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All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Real-time Optimal Dispatch of Behind-the-Meter DERs for Secondary Frequency Regulation

Active distribution networks (ADNs) can provide grid services such as peak load shaving, loss reduction, VoltNar control, congestion management, and frequency regulation. The fast response of inverter-based distributed energy resources (DERs) and battery storage systems enables them to provide ramping support and frequency control. This paper proposes a real-time optimization approach for behind-the-meter DERs to participate in the secondary frequency regulation. The proposed approach determines optimal set-points of output power of DERs to respond to requests from system operators (SOs) in realtime to maintain the frequency of the system at the nominal value. To satisfy the real-time requirement for the secondary frequency control, the nonlinear AC power flow model is linearized considering power losses in the system to achieve both high computational speed and acceptable accuracy. The optimization problem is rerun in a closed loop manner until the mismatch between the requested power by the system operators and actual delivered power at the substation reaches an acceptable tolerance. Furthermore, the proposed approach is validated using modified versions of the IEEE 33-bus and IEEE 69-bus distribution systems. Although the contribution of a single distribution system in the frequency regulation may not be significant, stacked and coordinated contributions from several distribution systems can provide frequency regulation and other grid services at scale.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Electric Vehicles Charging Time Constrained Deliverable Provision of Secondary Frequency Regulation

Aggregation of electric vehicles (EVs) is a promising technique for providing secondary frequency regulation (SFR) in highly renewable energy-penetrated power systems. Equipped with energy storage devices, EV aggregation can provide reliable SFR. However, the main challenge is to guarantee reliable intra-interval SFR capacities and inter-interval delivery following the automatic generation control (AGC) signal. Furthermore, aggregated EV SFR provision will be further complicated by the EV charging time anxiety because SFR provision might extend EV's charging time. This paper proposes a deliverable EV SFR provision with a charging-time-constrained control strategy. First, a charging-time-constrained EV aggregation is proposed to address the uncertainty of EV capacity based on the state-space model considering the charging-time restriction of EV owners. Second, a real-time economic dispatch and time domain simulation (RTED-TDS) cosimulation framework is proposed to verify financial results and the dynamic performance of the EV SFR provision. Last, the proposed charging time-constrained EV aggregation is validated on the IEEE 39-bus system. In conclusion, the results demonstrate that with charging time-constrained EV aggregation, the dynamic performance of the system can be improved with a marginal increase in total cost. More importantly, the charging time constraint can be respected in the proposed SFR provision of the EV aggregation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Cooperative Game Theory-based Secondary Frequency Regulation in Distribution Systems

Participation of distribution systems in frequency regulation has become an important factor for grid operation after the integration of distributed energy resources (DERs). While available reserves from a single distribution system may not be sufficient for frequency regulation, aggregated reserves from several distribution systems can provide frequency regulation at grid-scale. This paper proposes a cooperative game theory-based approach for secondary frequency regulation in distribution systems consisting of distributed energy resources (DERs). A two-stage strategy is proposed to effectively and precisely determine a change in active power set points of DERs following a command from system operators. In the first stage, the value or worth of each DER and their coalitions are determined using initial rates of change of frequency (ROCOF) for each DER/coalition. In the second stage, the Shapley value, one of the solution concepts of cooperative game theory, is used to determine changes in active power set points of DERs. The proposed method is implemented on several distribution systems including a modified IEEE 13-node system and modified 33-node distribution system.

Gautam, Mukesh↗
DOE OSTI2021

Secondary Frequency Regulation from Variable Generation through Uncertainty Decomposition: An Economic and Reliability Perspective

The rapid integration of variable generation (VG), such as photovoltaics (PV), necessitates an increase in the secondary frequency regulation (SFR) to handle the system intra-dispatch interval imbalance because of VG's variation. Although PV has the control capability to provide SFR, the main challenge is in guaranteeing the delivery of PV's energy and SFRs capacities in the automatic generation control (AGC) within each dispatch interval considering its uncertainty. This paper proposes a deliverable VG SFR provision model with endogenous VG's power uncertainty decomposition. First, the uncertainty of VG is decomposed using distributionally robust chance constraints through which the deliverable SFR provision is guaranteed. Next, the intra-interval frequency response of PV's SFR is validated with a user defined AGC model including the PV power plant. Finally, the economic benefits and the reliability improvements such as the frequency deviation reduction with PV providing SFRcan be integrated and evaluated. The proposed model is tested in a modified 18-bus system and in the Western Electricity Coordinating Council test system. Results demonstrate that with the deliverable SFR from PV, the system cost and the frequency reliability can be improved simultaneously. PV's SFR performance can be guaranteed with the proposed model.

