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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