Calculating broken PEN touch voltage with backup earth electrode

[timhoward]

My brain has been exercised a bit by this. Am I on the right lines with this extremely simplified example:
If we take:
-TNCS installation with a Ze of 0.2 ohms.
-Plastic services, nothing bonded, keeping it simple
-Line conductor resistance from supply transformer should be similar to PEFC and PSCC given equal conductor sizes. So 0.2 ohms. Or is this only to nearest PME point and would be larger?
-Resistance of average human being according to google is 300 ohms

If this installation is pulling 20 amps, it can be treated basically as a resistive load of 11.5 ohms. (given nominal 230v supply)

Can I just use the voltage divider resistor formula (R2/R1+R2) to calculate voltage in the middle?

So with broken PEN and only path back being through human, R1 is 11.7 ohms, R2 is 300 ohms, so voltage at point of contact is 222v (or pretty much full supply)
And in case where someone has installed a backup earth electrode at the cut-out, with the electrode having an impedance of 50 ohms, R2 becomes 50 ohms, and the potential at the installation's exposed conductive parts is about 186v

Does that basically stack up, main variables being:
-resistance of earth, resistance at humans feet etc.
-current draw of installation
-impedance of earth rod
-resistance of line and cpc conductors within installation (completely omitted above)

Would parallel paths to earth via bonded services be calculated by 1/R=(1/R2) + (1/R2) + (1/Rn) and substitute that value for R2?
Thank you to anyone who got to the end and is willing to comment!

 

[Marvo]

I'm short of time so I can't get deep into this but the nominal resistance of a person is 1000 ohms for the purpose of electrical calcs, so in formulas where Ztl is the resistance of a person a figure of 1000 ohms would be used.

 

[LastManOnline]

I'm short of time so I can't get deep into this

Me too.But the figures for me stack up and it sounds a realistic scenario.If I might suggest one adjustment. In your post title you refer to a "backup electrode". A standard domestic earth rod in a TNC-S system is commonly referred to as a "backup" in many countries. This is however misleading. Its function is to reduce touch voltage under fault conditions. It serves no other function.

 

[timhoward]

Me too.But the figures for me stack up and it sounds a realistic scenario.If I might suggest one adjustment. In your post title you refer to a "backup electrode". A standard domestic earth rod in a TNC-S system is commonly referred to as a "backup" in many countries. This is however misleading. Its function is to reduce touch voltage under fault conditions. It serves no other function.

Thanks. I respect that this could turn into an endless debate.
Without digging deep into the theory - my conclusion so far is that the value of an earth rod on a TCNS is to slightly reduce touch voltage, but not actually that much, and also to provide enough imbalance to trip an RCD should the very rare open PEN scenario happen. (EDIT this last bit is rubbish!)

 

[marcuswareham]

Thanks. I respect that this could turn into an endless debate.
Without digging deep into the theory - my conclusion so far is that the value of an earth rod on a TCNS is to slightly reduce touch voltage, but not actually that much, and also to provide enough imbalance to trip an RCD should the very rare open PEN scenario happen.

How will it trip an RCD?,

current though L and N will be balanced regardless of the electrode resistance.
as the connection of PE to N is before any RCDs, even if the current is returning via a CPC or some bonded pipe work it would still be balanced though the RCD

 

[timhoward]

How will it trip an RCD?,
current though L and N will be balanced regardless of the electrode resistance

of course it will....! Doh. A glass of red wine makes any installation safer it seems!

 

[marcuswareham]

of course it will....! Doh. A glass of red wine makes any installation safer it seems!

Haha ,

the calculation in A722.3 for the electrode resistance needed to keep touch voltages below 70v (not sure why they haven't used 50v) goes to show how low resistance is needed for any realistic load, makes it feel pointless sticking in a few rods on PME unless you can get in 1 ohm mark

 

[timhoward]

Haha ,

the calculation in A722.3 for the electrode resistance needed to keep touch voltages below 70v (not sure why they haven't used 50v) goes to show how low resistance is needed for any realistic load, makes it feel pointless sticking in a few rods on PME unless you can get in 1 ohm mark

That's exactly why I did this contrived exercise and exactly what I arrived at - for example a 50% loaded 60 Amp supply needs 2.1 ohms at the rod or less to achieve 50v.

 

[LastManOnline]

Haha ,

the calculation in A722.3 for the electrode resistance needed to keep touch voltages below 70v (not sure why they haven't used 50v)

Yes. Have also not read a satisfactory explanation for that 70 volt figure. It seems to have emerged along with the open PEN sensors for EV chargers.

 

[Lucien Nunes]

The take-away fact here is that if a rod is expected to sink a realistic installation neutral current without the touch voltage from the broken PEN to real earth exceeding 50V, it has to offer a resistance lower than can usually be achieved. For Uo=230V and 50V touch, it's (50/(230-50) * (230²/P) ohms, where P is the installation load (or unbalance, if 3-phase) in VA.

 

[timhoward]

The take-away fact here is that if a rod is expected to sink a realistic installation neutral current without the touch voltage from the broken PEN to real earth exceeding 50V, it has to offer a resistance lower than can usually be achieved. For Uo=230V and 50V touch, it's (50/(230-50) * (230²/P) ohms, where P is the installation load (or unbalance, if 3-phase) in VA.

Thank you very much.
I think I recognise the 2nd half of the formula as P=V^2 / R rearranged? (though using real power not apparent power)
I'll muse the first half later as don't quickly get why divisor is 230-50

 

[UKPN]

Thank you very much.
I think I recognise the 2nd half of the formula as P=V^2 / R rearranged? (though using real power not apparent power)
I'll muse the first half later as don't quickly get why divisor is 230-50

He doesnt do the bonding but installs a rod to reduce the "touch voltage"