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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

Ambient-Frequency-Data Based System-Level Inertia Estimation Using Physical Equation and its Practice on Hawaii Islands

Here, in this paper, a practical ambient-frequency-data-based inertia estimation method using a physical equation is proposed and validated by real measurement data from Hawaii island grids. With high renewable penetration, accurate inertia estimation is important and urgent. Ambient frequency oscillation always exists in power grids, so the proposed method has advantages of real-time inertia estimation and no need for additional disturbances. This paper first developed the physical equation for inertia estimation to offer a clear mechanism for easy implementation in practice. To apply the proposed method in actual grids, a practical method to extract the ambient frequency oscillation from frequency measurement is further proposed. The inertia estimation using the physical equation is validated by KIUC simulation data and HECO field data, in which error rates are around 2% and 8%, respectively. Practical inertia estimation is challenging due to the large amounts of resources contributing to the power grid's effective inertia, but the method provided in this paper can offer a novel way for practical inertia estimation, which can help renewable penetration to boost carbon-free grid.

14 SOLAR ENERGY↗
NASA NTRS2006

Spacecraft inertia estimation via constrained least squares

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

inertia estimation↗
DOE OSTI2024

Comparative Study of Data-Driven Area Inertia Estimation Approaches on WECC Power Systems

With the increasing integration of inverter-based resources into the power grid, there has been a notable reduction in system inertia, potentially compromising frequency stability. To assess the suitability of existing area inertia estimation techniques for real-world power systems, this paper presents a rigorous comparative analysis of system identification, measurement reconstruction, and electromechanical oscillation-based area inertia estimation methodologies, specifically applied to the large-scale and multi-area WECC 240-bus power system. Comprehensive results show that the system identification-based approach exhibits superior robustness and accuracy relative to its counterparts.

area inertia estimation↗
DOE OSTI2026

Inertia estimation for power grids: A review of methods, challenges, and future prospects

The electric power grid is undergoing a significant transformation, shifting from traditional synchronous generators to inverter-based resources (IBRs) such as solar photovoltaics, wind turbines, and energy storage systems. This evolution leads to a reduction in system inertia, a critical attribute for maintaining frequency stability in response to disturbances. Consequently, the ability to monitor and estimate system inertia has become increasingly essential. This paper provides a comprehensive review of existing inertia estimation methodologies, analyzing them from multiple perspectives, including the types of data utilized, underlying estimation principles, operational modes, and system-wide applicability. A comparative summary table is included to distill commonalities and key characteristics across various studies. In addition, the paper examines practical implementations of inertia estimation across several major power systems worldwide, including the U.S. interconnections, the Nordic power system, and the U.K. grid. Key challenges are identified, particularly in estimating contributions from virtual inertia sources and load-induced inertia in increasingly converter-dominated networks. To address these emerging challenges, the paper proposes an integrated framework for real-time inertia estimation and monitoring. This framework encompasses critical components such as data acquisition, inertia estimation from both synchronous and non-synchronous sources, load-induced effects, optimization techniques, forecasting, and virtual inertia scheduling. Collectively, these elements enable dynamic, system-wide monitoring and adaptive control of grid inertia.

Inertia estimation↗
DOE OSTI2024

Inertia Estimation and Trend Analysis of the United States Power Grid Interconnections

The transition from conventional to modern power systems is causing an increase in integration of inverter-based resources (IBRs). This generally leads to a decrease in total system inertia, which in-turn increases the system’s rate-of-change-of-frequency (RoCoF) during disturbances. This poses a threat to the frequency stability of the system and may falsely trigger protective devices. To monitor system status and plan for integrating renewable energy sources like photovoltaic, wind, and energy storage systems, a realistic study of inertia estimation and analysis in the United States (US) over the past decade is needed. This paper uses field-measured phasor measurement unit (PMU) data collected throughout the US from 2013 to 2023 via the Frequency Monitoring Network (FNET/GridEye) operated by the University of Tennessee, Knoxville (UTK) and Oak Ridge National Laboratory (ORNL). The collected PMU frequency data is utilized to estimate the system inertia of the three US interconnections: Eastern, Western, and Texas. Various RoCoF time windows are investigated for estimating the inertia of each interconnection by maximizing the correlation coefficient between the measured RoCoF and power mismatch. The resulting inertia trends over the past decade show approximately a 6% decline in inertia in the Eastern interconnection, a 15% decline in inertia in the Western interconnection, and a 16% increase in inertia in Texas. Key insights into how inertia is changing amidst the complex energy landscape are extracted using the fuel mix trend data. This provides valuable information for future energy strategies and planning.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

Regional Inertia Estimation Using Actual Event Measurements: Florida Case

As inverter-based resources’ integration in power grids increases, their uneven distribution across the electrical network leads to the formation of local regions that are weakly coupled to the larger interconnection. This signifies the necessity of regional frequency dynamics investigation and analyzing various inertia metrics. This paper presents a practical methodology for estimating regional rate-of-change of frequency (RoCoF) using actual event recordings, which is then used to evaluate regional inertia. Florida (FL) is selected as the region of interest due to its distinct regional frequency dynamics and the rising levels of solar generation. We identify and analyze confirmed events from 2017 to 2024 that occurred in FL. The results indicate that FL contributes about 14% to the total inertia of the US Eastern Interconnection, which approximately matches its share of generation capacity. Results also highlight seasonal fluctuations in energy generation, which play a significant role in influencing inertia and thus the RoCoF levels. This emphasizes the importance of estimating regional inertia to enhance grid operations for a future that focuses on distributed generation.

