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NASA NTRS2012

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition.

Watson, W. R.↗

NASA NTRS2013

Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces

High-speed serial communication (i.e., Gigabit Ethernet) requires differential transmission and controlled impedances. Impedance control is essential throughout cabling, connector, and circuit board construction. An impedance discontinuity arises at the interface of a high-speed quadrax and twinax connectors and the attached printed circuit board (PCB). This discontinuity usually is lower impedance since the relative dielectric constant of the board is higher (i.e., polyimide approx. = 4) than the connector (Teflon approx. = 2.25). The discontinuity can be observed in transmit or receive eye diagrams, and can reduce the effective link margin of serial data networks. High-speed serial data network transmission improvements can be made at the connector-to-board interfaces as well as improving differential via hole impedances. The impedance discontinuity was improved by 10 percent by drilling a 20-mil (approx. = 0.5-mm) hole in between the pin of a differential connector spaced 55 mils (approx. = 1.4 mm) apart as it is attached to the PCB. The effective dielectric constant of the board can be lowered by drilling holes into the board material between the differential lines in a quadrax or twinax connector attachment points. The differential impedance is inversely proportional to the square root of the relative dielectric constant. This increases the differential impedance and thus reduces the above described impedance discontinuity. The differential via hole impedance can also be increased in the same manner. This technique can be extended to multiple smaller drilled holes as well as tapered holes (i.e., big in the middle followed by smaller ones diagonally).

Navidi, Sal↗

DOE OSTI2024

Impedance Scan of Inverter-Based Resources and Diesel Generator for Stability Analysis

Impedance-based methods are widely used for power system stability analysis with inverter-based resources (IBRs), e.g., assessing dynamic interactions between the power grid and an IBR, control interactions between multiple IBRs, and the sub-synchronous oscillation and damping phenomenon. Since it is difficult to get a numerical model 100% matching with the hardware IBR, using the hardware inverter directly to obtain its output impedance has become a prominent approach nowadays. Therefore, this article presents the impedance scan using hardware IBRs, and also a hardware diesel generator as it still stays with the grid before the grid completely goes to renewable. The devices under test (DuTs) for the impedance scan includes two 3-..phi.., 480 V, 60 Hz commercial grid-forming IBRs (one of 250 kVA and another of 125 kVA rating) in series with ..delta..-Y transformers, one 3-..phi.., 480 V, 60 Hz commercial grid-following IBR (of 125 kVA rating), and a 3-..phi.., 480 V, 60 Hz commercial diesel generator (of 187.5 kVA rating). Using voltage signals perturbed with sub-, inter-, and higher harmonic components, and measuring the current response, the positive-sequence impedances are computed via an offline-based post-analysis. Moreover, best-fit transfer functions are estimated that closely resemble the measured data points of the positive-sequence impedances. Based on the observations from various outcomes of the hardware experiments, this article also provides some fundamental insights on the equivalent positive-sequence impedance of a combination of multiple hardware components by comparing the estimated and the empirically computed impedances. A comparative insight on the damping capability of the DuTs using the positive-sequence impedances of the hardware is also discussed.

current measurement↗

DOE OSTI2024

Impedance Scan of Inverter-Based Resources and Diesel Generator for Stability Analysis: Preprint

Impedance-based methods are widely used for power system stability analysis with inverter-based resources (IBRs), e.g., assessing dynamic interactions between the power grid and an IBR, control interactions between multiple IBRs, and the sub-synchronous oscillation and damping phenomenon. Since it is difficult to get a numerical model 100% matching with the hardware IBR, using the hardware inverter directly to obtain its output impedance has become a prominent approach nowadays. Therefore, this article presents the impedance scan using hardware IBRs, and also a hardware diesel generator as it still stays with the grid before the grid completely goes to renewable. The devices under test (DuTs) for the impedance scan includes two 3-..phi.., 480 V, 60 Hz commercial grid-forming IBRs (one of 250 kVA and another of 125 kVA rating) in series with ..delta..-Y transformers, one 3-..phi.., 480 V, 60 Hz commercial grid-following IBR (of 125 kVA rating), and a 3-..phi.., 480 V, 60 Hz commercial diesel generator (of 187.5 kVA rating). Using voltage signals perturbed with sub-, inter-, and higher harmonic components, and measuring the current response, the positive-sequence impedances are computed via an offline- based post-analysis. Moreover, best-fit transfer functions are estimated that closely resemble the measured data points of the positive-sequence impedances. Based on the observations from various outcomes of the hardware experiments, this article also provides some fundamental insights on the equivalent positive- sequence impedance of a combination of multiple hardware components by comparing the estimated and the empirically computed impedances. A comparative insight on the damping capability of the DuTs using the positive-sequence impedances of the hardware is also discussed.

