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When the system is in balance, with three equal phase currents, there is no current in the neutral 4th wire and it is not needed. However if the load is unbalanced, the neutral is needed to maintain the star point at zero volts.

So for example a street of houses fed by a 3-phase supply needs a neutral because the houses draw unequal currents from the different phase lines, although a large enough collection of houses would tend to balance itself out.

If a three-pase system has equal currents the current in the neutral is zero. If two phases draw equal current but the third has no load, there is an equal current in the neutral, and if one phase draws current but the other two have no load, there is again an equal current in the neutral.

ANOTHER ANSWER

A three-phase, four-wire, system comprises three line conductors and a neutral conductor. If the load supplied by this system is balanced (i.e. the loads connected between each line and neutral are identical in all respects), then no current will flow in the neutral conductor regardless of its impedance. If the load is unbalanced, then a neutral current will flow in the neutral conductor. In other words, the impedance of the neutral conductor plays no part in whether or not there is a neutral current.

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Is instead of neutral wire can you ground it by putting the wire in to earth if yes then why is extra wire used for neutral by eleminating netrual wire cost of transmission can be reduced?

Transmission lines do not use a neutral conductor, so your question isn't actually relevant. Neutral wires are only necessary where imbalance may be large, and under some conditions current may be flowing in the neutral. Under these conditions a low impedance path (the neutral wire) is more desireable than a high impedance path (the ground). In many overhead transmission lines, a fourth or fifth wire are placed above the current carrying conductors; these are shield wires (not neutral wires) and are used to minimize outages on the line due to lightning (the lightning will strike these instead of the phase wires, these will flash over to the structures and the energy will be shorted to ground without the line having to be removed from service). When you're dealing with things that cost ~$100,000 - 2M/mile, it may be worth the added expense of a shield wire to keep it in service as much as possible.


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