs). Prevailing stochastic optimization-based approaches for BES expansion planning for MGs are computationally complicated. This work proposes a data-driven bi-level multi-period BES expansion planning framework to determine the siting, sizing, and timing of BES installations. The proposed planning framework unifies deep reinforcement learning (DRL) and linear programming, thereby decoupling the determinations for the integer and continuous decision variables in two time scales, respectively. In the upper level, a rainbow DRL agent with quantile regression is trained to provide dynamic planning policies to accommodate stochastic renewable energy resources (RESs), load, and battery price changes efficiently. Further, the lower level computes the optimal operation of MGs with frequency constraints to hedge the islanding contingency. The two levels communicate with one another by exchanging storage configuration and operating expenses in order to accomplish the shared goal of minimizing investment and operation costs. Comparative case studies on an MG are carried out to demonstrate the superiority of the proposed DRL-based solution to the mixed-integer linear programming counterpart on efficiency, scalability, and adaptability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Distributed Load Shedding Application Architecture and Bi-Level Predictive Estimator Algorithm

Increasing penetrations of distributed renewables are decreasing the effectiveness of traditional decentralized under-frequency load shedding (UFLS) schemes. As more distribution circuits begin to back-feed the transmission system, operation of traditional UFLS may exacerbate frequency instability. This paper presents the conceptual framework for a data-rich environment to coordinate UFLS across multiple distribution providers based on the laminar coordination framework in order to ensure optimal adaptive setting of UFLS relays. Communication and control are enabled through a distributed implementation of the IEC 61968-1 Common Information Model message bus structure. In addition to the proposed architecture, a novel adaptive UFLS scheme informed by a bi-level state estimator to create optimal relay setpoints is introduced. Initial simulation results are presented for the IEEE 14-bus test system on scenarios leading to mis-operation of traditional UFLS.

Anderson, Alexander A.↗
DOE OSTI2021

AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]

Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.

Smith, Kandler [National Renewable Energy Lab. (NR↗
DOE OSTI2025

A sequential Attacker-Defender game for distribution systems resilience enhancement against extreme weather events

Improving distribution system resilience against frequent extreme weather events is important for reliable power system operations. Especially when dealing with events such as hurricanes that have short-term predictions, proactive pre-event preparedness plays a vital role in system resilience performance. In this paper, we propose a novel approach to construct pre-event resource allocation plans for system operators to cope with upcoming threats through a sequential attacker-defender game framework. The sequential attacker-defender game is designed to model the interaction between the extreme weather and the system operator. In each round of the game, the attacker and the defender sequentially update their current strategies by accounting for the opponent’s action set. The attacker model is formulated as a bi-level problem to identify the severe outage scenarios, and the defender model is formulated as a two-stage optimization problem to determine the allocation of restoration resources including mobile responsive resources and repair crews. Two scale-reduction strategies are proposed to ensure the scalability of the game scheme. Finally, case studies on the IEEE 33-bus and a 7149-node practical utility system validate the effectiveness of the proposed sequential game and the efficiency of the scale-reduction strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗
DOE OSTI2023

Bi-Level Linear Programming Model for Automatic Load Shedding: A Distributed Wide-Area Measurement System-based Solution

Load shedding is currently implemented as a two-step based approach. In the first step, manual load shedding is taken place, were system operators, using estimates, inform distribution utilities of predicted stressful conditions. Information provided include the potential use of energy reserves, as well as load shedding amount. In a second step, automatic load shedding is done. The latter is realized using protection relays. While considering frequency variation, pre-defined values of load to be shed and correspondent number of stages for such to be realized are transformed into relay settings. Under-frequency protection relays use only local measurements towards decision making, thus operate in a decentralized architecture. Decision making is done in milliseconds plus breaker time. While this approach has provided much system reliability, considering the new smart grid paradigm, where system dynamics are much faster due to increasing renewable resources penetration, in some operating conditions it will generate sub-optimal solutions, such as islanding. Phasor measurement units provide a source of information which can be useful for this problem. Centralized architecture-based solutions for automatic load shedding, as present in the state-of-the-art, require though total processing times which are not acceptable for real-life implementation. In this work, considering the above, a bi-level linear programming model is presented. The model is implemented considering a distributed architecture while leveraging phasor measurement units data. The upper-level model estimates the current system state. Results of this model are embedded in a lower-level model, which decision variables are the location and load value to be shed. Easy-to-implement model, built-on the classic weighted least squares solution, highlight potential aspects towards real-life applications.

