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This paper introduces the notion of chaos synthesis by means of evolutionary algorithms and develops a new method for chaotic systems synthesis. This method is similar to genetic programming and grammatical evolution and is being applied along with three evolutionary algorithms: differential evolution, self-organizing migration and genetic algorithm. The aim of this investigation is to synthesize new and "simple" chaotic systems based on some elements contained in a prechosen existing chaotic system and a properly defined cost function. The investigation consists of eleven case studies: the aforementioned three evolutionary algorithms in eleven versions. For all algorithms, 100 simulations of chaos synthesis were repeated and then averaged to guarantee the reliability and robustness of the proposed method. The most significant results were carefully selected, visualized and commented in this report.

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The transformation of the traditional transmission power systems due to the current rise of non-synchronous generation on it presents new engineering challenges. One of the challenges is the degradation of the inertial response due to the large penetration of high power converters used for the interconnection of renewables energy sources. The addition of a supplementary synthetic inertia control loop can contribute to the improvement of the inertial response. This paper proposes the application of a novel Fuzzy Adaptive Differential Evolution (FADE) algorithm for the tuning of a fuzzy controller for the improvement of the synthetic inertia control in power systems. The method is validated with two test power systems: (i) an aggregated power system and its purpose is to understand the controller-system behavior, and (ii) a two-area test power system where one of the synchronous machine has been replaced by a a full aggregated model of a Wind Turbine Generator (WTG), whereby different limits in the tuning process can be analyzed. Results demonstrate the evolution of the membership functions and the inertial response enhancement in the respective test cases. Moreover, the appropriate tuning of the controller shows that it is possible to substantially reduce the instantaneous frequency deviation.

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