Long cable runs, solutions to reduce losses...

Generally speaking, the cable run has to be pretty extreme to justify transformers, especially where the load is light / intermittent. Transformers incur two types of loss - copper loss which increases with the square of load just like cable losses, and iron loss which is more or less constant all the time the transformer is energised.
If you step up from 240, you will need a fully-rated transformer at both ends. There is an option to launch at 240 using just the two hot/line conductors, and either step down to 120 or recreate the split-phase neutral at the load end. That would mean only one transformer and with the split-phase system it only needs to be rated for half the load (because it is transforming any imbalance from 240 to 120) so the losses are lower. A fully balanced load on such a system would not incur any copper loss in the transformer.

It's worth considering how the voltage drops compare between different systems using the same cable size, length and load power. If we consider a load that causes 1% drop on a 240V system:

240V 2-wire single-phase source and load: 1%
120V 2-wire single-phase source and load: 4%
120/240V 3-wire split-phase source, balanced 120V load: 1%
120/240V 3-wire split-phase source, 50% load fully unbalanced: 2%

Compared with a single-phase 120V system, adding the third wire to make it split phase halves the worst case voltage drop as only half the load can ever operate at 120V ie when fully unbalanced. As soon as more load than half load is applied it must improve the balance and an increasing amount of the total power is then taken at 240V with 1/4 of the drop. In full balance and with any 240V loads, the drop is as per a 240V system.

Next step is to plug in the numbers for the actual loads and cables. So far you haven't listed the loads that you expect to be using, which we'll need to make a quantitative assessment.

As Lucian says, transformers are an option but rarely justified over modest distances due to the costs involved.

Certainly chaining them and stepping cable size down makes sense to keep overall cable cost to a minimum. Having voltage fluctuations could also be reduced by putting most major loads in the building closes to the incoming supply.

In terms of earth size you have what is known as the adiabatic limit to consider, which is the impact of a short-term fault heating the conductor. So short that you can neglect heat escaping, so it comes down to the I2t term let-through by the circuit breaker or fuse (that is designed to disconnect the fault) heating the conductor's metal. However, you also have to consider that you need the fault current to be big enough that the breaker opens fast, and you get less heating as well as less exposure to an elevated voltage during the fault. This means you need a low enough fault impedance/resistance which can set a lower limit on the conductor size as well.

If you know the circuit parameters (supply voltage, earth loop fault impedance, fuse or breaker characteristics) you can see if a given cable size is OK or not.

As a rule of thumb in the UK, you would have the earth conductor as half the size of the supply conductors for larger circuits (live > 16mm^2 so AWG below #5) and the same size below that, or you do the full adiabatic computation to justify an alternative size.

One way to minimise the cable cost is to consider 3 core SWA cable and to use the armour as the earth. Usually though this will not be low enough resistance to cause fast disconnection on over-current so you would need to have a delay-action RCD (GFCI) supplying the cable set to trip in, say, 0.2s and with a trip current of say 0.3-1A, but not too small so general accumulated leakage from normal operation does not cause it to trip spuriously. These RCD are not cheap, but you might just find the cost works out cheaper than having 4C cable to get a big enough CPC/earth/ground.

Lucien Nunes said:

Generally speaking, the cable run has to be pretty extreme to justify transformers, especially where the load is light / intermittent. Transformers incur two types of loss - copper loss which increases with the square of load just like cable losses, and iron loss which is more or less constant all the time the transformer is energised.
If you step up from 240, you will need a fully-rated transformer at both ends. There is an option to launch at 240 using just the two hot/line conductors, and either step down to 120 or recreate the split-phase neutral at the load end. That would mean only one transformer and with the split-phase system it only needs to be rated for half the load (because it is transforming any imbalance from 240 to 120) so the losses are lower. A fully balanced load on such a system would not incur any copper loss in the transformer.

It's worth considering how the voltage drops compare between different systems using the same cable size, length and load power. If we consider a load that causes 1% drop on a 240V system:

240V 2-wire single-phase source and load: 1%
120V 2-wire single-phase source and load: 4%
120/240V 3-wire split-phase source, balanced 120V load: 1%
120/240V 3-wire split-phase source, 50% load fully unbalanced: 2%

Compared with a single-phase 120V system, adding the third wire to make it split phase halves the worst case voltage drop as only half the load can ever operate at 120V ie when fully unbalanced. As soon as more load than half load is applied it must improve the balance and an increasing amount of the total power is then taken at 240V with 1/4 of the drop. In full balance and with any 240V loads, the drop is as per a 240V system.

Next step is to plug in the numbers for the actual loads and cables. So far you haven't listed the loads that you expect to be using, which we'll need to make a quantitative assessment.

Click to expand...

Thank you very much for that, very helpful information. I had not considered that a 3-wire split phase (in worst case unbalanced scenario) has only 50% the losses of single phase - at first glance it appeared that the drop would be the same, hence why I immediately thought of higher voltage... the 4 scenarios you present make it very clear.

