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

Modeling and control modes of PM synchronous motor drives
3
∗
Pe = pbΩmIm( Ψ
sABC
IsABC
)
(2.40)
2
In dq , frame the active power can be written:
3
Pe = pbΩm( ΨsdIsq −Ψ
sqIsd)
(2.41)
2
For the presented system (Fig. 2.4) the expression for instantaneous reactive power
supplied to the three-phase load system without neutral wire can be calculated as:
1
Q= ( IsAUsBC + IsBUsCA + IsCUsAB
)
(2.42)
3
Introducing the space vector definition into equation (2.42), after some arrangement,
and taking into account the relation: I + I + I = 0, one obtains:
sA sB sC
3 ∗
Q= Im[ U
sABC
IsABC
]
(2.43)
2
In dq , frame the reactive power is expressed as:
3
Q= ( UsqIsd − UsdIsq
)
(2.44)
2
Substituting voltage equation (2.4) into (2.43), adopting Ω
K
= pbΩ m
and made similar
arrangements like for active power calculation, the final expression for reactive power
is:
3
∗
Q= pbΩmRe( Ψ
sABC
I
sABC
)
(2.45)
2
In dq , frame the expression (2.45) for the reactive power becomes:
3
Q= pbΩm ( Ψ
sd
Isd +Ψ
sqIsq
)
(2.46)
2
The important quantity of the drive is the power factor cosφ , which can be calculated
as:
Q
cosφ = (2.47)
S
where S is module of apparent power vector S = P+ jQ:
2 2
S = P + Q
(2.48)
18