It must also be noted that wind turbines, unlike other forms of electricity production, are designed to generate under a spectrum of power levels [5], and thus must contend with transient loads within their drivetrains. A commonly used means to estimate the power-producing ability and drivetrain loads is to assume that it operates under a certain wind speed distribution. The distributions that are frequently used are Weibull (Fig. 18.5) and Rayleigh distributions [23, 24]. To determine the number of cycles of a drivetrain component at a given load, it is important to determine the total number of hours per year for a particular wind speed. This is done by finding the probability of a particular wind speed for the desired distribution and multiplying it by the number of hours per year. The probability that the wind lies between two wind speeds is given by

Fig. 18.5 Histogram of predicted and observed wind speeds, from [25]

where Pr is the probability function, and p(u) is the probability density function. For the Rayleigh distribution, the probability density function is given by

4 Ua

where ua is the average wind velocity. From this, the number of hours that a wind turbine is operated at a given speed is estimated as

where 8760 represents the total number of hours in a 365-day year [24]. From this analysis, designers can implement a damage criteria such as Palmgren-Miner's rule (as discussed in Sect. 18.5.2.4) to estimate the fatigue lives of components such as gears and bearings.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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