Formula for DC Decrement Curve
Formula for DC Decrement Curve
(OP)
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.
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.
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.






RE: Formula for DC Decrement Curve
RE: Formula for DC Decrement Curve
But I could be wrong. If you have proof, can you send it to me so I can check it out?
Thanks.
RE: Formula for DC Decrement Curve
RE: Formula for DC Decrement Curve
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.
RE: Formula for DC Decrement Curve
Bill
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"Why not the best?"
Jimmy Carter
RE: Formula for DC Decrement Curve
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!
RE: Formula for DC Decrement Curve
RE: Formula for DC Decrement Curve
RE: Formula for DC Decrement Curve
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