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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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