Does the power curve of any wind turbine depend upon the density of air.Either it varies with the air density or the power curve is always constructed on standard air density

A power curve prepared for a particular turbine by a manufacturer will typically state the assumptions made about the air in preparing the power curve. Typically, the air in a power curve would be assumed to be at sea-level atmospheric pressure and probably somewhere around 60 degrees F.

The equation for the available power in moving air is

P = 0.5 x rho x A x V^3

where A is the swept area of the turbine blades, the V represents the velocity of the air, and rho is the density of the air. Therefore, the power curve does depend on air density. Given that the air density depends on the pressure (things such as weather conditions and altitude) and the temperature of the air the available power in the air will change with changes in the aforementioned conditions.

In short, for simplicity power curves make some assumptions and would need to be adjusted to reflect conditions at a certain sight.