On parameter stability regions for several parameters using frequency response.
Parameter stability regions with frequency response, noting interpretation for several parameters
FREQUENCY RESPONSE↗
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Results for “frequency response”
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Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor
NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.
Tesch, W. A.↗
Quantified Fast Frequency Response of Inverter-Based Resources for Bulk-Power System Study
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.
Kim, Jinho↗
A multipurpose frequency-response analyzer
Closed loop frequency response analyzer with steepest descent computing procedure to obtain in-phase and quadrature signal components in linear or nonlinear systems
Kohr, R. H.↗
Comparative Assessment of Tactics to Improve Primary Frequency Response Without Curtailing Solar Output in High Photovoltaic Interconnection Grids
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.
14 SOLAR ENERGY↗
Eastern Frequency Response Study
This study was specifically designed to investigate the frequency response of the Eastern Interconnection that results from large loss-of-generation events of the type targeted by the North American Electric Reliability Corp. Standard BAL-003 Frequency Response and Frequency Bias Setting (NERC 2012a), under possible future system conditions with high levels of wind generation.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Frequency response of a gas ring laser with a variable-sign frequency bias in the case of frequency nonreciprocity comparable with the bias amplitude
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)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Frequency response in short thermocouple wires
Theoretical expressions are derived for the steady state frequency response of a thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for a nonuniform wire with unequal material properties and wire diameters across the junction. The amplitude ratio at low frequency omega approaches 0 agrees with the results of Scadron and Warshawsky (1952) for a steady state temperature distribution. Moreover, the frequency response for a nonuniform wire in the limit of infinite length l approaches infinity is shown to reduce to a simple expression that is analogous to the classic first order solution for a thermocouple wire with uniform properties. Theoretical expressions are also derived for the steady state frequency response of a supported thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for both a supported one material wire and a two material wire with unequal material properties across the junction. For the case of a one material supported wire, an exact solution is derived which compares favorably with an approximate expression that only matches temperatures at the support junction. Moreover, for the case of a two material supported wire, an analytical expression is derived that closely correlates numerical results. Experimental measurements are made for the steady state frequency response of a supported thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for both a supported one material wire (type K) and a two material wire (type T) with unequal material properties across the junction. The data for the amplitude ratio and phase angle are correlated to within 10 pct. with the theoretical predictions of Forney and Fralick (1991). This is accomplished by choosing a natural frequency omega sub n for the wire data to correlate the first order response at large gas temperature frequencies. It is found that a large bead size, however, will increase the amplitude ratio at low frequencies but decrease the natural frequency of the wire. The phase angle data are also distorted for imperfect junctions.
Forney, L. J.↗
Improving magnitude and phase comparison metrics for frequency response functions using cross-correlation and log-frequency shifting
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.
42 ENGINEERING↗
Application of several methods for determining transfer functions and frequency response of aircraft from flight data
In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author)
Eggleston, John M↗
Real-Time Estimation of Bare-Airframe Frequency Responses from Closed-Loop Data and Multisine Inputs
A method is presented for computing frequency responses of multiple-input multiple-output bare-airframe dynamics from flight test data containing feedback control and/or mixing of control effectors. Orthogonal phase-optimized multisines are used to simultaneously excite each input with unique harmonic frequencies, at which frequency responses are computed as ratios of output-to-input Fourier transform data. The confounding effects of feedback and mixing for frequency response estimation are resolved by interpolating the frequency responses among all the harmonic frequencies. The method can be run in batch for post-flight analysis, or in real time as the aircraft is flying. The effectiveness of the method was verified using closed-loop simulations of the subscale NASA T-2 generic transport airplane. The method was also demonstrated using flight test data from the X-56A MUTT aeroelastic airplane, which was flown with feedback control and mixing.
Jared A Grauer↗
Newton algorithm for fitting transfer functions to frequency response measurements
In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.
Spanos, J. T.↗
Model-free control for frequency response support in microgrids utilizing wind turbines
Islanded microgrids integrated with renewable energy resources bring additional challenges to the primary frequency control due to their power-electronic interfaced generations. Developing an efficient control strategy for inertia emulation and frequency response support of microgrids is becoming an important issue. Wind turbine dynamics, however, will degrade the emulated inertial and primary responses with most traditional control strategies. On the other hand, compensation methods often require the knowledge of system models at the design stage and state estimation for feedback once deployed online. To overcome these challenges, this paper explores a model-free control (MFC) strategy to emulate the desired inertia and support the frequency response of a diesel-wind microgrid system. Additionally, the proposed MFC strategy utilizes a model reference concept to obtain guaranteed inertial response and improve the frequency response of microgrids. This work considers different control strategies with different operating points. The proposed controller is implemented and verified using the modified 33-bus full nonlinear model of the three-phase diesel-wind system in Simulink. Simulation results demonstrate the improved frequency response by precisely emulating the desired inertia using the MFC strategy.
24 POWER TRANSMISSION AND DISTRIBUTION↗
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↗
Frequency Response of Pressure Sensitive Paints
An experimental method for measuring the frequency response of Pressure Sensitive Paints (PSP) is presented. These results lead to the development of a dynamic correction technique for PSP measurements which is of great importance to the advancement of PSP as a measurement technique. The ability to design such a dynamic corrector is most easily formed from the frequency response of the given system. An example of this correction technique is shown. In addition to the experimental data, an analytical model for the frequency response is developed from the one dimensional mass diffusion equation.
Winslow, Neal A.↗
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↗
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↗
Identification of Bare-Airframe Dynamics from Closed-Loop Data Using Multisine Inputs and Frequency Responses
Amethod is presented for computing multiple-input multiple-output frequency responses of bare-airframe dynamics for systems excited using orthogonal phase-optimized multisines and including correlated data arising from control mixing or feedback control. The estimation was posed as the solution to an underdetermined system of linear equations, for which additional information was supplied using interpolation of the frequency responses. A simulation model of the NASA T-2 aircraft having two inputs and two outputs was used to investigate the method in the open-loop configuration and under closed-loop control. The method was also applied to flight test data from the X-56A aeroelastic demonstrator having five inputs and ten outputs and flying under closed-loop control with additional control allocation mixing. Results demonstrated that the proposed method accurately estimates the bare airframe frequency responses in the presence of correlated data from control mixing and feedback control. Results also agreed with estimates obtained using different methods that are less sensitive to correlated inputs.
Grauer, Jared A.↗