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DOE OSTI2025

Consensus-Based Control and Optimization of Power System Inertia

The integration of distributed energy resources (DERs), such as solar, wind, and energy storage systems, into power grids through inverter-based resources reduces power system inertia, leading to faster frequency dynamics and potential grid instability. To address this challenge, this paper proposes a distributed, consensus-based approach for the real-time control and optimization of inertia sources (synchronous generators and/or DERs) during system disturbances, enhancing both system stability and economic performance. The distributed control and optimization approach assumes each inertia source exchanges information solely with its neighbor ones, making it easily scalable to large power grid networks. The impacts of the communication connectivity among the inertia sources as well as their generation capacity limits on the distributed approach are investigated. We also demonstrate the approach’s robustness in scenarios involving communication time delays and packet losses, validating its effectiveness through numerical simulations on a 4-bus test system and a two-area 8-bus test system.

Power system inertia↗

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↗

NASA NTRS2018

Change of Inertia Tensor Due to a Severed Radial Boom for Spinning Spacecraft

Many spinning spacecraft have long, flexible, radial booms to carry science instrumentation. These radial booms often have low mass but contribute significantly to the spacecraft moment of inertia due to their length. There are historical cases where radial booms have been severed or have failed to deploy. This paper presents models for the center of mass (CM) and inertia tensor that account for variable boom geometry and investigates how the CM and inertia tensor change when a radial boom is severed.The CM and inertia tensor models presented here will be included in the Attitude Ground System (AGS) for the Magnetospheric Multiscale (MMS) mission. This work prepares the AGS to provide uninterrupted support in the event of a radial boom anomaly. These models will improve the AGS computations for spin-axis precession prediction, Kalman filter propagation for the definitive attitude, and mass property generation needed for the onboard control system. As an additional application, a method is developed for approximating the location on the boom where the break occurred based on the new models and readily observable attitude parameters.

Inertia↗

NASA NTRSDate not supplied

Rise and Shine: Using Light as a Countermeasure to Sleep Inertia

INTRODUCTION: Sleep inertia describes the phenomenon of sleepiness and poor performance experienced after waking from sleep. This period of impaired alertness and performance is of significant concern to workers who nap on shift, or work on-call and are required to perform safety-critical tasks soon after waking (e.g., emergency services, healthcare, military). Light has been shown to acutely improve alertness during sleep deprivation and circadian misalignment. In this study, we assessed the efficacy of blue-enriched light to improve alertness and mood immediately after waking from SWS, i.e., during the sleep inertia period. METHODS: Twelve participants kept a sleep schedule of 8.5 h for 5 nights and 5 h for one night prior to the overnight laboratory visit (confirmed by actigraphy). Participants went to bed at their scheduled habitual bedtime in the laboratory and were monitored by standard polysomnography. After at least 5 min of SWS, participants were awoken and exposed to either red ambient light (control) or blue-enriched light (light) for 1 h. During this time, participants completed a subjective scale of alertness (Karolinska Sleepiness Scale, KSS) and visual analogue scales (VAS) of mood at 2 min, 17 min, 32 min, and 47 min after waking. Following this sleep inertia measurement period, all lights were turned off and participants were allowed to return to sleep. They were then awoken again from their subsequent SWS period and exposed to the opposite condition (control or light). A linear mixed-effects model with fixed effects of condition, time, and condition*time and a random effect of participant was used to determine the impact of light across the testing period. An average of baseline responses (pre-sleep) was included as a covariate. RESULTS: Compared to the control condition, participants exposed to blue-enriched light reported feeling more alert (KSS: F1,77=4.955, p=.029; VASalert: F1,77=8.226, p=.005), more cheerful (VAScheerful: F1,77=8.615, p=.004), less depressed (VASdepressed: F1,77=4.649, p=.034), and less lethargic (VASlethargic: F1,77=5.652, p=.020). DISCUSSION: Exposure to blue-enriched light immediately after waking from SWS may help to improve subjective alertness and mood. Future analyses will explore whether these findings extend to effects on cognitive performance. This countermeasure to sleep inertia may be suitable for implementation to alert crew members during mid-sleep emergencies but requires further testing in field settings.

alertness↗

DOE OSTI2025

Calculating Critical Inertia of a Power System

The increasing integration of renewable energy sources in modern power systems has led to a decline in system inertia, raising concerns about frequency stability following large disturbances. Determining critical inertia is essential to prevent excessive frequency decline and ensure grid stability. This paper evaluates four different methods for calculating critical inertia, using the Electric Reliability Council of Texas (ERCOT) system as a test case. The results highlight the importance of employing multiple methodologies to capture the full spectrum of inertia requirements.