Bretas, Arturo Suman↗
DOE OSTI2024

A hierarchical framework for aggregating grid-interactive buildings with thermal and battery energy storage

The behind-the-meter (BTM) thermal and battery energy storage can help improve energy efficiency, reduce energy costs, and enhance energy resilience, particularly in rural areas and for disadvantaged communities. Aggregating numerous BTM energy storage systems can act as a price influencer with a significant source of load shifting and peak demand reduction. An integrated and scalable control mechanism is required to effectively utilize energy storage systems and flexible building loads to maximize the economic benefits, considering various distribution system constraints. Here, this paper presents an innovative hierarchical coordination framework for energy storage and flexible load in buildings, considering various factors such as electricity prices, thermal comfort, and distribution system modeling and constraints. At the upper level, a distribution system operator optimizes the power flow to minimize its power procurement costs from the electricity wholesale market, while at the lower level, aggregators determine the optimal dispatch of battery and thermal energy storage systems in multiple buildings on behalf of end-users to minimize operating costs according to the power prices. These problems are solved using a game-theoretic approach through negotiations between the distribution system operator and aggregators as a bi-level decision model. Simulation case studies have been performed for a test distribution network with a number of building end-users using energy storage systems to quantify the performance of aggregators. The results demonstrate that the proposed strategy can reduce peak load for a reliable electricity distribution network while saving electricity bills for customers.

25 ENERGY STORAGE↗
DOE OSTI2023

Small-Signal Angle Stability-Oriented False Data Injection Cyber-Attacks on Power Systems

The small-signal angle stability (SSAS) of a power system is determined by the property of operation points. The widely applied false data injection (FDI) cyber-attack, however, is able to stealthily mislead the optimal power flow (OPF) and thus compromise operation points, leading to damages to the SSAS margin. Here, to provide insights for cyber defenders, this paper proposes and investigates a stealthy SSAS-oriented FDI cyber-attack focusing on two attacking purposes, i.e., the SSAS margin and operation cost, with higher priority on the former one. First, this paper establishes a novel bi-level model with an implicit SSAS constraint based on a structure preserving model to compromise operation points. Then, for the SSAS interarea mode in a typical two-area system, this paper formulates closed-form expressions of how the SSAS margin and operation cost behave with respect to stealthy injections. By comparison, for the SSAS local mode in general power systems, this paper proposes a moving target cyber-attack-based hierarchical solution algorithm. Simulation results on a two-area system, a Kundur 11 bus system, and a modified IEEE 14 bus system demonstrate the significant damaging effects of the proposed SSAS-oriented FDI cyber-attack and the conflict between the two attacking purposes.

Benders decomposition↗
DOE OSTI2024

A Model for Optimally Allocating Curbside Space Among Competing Uses

The emergence of various new forms of urban mobility services in recent years is leading to new pressures on curbside space. Municipalities, the entities typically responsible for managing the curbside, are in many instances handling these growing pressures by reallocating portions of the curbside away from traditional uses (such as metered and residential parking) in favor of uses such as ridehailing, scooter and bike-share corrals. As yet, however, such actions are being undertaken on an ad-hoc basis, due to the rapidly growing complexity of the curbside and the lack of standard analytical approaches. This lack of analytical capability is due to the traditional focus of transportation network modeling being focused predominantly on the interaction of supply and demand on links and nodes, with limited focus on link edges (the curbside). In this paper we address this research need by proposing a framework for modeling inter-modal competition for curbside space, inspired by the classical Bid-Rent Model of urban land use, intended to support curb managers to move towards maximizing the aspects of economic welfare that relate to curb access. In the bi-level model, choices made by the curbside manager impact travelers’ mode choices, and vice versa. We then present a simple numerical case study to demonstrate the properties of the proposed model, showing its tractability, flexibility, and intuitive sensitivity to systematic variation in inputs. The framework demonstrates the type of adaptive and evolving approach needed to maximize benefits from increasingly dynamic curb management strategies. The paper concludes with a brief discussion of future research needs to advance this line of inquiry.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Data Structure Alchemy

In an increasingly more data-driven world, the project set out to uncover the first principles of data-structure design, chart the immense design space they form, and build automation that can synthesize an optimal structure, or even a whole storage engine, for any given workload, hardware platform, and cost target. Data structures are at the center of every computational system and are directly responsible for its performance. Two core technical thrusts were defined: 1) Mapping design spaces for key data-centric abstractions (filters, hash functions, storage-engine layouts, neural-network topologies, blockchain protocols, image layouts, etc.). 2) Developing search & synthesis algorithms, initially analytical cost models, later neural-guided bi-level optimisers that navigate sextillions of candidate designs in seconds and materialise the best one as ready‐to-run code. This report distills the key insights, accomplishments, and impact.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