Attempt to quantify the impact of seasonal air density variation on operating tip-speed ratio of small wind turbines

This study presents the impact of seasonal variation in air density on the operating tip-speed ratio of small wind turbines. The air density, which varies depending on the temperature, atmospheric pressure, and relative humidity, has an annual amplitude of about 5% in Tokyo, Japan. This study quantified this impact using the rotational speed equation of motion in a small wind turbine informed by previous work. This governing equation has been simplified by expanding the aerodynamic torque coefficient profile for a wind turbine rotor to the tip-speed ratio. Furthermore, this governing equation is simplified by using non-dimensional forms of the air density, inflow wind velocity, and rotational speed with their characteristic values. In this study, the generator’s load is set to be constant based on a previous analysis of a small wind turbine. By considering the equilibrium between the aerodynamic torque and the load torque of the governing equation at the optimum tip-speed ratio, the impact of the variation in the air density on the operating tip-speed ratio was expressed using a simple mathematical form. As shown in this derived form, the operating tip-speed ratio was found to be less sensitive to a variation in air density than that in inflow wind velocity.