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Synchronization of Open Systems: Application to the Lossy Power Grid

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The transient stability assessment of multi-machine power systems has been a deeply explored research area in the power system community. The nonlinear nature of the evolving dynamics warrants distinctive control approaches, of which, the time domain simulations and Lyapunov based methods have been majorly applied for assessment and estimating the regions of attraction. However, these methods find limitations when applied to the lossy power grid and demand different modeling procedures. Treating the lossy grid as an open system aids in addressing the challenging problems of assessing their stability and achieving control. In this context, this paper explores the synchronization of open systems through the first order non-uniform Kuramoto model, which renders equivalence between rotor angle stability and phase synchronization of coupled oscillators. This paper investigates the distributed and decentralized control architectures for lossy networks and highlights the contexts under which they are applicable. The mean field Kuramoto model is central to the application of distributed control, whereas a generic framework for developing potential functions using notions of passivity to exercise decentralized control is also discussed.
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Integrability; Kuramoto Model; Open Systems; Power Grid; Stability; Synchronization

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W. Ren, R. W. Beard, E. M. Atkins, Information consensus in multivehicle cooperative control, IEEE Control Systems, vol. 27, no. 2, pp. 71–82, 2007

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a universal concept in nonlinear sciences (vol. 12, Cambridge university press, 2003).

F. Blanchini and S. Miani, Set-theoretic methods in control (Springer, 2008).

M. Zhu and S. Martínez, Distributed Optimization-Based Control of Multi-Agent Networks in Complex Environments (Springer, 2015).

U. A. Khan, S. Kar, and J. M. Moura, Distributed average consensus: Beyond the realm of linearity, in Signals, Systems and Computers, Conference Record of the Forty-Third Asilomar pp. 1337–1342, IEEE, 2009

L. Moreau, Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic control, vol. 50, no. 2, pp. 169–182, 2005

P. DeLellis, M. di Bernardo, and G. Russo, On quad, lipschitz, and contracting vector fields forconsensus and synchronization of networks, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 3, pp. 576–583, 2011.

M. di Bernardo, D. Fiore, G. Russo, and F. Scafuti, Convergence, consensus and synchronization of complex networks via contraction theory (Complex Systems and Networks, pp. 313–339, Springer, 2016.)

H. K. Khalil, Nonlinear Systems (Prentice-Hall, New Jersey, 1996).

S. C. Savulescu, Real-time stability assessment in modern power system control centers (vol. 42. John Wiley & Sons, 2009).

L. Reznik, O. Ghanayem, and A. Bourmistrov, Pidplus fuzzy controller structures as a design base for industrial applications, Engineering applications of artificial intelligence, vol. 13, no.4, pp. 419–430, 2000.

J. B. Burl, Linear optimal control: H_2/H_(∞ ) methods (Addison-Wesley Longman Publishing Co., Inc., 1998).;2-x

B. S. Chen, C. S. Tseng, and H.-J. Uang, MixedH_2/H_(∞ )fuzzy output feedback control design fornonlinear dynamic systems: an LMI approach, IEEE Transactions on Fuzzy Systems, vol. 8, no. 3, pp. 249–265, 2000

Kulkarni, S., Wagh, S., Singh, N., Challenges in Model Predictive Control Application for Transient Stability Improvement Using TCSC, (2015) International Review of Automatic Control (IREACO), 8 (2), pp. 163-169.

T. Athay, R. Podmore, and S. Virmani, A practical method for thedirect analysis of transient stability, IEEE Transactions on Power Apparatus and Systems, no. 2, pp. 573–584, 1979

A. Bose, Application of direct methods to transient stability analysis of power systems, IEEE transactions on power apparatus and systems, no. 7, pp. 1629–1636, 1984

K. Padiyar and K. Ghosh, “Direct stability evaluation of power systems with detailed generator models using structure-preserving energy functions, International Journal of Electrical Power & Energy Systems, vol. 11, no. 1, pp. 47–56, 1989

M. Parimi, S. Kulkarni, S. Wagh, K. Kumar, F.Kazi, and N. Singh, Synchronization andintegrability of N-machine system with transfer conductances, in Power and Energy Society General Meeting (PESGM), 2016, pp. 1–5

F. Dorfler and F. Bullo, Synchronization andtransient stability in power networks and nonuniform Kuramoto oscillators, SIAM Journal on Control and Optimization, vol. 50, no. 3, pp. 1616–1642, 2012

S. Kulkarni, S. Wagh, F. Kazi, and N. Singh, Synchronization and transient stability in multi-machine power system through edge control using TCSC, in Proceedings of the Mathematical Theory of Networks and Systems MTNS, 2014

M. Areak, Passivity as a design tool for group coordination, in American Control Conference, pp. 6, IEEE, 2006

H. D. Chiang, Direct methods for stability analysis of electric power systems: theoretical foundation, BCU methodologies, and applications (John Wiley & Sons, 2011).

C. E. Wayne, An introduction to kam theory:Dynamical systems and probabilistic methods in partial differential equations (Berkeley, 1994), pp. 3–29, 1996.

S. Kulkarni, M. Parimi, S. Wagh, and N. Singh, Decomposition of drift vector field: An application to multi-machine transient stability enhancement, in Power and Energy Society General Meeting (PESGM), 2016, pp. 1–5, IEEE, 2016.

R. Ortega, M. Galaz, A. Astolfi, Y. Sun, and T. Shen, Transient stabilization of multimachinepower systems with nontrivial transfer conductances, IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 60–75, 2005.


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