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Complexity
Volume 2017, Article ID 3815146, 18 pages
https://doi.org/10.1155/2017/3815146
Research Article

Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

Centre for Non-Linear Dynamics, Defense University, Bishoftu, Ethiopia

Correspondence should be addressed to Karthikeyan Rajagopal; moc.liamg@nayekeihtrakr

Received 16 January 2017; Revised 1 March 2017; Accepted 9 March 2017; Published 13 April 2017

Academic Editor: Viet-Thanh Pham

Copyright © 2017 Anitha Karthikeyan and Karthikeyan Rajagopal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.