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All sources NASA NTRS DOE OSTI

DOE OSTI2025

Small-Signal Stability of Grid-Forming Inverters Using Current-Limiting and Frequency Stabilization

This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.

current limiting↗

DOE OSTI2025

Proactive Frequency Stability Scheme Based on Bayesian Filters and Spectral Clustering

Not Available

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Software Control Program For Transportable Microgrid State-of-charge Balancing And Frequency Stability Controls

A deterministic state-of-charge (SOC) balancing approach software control code is introduced as an integral secondary management to primary control layer of an islanded small microgrid or nanogrid system made up of multiple grid-forming inverter/battery/solar combination systems, where each set of batteries with each inverter are on independent DC buses (i.e. non-paralleled on the DC sides). A DERMS-level control approach, algorithm and automation controller program was developed to improve coordination and enable microgrid asset compliance and SOC balancing, enabling provision of a system-level power stability support architecture, load support, and asset scalability. The architecture is configured to treat each unit or micro/nano-grid as a node in a microgrid network, allowing for autonomous DERMS control regarding load and SOC balancing and power stability. As the network grows with the addition of units, greater coordination efforts may be required. The ideal small network microgrid ranges from 2-10 inverter/battery units before additional control parameters must be considered in the existing architecture. The control approach focuses on a deterministic state-of-charge analysis as the primary level control process followed by a secondary control loop using a forced frequency-watt droop strategy to conform off-the-shelf components into behaving under a leader-follower configuration. Adopting this control scheme has been shown to allow for a balanced, unit-coordinated microgrid network, enabling stable power flow. The deterministic state-of-charge approach is introduced as an integral primary control layer of an islanded small network microgrid. A standard strategy for SOC balancing is implementing a battery management system (BMS) to control SOC on the DC side. An alternative approach is to determine how to coordinate sending and receiving power on the AC side with multiple units. The latter approach assesses all the integrated units in the microgrid network. Once the individual units are identified, further system data is required to calculate each unit's total kWh, provided information about its capability to supply or consume kWh and availability. The secondary control layer in the multi-layered small network microgrid methodology uses the primary layer’s decision to initiate frequency setpoint changes, initializing the SOC balancing. The secondary control layer considers numerous system-dependent variables to enable a charging and discharging profile based on adjustable frequency setpoints. The combined architecture will result in stable, coordinated power flow enhancing an AC microgrid's functionalities.

Myers, KurtS [Idaho National Laboratory (INL), Ida↗

DOE OSTI2026

Analytical small-signal stability analysis of low-inertia power system frequency response considering secondary frequency regulation

Modern power systems are increasingly vulnerable to frequency instability as inverter-based resources (IBRs) replace synchronous machines and reduce system rotational inertia. Existing small-signal frequency stability assessment methods are either computationally intensive, relying on simulation-driven approaches, or lack analytical stability regions that explicitly account for secondary frequency response (SFR). This paper introduces new analytical frameworks that enable evaluation small-signal frequency stability while explicitly incorporating tunable IBR and SFR parameters. Using Kharitonov’s theorem with an overbounding approach, explicit small-signal stability criteria are derived. In addition, based on Białas’ criterion and Hurwitz matrix, analytical stability regions are established to reveal feasible design spaces for SFR and IBR parameters tuning. Extensive Matlab/Simulink-based simulations validate the accuracy and computational efficiency of the proposed methods, demonstrating that coordinated tuning of SFR and IBR parameters can substantially enhance system resilience. By bridging analytical rigor with practical tunability, this work provides an analytical framework for assessing small-signal frequency stability in low-inertia grids, supporting the real-time, scalable, and resilient operation of sustainable power systems.

14 SOLAR ENERGY↗

DOE OSTI2026

Small-Signal Analysis of Current-Limiting Grid-Forming Inverters

Grid-forming (GFM) inverters are equipped with a current limiter to protect the device during grid disturbances. Because the intervention of the current limiter can compromise the transient stability of the GFM inverter, various types of current limiter designs and additional frequency-stabilization control methods have been proposed in recent literature to aid in transient GFM inverter stability; however, the small-signal stability implications of adding these additional control blocks during, in particular, off-nominal conditions are not fully understood. To address this challenge, this paper presents a generic small-signal model of a GFM inverter that incorporates various types of current limiters and frequency stability-enhancing controls. With the proposed model, we analyze the root causes of inverter instability, which reveals two critical design trade-offs. First, due to current-limiter engagement caused by a disturbance, the GFM inverter dynamics are altered, which can lead to voltage oscillations. Second, additional frequency-stabilization controls can improve the small-signal stability of the GFM inverter, but at the cost of reduced power and voltage support to the grid. Comprehensive hardware experiments validate the theoretical concept and analysis. The findings in this work underscore the importance of incorporating both transient-response and small-signal dynamics requirements into the design procedure of GFM current limiters and frequency-stabilization controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1993

