Editing Y-Δ transform (section)

{{short description|Technique in electrical circuit analysis}}
{{about|an application of a mathematical technique in electrical engineering|the mathematical technique itself|YΔ- and ΔY-transformations|the device which transforms three-phase electric power |delta-wye transformer|the application in statistical mechanics|Yang–Baxter equation|the regional airline brand name for Delta Air Lines|Delta Connection}}
{{Technical|date=January 2021}}

In [[circuit design]], the '''Y-Δ transform''', also written '''wye-delta''' and also known by many other names, is a mathematical technique to simplify [[Network analysis (electrical circuits)|the analysis]] of an [[electrical network]]. The name derives from the shapes of the [[circuit diagram]]s, which look respectively like the letter Y and the Greek capital letter [[Δ]]. This circuit transformation theory was published by [[Arthur Edwin Kennelly]] in 1899.<ref>{{cite journal |first=A. E. |last=Kennelly |title=Equivalence of triangles and three-pointed stars in conducting networks |journal=Electrical World and Engineer |volume=34 |pages=413–414 |year=1899}}</ref> It is widely used in analysis of [[three-phase electric power]] circuits. 

The Y-Δ transform can be considered a special case of the [[star-mesh transform]] for three [[resistor]]s.  In mathematics, the Y-Δ transform plays an important role in theory of circular [[planar graph]]s.<ref>{{Cite journal|doi = 10.1016/S0024-3795(98)10087-3|title = Circular planar graphs and resistor networks|year = 1998|last1 = Curtis|first1 = E.B.|last2 = Ingerman|first2 = D.|last3 = Morrow|first3 = J.A.|journal = Linear Algebra and Its Applications|volume = 283|issue = 1–3|pages = 115–150|doi-access = free}}</ref>