grid following inverter↗

NASA NTRS2004

Validation of an Impedance Education Method in Flow

This paper reports results of a research effort to validate a method for educing the normal incidence impedance of a locally reacting liner, located in a grazing incidence, nonprogressive acoustic wave environment with flow. The results presented in this paper test the ability of the method to reproduce the measured normal incidence impedance of a solid steel plate and two soft test liners in a uniform flow. The test liners are known to be locally react- ing and exhibit no measurable amplitude-dependent impedance nonlinearities or flow effects. Baseline impedance spectra for these liners were therefore established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method is shown to reproduce the measured normal incidence impedance spectrum for each of the test liners, thus validating its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers. Nomenclature

Watson, Willie R.↗

NASA NTRS2009

Micro-Horn Arrays for Ultrasonic Impedance Matching

Thin-layered structures containing arrays of micromachined horns, denoted solid micro-horn arrays (SMIHAs), have been conceived as improved means of matching acoustic impedances between ultrasonic transducers and the media with which the transducers are required to exchange acoustic energy. Typically, ultrasonic transducers (e.g., those used in medical imaging) are piezoelectric or similar devices, which produce small displacements at large stresses. However, larger displacements at smaller stresses are required in the target media (e.g., human tissues) with which acoustic energy is to be exchanged. Heretofore, efficiencies in transmission of acoustic energy between ultrasonic transducers and target media have been severely limited because substantial mismatches of acoustic impedances have remained, even when coupling material layers have been interposed between the transducers and the target media. In contrast, SMIHAs can, in principle, be designed to effect more nearly complete acoustic impedance matching, leading to power transmission efficiencies of 90 percent or even greater. The SMIHA concept is based on extension, into the higher-frequency/ lower-wavelength ultrasonic range, of the use of horns to match acoustic impedances in the audible and lower-frequency ultrasonic ranges. In matching acoustic impedance in transmission from a higher-impedance acoustic source (e.g., a piezoelectric transducer) and a lowerimpedance target medium (e.g., air or human tissue), a horn acts as a mechanical amplifier. The shape and size of the horn can be optimized for matching acoustic impedance in a specified frequency range. A typical SMIHA would consist of a base plate, a face plate, and an array of horns that would constitute pillars that connect the two plates (see figure). In use, the base plate would be connected to an ultrasonic transducer and the face plate would be placed in contact with the target medium. As at lower frequencies, the sizes and shapes of the pillars could be tailored for impedance matching in a specified ultrasonic frequency range. In a design that would be simplest to implement by micromachining, the horns would have constant cross-sectional areas as shown in the upper part of the figure. In this case, the dimensions of the horns could be chosen on the basis of a Mason equivalent-circuit model (a simplified model, well-known in the piezoelectric-transducer art, in which the electrical and mechanical dynamics, including electromechanical couplings, are expressed as electrical circuit elements that can include inductors, capacitors, and lumped-parameter complex impedances.) In a more complex, more nearly optimum design, the cross-sectional area of each horn would be either stepped or made to vary as a continuous function of through-the thickness position, as shown in the lower part of the figure.

Rao, Shanti↗

DOE OSTI2020

Real Time Effective Impedance Estimation for Power System State Estimation

Here, we introduce two tools-the Effective Impedance State Estimator (EISE), and the Real Time Effective Impedance Estimator (RTEIE). The EISE is novel in that it is an entirely data-driven state estimator, and does not require a network model. Thus, the EISE is well suited for applications in which an accurate network model is not available. Instead of using a network impedance model, the EISE uses an effective impedance network model that is learned online by the RTEIE. The RTEIE recursively estimates the effective impedance network model using phasor measurement unit (PMU) measurements. The mathematical reasoning for using an effective impedance model, rather than a full network impedance model, is given. The recursive estimation framework allows the RTEIE to take the entire history of phasor measurements into account to produce a model estimate, while still adjusting to changes in the network impedance due to external factors such as topology changes and temperature. The merits of the RTEIE and EISE are demonstrated by comparing the accuracy of the EISE with a conventional state estimator on a toy network.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2020

INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.

