On 26/07/2012 17:24, dennis@home wrote:
> John claims that the circuit will always balance while I claim its luck
> that it did.
No, if you recall I said "In the situation Adam described, luck had
nothing to do with it."
A statement I still maintain.
> Unless you put some very tight (IMO impossibly tight) tolerances on
> cable lengths it does not balance.
I don't believe that is true for reasons I will demonstrate shortly.
> You may notice that John probably understands this now as he has gone
> very quite.
No, I had intended to just let you wiggle and change arguments every 5
minutes as usual until you got bored. Since I figure no one would take
much notice anyway, it hardly seemed to matter. However since there
seems to be ongoing interest and no end in site, lets see if we can put
it to bed.
> But just for you I will go through it again..
>
> First the basics as I can't get certain posters to understand them.
>
> Wires have resistance proportional to their length (assuming they are
> normal wires)
>
> A ring circuit has two line wires in parallel feeding the load.
> A ring circuit has two neutral wires in parallel returning from the load.
So far so good...
> All the current has to pass through the load so its effects are a net
> zero on the balance of currents.
On the balance itself this is true. However the load effects the
magnitude of any imbalance. Unlike "normal" circumstances where an RCDs
imbalance will be typically caused by insulation failure and hence the
leakage very much dependant on circuit voltage, this situation is more
affected by total load current. So the load is very significant factor.
> The current through the two lines will be split in proportion to the
> resistance (length)
> The same applies to the neutral
yes
> Normally the two lines match the two neutrals as they are in the same
> pair of T&E cables
>
> This means you will get exactly the same current through the line and
> neutral in the one cable and the same applies to the other cable.
>
> Now on the faulty circuit these are tied at the ends to two RCDs and if
> they are exactly the same nothing happens, they don't trip.
Yes, we established that many posts back.
> Now if you make one core slightly longer anywhere in the circuit the
> current will be imbalanced on one of the cables (the resistances are
> different so the split is different).
>
> Now as you only need an imbalance of 30 mA to trip the RCD it doesn't
> take much difference in the length.
In a real world situation it actually takes quite a bit. Enough that its
unlikely to happen.
> In the *example* I gave with a 10A load you need 0.3% imbalance to get
> 30 mA.
> Now 0.3% of a cable is not much, its 3mm in a metre or in the example I
> gave its 30mm in 10 metres.
There are a number of aspects you are not considering here. The obvious
one being that 10m is rather short for a ring circuit[1]. You also seem
to be assuming that the extra length is at one end of the cable. If you
are maintaining that one might normally cut the neutral longer at the CU
(which I suspect is untrue for most electricians) that really ought to
apply to both ends of the wire, since they both terminate at the same CU.
[1] The shortest ring I recall wiring was for a kitchen approx 7' by
11'. That took around 22m of cable (wired in the ceiling void, with each
socket drop taking 2 - 3m of cable).
> A 30A load will only need a difference of 0.1%.
>
> Now do you understand why I said it was luck it didn't trip.
I understand why you said it, I just don't agree with the assessment.
Let's explore why...
If we take the following model of the circuit in question:
http://wiki.diyfaq.org.uk/index.php?title=File:RCDsCrosswired.gif
We have got a 230V supply at 50Hz with a Zs of 0.1 ohms (the supply
impedance has no effect on the result, but may as well be included for
completeness, along with a "book" TN-S value of Ze of 0.8 Ohms).
We have two ring circuits as you might find in a typical medium sized
semi, a downstairs one with a total of 40m of 2.5mm^2 T&E, and a
slightly longer upstairs one with 53m.
If we take the resistance of 2.5mm^2 wire as 7.41 mOhm/m, it means we
have a round trip resistance of about 0.4 ohm for the longer circuit,
and about 0.3 ohms for the shorter.
The situation as described was a new build, second fix wiring complete,
with a different electrician (Adam) commissioned to test the system. The
system is in use by other trades completing the building work. So I have
used in this example a total load of 10A on one circuit, and 2.5A on the
other, representing a mix of work lights, power tools, chargers etc. At
230V these correspond to load impedances of 23 and 92 ohms.
To demonstrate the position of the loads makes no difference, I have
placed the first a quarter of the way along the circuit, and the second
at about a third.
Now Dennis has been maintaining that small variations in conductor
length amounting to just a handful of mm will result in a trip. So for
this example I have included half a metre of extra neutral conductor on
each circuit, which I hope most will agree is excessive (if I were
reading that kind of difference on a loop round trip test, I would be
expecting a fault somewhere!)
At 7.41 mOhm/m that amounts to a total of 3.7 mOhms extra resistance,
which I have split equally between the ends. I have also introduced the
same mismatch on the second circuit.
Now for analysis, I have summed the currents in all of the cable ends
connected to the first RCD. In a perfectly balanced situation these
would obviously be zero. However in this case with an extra metre of
wire floating about in there, they are not.
(I have also summed current flow in the other ends as well however since
these are identical to the first, they line on the graph would be
obscured - so I have included an inversion in there just to make it visible)
So if you have a look at :
http://wiki.diyfaq.org.uk/index.php?title=File:RCDsCrosswiredCurrentBalanc.gif
You can see we only get around 19.5mA RMS of imbalance. Unlikely to trip
the RCD. In reality you would need to add another 10A or so of load to
be sure of doing it with this configuration. You can play with the
parameters to move in and out of trip scenarios, but the basic upshot is
that you are unlikely to trip the circuit with a typical (much smaller)
mismatch of conductor lengths, and with normal loads on it.
Now assuming that I have not made some glaring error in calculation,
this is why I disagree with Dennis' assessment of it just being "luck".
(if anyone wants the LT Spice model to play with, then let me know and I
will stick it on the FAQ web site)