The usual conventions are a little muddled - by the definitions, the customer's electrode is part of the consumer's installation, so is not external to it, so Ze does NOT include Ra (although it would, for TT, include the supplier's electrode(s) - Rb).  Hence you get things like statements like the max Ze for TT systems is 21Ω yet Ra can often be in the region of 200Ω.

Really things like Zs = Ze + R1+R2 should only be done for TN systems, originally the requirement for TT systems didn't depend on the loop impedance, just Ra (which technically actually included R2 already).

The point about using a loop meter is that it includes all of Ra ... plus extra bits for the supplier. As the supplier's bit are never going to provide a -ve impedance, if the loop meter gives you an acceptable number, you can be sure that Ra will be less than that - so always compliant. So is a quick, easy but still clean, method of showing compliance. The downside is that if the loop meter shows a value that's just a little too high, you can't then tell if it complies or not - the extra bit could be down to the supplier's side in which case Ra would be OK, or it might be down to Ra in which case it would be a fail - but you can't really tell using a test meter - so either just assume the worst or get hold of a more expensive instrument. In the real world though, electrodes buried in the ground are quite variable beasts - actual resistance figures varying considerably with the weather and season so any practical design and installation will have to include very substantial safety margins anyway - so the difference between loop figures and Ra are usually smaller than would be significant anyway.

            - Andy.

Thank you Andy. In this case of TT earthing system, is it still necessary to add a "Ze" value on the test certificate if it is not really known unless we could deduct the actual Ra from the loop measurement? Basically we only need to assess In x Ra < 50V. Should we just write down "max 21ohm" or just "n/a" for the Ze? I have also seen people using the loop test results (external impedance + Ra) for the Ze value on the test certificates, which is not correct based on your explanation above. many thanks 

Thank you Andy. In this case of TT earthing system, is it still necessary to add a "Ze" value on the test certificate if it is not really known unless we could deduct the actual Ra from the loop measurement? Basically we only need to assess In x Ra < 50V. Should we just write down "max 21ohm" or just "n/a" for the Ze? I have also seen people using the loop test results (external impedance + Ra) for the Ze value on the test certificates, which is not correct based on your explanation above. many thanks 

Ding Wang said:

Thank you Andy. In this case of TT earthing system, is it still necessary to add a "Ze" value on the test certificate if it is not really known unless we could deduct the actual Ra from the loop measurement? Basically we only need to assess In x Ra < 50V.

Where RCDs are used for fault protection, compliance with Regulation 411.5.3 is demonstrated by earth fault loop impedance Z_s being less than the values in Table 41.5. Similarly, if an OCPD is used for ADS in TT systems, Note 1 to Regulation 411.5.2 tells us to assess Z_s. So I would argue that earth fault loop impedance Z_s is what's verified (assessed) in TT systems, as required by BS 7671, and we do NOT directly verify (assess) either I_Δn×R_A<50 V or I_n×R_A<50 V.

I agree that strictly Z_e for a TT system does not include the consumer's earth electrode resistance R_EE, because the electrode is part of the installation, and the table of Symbols in Part 2 tells us that Ze is external to the installation.But that doesn't make Z_e less important to the installation, and verifying (Z_e+R_A)

However, for verification, as discussed above we have to verify Z_s (where RCDs are used for ADS, this is required to be less than the values in Table 41.5). Hence, if Z_e is measured to include R_EE, the formula Z_s=Z_e+(R₁+R₂) could still be used rather than measuring Zs directly. (Noting that, for armoured cables, for  the measured values would need modifying by the relevant formula from PD IEC/TR 50480 to get the value of (R₁+R₂) to use, see Guidance Note 6 and OSG ... and also noting that the armour needs a different temperature correction factor to copper conductors in SWA).

If you wanted to be more factual regarding the measured value, why not record '(Includes R_EE)' next to the value of Z_e recorded on the certificate?

Hi Graham thank you for your explanation. It is now clear to me. We will need to meet both 411.5.3 (i) and (ii). For a site with earth leakage protection, 411.5.3 (i) is very easy to meet even considering the worst Ze (as high as 21 ohms, thus conservative Zs). We will also use Ra (measured from the loop tester -> Ze + Ra) to assess if we meet 411.5.3 (ii). We will put down the measured Ze+Ra against Ze on the certificate and note down that it includes Ra. 

 Ding Wang , R_A is the sum of (R_EE+R₂) in this case -  If you wanted to measure R_A, you'd have to include R₂ to the exposed-conductive-parts (because  for 411.5.3, R_A includes that resistance).

and therefore you would be:

• measuring (Z_e+R_EE) at the origin (and recording the value for Z_e includes R_EE) - see Note to 643.7.1 b) (1); and
• measuring or determining Zs by other means at the extremity of each circuit to comply with either:
  • Table 41.5 where RCDs are used for ADS (see Regulation 411.5.3 and NOTE to 643.7.1); or
  • the formula Z_s ≤ U₀×C_min÷I_a  where OCPDs are used (see Regulation 411.5.4, I_a being the value of current causing operation of an OCPD according to the disconnection time of Regulation 411.3.2.2 or 411.3.2.4, usually 0.2 s or 1 s depending on circuit rating/function for 230/400 V TT supplies, although for installations within buildings where protective bonding is in place, disconnection times for TN systems may be used for circuits covered by Regulation 411.3.2.2)

Interesting, though, that, having discussed the designer's obligations, where RCDs are used for ADS, the person carrying out initial/periodic verification also needs to verify the effectiveness of protection by testing the RCD as well as verifying that the requirements of Chapter 41 are met (see Regulation 643.7.1 b) (2) and related NOTE). Having said that, this is the minimum standard.

Note: we ought to be careful, R_a is defined differently to R_A as well - see Page 47 of BS 7671:2018+A2:2022

Graham, thank you for your help.