Introducing MRAC-PSS-VI to Increase Small-Signal Stability of the Power System after Wind Power Integration

Table 5

The eigenvalues of the system in different DFIG access positions.

Mode	Case	Without the controller			PSS			Dominant states
		λ	f (Hz)	ξ (%)	Λ	f (Hz)	ξ (%)
1	d	−0.652 ± j6.546	1.042	9.908	−0.649 ± j6.546	1.042	9.879	G1, G2
	e	−0.651 ± j6.547	1.042	9.901	−0.651 ± j6.546	1.042	9.899
	f	−0.651 ± j6.547	1.042	9.896	−0.651 ± j6.547	1.042	9.896
2	d	−0.620 ± j6.393	1.017	9.662	−0.620 ± j6.393	1.017	9.656	G3, G4
	e	−0.621 ± j6.393	1.017	9.661	−0.619 ± j6.393	1.017	9.637
	f	−0.620 ± j6.393	1.017	9.654	−0.616 ± j6.392	1.017	9.597
3	d	−0.303 ± j3.128	0.498	9.639	−0.327 ± j2.994	0.476	10.864	G1−G4
	e	−0.302 ± j3.133	0.499	9.591	−0.257 ± j3.079	0.490	8.306
	f	−0.299 ± j3.137	0.499	9.500	−0.290 ± j3.172	0.505	9.121
4	d	−0.807 ± j3.051	0.486	25.571	−0.919 ± j3.063	0.487	28.742	G1−G4, DFIG
	e	−0.791 ± j3.010	0.479	25.419	−0.894 ± j3.147	0.501	27.339
	f	−0.807 ± j3.042	0.484	25.648	−0.892 ± j2.936	0.467	29.075
Mode	Case	PSS-VI			MRAC-PSS-VI			Dominant states
		λ	f (Hz)	ξ (%)	λ	f (Hz)	ξ (%)
1	d	−0.651 ± j6.545	1.042	9.892	−0.760 ± j6.267	0.997	12.030	G1, G2
	e	−0.651 ± j6.547	1.042	9.902	−0.668 ± j6.362	1.012	10.441
	f	−0.651 ± j6.547	1.042	9.896	−0.675 ± j6.351	1.011	10.563
2	d	−0.620 ± j6.393	1.017	9.658	−1.057 ± j6.632	1.055	15.745	G3, G4
	e	−0.619 ± j6.392	1.017	9.645	−1.426 ± j5.550	0.883	24.891
	f	−0.615 ± j6.390	1.017	9.589	−2.198 ± j7.205	1.146	29.187
3	d	−0.366 ± j3.187	0.507	11.405	−0.307 ± j3.048	0.485	10.011	G1−G4
	e	−0.360 ± j3.140	0.500	11.385	−0.303 ± j3.034	0.483	9.926
	f	−0.371 ± j3.059	0.487	12.049	−0.300 ± j3.036	0.483	9.829
4	d	−1.120 ± j2.927	0.466	35.749	−1.421 ± j3.720	0.592	35.692	G1−G4, DFIG
	e	−1.033 ± j2.844	0.453	34.144	−1.187 ± j3.174	0.505	35.035
	f	−1.375 ± j2.814	0.448	43.911	−1.225 ± j3.565	0.567	32.486