Want to calculate the energy loss due to unbalance current in the 3 phase star system grounded neutral
Neutral conductors are often made from thinner wire because they're not expected to carry full line current. So you will get some ohmic losses if they do carry high current. However it's much more likely that there is a major problem with the load if it passes high neutral currents and that is far, far more likely to cause losses than heating the neutral wire.
As Tony said, it will cause some ohmic losses based on the resistance of the neutral conductor and the ground path resistance in between that ground point and nearby(other) neutral point ..... But this impact is much less severe than the problems within the network caused by the unbalance ....for example over heating of induction motors and tripping of G/N relay which may further aggravate the problem......
conventionally the neutral should be designed for 10 % of rated current i.e for a normal balanced system , maximum asymmetry in loading is within 10 % .
However , under fault condition the neutral may be subjected to 3 times the rated current . Hence , it is safer to provide neutral conductor cross section equal to the Phase current .
The current in the neutral is a vectorial summation of the current in 3 phases . S, while calculating the loss due to neutral current ha sto involve the current distribution in all the 3 phases and the loss arise in them. The loss and current in the Neutral can not be treated in Isolation .
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