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DOE OSTI2022

Precise ROCOF estimation algorithm for low inertia power grids

The precise estimation of Rate Of Change Of Frequencies (ROCOFs) in a generation trip event can be helpful on power system inertia estimation, fast system response, and accurate event capturing. However, the ROCOF estimations from the existing Synchronized Measurement Devices (SMDs) are usually simply calculated by the finite difference between two adjacent frequency measurement points. The ineluctable noises, disturbances, and spikes from real-world frequency measurements can bring large dynamics to the ROCOF estimation and thus can result in an inaccurate estimation of the initial ROCOF. This issue becomes more serious when the target power grid has low inertia, and a large amount of distributed energy sources are deployed. To address this issue, a precise ROCOF estimation algorithm is designed based on least square method with flexible window size. In addition, a median filter is also designed and applied on the frequency measurements before using the proposed algorithm. The window size and thresholds in the proposed algorithm are determined with historical event data analysis. The proposed algorithm is deployed in a low cost, flexible, and distribution level universal grid analyzer (UGA) platform. In conclusion, multiple experiments are conducted in both a laboratory and the Hawaiian Islands to verify the effectiveness of the proposed algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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 OSTI2020

Long range frequency chirping of Alfvén eigenmodes

In this work, a theoretical framework has been developed for an NBI scenario to model the hard non-linear evolution of global Alfvén eigenmodes (GAEs) where the adiabatic motion of phase-space structures (holes and clumps), associated with frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements, which allows an update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper action-angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the non-linear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of the finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long-range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Quantified Fast Frequency Response of Inverter-Based Resources for Bulk-Power System Study

Quantifying fast frequency response (FFR) of inverter-based resources (IBRs) is crucial for robust frequency regulation, managing resources, and improving system reliability in the power grids with high penetration levels of IBRs. This paper proposes a concept of frequency response scheme that its response is quantifiable and applicable to the generic IBR models. To achieve this, a stepwise-energy function is derived as a control module by considering operational constraints of IBRs. Then the module is implemented along with generic IBR models in electromagnetic transient (EMT) and electromechanical-based software. To quantify the FFR, the implemented module calculates available incremental active power for a specific time duration. This energy profile is being updated depending on IBR’s operating conditions and is provided into a power grid upon detecting a frequency event. Thus, due to this characteristic, this scheme can quantify the FFR and enable applicable IBRs to provide their available headroom within frequency arrest period. Thereby, this scheme can help estimate IBRs’ frequency response and is more effective in improving the initial frequency response than frequency-dependent control schemes: rate-of-change-of-frequency based and droop-based control schemes. The performance of the proposed scheme was tested under different IBR penetration levels using PSLF and PSCAD simulators.

Kim, Jinho↗

NASA NTRS1973

Filter for third order phase locked loops

Filters for third-order phase-locked loops are used in receivers to acquire and track carrier signals, particularly signals subject to high doppler-rate changes in frequency. A loop filter with an open-loop transfer function and set of loop constants, setting the damping factor equal to unity are provided.

Crow, R. B.↗

NASA NTRS1982

ISEE 1 observations of VLF line radiation in the earth's magnetosphere

VLF line radiation in the magnetosphere is analyzed in an attempt to clarify the role of radiation from electric power lines in magnetospheric wave-particle interactions. Observations were made by the ISEE 1 satellite from October 1977 through August 1979 between L = 2 and L = 8 and 50 to 110 deg W longitude, a region encompassing the magnetic field lines linking the Eights, Siple and Roberval stations and in which VLF chorus activity had been linked to power line radiation. Line radiation was detected on 5 of 90 orbits, in all cases at frequencies below 4 kHz. The one event with a high S/N ratio exhibited lines changing frequency at rates from 22 to 6 Hz/min over a 9-min period. The radiation was detected at a time when whistler mode echoing was quite pronounced on lower L shells, and thus may have been a scattered component of line radiation echoing between hemispheres. It is concluded that very little of the background VLF wave energy in the outer magnetosphere is contained in line radiation, although the catalytic role of line radiation in controlling wave-particle interactions remains to be assessed.

Bell, T. F.↗

DOE OSTI2022

A scalable planning framework of energy storage systems under frequency dynamics constraints

As the penetration of renewables increases in power systems, the declining system inertia can cause frequency stability issues. Battery energy storage systems (BESSs) respond fast and therefore can relieve the low inertia difficulty but need to be appropriately sized considering the associated cost. This paper presents a novel stochastic optimization model for economically planning BESS capacity while considering the spatial–temporal correlation of wind generation and generator outages under frequency stability constraints, which include the rate-of-change of frequency (RoCoF), frequency nadir (FN), and quasi-steady-state (QSS) frequency. A set of new FN constraints that can be easily linearized is developed. To account for renewable uncertainties, a realistic uncertainty modeling approach, Random Field, is adopted to generate wind generation scenarios by considering both spatial and temporal evolutions of wind speed profiles. The ESS sizing is formulated as a mixed-integer linear programming problem and solved by using a scalable decomposition-and-coordination approach, Surrogate Absolute Value Lagrangian Relaxation (SAVLR). To further improve the scalability and reduce computational burdens, a rolling-horizon-based update is developed and incorporated into SAVLR for providing a practical solution to the long-term planning of very large-scale power systems. Finally, a modified IEEE 118-bus system and the Polish system are used to validate the effectiveness and scalability of the model and solution methodology.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Frequency Disturbance Event Detection Based on Synchrophasors and Deep Learning

