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Anomaly Identification of Synchronized Voltage Waveform for Situational Awareness of Low Inertia Systems

Inverter-based resources (IBRs) such as photovoltaics (PVs), wind turbines, and battery energy storage systems (BESSs) are widely deployed in low-carbon power systems. However, these resources typically do not provide the inertia needed for grid stability, resulting in a low-inertia power system. IBRs and lack of inertia have been known to cause anomalies such as waveform distortions and wideband oscillations in power systems due to the limited inertia level, leading to increased generation trips and load shedding. Here, to achieve effective anomaly identification, this paper proposes a synchro-waveform-based algorithm utilizing real-time synchronized voltage waveform measurements from waveform measurement units (WMUs). In the proposed method, different physical characteristics, as well as statistical features, are extracted from synchronized voltage waveform measurements to filter anomalies. Then, the anomaly identification approach based on the random forest is developed and deployed into the FNET/GridEye system considering trade-offs among accuracy, computational burden, and deployment cost. Moreover, four WMUs are specially designed and deployed on Kauai Island to receive instantaneous synchronized voltage waveform measurements. To verify the performance of the proposed algorithm, different experiments are carried out with collected field test data. The result demonstrates that the performance of the proposed synchro-waveform-based anomaly categorization algorithm can accurately identify anomalies 95.35% of the time, which has comparable performance among benchmarking algorithms.

Situational awareness

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

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

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

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

Thermal inertias in the upper millimeters of the Martian surace derived using Phobus' shadow

The first thermal images of Phobos' shadow on the surface of Mars, in addition to simultaneous visible images, were obtained by the Phobus '88 Termoskan instrument. The best observed shadow occurence was on the flanks of Arsia Mons. For this occurence, we combined the observed decrease in visible illumination of the surface with the observed decrease in brightness temperature to calculate thermal inertias of the Martian surface. The most realistic of our three models of eclipse cooling improves upon our preliminary model by including nonisothermal initial conditions and downward atmospheric flux. Most of our derived inertias fall within the range 38 to 59 J/Sq m/S(exp 0.5)K (0.9 to 1.4 10(exp -3)Cal/Sq m/S(exp 0.5)/K), corresponding to dust-sized particles (for a homogeneous surface), consistent with previous theories of Tharsis as a currrent area of dust deposition. Viking infrared thermal mapper (IRTM) inertias are diurnally derived and are sensitive to centimeter depths, whereas the shadow-derived inertias sample the upper tenths of a millimeter of the surface. The shadow-derived inertias are lower than those derived from Viking IRTM measurements (84 to 147), however, uncertainties in both sets of derived inertias make conclusions about layering tenuous. Thus, near-surface millimeter versus centimeter layering may exist in this region, but if it does, it is likely not very significant. Both eclipse and diurnal inertias appear to increase near the eastern end of the shadow occurence. We also analyzed a shadow occurence near the crater Herschel that showed no observed cooling. This analysis was limited by cool morning temperatures and instrument sensitivity, but yielded a lower bound of 80 on eclipse inertias in that region. Based upon our results, we strongly recommend future spacecraft thermal observations of Phobus' shadow, and suggest that they will be most useful if they improve upon Termoskan's geographic and temporal coverage and its accuracy.

Betts, Bruce H.

Thermal inertias in the upper millimeters of the Martian surface derived using Phobos' shadow

The first thermal images of Phobos' shadow on the surface of Mars, in addition to simultaneous visible images, were obtained by the Phobos'88 Termoskan instrument. The best observed shadow occurrence was on the flanks of Arsia Mons. For this occurrence, we combined the observed decrease in visible illumination of the surface with the observed decrease in brightness temperature to calculate thermal inertias of the Martian surface. The most realistic of our three models of eclipse cooling improves upon our preliminary model by including nonisothermal initial conditions and downward atmospheric flux. Most of our derived inertias fall within the range 38 to 59 J/(sq m s(exp 1/2) K), (0.9 to 1.4 x 10(exp -3) cal/(sq cm s(exp 1/2) K)) corresponding to dust-sized particles (for a homogeneous surface), consistent with previous theories of Tharsis as a current area of dust deposition. Viking infrared thermal mapper (IRTM) inertias are diurnally derived and are sensitive to centimeter depths, whereas the shadow-derived inertias sample the upper tenths of a millimeter of the surface. The shadow-derived inertias are lower than those derived from Viking IRTM measurements (84 to 147), however, uncertainties in both sets of derived inertias make conclusions about layering tenuous. Thus, near-surface millimeter versus centimeter layering may exist in this region, but if it does, it is likely not very significant. Both eclipse and diurnal inertias appear to increase near the eastern end of the shadow occurrence. We also analyzed a shadow occurrence near the crater Herschel that showed no observed cooling. This analysis was limited by cool morning temperatures and instrument sensitivity, but yielded a lower bound of 80 on eclipse inertias in that region. Based upon our results, we strongly recommend future spacecraft thermal observations of Phobos' shadow, and suggest that they will be most useful if they improve upon Terinoskan's geographic and temporal coverage and its accuracy.

