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DOE OSTI2020

Impedance-Based Prediction of SSR-Generated Harmonics in Doubly-Fed Induction Generators

Doubly-fed induction generators (DFIGs) are prone to subsynchronous resonance (SSR) with series-compensated transmission lines and experiencing SSR-generated harmonics of wide-ranging magnitudes. This paper presents a large-signal impedance-based approach for the prediction of the magnitude of SSR-generated harmonics in DFIGs. Note that the large-signal impedance of a network shows variation in its impedance response with the magnitude of perturbation at its terminals. It is discovered in this paper that the impedance of a series-compen- sated transmission line starts changing with the magnitude of SSR because of the metal-oxide varistor-based protection of series capacitors in the line. The changing line impedance halts the growth of the SSR beyond a certain point, where the DFIG forms a limit-cycle mode and emits harmonics at the SSR frequency. The discovered role of the protection of series capacitors in SSR not only enables the prediction of SSR-generated harmonics but also can be used for the timely detection of an SSR event to avoid system disruption and sudden loss of bulk generation. The large- signal impedance-based prediction of SSR-generated harmonics in DFIG-based wind and hydro generators is demonstrated using numerical simulations of a 2.5-MVA, 690-V DFIG supplying to a series-compensated transmission line.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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

Asynchronous Grid Connections Providing Fast-Frequency Response: System Integration Study

This paper presents an integration study for the recent power electronic-based fast-frequency response technology, "asynchronous grid connection" which operates as an aggregator for behind-the-meter resources and distributed generators. Both technical feasibility and techno-economic viability studies are presented. The fast-frequency response characteristics, validated against Power Hardware-in-the-Loop experiments, are integrated into an IEEE 9- bus system in DigSilent PowerFactory for system-level dynamic analysis. It demonstrates that droop-based control enhancements to local distributed generators allow their aggregation to provide grid-supporting functionalities and participate in the ancillary service markets. To this end, a long-term simulation embedding the system within the ancillary service market framework of PJM has been performed. The fast-frequency response regulation is subsequently used to calculate the potential revenue and project the results on a 15-year investment horizon. Finally, the techno-economic analysis provides recommendations for enhancements to access the full potential of distributed generators on a technical and regulatory level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

A Unified Analytical Method to Quantify Three Types of Fast Frequency Response from Inverter-Based Resources

With more inverter-based resources (IBRs), our power systems have lower frequency nadirs following N-1 contingencies, and undesired under-frequency load shedding (UFLS) can occur. To address this challenge, IBRs can be programmed to provide at least three types of fast frequency response (FFR), e.g., step response, proportional response (P/f droop response), and derivative response (synthetic inertia). However, these heterogeneous FFR challenge the study of power system frequency dynamics. Thus, this paper develops an analytical frequency nadir prediction method that allows for the consideration of all three potential forms of FFR provided by IBRs. The proposed method provides fast and accurate frequency nadir estimation after N-1 generation tripping contingencies. Our method is grounded on the closed-form solution for the frequency nadir, which is solved from the second-order system frequency response model considering the governor dynamics and three types of FFR. The simulation results in the IEEE 39-bus system with different types of FFR demonstrate that the proposed method provides an accurate and fast prediction of the frequency nadir under various disturbances.

fast frequency response↗

DOE OSTI2020

Adaptive PV Frequency Control Strategy Based on Real-time Inertia Estimation

The declining cost of solar Photovoltaics (PV) generation is driving its worldwide deployment. As conventional generation with large rotating masses is being replaced by renewable energy such as PV, the power system’s inertia will be affected. As a result, the system’s frequency may vary more dramatically in the case of a disturbance, and the frequency nadir may be low enough to trigger protection relays such as under-frequency load shedding. The existing frequency-watt function mandated in power inverters cannot provide grid frequency support in a loss-of-generation event, as PV plants usually do not have power reserves. Here, a novel adaptive PV frequency control strategy is proposed to reserve the minimum power required for grid frequency support. A machine learning model is trained to predict system frequency response under varying system conditions, and an adaptive allocation of PV headroom reserves is made based on the machine learning model as well as real-time system conditions including inertia. Case studies show the proposed control method meets the frequency nadir requirements using minimal power reserves compared to a fixed headroom control approach.

14 SOLAR ENERGY↗

DOE OSTI2022

Transmission-Distribution Dynamic Co-Simulation of Electric Vehicles Providing Grid Frequency Response

This paper investigates the impacts of electric vehicles (EVs) on power system frequency regulation based on an open-source transmission-and-distribution (T&D) dynamic co-simulation framework. The development of a EV dynamic model based on appropriate WECC dynamic model is introduced first, then the T&D dynamic co-simulation platform is described. The advantage of the overall platform is that DERs such as distributed photovoltaic (DPV) and EV are modeled explicitly in both transmission and distribution simulators for frequency dynamics and voltage, respectively. In the case studies, EVs frequency responses (i.e., primary and/or secondary) are simulated after the system is exposed to N-1 contingency such as a generation trip. Various EV frequency regulation participation strategies are investigated as well to study their impacts on system frequency response. The studies shows that EVs have potential capability to provide effective frequency regulation services.

electric vehicle↗

DOE OSTI2022

Transmission-Distribution Dynamic Co-Simulation of Electric Vehicles Providing Grid Frequency Response: Preprint

electric vehicle↗

DOE OSTI2021

A Two-Level Simulation-Assisted Sequential Distribution System Restoration Model With Frequency Dynamics Constraints

Not provided.