14 SOLAR ENERGY↗
DOE OSTI2021

Real-Time Dispatch With Secondary Frequency Regulation: A Pathway to Consider Intra-Interval Fluctuations

Real-time dispatch balances the power demand with minimized operating costs. For the current dispatch model, the demand is assumed to be constant within a time interval, while the intra-interval power balance is left to frequency regulation. Based on practical experience and simulations, this behavior may lead to insufficient frequency regulation and uneconomic regulation costs considering the increase in intra-interval fluctuations caused by renewables. Here, a real-time dispatch method with secondary frequency regulation behaviors is proposed. Without changing the interval of the real-time dispatch command, the system regulation mileage and intra-interval generation adjustment are explicitly formulated in a mixed-integer optimization model. To reduce the computational burden, an efficient two-stage calculation method is proposed. With practical utility data, this article finds that the proposed method can effectively improve the system frequency performance with the subminute net load forecasting curve obtained by an off-the-shelf forecasting approach. Time-domain simulations in IEEE and practical utility systems validate the effectiveness of the proposed method in terms of the frequency performance and total operating costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1991

A high-frequency, secondary instability of crossflow vortices that leads to transition

Three-dimensional boundary-layer transition experiments are currently being conducted on a 45 deg swept wing in the Arizona State University Unsteady Wind Tunnel. Crossflow-dominated transition is produced via a model with contoured end liners to simulate infinite swept-wing flow. Fixed-wavelength, stationary and travelling crossflow vortices are observed. The frequencies of the most amplified travelling waves are in agreement with linear-stability theory; however travelling waves at frequencies an order of magnitude higher than predicted are also observed near transition. Near the transition location, the distorted boundary layer is due to the stationary crossflow vortex and is subject to a Rayleigh-type instability in the stream direction. As a result, a high-frequency secondary instability is detected in the transition region and spatial relations of the process are well documented by coupled use of flow visualization and hot-wire measurements.

Kohama, Yasuaki↗
DOE OSTI2023

Secondary Frequency Control for Reconfigurable Interconnecting Microgrids

Microgrids and microgrid technologies offer an operations and control framework for realizing the needed aggregation of a growing share of distributed energy resources. As the number of microgrids increases, so will the incentive to interconnect them, leading to a combinatorial growth of potential operating states. At the same time, their growing complexity nudges interconnected microgrids conceptually closer to balancing authorities in the bulk power system. This paper focuses on secondary frequency control and leverages the conceptual similarity between balancing authorities and interconnected microgrids to adopt an automatic generation control design with some adaptations. Frequency control and restoration is demonstrated via several use-cases with switching and reconfiguration events.

Schweitzer, Eran↗
NASA NTRSDate not supplied

High-Frequency Secondary Instabilities Downstream of a Forward-Facing Step

Localized high-frequency velocity fluctuations were measured downstream of a forward-facing step on a 30◦swept flat plate with an imposed pressure gradient. Phase-locked time-resolved particle image velocimetry measurements were performed to determine the source of the fluctuations, which ultimately lead to transition. The steps result in localized regions of reversed flow for a short region downstream of the step. These regions are highly localized due to the impact of the stationary crossflow vortices. The velocity fluctuations typically increase significantly in amplitude shortly downstream of reattachment in these localized regions, indicating that the fluctuations are related to reattachment of the shear layer. The phase-averaged measurements confirm that the unsteadiness in the shear layer results in the shedding of a plethora of vortices, some oriented in the streamwise direction, and others in the spanwise direction. These vortices are impacted by the local properties of the mean flow, such as streamwise vorticity and streamwise velocity gradient. The origin of the unsteadiness in the shear layer is not definitively shown, but evidence suggests it is due to a shear-layer instability. Ultimately, the unsteadiness of the shear layer, and the vortices that are shed as a result of this unsteadiness, are responsible for transition in this scenario.

Jenna L Eppink↗
DOE OSTI2025

A Novel Secondary Frequency Regulation with Optimal Priority Selection of AGC Contributions

Automatic generation control (AGC) is used to maintain acceptable frequencies during operation owing to fluctuations in load and variable resources. In conventional industry applications, the AGC signal is allocated to each generator according to the predispatched frequency regulation capacity or the order of economic efficiency. However, with the increasing integration of inverter-based resources (IBRs), the retirement of conventional synchronous generators (SGs) has posed new challenges to frequency control schemes because fewer of them are optional for AGC regulation. In this paper, we propose a novel model predictive control (MPC)-based frequency regulation model to reduce control cost and ensure stability, by considering different critical dynamic factors when optimally selecting the AGC units. The proposed control model – developed in a general form – comprehensively embeds characteristics such as generator ramping rates, reserve capacity, and operation cost. The model predictive control–based two-timescale AGC scheme enhances the capability of immunizing the power disturbance from types of resources by coordinating the control signals between faster IBRs and slower SGs. The case study’s proposed model is verified to be effective in synergistically enforcing different dynamic properties of AGC units into the frequency regulation scheme.

