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

Table 4

The eigenvalues of the system in different tie line power conditions.

Mode	Case	Without the controller			PSS			Dominant states
		λ	f (Hz)	ξ (%)	λ	f (Hz)	ξ (%)
1	a	−0.671 ± j6.550	1.042	10.195	−0.671 ± j6.550	1.043	10.196	G1, G2
	b	−0.643 ± j6.542	1.041	9.790	−0.644 ± j6.542	1.041	9.789
	c	−0.618 ± j6.502	1.035	9.465	−0.618 ± j6.502	1.034	9.466
2	a	−0.589 ± j6.404	1.019	9.154	−0.583 ± j6.401	1.019	9.079	G3, G4
	b	−0.637 ± j6.386	1.016	9.921	−0.631 ± j6.383	1.016	9.839
	c	−0.704  ± j6.350	1.011	11.021	−0.697 ± j6.348	1.010	10.920
3	a	−0.295 ± j3.289	0.524	8.919	−0.259 ± j3.293	0.524	7.827	G1−G4
	b	−0.305 ± j3.031	0.482	10.039	−0.386 ± j3.055	0.486	12.539
	c	−0.343 ± j2.314	0.368	14.672	−0.432 ± j2.354	0.375	18.038
4	a	−0.513 ± j3.063	0.488	16.518	−0.513 ± j3.407	0.542	14.877	G1−G4, DFIG
	b	−0.512 ± j3.056	0.486	16.524	−0.379 ± j3.379	0.538	11.159
	c	−0.503 ± j3.028	0.482	16.387	−0.389 ± j3.390	0.540	11.412
Mode	Case	PSS-VI			MRAC-PSS-VI			Dominant states
		λ	f (Hz)	ξ (%)	λ	f (Hz)	ξ (%)
1	a	−0.671 ± j6.550	1.043	10.195	−0.628 ± j6.355	1.011	9.827	G1, G2
	b	−0.644 ± j6.542	1.041	9.789	−0.679 ± j6.335	1.008	10.669
	c	−0.618 ± j6.502	1.035	9.464	−0.746 ± j6.312	1.004	11.730
2	a	−0.589 ± j6.404	1.019	9.154	−1.059 ± j5.414	0.862	19.204	G3, G4
	b	−0.637 ± j6.386	1.016	9.920	−0.959 ± j5.660	0.901	16.713
	c	−0.704 ± j6.350	1.011	11.021	−1.153 ± j6.356	1.011	17.846
3	a	−0.293 ± j3.290	0.524	8.879	−0.297 ± j3.191	0.508	9.278	G1−G4
	b	−0.304 ± j3.034	0.482	9.970	−0.305 ± j2.928	0.466	10.345
	c	−0.342 ± j2.321	0.369	14.589	−0.332 ± j2.194	0.349	14.978
4	a	−0.687 ± j3.489	0.555	19.319	−1.050 ± j3.495	0.556	28.783	G1−G4, DFIG
	b	−0.689 ± j3.476	0.553	19.467	−1.081 ± j3.496	0.556	29.563
	c	−0.689 ± j3.431	0.546	19.694	−0.946 ± j3.281	0.522	27.713