Some background on Wind Turbines power output.

The dataset [1] consists of two columns each containing 500 floating numbers under the column names speed and power. There are no other features provided. Therefore before I go any further I do a little research into the dataset which may help in understanding and interpreting the relationship between wind speed and power output from a turbine and also in determining what conclusions can be reached based on the dataset alone. The research below also highlights the limitations and uncertainty in predicting power generated from wind turbines using local wind speed data.

Some background to the project was provided in a lecture. In the electricity supply market, the producers usually sell their electricity ahead of time and enter a contract where they agree to produce a certain number of kilowatts of electricity during a particular time frame. The price is negotiated in advance of generating electricity and pushing it onto the supply grid. Wind farms supply electricity to the supply grid and negotiate prices in advance. It is more difficult for wind farms to predict exactly how much electricity they can generate at a future date compared to other electricity producers as their generation of electricity depends on wind power. For this reason predictions can be estimated based on meterological data from a weather prediction agent such as Met Eireann. The aim is to be able to predict that when wind speed is a certain amount that the power produced from the turbines is a certain amount.

The Irish Wind Energy Association (IWEA)[2] is the representative body for the Irish wind industry, working to promote wind energy as an essential, economical and environmentally friendly part of the country’s low-carbon energy future. They note here that in 2018 wind energy provided 29 per cent of Ireland’s electricity. Each quarter, both EirGrid and ESBN publish updated wind farm statistics for Ireland at ESBN Connected Wind Farms. There is currently 4,130 MW of installed capacity in the Republic of Ireland. The amount of electricity a turbine can generate depends on the type of turbine and the wind conditions at any time. There are many different models of turbines that can generate different amounts of electricity. Ireland’s largest wind farm is the Galway Wind Park in Connemara which has 3 MW turbines. Eirgrid’s Smart grid dashboard[3] shows actual and forecast wind generation by day, week and month for all wind farms on the system while WindEurope[4] has some facts and issues about wind energy in Europe, in particular the section on Wind Energy Basics. Wind is caused by three things, the heating of the atmosphere by the sun, the rotation of the Earth and the Earth’s surface irregularities:

Air under high pressure moves toward areas of low pressure – and the greater the difference in pressure, the faster the air flows and the stronger the wind! [4]

Energy is the ability to do work and can be categorised into either kinetic energy (the energy of moving objects) or potential energy (energy that is stored). Wind turbines take the kinetic energy that’s in the wind and convert that kinetic energy into mechanical power which is mostly used in the form of electricity. Wind energy captures the energy of the wind and converts it to electricity and is an alternative to burning fossil fuels. It comes from a natural and renewable resourse and it is clean as it produces no greenhouse gas, emits no air pollutants and uses very little water. A wind turbine is a device that converts kinetic energy from the wind into electricity. Their output ranges from as small as 100 kilowatts to as big as 12 megawatts. This suggests that the power values in the dataset for this project is not in kilowatts but possibly megawatts or may represent a wind farm rather than a single turbine. However this is of no consequence to this project.

According to the https://windeurope.org website [4], there are three main variables determining how much electricity a turbine can produce: wind speed, blade radius and air density. Stronger winds allow more electricity to be produced with higher turbines being more receptive to strong winds. We only have the values for wind speed in the dataset here so will have to assume that the other variables are constant. Wind turbines generate electricity at wind speeds of 4 – 25 metres per second. [4] The same article also outlines what happens when the wind doesn’t blow. A wind farms location is usually chosen purposely and therefore when a wind turbine is not turning it is usually because of maintenance, or because it must be stopped for safety reasons in the case of strong winds or a storm. This should help account for the zero values we see in the dataset. The article does note that while sometimes there might not be enough wind to turn a turbine, the wind energy is not lost as the wind energy can be stored in energy storage systems for later use whenever wind levels are low. This may somewhat complicate the predictions from any machine learning models. The scatter plot above does show power values corresponding to wind speed values below 4 metres per second, with a few of these in the 10 to 15 power value range.

Another article looks at how to calculate power output of wind [5] and notes that most U.S. manufacturers rate their turbines by the amount of power they can safely produce at a particular wind speed, usually chosen between 24 mph or 10.5 m/s and 36 mph or 16 m/s. A formula illustrates the factors important to the performance of a wind turbine and notes that the wind speed V has an exponent of 3 applied to it meaning that even small increases in wind speeds result in a large increase in power. $Power=k.Cp \frac{1}{2}\rho AV^3$ where P = power output in kilowatts, Cp = Maximum power coefficient, $\rho$ is Air density, A = Rotor swept area, V = wind speed in mph, k = 0.000133 a constant to yield power in kilowatts. There are other more complex formulas mentioned in other articles but this is not relevent to this project. Additionally the article notes that although the calculation of wind power illustrates important features about wind turbines, the best measure of wind turbine performance is annual energy output. The difference between power and energy is that power (kilowatts kW) is the rate at which electricity is consumed, while energy (kilowatt-hours kWh) is the quantity consumed.

