NEC / Complex Imaginary Voltage Drop Confusion

[BigWheel]

So serious!

I guess you've never had Memphis BBQ....?  Dodged that one quicker than Hillary being quizzed about her rogue emails....

Hah! I like BBQ, man. I'm gonna smoke a butt next weekend for Mother's Day. 

 

[BigWheel]

Let us try to remove  and quantify the confusion.

In real sense as per textbook definition VD= IEI-IVI. Now the best way would be to find this out and be happy. To  get VD on V axis we draw an arc touching V axis at C; so the exact VD = OC in the figure. But if want to take approximation let us take take offset of vector VD or IZ on V axis i.e. OB in the figure attached. It comes I R Cos theta+I X sin theta meaning approximate Z is R cos theta+ X sin theta. The error in using the formula is BC. It depends on you whether the error in calculations is acceptable to you or not. The error is not constant but will vary on R and X. that is angle theta itself. That is the reason the figures for .85 pf should not be taken for other pf's calculations because then error will increase. This is a case of meeting point of technicians and Engineers so confusion has to happen.

View attachment 9444

Seriously, man, PROPS! Great job! I understood the intent, but you went and made me understand why the intent is valid. 

 

[BigWheel]

Please take AB = I X sin theta in figure and also in OA+AB. I am not able to take it out and edit.

I think we all picked up what you were laying down based on your diagram. Great job. 

 

[BigWheel]

As soon as I figure out how to give you rep, I'll do it. 

 

[TNPE]

Let us try to remove  and quantify the confusion.

In real sense as per textbook definition VD= IEI-IVI. Now the best way would be to find this out and be happy. To  get VD on V axis we draw an arc touching V axis at C; so the exact VD = OC in the figure. But if want to take approximation let us take take offset of vector VD or IZ on V axis i.e. OB in the figure attached. It comes I R Cos theta+I X sin theta meaning approximate Z is R cos theta+ X sin theta. The error in using the formula is BC. It depends on you whether the error in calculations is acceptable to you or not. The error is not constant but will vary on R and X. that is angle theta itself. That is the reason the figures for .85 pf should not be taken for other pf's calculations because then error will increase. This is a case of meeting point of technicians and Engineers so confusion has to happen.

View attachment 9444

There was no confusion, just cage rattling.

 

[TNPE]

Hah! I like BBQ, man. I'm gonna smoke a butt next weekend for Mother's Day. 

I told my wife that and....well... umm if looks could kill, I wouldn't be here telling you that.

 

[rg1]

I think we all picked up what you were laying down based on your diagram. Great job. 

I have not plotted but I think the error will further reduce if we take the offset of E (supply end or no load voltage) on V axis. I suppose the offset will fall some where between B and C. That is actual difference between IEI and IVI, called voltage drop, not the I VD I as I have simplified in above demo. I suppose when theta is zero, the error is zero (unity pf) and when theta is 90 (zero pf) the error is max. However we can prove it mathematically taking derivatives and finding maximum of the error function. But Engineers are not scientists, let us leave it. 

 

[cos90]

So is the rule to always ignore phase angle for PE style voltage drop calculations?

For example please see Complex Imaginary Exam 1 Problem 48. The phase angle doesn't affect the answer here but I'm trying to establish general rules in my head.

 

[rg1]

So is the rule to always ignore phase angle for PE style voltage drop calculations?

For example please see Complex Imaginary Exam 1 Problem 48. The phase angle doesn't affect the answer here but I'm trying to establish general rules in my head.

The phase angle is always taken into account while calculating voltage drop in AC circuits. In the example shown, also they have taken phase angle into account. You can also find the Vd with I<theta * X<phi. Please keep in mind while calculating Voltage regulation is it is the magnitudes of load and no load voltages. Somewhere in the thread I have posted a file showing the differences. See if that makes sense and helps you.

 

[BigWheel]

So is the rule to always ignore phase angle for PE style voltage drop calculations?

For example please see Complex Imaginary Exam 1 Problem 48. The phase angle doesn't affect the answer here but I'm trying to establish general rules in my head.

No, that's not the rule. Even the NEC approximation includes the phase angle (by way of the power factor).