an investigation of dual stator winding induction machines

nth-degree algebraic equations in his D-decomposition method. Here D-decomposition is
applied to determine the boundary of stable and unstable resigns from the system
characteristic equation in system parameter domain.
Consider a real polynomial, which is corresponding to the characteristic equation of a
transfer function,
n
i
F () s a ⋅ = 0
(10.109)
= ∑
i=
0
i s
where, s = σ + jω
is the complex variable and the coefficients a i are the continuous
function of r system parameters p , which is expressed as a a ( p p , L,
p )
388
i
= .
i
1,
2
Then the r-dimensional vector space can be decomposed into sets denoted by
( m n m)
D , − , which represent the polynomial having m zeros with negative real parts
and n − m zeros with positive real parts. Such a decomposition of the parameter space
into sets is called the D-decomposition.
The boundary of the sets D( m n − m)
, consists of surfaces determined by:
a 0,
a = 0
(10.110)
0 = n
The surface determined by a 0 = 0 corresponds to a zero at the origin of the s plane
while the surface determined by a = 0 corresponds to the zero at infinity of the s plane.
The boundary also consists of the surface determined by:
R =
I =
where i
∑
i=
0
n
n
∑
i=
0
a X
i
i
i
i
= 0
a Y = 0
a are the coefficients of ( s)
n
F and
r
(10.111)