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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.
Power networks have to withstand a variety of disturbances that affect system frequency, and the problem is compounded with the increasing integration of intermittent renewable generation. Following a large-signal generation or load disturbance, system frequency is arrested leveraging primary frequency control provided by governor action in synchronous generators. In this work, we propose a framework for distributed energy resources (DERs) deployed in distribution networks to provide (supplemental) primary frequency response. Particularly, we demonstrate how power-frequency droop slopes for individual DERs can be designed so that the distribution feeder presents a guaranteed frequency-regulation characteristic at the feeder head. Furthermore, the droop slopes are engineered such that injections of individual DERs conform to a well-defined fairness objective that does not penalize them for their location on the distribution feeder. Time-domain simulations for an illustrative network composed of a combined transmission network and distribution network with frequency-responsive DERs are provided to validate the approach.
Recent large penetrations of solar photovoltaic (PV) generation and the inertial characteristics of inverter-based generation technologies have caught the attention of those in the electric power industry in the United States. This paper presents a systematic approach to developing test cases of high penetrations of PV for the Western Interconnection. First, to examine the accuracy of the base case model, the Western Electricity Coordinating Council (WECC) model is validated by using measurement data from synchronized phasor measurement units. Based on the 2022 Light Spring case, we developed four high PV penetration cases for the WECC system that are of interest to the industry: 5% PV+15 % wind, 25% PV+15% wind, 45% PV+15% wind, 65% PV+15% wind). Additionally, a method to project PV is proposed that is based on collected, realistic PV distribution information, including the current and future PV power plant locations and penetrations in the WECC system. Both the utility-scale PV plant and residential rooftop PV are included in this study.
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.
The ongoing changes in the generation resource mix, driven by the rapid adoption of inverter-based resources (IBR) as well as the early retirement of synchronous generators, are bringing new challenges to the planning and operation of bulk electric power systems. Consequently, there is an increasing need to understand, design, and quantify the reliability service provision from IBRs by performing integrated scheduling and dynamic simulations. However, test systems that have consistent scheduling and dynamic models rarely exist largely because of the decoupled nature of the two simulations on a synchronous generator-dominated system. This paper develops the dynamic model of a reduced Western Electricity Coordinating Council (WECC) system. In conjunction with the existing scheduling model, it is suitable for integrating scheduling and dynamic simulations. The reduced 240-bus WECC model reflects the generation resource mix of the Western Interconnection as of 2018. Moreover, the developed dynamic model is validated against field frequency events measured by FNET/GridEye and preserves the dominant inter-area oscillation mode in WECC.
Increasing penetration levels of solar photovoltaic (PV) and the reduced inertia of inverter-based generation technologies have caught the attention of the electric power industry and academia in the United States. This paper conducts a comprehensive frequency response study of the Western Interconnection under high penetration levels of PV, which are up to 80% at the interconnection level and 100% at the regional level. Based on the 2022 Light Spring case, PV has been projected by areas for four PV penetration levels based on collected realistic PV distribution information. The overall system frequency response has been analyzed under different scenarios. In particular, the 100% regional PV penetration case has been developed to reveal local frequency issues in the Western Interconnection. The potential of using existing resources to improve frequency response has also been studied. New insights in this paper address the implications of the rapid deployment of solar generation in the Western Interconnection.
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.
The electrical frequency of an interconnected power system must be maintained close its nominal level at all times. Excessive under- and overfrequency excursions can lead to load shedding, instability, machine damage, and even blackouts. There is a rising concern in the electric power industry in recent years about the declining amount of inertia and primary frequency response (PFR) in many interconnections. This decline may continue due to increasing penetrations of inverter-coupled generation and the planned retirements of conventional thermal plants. Inverter-coupled variable wind generation is capable of contributing to PFR and inertia with a response that is different from that of conventional generation. It is not yet entirely understood how such a response will affect the system at different wind power penetration levels. The modeling work presented in this paper evaluates the impact of wind generation's provision of these active power control strategies on a large, synchronous interconnection. All simulations were conducted on the U.S. Western Interconnection with different levels of instantaneous wind power penetrations (up to 80%). The ability of wind power plants to provide PFR - and a combination of synthetic inertial response and PFR - significantly improved the frequency response performance of the system.
Premixed flames are sensitive to flow disturbances, which can arise from acoustic or vortical fluctuations. For transverse instabilities, it is known that a dominant mechanism for flame response is “injector coupling,” whereby pressure oscillations associated with transverse waves excite axial flow disturbances. These axial flow disturbances then excite heat release oscillations. The objective of this paper is to consider another mechanism—the direct sensitivity of the unsteady heat release to transverse acoustic waves—and to compare its significance relative to the induced axial disturbances, in a linear framework. The rate at which the flame adds energy to the disturbance field is quantified using the Rayleigh criterion and evaluated over a range of control parameters, such as flame length and swirl number. The results show that radial modes induce heat release fluctuations that always add energy to the acoustic field, whereas heat release fluctuations induced by mixed radial-azimuthal modes can add or remove energy. These amplification rates are then compared to the flame response from induced axial fluctuations. For combustor-centered flames, these results show that the direct excitation mechanism has negligible amplification rates relative to the induced axial mechanism for radial modes. For transverse modes, the fact that the nozzle is located at a pressure node indicates that negligible induced axial velocity disturbances are excited; as such, the direct mechanism dominates. As a result, for flames that are not centered on pressure nodes, the direct mechanism for mixed modes dominates for certain nozzle locations and flame angles.
