**4.2 Matrix method**

In the matrix methods the changes in the wind speed and direction (wind veer) are modelled through joint distributions fitted on the 'matrix' of wind speed bins and wind direction bins. The concurrent periods of the measured wind data are used to calculate the set of non-linear transfer functions, used for estimating wind speeds and directions from the reference site to the prospect site. Since real measurements suffer from data missing in bins in the dataset, this method needs a way to substitute the missing input bins. A basic assumption of the matrix method is that the long-term site data (wind speed and direction) can be expressed through the simultaneous measurements of on-site data and reference site data. How this joint distribution is modelled should actually depend on the data in question, suggesting that a combination of binned sample distributions and modelled joint Gaussian distributions are working well [73–77]. The transfer model, given as a conditional distribution, is actually the key distribution in the matrix method. When applying the matrix method this conditional distribution is stipulated to hold regardless of the time frame considered. Thus, for each measured sample it is necessary to calculate/measure pairs of the two quantities (a pair is data with identical timestamps):

$$
\Delta \boldsymbol{\nu} = \boldsymbol{\nu}\_{\text{site}} - \boldsymbol{\nu}\_{\text{ref}} \tag{65}
$$

$$
\Delta\theta = \theta\_{\text{site}} - \theta\_{\text{ref}} \tag{66}
$$

These parameters refer to the wind speeds and directions at the wind project site and the meteorological site, respectively. The joint distribution of *f(Δu, Δθ)* is modelled conditioned on the wind speed and the wind direction on the reference site. The joint distributions are represented as either through the samples (bootstrap model) or often through a joint Gaussian distribution. When the data has been measured and a match between the short-term data and the short-term reference data has been established, then the samples are sorted into bins with specific resolutions, such as 1 m/s and 10 degrees. The result from this binning is a set of joint sample distributions of wind veer and wind speeds. Since the data is binned with wind speed and wind direction, these sample distributions are conditioned on the mean wind speed at the reference position and the wind direction on the reference position. The calculated distributions are used directly in a bootstrapping technique when doing matrix MCP calculations. Based on the sample distributions, the statistics, calculated for the wind veer are the mean, the standard deviation, and the correlation coefficients. To enable interpolations and extrapolations into bins where no data is present, a spline is fitted to the sample distributions. This parametric distribution is represented by the two moments and the correlation, assuming that a joint Gaussian distribution. Note, that even if the Gaussian distribution assumption may seem a bit crude, then the parametric model can be applied in cases where limited or no sample data is available. Thus, the influence of this assumption is limited, as most long-term corrected samples are typically based on the resampling approach. The mean, standard deviation and correlation are now modelled as 'slices' of polynomial surfaces:

$$P(v, \theta) = \sum\_{i=0}^{N} a\_i(v\_i, \theta\_i) v\_{ref}^1 \tag{67}$$

where P denotes the sample statistical moment (or correlation) considered, N is the order of the polynomial is the polynomial coefficients, depending on the wind velocities. As in the case of regression MCP, the long-term corrected meteorological data is calculated using Bootstrap and Monte-Carlo techniques, i.e. probabilistic methods enabling generation of the long-term corrected wind distribution through an *artificial* time series.

#### **4.3 Hybrid MCP and the wind index MCP methods**

The hybrid MCP method [72–77] correlates the wind data at the targeted wind plant site with that at multiple reference stations. The strategy accounts for the local climate and the topography information. In the original hybrid MCP method, all component MCP estimations between the targeted wind plant site and each reference station use a single MCP method (e.g., linear regression, variance ratio, Weibull scale, or neural networks). The weight of each reference station in the hybrid strategy is determined based on: (i) the distance and (ii) the elevation differences between the target wind plant site and each reference station. The hypothesis here is that the weight of a reference station is larger when the reference station is closer (shorter distance and smaller elevation difference) to the target wind plant site. The weight of each reference station, *wi*, is determined by:

