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estimate method with nodal injection mutual correlation. Considering spatially
correlated power sources and loads in [6], a probabilistic power flow model is
constructed, which is then solved using an extended point estimate method.
The multivariate dependent random numbers with any given distribution are
generated in [7]-[8].
Motivated by the above observations, this paper investigates the POPF calcu-
lation including wind farms with correlated parameters which contain loads and
generation powers. The 2PEM and MCS are used to solve the POPF with cor-
related parameters. Finally, to analyze the impacts of correlated parameters on
the power system, the POPF with correlated parameters and with independent
parameters are made on the improved 5-bus test system.
2 Probabilistic Model in Wind Power Generation System
2.1 Wind Turbine Model
In the estimation of long-term wind speed, it is usually modeled as follows [9]:
ϕ
(
v
)=
k
c
(
v
(
v
c
)
k−
1
exp[
c
)
k
]
k>
0
,v>
0
,c>
1)
−
(1)
where
v
represents wind speed, and
φ
(
v
) is the Weibull probability density func-
tion with the shape parameter
k
and the scale parameter
c
.
The wind turbine model can be expressed as follows:
P
m
=
1
2
ρAv
3
C
p
(2)
where
ρ
is the density of air (
Kg/m
3
),
A
is the area swept out by the turbine
blades (
m
2
),
v
is the wind speed (m/s) and
C
p
is the dimensionless power co-
ecient.
C
p
can be expressed as a function of the blade tip speed ratio and be
obtained by interpolation method.
2.2 Induction Wind Generator Model
The induction generator's equivalent circuit can be simplified into
Γ
type
equivalent circuit when induction generator is used in wind farm [9]. In short,
the real power injected into grid and the reactive power absorbed from the grid
generated by induction wind generator can be expressed as
−
U
2
r
2
/s
(
r
2
/s
)
2
+
x
k
P
e
=
−
(3)
r
2
+
x
k
(
x
k
+
x
m
)
s
2
r
2
x
m
s
Q
e
=
−
P
e
(4)
where
x
1
is the stator reactance,
x
2
is the rotor reactance,
r
2
is the rotor resis-
tance,
x
k
=
x
1
+
x
2
,
x
m
is the magnetizing reactance,
s
is the slip of induction
machine,
U
is the generator voltage, respectively.
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