Dulal, Saurav [University of Tennessee, Knoxville ↗
DOE OSTI2024

Inertia Estimation Under High Penetration of Inverter-based Resources

Many types of renewable energy sources, especially solar and wind generation, are connected to the electric grid through power-electronic-based interfaces (inverters). These inverter-based resources (IBRs) are mechanically decoupled from the grid, which reduces system inertia and thus may compromise its stability and reliability. In this study, we examine the impact of high penetration of IBRs on the power grid’s inertia. To achieve this, we intentionally introduce disturbances into a simulation case study, such as a step load change, to observe and record the system’s frequency responses. This study offers a nuanced understanding of how the integration of IBRs affects grid stability, and it provides essential guidance for future grid management and resilience strategies.

Yadav, Ajay↗
NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗
DOE OSTI2025

Estimating Soil Thermal Inertia Profiles From the Passive Equilibration of a Temperature Probe

Knowledge of the distribution of soil thermal properties is important for understanding subsurface hydrological and biogeochemical processes. This study describes and evaluates quick thermal profiling (QTP), a new measurement technique aimed at providing rapid, depth-resolved measurements of soil thermal inertia at numerous locations across the landscape. A cylindrical probe with temperature sensors at multiple depths is quickly inserted into the ground, and soil thermal inertia is estimated from how quickly the probe temperature equilibrates with the soil. To this end, a finite volume heat transfer model is used to generate temperature equilibration time series across combinations of controlling factors, and a gridded search inversion approach is applied to infer soil thermal inertia. Field tests in the Arctic indicate that QTP measurements have a minimum uncertainty of 0.14 J m −2 K −1 s −1/2 and covary with dual-probe heat pulse thermal analyzer measurements (concordance correlation coefficient = 0.56) with a root-mean-square error of 0.40 J m −2 K −1 s −1/2 . Besides demonstrating the value of QTP for estimating thermal inertia, this study identifies various sources of measurement uncertainty, particularly probe-soil contact resistance and frictional heating. Further, analysis of soil samples indicates that thermal inertia can be used to estimate thermal conductivity and dry bulk density in the studied area, although such inferences are highly site-specific. Overall, the QTP method holds promise to generate thermal inertia data products and to complement other characterization approaches for advancing understanding of soil properties across far more locations than is currently possible.

Lamb, J. R. [Lawrence Berkeley National Laboratory↗
DOE OSTI2025

Open-Source Ambient-Signal-Based Inertia Monitoring Tool for Power systems [SWR-25-59]

This script, developed by NREL, implements an inertia estimation algorithm using a sliding window approach. The inertia (H) is estimated based on frequency deviations and active power deviations, utilizing the swing equation from power system dynamics. An example application is provided using the WECC 240-bus system.

Peng, Jiangkai [National Renewable Energy Laborato↗
DOE OSTI2026

Regional inertia dynamics of U.S. interconnections: An event-based measurement approach

Power grid inertia plays a vital role in frequency stability following large disturbances, yet its distribution across the U.S. grid is highly uneven. While interconnection-wide inertia benchmarks are useful, they can mask regional variability driven by resource mix, network coupling, and geographic separation. This paper extends event-driven inertia estimation to the regional scale using field measurements from the Frequency Monitoring Network (FNET/GridEye). Starting from balancing authority and independent system operator footprints, candidate regions are refined using a composite coherency score that combines frequency-trajectory shape similarity, timing spread, and lead/lag behavior to ensure dynamic consistency. A filtered sliding difference method (FSDM) is then used to construct regional frequency trajectories, detect disturbance onset, and compute robust regional rate-of-change of frequency (RoCoF). Regional, local, and interconnection inertia are estimated by combining RoCoF with event power imbalance, and additional indicators (regional-to-system inertia ratio and inertial-support arrival time) quantify regional-to-interconnection coupling and relative regional contributions. The method is demonstrated on eleven regions across the Eastern Interconnection (EI) and the Western Electricity Coordinating Council (WECC), with the Electric Reliability Council of Texas (ERCOT) used for validation. In ERCOT, estimates compared against energy management system (EMS) values achieve a mean absolute percentage error of 17.94%. WECC exhibits consistently shorter inertial-support arrival times (0.15–0.3 s) than EI (0.7–1.1 s), highlighting contrasting coupling and disturbance-propagation behavior. Overall, the results reveal pronounced spatial heterogeneity in inertia and coupling, underscoring the value of regional monitoring for both operational decision-making and long-term system planning.

