For techies - Potential Flaw in Zs/ADS calculations?

[JohnW2]

Here is the formula I used - the definitons here: .... The actual forumla here:

I have attempted, in haste, to reproduce your equation, but I don't think we can both be right, because I can see no way in which yours could be simplified to become mine! In view of my haste, it is very probably me who is wrong, so maybe you can spot the 'deliberate mistakes' in the following (I'm not sure how readable it will be when posted; if it doesn't look good after posting, I'll try a 'Plan B').

Kind Regards, John
Edit: it looks fairly readable to me, particularly if zoomed - but if you have a problem, please let me know.

 

[John D v2.0]

Hmmm. Are you sure that your model is correct, since that's something which I have not yet ever seen with any of my simulations. I've looked at a fairly wide range of situations and the ('per regs') Zs-based method has always under-estimated actual PFC, never overestimated it - which is why I thought I had at least reassured myself that errors in the estimates were always going to be in the 'safe' direction. When I have a little time, I'll see if I can reproduce your equation.

Kind Regards, John

Yes I even checked manually
PFC 0.95 is 30.01ish and actually fault current at 0.94 is 29.75ish

 

[John D v2.0]

I have attempted, in haste, to reproduce your equation, but I don't think we can both be right, because I can see no way in which yours could be simplified to become mine! In view of my haste, it is very probably me who is wrong, so maybe you can spot the 'deliberate mistakes' in the following (I'm not sure how readable it will be when posted; if it doesn't look good after posting, I'll try a 'Plan B').


Kind Regards, John
Edit: it looks fairly readable to me, particularly if zoomed - but if you have a problem, please let me know.

Yep I can read it well, your Ir is identical to mine, but your If is a lot simpler. Also, I don't make any idea about who is wrong, I think we've all had our fair share of confusion, but confusion leads to understanding! Your haste was happening while I was asleep by the looks of your timings! I'll have another look and post back.

 

[JohnW2]

Yep I can read it well, your Ir is identical to mine, but your If is a lot simpler. Also, I don't make any idea about who is wrong, I think we've all had our fair share of confusion, but confusion leads to understanding! Your haste was happening while I was asleep by the looks of your timings! I'll have another look and post back.

Thanks. As I said, I wouldn't be at all surprised if there is a mistake in there somewhere - as you observe, it was not only done in haste, but also 'in the middle of the night'! Let me know if/when you find my error!

Kind Regards, John

 

[JohnW2]

Yes I even checked manually ... PFC 0.95 is 30.01ish and actually fault current at 0.94 is 29.75ish

Thanks. I can't fault your arithmetic.

I need to think. As you have no doubt realised, if you had calculated a "PFC 0.94", it would have been fractionally below the true fault current.

I'm going to be tied up for much of this afternoon, so will probably be quiet until this evening!

Kind Regards, John

 

[John D v2.0]

You're doing my trick of editing your posts!
I have checked both your and my equations and I still can't find the fault. I also can't rearrange mine to get yours. I'm thinking of plotting them both just to prove they are different, although I'm pretty sure they are.
Have a nice afternoon!

 

[JohnW2]

You're doing my trick of editing your posts!
I have checked both your and my equations and I still can't find the fault. I also can't rearrange mine to get yours. I'm thinking of plotting them both just to prove they are different, although I'm pretty sure they are. Have a nice afternoon!

See my edit. I produced that graphic a while ago when I thought you had made a mistake, but the mistake was mine. However, I can't delete the image or post - so I have asked the mods to. Sorry about the confusion!

Yes, I was planning on plotting both - or, at least, put them in a spreradsheet and comparing results over a range of situations - but you'll probably beat me!

Kind Regards, John

 

[John D v2.0]

Oh ok I derived your forumla accidentally while checking mine. So I plotted both your If/Vt and my If/Vt and I found they're identical.

I managed to simplify mine to
If/Vt=(Ro^2+RoRf)/(ZeRo^2+2ZeRoRf+ZeRf^2+Ro^2Rf+RoRf^2)
Yours is
If/Vt=Ro/(RfRo+ZeRo+RfZe)

Then if I factor out (Ro+Rf) from the top and bottom of mine, I get the same as yours!

 

[John D v2.0]

So, possible conclusions from this thread:

Using the regs, it's possible to oversize a relatively high current circuit by a maximum of 17% (Vt=253, Vo=216.2, maximum reached as the Rf << Ze)

Using the regs, it's possible to undersize a relatively low current circuit by a maximum of 1% (Vt=253, Vo=216.2, maximum reached as the Rf >> Ze)

 

[JohnW2]

I've just found a few spare moments! ....

Oh ok I derived your forumla accidentally while checking mine. So I plotted both your If/Vt and my If/Vt and I found they're identical.

Thanks, and that's reassuring - in that case I'd be more inclined to use mine, since it's a lot simpler
I'm just found a few spare moments! ....

