# Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

_{i}, are the yearly means, x the long-term mean, and n = 11 (number of years). For the consideration of the spatial variability of the long-term mean wind speed, a method similar to that used in [12] is applied. For a given number of cells, n, around the central cell in question, the standard deviation is calculated as in equation 2, where the mean, x , is taken to be the long-term (11-year) mean of the central cell and x

_{i}is the long-term mean of each of the surrounding cells.

_{centre}is the elevation of the centre cell, and H

_{i}is the elevation of each of its 8 surrounding cells. Figure 1 also indicates the location of the met stations cited in [2].

Site | Name | General classification | Capacity in zone (MW) | Mean height (m) | Height range (m) | Ruggedness Index (RIX) (m) |
---|---|---|---|---|---|---|

1 | Ayrshire | Inland | 764 | 172 | 332 | 128 |

2 | The Wash | Coastal | 190 | 14 | 36 | 15 |

3 | Central Wales | Inland | 256 | 276 | 477 | 107 |

4 | South Wales | Coastal | 136 | 208 | 572 | 170 |

5 | Yorkshire | Inland | 140 | 25 | 120 | 9 |

6 | Galloway | Coastal | 347 | 126 | 461 | 146 |

7 | Sperrins | Inland | 141 | 151 | 314 | 69 |

8 | Lancashire | Inland | 146 | 227 | 453 | 205 |

9 | Grampian | Coastal | 305 | 178 | 732 | 168 |

10 | Barrow | Offshore | 608 | 0 | 0 | 0 |

11 | Kent | Offshore | 1205 | 0 | 0 | 0 |

12 | Norfollk | Offshore | 464 | 0 | 0 | 0 |

13 | Aberdeen | Offshore | 10 | 0 | 0 | 0 |

## 3. Results

#### 3.1. Interannual Variability

**Figure 2.**Interannual co-efficient of variation (%) for the annual mean 10 m (

**A**) and 80 m (

**B**) wind speed in a 10 year hindcast.

#### 3.2. Spatial Variability of the Long-Term Mean

^{2}), increasing to 99 by 99, the long-term mean annual wind speeds have been used to derive the coefficient of variation for the centremost cell as in [12]. Referring to Equations (1) and (2), x

_{i}represents the mean annual wind speeds of the n individual cells in the window; x is then the long term mean of the central cell, so that the variation over the region is calculated relative to the cell in question.

**Figure 4.**Coefficient of variation in long-term mean wind speed from 11 year hindcast for varying spatial windows—(

**A**) 3 by 3; (

**B**) 15 by 15; (

**C**) 35 by 35; (

**D**) 59 by 59.

**Figure 5.**Correlation between the ruggedness index (RIX) and coefficient of variation for differing window size.

- ▪
- The offshore points (10–13, shown in the upper panel) initially show a steady increase in variability with increasing window size; this rate of increase reduces at greater distances;
- ▪
- The two very flat onshore locations (2 and 5) show similar trends to the offshore points and are plotted with the offshore points in the upper panel;
- ▪
- The points located in more complex terrain (lower panel), however, show a lot of changes, both increases and decreases in the CVar, with increasing distance. This would be indicative that hills and valleys are causing peaks and troughs in the mean wind speeds of cells within the windows, but their effects are averaged out as the window size increases;
- ▪
- Point 9 is a “rogue” point, compared to the others—it has a much larger variability from the beginning, and as the window size increases beyond 60 cells, it continues to trend upwards. This may reflect its location in both complex and coastal terrain;
- ▪
- After a certain distance—depending on the location—the influence of terrain will be minimised and it is postulated that it is overtaken by the influence of mesoscale weather systems.

**Figure 6.**Change in coefficient of variation (CVar) with window size (

**A**) offshore and flat onshore sites; (

**B**) more complex onshore and coastal sites.

#### 3.3. Effects of Spatial Aggregation

^{2}) around the centre cell is shown in Figure 8, whilst Figure 9 shows a 9 by 9 window (~27 km

^{2}).

**Figure 7.**Coefficient of variation for 2004 (calculated from fitted Weibull parameters at each cell).

**Figure 8.**Coefficient of variation for 2004 (calculated from fitted Weibull parameters from the average of a 3 by 3 window around each cell).

**Figure 9.**Coefficient of variation for 2004 (calculated from fitted Weibull parameters from the average of a 9 by 9 window around each cell).

**Figure 10.**Coefficient of variation with averaging of cells for different points. (

**A**) offshore and flat onshore sites; (

**B**) more complex onshore and coastal sites.

#### 3.4. Discussion of Wind Variability Analysis

## 4. Impact on Power Analyses

- ▪
- Pseudo-Met Station: The capacity factor of the central cell is taken as the capacity factor for the whole region;
- ▪
- Lower resolution model: An 80m wind speed time series has been created as the mean wind speed of all the cells falling within the specified ~50 km × 50 km zone, and converted to capacity factor using the aggregate power curve;
- ▪
- True”: The 80 m wind speed for the relevant WRF cell for each wind farm within the given radius is extracted and converted to power using the aggregate power curve scaled to the capacity of that farm. All the farms in the zone are then summed and the hourly regional capacity factor calculated as the aggregate power divided by the regional capacity;
- ▪
- For 4 of the 50 km × 50 km areas (1, 5, 6 and 8), a met station falls within the zone, and for zone 2, one lies 10 km outside the boundary. Wind speeds for these met stations have been extracted for the time period of analysis, extrapolated from 10 m to 80 m turbine hub height (using a 1/7 power law) and the aggregate power curve applied to give a regional capacity factor.

**Figure 12.**Mean capacity factors, standard deviations and coefficient of variation per region (1–13).

## 5. Conclusions

## Nomenclature

a.g.l | Above ground level |

GB | Great Britain |

MERRA | Modern-Era Retrospective Analysis for Research and Applications |

met | Meteorological |

RIX | Ruggedness index |

ROC | Renewables Obligation Certificate |

UK | United Kingdom |

WRF | Weather Research and Forecasting (mesoscale model |

## Acknowledgements

## Conflicts of Interest

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**MDPI and ACS Style**

Cradden, L.C.; Restuccia, F.; Hawkins, S.L.; Harrison, G.P. Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series. *Resources* **2014**, *3*, 215-234.
https://doi.org/10.3390/resources3010215

**AMA Style**

Cradden LC, Restuccia F, Hawkins SL, Harrison GP. Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series. *Resources*. 2014; 3(1):215-234.
https://doi.org/10.3390/resources3010215

**Chicago/Turabian Style**

Cradden, Lucy C., Francesco Restuccia, Samuel L. Hawkins, and Gareth P. Harrison. 2014. "Consideration of Wind Speed Variability in Creating a Regional Aggregate Wind Power Time Series" *Resources* 3, no. 1: 215-234.
https://doi.org/10.3390/resources3010215