The Flight Performance of the Galileo Orbiter USO

Results are presented from an analysis of radio metric data received by the DSN stations from the Galileo spacecraft using an Ultrastable Oscillator (USO) as a signal source. These results allow the health and performance of the Galileo USO to be evaluated, and are used to calibrate this Radio Science instrument and the data acquired for Radio Science experiments such as the Red-shift Observation, Solar Conjunction, and Jovian occultations. Estimates for the USO-referenced spacecraft-transmitted frequency and frequency stability were made for 82 data acquisition passes conducted between launch (October 1989) and November 1991. Analyses of the spacecraft-transmitted frequencies show that the USO is behaving as expected. The USO was powered off and then back on in August 1991 with no adverse effect on its performance. The frequency stabilities measured by Allan deviation are consistent with expected values due to thermal wideband noise and the USO itself at the appropriate time intervals. The Galileo USO appears to be healthy and functioning normally in a reasonable manner.

D D Morabito↗

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↗

NASA NTRS1993

Stability Measurements of the Radio Science System at the 34-m High-Efficiency Antennas

From 1991 to 1993 the fractional frequency stability of the operational Radio Science System was measured at DSS's 15, 45, and 65. These stations are designed to have the most stable uplink and downlink equipment in the Deep Space Network (DSN). Some measurements were performed when the antenna was moving and the frequency was ramped. The stability, including contributions of all elements in the station except for the antenna and the hydrogen maser, was measured to be 0.3 to 1.3 x 10 -15 when the frequency was fixed, and 0.6 to 6.0 x 10 -15 when the frequency was ramped (sample interval, 1000 sec). Only one measurement out of fifteen exceeded specification. In all other cases, when previous measurements on the antenna and the hydrogen maser were added, a total system stability requirement of 5.0 x 10 -15 as met. In addition, ambient temperature was found to cause phase variation in the measurements at a rate of 5.5 deg of phase per deg C.

T T Pham↗

DOE OSTI2025

Toward 100% Renewable Power Grids: A Review

The transition to a 100% renewable power grid remains beset by significant technical challenges. This paper critically examines the obstacles arising from the variability and unpredictability of renewable energy sources (RES), which complicate the real-time balancing of power generation and load demand. In addition to traditional stability concerns (e.g., rotor angle, voltage, and frequency stability), the increasing penetration of inverter-based resources (IBRs) introduces novel challenges, including resonance stability issues and converter-driven dynamics. Moreover, the dynamic behavior and fault response of IBRs diverge markedly from those of conventional synchronous generators, rendering traditional protection schemes increasingly inadequate. This paper reviews state-of-the-art solutions in power balancing, grid flexibility, stability enhancement, and advanced protection strategies, discussing their implications for future grid design. The analysis provides a comprehensive assessment of recent technological advancements, thereby outlining critical research directions essential for achieving a resilient, 100% renewable power grid.

100% renewable power grid↗

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↗

DOE OSTI2025

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗

DOE OSTI2026

Grid and Wind Transient Ride Through Assessment of Type-5 Synchronous Wind Turbine

The integration of the inverter-based renewable energy resources is increasing and replacing conventional synchronous generators in the evolving bulk power system (BPS), impacting the system inertia along the way. Also, the limited over-current capability of power electronic converters continues to deteriorate the grid strength of the evolving power systems. Type-5 wind turbines have the potential to mitigate these problems because this configuration interfaces with the grid through a synchronous generator; hence, its operation and consequent grid impacts might mimic the conventional synchronous generator. The drivetrain of this type of turbines, however, is different from the more common Type-3 and Type-4 turbines. A hydraulic torque converter and gearbox with torque limiting feature are integral parts of a Type-5 wind turbine drivetrain, to isolate the wind speed variations at the wind turbine rotor from the grid connected generator side. This supports the synchronous operation of the generator. However, high fidelity models of Type-5 wind turbine drivetrain including these core components are not openly and widely available for grid integration and transient stability studies. Moreover, Type-5 turbines are not commonly deployed and hence its power generation and frequency stability characteristics are not widely publicized. This hinders appropriate assessment of Type-5 wind power plant's contribution to bulk grid resilience. This work provides transient stability assessment of a standalone Type-5 wind turbine. Normal operation and grid transient studies are performed to see the step load change and wind speed disturbance impacts on the Type-5 drivetrain and generation dispatch. Preliminary results show that Type-5 wind turbines can support load changes of between 0.6 p.u to 1.15 p.u. Beyond this point, the synchronization of the generator starts to deviate from its set point.

