V=Vmax sin(wt +/- phase angle) 3

[steviesparkie]

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.

 

[electricpete]

Vr=Vmaxsin 0,Vy=Vmax sin 120, Vb=Vmax sin -120

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.

 

[stevenal]

The equations stated left out the time varying component, so they are only valid for the instant when t=o. To get a time varying expression, add omega*t to the angular displacement. t is time, omega is the system frequency expressed in the proper units. Degrees/s in this case, assuming t is in seconds.

 

[stevenal]

On second look, the expression was correct in the subject line, but not in the body of the question.

 

[electricpete]

Steve is right. A little bit of a typo.

 

[jbartos]

Suggestion: The balanced three-phase source can be described as:
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.

 

[stevenal]

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.

 

[jbartos]

Suggestion to the previous posting marked ///\\\:
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.\\

 

[steviesparkie]

thanks guys-i realised my mistake was leaving the angular displacement/time out of my answers.
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.

 

[jbartos]

Suggestion: I have done some small survey regarding the abuse of dimensions in the sin(wt + 120°) and sin(wt - 120°). Additional books that have it this way are:
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"

 

[steviesparkie]

to jbartos-thanks-the equations required refer to an instantainous value using red phase as the reference vector , therefore the -assumption- is that in an ideal situation with exact phase angle differences on the coils
the other phases are exactly 120 degrees displaced at any given moment.(assuming constant speed of rotation)