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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.
Flexibility in inverter-based loads could be used to support the converter-dominated power grid by offering a rapid, autonomous, and adjustable power reserve during system transients to help maintain system stability. Based on technical potential, ancillary service (AS) value, and implementation costs, this study illustrates the cost-benefit analysis of grid-supportive loads (GSLs) for the supply of fast frequency response (FFR). The net benefit for each GSL is demonstrated using a case study and relevant data sources. The findings suggest that implementation costs for enabling GSL features are low compared to the value that grid operators get from the acquisition of responsive reserve services. The authors believe that, given the rising popularity of renewable energy sources, GSLs can be a useful tool for grid stability in low-inertia 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.
This paper provides a new method for matching dominant features of Frequency Response Functions (FRFs). In particular, this paper proposes a slicing and shifting method where the key features (in this case, resonant amplitudes) of a baseline FRF are compared with a similar FRF using cross-correlation and a Log-Frequency Shift (LFS). Here, the goal is to provide an alternative to classic point-to-point methods for FRF comparison and instead to match the dominant features of two FRFs in a way similar to visual inspection. This enables existing FRF comparison metrics to then be applied with greater fidelity. Additionally, this paper introduces the Phase Similarity Metric (PSM) for comparing phases of two FRFs and illustrates the improvement of using LFS for phase comparisons as well. This paper uses a cantilever beam experiment in multiple configurations to provide a benchmark case for FRF comparison improvements.
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.
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.
The rapid deployment of distributed energy resources (DERs) in distribution networks has made it challenging to balance the transmission system and stabilize frequency. DERs have the ability to provide frequency regulation services; however, existing frequency dynamic simulation tools - which were developed mainly for the transmission system - lack the capability to simulate distribution network dynamics with high penetrations of DERs. Although electromagnetic transient simulation tools can simulate distribution network dynamics, the computation efficiency limits their use for large-scale transmission-and-distribution (T&D) co-simulation. This paper presents an efficient open-source T&D dynamic co-simulation framework for DER frequency response based on the HELICS platform and off-the-shelf T&D simulators. The challenge of synchronizing the simulation time between the transmission network and the DERs in the distribution network is solved through the detailed modeling of DERs in frequency dynamic models while DER power flow models are also preserved in the distribution networks, thereby respecting local voltage constraints when dispatching DER power for frequency response. DER frequency response (primary and secondary) is simulated in case studies to validate the proposed framework. Last, the accuracy of the proposed co-simulation model is benchmarked, and a large T&D system simulation (2k transmission and 1M distribution nodes) is presented to demonstrate the efficiency and effectiveness of the overall framework.
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.
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.
Fast frequency response (FFR) is a critical tool for grid operators to manage contingency events in low-inertia systems. While large generators and loads are more commonly used, many smaller end use loads, in aggregate, can provide FFR across a large system. This work considers the technical potential of power electronics-based loads for autonomous FFR in low-inertia grids. We consider multiple factors that might influence the impact of FFR for various end use loads, with a focus on residential loads.
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.
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.
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.
As renewable penetration increases in the United States, maintaining stability and reliability of low-inertia power grid by providing sufficient frequency control capability becomes a challenge. Advanced pumped storage hydro technologies (APSH) will be expected to play an important role for future grid as not only an energy supplier, but also as an ancillary services provider. This paper studies the impact of using quaternary pumped storage hydropower (Q-PSH), as one of the newly proposed APSH technology, to provide primary frequency response. To quantify the impact of Q-PSH on frequency response of the U.S. Western Interconnection, a user-defined dynamic model of Q-PSH is developed on the GE Positive Sequence Load Flow (PSLF) platform and is implemented in a set of detailed U.S. Western Electricity Coordination Council (WECC) planning cases in which renewable penetration levels are 20%, 40%, 60% and 80%. Simulation results show that Q-PSH can help improve frequency nadir and settling frequency comparing to the conventional PSH.