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Table 1 Bus voltage angle- and magnitude-based sensitivity analysis for WIS

From: Sensitivity analysis-based performance and economic operation of wind-integrated system with FACTS devices for optimum load dispatch

No. Bus no. Tangent vector for voltage angle Voltage angle sensitivity \(\frac{{\partial \delta_{i} }}{{{\text{d}}\lambda }}\) Tangent vector for voltage magnitude (\(V_{i}\)) Voltage mag. sensitivity \(\frac{{\partial V_{i} }}{{{\text{d}}\lambda }}\)
1 3 0.17206 1.0000 1.0000 1.0000
2 1 0.17119 0.9952 −0.9981 −0.9981
3 8 0.16209 0.9712 −0.9669 −0.9669
4 6 0.16113 0.9253 −0.9571 −0.9571
5 11 0.15792 0.8825 −0.9333 −0.9333
6 2 0.15348 0.8695 −0.8997 −0.8997
7 4 0.15111 0.8313 −0.8649 −0.8649
8 5 0.14881 0.7976 −0.8412 −0.8412
9 14 0.14628 0.7761 −0.8111 −0.8111
10 9 0.13667 0.7123 −0.7939 −0.7939
11 10 0.13419 0.6912 −0.7775 −0.7775
12 7 0.13291 0.6777 −0.7558 −0.7558
13 12 0.12825 0.6485 −0.7113 −0.7113
14 13 0.12344 0.6117 −0.6999 −0.6999