Transformation of the circuits and equivalences
1) Property of the symmetrical attice:
to) a bipole place in parallel it is to the longitudinal coppers that cross-sectional of a symmetrical attice pu² to be brought back in parallel to the income or the escape of the attice.
b) a bipole place in series is to the longitudinal coppers that cross-sectional of a symmetrical attice pu² to be brought back in series to the income or the escape of the attice.
2) bisezionabile Net:
It is a net that can be decomposed in two equal semicircuits which are connected between of they for means of conductors, which can be interlaces to you or not.
3) Theorem of Bartlett:
It is always possible to decompose an not interlaced
bisezionabile net in a net to symmetrical attice in which the
longitudinal stiffnesses Zl
are equal to the stiffness 
seen from the income of
the seminet when its escapes are cortocircuitate, while the
cross-sectional stiffnesses Zt
are equal to the stiffness 
seen from the income of
the seminet when its escapes are opened.
It is demonstrated applying the substitution theorem and
therefore closing the net as an example on deu generating of tension Vg1 and Vg2 that does not have necessarily to be equal
because it can applying to the superimposition of the effects us it
can lead back to study the case in which the net it is sluice on two
generators who realize an equal feeding, and the
case in which the net it is sluice on two 
generators that realize one uneven feeding. The
demonstration is carried out in two is made:
to) Calculation of the matrix [ Z ] of one bisezionabile net:
Applying an equal feeding in the conductors who connect
the two seminets current does not slide, therefore the two seminets
can be separated, from
replacing 
but the two equations they say the same thing inasmuch as
the bisezionabile net is symmetrical and therefore 11Z = 22Z and 12Z = Z21 therefore is had 
.
Applying instead an uneven feeding one obtains that every
brace of the conductors who connect the 2 seminets, is found to the
same one upgrades them therefore these can be considers you in short
circuit. The 2 seminets can be separated, from 
replacing 
but the two equations they say
the same thing inasmuch as the bisezionabile net is symmetrical and
therefore 11Z = 22Z and 12Z = Z21 therefore
has 
Adding and embezzling the two it turns out can be obtained 11 Zto you and 22Z and therefore the entire matrix [ Z ] of one bisezionabile net.
b) I find the value of 
and 
for the symmetrical attice:
Applying to the attice an equal feeding, we find 
while applying an uneven feeding we find 
therefore confronting with the result found for the net
bisezionabilesi has 
e 
.
4) Scope of the transformation star-triangle:
To reduce of an unit the number of the nodes, iterando such passage in conjunction with the parallels and the series of stiffnesses, can be reduced in consisting way the circuits pass to you.
5) Value of the admittances YAB , YBC and YAC of the triangle in function of the admittances of the star:
Where YAC is the longitudinal stiffness of the net to triangle while Zc is the stiffness trasversa of the net to star.
The relations are obtained inverting the matrix of
the 
stiffnessesof the
net to star that is equivalent to a net to T , obtaining in such a way the matrix of the
admittances for the net to star and uguagliando it to the matrix of
the admittances of the net to triangle that is equivalent to a net to p and for which 
is had well-known.