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Table 6 Comparison of damping ratios—Kerala grid with wind and solar power

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

Most associated states Before maximization of renewable generation After maximization of renewable generation After optimization of damping ratio
Complex eigenvalue Damping ratio Complex eigenvalue Damping ratio Complex eigenvalue Damping ratio
vr1_Exc_4, e2q_Syn_3 − 45.1074 ± 4.6881i 0.995 − 45.0517 ± 4.7378i 0.995 1
vr1_Exc_2, e2q_Syn_1 − 45.3261 ± 2.7426i 0.998 1 1
vr1_Exc_3, e2q_Syn_2 − 45.1933 ± 3.5004i 0.997 − 45.0827 ± 3.6811i 0.997 1
omega_Syn_1, delta_Syn_1 − 0.5605 ± 7.6214i 0.076 − 0.5715 ± 7.5274i 0.076 − 0.6046 ± 7.447i 0.082
omega_Syn_2, delta_Syn_2 − 0.3286 ± 8.85i 0.0371 − 0.41918 ± 10.9843i 0.038 − 0.4534 ± 0.9322i 0.042
omega_Syn_3, delta_Syn_3 − 0.2935 ± 7.0098i 0.0418 − 0.35146 ± 7.0287i 0.05 − 0.3113 ± 7.064i 0.047
e1q_Syn_3, vf_Exc_4 − 3.0218 ± 4.0428i 0.599 − 3.0404 ± 4.1021i 0.595 1
e1q_Syn_2, vf_Exc_3 − 0.34682 ± 1.5612i 0.217 − 3.7871 ± 0.77427i 0.98 1
e1q_Syn_1, vr2_Exc_2 1 − 0.6291 ± 0.49498i 0.786 1
omega_Syn_4, omega_Syn_3 − 0.6992 ± 1.7335i 0.374 − 0.39893 ± 2.0688i 0.189 − 0.689 ± 1.7435i 0.375