LA ONEROSIDAD Y LA GRATUIDAD DEL PROCESO

∑

=

=

2 2 n

HDn

THD

The THD is 3.67% and the highest harmonic distortion of any individual harmonic is 2.15%. Thus, these harmonics are within the allowable range of IEEE 519.

9.7 The data file ‘Site1 v Site2 For MCP.csv’ includes five years of wind speed and direction data from Site 1 (the reference site) and Site 2 (the candidate or project site). Data that was determined to be incorrect (due to sensor icing or other problems, for example) is indicated by -999. Use this data to determine the appropriate Variance MCP relationship between the two sites using three different years of concurrent data: 1999, 2001 and 2002.

What are the slopes and offsets determined from these three different concurrent data sets?

What is the data recovery of the data sets used for the analysis expressed as a percentage of a year worth of data? What might be the cause of the difference between the results for different years?

SOLUTION

The calculations have been done in Site1 v Site2 For MCP_Years 1999, 2001, 2002 Solution.xls. The results are shown here:

Year of Concurrent Data Slope Offset Data Recovery

1999 0.998 0.214 0.958

2001 0.912 0.347 0.914

2002 0.915 0.492 0.948

There is a significant variability between the slopes, which range from 1.00 to 0.91. There is some variability between the offsets that were determined. All of the data recovery percentages were over 91%. The causes of the variability is unknown but could be due to sensor changes, changes in the ground cover upwind of either site over the four year period or variability in the relationship between the winds at the two locations.

9.8 A study determines that the maximum chord size in meters of blades can be expressed as:

4 . 1 024 . 0 0005 .

0 ²+ +

= L L

c

where L is the blade length and the mass of blades in kilograms can be approximated as 6300

340 043 .

9 ²− +

= L L

m

The clearance under the bridges on the only road to a proposed project are 5.5 m and the trailer carrying the blades to the project must maintain a clearance between the blade and the road of 1 m. Additionally, the overpasses on the road are only rated for loads (tractor trailer plus cargo) of 36,000 kg. Note that the empty tractor trailer has a mass is 16,000 kg.

a) If the underpass clearances are determined by the maximum blade chord what is the largest blade that can be transported to the project that will fit under the road underpasses and over the bridges?

b) Final access to the project is along a narrow dirt road. The minimum radius of curvature of the road, r, that will accommodate a blade of length L when the road width is w is:

w L w

r 2

2

2 2

⎟ −

⎠

⎜ ⎞

⎝

⎛

=

What is the minimum radius of curvature that will accommodate the blade chosen in part a if w = 8 m?

SOLUTION

a. The available clearance is 4.5 m between the trailer and the top of the underpasses. The available blade weight is only 20,000 kg due to the weight of the tractor and trailer. The 4.5 m maximum chord length limits the blades to 58.5 m. The mass limit of 20,000 kg limits the blades to about 62 m long. Thus, the underpass limit is the more restrictive and the project must use wind turbines with blades no longer than 58.5 m long.

b. Plugging the values into the formula, the minimum radius of curvature is 68.3 m.

9.9 A developer decides to install a 45 turbine offshore wind farm. The wind map of the proposed project is shown in the Figure B-11. The rows are 2 km apart in the north-south direction and 1 km apart in the east-west direction. The closet turbine to land is 4 km to the east of Eastern Point.

Figure B.11 Map of proposed project.

The wind map shows the expected range of mean hub height wind speeds at the site in each shaded area. The Weibull shape factors found at this site are 2.4. As the permitting for the project moves forward, the developer realizes that he will need to eliminate 4 turbines in the higher wind speed region due to concerns at archeologically valuable shipwrecks nearby. He also decides to eliminate all turbines within 5.7 km of Eastern Point to avoid conflicts with lobstermen who are concerned about environmental damage to lobster beds.

What is the expected range of annual energy generation if the turbines that will be used have a rated power of 4.0 MW above 13 m/s and has a cubic power curve from 4 m/s to rated and a cut-out wind speed of 24 m/s?

SOLUTION

The final number of wind turbines in the lower wind speed area is 14 and in the high wind area it is 17. The average capacity factors are shown in the table below. The analysis can be found in OffshoreWindFarmSolution.xls.

Minimum expected CF 0.277 Maximum expected CF 0.315

9.10 A proposed wind farm will have 18 wind turbines in a row. Each will be 8 rotor diameters apart. The wind speeds in each 30 degree direction bin are characterized in the Table B.10. The turbine that will be used in this project generates rated power of 2.0 MW above 11 m/s and has a cubic power curve from 4 m/s to rated and a cut-out wind speed of 24 m/s. The array losses are assumed to be 15% when the wind is from the north (0 degrees) and 0% when the wind is from other directions. Additionally, it is assumed that other losses (downtime, electrical losses, weather conditions, etc.) will be 20%. Under these assumptions, what will the total generation of the wind farm be? After consulting the manufacturer, the developer learned that the wind turbine manufacturer would not honor the turbine warranty if the wind turbines were operated when the wind was directly along the row of the turbines (in direction sectors bins of 0 and 180 degrees) due to excessive wake turbulence. Given this new information, how much can the developer expect to generate at this wind farm and preserve the warranty on his turbines?

Table B.10 Wind speed and directiondata Direction

Bin Center Mean Wind Speed, m/s Weibull Shape Factor Percent of Time

0 7.9 2.0 8.0

30 7.0 2.1 6.0

60 6.7 2.0 4.0

90 5.6 2.1 10.0

120 6.9 2.3 8.0

150 7.2 2.1 7.0

180 8.8 2.2 7.0

210 9.2 2.1 10.0

240 9.0 2.0 8.0

270 8.3 2.1 14.0

300 8.4 2.1 12.0

330 7.6 2.2 6.0

SOLUTION

The answers are presented in the table below and the details of the analysis are in DirSectorMgtSolution.xls.

Project CF including array losses 0.430

Net Project CF including all losses 0.344

Project CF w/ Dir. Sector Management including array losses 0.368 Net Project CF w/ Dir. Sector Management, incl. all losses 0.294 9.11 HourlyLoadAndPowerOneYearGW.csv contains average hourly electrical load (GW) in a utility control area and the wind power that is expected to be generated by future planned wind farms.

a. Determine the total GWh, mean, maximum, minimum and standard deviation of the gird load and the generated wind power. Graph the load duration curve of the utility with the existing load (before the installation of the wind plants).

b. Determine the total GWh, mean, maximum, minimum and standard deviation of the net load once the wind power plants are installed. Graph the load duration curve of the net load of the utility after the installation of the wind plants.

c. How much does the mean electrical load decrease with the installation of the wind power plants? How much does the standard deviation of the load seen by the grid operators (the net load) increase with the inclusion of wind? How much does the peak net load change?

SOLUTION

Answers to a) and b): The statistics of the data are:

Original Load

Wind Power

Net Load

Average GW 26.26 3.67 22.58

Total GWh 229,995 32,183 197,812

Standard Deviation,

GW 4.96 4.16 6.43

Max GW 43.06 12.00 43.06

Min GW 11.03 0.00 0.24

The cumulative distributions are (see LoadGWSolution.xls):

0 5 10 15 20 25 30 35 40 45 50

0 0.2 0.4 0.6 0.8 1

Cummulative Probability

Load Net Load

Original Load

c. The mean electrical net load decreased from 26.26 GW to 22.58 GW but the standard deviation increased from 4.96 GW to 6.43 GW. Meanwhile the peak net electrical load remains the same.