an investigation of dual stator winding induction machines

dλ
v = R ⋅ i +
(3.58)
dt
where, v , i and λ are the terminal voltage, current flow and flux linkage in each circuit;
R is the matrix of resistance. Applying this general equation to the dual stator winding
induction machine leads to the full model.
3.7.1 Stator Voltage Equation
For the ABC winding set, the stator voltage equation is expressed as:
v = R i + pλ
(3.59)
abc
abc abc
abc
where, R abc is a diagonal 3× 3 matrix, in which the diagonal value depends on the
d
resistances per phase of the ABC winding set; p represents the operator and
dt
⎛v
a ⎞ ⎛ia
⎞ ⎛λ
a ⎞
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
v abc = ⎜v
b ⎟ , i abc = ⎜ib
⎟ , λ abc = ⎜λ
b ⎟ .
⎜ ⎟
⎝v
⎜ ⎟
c ⎠ ⎝i
⎜ ⎟
c ⎠ ⎝ λc
⎠
The flux linkage can be written as the contribution of three components as:
λ = λ + λ + λ
(3.60)
abc s1s1
s1s2
s1r
The first term in equation (3.60) represents the ABC winding set stator flux linkage
due to the ABC winding stator currents, the second term is the flux linkage due to the
XYZ winding set stator currents and the last term is the contribution of the rotor current.
More detailed explanations of each term will be developed separately in the following
sub-sections.
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