Güç sistemlerinde ferrorezonans olayının çok çözünürlüklü dalgacık analizi ile incelenmesi ve doğrusal olmayan dinamiklerinin çıkartılması

Power systems are one of the most important infrastructures of a country. The healthy working condition of a power system is crucial. Utilities are making great effort in order to keep the power systems healthy. Nevertheless, it is not always possible to keep these conditions. Power systems face many incidents. As the systems are usually located outdoors, they are very vulnerable to the enviromental effects which can cause serious damage. In addition, the physical parameters of the power system equipment can affect the system operation. Ferroresonance is one of the incidents that power systems might face. It is defined as well as the interaction between the nonlinear inductance and capacitance of the system. In the power system, nonlinear inductance stands for the transformer core and the capacitance is the power line capacitor. Main causes of ferroresonance are short circuits, capacitor switching, transformer switching, insulation faults, lighting, turning the load off suddenly and switching out the transmission line. It is an unpredictable phenomenon and its consequences are destructive. Over voltages, over currents and harmonic frequency components are main results of this phenomenon. This PhD thesis is focused on identifying the ferroresonance phenomenon and its nonlinear dynamics. In the introduction chapter, the motivation for this study in several studies in the literature is given. Although ferroresonance was studied on power transformers, it is not common to take into consideration all power system component. Previous studies mostly focus on change of transformer parameters. On the other hand, it is not the case on an actual power system as it is not possible to change these parameters. By increasing in the usage of condition monitoring and data collecting systems on power systems, improving new techniques become a necessity. The ferroresonance data are nonstationary and wavelet transform is a powerful tool for analysing this type of data. In this study, the harmonic frequency components are identified by multi resolution wavelet transform in order to interpret related nonlinear dynamics. In addition, related literature survey can be found in introduction chapter. In the second chapter, theoretical bakcground of ferroresonance phenomenon is described. First, the difference between classical resonance circuits and ferroresonance is described. The equivalent circuits for ferroresonance are given and the phenomenon is described in mathematical manners. Even though ferroresonance is unpredictable, there are numerous approaches for preventing and mitigating the phenomenon. These approaches are also explained in this chapter. In the third chapter, mathematical methods and signal processing techniques used in this study are explained. Short time Fourier transform, multi resolution wavelet transform and Lyapunov exponents are used for identifying ferroresonance and its nonlinear dynamics. Related mathematical background can be found in this chapter. In the fourth chapter, the power system modeling is given. The SIMULINK model, and power system parameters are given briefly. The necessary calculations for the equivalent circuit are identified in this chapter. In the fifth chapter, spectral methods are applied on ferroresonance data. Short time Fourier transform and multi resolution wavelet transform are applied and harmonic frequency components are identified. It is observed that, sub harmonic and quasi periodic harmonic frequency components are created. In addition, phase portraits are constructed in order to understand the evolution of the system. In the sixth chapter, the largest Lyapunov exponent of the system is estimated. First the dimensions of the system are specified and an estimation method is utilized. As the largest Lyapunov exponent is estimated to be greater than zero, further calculations are applied and by using cross recurrence plots. In the seventh chapter, nonlinearities calculated by multi resolution wavelet analysis are checked by ordinary differential equations. A new approach for the hysteresis curve is given and it is proven that, the new approach is as useful as the classical approach for modeling the nonlinear curve. The sub harmonic and quasi periodic harmonic frequency components are used as driving force frequencies for differential equations. The phase portraits are plotted seperately and it is proven that, ferroresonance is creating harmonic frequency components. The detailed comments for outputs and novelties of the thesis are explained in conclusions and discussions chapter.