Formula for DC Decrement Curve

[corvalan]

I want to plot the DC Decrement curve with an Asymmetrical curve in the same graph.

According to IEEE Std. 141-1993 (Red Book, page 118) the formula for the DC Decrement curve is as follows:

DC Decrement = e^-(R*t/L). Converting the L to X/R with a frequency of 60 Hz, we have the following equation:

​

DC Decrement = e^-(120*Pi*t/(X/R)) where t is in seconds.

Now for the symmetrical curve.

The symmetrical curve equation, when the short circuit occurs when the voltage wave is at 0 degrees and there is no R, only X, is as follows.

sin (2*Pi*x-90*Pi/180)​

The x in this equation is not the X from the X/R ratio of the short circuit. It is any value and is used to plot the sine wave. It is dimensionless. But the resultant value of 2*Pi*x is in radians. So we plot the sine function with the dimensionless variable x in the horizontal axis.

On the other hand, the value of the variable t in the DC Decrement curve is in seconds. So we plot the DC Decrement curve with the variable t in seconds in the horizontal axis.

And here is the challenge, The curves can't interact with one another because they have a different horizontal axis. For example, I would like to add the DC Decrement curve to the symmetrical curve to obtain the asymmetrical curve through time as follows:

​

sin (2*Pi*x-90*Pi/180)+ e^-(120*Pi*t/(X/R))

But I believe I can't do this because one curve is based on x and another is based on t on the horizontal axis.

So here is the question.

How can I make these two curves have a common horizontal axis so I can add them?

Thanks.

 

[magoo2]

I believe the x in your second sine equation should be t.

 

[corvalan]

I do not think that the x in the second equation (the sine equation) should be replaced by t in seconds. The sine equation is based upon radians.

But I could be wrong. If you have proof, can you send it to me so I can check it out?

Thanks.

 

[magoo2]

You can work it out the angle in in radians or degrees, but you still have time (t) in both equations. I'll see if I have a link to send you.

 

[magoo2]

Allan Greenwood in the 2nd Edition of Electrical Transients in Power Systems analyzes the closing transient for an R-L circuit in the attachment. He starts out with LaPlace transforms and then winds up with the time based solution.

In the Red Book, it looks like their analysis for the total current took some shortcuts if you read page 117. I suspect the two results will be close, but I have more confidence in Greenwood's work.

 

[waross]

Can you use (2 pi r) and (60 Hz) to convert x to t?

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[corvalan]

Thanks so much for all your answers.

I checked the equations that magoo2 sent me. That is exactly what I wanted. Thanks so much.

Just before I opened your response, I read the IEEE Violet Book and also found the equations I needed.

I ended up using the equation 2.3 from the IEEE Violet Book (IEEE Std 551-2006) in page 19, which shows the decrement curve equation and the symmetrical curves equation, both with the same variable t in seconds. This equation is the same as what magoo2 sent me but in a different forma.

I have not yet analyzed the response of waross, regarding the conversion from x to t. I will analyze this latter.

Thanks again, great forum!

 

[cuky2000]

See if the enclosed file could help.

 

[magoo2]

Nice work, cuky2000!

 

[Hector04]

quote waross: Can you use (2 pi r) and (60 Hz) to convert x to t...
In imperative affirmative, the angular and temporal variables are related
as a result, an equation can be expressed in both ways, so when adding them are with the same variable