Individual microgrids can improve the reliability of power grids during extreme events, and networked microgrids can further improve efficiency through resource sharing and increase the resilience of critical end-use loads. However, networked microgrid operations are subject to large switching transients, which can cause dynamic instability and lead to system collapse. These transients are especially prevalent in microgrids with high penetrations of inverter-connected renewable energy resources, which do not provide the system inertia needed to mitigate the transients. Existing generator controls can be modified to invoke a drop in terminal voltage in response to a frequency deviation, thereby reducing load and improving frequency response. This paper investigates the use of a reinforcement-learning--based controller trained over several switching transient scenarios to modify generator controls during large frequency deviations. Compared to previously used proportional integral controllers, the proposed controller can improve primary frequency response while adapting to changes in system topologies and events.
The Multi-Area Frequency Response Integration Tool (MAFRIT) is the only software tool of its kind that integrates primary frequency response (turbine governor control) with secondary frequency response (automatic generation control). It simulates the power system dynamic response in full time spectrum with variable time steps from millisecond to minutes to hours and days. Capable of simulating both normal and event conditions, this tool can represent real power system operations and thus evaluate the primary and secondary reserves adequacy. This unique interaction of a turbine governor model and a novel automatic generation control model places special emphasis on electric power systems with high penetrations of renewable generation.
This paper presents an impedance-based noninvasive approach for the characterization of power system frequency response in real time in the absence of a transient event. It measures transfer function response from the injected active power to the frequency at the point of interconnection for the estimation of inertia and primary frequency response of the system. The so-called frequency response function also shows the effects of the speed of primary frequency control. The paper also derives the relationship between the frequency response function and the network impedance seen from the point of interconnection. This relationship highlights how impedance captures the frequency response behavior of a network. The proposed methodology is demonstrated on a modified IEEE 9-bus system with 25% penetration of wind and PV generation; a 5-MW battery energy storage system is used for the injection of active power perturbations for the measurement of the frequency response function.
Demand-side frequency control can complement traditional generator controls to maintain the stability of large electric systems in the face of rising uncertainty and variability associated with renewable energy resources. This paper presents a hierarchical frequency-based load control strategy that uses a supervisor to flexibly adjust control gains that a population of end-use loads respond to in a decentralized manner to help meet the NERC BAL-003-1 frequency response standard at both the area level and interconnection level. The load model is calibrated and used to model populations of frequency-responsive water heaters in a PowerWorld simulation of the U.S. Western Interconnection (WECC). The proposed design is implemented and demonstrated on physical water heaters in a laboratory setting. A significant fraction of the required frequency response in the WECC could be supplied by electric water heaters alone at penetration levels of less than 15%, while contributing to NERC requirements at the interconnection and area levels.
We report a theoretical study of the dependence of the beat frequency of counterpropagating waves on the rotation velocity in a gas ring laser with a periodic alternating frequency bias. Rectangular biases of two types are considered: with constant amplitude and with periodic amplitude modulation. We have found dynamic zones for locking-in the counterpropagating wave frequencies and determined deviations of the frequency response from the ideal one that arise when measuring frequency nonreciprocities, close in magnitude to the amplitude of an alternating frequency bias. It is shown that in the case of a rectangular bias with periodic amplitude modulation, nonlinear distortions of the frequency response can be reduced by an order of magnitude. (paper)
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.
Power grid primary frequency response will be significantly impaired by Photovoltaic (PV) penetration increase because of the decrease in inertia and governor response. PV inertia and governor emulation requires reserving PV output and leads to solar energy waste. This paper exploits current grid resources and explores energy storage for primary frequency response under high PV penetration at the interconnection level. Based on the actual models of the U.S. Eastern Interconnection grid and the Texas grid, effects of multiple factors associated with primary frequency response, including the governor ratio, governor deadband, droop rate, fast load response. are assessed under high PV penetration scenarios. In addition, performance of batteries and supercapacitors using different control strategies is studied in the two interconnections. The paper quantifies the potential of various resources to improve interconnection-level primary frequency response under high PV penetration without curtailing solar output.
The dependence of the beat frequency of counterpropagating waves on the rotation rate is studied theoretically and experimentally in a gas ring laser (GRL) with a Zeeman effect-based, variable-sign frequency bias. Use is made of magneto-optical biases of two types, namely, a rectangular (meander) bias and a combined bias consisting of fast and slow meanders. At high rotation rates, when the frequency nonreciprocity determined by the rotation rate is close in magnitude to the amplitude of the variable-sign frequency bias, the dynamic locking bands take maximum values and there arise the most extensive deviations of the frequency response from the ideal response. Comparison of experimental and theoretical results for the widths of dynamic bands that appear in this region of the measured rotation rates shows good agreement between theory and experiment. The results suggest that the frequency response of a GRL in this region can be described by one differential equation for the phase difference of counterpropagating waves. (laser gyroscopes)
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.