computational mathematics↗

DOE OSTI2025

Evaluating Variable-Impedance Magnetically-Insulated Transmission Lines as a Risk-Mitigation Measure for Next-Generation Pulsed Power

This project has produced the first detailed characterizations of power flow resulting from applying the “variable-impedance MITL” concept to real-life systems in Sandia’s pulsed power program (Z and next-generation pulsed power (NGPP)). We present simulation results and analyses for constant-impedance versions of both Z and NGPP and survey the operational viability of several variable-impedance re-designs in the parameter space of linear tapers. Circuit modeling (SCREAMER/Bertha) was used to pinpoint promising candidate designs, and EM-PIC (Empire) simulations were used to evaluate these candidates more rigorously. This approach was particularly successful in the Z regime which resulted in the identification of several viable variable-impedance MITL designs for each level. The approach was more challenged in the operating space NGPP occupies, producing data points that speak to a more restrictive design space due to anode plasma turn-on. In the end, we were able to converge on one viable variable-impedance design for the highest inductance line (level “F”) and one for the highest current line (level “A”). Altogether, the body of simulation evidence presented in this report suggest there does exist flexibility in operating space for magnetically-insulated transmission lines (MITLs) having variable geometric impedance to be a potential enabling technology for safely increasing current delivery (and potentially lowering stack voltage) in pulsed-power drivers by manipulating electron losses; however, operating points for a particular design must be carefully screened. Circuit and EM-PIC modeling provided consistent verdicts in safe operating regimes for operational viability, but additional physics such as anode plasma turn-on which is included in Empire but not in SCREAMER/Bertha was found to be a critical factor affecting power flow that lead to different assessments between the codes. It is not always the case that the occurrence of anode plasma caused a design to fail (some designs turned on anode plasma yet still delivered load currents meeting design targets); the details matter such as how early in the pulse anode surfaces break down (and how large a region). However, in every case that it did fail it was found that the feedback from anode plasma was the cause (i.e., turning off the anode plasma model in Empire restored agreement with the circuit model prediction). As circuit simulations represent an efficient and practical means of surveying design space compared to more computationally-expensive approaches such as EM-PIC, it could be prudent to invest in the research and development of models to include the effects of anode plasma such as ion emission in circuit codes. The variable-impedance MITL design is a new concept that enables controlled manipulation of the initial electron losses in the outer MITL and can be tested on Z today. We encourage follow-on work to explore further optimization (including alternative variable-impedance profiles, e.g., having constant dZ/dR), and to confirm the major findings presented in this report by fielding test hardware on actual Z shots.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1989

Impedance studies of Ni/Cd and Ni/H cells using the cell case as reference electrode

Many impedance studies were carried out on Ni electrodes and Ni/Cd and Ni/H batteries. In order for impedance to become a diagnostic tool, accurate and reproducible measurements must be made, and some way of separating the contributions of the individual electrodes must be found. Using the PAR and the Solartron impedance equipment, studies have found that consistent measurements can be made if the cells or electrodes are equilibrated at the voltage of interest. In the charged state, equilibration times required are short, on the order of a few hours or less, but the equilibration time required becomes progessively longer as the voltage is lowered. The cell case can be used as a reference electrode during impedance measurements. The voltage of the case with respect to the electrodes is unimportant provided that it does not change appreciably during the course of the measurement. Measurements were made with several uncycled Ni/Cd cells, one from a lot which was known to have faulty Cd electrodes and another from a lot which showed excellent cycle life and presumably had good Cd electrodes. The impedances of the Ni electrodes vs. the case were similar, while the impedance of the poor Cd electrodes vs. the case. A 50 AH Ni/H cell was also investigated. After subtraction of the ohmic resistances, the sums of the impedances of the individual electrodes were very close to the impedance of the total cell. This indicates that the method is valid for examining the characteristics of the individual electrodes in situ.

Reid, Margaret A.↗

NASA NTRS1993

Scattering by a groove in an impedance plane

An analysis of two-dimensional scattering from a narrow groove in an impedance plane is presented. The groove is represented by a impedance surface and the problem reduces to that of scattering from an impedance strip in an otherwise uniform impedance plane. On the basis of this model, appropriate integral equations are constructed using a form of the impedance plane Green's functions involving rapidly convergent integrals. The integral equations are solved by introducing a single basis representation of the equivalent current on the narrow impedance insert. Both transverse electric (TE) and transverse magnetic (TM) polarizations are treated. The resulting solution is validated by comparison with results from the standard boundary integral method (BIM) and a high frequency solution. It is found that the presented solution for narrow impedance inserts can be used in conjunction with the high frequency solution for the characterization of impedance inserts of any given width.

