Frequency-Domain Fitting Techniques: A Review

Morales-Rodriguez, Jesus; Medina, Edgar; Mahseredjian, Jean; Ramirez, Abner; Sheshyekani, Keyhan; Koçar, Ilhan

doi:10.1109/tpwrd.2019.2932395

Cited by 19 publications

(4 citation statements)

References 22 publications

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“…It identifies the poles and residues by iteratively relocating an initial pole set which can be either real or complex conjugate pairs to better positions via a scaling function, each iterative step corresponding to the solution of simple well-conditioned linear systems. Thanks to its superior fitting performance, as demonstrated by the findings in [13], [14], several engineering fields have attempted to improve the VF since its invention, among which power electronic domain [5]- [9], [15], [16], power system domain [17]- [24], and electromagnetic compatibility domain [25]- [28] are relatively active.…”

Section: Introductionmentioning

confidence: 99%

Application of Extrapolation Capability of Vector Fitting for Out-of-Band Dominant Modal Synthesis of Voltage-Source Converters

Zhou,

Beerten

2024

IEEE Open J. Power Energy

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Conventional state-space-based stability assessment method of voltage-source converters (VSCs) can be hindered by the black-box feature. Black box-based state-space model identification method using the terminal admittance/impedance frequency responses has thus been drawing increasing research attentions recently. However, the estimation of out-of-band modes commonly suffers from narrow bandwidth of frequency responses. This article presents, for the first time, the potential identification of several critical out-of-band modes of an artificially created rational function and a grid-connected VSC. This identification is achieved through their band-limited frequency responses using the vector fitting (VF) algorithm. On its basis, a sensitivity index of a partial fraction term is derived to explain the out-of-band modal identification behavior of the VF. The effects of the pole, residue, and fitting frequency interval width on the sensitivity index are further investigated and demonstrated. The numerical analysis shows that, with the help of the proposed sensitivity index, the extrapolation behavior of the VF can be explained, and several invisible out-of-band modes can further be identified or synthesized from a band-limited frequency response. This extrapolation feature may strengthen the curve fitting capability of the VF, i.e., compared to the VSC's band-limited frequency responses, more modal information can be obtained and further used for eigenvalue-based stability analysis.

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Section: Introductionmentioning

confidence: 99%

Application of Extrapolation Capability of Vector Fitting for Out-of-Band Dominant Modal Synthesis of Voltage-Source Converters

Zhou,

Beerten

2024

IEEE Open J. Power Energy

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“…For a specific fitting order, the VF can achieve the most accurate fitting result, whereas the other two techniques can reach the same accuracy as that of the VF at the cost of higher fitting order [9]. In addition, it has high robustness when fitting noisy or contaminated frequency samples [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

Extrapolation of Band-Limited Frequency Responses for Out-of-Band Modal Synthesis

Zhou

Beerten

2022

2022 International Power Electronics Conference (IPEC-Himeji 2022- ECCE Asia)

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The bandwidth of the measured or simulated frequency responses is sometimes relatively narrow, resulting in that some out-of-band modes of interest cannot be directly observed from the band-limited frequency responses. Although various kinds of curve fitting algorithms aim at generating linear or nonlinear transfer functions for these frequency samples, their fitting objective is commonly minimizing the in-band fitting errors, whereas their reproduction/identification capabilities for the out-of-band modes are usually ignored and may be not satisfying. To fill this research gap, this paper, based on the sufficient excavation of the in-band frequency responses information induced by the out-of-band partial fraction terms, develops an extrapolation method for the band-limited frequency responses in order to identify or synthesize the out-of-band modes. The effectiveness of the proposed out-of-band modal synthesis method is validated on artificially created rational functions with different numbers of out-of-band modes. The proposed frequency-domain extrapolation method can obtain unknown and much modal information from known and little modal information, which would be a desirable tool to identify the modes of interest not located within the available frequency interval.

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“…Finally, the model is subjected to passivity enforcement by perturbation of the model's parameters, thereby ensuring stable time domain simulation results with any terminal condition. While the initial model can be reliably calculated using methods such as vector fitting [10] or Löwner tangential interpolation [11], [12], the passivity enforcement is much more difficult and has hampered the widespread use of FDNEs in electromagnetic transient simulations. The lack of a good passivity enforcement method is also a major obstacle in some other modeling applications, e.g.…”

Section: Introductionmentioning

confidence: 99%

Passivity Enforcement by Residue Perturbation via Constrained Non-Negative Least Squares

Gustavsen

2021

IEEE Trans. Power Delivery

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Passivity is a fundamental requirement for rational models to guarantee stable behavior when included in general time domain simulations. This paper introduces a new variant of one passivity enforcement scheme that is based on residue matrix perturbation. The constrained least squares problem associated with the passivity condition is transformed into a least distance problem which is solved as a non-negative least squares problem while utilizing the sparsity pattern that arises with multi-terminal problems. The resulting method is very fast and requires only a small amount of computer memory, thereby being applicable to models with many terminals and high orders. The method is demonstrated to be suitable for frequency-dependent modeling of subnetworks, transformer winding branch impedances, and measured transformer admittance data.

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Frequency-Domain Fitting Techniques: A Review

Cited by 19 publications

References 22 publications

Application of Extrapolation Capability of Vector Fitting for Out-of-Band Dominant Modal Synthesis of Voltage-Source Converters

Application of Extrapolation Capability of Vector Fitting for Out-of-Band Dominant Modal Synthesis of Voltage-Source Converters

Extrapolation of Band-Limited Frequency Responses for Out-of-Band Modal Synthesis

Passivity Enforcement by Residue Perturbation via Constrained Non-Negative Least Squares

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