For techies - Potential Flaw in Zs/ADS calculations?

[JohnW2]

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.

OK, I think I'm gradually getting unconfused. To be frank, I'd actually forgotten that there had been an 'earlier equation'. Just to be clear, everything I've done and written in the last couple of days has related to the 'second' equation, per your message #58

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.

Fair enough, but I'm not too sure how you could have thought that. What did you think the different rows in my tabulated simulations were - they were each for a different supply voltage (ranging from 122V to 238V in my first simulation), achieved by varying Ro.

Returning to the 'second' equation, it's easy enough to modify that so that Ir really is the PFC determined per the regs' method, but that creates a practical problem ...

Since the transformer voltage (Vt) terms no longer cancel, we are stuck with a Vt term in the final expression, and we will not normally (if ever!) know the value of that. All one can do (and I will try) is to explore the effect of varying Vt, with Ro constrained to values which result in supply voltages between 216.2 and 253V. I suspect that that constraint will seriously limit the range of transformer voltages that can be sensibly considered (i.e. without invoking ridiculous load currents). There is also now going to be a practical issue in relation to presenting this graphically (without having dozens of graphs), since we now have 5 variables to consider (Vt, Vs, Ze, Rf and 'error') - it was bad enough with the 4 variables I presented graphically yesterday, so I need to think how best to do this! Watch this space.

Anyway hope that makes sense. Far better to discuss this kind of thing over a pint anyway...

Very true, but I suspect that geography could present a problem. If it's any consolation, I've consumed a good few glasses of wine whilst partaking in this discussion, and there are probably more to be drunk before it's finished!!

Kind Regards, John

 

[John D v2.0]

Sounds good, actually I was just unable to grasp so many variables at once! But hence why I worked out the first equation first and then moved on to the second.
Actually for the second I assumed Vt was 253 volts but I could believe it's more in reality.

If you're struggling with 5 variables, just do what I did without telling you! Worked out that Max voltage drop gives the biggest error from my "first" equation, then assumed Vt is 253, then I also knew the ratio Ze to Ro for max voltage drop. Then I only had to play with Rf relative to Ze really to get my error.
Then I found minimising Rf gives the biggest error, and maximising it gives the biggest error the other way.

 

[JohnW2]

Sounds good, actually I was just unable to grasp so many variables at once! But hence why I worked out the first equation first and then moved on to the second. Actually for the second I assumed Vt was 253 volts but I could believe it's more in reality.

Fair enough. I imagine that the transformer voltage may well be a little over 253V, but I doubt that it's often a lot above that (unless the substation is fairly remote from the first consumer), since there would otherwise be a risk that the supply voltage to the nearest consumers would rise above the 'permitted maximum' of 253V.

If you're struggling with 5 variables, just do what I did without telling you! Worked out that Max voltage drop gives the biggest error from my "first" equation, then assumed Vt is 253, then I also knew the ratio Ze to Ro for max voltage drop. Then I only had to play with Rf relative to Ze really to get my error. Then I found minimising Rf gives the biggest error, and maximising it gives the biggest error the other way.

OK. What I've done with these 5 variables is to produce one set of six plots (for a range of Ze values) for each of three transformer voltages - 253V (which, as above, is probably not far short of the highest voltage they would often 'dare' to use), 245V and 235V (probably the lowest likely). I could obviously produce sets of plots for any other transformer voltages that you wanted, but I think what I have done is probably adequate, and basically confirms the 'conclusions' you gave in msg #99.

The 'error' plotted in all of these graphs is that between the actual/true fault current and that using the actual regs' method (i.e. 218.5/Zs) - and, as you said, usually represents an under-estimate (up to about 13%) by the regs' method, but (under fairly 'extreme' circumstances) just occasionally an over-estimate (but never more than 1%, if that):

Kind Regards, John

 

[John D v2.0]

Looks great! Excellent graphs.

And just a note that the reason yours "only" goes to 13% is because you didn't go as extreme as you could have. In the graphs worst oversizing (at the min permissible voltage of 0.94x) at Vt=253V is 12% ish

however I pushed Rf to zero and got an Ir/If of 0.8545454545 which I think is about 17%. Interestingly, it only depends on the ratio of supply voltage to transformer voltage, and not dependent on the Ze at all.