Bindiganavale, Sunil↗

NASA NTRS2001

Comparison of Two Acoustic Waveguide Methods for Determining Liner Impedance

Acoustic measurements taken in a flow impedance tube are used to assess the relative accuracy of two waveguide methods for impedance eduction in the presence of grazing flow. The aeroacoustic environment is assumed to contain forward and backward-traveling acoustic waves, consisting of multiple modes, and uniform mean flow. Both methods require a measurement of the complex acoustic pressure profile over the length of the test liner. The Single Mode Method assumes that the sound pressure level and phase decay-rates of a single progressive mode can be extracted from this measured complex acoustic pressure profile. No a priori assumptions are made in the Finite Element. Method regarding the modal or reflection content in the measured acoustic pressure profile. The integrity of each method is initially demonstrated by how well their no-flow impedances match those acquired in a normal incidence impedance tube. These tests were conducted using ceramic tubular and conventional perforate liners. Ceramic tubular liners were included because of their impedance insensitivity to mean flow effects. Conversely, the conventional perforate liner was included because its impedance is known to be sensitive to mean flow velocity effects. Excellent comparisons between impedance values educed with the two waveguide methods in the absence of mean flow and the corresponding values educed with the normal incident impedance tube were observed. The two methods are then compared for mean flow Mach numbers up to 0.5, and are shown to give consistent results for both types of test liners. The quality of the results indicates that the Single Mode Method should be used when the measured acoustic pressure profile is clearly dominated by a single progressive mode, and the Finite Element Method should be used for all other cases.

Jones, Michael G.↗

NASA NTRS2005

A Quasi-3-D Theory for Impedance Eduction in Uniform Grazing Flow

A 2-D impedance eduction methodology is extended to quasi-3-D sound fields in uniform or shearing mean flow. We introduce a nonlocal, nonreflecting boundary condition to terminate the duct and then educe the impedance by minimizing an objective function. The introduction of a parallel, sparse, equation solver significantly reduces the wall clock time for educing the impedance when compared to that of the sequential band solver used in the 2-D methodology. The accuracy, efficiency, and robustness of the methodology is demonstrated using two examples. In the first example, we show that the method reproduces the known impedance of a ceramic tubular test liner. In the second example, we illustrate that the approach educes the impedance of a four-segment liner where the first, second, and fourth segments consist of a perforated face sheet bonded to honeycomb, and the third segment is a cut from the ceramic tubular test liner. The ability of the method to educe the impedances of multisegmented liners has the potential to significantly reduce the amount of time and cost required to determine the impedance of several uniform liners by allowing them to be placed in series in the test section and to educe the impedance of each segment using a single numerical experiment. Finally, we probe the objective function in great detail and show that it contains a single minimum. Thus, our objective function is ideal for use with local, inexpensive, gradient-based optimizers.

Watson, W. R.↗

NASA NTRS2014

Single Mode Theory for Impedance Eduction in Large-Scale Ducts with Grazing Flow

An impedance eduction theory for a rigid wall duct containing an acoustic liner with an unknown impedance and uniform grazing flow is presented. The unique features of the theory are: 1) non-planar waves propagate in the hard wall sections of the duct, 2) input data consist solely of complex acoustic pressures acquired on a wall adjacent to the liner, and 3) multiple higher-order modes may exist in the direction perpendicular to the liner and the opposite rigid wall. The approach is to first measure the axial propagation constant of a dominant higher-order mode in the liner sample section. This axial propagation constant is then used in conjunction with a closed-form solution to a reduced form of the convected Helmholtz equation and the wall impedance boundary condition to educe the liner impedance. The theory is validated on a conventional liner whose impedance spectrum is educed in two flow ducts with different cross sections. For the frequencies and Mach numbers of interest, no higher-order modes propagate in the hard wall sections of the smaller duct. A benchmark method is used to educe the impedance spectrum in this duct. A dominant higher-order vertical mode propagates in the larger duct for similar test conditions, and the current theory is applied to educe the impedance spectrum. Results show that when the theory is applied to data acquired in the larger duct with a dominant higher-order vertical mode, the same impedance spectra is educed as that obtained in the small duct where only the plane wave mode is present and the benchmark method is used. This result holds for each higher-order vertical mode that is considered.