I managed to simplify mine to .... then if I factor out (Ro+Rf) from the top and bottom of mine, I get the same as yours!

Ah - so algebra really does work

So, we're at least reading from the same hymn sheet, maths-speaking.

Kind Regards, John

 

[JohnW2]

So, possible conclusions from this thread:
Using the regs, it's possible to oversize a relatively high current circuit by a maximum of 17% (Vt=253, Vo=216.2, maximum reached as the Rf << Ze)
Using the regs, it's possible to undersize a relatively low current circuit by a maximum of 1% (Vt=253, Vo=216.2, maximum reached as the Rf >> Ze)

That sounds very credible; I look at the figures in more detail later, and will comment if necessary. The reason, of course, that I saw some very large errors was that, in the interests of theoretical generalisation, I was looking at a ridiculous range of supply voltages, to see what happened at the extremes - not just the range of interest (216.2V - 253V).

Of course, in practical terms, cable sizes come in large discrete jumps, so that underestimating PFC by 'a maximum of 17%) could sometimes lead to going up to the next cable size 'unnecessarily'.

Kind Regards, John

 

[JohnW2]

Yes I even checked manually ... PFC 0.95 is 30.01ish and actually fault current at 0.94 is 29.75ish

Oh ok I derived your forumla accidentally while checking mine. So I plotted both your If/Vt and my If/Vt and I found they're identical ..... Then if I factor out (Ro+Rf) from the top and bottom of mine, I get the same as yours!

Something is wrong. Although (after my initial boob!) I agree with your manual calculation example, which gave the regs' method slightly over-estimating fault current (figures above), if one plugs those figures into my/your equation, one gets Ir/If=0.998 - i.e. with the regs method very slightly under-estimating actual fault current.

Having examined the behaviour of my/our equation (for Ir/If) over a wide range of situations, it seems consistent with my simulations in that it appears never to show the regs' method over-estimating fault current. I'm not sure how clearly the following will post, but they illustrate what my/our equation does (with 253V transformer voltage and 'supply voltages' from 216.2 - 253V); if there's a problem of clarity of the graphs, I'll try some other approach: Edit: NB please note a typo which I realised only after I'd posted these graphs "Zs=xx" in the title of each graph should read "Ze=":

Kind Regards, John

 

[John D v2.0]

Don't forget the equation was before we even thought about the 0.95 against 0.94 issue. So plugging it into the equation gives actual fault current against PFC at a given voltage.

The later comment about 0.94 is a new formula (with rather a lot of funny terms/multipliers), that assumes we worked out PFC for 0.95 voltage and measured actual fault current at 0.94 times nominal voltage. Where Vt is 1.1 times.

 

[JohnW2]

Don't forget the equation was before we even thought about the 0.95 against 0.94 issue.

I can't accept that I introduced the 0.94/0.95 issue in my initial post on page 1, and we discussed it quite a lot in the 5-6 pages before you introduced your equation!

So plugging it into the equation gives actual fault current against PFC at a given voltage.

I think you may have 'led me astray' to some extent. What I sought to do was to 're-derive/produce your equation (for "Ir/If"), but you now make me realise that I based that on what you had done, which, in turn, was based on what is probably an inappropriate premise. Your equation started with the assertion that "Ir (regs) = V/(Ze+Ro)" (where V is the supply voltage of the premises), but that does not correspond (at least, not exactly) with the regs calculation, which would be (for Cmin=0.95) "Ir=218.5/Zs" - or, if you prefer, "Ir=218.5/(Re+Rf) - so the equation would seem to be of limited usefulness. Your 'manual confirmation' of your equation perhaps confused me even more because (although I didn't think of this at the time I re-derived the equation) you didn't actually ('manually') use your equation but, rather, used a 218.5V-based calculation!

The later comment about 0.94 is a new formula (with rather a lot of funny terms/multipliers), that assumes we worked out PFC for 0.95 voltage and measured actual fault current at 0.94 times nominal voltage. Where Vt is 1.1 times.

I'm a bit confused as to what the 'new formula' is and what the (by implication) 'old formula' was. Are the comments above perhaps in relation to some formula other than the one we have been discussing for the past couple of days?

Kind Regards, John

 

[John D v2.0]

OK sorry let me rephrase, the earlier equation I was trying to derive was simply what the difference between Ir and If in any given situation with *constant* voltage. That we indeed found the regs always asked for a better Rf.
Then once I was clear on that I worked out the ratio of Ze to Ro to give the 0.94 voltage drop and plugged that in to the equation to derive the graph. However that kind of got lost in the noise as we were still clarifying the first equation.
When you first posted your simulation I thought you were also simulating the constant voltage situation too, so sorry for not pointing it out explicitly that I was doing that.
Anyway hope that makes sense. Far better to discuss this kind of thing over a pint anyway...