Method of vector fitting and symplectic geometry

M. Kh. Zakhar-Itkin

doi:10.1007/bf01681441

Symplectic Geometry

10.1017/cbo9780511526343 ◽

1994 ◽

Cited By ~ 10

Keyword(s):

Symplectic Geometry

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Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

Energies ◽

10.3390/en14092471 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2471

Author(s):

Tommaso Bradde ◽

Samuel Chevalier ◽

Marco De Stefano ◽

Stefano Grivet-Talocia ◽

Luca Daniel

Keyword(s):

Dynamical Systems ◽

Power System ◽

System Dynamics ◽

Real Time ◽

Initial Conditions ◽

Test System ◽

Initial State ◽

Power System Dynamics ◽

Vector Fitting ◽

Time Modeling

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

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A discussion concerning the floor of the northwest Indian Ocean - An area on the crest of the Carlsberg Ridge: petrology and magnetic survey

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1966.0007 ◽

1966 ◽

Vol 259 (1099) ◽

pp. 198-217 ◽

Cited By ~ 54

Keyword(s):

Remanent Magnetization ◽

Ultramafic Rocks ◽

Magnetic Survey ◽

Vector Fitting ◽

Uniform Magnetization ◽

Ocean Floor Spreading ◽

Carlsberg Ridge ◽

History Of ◽

Magnetic Gradients ◽

Basalt Glasses

Rocks collected in the vicinity of a transcurrent fault cutting the crest of the Ridge have been affected by brecciation and, in some cases, metamorphism and hydrothermal action. These processes have led to the formation of spilites from crystalline basalts, and ultramafic rocks from basalt glasses Further hydrothermal action has taken the form of replacement of some ultramafic rocks by quartz, ending in a nearly pure quartzite. The mineralogy is characteristic of greenschist facies meta-morphism. Fresh basalts were collected from a nearby hill, which seems to be a recent volcano post-dating the faulting and metamorphism. The magnetic survey reveals a marked parallelism between the anomalies and the trend of the ridge, regardless of bathymetry. Computations confirm that uniform magnetization of the material represented by the bathymetry can in no way simulate the observed anomalies. Application of the vector fitting technique suggests that the remanent magnetization of this material is often reversed and from this a very crude and simple model is developed to account for the observed anomalies. The model is consistent with an ocean floor spreading hypothesis and periodic reversals in the earth's magnetic field. If substantiated it would have important implications in deducing the history of the ocean basins. Above all it provides a plausible explanation to account for the magnetic gradients and amplitudes observed over ridges without implying improbable magnetic contrasts, structures, or changes in petrology.

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