V=Vmax sin(wt +/- phase angle)
V=Vmax sin(wt +/- phase angle)
(OP)
3 phase ac generation, i need help in expressing the voltage equations for 3 phase.
is it simply Vr=Vmaxsin 0,Vy=Vmax sin 120, Vb=Vmax sin -120,
yr 2 of hnc electrical engineering.
sorry but im a bit dim.
is it simply Vr=Vmaxsin 0,Vy=Vmax sin 120, Vb=Vmax sin -120,
yr 2 of hnc electrical engineering.
sorry but im a bit dim.






RE: V=Vmax sin(wt +/- phase angle)
That would correctly describe a set of three phase voltages.
Depending on choice of Vmax, that might represent line-to-line or line-to-ground voltages. Systems are typically characterized by their line-to-line voltages.
Also note that Vmax represents a peak voltage value... but typical voltages are represented in rms.
So if you have a "standard" 480vac system, then 480vac represents the line-to-line rms value. Line to line peak is 480*sqrt(2). Line to neutral peak would be 480*sqrt(2)/sqrt(3).... and line to neutral voltage functions would look like Vline_neutral=480*sqrt(2)/sqrt(3) *sin(wt+theta) where theta takes on three values separated by 120 degrees each.
RE: V=Vmax sin(wt +/- phase angle)
RE: V=Vmax sin(wt +/- phase angle)
RE: V=Vmax sin(wt +/- phase angle)
RE: V=Vmax sin(wt +/- phase angle)
vab=Vm x cos(377t)
vbc=Vm x cos(377t - 120°)
vca=Vm x cos(377t + 120°)
where 377=2 x pi x f=2 x 3.13 x 60
in time format, for example, or
vab=Vm x exp(j0°)
vbc=Vm x exp(-j120°)
vca=Vm x exp(+j120°)
in phasor format.
There are many books in your library including this, e.g. Standard Handbook for Electrical Engineers.
RE: V=Vmax sin(wt +/- phase angle)
RE: V=Vmax sin(wt +/- phase angle)
Just watch those conversions. Jbartos converted cycles per sec to radians per sec, and still does't have something that can be added directly to angular displacement expressed in degrees. Fancier calculators probably don't care if units are properly entered.
///I am in agreement with
Donald G. Fink, H. Wayne Beaty, "Standard Handbook for Electrical Engineers," 14th Edition, McGraw-Hill, 2000, Section 2.1.16 "Electric Energy Distribution in 3-Phase Systems"
377=2 x pi x f is in radians/second
2 is in Per Unit
pi=3.14 in Per Unit
f=60Hz=60cycles/second
It is true that the 120° shall be shown as 2 x pi / 3; however, since the rotating frame is involved and degree displacements are shown properly, it does not matter much about the rest, if the mathematics is somewhat abused. Other books are using this too as the above-mentioned reference. E.g. see
Vincent Del Toro, " Electric Power Systems," Prentice Hall, Englewood Cliffs, New Jersey, 07632, 1992, page 28, eq. 1-23, eq. 1-24 and eq. 1-25
So they are really inaccurate. Apparently, one has to adjust degrees to radians or vice versa to obtain correct results. I am glad that you pointed it out, and that these small discrepancies from books are revealed thanks to this Forum. I have been running into many of these so that I know what I have to do to obtain correct results. Apparently, it then belongs to the profession not to complain much.\\\
RE: V=Vmax sin(wt +/- phase angle)
yeah i understand the cos equations but for the purpose of this exercise i have to show the sin formula.
many thanks for jogging my memory
steviesparkie.
RE: V=Vmax sin(wt +/- phase angle)
1. Gross C. A. "Power System Analysis"
2. Gungor B. R. "Power Systems"
3. Wadhwa C. L. "Electrical Power Systems"
Books that avoid this problem by not including it:
1. Stevenson W. D. "Elements of Power System Analysis"
Correctly stated (at least, in a similar application such as power equations):
1. Bergen A. R. "Power Systems Analysis"
RE: V=Vmax sin(wt +/- phase angle)
the other phases are exactly 120 degrees displaced at any given moment.(assuming constant speed of rotation)