Power system frequency disturbances are caused by various generation and transmission events including generator trips, load disconnections, line trips, etc. Accurate detections of the events are crucial to bulk power system situation awareness and event investigation. This paper utilizes the recent advances of deep learning to build a convolutional neural network model to detect events in an accurate yet straightforward manner. Herein, the rate of change of frequency and the relative angle shift are converted to images as the inputs of the proposed model. Finally, this paper uses two convolutional neural networks and classifier fusion to achieve the detection result. Compared with the conventional event detection algorithm and the frequency only deep learning model, the proposed model improves the detection accuracy by over 48%. As a promising tool for bulk power system situation awareness, the proposed model requires a short decision time, which is suitable for practical scenarios.

42 ENGINEERING↗

DOE OSTI2025

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 ↗

DOE OSTI2021

“Frequency” and the PMU standard

The Phasor Measurement Unit (PMU) has revolutionized power system management by providing high-resolution, time-stamped, spatial, and temporal measure¬ments of the state of power systems. However, the standards defining the measured quantities have ambiguities that cause uncertainty, irreproducibility, and loss of interoperability during periods of change where the measurements should have the greatest value. This paper examines PMU frequency measurement to highlight the problems. It develops some suggestions for the scope and the next evolutionary improvements to the documentary standards. The aim is to improve the meaningfulness and trustworthiness of dynamic power system measurements.

Frequency, rate of change of frequency, definition↗

DOE OSTI2023

Frequency Resilience Enhancement for Power Systems with High Penetration of Grid-Forming Inverters

Abstract—Grid following inverter-based renewable generation has replaced conventional generation in recent years, resulting in lower system inertia. The frequency resilience in such a lower inertia system is critical for emergency mitigation. In this paper, we propose a resilience metric based on frequency recovery to quantitatively represent system resilience in terms of the rate of change of frequency. Application of grid-forming converters provides a means to improve system resilience by providing virtual inertia. An under-frequency load shedding strategy is applied to further support frequency recovery in cases with high penetration of grid-forming inverters. Case studies are designed and performed in a modified IEEE 9-bus test system using the PSCAD/EMTDC platform. Simulation results demonstrate the validity of the proposed resilience metric and the effectiveness of the strategy for reducing frequency excursion in inverter-based power systems. citation: J. Gui, H. Lei, T. R. McJunkin and B. K. Johnson, "Frequency Resilience Enhancement for Power Systems with High Penetration of Grid-Forming Inverters," 2023 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA, 2023, pp. 1-5, doi: 10.1109/ISGT51731.2023.10066357.

14 SOLAR ENERGY↗

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 OSTI2022

Practical Event Location Estimation Algorithm for Power Transmission System Based on Triangulation and Oscillation Intensity

Event location in power systems is quite essential information for system operators to enhance control-room situational awareness capability. Therefore, it is of great importance to develop an event location estimation algorithm for transmission systems with high accuracy. With the development of wide-area measurement system (WAMS) such as FNET/GridEye, and the synchrophasor measurement devices (SMDs) such as frequency disturbance recorders (FDRs), the synchronous measurement data including frequency, voltage amplitude and phase angle can be collected and used for event location estimation. First, the phase angle and rate of change of frequency (RoCoF) trajectories are respectively used for determining two sets of wave arrival time associated with each FDR. Then, a convolutional neural network (CNN) is utilized to determine the wave arrival order to select the more suitable set of wave arrival times for a given case and to perform corresponding modifications. Next, the oscillation intensity associated with each FDR is determined based on phase angle trajectories in the center of inertia (COI) coordinate system. Finally, the multiple criteria for event location estimation are represented. In conclusion, case studies and comparisons between the proposed and previous algorithms using actual and confirmed cases in U.S. power systems are performed to demonstrate the effectiveness and improvement of the proposed algorithm in practical applications.

frequency disturbance recorder (FDR)↗

DOE OSTI2020

Optimization-Based Fast-Frequency Estimation and Control of Low-Inertia Microgrids

The lack of inertial response from non-synchronous, inverter-based generation in microgrids makes the power system vulnerable to a large rate of change of frequency (ROCOF) and frequency excursions. Energy storage systems (ESSs) can be utilized to provide fast-frequency support to prevent such large excursions in the system. However, fast-frequency support is a power-intensive application that has a significant impact on the ESS lifetime. In this paper, a framework that allows the ESS operator to provide fast-frequency support as a service is proposed. The framework maintains the desired quality-of-service (limiting the ROCOF and frequency) while taking into account the ESS lifetime and physical limits. The framework utilizes moving horizon estimation (MHE) to estimate the frequency deviation and ROCOF from noisy phase-locked loop (PLL) measurements. These estimates are employed by a model predictive control (MPC) algorithm that computes control actions by solving a finite-horizon, online optimization problem. Additionally, this approach avoids oscillatory behavior induced by delays that are common when using low-pass filters as with traditional derivative-based (virtual inertia) controllers. MATLAB/Simulink simulations on a test system from Cordova, Alaska, show the effectiveness of the MHE-MPC approach to reduce frequency deviations and ROCOF of a low-inertia microgrid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Interactive Power to Frequency Dynamics Between Grid-Forming Inverters and Synchronous Generators in Power Electronics-Dominated Power Systems

