Small-Signal Stability Analysis for Power System Frequency Regulation with Renewable Energy Participation

Table 1

Eigenvalues of the system.

Case	Characteristic root	Fluctuating frequency (Hz)	Damping ratio	Relevant units
Without wind or PV	−0.9789 ± j6.8784	1.0947	0.1408	G1, G2
	−1.2415 ± j7.4895	1.2332	0.1582	G1, G3
	−0.3021 ± j4.1298	0.6573	0.0730	G1, G5
	−0.8243 ± j7.1776	1.0065	0.1292	G1, G8
	−0.5194 ± j7.9844	0.9476	0.0869	G1, G9
	−0.4123 ± j4.4777	0.7937	0.0824	G1, G10
	−0.6512 ± j6.6744	0.8156	0.1260	G2, G3
	−1.1654 ± j6.2732	0.7402	0.2430	G2, G4
	−0.9426 ± j5.0038	1.1116	0.1337	G2, G5
Only wind	−1.1584 ± j7.1777	1.1423	0.1593	G1, G2
	−1.3828 ± j7.9844	1.2707	0.1706	G1, G3
	−0.5108 ± j4.4778	0.7126	0.1133	G1, G5
	−1.0342 ± j6.6744	1.0622	0.1531	G1, G8
	−0.7109 ± j6.2732	0.9984	0.1126	G1, G9
	−0.4223 ± j5.0038	0.7963	0.0841	G1, G10
	−0.6718 ± j5.1594	0.8211	0.1291	G2, G3
	−1.2612 ± j4.8112	0.7657	0.2535	G2, G4
	−1.1018 ± j7.2496	1.1538	0.1502	G2, G5
	−0.4291 ± j0.7962	0.1267	0.4744	G1-G10, DFIG
Only PV	−1.3548 ± j7.5049	1.1944	0.1776	G1, G2
	−1.5051 ± j8.1882	1.3031	0.1807	G1, G3
	−0.7568 ± j4.8878	0.7779	0.1530	G1, G5
	−1.2497 ± j7.0336	1.1194	0.1749	G1, G8
	−1.0015 ± j6.7575	1.0755	0.1466	G1, G9
	−0.5817 ± j5.2695	0.8386	0.1097	G1, G10
	−0.7693 ± j5.3220	0.8470	0.1431	G2, G3
	−1.2929 ± j4.8640	0.7741	0.2569	G2, G4
	−1.2851 ± j7.5551	1.2024	0.1677	G2, G5
	−0.6627 ± j1.1856	0.1886	0.4879	G1-G10, PV
Combination of wind and PV	−1.4818 ± j7.7166	1.2281	0.1885	G1, G2
	−1.5323 ± j8.2336	1.3104	0.1829	G1, G3
	−0.8368 ± j5.0210	0.7991	0.1643	G1, G5
	−1.2958 ± j7.1105	1.1316	0.1792	G1, G8
	−1.0858 ± j6.8981	1.0978	0.1554	G1, G9
	−0.7138 ± j5.4895	0.8736	0.1289	G1, G10
	−0.9275 ± j5.5855	0.8889	0.1638	G2, G3
	−1.4302 ± j5.0927	0.8105	0.2703	G2, G4
	−1.5478 ± j7.9928	1.2721	0.1901	G2, G5
	−0.8182 ± j1.4446	0.2299	0.4928	G1-G10, DFIG
	−0.7283 ± j5.0665	0.8064	0.1423	G1-G10, PV