Load changes in a microgrid comprising diesel generators and wind turbines cause oscillations in system frequency. In this paper, an analytical model that takes wind generator speed deviation into account is proposed to evaluate the oscillation frequency and damping ratio of the frequency mode oscillation when the wind turbines participate in ancillary frequency control. Because the frequency mode oscillation may excite torsional modes, a complete linearized model comprising the diesel generators and the five‐mass drivetrain of the wind turbine is formulated, and the mode shapes as well as the frequencies and damping ratios of the torsional modes are analyzed. To improve damping for the torsional modes, a constant damping ratio design method is proposed to move the eigenvalues of poorly damped modes to points along a line with a constant damping ratio on the complex plane. Dynamic simulations are performed on the microgrid subject to load changes and wind fluctuations in order to validate the results from mode shape analyses as well as demonstrate the effectiveness of the designed torsional damper.
In this paper, analysis of dipole antenna array with each element loaded with an active device (i.e., two-terminal oscillator) is presented. The analysis is equivalent to solving a multiport network circuit with each port shunt with a twoterminal oscillator and an equivalent exciting source. A characteristic equation with the order of 2N is derived to describe the stability condition of a N-element injectionlocked active antenna array. The Routh-Hunvitz stability criterion is then applied to remove the unstable solutions. Numerical results show that the array performance such
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