$$w\_j = F(n\_{\rm ref}, \Delta d\_j, \Delta h\_j) \tag{68}$$

where *nref* is the number of reference stations; and Δ*dj* and Δℎ*<sup>j</sup>* represent the distance and the elevation difference between the target site and *jt*ℎ reference station, respectively. Each wind data point is allocated to a bin according to the wind direction sector at the target wind plant site. Within each sector, the longterm wind speed is predicted by a hybrid MCP strategy based on the concurrent short-term wind speed data within that specific sector. By setting the wind speed data in each sector together, the long-term wind data at the target wind plant site can be obtained. The predicted long-term wind data quality is usually evaluated using the performance metrics. ANNs are used to correlate and predict wind conditions because of their ability to recognize patterns in noisy or complex data. A neural network contains an input layer, one or more hidden layers, and an output layer, being defined the following parameters: input and output connections, number of neuron layers, the weights, and transfer functions, the interconnection pattern between different neuron layers, the learning process for updating the weights of the interconnections, and the activation function that converts the input into outputs. The Levenberg–Marquardt algorithm is usually used for neural network training.

The index correlation method is a method creating the MCP analysis by means of monthly averages of the energy yield, disregarding the wind directional distributions [72–77]. Even though this method may seem rather crude and primitive when comparing to other more advanced MCP methods, which takes the wind veer into account; this method has the advantages in stability and performance as it may even succeed in the cases where other MCP methods may fail. This is due to the fact, that the wind indexes are related directly to WTG energy yield and that the method allows the production calculation to be completed using actual measured data before applying the correction. The Wind Index MCP method offers the opportunity to calculate the wind indexes using real power curves of the wind turbines. A generic power curve based on a truncated squared wind speed approach may be chosen. When the wind indexes are calculated, the MCP correction is done on the estimated WTG energy yield, i.e. by multiplying the production estimated

#### *Assessment and Analysis of Offshore Wind Energy Potential DOI: http://dx.doi.org/10.5772/intechopen.95346*

with a correction factor based on the difference in the wind index from the shortterm site data to the long-term site estimated data. However, since the power curve of a WTG is a non-linear function of the wind speed the wind index is typically modelled using power curve common models. For the power output, calculated for the target site and the reference to be comparable they must be based on a similar mean wind speed. This is done by assuming a sector uniform shear that can be applied so that both concurrent mean wind speeds are set to a fixed user-inferred wind speed, typically the expected mean wind speed at hub height. The individual wind speed measurements are thus multiplied with the relevant factor. Full time series wind speeds are adjusted with the same ratio as the one applied to the respective concurrent time series. The argument for this operation is that the variations in wind speed will only be interpreted correctly in terms of wind energy if a comparable section of the power curve is considered.

As discussed in [4, 9, 14, 72–77], once a regression equation has been conditioned based on the measurement overlap period, the regression parameters can then be used to derive an extended data record for the site of interest. MCP methods are generally applied using some sort of regression analysis for each wind direction sector. An issue of using MCP methods based on wind velocity data from the land sites, due to the scarcity of offshore wind velocity observations is that most applications use linear regression which cannot account for observed differences in the wind speed distribution between the land site and the offshore sites. In [9, 14] was proposed in such cases to apply wind velocity corrections of the probability distribution functions, e.g. Weibull parameter corrections. In this method, the Weibull parameters of the short-term data series are modified to characterize longer data sampling periods. It compares sector-based wind speed distributions at the onshore and the off-shore sites considering the on-shore long-term time series as representative of the area of interests. Weibull scale (c) and shape (k) factors are determined for each of several wind sectors and for the mean values in each point of the grid, for data sets from overlapping periods. The differences between the two datasets are expressed in terms of the ratios of Eq. (69). These correction factors are applied to the Weibull factors estimated for the short-term data sets.

$$Corr\_{\text{Scale}} = \frac{c(\text{off-show})}{c(\text{on-show})}, \text{and } Corr\_{\text{Shape}} = \frac{k(\text{off-show})}{k(\text{on-show})} \tag{69}$$

The Weibull correction method, as discussed in [9, 14] gave better wind velocity estimated for both onshore and offshore flow where the wind speeds were overestimated.