Betts, Bruce H.

Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix

In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.

Llama, Eduardo Garcia

Measurement-Based Approach for Inertia-Trend Analysis of the US Western Interconnection

Rising deployment of inverter-based resources (IBRs), characterized by a lack of rotating mass, is decreasing the total inertia of the system. This can lead to an increased Rate of Change of Frequency (RoCoF) during the disturbance and false activation of protective devices. There is a need to assess the inertia over the past decade amidst the evolving landscape of renewable energy sources to develop strategies for integrating energy storage, enhancing resilience measures, and ensuring the stable and reliable operation of the grid. Therefore, a realistic assessment of the inertia trend using a measurement-based approach that addresses the limitations of existing models is proposed. An inertia study of the Western Interconnection in the United States is performed utilizing the data from 2013 to 2022, obtained from FNET/ GridEye network. The three-second RoCoF time window is chosen for the study as it showed an optimum balance between a strong correlation with the power imbalance (ΔP) and minimum inclusion of primary response from governor. The obtained inertia trend result shows a small percentage declination of inertia over the decade. By examining the result alongside a generation mix graph, insights are gained into the dynamic interplay between shifting energy landscape and system inertia.

Dulal, Saurav

A Practical Approach to Inertia Assessment: Analyzing New York's Grid Response to Real Events

The non-uniform distribution of inverter-based resources (IBRs) such as solar and wind energy leads to the formation of weakly coupled regions within the broader interconnection. This highlights the urgency of investigating regional dynamics. This paper proposes a practical framework for estimating regional inertia using actual event measurements from the New York (NY) region. The regional frequency is determined using measurement data from frequency disturbance recorders (FDRs) deployed across NY. The rate-of-change of frequency (RoCoF) is estimated using a hybrid methodology that combines the benefits of both moving and non-moving window techniques. By utilizing the power mismatch value and the estimated RoCoF, various inertia metrics such as regional RoCoF, inertia arrival time, and inertia percentage relative to the interconnection inertia are calculated. The identified confirmed-events that took place between 2017–2022 in NY are used in the study. This assessment of inertia using real event data reveals the true behavior of the grid under stress. The results indicate that as the generation mix in NY evolves with the rise of IBRs, both the RoCoF levels and the regional inertia undergo significant changes.

Dulal, Saurav [University of Tennessee, Knoxville

Understanding Regional Inertia Dynamics in CAISO from Real Grid Disturbances

The shift from synchronous generators to inverter-based resources has caused power system inertia to be unevenly distributed across power grids. As a result, certain grid regions are more vulnerable to high rate-of-change of frequency (RoCoF) during disturbances. This paper presents a measurement-based framework for estimating grid inertia in CAISO (California Independent System Operator) region using real disturbance-driven frequency data from the Frequency Monitoring Network (FNET/GridEye). By analyzing confirmed disturbances from 2013 to 2024, we identify trends in regional inertia and frequency dynamics, highlighting their relationship with renewable generation and the evolving duck curve. Regional RoCoF values were up to six times higher than interconnection-wide values, coinciding with declining inertia. Recent recovery in inertia is attributed to the increased deployment of battery energy storage systems with synthetic inertia capabilities. These findings underscore the importance of regional inertia monitoring, strategic resource planning, and adaptive operational practices to ensure grid reliability amid growing renewable integration.