I came across a blog post [6] that use a linear equation to calculate ideal wind production, where the author notes that modeling results can be enhanced via statistical analysis of hyper-local time series such as meteorological data and energy production data. Each wind turbine manufacturer provides an ideal energy production curve for their turbines. The article provides a brief overview which is taken from another research article [7]. Of particular relevance is that a typical wind turbine has three main characteristic speeds, the cut-in speeds (Vc), rated speeds (Vr) and cut-out (Vs) speeds which explain the s-shaped curve we see for this dataset.

• The turbine starts generating power when the wind speed reaches the cut-in value.
• The rated speed is the wind speed at which the generator is producing the machine’s rated power.
• The power generation is shut down to prevent defects and damage when the wind speed reaches the cut-out speed. It also mentions the differences between the ideal power curves which just describe the potentially maximum output versus reality taking into account many factors as well as measurement variations. In practice, however, wind turbines are never used under ideal conditions, and the empirical power curves could be substantially different from the theoretical ones due to the location of the turbine, air density, wind velocity distribution, wind direction, mechanical and control issues, as well as uncertainties in measurements. [7]

While the ideal power curves simply describe potentially maximum output, accuracy could be improved by using more accurate accurate weather forecasts or various statistical methods such as machine learning. We do not have historical data which we could use for statistical improvements but nor do we have hyper-local forecasts as we don’t know the source or time frame of this particular dataset. Another article notes that real wind turbines do not achieve their theoretical limit as their performance is a function to of aerodynamics and the need to limit power capture once the rated generator power is reached, at ‘rated’ windspeed. The generator power, turbine diameter and bladeshape are optimized based on site characteristics such as annual average wind speed and the wind speed distribution. [8]

Turbine manufacturers measure their turbine’s ‘powercurve’ (the relationship between power output and windspeed) at turbine test sites where it is calculated from 10 minute averaged wind speed ($U=\bar{\mu}$) and power. The typical power curves have an s-shape where at wind speeds less than rated the energy capture is approximately proportional to $U^3$ (known as Region II). At wind speeds above rated, the bladepitch and generator torque are actively controlled to limit the power to the generator’s rated power (Region III). [8]

Variations in atmospheric conditions can lead to changes in turbine power output of 10% or more at the same wind speed. Turbulence and shear and not usually used in the power curves as they are considered difficult to include in turbine power predictions. The article also mentions that because of intermittency in the wind, wind turbines typically produce 20%–40% of their maximum possible output over the course of a year. They note that there is a lot of uncertainty in predicting power generation from a turbine using local wind speed data. If the amount of energy is overestimated then the site might not be as profitable as expected while underestimating the energy available at a site might lead to a site not being developed at all. This study also simulated the aerodynamic forces on the turbines blades and structures using an aerostructuraland simulator and created 1796 10-minute wind fields from a stochastic turbulence simulator. The data from the wind fields from the simulations were used to form a database of 1796 observations of 10-min average power (the response) as a function of wind speed, turbulence intensity, and shear exponent (the forcing). The researchers binned the power data into 1 m s$^{-1}$ wide bins and included a plot (figure 3 in the article) of the power curve which shows a Region II between 0.3 metres per second and about 11.5 metres per second, region III is from end the end of region II up to 25 which correspond exactly with our dataset.

The authors also noted that although the forcing variables are evenly distributed, variance in power is largest near rated wind speed. This sensitivity may result in large variation between predicted power output and observed power output. Furthermore, the mean power generated in simulations that include turbulence is lower than the no-turbulence cases near rated wind speed. At wind speeds below 8 m s$^{-1}$, power increases with turbulence intensity and shear. The increase in power due to turbulence arises because turbulent flow with mean speed U carries more power than laminar flow of the same U. The changes in power output of +/-20% associated with turbulence are approximately half of the change due to a change in wind speed from 7 to 8 m s$^{−1}$. In contrast, at wind speeds just above and below rated speed, increasing turbulence intensity reduces power output as the turbine cannot capture the extra energy that gusts bring, but a short duration slow down to wind speeds below rated results in a loss of energy. As the mean wind speed increases, the total amount of time with the blades pitched toward feather increases and the wind turbine is more often operating at rated power. At wind speeds much greater than rated, larger turbulence intensities are required to reduce the output of the machine to less than rated power, regardless of shear.

