Wind Energy Forecasting
By comparison with other renewable energy sources, wind energy is associated with one of the lowest costs of electricity production, the largest resource availability, a level of technical efficiency presently mature enough to create a substantial contribution, and a strong political intent for expansion. The British government has announced a target of 10% of electricity to be generated by renewable sources by the year 2010, and an aspiration for 20% by 2020. The intermittent nature of wind power generation presents a challenge for the operation of wind farms and the management of the electricity system. Accurate short- to medium-term forecasts of wind power output are crucial both for technical and financial reasons. For example, wind farm operators will be penalised by the system operator if generated power is not as suggested, extreme gusts must be predicted so that the operators have sufficient time to shut down the turbines, and the scheduling of maintenance should certainly take account of the wind conditions. A common theme in these issues is a need to manage risk. The following projects are currently in progress:
Wind speed characteristics
Wind speed observations demonstrate an annual seasonality with stronger wind speeds experienced in winter than
summer (figure to the right: daily wind speed observations at Malin Head plotted against the day of the year.)
Wind speed values can be deseasonalised by fitting a curve to describe this intra-annual variability. For example,
fitting a series of harmonic functions provides the basis of one such
technique. A square root transform can be used to produce a time series which approximates a normal distribution,
thereby offering advantages for modelling and forecasting.
Wind speeds are positively correlation over the short term (day to day) in that low values tend to follow low values and high values tend to follow high values. Furthermore, wind speeds have a property known as long-memory and its hallmark is a slowly decaying autocorrelation function. The existence of long-memory is important when attempting to forecast and quantify the risk associated with wind. Long-memory may be estimated by calculating the power-spectral density, S(f), and estimating the power-law scaling exponent, β, that satisfies S(f) ≈ f−β. Wind speeds at Malin Head have β=0.29 suggesting a scaling closer to that of white noise (β=0) than either pink noise (β=1) or a random walk (β=2). See [1] for further details of quantifying long-memory using time series data.
The probability of exceeding a particular wind speed can be employed to investigate the distribution of wind speeds.
These give the likelihood of strong wind on a number of consecutive days (see figure to the left: probabilities of observations
exceeding given wind speed thresholds at Malin Head, with idealised wind power generated as a function of wind speed.)
While the probability of having one day with wind speeds greater than 10m/s is 0.26, the probability of this occurring
on four consecutive days decreases to 0.05. Conditional autoregressive models may be used to quantify risk by forecasting
the quantiles in the upper tail of the distribution of wind speeds.
Wind power forecasts
The importance of risk management motivates the estimation of the probability density function of the wind power output, rather than just a single point forecast. As the power output from a wind turbine is heavily dependent on wind speed (see figure above), the problem of wind power density forecasting translates to one of wind speed density forecasting. We consider three approaches for generating both point forecasts and density forecasts of wind speed (see [2]).
1. Statistical time series modelling
A wind power density forecast can be generated using Monte Carlo simulation based on a statistical model for the variation
in the level and volatility of wind speed. One of the statistical challenges to be addressed is the fact that wind speed
is bounded below by zero. We have found that the volatile nature of wind speed can be adequately described by volatility
models used in the financial sector.
The movie on the right shows forecasts obtained from a seasonal autoregressive moving average (SARMA) model (red) for hourly wind speed observations (black) over a range of forecast horizons from 1 to 72 hours ahead. Its performance is compared with two simple benchmarks, persistence (blue) and a seasonal mean (yellow).
2. Methods based on the predictions from an atmospheric model
In order to develop wind speed density forecasts, we also consider a relatively new type of weather forecast called weather ensemble predictions. These predictions are produced by large meteorological models of the earth’s atmosphere. Ensemble prediction systems generate multiple realisations of weather variables by using a range of different initial conditions in the numerical model of the atmosphere. The frequency distribution of the different realisations provides an estimate of the density function. At present, the European Centre for Medium-Range Weather Forecasts (ECMWF) produces forecasts with 51 ensemble members. Previous work has shown that, although ensemble predictions are able to capture the dynamic change over time in the density of a weather variable, they tend to underestimate the spread of the density. For this reason, the ensemble forecasts need to be calibrated when transforming to a forecast density.
3. Hybrid techniques
Both the statistical time series models and the atmospheric models have advantages and disadvantages and their performance varies with the forecast horizon. Hybrid predictions formed using state-of-the-art combination methods offers a superior forecasting system.
[1] P.E. McSharry, B.D. Malamud (2005), Quantifying self-similarity in cardiac inter-beat interval time series in Computers in Cardiology 2005, IEEE: New York, (in press).
[2] J.W. Taylor, P.E. McSharry, R. Buizza (2006), Wind power density forecasting using ensemble predictions and time series models. (in preparation).