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Extra info for Geometrical Methods for Power Network Analysis
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S. Reall, General supersymmetric AdS5 black holes. JHEP 0404P, 048 (2004); arXiv:hep-th/0401129v3 42. I. P. Warner, One ring to rule them all ... and in the darkness bind them?. Adv. Theor. Math. Phys. 9P, 667–701 (2005); arXiv:hep-th/0408106v2 43. P. B. Gutowski, General concentric black rings. Phys. Rev. D 71, 045002 (2005); arXiv:hep-th/0408122v3 44. S. Ferrara, R. Kallosh, A. Strominger, N = 2 extremal black holes. Phys. Rev. D 52, R5412– R5416 (1995); arXiv:hep-th/9508072v3 45. A. Strominger, Macroscopic entropy of N = 2 extremal black holes.
Compensation must therefore be provided for all the transmission lines except the first line. In this case, this illustrates the physical quantification of the fluctuations shown in the Figs. 3. Chapter 6 Phases of Power Network In this chapter, we describe the intrinsic geometric design of power flow and the parametric stability of power networks by focusing our attention on the admissible values of the parameters {L , C, R} for the real power flow, the imaginary power flow, and their arbitrary linear combinations as the unified description of the network power flow.
Furthermore, an extension of the present investigation could be made for general finite network configurations by defining the effective Hessian gi j = Di D j P(xi ) of the net power. The analogy follows from intrinsic manifolds and moduli space geometry in string theory [51–56]. Although the underlying physical interpretations of network theory may not remain quite the same as those of the chosen component network configurations, it should be noted that the parameters defining the underlying parameter manifold may not be globally stabilized in general.