Modeling and simulation of chaotic phenomena in electrical power systems |
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| Authors: | Deepak Kumar Lal K.S. Swarup |
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| Affiliation: | 1. Departamento de Ciencias Integradas, Centro de Estudios Avanzados en Física, Matemática y Computación, Universidad de Huelva, Huelva 21071, Spain;2. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;3. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;4. Departamento de Matemática Aplicada II, E.T.S. Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain;1. CTS, UNINOVA and DEE, Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Caparica 2829 - 516, Portugal;2. Institute of Engineering of Polytechnic of Porto, Department of Electrical Engineering, Porto 4249-015, Portugal;1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. School of Mathematics Sciences, Qufu Normal University, Qufu 273165, China;3. Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor SI-2000, Slovenia;4. Institute of Mathematics, Physics and Mechanics, Ljubljana SI-1000, Slovenia;5. Center for Applied Mathematics and Theoretical Physics, Maribor SI-2000, Slovenia;6. Faculty of Natural Science and Mathematics, University of Maribor, Maribor SI-2000, Slovenia |
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| Abstract: | Modeling and simulation of nonlinear systems under chaotic behavior is presented. Nonlinear systems and their relation to chaos as a result of nonlinear interaction of different elements in the system are presented. Application of chaotic theory for power systems is discussed through simulation results. Simulation of some mathematical equations, e.g. Vander Pol's equation, Lorenz's equation, Duffing's equation and double scroll equations are presented. Theoretical aspects of dynamical systems, the existence of chaos in power system and their dependency on system parameters and initial conditions using computer simulations are discussed. From the results one can easily understand the strange attractor and transient stages to voltage collapse, angle instability or voltage collapse and angle divergence simultaneously. Important simulation results of chaos for a model three bus system are presented and discussed. |
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