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In Europe, houses often have all breakers chained beneath one or more RCDs (their word for GFCI). I would not want the nuisance of multiple circuits shutting off at once, so I'm glad in the US we have GFCI on individual breakers or outlets. But, I would like to have some sort of alarm sound when leakage current of my home as a whole exceeds some level or increases rapidly.

At first thought a CT around the grounding conductor in the main panel would do this. But this would not detect leakage through Earth/water/communications cables. Paths to ground are essentially unlimited, and impossible to enumerate.

So what about measuring the utility conductors? With a single hot like they have in Europe this would be easy because there's only one path current should be taking for each customer. If the current on their utility's hot != the current on their utility's neutral, then the difference is leakage.

But with the NorthAmerican split-phase system you can't assume L1=L2 or L1+L2=N can you?

Is there mathematically, a way to detect the amount of leakage current by measuring only L1, L2, and N in a standard North American residence? I'm guessing not, but I'm hoping someone here can blow my mind.

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What about one big CT around all three service conductors? (and NOT around the grounding wire) They SHOULD all cancel each other out in the absence of leakage, and the CT / Amp clamp would measure only the leakage. Did I just solve this?

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Your service panel has the neutral bonded to the ground. Any current which flows down that bonding path reveals a ground fault. Sense that, and you're all set. On locomotives, the traction circuits (main gen, switchgear and traction motors) are entirely isolated from chassis, except for the ground fault relay. Any leakage anywhere else closes the loop through the ground relay. Similarly, look for current flow on that ground-neutral bond. This is very sensitive because a fault is any current at all.

The only problem is if you share the transformer with other houses, because a fraction of their ground faults will travel to your house to use your ground bond. In that case, you can compare your 3 wires - L1, L2 and neutral, but this is not as sensitive because you're measuring tiny differences in large amounts of current. Think of a whole house as a giant MWBC. Add up the current flow (counting flow direction as positive or negative) in all 3 wires - both hots and the neutral. The total should always equal zero.

An old style ground fault relay would have all 3 wires wound several turns around its core. In normal operation, the magnetic flux cancels each other out. Any remaining flux is proportionate to the leakage.

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