Engineering↗

DOE OSTI2024

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel-wind energy system is considered and modeled as a switching system between normal, faulted, and post-fault modes. Further, a safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33-bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

barrier function↗

DOE OSTI2022

Enhanced Inertial Support: Modeling Fast Frequency Response Controls for Energy Storage System Inverters

Reduction of power system inertia is a growing concern for grid operators given the transition under way from conventional fossil generators to inverter-based resources. One key concern is the rapid and severe dip in power system frequency following a large disturbance which could trigger remedial actions including operation of under frequency load shedding (UFLS) relays. A potential solution is to utilize battery energy storage systems (BESS) to provide fast frequency response(FFR) to mitigate the system frequency impact of low system inertia. In this work, we investigate different control parameters to achieve modeled FFR response from BESS in the simulated US Western Interconnection. First, a very low inertia model is developed from an existing positive sequence model of the Western Interconnection. Afterwards, we tune the BESS dynamic response parameters to eliminate any risks of reaching UFLS relay thresholds following the loss of large generators. Finally, we investigate the relative impact of having large BESS units in comparison of multiple smaller units in the same area. The results of the analyses indicate that 1 GW of transmission-connected BESS can help mitigate the frequency drop caused by large generators outages in the Western Interconnection, and significantly reduce the risk of under frequency load shedding.

power system dynamic performance, Low Inertia, Fas↗

DOE OSTI2024

Bayesian stability and force modeling for uncertain machining processes

Accurately simulating machining operations requires knowledge of the cutting force model and system frequency response. However, this data is collected using specialized instruments in an ex-situ manner. Bayesian statistical methods instead learn the system parameters using cutting test data, but to date, these approaches have only considered milling stability. This paper presents a physics-based Bayesian framework which incorporates both spindle power and milling stability. Initial probabilistic descriptions of the system parameters are propagated through a set of physics functions to form probabilistic predictions about the milling process. The system parameters are then updated using automatically selected cutting tests to reduce parameter uncertainty and identify more productive cutting conditions, where spindle power measurements are used to learn the cutting force model. The framework is demonstrated through both numerical and experimental case studies. Results show that the approach accurately identifies both the system natural frequency and cutting force model.

42 ENGINEERING↗

DOE OSTI2023

Impact of Transportation Electrification on the System's Dynamic Frequency Response

Transportation electrification is an integral component of the energy decarbonization transition. This paper investigates the impact of distributed energy resources (DERs), including distributed photovoltaics (DPV) and electric vehicles (EVs), in the primary frequency response of the power grid. Increasing DER adoption poses challenges to maintaining grid frequency stability. However, DERs' ability to provide fast frequency regulation services-primary frequency response (PFR) and secondary frequency response (SFR)-can be exploited to recover the frequency after an N-1 contingency event in the system. This paper also investigates the importance of a droop control strategy through dynamic models of DPV and EV to provide the primary frequency regulation services following the contingency event. A dynamic EV model, based on the PVD1 model Western Electricity Coordinating Council (WECC) introduced, has been used for the simulation. Further, DERs' primary frequency response is studied for five different cases of DER penetration levels after the system is exposed to the generator trip. Additionally, different frequency regulation capacities of EVs are analyzed. The studies show that an increment in DERs capacity providing effective PFR can improve the system frequency nadir and stabilize the frequency faster after the generation trip contingency.

distributed energy resources↗

DOE OSTI2023

Impact of Transportation Electrification on the System's Dynamic Frequency Response: Preprint

Transportation electrification is an integral component of the energy decarbonization transition. This paper investigates the impact of distributed energy resources (DERs), including distributed photovoltaics (DPV) and electric vehicles (EVs), in the primary frequency response of the power grid. Increasing DER adoption poses challenges to maintaining grid frequency stability. However, DERs' ability to provide fast frequency regulation services-primary frequency response (PFR) and secondary frequency response (SFR)-can be exploited to recover the frequency after an N-1 contingency event in the system. This paper also investigates the importance of a droop control strategy through dynamic models of DPV and EV to provide the primary frequency regulation services following the contingency event. A dynamic EV model, based on the PVDl model Western Electricity Coordinating Council (WECC) introduced, has been used for the simulation. Further, DERs' primary frequency response is studied for five different cases of DER penetration levels after the system is exposed to the generator trip. Additionally, different frequency regulation capacities of EVs are analyzed. The studies show that an increment in DERs capacity providing effective PFR can improve the system frequency nadir and stabilize the frequency faster after the generation trip contingency.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2025

Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.

frequency↗

DOE OSTI2020

Shape-constrained Input Estimation for Efficient Multi-shaker Vibration Testing

Multi-shaker vibration testing is gaining interest from structural dynamics test engineers as it can provide a much more accurate match to complicated field vibration responses than traditional single-axis shaker tests. However, the force capabilities of the small modal shakers typically used in multi-shaker vibration tests has limited the achievable response levels. To date, most multi-shaker vibration tests have been performed using a variety of standard, commercially-available control systems. While these control systems are adequate for a wide range of multiple-input/multiple-output tests, their control algorithms have not been tailored for the specific problem of multi-shaker vibration tests: efficiently coordinating the various shakers to work together to achieve a desired response. Here, a new input estimation algorithm is developed and demonstrated using simulations and actual test data. This algorithm, dubbed shape-constrained input estimation, is shown to effectively coordinate multiple shakers using a set of constraint vectors based on the deflection shapes of the test structure. This is accomplished by using the singular vector shapes of the system frequency response matrix, which allows the constraint vectors to automatically change as a function of frequency. Simulation and test results indicate a significant reduction in the input forces required to achieve a desired response. Finally, the results indicate that shape-constrained input estimation is an effective method to achieve higher response levels from limited shaker forces which will enable higher level multi-shaker vibration tests to be performed.

42 ENGINEERING↗

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

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↗

DOE OSTI2024

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↗