Viable Computation of the Largest Lyapunov Characteristic Exponent for Power Systems

Stochastic Differential Algebraic Equations (SDAEs) are used to model power systems. However, there is no universally accepted method to properly evaluate the stability of such models. The theoretical and numerical aspects of the computation of the largest Lyapunov Characteristic Exponent (LCE) for power systems with the inclusion of stochastic processes is discussed as a method to provide a measure of stability. A semi-implicit formulation of power systems is employed in order to exploit parallelism, sparsity and to have low memory requirements. Three case studies are considered, two based on the IEEE 14-bus system as well as a 1,479-bus model of the all island Irish transmission grid.

[1]  Humberto Verdejo,et al.  Stability region and radius in electric power systems under sustained random perturbations , 2015 .

[2]  R. Brayton,et al.  A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas , 1972 .

[3]  A. Bihain,et al.  The mixed Adams-BDF variable step size algorithm to simulate transient and long term phenomena in power systems , 1994 .

[4]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[5]  Sairaj V. Dhople,et al.  Analysis of Power System Dynamics Subject to Stochastic Power Injections , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  W. Kliemann,et al.  Application of linear stability via Lyapunov exponents in high dimensional electrical power systems , 2015 .

[7]  Federico Milano,et al.  Power System Modelling and Scripting , 2010 .

[8]  Federico Milano,et al.  Impact of variability, uncertainty and frequency regulation on power system frequency distribution , 2016, 2016 Power Systems Computation Conference (PSCC).

[9]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[10]  Federico Milano,et al.  Semi-implicit formulation of differential-algebraic equations for transient stability analysis , 2017, 2017 IEEE Power & Energy Society General Meeting.

[11]  S. M. Shahidehpour,et al.  Stochastic Approach to Small Disturbance Stability Analysis , 1992, IEEE Power Engineering Review.

[12]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[13]  M. Crow,et al.  Numerical simulation of Stochastic Differential Algebraic Equations for power system transient stability with random loads , 2011, 2011 IEEE Power and Energy Society General Meeting.

[14]  D. Hill,et al.  Numerical Simulation for Stochastic Transient Stability Assessment , 2012, IEEE Transactions on Power Systems.

[15]  X. Li,et al.  Chaotic behavior observations in a power system model , 2009, 2009 IEEE Bucharest PowerTech.

[16]  Federico Milano,et al.  A python-based software tool for power system analysis , 2013, 2013 IEEE Power & Energy Society General Meeting.

[17]  F. Milano,et al.  A Systematic Method to Model Power Systems as Stochastic Differential Algebraic Equations , 2013, IEEE Transactions on Power Systems.

[18]  H. Chiang,et al.  Effects of the stochastic load model on power system voltage stability based on bifurcation theory , 2008, 2008 IEEE/PES Transmission and Distribution Conference and Exposition.