Two-Point Estimate Method for Probabilistic Optimal Power Flow Computation Including Wind Farms with Correlated Parameters - Intelligent Computing for Sustainable Energy and Environment - page 422

From the Table 1, it can be seen that the 2PEM provides good means and
standard deviations, except few poor standard deviations. Meanwhile, it can also
be noted that the standard deviation average errors are greater than the mean
ones in almost all the cases. It indicates that the accuracy of the point estimate
method deteriorates as the order of the estimated statistical moment becomes
higher.

6 1.4

MCS
2PEM

MCS
MCS fit
2PEM

1.2

5

1

4

0.8

3

0.6

2

0.4

1

0.2

0 0

−2 −1.9 −1.8 −1.7 −1.6 −1.5 −1.4 −1.3 −1.2 −2.5 −2 −1.5 −1 −0.5

PDF of injection real power in no.1 node. CDF of injection real power in no. 1 node

Fig. 2. PDF and CDF of injection real power in no. 1 node with independent param-
eters

6 1.4

MCS
MCS fit
2PEM

MCS
2PEM

1.2

5

1

4

0.8

3

0.6

2

0.4

1

0.2

0 0

−2 −1.9 −1.8 −1.7 −1.6 −1.5 −1.4 −1.3 −1.2 −2.5 −2 −1.5 −1 −0.5

PDF of injection real power in no. 1 node CDF of injection real power in no. 1 node

Fig. 3. PDF and CDF of injection real power in no. 1 node with correlated parameters

For the POPF with independent parameters, from the Fig. 2, it can be found
that the PDF and CDF of injection real power in no. 1 node obtained by the
2PEM coincide with the results obtained by MCS basically. Therefore, the effec-
tiveness and feasibility of the 2PEM are confirmed. For the POPF with corre-
lated parameters, from the Fig. 3, it can be noted that the impacts of considering
the correlated parameters and introducing wind farms on the power system are
existed because the PDF of injection real power obtained by the 2PEM are de-
viated to that by MCS wherein the peak value of PDF of injection real power
in no. 1 node.