With increased attention on grid-forming inverters as a power system stabilizing device during high shares of inverter-based resource operations, there is a present need for a transparent and methodical investigation of the inverted and direct power to frequency control capabilities and impacts of these devices on emerging power systems. Here, analysis of the frequency dynamics of the droop-controlled grid-forming inverter and the synchronous generator illuminates the inverted active power-frequency relationship and the frequency response order reduction, forming the basis for novel, nonlinear frequency control approaches. Device-level electromagnetic transient domain simulations corroborate the order-reduction findings, establish that a properly designed dc-side system has a negligible impact on power transfer and will not impede frequency regulation, and confirm the primary frequency response improvement with nonlinear control. Simulations of the 9- and 39-bus test systems validate the order reduction and associated decoupling of the nadir and rate of change of frequency in larger networks. Oscillatory mode analysis confirms the grid-forming benefit of increased damping; decreased damping is observed at shares above 80%, but not at 100%. Finally, simulations on a validated Maui power system model with a 96% of inverter-based resources model yield a trend toward a first-order response.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Inertia Emulation Control using Demand Response via 5G Communications

Building energy equipment is moving rapidly towards Internet of Things (IoT)-driven devices to provide consumer connectivity and device management. These device-level interfaces along with 5G communications will be leveraged to develop control architectures to engage a large number of monitoring and control devices and provide real-time and reliable energy services. Emerging 5G networks have high potential to provide the communication technology for demand response, with fast transfer speed, high reliability, and high number of connections. Guaranteed inertial response to limit frequency fluctuations is one of the main challenges in modern power systems due to the increased penetration of renewable generation, and it is largely affected by communication delays and packet losses. This paper analyzes inertial response and rate of change of frequency in a power system model with inverter-interfaced air conditioners. The control loop considers time delays and packet losses to show the need to switch to 5G networks in future smart grids.

Morovati, Samaneh↗

NASA NTRS1993

Evaluation of simulation motion fidelity criteria in the vertical and directional axes

An evaluation of existing motion fidelity criteria was conducted on the NASA Ames Vertical Motion Simulator. Experienced test pilots flew single-axis repositioning tasks in both the vertical and the directional axes. Using a first-order approximation of a hovering helicopter, tasks were flown with variations only in the filters that attenuate the commands to the simulator motion system. These filters had second-order high-pass characteristics, and the variations were made in the filter gain and natural frequency. The variations spanned motion response characteristics from nearly full math-model motion to fixed-base. Between configurations, pilots recalibrated their motion response perception by flying the task with full motion. Pilots subjectively rated the motion fidelity of subsequent configurations relative to this full motion case, which was considered the standard for comparison. The results suggested that the existing vertical-axis criterion was accurate for combinations of gain and natural frequency changes. However, if only the gain or the natural frequency was changed, the rated motion fidelity was better than the criterion predicted. In the vertical axis, the objective and subjective results indicated that a larger gain reduction was tolerated than the existing criterion allowed. The limited data collected in the yaw axis revealed that pilots had difficulty in distinguishing among the variations in the pure yaw motion cues.

Schroeder, Jeffery A.↗

DOE OSTI2022

Using a Grid-Forming Inverter to Stabilize a Low-Inertia Power System - Maui Hawaiian Island

As power systems around the world integrate greater amounts of wind and solar photovoltaic power, periods of very high instantaneous power shares of inverters, the primary interfacing technology for these generation sources, are complicating system stability and control. The contemporary, primary mode of inverter operation, grid-following, which explicitly assumes the presence of a local, stable voltage waveform, yields operational inadequacy at high instantaneous power shares potentially leading to instability due to the low-inertia conditions, as well as the correlated reduced voltage forming capacity on the respective system. Parallel connected grid-forming inverters, which directly regulate the local voltage, are a solution that is expected to bolster system stability and mitigate the shortcomings of the grid-following technology. In this paper, grid-following and two types of grid-forming inverter control, the traditional linear droop and the recently introduced nonlinear exponential droop (Droop-e), are simulated on a low-inertia, H = 0.48s, high inverter-based resource scenario, 97%, with a validated electromagentic transient domain model of the Hawaiian island of Maui power system. The benefit of a single grid-forming device over its grid-following counterpart is significant, both in terms frequency deviation and voltage stability. Further, the superiority of the Droop-e and the associated secondary power sharing control over both grid-following and linear droop grid-forming technologies is displayed, with improved nadir and rate of change of frequency over the linear droop control.

droop control↗