Wind power outputs from normal wind speed errors to pathological power distributions

The estimated energy production from wind is a key consideration to determine how a wind project will be financed. The input to estimate energy is the wind resource expected. To secure project finance, a thorough evaluation of the uncertainty in the wind resource is needed.?

At the IEA we are always interested in how wind simulation errors propagate through our power modelling software, EnergyMetric. Errors on weather forecasts of wind speed typically follow a normal distribution (the ‘bell curve’).?

However, the non-linear nature of the power curves used to estimate the resulting wind energy produced have the effect of transforming the wind speed errors into a family of non-normal distributions for the power estimates. This can be seen in the following 4 examples:

1. Low wind speeds?

At low wind speeds, the distribution of wind power estimates is truncated to the right as the turbine fails to cut in for the lowest wind speed samples.

2.?Mid wind speeds

As the wind speed increases and enters the ‘ramping’ part of the power curve, the gradient acts to amplify the uncertainty in the wind and the standard deviation of the power estimates increases.

3. High wind speeds

At higher wind speeds toward the top of the ramp, the distribution of wind power estimates is truncated to the left as the turbine maxes out for the highest wind speed samples.

4. Very high wind speeds

Finally, for very high wind speeds close to the turbine limit, the distribution of wind power estimates becomes pathologically bimodal as some samples max and other cut out. Taking the mean of the power estimates as representative here would be very misleading.

Final thought

The analysis above assumes that the power curve is known and can be represented by a nice clean line. In reality, this isn’t the case and a probabilistic model is required. Overlapping Mixtures of Gaussian Processes (OMGP) provide such a model and this will be discussed in a subsequent post.