The same article next looked at using machine learning to predict power output under different conditions by incorporating turbulence intensity and wind shear into power prediction tools. They note that the power output from the turbine is not a linear function of wind speed and so linear regression is not an appropriate technique. Non-linear regression assumes that the relationships are constant throughout the model space (i.e. power output is always proportional to $U^n$ ), which is incorrect, so non-linear regression is also inappropriate. Also, as multivariate bins only work where the training data includes data in all bins this would be computationally or observationally more expensive. Instead they chose a machine learning technique regression trees for capturing non-linear changes in response to forcing. Regression trees are models that use simple branching question paths to predict an outcome based on inputs. I don’t think this is really an option for this project though as this particular dataset has only a single feature.

The turbines responds differently to changes in shear and turbulence at different wind speeds. In Region II, at wind speeds below 8 m s$^{−1}$, power output increases by up to 10% as turbulence increases or as the magnitude of the shear increases. At wind speeds greater than 8 m s$^{−1}$ and in Region III, the regression tree modeled power is consistent with the simulated power output: power decreases as turbulence intensity increases and shows weak or no dependence on shear.

The article concludes:

simulations suggest and the model clearly demonstrates that the response of the turbine is a complex non-linear function of hub height wind speed, turbulence intensity, and rotor disk shear. At wind speeds below rated speed, the turbine power output is most sensitive to changes in wind speed and speed, turbulence. At rated speed, the turbine is most sensitive to turbulence intensity and shear, and power can change by 10% under typical atmospheric conditions. At wind speeds greater than rated, the turbine responds most to changes in turbulence intensity.

The article also includes a figure of the power curves for different utility-scale wind turbines which all reach higher maximum powers than the values in this dataset. [8] The cut-in speeds quoted here are in miles per hour which can be converted to metres per second by divide by 2.237. Rated windspeed is the wind speed at which a turbine hits its maximum rated power output.

Wikipedia describes wind turbine design as follows:

A wind turbine is designed to produce power over a range of wind speeds. The cut-in speed is around 3–4 m/s for most turbines, and cut-out at 25 m/s. If the rated wind speed is exceeded the power has to be limited. There are various ways to achieve this. All wind turbines are designed for a maximum wind speed, called the survival speed, above which they will be damaged. The survival speed of commercial wind turbines is in the range of 40 m/s (144 km/h, 89 MPH) to 72 m/s (259 km/h, 161 MPH). The most common survival speed is 60 m/s (216 km/h, 134 MPH). Some have been designed to survive 80 metres per second (290 km/h; 180 mph) [9]

Every wind turbine design has a cut-in wind speed, a rated wind speed, and a cut-out wind speed. At the cut-in wind speed, the blades start to turn and a trickle of electricity starts to be produced. Around cut-in, the generator may be used as a motor to help the wind overcome inertia and start the blades turning.[10] The cut-in speed is typically 7 to 9 mph or equivalently to 3 to 4 meters per second. At the rated wind speed, the turbine is able to generate electricity at its maximum, or rated, capacity. The rated speed is usually in the range of 25 to 35 mph (equivalent to 11 to 13.5 metres per second). At the cut-out wind speed, the turbine shuts down to avoid damage. The pitch controllers feather the blades to let the wind flow past them and the rotor hub is braked. The wind usually has to return to a much lower speed, called the cut-back-in wind speed, for a certain amount of time before the turbine will restart. The cut-out speed is generally around 55 mph (24.6 metres per second). The cut-back-in speed is around 45 mph (20 metres per second).[10]

Some notable facts from this research that may be of relevance to this project:

• Wind speed is measured in metres per second. (The actual metrics are not provided in the dataset)
• Wind turbines generate electricity at wind speeds of 4 – 25 metres per second [4]
• A wind farms location is usually chosen purposely and therefore when a wind turbine is not turning it is usually because of maintenance, or because it must be stopped for safety reasons in the case of strong winds or a storm. This would account for the zero values in the dataset.
• Sometimes there might not be enough wind to turn a turbine but the wind energy is not lost as it can be stored up to be used later whenever wind levels are low. This might explain the higher than expected values of power for low levels of wind speed that we see in the dataset.
• Turbines are rated by the amount of power they can safely produce at a particular wind speed, usually chosen between 24 mph or 10.5 m/s and 36 mph or 16 m/s [5].
• In formulas used to illustrate the factors important to the performance of a wind turbine, an exponent of 3 is applied to wind speed. Small increases in wind speeds result in a large increase in power. [5]
• Of particular relevance is that a typical wind turbine has three main characteristic speeds, the cut-in speeds (Vc), rated speeds (Vr) and cut-out (Vs) speeds. This helps explain the s-shaped curve we see for this dataset [7]
  • The turbine starts generating power when the wind speed reaches the cut-in value.
  • The rated speed is the wind speed at which the generator is producing the machine’s rated power.
  • The power generation is shut down to prevent defects and damage when the wind speed reaches the cut-out speed.
• There is a lot of uncertainty around the prediction of power generation from a turbine using local wind speed data.
• Variance in power is largest near rated wind speed and this sensitivity may result in large variation between predicted power output and observed power output.