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In order to analyze harmonic problems effectively, system resonant behavior in addition to harmonic sources has to be concerned. Resonant frequencies are known as the critical frequencies of electrical power systems, where systems could be sensitively excited. Harmonic sources which normally behave like frequency-dependent current sources could excite system parallel resonant frequencies. These results in extremely high overvoltage which could be dangerous to electrical power system elements as well as affect power system operation negatively. Conventionally parallel resonant frequencies will be detected by observing the positions at nodal impedance-frequency curves where impedances are especially high. However, resonant frequencies determined from different nodal impedance-frequency curves might not be identical. Moreover, some resonant frequencies could not be obviously identified. In contrast, system parallel resonant frequencies will be obviously identified at modal impedance-frequency curves in modal coordinate system by using the method of Resonance Mode Analysis or RMA. In modal coordinate system, it is more effective to identify parallel resonant frequencies and also analyze individual resonances. The theory of RMA and its application for determining system resonances in a test system are shown in this paper. As the basis for resonance analysis with RMA in correspondence with switching operations, formulation of the modified nodal admittance matrices for series and shunt power system elements based on the fault matrix method is demonstrated. At the end of this paper, the results of resonance analyses in an Extra High Voltage (EHV) transmission system in Germany at different operating conditions by using the methods presented in this paper are shown and discussed.