Answer Posted / amol wazalwar

multiphase systems are very much possible but the problem is
the higher cost. we need a minimum of two phases for
production of a rotating magnetic field , this is one of the
reasons why the earliest generation was done in two phases.
But three phase provides us with the optimum compromise
between the power transfer capability and the the cost of
generation and transmission of electricity. i will give you
a brief mathematical derivation of why we use three phase
and not more than three phases.

let us assume a single phase system with the induced and
current I .
power output = E*I
assuming unity pf

for a two phase system , let us suppose that the induced
voltage is still E and current I
per phase voltage in a two phase system = 1/root(2) * E
(with two conductors in series and 90 deg electrically apart.
so power output = 2*1/root(2) * E *I
= root(2) *E*I
= 1.414 EI

for a three phase system , let the induced voltage still be
E and the current I
per phase voltage in a three phase system = 1/2 * E (with
three conductors in series and 120 deg electrically apart.
so power output = 3/2 * E *I = 1.5 EI

thus for a n phase system let the induced voltage still be E
and the current I
per phase voltage in a n phase system = piE/2n
so power output = n * piE/2n * I = 1.57 EI

thus from the above it can be seen that when we move from
single phase to two phase the power delivered increases by
42% then in three phase by 50% and in a n phase or higher
phases maximum by 57 %

thus 3 phase provides the optimum compromise between the
power delivered and the economics of laying n no of wires.

note * - well the last derivation i had given assumes a very
large no of phases. the problem can be visualized as trying
to fit n no of phases in a semicircle with dia as E. so for
a large no of phases emf per conductor can be taken as
length of the semicircle / no of phases
(pi *E/2)/ n
pi E/ 2n

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