Protection and Control of Modern Power Systems

Table 3 Relative stability and minimum damping ratio for ±30% changes in field time constant T_do^’

From: Design of a robust PID-PSS for an uncertain power system with simplified stability conditions

*Q p.u*	% T_do^’	*P in p.u*
*Q p.u*	% T_do^’	0.2	0.4	0.6	0.8	1	1.2
Relative Stability(σ_max)
− 0.4	+ 30	− 0.5076	−0.7046	− 1.0904	− 1.4206	− 1.4081	− 1.3942
− 0.4	−30	−0.7729	− 1.1345	− 1.1350	− 1.1292	− 1.1292	− 1.1121
− 0.2	+ 30	− 1.4266	− 1.1834	− 1.4920	− 1.4981	− 1.4954	− 1.4882
− 0.2	−30	− 1.0820	− 1.1360	− 1.1569	− 1.1628	− 1.1620	− 1.1578
0	+ 30	− 1.7710	− 1.5991	− 1.5876	− 1.5888	− 1.5878	− 1.5834
0	− 30	−1.1817	− 1.1782	− 1.1923	− 1.2009	− 1.2038	− 1.2030
0.2	+ 30	− 2.5395	− 1.8636	− 1.7504	− 1.7163	− 1.7015	− 1.6916
0.2	− 30	− 1.3693	− 1.2740	− 1.2568	− 1.2549	− 1.2547	− 1.2535
0.4	+ 30	− 3.6341	− 2.2863	− 1.9956	− 1.8943	− 1.8479	− 1.8217
0.4	− 30	− 1.6257	− 1.4180	− 1.3539	− 1.3303	− 1.3197	− 1.3134
Minimum damping ratio (ζ_min)
− 0.4	+ 30	0.4167	0.3952	0.3906	0.3888	0.3877	0.3869
− 0.4	− 30	0.3153	0.3003	0.2970	0.2956	0.2947	0.2939
−0.2	+ 30	0.5246	0.4312	0.4050	0.3945	0.3892	0.3861
−0.2	−30	0.3921	0.3272	0.3087	0.3012	0.2973	0.2950
0	+ 30	0.6237	0.4797	0.4308	0.4086	0.3969	0.3901
0	−30	0.4619	0.3638	0.3290	0.3131	0.3046	0.2996
0.2	+ 30	0.7055	0.5240	0.4587	0.4263	0.4081	0.3970
0.2	−30	0.5156	0.3986	0.3517	0.3281	0.3147	0.3065
0.4	+ 30	0.6827	0.5587	0.4836	0.4438	0.4202	0.4052
0.4	−30	0.5159	0.4284	0.3734	0.3438	0.3261	0.3148

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