Disturbance events↗
DOE OSTI2024

Probing Signal-Based Inertia and Frequency Response Estimation for Power Systems With High Levels of Inverter-Based Resources

Power system inertia is the inherent capability of a power system to resist changes in its frequency during disturbances. Real-time inertia estimation technology has become more important due to the low-inertia issues caused by the increasing integration levels of inverter-based resources (IBRs) from renewable energy; however, existing inertia estimation methods hardly consider multiple frequency response controls that act within the same time frame as conventional inertial response, thus making measured inertia values vary under different testing conditions. To resolve this issue, this paper proposes a novel real-time estimation method to simultaneously estimate a power system's inertia constant and frequency response droop constant using a well-designed probing signal. First, we formulate the inertia and frequency response model of a power system with IBRs. Second, through the integration and manipulation of the developed model, we propose a multivariate linear regression-based estimation method that is resilient to measurement noise. Third, we design a probing signal that can be injected by IBRs to incite the required transients for estimation. Finally, we validate the proposed estimation method through comprehensive power-hardware-in-the-loop experiments using inverter hardware and a realistic island power system model. The results demonstrate that the proposed method can accurately estimate the inertia and droop value of the power system with grid-following IBRs and grid-forming IBRs with virtual synchronous machine control.

frequency response↗
DOE OSTI2024

Probing Signal-Based Inertia and Frequency Response Estimation for Power Systems with High Penetration of Inverter-Based Resources: Preprint

Power system inertia is the inherent capability of a power system to resist changes in its frequency during disturbances. Real-time inertia estimation technology has become more important due to the low-inertia issues caused by the increasing integration levels of inverter-based resources (IBRs) from renewable energy; however, existing inertia estimation methods hardly consider multiple frequency response controls that act within the same time frame as conventional inertial response, thus making measured inertia values vary under different testing conditions. To resolve this issue, this paper proposes a novel real-time estimation method to simultaneously estimate a power system's inertia constant and frequency response droop constant using a well-designed probing signal. First, we formulate the inertia and frequency response model of a power system with IBRs. Second, through the integration and manipulation of the developed model, we propose a multivariate linear regression- based estimation method that is resilient to measurement noise. Third, we design a probing signal that can be injected by IBRs to incite the required transients for estimation. Finally, we validate the proposed estimation method through comprehensive power- hardware-in-the-loop experiments using inverter hardware and a realistic island power system model. The results demonstrate that the proposed method can accurately estimate the inertia and droop value of the power system with grid-following IBRs and grid-forming IBRs with virtual synchronous machine control.

frequency response↗
NASA NTRS1979

Moderate resolution thermal mapping of Mars - The channel terrain around the Chryse basin

Moderate resolution (about 30 km) thermal inertia estimates have been made for several regions in the northern hemisphere of Mars. Examples of these maps are presented for the region 0-45 deg N, 0-90 deg W. In the region adjoining the Chryse basin there are two major channels, Kasei Vallis and Ares Vallis, whose floor materials have higher thermal inertia than the surrounding upland regions. Moreover, there are numerous craters in the region which have high inertia-low albedo features on the crater floor.

Christensen, P. R.↗
NASA NTRS1992

Adaptive control of Space Station with control moment gyros

An adaptive approach to Space Station attitude control is investigated. The main components of the controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is a full-state feedback space station baseline control law. The control gain calculation is based on linear-quadratic regulator theory with eigenvalues placement in a vertical strip. The parameter identification scheme is a recursive extended Kalman filter that estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to estimate Space Station inertias accurately during nominal control moment gyro operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, Robert H.↗
NASA NTRS1991

Adaptive control of Space Station during nominal operations with CMGs

An adaptive control approach is investigated for the Space Station. The main components of the adaptive controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is the Space Station baseline control law. The control gain calculation is based on linear quadratic regulator theory with eigenvalue placement in a vertical strip. The parameter identification scheme is a real-time recursive extended Kalman filter which estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to compute accurate estimates of the Space Station inertias during nominal CMG (control moment gyro) operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, R. H.↗
NASA NTRS1936

Estimation of moments of inertia of airplanes from design data

A method of determining the moments of inertia of an airplane from design data pertaining to the weights and locations of the component parts is described. The computations required to ascertain the center-of-gravity position are incorporated with the calculations of moments of inertia. A complete set of data and calculations for a modern airplane is given to illustrate the procedure. From a comparison between calculated values and measured values it is believed that the moments of inertia can be estimated within 10 percent by the use of this method.

AIRPLANES - DESIGN↗