A port-Hamiltonian approach to power network modeling and analysis

In this paper we present a systematic framework for modeling of power networks. The basic idea is to view the complete power network as a port-Hamiltonian system on a graph where edges correspond to components of the power network and nodes are buses. The interconnection constraints are given by the graph incidence matrix which captures the interconnection structure of the network. As a special case we focus on the system obtained by interconnecting a synchronous generator with a resistive load. We use Park's state transformation to decouple the dynamics of the state variables from the dynamics of the rotor angle, resulting in a quotient system admitting equilibria. We analyze the stability of the quotient system when it is given constant input mechanical torque and electrical excitation.

[1]  P. Moylan,et al.  Lyapunov function for power system with transfer conductances , 1985, IEEE Transactions on Automatic Control.

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

[3]  Leon Y. Bahar,et al.  Energy-like Lyapunov functions for power system stability analysis , 1985 .

[4]  Pravin Varaiya,et al.  A structure preserving energy function for power system transient stability analysis , 1985 .

[5]  V. Henner.  Comments on "On Lyanupov functions for power systems with transfer conductances" , 1974 .

[6]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[7]  Diego Langarica-Córdoba,et al.  A solution to the problem of transient stability of multimachine power systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Arjan van der Schaft,et al.  On port-Hamiltonian Modeling of the Synchronous Generator and Ultimate Boundedness of its solutions , 2012 .

[9]  Romeo Ortega,et al.  A “Globally” Convergent Controller for Multi-Machine Power Systems Using Structure-Preserving Models , 2009, IEEE Transactions on Automatic Control.

[10]  David J. Hill,et al.  Energy Functions, Transient Stability and Voltage Behaviour in Power Systems with Nonlinear Loads , 1989, IEEE Power Engineering Review.

[11]  M. A. Pai,et al.  On Lyapunov functions for power systems with transfer conductances , 1973 .

[12]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[13]  M. Pai.  Energy function analysis for power system stability , 1989 .

[14]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[15]  Alessandro Astolfi,et al.  Transient stabilization of multimachine power systems with nontrivial transfer conductances , 2005, IEEE Transactions on Automatic Control.

[16]  H. Chiang.  Study of the existence of energy functions for power systems with losses , 1989 .

[17]  Stefano Stramigioli,et al.  Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach , 2014 .

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

[19]  Florian Dörfler,et al.  Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators , 2009, Proceedings of the 2010 American Control Conference.

[20]  Libao Shi,et al.  Nonlinear Decentralized Disturbance Attenuation Excitation Control for Power Systems With Nonlinear Loads Based on the Hamiltonian Theory , 2007, IEEE Transactions on Energy Conversion.

[21]  N. Bretas,et al.  Lyapunov function for power systems with transfer conductances: extension of the Invariance principle , 2003 .

[22]  David J. Hill,et al.  Power systems as dynamic networks , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[23]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[24]  P. Kundur,et al.  Power system stability and control , 1994 .

[25]  F.F. Wu,et al.  Direct methods for transient stability analysis of power systems: Recent results , 1985, Proceedings of the IEEE.

[26]  A.R. Bergen,et al.  A Structure Preserving Model for Power System Stability Analysis , 1981, IEEE Transactions on Power Apparatus and Systems.