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q
d
s
e
λ
q
s
θ
ω
e
e
d
s
Fig. 8.
Stator flux vector orientation along the rotating reference frame
Substituting (31) in (29) and (30) with vector control and re-arranging, we obtain (32)
and (33)
L
3
2
*
P
=−
m
v i
(32)
s
s qr
L
s
3
v
2
*
Q
=
s
−
v L i
(33)
s
s
m
dr
2
L
ω
s
s
The rotor voltage equation governing the active and reactive power control can be
obtained by rearranging equation (19)-(26) and is given by (34) and (35)
d
(34)
vr i
=
σ
Li
−ω−ωσ
(
)(
Li
)
dr
r
dr
r
dr
e
r
r
qr
dt
L
d
vr i
=
σ
Li
+ω−ωσ+ω−ω λ
(
) Li
(
)
m
(35)
qr
rqr
r
qr
e
r
rdr
e
r
ds
dt
L
s
Where
L
2
m
σ= −
1
LL
rs
Equations (34) and (35) can be rewritten as (36) and (37) to form the decoupled
control of active and reactive power.
(
k
=+
)
(
)
*
di
*
v
k
i
−−−
i
ωωσ
L i
(36)
dr
dp
dr
dr
e
r
r
qr
s
k
=+
L
(
)
qi
(
)
*
*
m
v
k
i
−−−
i
ωωσ
(
i
−
λ
)
(37)
qr
qp
qr
qr
e
r
r dr
s
s
L
s
where,
k
,
d
k
are the PI proportional and integral constant for the d-axis for the
control of reactive power while gain
dp
k
,
k
are the PI constant for controlling the
qp
qi
i
*
qr
*
dr
active power.
and
i
are the reference current for the active and reactive power
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