Hakim sneha, Fariha [University of Tennessee, Knox↗

NASA NTRS1974

Experimental determination of the principal moments of inertia of the Helios prototype spacecraft

The moment of inertia of the Helios Spacecraft about its spin axis was determined by use of a roll-fixture using two sets of crossed flexure pivots as elastic constraints. The test procedure entailed measurement of a system oscillation period with each of a set of added moment-of-inertia increments. The tare effect of the fixture was determined by a like process and was subtracted from the gross value to yield the spacecraft roll moment of inertia to an estimated accuracy of 0.2%. Lateral moments of inertia (i.e., about each of three axes normal to the spin axis) were determined by a gravity pendulum method that makes use of the fact that any physical pendulum has a minimum period of oscillation determined by a particular distance from the axis of rotation to the system center of gravity.

Gayman, W. H.↗

NASA NTRS1977

Evaluation of algorithms for geological thermal-inertia mapping

The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).

Miller, S. H.↗

NASA NTRS1981

Geologic applications of thermal-inertia mapping from satellite

In the Powder River Basin, Wyo., narrow geologic units having thermal inertias which contrast with their surroundings can be discriminated in optimal images. A few subtle thermal inertia anomalies coincide with areas of helium leakage believed to be associated with deep oil and gas concentrations. The most important results involved delineation of tectonic framework elements some of which were not previously recognized. Thermal and thermal inertia images also permit mapping of geomorphic textural domains. A thermal lineament appears to reveal a basement discontinuity which involves the Homestake Mine in the Black Hill, a zone of Tertiary igneous activity and facies control in oil producing horizons. Applications of these data to the Cabeza Prieta, Ariz., area illustrate their potential for igneous rock type discrimination. Extension to Yellowstone National Park resulted in the detection of additional structural information but surface hydrothermal features could not be distinguished with any confidence. A thermal inertia mapping algorithm, a fast and accurate image registration technique, and an efficient topographic slope and elevation correction method were developed.

Offield, T. W.↗

NASA NTRS1987

Thermal inertia characteristics of the Martian crater Curie

Thermal inertia characteristics have been determined for the martian crater Curie from high resolution groundtracks of Viking Thermal Infrared Mapper (IRTM) data. Flow features near the southeastern edge of the ejecta indicate that at least part of the Curie ejecta was emplaced in a manner similar to the ejecta of rampart craters. Within the study region there appears to be a general southeastern trend towards lower thermal inertia values. This trend may be related to the proximity of the Arabia region, which is mainly to the south and east of Curie. Curie is in a region where the overall thermal inertias change over relatively short distances radial to Arabia. Therefore, the observed general decrease in thermal inertia may represent increasing regional dust accumulation in the direction of Arabia.

Horner, V. M.↗

NASA NTRS1994

Atmospheric effects on the mapping of Martian thermal inertia and thermally derived albedo

The most widely used thermal inertia data for Mars assumes the atmospheric contribution is constant and equal to 2 percent of the maximum solar insolation. Haberle and Jakosky investigated the effect of including a dusty CO2 atmosphere and sensible heat exchange with the surface on thermal inertia. We recently utilized Haberle and Jakosky's coupled surface-atmosphere model to investigate the effects of such an atmosphere on the thermally derived albedo. The thermally derived albedo is the albedo which, together with the thermal inertia, provides model surface temperatures which best match the observed temperatures. New maps are presented of thermal inertia and thermally derived albedo which incorporate dust opacities derived from IRTM data.

Hayashi, J. N.↗

NASA NTRS1995

Closed-form Static Analysis with Inertia Relief and Displacement-Dependent Loads Using a MSC/NASTRAN DMAP Alter

Solving for the displacements of free-free coupled systems acted upon by static loads is commonly performed throughout the aerospace industry. Many times, these problems are solved using static analysis with inertia relief. This solution technique allows for a free-free static analysis by balancing the applied loads with inertia loads generated by the applied loads. For some engineering applications, the displacements of the free-free coupled system induce additional static loads. Hence, the applied loads are equal to the original loads plus displacement-dependent loads. Solving for the final displacements of such systems is commonly performed using iterative solution techniques. Unfortunately, these techniques can be time-consuming and labor-intensive. Since the coupled system equations for free-free systems with displacement-dependent loads can be written in closed-form, it is advantageous to solve for the displacements in this manner. Implementing closed-form equations in static analysis with inertia relief is analogous to implementing transfer functions in dynamic analysis. Using a MSC/NASTRAN DMAP Alter, displacement-dependent loads have been included in static analysis with inertia relief. Such an Alter has been used successfully to solve efficiently a common aerospace problem typically solved using an iterative technique.

