Fractional Order Chaos Synchronization for Real-Time Intelligent Diagnosis of Islanding in Solar Power Grid Systems

Abstract

Many different methods have been proposed for determining islanding and most of them have drawbacks. The main issue is the difficulty of detecting islanding when the current and voltage values are of the same phase or the frequency remains within the normal range of the grid when islanding occurs. In this study, a non-autonomous Chua's circuit was used to preprocess the grid signal after which a method based on the fractional Lorenz chaotic system and extension theory was used to analyze the preprocessed voltage signal. The capability of a chaotic system to amplify an extremely small signal was effectively utilized for the diagnosis of grid islanding. Simulation results showed that the diagnostic accuracy of the proposed method could be 100% and no other diagnostic method has offered such accuracy. Furthermore, the method proposed in this study is simple, easy to implement, and could be used as a portable system for the real-time monitoring and diagnosis of islanding in a conventional home grid system. detection based on new active disturbance [7] and one for active movement frequency anti-islanding detection [8]. Even though these methods can reduce the time taken to detect islanding, they can also affect the stability of the system or even lead to overall harmonic distortion. Furthermore, if the operating area (for islanding detection) includes other relatively stable power sources connected in parallel such as cogeneration systems. These methods will fail. New algorithms such as the Neural Network Algorithm (NNA) [9] have also been used in detecting islanding. Even though the neural network learns fast, it has a free mode and error tolerance and allows the use of reverse transmission direction to modify the weight and make corrections after repetition. It has a complicated training process that takes a long time. Accurate determinations cannot be made with other algorithms such as Fuzzy Theory [10] or the Genetic Algorithm (GA) [11] when the voltage, frequency, and phase differences are small. The Goertzel Algorithm [12], which is a Discrete Fourier Transformation (DFT) [13], has been recommended in some studies, but the conversion time is long and the width of the Fourier conversion window is fixed. This means that, when the time domain requires high resolution, the harmonic resolution will drop and the method is less than optimal. In 2015, a new, very accurate method has been proposed by Wang et al., which uses the Lorenz integer order [14] to detect islanding. However, many nonlinear systems exhibit fractional-order behavior. Therefore, if the fractional-order concept is considered in the diagnosis system, more accuracy can be obtained with a real physical system. In this study, the use of a non-autonomous Chua's circuit [14] for preliminary processing of the grid signal is described. This is followed by fractional Lorenz chaotic synchronization [15] and the product element model characteristics of the self-synchronization dynamic error are then analyzed. Afterward, the extension method is used to detect th...

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Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

“…The literature is long, but we give a brief presentation. In [1], Cheng et al investigate the synchronization of the fractional Chua's chaotic model. In [2], Chua et al introduce an electrical circuit chaotic model and study the synchronization of this proposed model as well.…”