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Given that I don't have neutral, sounds like, even for just running a simple irrigation controller, that I don't want to use the ground wire for my neutral and simply pull 120v off the split phase 240V since a potential short would energize the ground wire.

It seems like running a small transformer is the way to go. However often recommendations I have found mention adding a sub panel breaker after the transformer, which seems like overkill for my need. Would adding a 5A fuse to new transformed 120V be fine instead of a whole breaker box?

I'm surprised how much transformers are, and most of them are for transforming single phase Euro 220v to US 110v, anyone have a good source?

As an aside, if this existing ground to the 240V did connect directly to ground at the main panel instead of neutral (haven't looked yet, in the neighbor's panel) then to me it would be ok to just pull L1 and ground off the 240V and skip the transformer right? These are very large wires running a 20A load to a well pump, might 1000' away, so I think this is the only load on that breaker.

At 0.15A x 120V, this thing is about 18 VA (similar to watts). That is significantly less than 40 VA.

As it happens, 40VA thermostat transformers are cheap and common as dirt, typically around $13. They make them with both 240V and 120V primaries. Get one of each.

You connect the two 24V secondaries to each other. The 240V primary goes to the 240V main via a 1 amp fuse. The 120V primary feeds your controller. This is double-isolated from 240V, so it won't be terribly dangerous.

If you really want to, you can call it a separately derived service and add a neutral-ground equipotential bond to whichever leg of the 120V you want to call "neutral", but given that it is going straight into another transformer that will also isolate it, that seems like much ado about nothing.

I recommend to snip the plug off the cord and hardwire this thing, to avoid the temptation of someone plugging a circular saw into the outlet.

Wow, that was easy and cheap.

For the specific irrigation controller you linked, there's almost certainly a way to configure it to accept 240V directly.

From the international manual on their website:

Rated input:

Australia—240V AC 50/60Hz 0.15A

Europe—230V AC 50/60Hz 0.15A

USA—120V AC 60Hz 0.15A

I'd recommend contacting them to see if you can plug the one you have into 240V directly, or if there's some internal wires or jumpers that need to be reconfigured first.

Something similar to this comes up all the time in industrial applications. For example there may be a three phase 480V supply to a motor, but you need lower voltage for the controls.

The usual solution is a control transformer. These are modestly priced, especially for tiny loads. For example one brand, Hammond, makes control transformers as small as 50VA for under $50. (USD)

Take a look at this document from Hammond for wiring diagrams for various primary / secondary configurations:

https://www.hammondpowersolutions.com/files/HPS_Instruction_Sheet_Control_Transformer_WiringDiagram_PHWD1.pdf

With these products, there are fuse holders built in, and you can also buy enclosures ready made for the device for a finished install with minimal fuss, and there are enclosed versions that are built in an enclosure - lots of options.