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Oscillations have been observed in wind farms with weak grid interconnections. While Texas observes 4 Hz low-frequency oscillations, the west region in China observes subsynchronous oscillations at 30 Hz. Furthermore, this oscillation mode caused torsional interactions with a remote synchronous generator and led to shutdown of the power plant. Inspired by those real-world events, this paper aims to present an analytical model of type-4 wind in weak grids that can demonstrate both low-frequency and subsynchronous frequency oscillations. Critical factors, e.g., the parameters of the phase-locked loop (PLL), are examined using small-signal analysis. The analysis results are validated using a testbed built in MATLAB/SimPowerSystems. Except power electronic switching sequences, the testbed has controls (e.g., wind turbine pitch control, maximum power point control, converter controls), machine dynamics and power system dynamics modeled. This testbed includes a 100 MW Type-4 wind farm, a 600 MW synchronous generator, a long transmission line and a grid. The testbed successfully demonstrates two types of dominant oscillations under different PLLs. In addition, the testbed demonstrates torsional interactions due to the proximity of the subsynchronous mode and one of the torsional modes. [ABSTRACT FROM AUTHOR]