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A Novel Analysis Method Based on Quadratic Eigenvalue Problem for Multirelay Magnetic Coupling Wireless Power Transfer

To simplify the analysis process of the multirelay magnetic coupling wireless power transfer system, a novel analysis method based on the quadratic eigenvalue problem (QEP) has been proposed. The second-order underlying equation of the system is given. The eigensolution represents the inherent properties of the entire system and provides important and useful information. The analytical solutions of currents induced in each coil are expressed in terms of the eigensolution of the corresponding QEP. Real parts and imaginary parts of the eigenvalues represent attenuation coefficients and system resonance frequencies, respectively. The effect of the load resistance on the eigenvalues is studied. It is found that the attenuation coefficient of an eigenvalue increases as the load resistance increases so that it can be ignored. The relationships between eigenvalues and some key frequencies are discussed, such as system resonance frequencies, zero-phase angular frequencies, and constant voltage/current frequencies. The results show that fixed zero-phase angular frequencies and constant current frequencies are equal to the imaginary parts of the eigenvalues with load resistance is equal to zero, and the constant voltage frequencies are equal to the imaginary parts of the complex eigenvalues in a strong damping stage. Finally, experimental results verify the theoretical analysis.