This research focused on the design and dynamic modeling of a broadband electromagnetic Vortex Bladeless Wind Turbine (VBWT) with a non-linear tuned mechanism. Two progressive-rate springs are part of the tunable mechanism, which are connected to two oscillating magnets inside an electromagnetic coil. The Vortex-Induced Vibration (VIV) caused by the wind flow crossing over the oscillating mast is tuned to match the shedding frequency by gradually adjusting the spring stiffness as the wind speed varies. Using the lumped-mass model and Newton formulation, the coupled nonlinear equations of motion for the tunable turbine are derived. The tunable bladeless turbine operates well at high average wind speeds, as demonstrated by numerical data, without experiencing any structural failures (i.e., good damping). The optimum turbine's mechanical fundamental frequency is expressed analytically, with respect to the non-linear stiffnesses and displacement. The numerical evaluations and the analytical results agree rather well. The output power of the tunable turbine reaches its maximum value at a particular non-linear stiffness beyond the threshold. Comparing the 2 m long tunable turbine to a typical bladeless turbine under identical conditions and at higher wind speeds, numerical studies also demonstrate that the output power of the former is superior. For instance, the output RMS power of the tunable turbine is approximately 37.5 W at a wind speed of around 24 m/s, compared to almost zero watts for the traditional VBWT. Strong winds cause a decoupling between the emergence of vortices and the structural oscillation frequency in the case of traditional VIV resonant wind turbines. As lift forces become less significant than drag forces, resonance and oscillation vanish. An ideal external load can help increase the power even more. Conventional small bladeless wind turbines violently oscillate at high wind speeds, which primarily results in uncontrollable resonance and system failure. In contrast, tuned turbines effectively sustain wind speeds beyond 20 m/s. This study proved the viability and benefits of the suggested tuned mechanism to improve the bladeless wind turbine's overall performance at high wind speeds, particularly in urban grounds like Oman (i.e., 16-31 m/s). To boost the harvester output power and expand the bandwidth frequency, a subset of the geometrical parameters of the suggested harvester are optimized using the fundamental Cat Swarm optimization algorithm (CSO). It has been discovered that the recommended harvester's maximum power, when operating at its third natural frequency, is roughly 37.5 W. This can be achieved by optimizing the harvester's physical parameters using a variety of objectives or fitness functions.