Jiang, Sufan [The University of North Carolina at ↗
NASA NTRS1983

Programmable, secondary frequency standard based infrared synthesizer using tunable lead-salt diode lasers

Quantum phase noise limited Lorentzian power spectral densities were achieved with tunable lead-salt diode lasers. Linewidths as narrow as 22 kHz were observed. A truly programmable infrared synthesizer was produced by frequency-offset-locking the tunable diode lasers to the combination of a stable CO2 (or CO) reference laser and a programmable microwave frequency synthesizer. Absolute frequency accuracy and reproducibility of about + or - 30 kHz (0.000001 kaysers) relative to the primary Cs frequency standard may now be obtained with this technique.

Freed, C.↗
NASA NTRS1990

Secondary frequencies in the wake of a circular cylinder with vortex shedding

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers was conducted using three different numerical algorithms for solving the time-dependent compressible Navier-Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well-predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behavior.

Abarbanel, Saul S.↗
NASA NTRS1991

Secondary frequencies in the wake of a circular cylinder with vortex shedding

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers was conducted using three different numerical algorithms for solving the time-dependent compressible Navier-Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well-predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behavior.

Abarbanel, Saul S.↗
DOE OSTI2020

A machine learning-based fast frequency response control for a VSC-HVDC system

An HVDC system can realize a very fast frequency response to the disturbed system under a contingency because its active power control is decoupled from the frequency deviation. However, most of existing HVDC frequency control strategies are coupled with system primary frequency control and secondary frequency control. Since the traditional system frequency control is dominated by the thermal generators, the advantage of the fast response of the HVDC system is not made fully used. The development of a frequency response estimation based on a machine learning algorithm provides another approach to improve the frequency response capability of the HVDC system. Different from other frequency deviation tracking strategies, a machine learning based HVDC frequency response control can directly increase the power flow of a HVDC system by estimation of the system generator or load lost. In this paper, a fast frequency response control using a HVDC system for a large power system disturbance based on the multivariate random forest regression (MRFR) algorithm is proposed. The simulation is carried out with an integrated power system model based on the North American interconnections. The simulation results indicate that the proposed MRFR based frequency response control can significantly improve the frequency low point during an event, while stabilizing the frequency in advance.

42 ENGINEERING↗
DOE OSTI2024

Towards the Flexibility of HVDC-Interconnected Systems: A Novel Emergency Freqeuncy Response Model

In this paper, we propose a novel multi-time scale emergency frequency response model by unlocking the flexibility of High Voltage Direct Current (HVDC) systems. Unlike assigning power ramping rates for FACTS to regulate frequency in traditional methods, this paper designs a step-change electromagnetic power frequency response (EPFR) scheme, by leveraging the temporal over/under DC voltage capability of HVDC. Wherein the Kullback-Leibler Divergence is adopted to convexify the modified swing equation after integrating the step-change power. Further, to avoid the complicated differential equations, we equivalently reformulate the duration limits of DC voltage deviation into the HVDC decreasing power ramping rates, which participate in the system primary frequency response. Finally, the new steady-state operation level of HVDC is involved with the secondary frequency response. As a result, an improved three-level algorithm is developed to solve the model, wherein the instant step-change, primary, and secondary frequency response are coordinated together. After applying the proposed frequency response scheme on the test system, the EPFR is validated to effectively provide the most instantaneous supports when faced with bulk power loss due to extreme contingencies, and the resilience is ensured within acceptable expenditures.

Jiang, Sufan↗
NASA NTRS2009

Precise Stabilization of the Optical Frequency of WGMRs

Crystalline whispering gallery mode resonators (CWGMRs) made of crystals with axial symmetry have ordinary and extraordinary families of optical modes. These modes have substantially different thermo-refractive constants. This results in a very sharp dependence of differential detuning of optical frequency on effective temperature. This frequency difference compared with clock gives an error signal for precise compensation of the random fluctuations of optical frequency. Certain crystals, like MgF2, have turnover points where the thermo-refractive effect is completely nullified. An advantage for applications using WGMRs for frequency stabilization is in the possibility of manufacturing resonators out of practically any optically transparent crystal. It is known that there are crystals with negative and zero thermal expansion at some specific temperatures. Doping changes properties of the crystals and it is possible to create an optically transparent crystal with zero thermal expansion at room temperature. With this innovation s stabilization technique, the resultant WGMR will have absolute frequency stability The expansion of the resonator s body can be completely compensated for by nonlinear elements. This results in compensation of linear thermal expansion (see figure). In three-mode, the MgF2 resonator, if tuned at the turnover thermal point, can compensate for all types of random thermal-related frequency drift. Simplified dual-mode method is also available. This creates miniature optical resonators with good short- and long-term stability for passive secondary frequency ethalon and an active resonator for active secondary frequency standard (a narrowband laser with long-term stability).

Savchenkov, Anatoliy↗