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Table 4 Relative stability and minimum damping ratio for ±30% changes in machine inertia constant (M)

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

Q
p.u.
%
M
P in p.u.
0.2 0.4 0.6 0.8 1 1.2
Relative Stability(σmax)
−0.4 + 30 − 0.6026 − 0.9114 −1.2797 − 1.2690 − 1.2551 − 1.2400
− 30 − 0.5956 −0.8983 − 1.2757 −1.2713 − 1.2647 −1.2571
− 0.2 + 30 − 1.2207 − 1.2870 − 1.3128 −1.3186 − 1.3151 −1.3069
− 30 −1.2629 − 1.3023 − 1.3234 −1.3305 − 1.3309 −1.3280
0 + 30 −1.3869 −1.3558 − 1.3678 −1.3758 − 1.3770 −1.3733
−30 −1.4846 −1.3943 − 1.3932 −1.3980 − 1.4001 −1.3994
0.2 + 30 −1.7087 −1.5090 − 1.4679 −1.4577 − 1.4529 −1.4479
− 30 −1.8812 − 1.5722 − 1.5084 −1.4905 − 1.4838 −1.4796
0.4 + 30 − 2.2016 −1.7473 − 1.6206 − 1.5733 −1.5509 − 1.5372
−30 − 2.4677 − 1.8335 −1.6755 − 1.6164 −1.5895 − 1.5748
Minimum damping ratio (ζmin)
−0.4 + 30 0.4230 0.4024 0.3980 0.3960 0.3946 0.3935
−30 0.3089 0.2932 0.2899 0.2886 0.2878 0.2873
−0.2 + 30 0.5275 0.4379 0.4126 0.4023 0.3970 0.3938
−30 0.3870 0.3202 0.3013 0.2937 0.2899 0.2876
0 + 30 0.6247 0.4869 0.4391 0.4173 0.4057 0.3988
−30 0.4554 0.3559 0.3208 0.3048 0.2963 0.2913
0.2 + 30 0.6329 0.5339 0.4689 0.4366 0.4183 0.4071
−30 0.5038 0.3882 0.3419 0.3185 0.3053 0.2972
0.4 + 30 0.6203 0.5748 0.4973 0.4566 0.4325 0.4172
−30 0.5333 0.4135 0.3609 0.3323 0.3151 0.3041