Partitioning power grids via nonlinear Koopman Mode Analysis

This paper proposes a new method for partitioning power grids based on the nonlinear Koopman Mode Analysis (KMA). Grid partitioning is the fundamental problem in the controlled islanding strategy. The KMA is a new technique of nonlinear modal decomposition based on properties of the point spectrum of the so-called Koopman operator. The key idea in the proposed method is to determine a set of islanded sub-grids using KMA of data on voltage angle dynamics of every bus. The method is numerically investigated with the IEEE 118-bus test system. It is shown that the proposed method provides partitions on a multiple frequency scale as well as captures the intrinsic structural properties of a grid characterized by spectral graph theory.

[1]  V. Vittal,et al.  Slow coherency-based islanding , 2004, IEEE Transactions on Power Systems.

[2]  I. Mezic,et al.  Nonlinear Koopman Modes and Coherency Identification of Coupled Swing Dynamics , 2011, IEEE Transactions on Power Systems.

[3]  I. Mezic,et al.  Nonlinear Koopman Modes and a Precursor to Power System Swing Instabilities , 2012, IEEE Transactions on Power Systems.

[4]  I. Mezić,et al.  Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.

[5]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[6]  R. Moreno,et al.  Security of the power system based on the separation into islands , 2011, 2011 IEEE PES CONFERENCE ON INNOVATIVE SMART GRID TECHNOLOGIES LATIN AMERICA (ISGT LA).

[7]  Kai Sun,et al.  Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods , 2003 .

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

[9]  G.T. Heydt,et al.  Slow-Coherency-Based Controlled Islanding—A Demonstration of the Approach on the August 14, 2003 Blackout Scenario , 2006, IEEE Transactions on Power Systems.

[10]  Kai Sun,et al.  A simulation study of OBDD-based proper splitting strategies for power systems under consideration of transient stability , 2005 .

[11]  M. Fiedler.  A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory , 1975 .

[12]  K. alik.  An efficient k'-means clustering algorithm , 2008 .

[13]  V. Vittal,et al.  System islanding using minimal cutsets with minimum net flow , 2004, IEEE PES Power Systems Conference and Exposition, 2004..

[14]  Hikihara Takashi,et al.  Investigation of Power Grid Islanding Based on Nonlinear Koopman Modes , 2013 .

[15]  Charles A. Desoer,et al.  Basic Circuit Theory , 1969 .

[16]  I. Mezić.  Spectral Properties of Dynamical Systems, Model Reduction and Decompositions , 2005 .

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

[18]  James S. Thorp,et al.  Synchronized Phasor Measurement Applications in Power Systems , 2010, IEEE Transactions on Smart Grid.

[19]  F. Milano,et al.  An open source power system analysis toolbox , 2005, 2006 IEEE Power Engineering Society General Meeting.

[20]  Mohammad Reza Aghamohammadi,et al.  Intentional islanding using a new algorithm based on ant search mechanism , 2012 .

[21]  P. Olver.  Nonlinear Systems , 2013 .

[22]  I. Mezić,et al.  Applied Koopmanism. , 2012, Chaos.