Kron Reduction of Generalized Electrical Networks

Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. In this paper we show how to perform Kron reduction for a class of electrical networks without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.

[1]  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.

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

[3]  P. Rowlinson.  ALGEBRAIC GRAPH THEORY (Graduate Texts in Mathematics 207) By CHRIS GODSIL and GORDON ROYLE: 439 pp., £30.50, ISBN 0-387-95220-9 (Springer, New York, 2001). , 2002 .

[4]  Paulo Tabuada,et al.  Kron reduction of power networks with lossy and dynamic transmission lines , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[5]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

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

[7]  M. V Deshpande,et al.  Electrical power system design. , 1985 .

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

[9]  H. W. Dommel,et al.  Techniques for analyzing electromagnetic transients , 1997 .

[10]  M. Pavella,et al.  Transient stability of power systems: Theory and practice , 1994 .

[11]  Hadi Saadat,et al.  Power System Analysis , 1998 .

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