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GISdude
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AC Waveform

08/13/2014 10:50 PM

Hi all,

This may be a dumb question, so bear with me. Why is a typical AC wave represented by the equation:

x(t) = Xm (cos wt +Ø). Why wouldn't this a sin instead?

Thanks

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IdeaSmith
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#1

Re: AC waveform

08/13/2014 11:07 PM

I am sure you could express this in sin as well by turning it the other way.

Its all to do with the circular movement of the generator.

This is not meant as a scientific or even correct engineering answer.

Others will kick in with a better explanation. I just think its mathematics.

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SolarEagle
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#2

Re: AC waveform

08/14/2014 6:58 AM

It can be given either way....the sine version measures from the beginning of the wave at center and cosine at peak....

http://agni.phys.iit.edu/~vpa/wavesosci.html

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GISdude
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#7
In reply to #2

Re: AC waveform

08/14/2014 12:46 PM

thanks for all the reply's.

I saw this formula in a paper called"Syncrophasors:definition,measurement, and application:" I work in substations and it seems like my work (and the industry in general) is headed to more syncrophasors on the sub-distribution side of the sub, <69kV. But I think these tie into the relay ct's to monitor the get-aways from the sub.

Thanks again.

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Codemaster
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#3

Re: AC Waveform

08/14/2014 8:27 AM

#2 answers it, but it should be x(t) = Xm*cos (wt +Ø)

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Rixter
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#4

Re: AC Waveform

08/14/2014 9:09 AM

A sine wave is just cosine shifted by 90 degrees.

There are two parameters that you have to specify to describe any "sine" wave: amplitude (Xm) and phase (Φ). So the general formula "x(t) = Xm (cos wt +Ø)" will produce any "sine" wave by filling in these parameters.
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#5
In reply to #4

Re: AC Waveform

08/14/2014 9:28 AM

Except that it should be "x(t) = Xm*cos (wt +Ø)"

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JRaef
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#6

Re: AC Waveform

08/14/2014 12:33 PM

Since we measure the power factor wave form by using the cosine, it presents a clearer definition of what you are discussing when discussing both.

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70AARCuda
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#8

Re: AC Waveform

08/14/2014 1:10 PM

Depends upon WHAT you look at to represent the AC waveform, VOLTAGE or CURRENT, ie:

• ELI = Voltage LEADS current across an inductive (L) load...associated with SIN.

• ICE = Current LEADS voltage across a capacitive (C) load...associated with COS.

• E:I = Voltage & current in-phase across a purely resistive (R) load.

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#9

Re: AC Waveform

08/15/2014 1:02 AM

Dear Mr.GISdude,

In terms of SINE function AC Wave Form is expressed as e = Emax x Sin Ø

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cjanand
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#10
In reply to #9

Re: AC Waveform

08/15/2014 10:49 AM

Hello folks,

Had a quick look at the paper mentioned earlier in these postings. The synchrophasors use UTC as time and per real life and standards time has only one arrow - always moving forward. Per standards that synchrophasors will follow globally, phase information is transmitted as time information with no provision (rightly so) for negative time. Considerng that phase is either + or - 90 degrees and this information is to be conveyed with only a positive going reference, start of the sine wave is offset by 90 degrees - hence the cosine.

Otherwise, generic expressions of electrical AC waves are still sine, and cosine (the other side of the same coin) is a ledgerdemain to accommodate an always forward progressing time information.
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GISdude
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#11
In reply to #10

Re: AC Waveform

08/15/2014 3:33 PM

Thanks cjanand! I would not have thought about the time domain of the wave form (maybe I should from now on) going positive.

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James Stewart
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#12
In reply to #11

Re: AC Waveform

09/18/2014 2:56 PM

Go ahead and mark this as OT, but it is only a SIN if you touch it!

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