Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Modeling and control modes of PM synchronous motor drives
where
U ,
sA, U
sB
U
sC
are the instantaneous stator voltage values, I
sA
I
sB
, I
sC
, are
instantaneous values of the current,
R = R = R = R is the resistance of the stator
s
sA
sB
sC
windings, and ΨsA,
Ψ
sB
and Ψ
sC
are magnetic flux linkages stator windings A, B and
C , respectively.
Using the space vector theory to voltage equations we can written in vector form
where:
U
d Ψ
dt
sABC
sABC
= Rs
I
sABC
+ (2.4)
2 2
U
sABC
= (1 UsA + aUsB + a UsC
) ,
2 2
2 2
I
sABC
= (1 IsA + aIsB + a IsC
) ,
sABC (1
sA
a
sB
a
sC )
3
3
3
stator voltage, current and flux space vectors, respectively.
Ψ = Ψ + Ψ + Ψ are the
The stator winding flux consist of rotor flux and stator flux linkages:
where,
Ψ
sABC
=Ψ
ABC ( s) +Ψ
ABC( r)
(2.5)
⎡ LsA MsAB MsAC⎤⎡IsA⎤
⎢
M L M
⎥⎢
I
⎥
Ψ
ABC( s)
= ⎢ sBA sB sBC ⎥⎢ sB ⎥
⎢⎣ M
sCA
MsCB L ⎥⎢
sC ⎦⎣I
⎥
sC ⎦
(2.6)
⎡
⎤
⎢ cosθ
⎥
r
⎢
⎥
2π
Ψ
ABC ( r)
=Ψ ⎢
PM
cos( θr
− ) ⎥
⎢ 3 ⎥
⎢
2π
⎥
cos( θr
+ )
⎢⎣
3 ⎥⎦
(2.7)
and, θr
is electrical rotor position. Mechanical rotor position is defined as:
θ = p γ
(2.8)
r b m
where: pb
- number of pole pairs, γ
m
- mechanical position.
In equation (2.6) LsA
is the self-inductance of phase A winding, M
sAB
and M
sAC
are the
mutual inductances between A and B phase, A and C phase, respectively. For self and
mutual inductances of B and C phase the same notations used. In (2.7),
Ψ
PM
is the
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