using single phase or three phase depends upon the load connected for house hold appliances they run on single phase but industries require three phase power there r no appliances which run on two phase or 4 phase supply
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As we increase the phase, output rating of machine also increases(like output rating of 3ph is 1.5 times more than 1 ph),pulsation in output decreases, this really encourage to have greater phase
BUT this may also lead high generation cost, high transmission cost, and many practical problem. So, we choose something which is beneficial considering both above mentioned criteria. and found 3-ph is best to use.
That's the reason we don't use not only 4ph while any other higher phase system.
There are many home appliances(like bulb n all) which works fine and easier with single phase and we don't have to spent more cost for 3ph wiring in household circuit, So, choose single phase for these.
Differentiating single and double phase is really a big task. As single phase stand alone don't work, it always need neutral(returning path), U may consider it as double phase(L-N).
Sometime split phase distribution is also (which is practiced as in American countries) assumed as double phase supply. Actually a center tap transformer is used having two live wire(at a instant, let L1=120v and L2=-120v)
and one neutral(center tap=0v). Houseshold needed 120v only get supply with neutral and one live wire.
But who needs 240 v got supply through both live wire(120v & -120v). Sometimes this can be referred as double phase........ So, yes double phase is also used
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Continuing my answer...............
I wrote above "Differentiating single and double phase is really a big task. As single phase stand alone don't work, it always need neutral(returning path), U may consider it as double phase(L-N)."
Please ignore it, Its my mistake, I was confused and considered 2 wire system as double phase
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