View source for Time-varying phasor

{{Short description|Analysing signals}}
In communication theory, '''time-varying phasors''' are used for analyzing narrow-band signals, whose signal bandwidths in the [[frequency domain]] are considerably smaller than the carrier frequency.<ref name=":0">{{Cite journal|last=Venkatasubramanian|first=V.|date=1994|title=Tools for dynamic analysis of the general large power system using time-varying phasors|journal=International Journal of Electrical Power & Energy Systems|volume=16|issue=6|pages=365–376|doi=10.1016/0142-0615(94)90023-X|s2cid=109676900}}</ref><ref name=":1">{{Cite journal|last=Jeltsema|first=Dimitri|date=2015|editor-last=Camlibel|editor-first=M. Kanat|editor2-last=Julius|editor2-first=A. Agung|editor3-last=Pasumarthy|editor3-first=Ramkrishna|editor4-last=Scherpen|editor4-first=Jacquelien M.A.|editor4-link=Jacquelien Scherpen|title=Time-Varying Phasors and Their Application to Power Analysis|url=https://link.springer.com/chapter/10.1007/978-3-319-20988-3_4|journal=Mathematical Control Theory I|series=Lecture Notes in Control and Information Sciences|volume=461|language=en|location=Cham|publisher=Springer International Publishing|pages=51–72|doi=10.1007/978-3-319-20988-3_4|isbn=978-3-319-20988-3}}</ref> Time-varying [[phasor]]s are mostly used for analysis of frequency domain of band-pass systems.<ref name=":1" /><ref name=":0" /> The method uses classical impulse response.<ref name=":0" />

In electrical power system, phasors are used for [[transient analysis]] of the power system keeping the quasi-stationary conditions.<ref name=":0" /><ref name=":2">{{Cite journal|last1=Venkatasubramanian|first1=V.|last2=Schattler|first2=H.|last3=Zaborszky|first3=J.|date=November 1995|title=Fast time-varying phasor analysis in the balanced three-phase large electric power system|url=https://ieeexplore.ieee.org/document/471228|journal=IEEE Transactions on Automatic Control|volume=40|issue=11|pages=1975–1982|doi=10.1109/9.471228|issn=1558-2523}}</ref><ref name=":3">{{Cite journal|last1=Belikov|first1=J.|last2=Levron|first2=Y.|date=December 2018|title=Uses and Misuses of Quasi-Static Time-Varying Phasor Models in Power Systems|url=https://ieeexplore.ieee.org/document/8403297|journal=IEEE Transactions on Power Delivery|volume=33|issue=6|pages=3263–3266|doi=10.1109/TPWRD.2018.2852950|s2cid=53741086|issn=1937-4208}}</ref> They were introduced to facilitate the computation and analysis of power systems in stationary operation.<ref name=":2" /> Time-varying phasors are used in dynamic analysis of a large power system.<ref name=":0" /><ref name=":4">{{Cite web|title=Comparison of time-varying phasor and dq0 dynamic models for large transmission networks|url=https://www.researchgate.net/publication/317252520|access-date=2021-01-28|website=ResearchGate|language=en}}</ref> The phasor representation of [[sinusoidal]] [[voltage]]s and [[Electric current|currents]] is generalized to [[Arbitrary waveform generator|arbitrary waveforms]].<ref name=":1" /> This mathematical transformation eliminates the 60 [[Hertz]] (Hz) carrier which is the only time-varying element in the stationary case.<ref name=":2" /> The longer usage of time-varying phasors in large power systems since 1920s have created many misconceptions. One of the misuses suggest that [[Quasi-stationary distribution|quasi-stationary]] models are always accurate, but only when the system dynamics are slow as compared to nominal system frequency which is usually 60&nbsp;Hz.<ref name=":3" />

The concern to study time-varying phasors is raised to understand in-depth the fast amplitude and phase variations of emerging electrical power generator technologies.<ref name=":3" /> This is because current and voltage signals of latest machines may have harmonic components and they can damage the entire [[transmission system]] which is coupled with the machine.<ref name=":2" /><ref name=":3" /> However, if we employ quasi-static model, we can accurately model AC signals by using time-varying phasors as opposed to traditional quasi-static model which supports constant voltage and current signals throughout the network.<ref name=":4" />

== References ==
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[[Category:Electric power generation]]
[[Category:AC power]]
[[Category:Interference]]
[[Category:Trigonometry]]