Environmental Engineering Reference
In-Depth Information
P
δ
Ω
=
P
mech
+
P
fw
Ω
T
δ
=
syn
(1
−
s
)
syn
(3.9)
P
fw
Ω
syn
(1
T
=
T
δ
−
T
fw
=
T
δ
−
−
s
)
Eventually the efficiency can be calculated:
η
M
=
P
mech
P
el
P
el
P
mech
;
η
G
=
for motor and generator operation
,
respectively
.
3.2.2.5 Per Unit Representation
Often quantities are given in per unit; this is useful for comparing performance
or checking parameters of electrical machines and drives. This has been done in
Fig. 3.6 for current and torque. The concept is to refer a set of independent state
variables to reference values, yielding both variables and parameters as ratios in
dimensionless form, expressed as fraction or in %. The method is widely used in the
field of power generation and distribution. Preferably rated values are chosen as the
reference values.
Use of per unit representation was made for a wind energy converter in the algo-
rithms of 2.3.3.
For application with the induction machine, expressing voltage and currents as
r.m.s. quantities and assuming a three-phase star-connected winding, the reference
values are
U
N
,
I
N
, together with the rated frequency
f
N
or the related angular fre-
quency
ω
N
= 2
π
f
N
. Knowing the number
z
p
of pole pairs, the synchronous angular
speed
N
is also known from (3.1). Then the derived reference values of impedance
Z
N
, apparent power
S
N
torque
T
N
are as follows:
Ω
Z
N
=
U
N
I
N
S
N
Ω
N
;
S
N
= 3
U
N
I
N
;
T
N
=
(3.10)
Also a reference flux linkage
Ψ
N
and a reference inductance
L
N
can be defined:
U
N
z
p
L
N
=
Ψ
N
I
N
Ψ
N
=
;
(3.11)
Ω
N
Usually quantities in per unit are denoted by lower-case letters, e.g.
Z
N
=
3
R
1
I
N
r
1
=
R
1
X
k
Z
N
=
X
k
I
N
;
x
k
=
S
N
U
N
This means that
r
1
is the ohmic loss in the winding resistance referred to rated
apparent power; and
x
k
is the voltage drop on the short-circuit reactance at rated
current referred to rated voltage.
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