Skip to main content

Advertisement

Table 2 The eigenvalues, damping ratios and associated states of the IEEE 14 bus system before and after maximization with solar and wind power

From: An enhanced particle swarm optimization algorithm for improving the renewable energy penetration and small signal stability in power system

Before maximization with solar and wind power After maximization with wind and solar power
Eigen numbers Eigenvalues Damping ratio Most associated states Eigen numbers Eigen values Damping ratio Associated states
1 − 1000 1 vm_Exc_2 1 − 1000 1 vm_Exc_2
2 − 1000 1 vm_Exc_1 2 − 1000 1 vm_Exc_1
3 − 99.2985 1 iqr_Dfig_1 3 − 92.859 1 iqr_Dfig_1
4 − 73.0801 1 iq_Spv_1 4 − 68.3848 1 iq_Spv_1
5 − 53.4892 1 id_Spv_1 5 − 56.1733 1 id_Spv_1
6 − 49.9798 1 vr1_Exc_2 6 and 7 − 44.4131 ± 7.7136i 0.985 vr1_Exc_1, e2q_Syn_1, vf_Exc_1
7 and 8 − 44.0346 ± 8.2427i 0.983 vr1_Exc_1, e2q_Syn_2 8 − 36.7227 1 e2d_Syn_1, e2d_Syn_2
9 − 37.0999 1 e2d_Syn_1 9 − 33.2848 1 e2q_Syn_2
10 − 33.1002 1 e2q_Syn_2 10 − 25.6455 1 e2q_Syn_3
11 − 25.6419 1 e2q_Syn_3 11 − 22.3182 1 e2q_Syn_4
12 − 21.3858 1 e2q_Syn_4 12 − 17.855 1 e2d_Syn_2, e1d_Syn_2
13 − 16.7754 1 e2d_Syn_2 13 and 14 − 2.2759 ± 11.6701i 0.191 omega_Syn_2, delta_Syn_2
14 and 15 − 3.3659 ± 9.8278i 0.324 omega_Syn_3, delta_Syn_3 15 and 16 − 3.1892 ± 9.8849i 0.307 omega_Syn_3, delta_Syn_3
16 and 17 − 1.1061 ± 9.3197i 0.118 e1q_Syn_1, vf_Exc_1 17 and 18 − 0.74009 ± 9.4357i 0.078 e1q_Syn_1, vf_Exc_1
18 and 19 − 2.9434 ± 8.7538i 0.319 omega_Syn_2, delta_Syn_2 19 and 20 − 1.3519 ± 7.3681i 0.18 omega_Syn_4, delta_Syn_4, e2d_Syn_4
20 and 21 − 1.0872 ± 7.5138i 0.143 omega_Syn_4, delta_Syn_4 21 − 11.8806 1 e2d_Syn_3, delta_Syn_3,, omega_Syn_3
22 − 12.0538 1 e2d_Syn_3 22 − 11.0187 1 btx1_Spv_1, e2d_Syn_4,
23 and 24 − 10.459 ± 0.03002i 1 btx1_Spv_1, e2d_Syn_4 23 − 9.6637 1 tg_Tg_2,e1d_Syn_2, e2d_Syn_2
25 − 9.5669 1 tg_Tg_2 24 − 9.1454 1 tg_Tg_1, e2d_Syn_4, omega_Syn_
26 − 8.9995 1 tg_Tg_1 25 − 8.5301 1 e2d_Syn_4, e1d_Syn_2
27 − 7.4985 1 e1d_Syn_2 26 − 8.3408 1 e1d_Syn_2, e2d_Syn_2,
28 and 29 − 0.50581 ± 1.9977i 0.245 omega_Syn_1, delta_Syn_1 27 and 28 − 0.34253 ± 2.2326i 0.0757 omega_Syn_1, delta_Syn_1
30 − 2.5454 1 idr_Dfig_1 29 − 2.8708 1 idr_Dfig_1
31 − 0.24538 1 e1q_Syn_4 30 − 0.68888 1 e1q_Syn_4, e1d_Syn_4
32 and 33 − 0.56184 ± 0.38565 0.824 e1q_Syn_2, vf_Exc_2 31 − 0.99054 1 omega_m_Dfig_1
34 − 0.79035 1 omega_m_Dfig_1 32 − 1.0116 1 vr2_Exc_1
35 − 0.89037 1 e1d_Syn_3 33 − 0.82144 1 e1q_Syn_2, e1d_Syn_4, e1q_Syn_3
36 − 0.89365 1 e1q_Syn_3 34 − 0.83365 1 e1q_Syn_2, e1d_Syn_4
37 − 1.0228 1 vr2_Exc_1 35 − 0.89925 1 e1d_Syn_3
38 − 1.0181 1 e1d_Syn_4 36 − 0.90227 1 e1q_Syn_3
39 − 1.0092 1 vr2_Exc_2 37 − 30.303 1 e1d_Syn_1
40 − 1.25 1 e1d_Syn_1 38 − 50 1 vr1_Exc_2
41 − 0.25 1 vw_Wind_1 39 − 1 1 vr2_Exc_2
42 − 0.33333 1 theta_p_Dfig_1 40 − 0.78592 1 vf_Exc_2
     41 − 0.25 1 vw_Wind_1
     42 − 0.33333 1 theta_p_Dfig_1