Rate-induced transitions and advanced takeoff in power systems.

One of the most common causes of failures in complex systems in nature or engineering is an abrupt transition from a stable to an alternate stable state. Such transitions cause failures in the dynamic power systems. We focus on this transition from a stable to an unstable manifold for a rate-dependent mechanical power input via a numerical investigation in a theoretical power system model. Our studies uncover early transitions that depend on the rate of variation of mechanical input. Furthermore, we determine the dependency of a critical rate on initial conditions of the system. Accordingly, this knowledge of the critical rate can be used in devising an effective control strategy based on artificial intelligence (AI).

[1]  Apala Majumdar,et al.  Transitions through critical temperatures in nematic liquid crystals. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Peter Cox,et al.  Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  I. Dobson.  Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems , 1992 .

[4]  E. Gopalakrishnan,et al.  Experimental investigation on preconditioned rate induced tipping in a thermoacoustic system , 2017, Scientific Reports.

[5]  Renke Huang,et al.  Adaptive Power System Emergency Control Using Deep Reinforcement Learning , 2019, IEEE Transactions on Smart Grid.

[6]  Peter J. Menck,et al.  How basin stability complements the linear-stability paradigm , 2013, Nature Physics.

[7]  W. Ji.  Hard-limit induced chaos in a fundamental power system model , 2003 .

[8]  A. Feijoo,et al.  A Linear Dynamic Model for Asynchronous Wind Turbines with Mechanical Fluctuations , 2002, IEEE Power Engineering Review.

[9]  Hui Ren,et al.  Early warning signals for critical transitions in power systems , 2015 .

[10]  R. Grondin,et al.  Recurrent neural networks for phasor detection and adaptive identification in power system control and protection , 1995, Proceedings of 1995 IEEE Instrumentation and Measurement Technology Conference - IMTC '95.

[11]  J. Bialek,et al.  Why has it happened again? Comparison between the UCTE blackout in 2006 and the blackouts of 2003 , 2007, 2007 IEEE Lausanne Power Tech.

[12]  Jobst Heitzig,et al.  How dead ends undermine power grid stability , 2014, Nature Communications.

[13]  Peter J. Schmid,et al.  Experimental Investigation of Non-Normality of Thermoacoustic Interaction in an Electrically Heated Rijke Tube , 2015 .

[14]  J. Rinzel,et al.  The slow passage through a Hopf bifurcation: delay, memory effects, and resonance , 1989 .

[15]  Muhammad Aslam Noor,et al.  Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems , 2007 .

[16]  Yoshisuke Ueda,et al.  GLOBAL BASIN STRUCTURE OF ATTRACTION OF TWO DEGREES OF FREEDOM SWING EQUATION SYSTEM , 1999 .

[17]  Michael Egmont-Petersen,et al.  Image processing with neural networks - a review , 2002, Pattern Recognit..

[18]  Sakshi Pahwa,et al.  Abruptness of Cascade Failures in Power Grids , 2014, Scientific Reports.

[19]  S. Blume,et al.  Effects of stressor characteristics on early warning signs of critical transitions and "critical coupling" in complex dynamical systems. , 2017, Chaos.

[20]  J. Kurths,et al.  Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect , 2016, PloS one.

[21]  P. Hines,et al.  Large blackouts in North America: Historical trends and policy implications , 2009 .

[22]  V. Ajjarapu,et al.  Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system , 1991 .

[23]  Jorge L. Moiola,et al.  Bifurcation Analysis on a Multimachine Power System Model , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Dirk Witthaut,et al.  Rotor-angle versus voltage instability in the third-order model for synchronous generators. , 2017, Chaos.

[25]  Marc Timme,et al.  Dynamically induced cascading failures in power grids , 2017, Nature Communications.

[26]  Christopher M. Danforth,et al.  Predicting Critical Transitions From Time Series Synchrophasor Data , 2012, IEEE Transactions on Smart Grid.

[27]  P. Varaiya,et al.  Nonlinear oscillations in power systems , 1984 .

[28]  E. Gopalakrishnan,et al.  Rate Dependent Transitions in Power Systems , 2018, 2018 International Conference and Utility Exhibition on Green Energy for Sustainable Development (ICUE).