TLDR: Shield excludes dielectric losses and evens the stress on inner dielectric.
Real EE stuff below:
Disagree with answers above (below) about safety aspect. No, it is not for safety. The dominating aspect in power distribution is losses. Having AC electric field contained in predictable space will exclude lossy dielectrics and conductors from participating in dissipation of energy (money).
If cable is not shielded, then for 3 of this in 3-phase line, the surrounding air, concrete, soil will be part of line, acting as lossy dielectric in 100 microfarad AC capacitor stretched for several kilometers and having massive dielectric losses.
In extreme case sharp conductive object next to cable will focus potential gradient lines and peirce dielectric. Shield removes this kind of stress completely. Same stress for field closest to central conductor is excluded by using semiconductor layer.
The mystery is why is it a copper. Possibly, if one do the math, the aluminum or iron will not be as efficient for the same (dielectric loss imunnity) aspect.
Digging firther: If shield is not conductive well enough, then ohmic voltage drop at shield at far point of the line (induced by zero-turn coax transformer + line as capacitor) can get to hundreds volts and cause other troubles. Here you have partly safety and losses covered better with copper than with aluminum.
And perhaps the shield is also have to be grounded and cross connected for 3 cables in few middle points of line for the same "loss reasons" to reduce induced current and shorten the shiled current path as 3 phase trigonometry give such advantage (advantage to create virtual floating ground midway on long line or just real ground).
Another observation: If it is russian customer in Moskow, then there probably is very limited space for power transformers in city, so such cable is economically reasonable, when there is need to deliver relatively low voltage with very high current from the parcels with less land cost to very expensive land parcels.
About zero-turn coax: One power station generator in Ukraine has 50KV/10KA outputs shielded with massive copper tube, opened on one end and grounded to generator's frame. At open end the voltage is about 500V. The AC current of the tube is unknown, but maybe be close to zero or few amperes. If not for this tube, then much higher current induced by open 3-phase capacitor could run through iron rods inside building walls, D/E losses will also heat the concrete walls and melt everything.
Given that safety must always be adequate, you then want
low final resistance,
durability,
low price
in descending order of priority.
If welding cable gives all 3 (as seems likely), use it.
Sheath may not be as resistant to sharp object penetration as TPS but is liable to be more drag and scuff resistant.
Test voltage may not be as high but would, I imagine, be adequate.
If you have a 100+ V battery system then you may well have regulatory requirements to meet re allowable wiring type. Maybe not.
At 130 Amp, 0.1 ohm drops 13V. In a ~ 100 V system that's ~ 13% loss.
Even 0.01 ohm gives say 1.5% loss.
Every 0.01 ohm improvement you can make adds ~= 1.5% to your available energy.
What sort of solar car has 105V, 130A peak specs ~= 14 kW
Sounds like fun.
Best Answer
I think you have a few misunderstandings about wire gauge, voltage, amperage and power.
Wire gauge, or its thickness or cross-sectional area, is directly related to how much current it can carry. The insulation determines how much voltage can be safely used and at what temperatures.
A thicker wire (lower gauge number) can carry more current. This is because it has less resistance. If you are replacing a thin wire with a thick one, you are effectively increasing the amount of current that can be safely carried. There is almost never harm in doing this. This might cause you do wonder: "Why wouldn't the manufacturer use a thicker wire in the first place?" Thicker wires occupy more physical space, cost more, and add additional weight. When manufacturing at high volume, these factors add up, so the manufacturer will select whatever is cheapest that still meets safety requirements. (Unless they don't care about safety requirements, which can happen (fake phone chargers) (teardown video).)
The "length of cable" (wire vs cable) that you have is probably safe if it was used for mains voltages. Again, the voltage that a wire can carry is a function of its insulation, not its gauge. Therefore, using a thicker wire as a replacement is not always a guaranteed safe move, because voltage and insulation properties must be taken into consideration. Wire characteristics, or at least a manufacturer code, are usually printed somewhere on the jacket; look for it when in doubt.
In short, insulation that is sufficient for 230V is more than adequate for your 3.7V application. You don't mention what current will be needed for the device at the lower voltage (nor does the eGo-T web site), so you just need to make sure the wire gauge meets or exceeds the intended current. Current carrying capacity (also known as ampacity) charts can be found online. I would assume since the device used thinner gauge wires, that its current requirements are less than that of the replacement wire.