17 - WIND ENERGY↗

NASA NTRS1992

Radiation sensitivity of quartz crystal oscillators experiment for the Long Duration Exposure Facility (LDEF)

Factors determining the radiation sensitivity of quartz crystal oscillators were studied on NASA's LDEF. Quartz materials were examined in the transmission electron microscope (TEM) and classified as to their sensitivity to radiation damage by establishing the rate of damage caused by the electron beam in the microscope. Two types of materials, i.e., swept premium Q quartz and natural quartz were chosen because clear differences were observed in their response to the electron beam in the TEM studies. Quartz resonators were then fabricated from them, tested for frequency stability over a greater than 6 mo. period and flown on the LDEF satellite. After retrieval (more than 7 yrs in space) the stability of the resonators was again determined. All of the space exposed resonators fabricated with swept premium Q material exhibited a frequency shift above that of the control resonators: none of the resonators fabricated from the natural quartz materials exhibited such a shift. The significant differences observed between the two types of materials in both the ground-based TEM studies and the space radiation induced frequency changes suggest that there may be a correlation between the two observations.

J. S. Ahearn↗

DOE OSTI2026

Frequency Control and Dynamics (Part 1) [Slides]

This presentation provides an introductory overview of system dynamics and frequency control in electric power systems, with a focus on concepts relevant to small and interconnected grids such as those in Malawi. It explains foundational principles of AC system frequency, the relationship between generation-demand balance and frequency deviations, and the operational limits of generators and end-use equipment. The deck discusses frequency stability within broader system stability classifications and illustrates how inertia and turbine-governor dynamics shape system response to disturbances. It then outlines the tiered approach to frequency control - primary, secondary, and tertiary - detailing the roles, characteristics, timescales, and response mechanisms of each. Special emphasis is placed on hydro and thermal unit behavior, area control error (ACE), automatic generation control (AGC), and the operational implications of interconnecting small systems with larger grids. The material was developed to support Malawi's electricity sector and the establishment of the Southern Africa Battery Energy Storage Center of Excellence (SABESS CoE).

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Frequency Control and Dynamics (Part 2) [Slides]

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Stochastic Adaptive Droop Control in Frequency Regulation of Power Systems With Intermittent Generators

Modern power systems (MPSs), including microgrids (MGs), are increasingly incorporating multiple renewable energy sources (RESs) such as wind and solar power, as well as battery storage and controllable loads. While environmentally beneficial, these sources pose challenges for control and management due to their intermittent and stochastic nature, especially in maintaining frequency stability with multiple interconnected generators of varying capacities. Traditional droop control methods are effective in systems with generators that are dispatchable and have fixed generation capacities, but they fall short when applied to systems with RESs, where generation capacities are dynamic and affected by unpredictable environmental conditions. To address these challenges, this paper introduces a novel stochastic adaptive droop control (SADC) method for load frequency control (LFC). The proposed method adapts droop coefficients in real time, based on the measured stochastic data of power generation capacities, enabling more effective frequency regulation in systems with variable and intermittent power generation. Unlike traditional adaptive control methods, which assume constant or slowly-varying system parameters, this approach accounts for stochastic processes by modeling them as Markov chains, enabling robust performance under highly dynamic and unpredictable conditions. The key contributions of this work include the development of real-time droop coefficient adaptation algorithms, derivation of their stability and convergence properties, and the demonstration of the advantages of the method through simulations. Case studies highlight the improved performance of frequency regulation, particularly in addressing the impact of stochastic weather conditions and the benefits of reducing dependence on battery reserves in dealing with intermittency of RESs. Finally, this paper provides a comprehensive analysis of the theoretical foundations of the method, as well as practical implementation insights for future power systems with high penetration of RESs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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 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↗