View source for V curve

[[File:V curve synchronous motor.svg|thumb|V curve for a [[synchronous motor]]]]

In [[synchronous machine]]s, the '''V curve''' (also spelled as '''V-curve''') is the graph showing the relation of [[Armature (electrical engineering)|armature current]] as a function of [[Stator|field current]] in [[synchronous motor]]s keeping the load constant. The name comes from an observation made by [[William Morris Mordey|W. M. Mordey]] in 1893 that the curve resembles a letter V.{{sfn|M.I.E.E.|1906|p=591}}

The lowest point of the curve corresponds to the [[unity power factor]]. For a motor, points on the left of the minimum correspond to underexcitation (and therefore the armature current would "[[Power factor#Lagging, leading and unity power factors|lag]]" the voltage), on the right - to overexcitation (and "[[Power factor#Lagging, leading and unity power factors|lead]]"). Typically multiple V curves are plotted based on the experiments, each corresponding to its own load value.{{sfn|Dawes|1922|pp=315-317}}

The minimum at unity power factor (<math>\cos \phi</math>) is due to the general formula for the power {{mvar|P}} of a synchronous motor, <math>P = \sqrt 3 V_A I_A \cos \phi</math>. In order to keep the power constant, with the [[Line voltage (three-phase)|line voltage]] at the terminals of the armature <math>V_A</math> also constant, any decrease in power factor has to be accommodated by a corresponding increase in the armature current <math>I_A</math>.{{sfn|Dawes|1922|p=315}} At the low values of the [[field current]], the power factor is low, so the armature current is high (and lagging). As the field current increases, the power factor increases too, until the unity power factor is reached (the armature current decreases to its minimum when the motor reaches this ''normal excitation''). If the field current is increased beyond this point, the armature current becomes leading, power factor decreases, and <math>I_A</math> grows again.{{sfn|Dawes|1922|p=317}}

The data from the V curves can be used to set up the synchronous motor to [[power factor correction|correct the power factor]] of the overall system, as the power factor of the motor can be changed by simply adjusting the field current.{{sfn|Dawes|1922|p=315}} While performing the correction, the motor can either provide the mechanical power also, or run in the idle mode ("float"), working as a [[synchronous condenser]].{{sfn|Dawes|1916|p=75}}

==Inverted V curve==
The '''inverted V curve''' is a graph showing the relation of [[power factor]] as a function of field current. The shape of this curve resembles a dome.

==See also==
* [[Synchronous motor]]

==References==
{{reflist}}

== Sources ==
* {{cite book|last=Dawes|first=C.L.|title=Electrical Measurements and Testing, Direct and Alternating Current|publisher=J. Wiley & sons, Incorporated|series=The Wiley technical series| editor-first = J. M. | editor-last = Jameson|year=1916|url=https://books.google.com/books?id=CDqblzc3QWYC&pg=PP75|access-date=2024-12-03}}
* {{cite journal|journal=English Mechanics and the World of Science|publisher=E. J. Kibblewhite|volume=83|year=1906|url=https://books.google.com/books?id=YORf6fJzVe0C&pg=PA591|ref=|access-date=2024-12-03|title=The Electric Transmission of Power|last=M.I.E.E.|pages=590–592}}
* {{cite book|last=Dawes|first=C.L.|title=A Course in Electrical Engineering: Alternating currents|publisher=McGraw-Hill Book Company, Incorporated|series=A Course in Electrical Engineering|year=1922|url=https://books.google.com/books?id=EpFEAAAAIAAJ&pg=PA315|access-date=2024-12-03}}
* Saadat, Hadi. 2004. ''Power Systems Analysis''. 2nd Ed. McGraw Hill. International Edition. {{ISBN|978-0-07-128184-3}}.

{{Characteristics of synchronous machines}}

[[Category:Electrical generators]]
[[Category:Synchronous machines]]
[[Category:Electromechanical engineering]]


{{electric-power-stub}}