3 phase power generating and delivering is more efficient than 2 phase which in turn is more efficient than 1 phase. Similarly, going up in the number of phases result in increased efficiency as well, i.e. 4 phase is more efficient than 3 phase and 5 phase is more efficient than 4 phase,...etc. The increase of efficiency as the number of phases increase is attributed to that power delivery becomes more continuous as the number of phases increases. A single phase (with resistive load) power delivery will have zero instantaneous power twice a cycle but no zero instantaneous power in the case of 3 phase power and higher phases number with a more smooth power delivery as phases go up. It can be easily calculated to show that 3 phase delivery is about 150% more efficient than single phase. This is the optimum choice as going higher than that the increased efficiency does not justify the increased complexity of using more phases.

I am not sure for the case of Aluminum melting industry which you say it uses 48 phase for melting, I can only make an intelligent guess and let others judge it. Aluminum melting uses induction heating which involves high currents(powers). Hence it may be justified to increase the complexity and use a high number of phases in order to increase the efficiency of the melting process as possible. The complexity can be justified as control is probably using high power diodes and thyristors. It is not like in the case of power generation where having a 3 phase generator/ motor is optimum and more than that means more brushes, sliprings and complex winding for less benefits. Hope I am correct. Thanks @AlDmour.

3 phase power generating and delivering is more efficient than 2 phase which in turn is more efficient than 1 phase. Similarly, going up in the number of phases result in increased efficiency as well, i.e. 4 phase is more efficient than 3 phase and 5 phase is more efficient than 4 phase,...etc. The increase of efficiency as the number of phases increase is attributed to that power delivery becomes more continuous as the number of phases increases. A single phase (with resistive load) power delivery will have zero instantaneous power twice a cycle but no zero instantaneous power in the case of 3 phase power and higher phases number with a more smooth power delivery as phases go up. It can be easily calculated to show that 3 phase delivery is about 150% more efficient than single phase. This is the optimum choice as going higher than that the increased efficiency does not justify the increased complexity of using more phases.

I am not sure for the case of Aluminum melting industry which you say it uses 48 phase for melting, I can only make an intelligent guess and let others judge it. Aluminum melting uses induction heating which involves high currents(powers). Hence it may be justified to increase the complexity and use a high number of phases in order to increase the efficiency of the melting process as possible. The complexity can be justified as control is probably using high power diodes and thyristors. It is not like in the case of power generation where having a 3 phase generator/ motor is optimum and more than that means more brushes, sliprings and complex winding for less benefits. Hope I am correct. Thanks @AlDmour.

Thank you sir I had confusion regarding multiple of 3 i.e. 6,12 or higher lines and after analyzing for higher phases , power transfer curve would be a drooping one e.g. 6 phases would add twice power than three phases but 12 phases do not add power double than that of 6 phases. Also higher phases would cause more constrain at grid.

PLEASE comment if I am correct or add suggestion.

As for aluminium melting I think thyristor diode arrangement can work.

thanks

Going from 1 phase to 3 phase gives efficient improvement by 50% increase (which can be utilized toward reduced copper by 75%). Increasing the number of phases arbitrary more than that (infinite) can only increase efficiency very little (some thing of the order of 7%). This is efficiency comparison only. In any case using 3 phase you can get 3 times the power of the single phase (if you generate same voltage and current in any one phase as that of a 1 phase generator) and so on. I can't see how 6 phase/12 phase are different on this. Thanks. @AlDmour.

Also, Neeraj, one more thing to add: There are LOCAL power delivery networks, and even smaller LOCAL ones. I even have a transformer in front of my house for a delivery from a higher voltage that was delivered to the front my house (by the electric company), into my house. This is as "local" as it will get !

Deliveries over long distances are done by using very high voltages (600 KV etc ...) to prevent high amperages, causing excessive copper losses. However, Local deliveries require local transformers that reduce the voltage. These local deliveries can be done using different phases, etc ...

When you say 48 phases, this could very well be a localized delivery network specialized for an industrial complex requiring extremely high amperages (e.g., for induction ovens). Such SPECIALIZED deliveries could be achieved with more phases to provide the smoothness of the delivery that Ismat is talking about. My guess is this:

A local transformer station just before the industrial complex "aggregates" 16 transformers, with 3 phases each, and delivers the power using a single 48-phase. This will allow the industrial complex to reduce the amperages it is requiring by 16x, thereby significantly reducing the copper losses. At the same time, the deliveries INTO THIS AGGREGATION STATION are really only being done by the industrially-standard three-phase deliveries.

3phase to 6phase(3==>3*2)

6phase to 12 phase(6==>6*2)

12phase to 24phase(12==>12*2)

24phase to 48phase(24==>24*2)

higher you go more Numbers of bus and conductors

Aluminium industry requires DC power at around 5 V, 70 kilo Ampere per furnace. Normally large number of furnaces are connected in Series, requiring DC voltage 5V multiplied by number of furnaces. In these industries, it is desired to control the ripple factor which ultimately requires multi phase transformer for rectification. Though the factory atmosphere has presence of large DC flux density- you can in fact hang several coins in series. This DC flux density is not so harmful as the AC flux density, which can be minimised by minimising ripple contents. A three phase can be converted into multi phase system using several transgormers. you can refer Power Electronics book by G.K. Dubey

For 3 Phase system the phase angel between transmission line is 360/3=120 Degree. As the number of phase increases the phase difference will decrease and more number of times transposition is required. It affects the Installation cost of transmission of Transmission towers.

Three phases systems are really more efficient than single and two phases system. However, behind of all the industry of electricity there is a constant need in teaching basics in electricity to all the future electricians and even future electrical engineers. In this context, try to teach to someone a system with a number of phases higher than three .Soon you will discover that whereas for the three phase systems there are only two voltages : Line voltage and phase voltage, things will increase exponentially in complication for four phases and others with more phases. Thus, unless you may consider as feasible to pay for a doctor to install your home facilty, be sure that teaching is an important process for making alive the industry of electricity. Therefore, systems with more than 3 phases are like very complicate and thus no one will be interested in adopting it.

There is no reason besides this !