 

[JohnW2]

Looks great! Excellent graphs.

Thanks. I hate to think how may graphs I have created over the years/decades, so I've had plenty of practice

And just a note that the reason yours "only" goes to 13% is because you didn't go as extreme as you could have. In the graphs worst oversizing (at the min permissible voltage of 0.94x) at Vt=253V is 12% ish

I'm not sure what sort of 'extreme' you're talking about - are you merely commenting on the fact that I didn't look at values of Rf (i.e. R1+R2) less than 0.1Ω ? If so, I though that reasonable as the lowest probable R1+R2 of any real-world circuit, but I could obvioulsy go lower if you really wanted!

however I pushed Rf to zero and got an Ir/If of 0.8545454545 which I think is about 17%.

As above, I stopped at 0.1Ω, since that seemed a reasonable lower limit of real-world R1+R2.

Interestingly, it only depends on the ratio of supply voltage to transformer voltage, and not dependent on the Ze at all.

Indeed. When Rf=0, my latest equation (shall we call it 'third'?!) reduces to:

Ir/If = 218.5 / Vt

... which, as you say, is not dependent on Ze (although it is dependent on Vt, which we don't know) - not the ratio of supply voltage to transformer voltage but, rather, the ratio of (Uo x Cmin) to transformer voltage. As such, Ir/IF could theoretically go as high as you like - since as Vt approaches zero, Ir/If approaches infinity (although one would then have a supply voltage also approaching zero!).

Kind Regards, John

 

[JohnW2]

however I pushed Rf to zero and got an Ir/If of 0.8545454545 which I think is about 17%.

What value of Vt did you use for that? With Vt=253 and Ze=0.05, I don't seem to be getting errors even as high as 14%, even if I use ridiculously small values for Rf (i.e. R1+R2). Does that mean that something is wrong with my plots?:

Kind Regards, John

 

[John D v2.0]

My Post: """ And just a note that the reason yours "only" goes to 13% is because you didn't go as extreme as you could have. In the graphs worst oversizing (at the min permissible voltage of 0.94x) at Vt=253V is 12% ish
"""

I'm not sure what sort of 'extreme' you're talking about - are you merely commenting on the fact that I didn't look at values of Rf (i.e. R1+R2) less than 0.1Ω ?

If so, I though that reasonable as the lowest probable R1+R2 of any real-world circuit, but I could obvioulsy go lower if you really wanted!As above, I stopped at 0.1Ω, since that seemed a reasonable lower limit of real-world R1+R2.
Indeed. When Rf=0, my latest equation (shall we call it 'third'?!) reduces to:

Ir/If = 218.5 / Vt

... which, as you say, is not dependent on Ze (although it is dependent on Vt, which we don't know) - not the ratio of supply voltage to transformer voltage but, rather, the ratio of (Uo x Cmin) to transformer voltage. As such, Ir/IF could theoretically go as high as you like - since as Vt approaches zero, Ir/If approaches infinity (although one would then have a supply voltage also approaching zero!).

YEah that whole thing was literally just a note, not a serious point - as you say it's not likely in the real world.

As I said it was at the min permissible voltage of 0.94x so that matches with what you said. If you go lower than that then all bets are off!

I didn't try to simplify things beforehand, but now you mention it mine turned out to be Ir/If = 216.2/253. Not sure which of us used the 0.95 by mistake.

What value of Vt did you use for that? With Vt=253 and Ze=0.05, I don't seem to be getting errors even as high as 14%, even if I use ridiculously small values for Rf (i.e. R1+R2). Does that mean that something is wrong with my plots?:

View attachment 109065

Kind Regards, John

No I get the same as you for those values put into my spreadsheet, although I make 0.873 about 14.5%*, see the third row below. Try Vt 253 and Ze whatever you like if Rf is zero, as long as the ratio of Ze to Ro gives a supply voltage of 0.94:

*I'm describing in terms of how much percent bigger (or smaller) the cables would be than necessary so really it would be If/Ir

 

[JohnW2]

I didn't try to simplify things beforehand, but now you mention it mine turned out to be Ir/If = 216.2/253. Not sure which of us used the 0.95 by mistake.

