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

Modeling and control modes of PM synchronous motor drives
2.1.2 Instantaneous power and electromagnetic torque
The three-phase star-connection system without neutral wire is shown in Fig. 2.4. This
is classical configuration for AC motor windings connections.
A
I sA
U sAC
U sAB
B
U sA
Z sC
Z sA
U sAB
Z sB
C
U sBC
I sC
U sC U sB
I sB
Figure 2.4. Three-phase star connection system without neutral wire.
For this configuration the expression for instantaneous active power supplied to load
can be expressed as:
P= UsAIsA+ UsBIsB+ UsCIsC
(2.35)
Introducing space vector definition, after some arrangement and taking into account the
relation: I + I + I = 0, the equation (2.35) can be written as:
sA sB sC
3 ∗
P= Re[ U
sABC
IsABC
]
(2.36)
2
For dq , frame, the equation (2.35) for the active power can be expressed as:
3
P= ( UsdIsd + UsqIsq
)
(2.37)
2
Substituting voltage equation (2.4) into (2.36), and adopting Ω
K
= pbΩmone obtains
3 ∗ d Ψ
[Re(
sABC ∗ ∗
P= RsIsABC IsABC + IsABC − jpbΩmΨ sABCIsABC
)] (2.38)
2
dt
Note that
sABC
sABC
2
s
I I ∗ = I and:
3 2 d Ψ
[ Re(
sABC ∗
∗
P= Rs Is + IsABC ) + Re( −jpbΩmΨ sABC
IsABC
)] (2.39)
2
dt
d ΨsABC
Hence, neglecting the losses in stator resistance R
s
and assuming that = 0 , the
dt
electromagnetic power is expressed:
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