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Keywords
(8)
Constrained Minimization
Frequency Domain
Positive Definite
Power System
Quadratic Program
Rational Approximation
Rational Function
Satisfiability
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Enforcing passivity for admittance matrices approximated by rational functions
Enforcing passivity for admittance matrices approximated by rational functions,10.1109/59.910786,IEEE Transactions on Power Systems,Bjørn Gustavsen,Ad
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Enforcing passivity for admittance matrices approximated by rational functions
(
Citations: 181
)
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Bjørn Gustavsen
,
Adam Semlyen
A linear
power system
component can be included in a transient simulation as a terminal equivalent by approximating its admittance matrix Y by rational functions in the frequency domain. Physical behavior of the resulting model entails that it should absorb active power for any set of applied voltages, at any frequency. This requires the real part of Y to be
positive definite
(PD). We calculate a correction to the
rational approximation
of Y which enforces the PDcriterion to be satisfied. The correction is minimal with respect to the fitting error. The method is based on linearization and
constrained minimization
by quadratic programming. Examples show that models not satisfying the PDcriterion can lead to an unstable simulation, even though the
rational approximation
has stable poles only. Enforcement of the PDcriterion is demonstrated to give a stable result
Journal:
IEEE Transactions on Power Systems  IEEE TRANS POWER SYST
, vol. 16, no. 1, pp. 97104, 2001
DOI:
10.1109/59.910786
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Citation Context
(120)
...The model extraction is done via rational functions using techniques, such as vector fitting [12] followed by passivity enforcement by residue perturbation [
13
]...
...1) Wide Band (Blackbox) Model: The wideband model is obtained by subjecting to rational approximation via (fast, relaxed) vector fitting (FRVF) [12], [22], [23] and passivity enforcement by residue perturbation via residue matrix eigenvalues [
13
], [24] with the implementation available in the Matrix Fitting Toolbox [25]...
Bjørn Gustavsen
,
et al.
Multivariate Analysis of Transformer Resonant Overvoltages in Power St...
...However, inherent approximations in the fitting process may cause to have passivity violation at certain frequency ranges [
12
]...
...ductance) of the admittance matrix must be positive definite (PD) at any frequency [
12
]...
...This paper adopts an alternate improved formulation based on [
12
], which enforces passivity using linearization and constrained optimization...
Yuefeng Liang
,
et al.
Improved CoherencyBased WideBand Equivalents for RealTime Digital S...
...The VF has guaranteed stable poles by flipping unstable poles into the left halfplane [
23
]...
...It has been proven that this correction is minimal in terms of the fitting error [
23
]...
Huang Wang
,
et al.
Transfer Function Analysis and Broadband Scalable Model for OnChip Sp...
...In a final step, the passivity conditions [8] are verified to assess the passivity of the model, and possible violations are corrected by a perturbation of the model coefficients [
9
]...
D. Vande Ginste
,
et al.
Broadband passive RLGC(f) modeling for onchip interconnect design
...The obtained model is next subjected to passivity enforcement in order to guarantee a stable simulation, for instance using approaches in [
812
]...
Andrea Ubolli
,
et al.
A digital filtering approach for Time Domain Vector Fitting
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