Barnett, Alan R.↗

NASA NTRS1994

Dynamical influences on the moment of inertia tensor from lateral viscosity variations inferred from seismic tomographic models

We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements delta I(sub xz) and delta I(sub yz) in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered (less than 300), delta I(sub xz) and delta I(sub yz) can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of delta I(sub xz) and delta I(sub yz). This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the delta I(sub xz) and delta I(sub yz) terms are directly responsible for exciting rotational movements.

Zhang, Shuxia↗

NASA NTRS2001

Thermal Inertia of Rocks and Rock Populations

The effective thermal inertia of rock populations on Mars and Earth is derived from a model of effective inertia versus rock diameter. Results allow a parameterization of the effective rock inertia versus rock abundance and bulk and fine component inertia. Additional information is contained in the original extended abstract.

Golombek, M. P.↗

NASA NTRS1960

Satellite Attitude Control Using a Combination of Inertia Wheels and a Bar Magnet

The use of inertia wheels to control the attitude of a satellite has currently aroused much interest. The stability of such a system has been studied in this investigation. A single-degree-of-freedom analysis indicates that a response with suitable dynamic characteristics and precise control can be achieved by commanding the angular velocity of the inertia wheel with an error signal that is the sum of the attitude error, the attitude rate, and the integral of the attitude error. A digital computer was used to study the three-degree-of-freedom response to step displacements, and the results indicate that the cross-coupling effects of inertia coupling and precession coupling had no effect on system stability. A study was also made of the use of a bar magnet to supplement the inertia wheels by providing a means of removing any momentum introduced into the system by disturbances such as aerodynamic torques. A study of a case with large aerodynamic torques, with a typical orbit, indicated that the magnet was a suitable device for supplying the essential trimming force. Single-degree-of-freedom bench tests generally verified the dynamic response predicted by the analytical study. the test table to within plus or minus 9 arc-seconds of the reference direction, even though the hardware components that were used in these tests were not specifically designed for the control system.

Adams, James J.↗

NASA NTRS1996

MSC/NASTRAN DMAP Alter Used for Closed-Form Static Analysis With Inertia Relief and Displacement-Dependent Loads

Solving for the displacements of free-free coupled systems acted upon by static loads is a common task in the aerospace industry. Often, these problems are solved by static analysis with inertia relief. This technique allows for a free-free static analysis by balancing the applied loads with the inertia loads generated by the applied loads. For some engineering applications, the displacements of the free-free coupled system induce additional static loads. Hence, the applied loads are equal to the original loads plus the displacement-dependent loads. A launch vehicle being acted upon by an aerodynamic loading can have such applied loads. The final displacements of such systems are commonly determined with iterative solution techniques. Unfortunately, these techniques can be time consuming and labor intensive. Because the coupled system equations for free-free systems with displacement-dependent loads can be written in closed form, it is advantageous to solve for the displacements in this manner. Implementing closed-form equations in static analysis with inertia relief is analogous to implementing transfer functions in dynamic analysis. An MSC/NASTRAN (MacNeal-Schwendler Corporation/NASA Structural Analysis) DMAP (Direct Matrix Abstraction Program) Alter was used to include displacement-dependent loads in static analysis with inertia relief. It efficiently solved a common aerospace problem that typically has been solved with an iterative technique.

Source record↗

NASA NTRS2018

Change of Inertia Tensor Due to a Severed Radial Boom for Spinning Spacecraft

Sedlak, Joseph E.↗

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↗

NASA NTRS1962

Use of an Inertia Sphere to Damp the Angular Motions of Spinning Space Vehicles

A theoretical study was made of a device which might be used to damp the angular motions of spin-stabilized space vehicles with constant moments of inertia. the device was assumed to consist of a rate gyro, a servo control, and a rotor mounted in a single gimbal. The investigation was conducted by considering the general equations of motion of the vehicle-damper system and noting that simplification would result if the damper had a spherical inertia distribution. Such a distribution was assumed thereafter, and a control command was defined so that the gimbal angle would be proportional to the angular velocity of the vehicle about the gimbal axis. The resulting equations were linearized, and the Routh-Hurwitz criterion was applied to determine the conditions for stability. The study included two numerical examples showing possible application of inertia-sphere rate dampers. The general conditions for stability were found to be feasible for practical applications. A simplified stability criterion covers a large class of practical problems.

SPHERE↗