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

Modeling and control modes of PM synchronous motor drives
1 π 1 2π
MsAC = MsCA =− LA − LB cos 2( θr + ) =− LA − LB cos(2 θr
+ ) (2.12b)
2 3 2 3
1 1
MsBC = MsCB =− LA − LB cos 2( θr + π) =− LA − LB cos(2θr
+ 2 π)
2 2
1
=− LA −LBcos 2θ
r
2
(2.12c)
Using the space vector theory, the flux linkage
Ψ
sABC
space vector can be written as:
3 3
∗ j2θr
jθr
Ψ
sABC
= ( Lls + LA)
IsABC − LB IsABC
e +Ψ
PM
e
(2.13)
2 2
where,
2 2
(1
sA sB sC )
IsABC
= I + aI + a I ,
3
space vector and conjugate stator current space vector.
2 2 (1
sA sB sC )
I ∗ sABC
= I + a I + aI are the stator current
3
Taking into account that:
Ld = Lls + Lmd
(2.14a)
Lq = Lls + Lmq
(2.14b)
3 3
where, Lmd = ( LA + LB
) , Lmq = ( LA − LB
) are d and q magnetizing inductances and
2
2
are defined as [5].
Finally, equations (2.13) comes as:
where, L
d
, L
q
are d and q inductances.
Ld + Lq Lq −Ld ∗ j2θr
jθ
r
Ψ
sABC
= ( ) I
sABC
− ( ) IsABC
e +Ψ
PM
e
(2.15)
2 2
Space vector form of machine equations (2.4, 2.15) becomes more compact, but the
rotor position dependent parameters still exist in that form of expressions for the stator
flux linkage space vector. Therefore, the space vector model is still not simple to use for
the analysis. A simplification can be made if the space vector model is referred to a
suitably selected rotating frame.
12