Three-Phase Wye Transformer connection
Three-Phase Wye Transformer connection
(OP)
I have a question related to a three-phase wye-connected secondary
> transformer. I know that if the phase to phase voltage is 208 on the
> secondary, the voltage from one phase to the neutral will be 120 volts. I
> also know that if you multiply 120 volts by 1.73 you get the phase to
phase
> voltage of 208. I also know that the 1.73 is the square root of 3.
>
> My question is this: Where does this 1.73 or square root of three come
> from? I know it has something to do with it being three-phase voltage.
Can
> you help? Thanks.
> transformer. I know that if the phase to phase voltage is 208 on the
> secondary, the voltage from one phase to the neutral will be 120 volts. I
> also know that if you multiply 120 volts by 1.73 you get the phase to
phase
> voltage of 208. I also know that the 1.73 is the square root of 3.
>
> My question is this: Where does this 1.73 or square root of three come
> from? I know it has something to do with it being three-phase voltage.
Can
> you help? Thanks.






RE: Three-Phase Wye Transformer connection
Consider the vector Vab former as the sum of Van and Vbn. The rest is simple geometric problem with a triangle 120 degrees in n and 30 degrees between Van and Vab related as follow:
Cos(30o)=(Vab/2)/Van=SQRT(3)/2.
Thus Vab = 1.73Van.
In any circuit or basic power system book you could find plenty information in this subget.
RE: Three-Phase Wye Transformer connection
For balanced systems, that makes three identical (isosceles; not equilateral) triangles nested within the larger equilateral triangle.
For those inner triangles, the two sides opposite each 120° angle (also the large outer triangle sides) represent phase-to-phase voltage, and the three adjacent lines represent the phase-to-neutral voltages. The ratio of ø-ø to ø-n voltages corresponds to the tangent of 120°=1.732, (square root of 3.) This is literally the ratio of the opposite side length (ø-ø) to the adjacent side length (ø-n). Besides voltage, it shows up in current ratios and in various power/energy/impedance calculations for balanced 3ø circuits.
In the most basic sense, “delta” and “wye” represent the physical layout of transformer-secondary winding interconnections, as well as the nominal voltage of the windings; e.g., 4-wire 480Y/277V or 3-wire 480V∆.
It is a worthwhile, not-soon-forgotten exercise to wire up and power small transformers in various delta, wye and zigzag configurations and measure/record/plot voltage relationships. Transformers and polyphase circuits brought power delivery out of the electrical stone age.
Consult textbooks for gaining a more thorough understanding of transformer circuits and root-3 relationships. For general but limited information, see: http://www.elec-toolbox.com/usefulinfo/xfmr-3ph.htm and http://www.cooperpower.com/Library/pdf/R201902.pdf
In the US, IEEE standards are extensively used. The granddaddy couple-of-thousand-page book on transformers is: Distribution, Power, and Regulating Transformers Standards Collection 1998 Edition; indexed at: http://standards.ieee.org/catalog/distribution.html
Specifically, C57.105-1978 (R1999) IEEE Guide for Application of Transformer Connections in Three-Phase Distribution Systems; outlined at: http://standards.ieee.org/reading/ieee/std_public/description/dtransformers/C57.105-1978_desc.html
And, C57.12.70-2001 IEEE Standard Terminal Markings and Connections for Distribution and Power Transformers; outlined at: http://standards.ieee.org/reading/ieee/std_public/description/dtransformers/C57.12.70-1978_desc.html
Related general references are described at: http://standards.ieee.org/colorbooks/index.html
RE: Three-Phase Wye Transformer connection
Phase A: ua(t) = 120.sqrt2.sin(wt) (Sqrt2 = Rate Amplitude/r.m.s. values)
Phase B: ub(t) = 120.sqrt2.sin(wt-2.pi/3) (2.pi/3 = 120º phase shift in radians)
Phase B: ub(t) = 120.sqrt2.sin(wt-4.pi/3)
Phase to phase voltage is the difference between two phase to neutral voltages. For instance:
Voltage A-B:
uab(t) = ua(t) - ub(t) = 120.sqrt2.sin(wt) + 120.sqrt2.sin(wt-2.pi/3+pi)
And using the following trigonometric properties:
A.sin(wt+a) + B.sin(wt+b) = C.sin(wt+c)
where:
C = sqrt[A^2 + B^2 + 2.A.B.cos(a-b)] and tan c =(A.sina+B.sinb)/(A.cosa+B.cosb)
uab(t) = Sqrt[120^2 + 120^2 + 2.120.120.cos(pi/6)]sin(wt + pi/6) =
= sqrt3.120.sqrt2.sin(wt + pi/6) = 208.sqrt2.sin(wt + pi/6)
Julian
RE: Three-Phase Wye Transformer connection
V=Vmax sin(wt +/- phase angle)
thread no. 238-10803