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Extra resources for Geometrical Methods for Power Network Analysis
U. , as e22 , to a large negative value. The general expression for the minor is not very elegant. Specifically, for r = 0, we find that the surface minor of the LC oscillations becomes unstable with the following value for the limiting minor: 36 5 A Test of Voltage Stability Fig. 14) where P˜2 = 1 − 20ω6 L 3 C 3 − 20ω8 L 3 C 5 + 15ω10 L 4 C 6 + 15ω8 L 4 C 4 − 6ω4 C 3 L − 6ω10 L 5 C 5 − 6ω2 LC − 6ω12L 5 C 7 + 15ω4 L 2 C 2 + 15ω6 L 2 C 4 + ω14 L 6 C 8 + ω12 L 6 C 6 + ω2 C 2 . 2 Volume Stability The determinant of the metric tensor defining voltage stability of the LRC variations has been depicted in Fig.
For the above type of two-component network, the Ricci scalar is given by R= 2 RX r X r . 6) From the hypothesis of power system planning, the intrinsic geometry gives the following local and global stability criteria: • A novel aspect of our proposal is that its methodology allows one to predict both the reliability and the stability of the desired power system and its operation. • For an arbitrary component finite network, the proposed intrinsic geometric formulation shows that reliability corresponds to hyperspace positivity, while stability is determined by positivity of the determinant of the state-space metric tensor.
Tiwari, On the thermodynamic geometry of BTZ black holes. JHEP 0611, 015 (2006); arXiv:hep-th/0606084v1 14. T. Sarkar, G. N. Tiwari, Thermodynamic geometry and extremal black holes in string theory. 3513v1 [hep-th] References 27 15. N. 3402v2 [hep-th] 16. N. 4087v2 [hep-th] 17. N. 4654v2 [hep-th] 18. S. N. Tiwari, On the microscopic perspective of black branes thermodynamic geometry. 3921v1 19. S. N. Tiwari, An exact fluctuating 1/2 BPS configuration. Springer J. High Energy Phys. 5314v1 20. S.