I'm actually thinking to take your advice and use only the two 110v hots (ignore the neutral) to give me 220v on 2 wires only. This obviously saves me a wire (to each building) and halves the conductor size of the remaining... But instead of stepping back down I think I will keep the whole property at 220v... there is a 220v 60Hz receptacle (wall socket) available and I've since learned that about 25% of the island houses are actually wired as 220v (it will make sourcing appliances a little more tricky as the store mostly stocks 110v items, but given the long cable lengths it makes sense to be higher voltage)

LOADS - (this was all originally planned for 110v split phase, so will be different if I go single phase 220v). The original plan was each bedroom building will have a 15A lighting circuit (on one 110v phase), and a 20A main (on the other 110v phase), and finally a 20A air-conditioning circuit (220V across both phases). Then the main building was 2 x 15A lighting circuits & 2 x 20A ring mains, 20A water heater circuit (doesn't sound enough amps, but this is a heat pump style WH requiring 7A min circuit), 30A water well pump, 30A swimming pool pump. Main breaker for bedrooms = 30A each, main breaker for main house = 70A. Utility feed main breaker at road = 100A. All main breakers would've been double breakers (due to split phase).

FYI here is the site plan, with power coming in at far right. Then coming up the hill (from right to left) you have bed 3, bed 2, pool, main house, bed 1:



FYI elevation:



P.S. Sorry if it seems I am being tight on cable costs! But the cost of cable here is very expensive (maybe it is everywhere, copper? I'm probably out of touch). These are the prices per reel (500ft) from the local hardware store:

2 AWG - $4,650
4 AWG - $3,585
6 AWG - $2,305

Prices are in EC dollars per 500ft, it's about $3.50 to the £ pound sterling so a reel of #2 is £1300 for 500ft/150m. So you can see it will soon add up to a ridiculous budget if I don't get this right!

pc1966 said:

As Lucian says, transformers are an option but rarely justified over modest distances due to the costs involved.

Certainly chaining them and stepping cable size down makes sense to keep overall cable cost to a minimum. Having voltage fluctuations could also be reduced by putting most major loads in the building closes to the incoming supply.

In terms of earth size you have what is known as the adiabatic limit to consider, which is the impact of a short-term fault heating the conductor. So short that you can neglect heat escaping, so it comes down to the I2t term let-through by the circuit breaker or fuse (that is designed to disconnect the fault) heating the conductor's metal. However, you also have to consider that you need the fault current to be big enough that the breaker opens fast, and you get less heating as well as less exposure to an elevated voltage during the fault. This means you need a low enough fault impedance/resistance which can set a lower limit on the conductor size as well.

If you know the circuit parameters (supply voltage, earth loop fault impedance, fuse or breaker characteristics) you can see if a given cable size is OK or not.

As a rule of thumb in the UK, you would have the earth conductor as half the size of the supply conductors for larger circuits (live > 16mm^2 so AWG below #5) and the same size below that, or you do the full adiabatic computation to justify an alternative size.

One way to minimise the cable cost is to consider 3 core SWA cable and to use the armour as the earth. Usually though this will not be low enough resistance to cause fast disconnection on over-current so you would need to have a delay-action RCD (GFCI) supplying the cable set to trip in, say, 0.2s and with a trip current of say 0.3-1A, but not too small so general accumulated leakage from normal operation does not cause it to trip spuriously. These RCD are not cheap, but you might just find the cost works out cheaper than having 4C cable to get a big enough CPC/earth/ground.

Click to expand...

Thanks a lot, that is very helpful. I will do some calcs to work out the earth cable size. I've replied in detail above to the other chap "Lucien" but I am now leaning towards a single phase 220v, and chaining the buildings like you say to keep cable costs down. I've not done calcs yet, but my gut feeling is to have a 2 AWG x 2 wire backbone (plus earth) run straight up the hill (see site plan in reply above). This will run through a junction box on the side of each building which can then spur off into a fuse box for that building.

My only concern about this approach is light flicker. When the water pump kicks in or other inductive loads there tends to be a very large surge current...now normally that wouldn't be an issue with lighting normally being on an independent circuit right back to the main feed... I am wondering if there is a simple solution to put some sort of smoothing device at each building (or on each lighting circuit) to deal with surges and provide temporary smoothing, e.g. a capacitor bank or an inline inductor, or any off the shelf solutions?

Thanks again to you both for taking the time to help me.

EDIT: Having done some quick calcs it looks more like I will need 1 AWG backbone in order to keep voltage drop to 3% when fully loaded. Guess that will keep flickering down too having a little more headroom. Can't get 1 AWG but can get 4 AWG so I'll double up. Would it make a difference if I just paralleled them up, or better to make a ring? (i.e. one 4 AWG daisy chaining up, and the other just running straight back from the furthest building)