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We prove that virtual friction can stabilize a power grid containing several virtual synchronous machines (VSMs), connecting line impedances and loads. Virtual friction is a torque added to the swing equation of each VSM, proportional to the deviation of its frequency from the overall center of inertia (COI) frequency. Our analysis is based on the network reduced power system (NRPS) model. We support our results with simulations for a two-area network of four VSMs, looking at the transients induced by a change of tie-line impedance and an asymmetric load change. We compare the results for the NRPS model with the corresponding results using detailed models of synchronverters and line impedances. We find that virtual friction has a strong stabilizing effect both for the NRPS model and for the detailed model. Furthermore we show simulation results on the influence of time delays in the communication between the inverters. This communication is used to compute the COI frequency. It turns out that communication delays of less than 100ms have practically no effect on the overall system. [ABSTRACT FROM AUTHOR]

Wind-tunnel experiments were conducted on two symmetric airfoils with different thickness ratios as a test of the ability of Goman-Khrabrov-type models to predict the lift coefficient history during pitching maneuvers. The primary difference between the two airfoils was that the thin airfoil had no hysteresis in its lift curve during quasi-steady maneuvers, but static hysteresis was observed with the thick airfoil over a range of 16 < α < 22 deg. Both airfoils exhibited dynamic hysteresis in the lift coefficient when the wing was pitching. The existence of static hysteresis had a strong effect on the lift response during periodic pitching and must be accounted for in the model. A modified version of the Goman-Khrabrov model was introduced that captured the static hysteresis behavior and the large-scale features of the dynamic hysteresis for the thick airfoil, even when the thick airfoil was in a deep-stall condition. Some deviations between model and experiment were observed at the highest angles of attack, which were attributed to the convection of the dynamic stall vortex and its backwash effect as it leaves the airfoil. [ABSTRACT FROM AUTHOR]

Measurements of the lift coefficient history obtained from a NACA 0018 airfoil undergoing pitching maneuvers with blowing-type active flow control were used to obtain low-dimensional models for control. Disturbance models for the lift response to pitching at different steady-state blowing amplitudes were identified based on a variation of the Goman-Khrabrov model. A plant model for the lift response to sinusoidal blowing amplitude had the form of a time-delay system. The models were used to design a feed-forward controller. The ability of the controller to compensate for lift oscillations during pitching maneuvers was evaluated using a Simulink® model. [ABSTRACT FROM AUTHOR]