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

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

Q p.u %
Tdo
P in p.u
0.2 0.4 0.6 0.8 1 1.2
Relative Stability(σmax)
− 0.4 + 30 − 0.5076 −0.7046 − 1.0904 − 1.4206 − 1.4081 − 1.3942
−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
−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
− 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
− 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
− 30 − 1.6257 − 1.4180 − 1.3539 − 1.3303 − 1.3197 − 1.3134
Minimum damping ratio (ζmin)
− 0.4 + 30 0.4167 0.3952 0.3906 0.3888 0.3877 0.3869
− 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
−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
−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
−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
−30 0.5159 0.4284 0.3734 0.3438 0.3261 0.3148