Watson, Willie R.↗

NASA NTRS2018

Impedance Eduction in a Duct Using the Linearized Euler Equations

An impedance eduction technique that is based upon a numerical solution to the linearized Euler equations coupled with the minimization of an objective function is presented. The linearized Euler equations are solved numerically using a cubic finite element method and the minimum of the objective function is obtained via a gradient based optimizer. The mean flow is allowed to have a gradient in two coordinate directions and the impedance of the liner may vary arbitrarily over the liner surface. A new regularized wall impedance boundary condition presented by Rienstra which contains the effects of the mean boundary layer thickness is implemented. Impedances are educed for a perforate over honeycomb liner using test data acquired in the Langley Grazing Flow Impedance Tube. The impedance of the liner is educed both with an upstream source and a downstream source. The method is validated by comparing the educed impedance to a benchmark method. The primary conclusion of the study is that the impedances educed for upstream and downstream sources are not well matched and that the primary effect of the boundary thickness is to reduce the resistance of the liner.

Watson, Willie R.↗

NASA NTRS2019

Influence of Source Propagation Direction and Shear Flow Profile in Impedance Eduction of Acoustic Liners

The acoustic impedance of liners is a key parameter for their design, and depends on the flow conditions, i.e., the sound pressure level and the presence of a grazing flow. The surface impedance of a locally reacting liner is defined as a local intrinsic property relating the acoustic pressure to the normal acoustic particle velocity at the liner surface. Impedance eduction techniques are now widely used to retrieve the impedance of liners in aeroacoustic facilities in the presence of a shear grazing flow. While surface impedance is intrinsic by definition, the educed impedance has recently been shown to depend on the direction of the incident waves relative to the mean flow. Different studies have investigated this issue by considering different acoustic propagation models used in the education process in the hope of matching the educed values. The purpose of the present work is to continue the previous investigations by evaluating the influence of the shear flow profile on the educed impedance, while considering a Bayesian inference process in order to evaluate the uncertainty on the educed values. The identified uncertainties were not able to totally account for the observed discrepancies between educed impedances.

Roncen, R.↗

DOE OSTI2022

Virtual Dynamic Grid Impedance and Its Impacts on Harmonics and Stability of Inverter Based Resources Plant

Nowadays, a large number of inverter-based resources (IBRs) are integrated into the grid at a single connection point as an IBR plant. In this article, a virtual dynamic grid impedance concept is introduced to evaluate the harmonics and stability for grid integration of an IBR plant containing multiple IBRs. First, a detailed theoretical study is conducted to build a foundation of the virtual grid impedance concept, which is a dynamic impedance that changes with the number of IBRs added into an IBR plant. Then, based on the new virtual dynamic grid impedance concept, frequency spectrum analysis is performed to explore harmonic impact at the interconnection point for an IBR plant with IBRs having L, LC, and LCL filters, respectively. An electromagnetic transient (EMT) simulation model of a grid-connected IBR plant is developed to explore the harmonics and stability of the IBR plant connected to the grid as well as the reliable operation of IBRs within the plant from the novel virtual equivalent dynamic grid impedance point of view. Hardware experiments are conducted to validate the EMT simulation evaluation. The results show that the number of IBRs added into an IBR plant influences the grid impedance, i.e., grid strength, and the grid impedance variation has multiple impacts on the IBR plant and IBRs within the plant depending on the grid-connected filters of the IBRs.

grid impedance↗

DOE OSTI2024

Wideband Impedance Passivation of MMCs for Suppressing Harmonic Oscillations

Harmonic instability and associated oscillation events have become one of the main concerns in MMC-based HVdc systems. These oscillations can appear in the range from a few hundred hertz to several kilohertz, and the root cause is identified as delay-induced negative damping of MMC impedance appearing at the system resonance frequency. Here, this paper introduces a wideband impedance reshaping method through MMC control to eliminate such negative damping for both grid-following (GFL) and grid-forming (GFM) MMCs, which makes the MMC impedance completely passive from the second harmonic frequency upward, thus preventing all harmonic oscillations. First, simplified impedance models of MMCs are derived for the harmonic stability analysis and the impedance reshaping control design. Next, a passivity-based impedance reshaping method is presented, as well as practical considerations for its implementation. In addition, to maintain the MMC's disturbance ride-through capability, an adaptive activation scheme is developed, which enables the wideband impedance reshaping control only in the presence of harmonic oscillation events. The effectiveness of the proposed method is validated by frequency domain analysis and by electromagnetic transient (EMT) simulations of two typical MMC-based power systems.

17 WIND ENERGY↗