Due to a large share of the modern electrical devices being connected to the power grid through power electronics converters, impedance resonances are an important issue. Namely, certain combinations of inductive and capacitive elements located in a power network may, depending on the network topology, result in substantial increase or decrease of the network impedances. This may result in a parallel or series resonance which is a phenomenon that occurs when a relatively small current injection causes a large voltage drop or a relatively small voltage causes a large current, respectively. A resonance has negative effect on a power network as it shortens the life span of the network components. It is especially critical when the impedance resonance frequency is close to a frequency that a distorted voltage or current signal contains as the amplification of the harmonic components is the largest in this case. The classical harmonic resonance analysis approach using frequency scan and harmonic power flow calculations cannot directly offer enough information for a comprehensive analysis. Because of this, the modal analysis technique, which is addressed in this master's thesis, has been developed in order to bypass the aforementioned limitations.
The fundamental step of the harmonic resonance mode analysis is eigen-decomposition of network admittance matrix. This enables the individual study of different resonance phenomena. The key steps of the analysis are as follows. Admittance matrix eigen-decomposition yields the eigenvalues and the eigenvectors, which are used to determine network bus harmonic excitability and observability. The modal sensitivity indices are used next to determine the effect that network parameters have on a modal impedance magnitude and resonance frequency. The calculation is performed using the eigen-decomposition results. Furthermore, the modifications needed in order to perform the series resonance analysis and the modal resonance frequency shift method using Newton's method are presented. In addition to the theoretical overview, the analysis results for different network models are also presented, including demonstrative proposals of the possible parallel harmonic resonance mitigation solutions.
The analysis of the calculation results shows that the modal analysis is an effective tool for the resonance harmonic analysis. Namely, bus participation in different resonance phenomena and network parameter influence on modal impedance charasteristics were successfully evaluated. Moreover, by successful modal resonance frequency shift calculations the possibilities for parallel harmonic resonance has been successfully mitigated.
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