Environmental Engineering Reference
In-Depth Information
where
2
δ
=
K
D
ω
s
/
(
P
N
τ
J
)
and
s
P
N
τ
J
0
=
T
s
0
ω
ν
2
2
0
>
For
ν
δ
it has a conjugate complex solution:
j
2
p
1
,
2
=
−
δ
±
ν
0
−
δ
2
(6.42)
2
which is mostly the case, except for drives with
large inertia values, the system features an electro-mechanical eigenfrequency which
is observed in rotor oscillations. Typical frequency values are a few Hz, their values
decreasing with increasing unit acceleration time.
2
0
Under the condition
ν
>
δ
6.2.3.4 Machine with a Damper Cage
In order to take transient rotor currents into account, the model of Fig. 6.5 must be
amended. The simplest way is to add one damper (amortisseur) mesh on the rotor in
each axis. The equivalent damper windings D, Q are short-circuited. The machine
may then be represented by an equivalent circuit model in d,q-components with five
windings
The voltage equation is an extension of (6.22) and given by:
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
u
d
u
q
0
0
u
f
R
s
i
d
i
q
i
D
i
Q
i
f
ψ
d
ψ
q
ψ
D
ψ
Q
ψ
f
−
ψ
q
ψ
d
0
0
0
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
R
s
0
d
dt
+
d
dt
=
R
D
+
(6.43)
R
Q
0
R
f
The flux linkages are expressed with the reactances as parameters:
⎡
⎤
⎡
⎤
⎡
⎤
ωψ
Q
ωψ
Q
=
X
q
X
mq
X
mq
X
Q
i
q
i
Q
ωψ
d
ωψ
D
ωψ
f
X
d
X
md
X
md
i
d
i
D
i
f
⎣
⎦
=
⎣
⎦
⎣
⎦
X
md
X
D
X
Df
;
X
md
X
Df
X
f
The reactance components are
X
d
=
X
md
+
X
σ s
X
D
=
X
Df
+
X
σ D
=
X
md
+
X
rc
+
X
σ D
X
d
=
X
Df
+
X
σ f
=
X
md
+
X
rc
+
X
σ f
X
q
=
X
mq
+
X
σ s
X
Q
=
X
mq
+
X
σ
Q
;
The model in Fig. 6.6, based on a salient pole machine, contains provisions for
a magnetic leakage flux coupling of field and direct axis damper windings. The
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