Michael Graham - Wind Energy Handbook

According to Cook (1985), a better estimate of the probability of extreme winds is obtained by fitting a Gumbel distribution to extreme values of wind speed squared. This is because the cumulative probability distribution function of wind speed squared is closer to exponential than the distribution of wind speed itself, and it converges much more rapidly to the Gumbel distribution. Therefore, by using this method to predict extreme values of wind speed squared, more reliable estimates can be obtained from a given number of observations.

Figure 2.9 Illustration of the Gumbel method

The design of wind turbines must allow them to withstand extremes of wind speed as well as responding well to the more ‘typical’ conditions described earlier. Therefore the various standards also specify the extremes of wind speed that must be designed for. This includes extreme mean wind speeds as well as various types of severe gust.

Extreme conditions may be experienced with the machine operating, parked or idling with or without various types of fault or grid loss, or during a particular operation such as a shut‐down event. The extreme wind conditions may be characterised by a ‘return time’: for example, a 50‐year gust is one that is so severe that it can be expected to occur on average only once every 50 years. It would be reasonable to expect a turbine to survive such a gust, provided there was no fault on the turbine.

It is always possible that the turbine happens to be shut down on account of a fault when a gust occurs. If the fault impairs the turbine's ability to cope with a gust, for example, if the yaw system has failed and the turbine is parked at the wrong angle to the wind, then the turbine may have to withstand even greater loads. However, the probability of the most extreme gusts occurring at the same time as a turbine fault is very small, and so it is usual to specify that a turbine with a fault need only be designed to withstand, for example, the annual extreme gust and not the 50‐year extreme gust.

For this to be valid, it is important that the faults in question are not correlated with extreme wind conditions. Grid loss is not considered to be a fault with the turbine and is actually quite likely to be correlated with extreme wind conditions.

Clearly the extreme wind speeds and gusts (both in terms of magnitude and shape) may be quite site‐specific. They may differ considerably between flat coastal sites and rugged hill tops, for example.

The IEC standard, for example, specifies a ‘reference wind speed’ V refthat is five times the annual mean wind speed. The 50‐year extreme wind speed is then given by 1.4 times V refat hub height and varying with height using a power law exponent of 0.11. The annual extreme wind speed is taken as 75% of the 50‐year value in the 1999 edition 2 standard, or 80% in the 2004 edition 3 standard.

The IEC edition 2 standard goes on to define a number of transient events that the turbine must be designed to withstand. These include:

Extreme operating gust (EOG): A decrease in speed, followed by a steep rise, a steep drop, and a rise back to the original value. The gust amplitude and duration vary with the return period.

Extreme direction change (EDC): This is a sustained change in wind direction, following a cosine‐shaped curve. The amplitude and duration of the change once again depend on the return period.

Extreme coherent gust (ECG): This is a sustained change in wind speed, again following a cosine‐shaped curve with the amplitude and duration depending on the return period.

Extreme coherent gust with direction change (ECD): Simultaneous speed and direction transients similar to EDC and ECG.

Extreme wind shear (EWS): A transient variation in the horizontal and vertical wind gradient across the rotor. The gradient first increases and then falls back to the initial level, following a cosine‐shaped curve.

These transient events are deterministic gusts intended to represent the extreme turbulent variations that would be expected to occur at the specified return period. They are not intended to occur in addition to the normal turbulence described previously. Such deterministic coherent gusts, however, have little basis in terms of actual measured or theoretical wind characteristics. Therefore in the later editions of the standard, some of the extreme loads are estimated instead by carrying out a large number of simulations and applying statistical extrapolation methods to the peak loads from each simulation. Appropriate probability distributions are fitted to the simulated peaks, and the 50‐year extreme load is estimated from the tail of the distribution – see Section 5.14.

Because of the variable nature of the wind resource, the ability to forecast wind speed some time ahead is often valuable. Such forecasts fall broadly into two categories: predicting short‐term turbulent variations over a timescale of seconds to minutes ahead, which may be useful for assisting with the operational control of wind turbines or wind farms, and longer‐term forecasts over periods of a few hours or days, which may be useful for planning the deployment of other power stations on the network.

Short‐term forecasts necessarily rely on statistical techniques for extrapolating the recent past, whereas the longer‐term forecasts can make use of meteorological methods. A combination of meteorological and statistical forecasts can give very useful predictions of wind farm power output.

The simplest statistical prediction is known as a persistence forecast : the prediction is set equal to the last available measurement. In other words, the last measured value is assumed to persist into the future without any change:

(2.49)

where y k−1is the measured value at step k −1 and is the prediction for the next step.

A more sophisticated prediction might be some linear combination of the last n measured values, that is,

(2.50)

This is known as an n th order autoregressive model , or AR(n) . We can now define the prediction error at step k by

(2.51)

and then use the recent prediction errors to improve the prediction:

(2.52)

This is known as an n th order autoregressive , m th order moving average model , or ARMA(n,m) . This can be further extended to an ARMAX model, where the X stands for an ‘exogenous’ variable: another measured variable that is included in the prediction because it influences y .