Identification of Coherent Generators Using Fuzzy C-Means ...

Table (2) the first proposed coherency measures between generators of 14-Bus system∆δ 1 ∆δ 2 ∆δ 3 ∆δ 4 ∆δ 5∆δ 1 1 0.9342 0.9101 0.3022 0∆δ 2 0.9342 1 0.9755 0.3677 0.0654∆δ 3 0.9101 0.9755 1 0.3912 0.0888∆δ 4 0.3022 0.3677 0.3912 1 0.6975∆δ 5 0 0.0654 0.0888 0.6975 1Table (3) The Elements of convergent membership matrix at the final sampling instant ofthe 3-cluster scheme for 14-Bus system due to ISEδG 1 G 2 G 3 G 4 G 5Cluster 1 0.0094 0.0007 0.0078 1.0000 0.0000Cluster 2 0.0041 0.0003 0.0030 0.0000 1.0000Cluster3 0.9864 0.9990 0.9892 0.0000 0.0000In the cluster group 3, the elements of G 1 , G 2 and G 3 are, respectively, 0.9864, 0.9990and0.9892, and are very close to 1, which proves that they form this cluster. From Table (3)one can derive that there are three cluster groups: Cluster group 1 contains G 4 . Clustergroup 2 contains G 5 . Cluster group 3 contains G 1 , G 2 and G 3 . Table (4) shows the secondproposed coherency measures that represent ISEω.Table (4) the second proposed coherency measures between generators of 14-Bus system∆ω 1 ∆ω 2 ∆ω 3 ∆ω 4 ∆ω 5∆ω 1 1 0.9179 0.8432 0.3331 0∆ω 2 0.9179 1 0.9058 0.3791 0.0368∆ω 3 0.8432 0.9058 1 0.3860 0.0327∆ω 4 0.3331 0.3791 0.3860 1 0.6244∆ω 5 0 0.0368 0.0327 0.6244 1The elements of convergent membership matrix at the final sampling instant of the 3-clusterscheme are sown in Table (5).Table (5) The Elements of convergent membership matrix at the final sampling instant ofthe 3-cluster scheme for 14-Bus system due to ISE ωG 1 G 2 G 3 G 4 G 5Cluster 1 0.010855 0.00080401 0.0092877 1 9.2977e-9Cluster 2 0.98443 0.99888 0.98724 4.4448e-8 1.2494e-9Cluster 3 0.0047113 0.00031601 0.0034753 1.329e-7 1From Table (5) one can derive that there are three cluster groups: Cluster Group 1 containsG 4 . Cluster Group 2 contains G 1 , G 2 and G 3 . Cluster Group 5 contains G 5 . It is derived thatthe obtained results for using ISEω as the coherency measures is the same for using ISEδ asthe coherency measures. Fig. (7) show the clusters group’s centers and the membershipmatrix for each iteration. It is clear that the results obtained by the proposed FCM algorithmare the same results obtained by the first proposed technique. Table (6) shows the12