Well, I haven't used 216.2V at all, other than as the value below which I truncated my plots (my actual calculations went down to incredibly low supply voltages, but I only plotted those which were in the 'permitted range').

No I get the same as you for those values put into my spreadsheet, although I make 0.873 about 14.5%*, see the third row below. Try Vt 253 and Ze whatever you like if Rf is zero, as long as the ratio of Ze to Ro gives a supply voltage of 0.94:

Well, that's pretty similar (but not identical) to what I'm getting, if you look at 216.2V on the last graph I posted (i.e. the truncated left-hand end of the line plotted for Rf=0.0001Ω), you'll see that the error is just slightly below 14%.

Kind Regards, John

 

[John D v2.0]

In that case it must be me that's used the wrong voltage somewhere!
I think this thread just wants to go off and curl up somewhere without us!
Anyone else still reading? If so hit Like on this post so we know!

 

[JohnW2]

In that case it must be me that's used the wrong voltage somewhere!

Maybe - only you can tell us that.

I think this thread just wants to go off and curl up somewhere without us! Anyone else still reading? If so hit Like on this post so we know!

Yes, I've been wondering the same. The 114 posts in this thread (not counting this one) have has 1,099 views - hence an average of about 9.6 'views' per post. However, I suspect that many/most of those 'views' consist of you and I having 'multiple looks' at the same messages - so it doesn't really give any sure indication of whether (or how much) anyone else is reading. I think the bottom-line conclusions might actually be of interest to some (even if they haven't been following the thread) - so, maybe, once we've done it to death, I/we could post a new 'conclusions' thread, since I imagine that a good few people would look at the initial post in a new thread!

Kind Regards, John

 

[John D v2.0]

I'm not going back over the equations now, I've already chucked out all my notes! They've covered in orange peels etc now!

I'll let you post the conclusions thread!

Thought about going over to the iet forums to mention it? They do exist, and I bet more people would have an opinion than here! Also there's electricians forums which I've used and they might have opinions.

 

[JohnW2]

I'll let you post the conclusions thread!

I might, in due course. I still make no apology for starting all this, because I thought that there might be a far greater 'flaw' in the regs' calculations than is actually the case.

However, I wouldn't mind betting that the great majority of electricians (very few of whom will have thought/played as deeply as we have ) believe that the per-regs method give an accurate/true value for PFC, rather than a (usually under-) estimate of it.

The bottom line is basically just reassurance about something one would have hoped in the first place - that the "reg's method" will very rarely over-estimate PFC (and, at worst, by under 1% - and very few circuits are that close to the limit) and that it will generally under-estimate the PFC by a bit (but probably never more than about 15%) - only pretty rarely resulting in one 'unnecessarily' using larger cable than would actually be adequate.

Thought about going over to the iet forums to mention it? They do exist, and I bet more people would have an opinion than here! Also there's electricians forums which I've used and they might have opinions.

You're obviously welcome to do that if you wish, but, personally speaking, I certainly don't want to have to go over all this ground again, even though it would be a fair bit simpler now that we have 'the benefit of hindsight'!

However, it's been 'fun', and intellectually fairly satisfying. Thanks!

Kind Regards, John

 

[333rocky333]

Anyone else still reading?

Lost me on 1st page
That formula on post #106 would do my head in.
Like the graphs though

 

[JohnW2]

Lost me on 1st page

Fair enough - but it seems as if you've nevertheless 'kept looking'!

That formula on post #106 would do my head in.

You haven't lived - look at the one in post #91 It did my head in as well, but more in typing it into an equation editor than actually doing the algebra!

Like the graphs though

Thanks!

Kind Regards, John

 

[333rocky333]

look at the one in post #91

Im lost for words john, never seen anything like it
Closest i got to that was when i took my city and quilds "C" course, nowadays would not know where to start