Observation of Chaos in Smart Grid and Stabilization Condition via Generalized Fuzzy Hyperbolic Model

Abstract

As is well known, Smart Grid is a complex nonlinear system whose dynamical behavior has many complicated forms such as low frequency oscillation, subsynchronous oscillation and even chaos. Thus this paper focuses on the chaotic phenomenon of the widely concerned Smart Grid and presents its stabilization condition via establishing generalized fuzzy hyperbolic model. Firstly, the concept of Smart Grid and its characteristic is introduced. The fourth-order model of a typical Smart Grid is put forward in which the wind turbine generator is considered as the distributed generator. According to numerical method, the Lyapunov exponents of the system are calculated. Chaotic phenomenon, which is harmful in power grid is discovered when the system parameters are in a special state. This moment, there is one positive Lyapunov exponent and the sum of all Lyapunov exponents is negative which verifies Smart Grid is in chaotic state. Secondly, because of difficulty in controlling the strong nonlinear chaotic system and universal approximation of generalized fuzzy hyperbolic model, the chaotic Smart Grid system can be approximated by generalized fuzzy hyperbolic model in any precision. Hence, the generalized fuzzy hyperbolic model is established to represent the complex nonlinear system. Controller of the generalized fuzzy hyperbolic model can be designed according to intelligent control theory. Then the complex problem of controlling a strong nonlinear system is converted to a problem of solving a linear matrix inequality (LMI). Finally, numerical simulation is given to demonstrate the effectiveness of the proposed control strategy.