Two-Point Estimate Method for Probabilistic Optimal Power Flow Computation Including Wind Farms with Correlated Parameters - Intelligent Computing for Sustainable Energy and Environment - page 421

Fig. 1. The 5-bus system connected with wind farms

data were taken as per-unit value and the base value was 100MVA. A computer
program was implemented in MATLAB to solve the POPF problem.
There are 20 identical wind turbines in the wind farms, each of which has
the nominal capacities equal to 600 KW. The parameters of wind farms are
given as follows. ρ =1.2245 Kg/m 3 , A =1840 m 2 . The identical cut-in wind speeds,
cut-out wind speeds and rated wind speeds of wind farms are set as 3m/s,
20m/s, and 14m/s, respectively. The parameters of a wind generator are stator
impedence r 1 + jx 1 =1 . 3883 + j 16 . 6417, rotor impedance r 2 + jx 2 =0 . 6217 +
j 18 . 1767, magnetizing reactance x m = 591 . 18. By simulating (1) with the shape
parameter ( k =2) and the scale parameter ( c =6.7703), 10000 wind speed samples
were generated. Using (2), 10000 wind power outputs were calculated.
The results from MCS were treated as the normorlized values. The average
error indices [3] for 5-bus test system are shown in Table 1, where ε e , ε f are the
average relative errors of real part and imaginary part of nodal voltage, ε P and
ε Q , are the average relative errors of active power and reactive power of nodal
power, respectively. Meanwhile, the PDF and CDF of nodal injection real power
in no. 1 node with independent parameters and with correlated parameters are
shown in Figs. 2-3.

Tabl e 1. Average error indices for 5-bus test system

Average error With independent With correlated
parameters parameters

μ 0.1900 0.1425

ε e (%)

σ

24.1966 22.8479

μ

1.1043 4.3279

ε f (%)

σ

7.0584 11.7695

μ 1.7221 2.1980

ε P (%)

σ 9.9744 17.8061

μ 0.3996 0.5799

ε Q (%)

σ 2.6794 10.6935