Dulal, Saurav [University of Tennessee, Knoxville

Investigation of Aerodynamic and Icing Characteristics of Water-Inertia-Separation Inlets for Turbojet Engines

The results of an investigation of several internal water-inertia-separation inlets consisting of a main duct and an alternate duct designed to prevent automatically the entrance of large quantities of water into a turbojet engine in icing conditions are presented. Total-pressure losses and icing characteristics for a direct-ram inlet and the inertia-separation inlets are compared at similar aerodynamic and simulated icing conditions. Complete ice protection for inlet guide vanes could not be achieved with the inertia-separation inlets investigated. Approximately 8 percent of the volume of water entering the nacelles remained. In the air passing into the compressor inlet. Heavy alternate-duct-elbow ice formations caused by secondary inertia separation resulted in rapid total-pressure losses and decreases in mass flow. The duration in an icing condition for an inertia-separation- inlet, without local surface heating, was increased approximately four times above that for a direct-ram inlet with a compressor-inlet screen. For normal nonicing operation, the inertia-separation- inlet total-pressure losses were comparable to a direct-ram installation. The pressure losses and the circumferential uniformity of the mass flow in all the inlets were relatively independent of angle of attack. Use of an inertia-separation inlet would in most cases require a larger diameter nacelle than a direct-ram inlet in order to obtain an alternate duct sufficiently large to pass the required engine air flow at duct Mach numbers below 1.0 at the minimum area.

VonGlahn, Uwe

Flapping inertia for selected rotor blades

Aerodynamics of helicopter rotor systems cannot be investigated without consideration for the dynamics of the rotor. One of the principal properties of the rotor which affects the rotor dynamics is the inertia of the rotor blade about its root attachment. Previous aerodynamic investigation have been performed on rotor blades with a variety of planforms to determine the performance differences due to blade planform. The blades tested for this investigation have been tested on the U.S. Army 2 meter rotor test system (2MRTS) in the NASA Langley 14 by 22 foot subsonic tunnel for hover performance. This investigation was intended to provide fundamental information on the flapping inertia of five rotor blades with differing planforms. The inertia of the bare cuff and the cuff with a blade extension were also measured for comparison with the inertia of the blades. Inertia was determined using a swing testing technique, using the period of oscillation to determine the effective flapping inertia. The effect of damping in the swing test was measured and described. A comparison of the flapping inertials for rectangular and tapered planform blades of approximately the same mass showed the tapered blades to have a lower inertia, as expected.

Berry, John D.

Determining the Products of Inertia for Small Scale UAVs

Moments of inertia and products of inertia often need to be determined for aircraft. As complex bodies, their mass properties need to be determined experimentally for best accuracy. While several moment of inertia experimental techniques have been developed, there are few to determine the products of inertia. Products of inertia can be easily determined mathematically if the angle between the aircraft x body axis and principal x axis is known. This method finds the principal inclination angle by mathematically correlating the measured moments of inertia about a range of axes of the aircraft. This correlation uses a least squares error minimization of a mathematical model that describes the ellipse of inertia in the aircraft's x-z axes plane. Results from a test conducted on a small scale UAV (Unmanned Aerial Vehicle) at NASA Armstrong Flight Research Center is also presented, which is an example of the intended application of this technique.

mass properties

Improving Slip Prediction on Mars Using Thermal Inertia Measurements

Rovers operating on Mars have been delayed, diverted, and trapped by loose granular materials. Vision-based mobility prediction approaches often fail because hazardous sand is difficult to distinguish from safe sand based on surface appearance alone. Unlike surface appearance, the thermal inertia of terrain is directly correlated to the same geophysical properties that control slip. This paper presents a quantitative analysis showing that considering thermal inertia improves rover slip prediction on Mars using in-situ data from the Curiosity rover. Thermal inertia is estimated for each slip measurement in sand using both on-board and orbital instruments. Slip models are learned using a mixture of experts approach where the experts are identified using thermal inertia. Two-expert models are compared to a single-expert, vision-only model to show that slip predictions are improved by separating high-slip, low thermal inertia sand from low-slip, high thermal inertia sand. These results support the hypothesis that the consideration of thermal inertia improves mobility estimates for rovers on Mars.

Nesnas, Issa A.

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

Formulas for additional mass corrections to the moments of inertia of airplanes

Formulas are presented for the calculation of the additional mass corrections to the moments of inertia of airplanes. These formulas are of particular value in converting the virtual moments of inertia of airplanes or models experimentally determined in air to the true moments of inertia. A correlation of additional moments of inertia calculated by these formulas with experimental additional moments of inertia obtained from vacuum chamber tests of 40 spin-tunnel models indicates that formulas give satisfactory estimations of the additional moments of inertia.

MOMENTS OF INERTIA