In transmission and distribution three phase systems.
Hi Salah,
some time ago I tried to estimate the power losses in a LV distribution grid, under the assumption of electric vehicles' controlled charging, and including an analysis with respect to unbalance load of the three phases. The results were published in a conference paper, and a copy can also be found here: http://www.smartgridcontest.com/attachments/idea_835_118_1308070088.5252_[2].pdf
I hope this might be helpful for you.
Kind regards,
Ioannis
Power loss in line is due to the,resistance offered by line to the flow of current, is equal to,((Current)sqr(Resistance of line). Total resistance of line, is (Resistivity of material)(length of line)/(Cross section area of line). Hence line with small cross section area,and long length will offer high resistance(more voltage drop), also it depends on resistivity of line material means aluminum conductor,line will offer high resistance than cooper. When load is balance the load (equal current in all three phase)star point would be at zero potential, as ground, for the balanced three phase voltages, hence the transmission of power is by three phase three wire or four wire will not make any difference(hence H.V transmission is by three phase three wire,as load is balanced). For distribution net work, as consumers need, single phase supply only for lightning and apliences, supply company give them single phase connection,by equally distributing the load, on all three phase,looking to there demand and time of the day/night,using forth wire the neutral wire,along with phase wire,called three phase fore wire system. Though while giving connection, of consumers the load was calculated,yet some unbalance in load(current) takes place,and hence some unbalanced current needs,flow from neutral,to keep,supply voltage constant,which is vector addition of all three phase currents.
From above discussion it is clear that,the main cause to generate,more loss of power in system is the current flowing from neutral wire, the forth wire.Hence by finding the resistance of neutral wire network,and the neutral current flowing in network,the extra loss can be calculated,which would be different for different system configuration,specially like traction etc.