The flow equations of linear resistive electrical networks

Resistive electrical networks constitute a beautiful example of open, interconnected, large-scale systems, giving rise to an elegant classical mathematical theory, still posing open problems and suggesting important extensions.

[1]  E. Haynsworth,et al.  An identity for the Schur complement of a matrix , 1969 .

[2]  John W. Simpson-Porco,et al.  A Theory of Solvability for Lossless Power Flow Equations—Part I: Fixed-Point Power Flow , 2017, IEEE Transactions on Control of Network Systems.

[3]  Gabriel Kron,et al.  Tensor analysis of networks , 1967 .

[4]  Edward B Curtis,et al.  The Dirichlet to Neumann map for a resistor network , 1991 .

[5]  Arjan van der Schaft,et al.  Characterization and partial synthesis of the behavior of resistive circuits at their terminals , 2010, Syst. Control. Lett..

[6]  John W. Simpson-Porco,et al.  A Theory of Solvability for Lossless Power Flow Equations—Part II: Conditions for Radial Networks , 2017, IEEE Transactions on Control of Network Systems.

[7]  Edward B Curtis,et al.  Determining the resistors in a network , 1990 .

[8]  A. Calderón,et al.  On an inverse boundary value problem , 2006 .

[9]  Francesco Bullo,et al.  Electrical Networks and Algebraic Graph Theory: Models, Properties, and Applications , 2018, Proceedings of the IEEE.

[10]  Arjan van der Schaft,et al.  Modeling of physical network systems , 2015, Syst. Control. Lett..

[11]  James A. Morrow,et al.  Circular planar graphs and resistor networks , 1998 .

[12]  Joost Rommes,et al.  Efficient Methods for Large Resistor Networks , 2010, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[13]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[14]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems Theory: An Introductory Overview , 2014, Found. Trends Syst. Control..

[15]  Florian Dörfler,et al.  Kron Reduction of Graphs With Applications to Electrical Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Francesco Bullo,et al.  Voltage collapse in complex power grids , 2016, Nature Communications.

[17]  Jan C. Willems,et al.  The behavior of resistive circuits , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[18]  Jan C. Willems,et al.  Terminals and ports , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[19]  N. Holmer,et al.  Electrical Impedance Tomography , 1991 .

[20]  S. Zampieri,et al.  On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks , 2014, IEEE Transactions on Power Systems.

[21]  G. Kirchhoff.  Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[22]  Jan C. Willems,et al.  The behavior of linear time invariant RLC circuits , 2010, 49th IEEE Conference on Decision and Control (CDC).

[23]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[24]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems on Graphs , 2011, SIAM J. Control. Optim..