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Frequency Response of the full length of the Prysmian Cable with 100 ft the cable placed in the oven. One set of S-parameter data was collected at room temperature (22 °C) and the second at 300 °C after 5 days of baking.
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.
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.
Monitoring and analyzing the frequency response performance of power generation units is essential for maintaining reliable and secure power system operation. To address this need, an automation tool has been developed to provide a pipeline for processing historical power plant generation data, including large-scale SCADA archives. The tool performs end-to-end processing, including event detection, frequency response (FR) analysis in accordance with NERC standards, and estimation of speed governor droop characteristics. The tool is designed with a modular architecture, allowing individual components of the workflow to be extended, customized, or deployed independently. In addition, the tool provides an API that enables seamless integration with other production systems and operational analytics platforms.
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.
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.
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.
Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.
Data is proving to be the backbone of today's and, more importantly, tomorrow's grid. As the system changes and introduces fast-acting devices like power electronics, overall observability tends to decrease from the utility point-of-view. This can be mitigated by adding more high-fidelity sensors onto the grid, although this incurs a cost. These sensors are never ideal, and each have unique frequency responses that may influence the data produced. This may, in turn, impact the protection and control of the power grid. This paper presents a methodology of representing these point-on-wave sensors digitally by estimating digital-filter representations of them, thereby introducing means of improving the sensor models used in electromagnetic-transient (EMT) simulations. This may help with identifying potential high-frequency, sensor-induced distortions, and system resonance compensation. Three commercial-grade medium-voltage point-on-wave sensors are utilized in a lab environment to obtain experimental frequency responses with a frequency sweep, and it is shown that both Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filter representations may approximate these responses with varying degrees of accuracy, though each has their own strengths and weaknesses. It is found that, in general, FIR estimation better approximates these sensors than IIR estimation does.
Experimental evaluations of the surface height response of an interference microscope using a binary pseudo-random array test sample are compared with a theory based on a Fourier optics model. Measurements of key instrument characteristics, including the illumination, imaging, and obscuring apertures of three different Mirau objectives, support the theoretical calculations. Agreement between experimental and theoretical modeling confirms the predictability of the spatial frequency response for the purpose of specification and optimization of instrument configuration for specific metrology tasks. The results also provide confidence in methods of compensating for the decrease in instrument response with spatial frequency.
This three‐year research project was focused on two outstanding condensed matter problems (i) Real‐frequency response functions in Coulomb systems at finite temperature, and Fermi surface (FS) reconstruction in the Spin-Fermion (SF) model. The uniform electron gas (jellium) model, describing electrons interacting via long‐range Coulomb forces on positive neutralizing background, is fundamentally important both for understanding the physics of correlated electrons and for formulation of the time‐dependent density functional theory (TDDFT). The spin-fermion model has found a wide range of applications in the physics of cuprates and iron‐based superconductors to explain the “strange metal" behavior and to suggest a possible pairing mechanism for high‐temperature superconductivity. The project’s goals were development and application of the Diagrammatic Monte Carlo (DiagMC) techniques for solving the above problems.
The grid-forming inverter is regarded as the solution for integrating high levels of renewable resources into future power systems. Ensuring the stable operation of grids necessitates that grid-forming inverters offer fast frequency response. This report introduces an optimal control method that coordinates the embedded storage within the grid-forming control model with conventional synchronous generators. The optimized active power reference for the embedded storage is generated using receding horizon optimization control, aiming to keep the center of inertia frequency within acceptable limits. The effectiveness of the proposed control is verified through testing in the IEEE 39-bus system. In addition, with grid-forming capability, we will also investigate the application of using mobile embedded storages as black-start units to provide cranking power to energize non-blackstart generators in a black-start process.
In order to fulfill vital auxiliary grid services, such as load regulation, spin and non-spin reserve provision, and frequency support during emergencies, there is often a requirement for certain wind farms to operate in de-loaded modes. Leveraging the swift response capabilities of wind farms, this study demonstrates that reserving power in de-loaded modes can significantly enhance power grid stability and reliability during system contingencies. Controlling wind farms optimally for frequency support is intricate due to the nonlinearity of models and controllers and the complexity of wind farm interactions with power systems. Here, to address this challenge, this paper introduces a novel approach that integrates wind turbines into reinforcement learning-based solutions for frequency response. This innovative methodology utilizes the state-of-the-art reinforcement learning algorithm known as the surrogate-gradient-based evolutionary strategy. The proposed learning-based algorithm provides continuous control of wind farm output to rapidly stabilize system frequency and prevent unnecessary trips of under-frequency load shedding relays. To facilitate efficient training, parallel computing techniques are employed. The proposed methodology is evaluated on a modified IEEE-39 bus system, and simulation results reveal its efficacy in reliably supporting power system frequency and preventing the need for unnecessary load shedding.
An accelerometer mounting technique has large implications on the frequency range and accuracy of the measurement, with stiffness and the mass relative to the monitored structure as the primary concerns. The International Organization for Standardization (ISO) gives an extensive list in 5348:2021, detailing mounting methods, and provides recommendations for testing mounts that are not specifically defined. In the nuclear industry on the laboratory scale, there is a need for vibration measurements for predictive maintenance and process monitoring that are nondestructive and capable of working in high-temperature environments. Commercial adhesive products with easy application and removal were tested as nondestructive methods, while quick mounts to a commonly used aluminum frame were tested as nondestructive and have potential applicability in high-temperature environments. The sinusoidal excitation method was used, measuring frequencies from 50 Hz to 10 kHz in one-third octave band intervals, utilizing three accelerometers and comparing the results to those obtained with the stud-mounting method. Using the lowest ±3 dB threshold across each accelerometer, foam dots and poster strips were not successful, and foam tapes were accurate up to 2000 Hz, hose clamps and zip ties up to 800 Hz, and a custom 3D printed mount up to 1000 Hz. Knowing the limitations of each mounting technique allows for accurate measurements within the appropriate range.
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.
The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between the energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid generation-demand imbalances is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS systems provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 seconds from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS with a high-inertia motor may be able operate over a broader range of frequency variations whereas a low-inertia system may be limited by thermal constraints of the motor.
The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid imbalances in generation and demand is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS scenarios provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 s from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS based on a highinertia motor may be able to operate over a broader range of frequency variations, whereas a low-inertia system may be limited by thermal constraints of the motor.
The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid imbalances in generation and demand is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS scenarios provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 s from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS based on a high-inertia motor may be able to operate over a broader range of frequency variations, whereas a low-inertia system may be limited by thermal constraints of the motor.