### **5. Wind energy resources in climate projections**

Just as with the other aspects of climate, wind statistics are subject to natural variability on a wide range of time scales. Like other meteorological parameters, such as temperature, rainfall, or other climate variables, wind speeds and directions change on time scales of minutes, hours, months, years, and decades. Future climate change is expected to alter the spatio-temporal distribution of surface wind speeds and directions, with impacts on wind-based electricity generation. Long term trends in wind speeds are difficult to quantify and large historical data sets are required to accurately capture and describe such variations. This is a more evident in the case of the offshore wind energy resources. Wind energy resources at any location vary on a range of time scales, and hence any resource assessment should address issues of climate variability and change. However, due to scarcity of

complete datasets offshore, comparisons have generally been performed with the hypothesis that local wind regimes have not changed during the last 10–20 years. The assumption validity is questionable, being likely to be regionally variable [78–81]. Even in the absence of climate non-stationarity, wind energy measurement sites typically have data periods up to 3 years and hence are not representative of wind climates over the 20–30 year lifetime of the wind farms. A further confounding influence is that homogeneous wind speed time series are rarely available for long periods because many monitoring locations have undergone change in land use and instrumentation. Accordingly, one can conceptualize the wind resource assessment as a two-step process: (1) an evaluation of wind resources at the regional scale to locate promising wind farm sites and (2) a site specific evaluation of wind climatology and vertical profiles of wind and atmospheric turbulence, in addition to an assessment of historical and possibly future changes due to climate variability.

In the context of wind energy generation, even small changes in the wind speed magnitude can have major impacts on the productivity of wind power plants, as the wind power relationship is directly proportional to the cube of the wind speed. However, the predictions for the direction and magnitude of these changes hinge critically on the assessment methods used. Decadal and multi-decadal variability in wind speed statistics currently introduce an element of risk into the decision process for siting new wind power generation facilities. Recent findings from the atmospheric science community suggest that climate change may introduce an added risk to this process. Many climate change impact analyses, including those focused on wind energy, use individual climate models and/or statistical downscaling methods rooted in historical observations. Wind speed and direction vary on small scales and respond in complex ways to changes in large-scale circulation, surface energy fluxes, and topography. Thus, whereas multiple climate models often agree qualitatively on temperature projections, wind estimates are less robust. The spatial variability of wind and its sensitivity to model structure suggest that higher resolution models and multi-model comparisons are particularly valuable for wind energy projections. For long-term planning of wind resources, it is imperative to analyze historical datasets and establish monitoring at hub-height using meteorological towers and remote sensing. A comprehensive review of climate change impacts on wind energy is shown in [78–81], discussing the main changes in the wind resources due to climate evolution, focused on northern Europe, with significant wind energy installations.

According to the analysis, until the middle of the current century natural variability will exceed the effect of climate change in the wind energy resources [78–81]. They conclude that there is no detectable trend in the wind resources that would impact future planning and development of wind industry in northern Europe. Pryor et al. (2006) down-scaled winds from ten global climate models at locations in northern Europe and found no evidence of significant changes in the 21st century wind regime compared to the 20th century. Predicted changes are found to be small and comparable to the variability associated with different global climate models. Using another approach, Ren [79] proposed a power-law relationship between global warming and the usable wind energy. The power-law exponent was calibrated using results from eight global climate models. He found that reduction of wind power scales with the degree of warming according to method and estimated that about 4 Celsius degrees increase in the temperatures in mid to high latitudes would result in up to 12% decrease in wind speeds in northern latitudes. Ren [79] suggested that an early maximized harvesting is beneficial and should be carried out. However, more studies are needed to solve all uncertainties in climate projections of wind resources under various future climate scenarios [4].
