## Energy Distribution

If we define the energy distribution function:

e _ kWh contribution in the year by the wind between v and (v + Av)

Then, it would look like that in Figure 4-12, which is for the Rayleigh speed distribution. The wind speed curve has the mode at 5.5 m/s and the mean at 6.35 m/s. However, because of the cubic relation with the speed, the maximum energy contribution comes from the wind speed at 9.45 m/s. Above this speed, although V3 continues to increase in cubic manner, the number of hours at those speeds decreases faster than V3. The result is an overall decrease in the yearly energy contribution. For this reason, it is advantageous to design the wind power to operate at variable speeds in order to capture the maximum energy available during high wind periods.

Figure 4-13 is a similar chart showing the speed and energy distribution functions for shape parameter 1.5 and scale parameter 15 mph. The mode speed is 10.6 mph, the mean speed is 13.3 and the rmc speed is 16.5 mph.

— Wind Speed Fr (h/y)/(m/s)

i equency

/ UA, A* / Spe*

/erac id 6.v

|e Wind \ 35 m/s

i

— Energy lllC^ Frequer

Density icy (kWh/y)/(m/s)

••••:.»•:: Speed W.4•••ri

i Wind ill^w 15 m/s

Steady Wind Speed at Reference Elevation, UR (m/s)

5 10 15

Steady Wind Speed at Reference Elevation, UR (m/s)

FIGURE 4-12

Rayleigh distributions of hours and energy per year versus wind speed with c = 10 and k = 2.

FIGURE 4-12

Rayleigh distributions of hours and energy per year versus wind speed with c = 10 and k = 2.

The energy distribution function has the mode at 28.5 mph. That is, the most energy is captured at 28.5 mph wind speed, although the probability of wind blowing at that speed is low.

The comparison of Figures 4-12 and 4-13 shows that as the shape parameter value decreases from 2.0 to 1.5, the speed and the energy modes move farther apart. On the other hand, as the speed distribution approaches the bell shape for k > 3, the speed and the energy modes get closer to each other.

10 20 30 40

FIGURE 4-14

Rayleigh distributions of hours and energy per year with k = 2 and c = 10, 15, and 20 mph.

10 20 30 40

FIGURE 4-14

Rayleigh distributions of hours and energy per year with k = 2 and c = 10, 15, and 20 mph.

Figure 4-14 compares the speed and the energy distributions with k = 2 (Rayleigh) and c = 10, 15, and 20 mph. As seen here, the relative spread between the speed mode and the energy mode remains about the same, although both shift to the right as c increases.

### 4.6.6 Digital Data Loggers

The mean wind speed over a period of time is obtained by adding numerous readings taken over the period and dividing the sum by the number of readings. Many digital data loggers installed over the last few decades collected average wind speed data primarily for the meteorological purpose, as opposed to assessing the wind power. They logged the speed every hour, and then averaged over the day, which in turn, was averaged over the month and over the year. The averaging was done as follows:

As seen earlier, for assessing the wind power, the rmc speed is what matters. The rmc equivalent of the digital data logging is as follows:

The above equation does not take into account the variation in the air mass density, which is also a parameter (although of second order) in the wind power density. Therefore, a better method of collecting the wind power data is to digitize the yearly average power density as follows:

i=l where n = number of observations in the averaging period pi = air density (kg/m3), and Vi = wind speed (m/s) at the ith observation time.

4.6.7 Effect of Height

The wind shear at ground surface causes the the wind speed increase with height in accordance with the expression

where Vj = wind speed measured at the reference height h V2 = wind speed estimated at height h2, and a = ground surface friction coefficient.

The friction coefficient is low for smooth terrain and high for rough ones (Figure 4-15). The values of a for typical terrain classes are given in Table 4-3.

The wind speed does not increase with height indefinitely. The data collected at Merida airport in Mexico show that typically the wind speed increases with height up to about 450 meter height, and then decreases (Figure 4-16)1. The wind speed at 450 meters height can be four to five times greater than that near the ground surface.

0 100 200 300 400 500

Height from ground (meters)

0 100 200 300 400 500

Height from ground (meters)

FIGURE 4-15

Wind speeds variation with height over different terrain. Smooth terrain has lower friction, developing a thin layer above.

TABLE 4-3

Friction Coefficient of Various Terrain

TABLE 4-3

Friction Coefficient of Various Terrain

 Friction Coefficient Terrain Type a Lake, ocean and smooth hard ground 0.10 Foot high grass on level ground 0.15 Tall crops, hedges, and shrubs 0.20 Wooded country with many trees 0.25 Small town with some trees and shrubs 0.30 City area with tall buildings 0.40

4.6.8 Importance of Reliable Data

Some of the old wind-speed data around the world may have been primarily collected for meteorological use with rough instruments and relatively poor exposure to the wind. This is highlighted by the recent wind resource study of Mexico.1 Significant differences in the old and the new data have been found, as listed in Table 4-4. The 1983 OLADE Atlas of Mexico indicates very low energy potential, whereas the 1995 NREL data reports several times more energy potential. The values from the OLADE Atlas are from a few urban locations where anemometers could be poorly exposed to the prevailing

FIGURE 4-16

Wind-speed variations with height measured at Merida airport in Mexico. (Source: Schwartz and Elliott, DOE/NREL Report DE95009202, May 1995.)

FIGURE 4-16

Wind-speed variations with height measured at Merida airport in Mexico. (Source: Schwartz and Elliott, DOE/NREL Report DE95009202, May 1995.)

TABLE 4-4

Comparison of Calculated Average Wind Power Density Between 1983 OLADE Atlas and 1995 NREL Analysis for Several Locations in Mexico

 OLADE NREL Atlas Data Region in Mexico Data Site (1983) (1995) Yucatan Peninsula Merida 22 165 Campeche 23 120 Chetumal 28 205 Northern Gulf Plain Tampico 8 205 Ciudad Victoria 32 170 Matamoros 32 165 Central Highlands Durango 8 140 San Luis Potosi 35 155 Zacatecas 94 270 Northwest Chihuahua 27 120 Hermosillo 3 80 La Paz 10 85

Data at 10 meters height.

### Data at 10 meters height.

winds. In contrast, the new NREL wind data comes from a large number of stations, including open airport locations, and has incorporated the terrain effect in the final numbers. The message here is clear. It is important to have reliable data on the annual wind speed distribution over at least a few years before siting a wind farm with a high degree of confidence.

### 4.7 Wind Speed Prediction

The available wind energy depends on the wind speed, which is a random variable. For the wind-farm operator, this poses difficulty in the system scheduling and energy dispatching, as the schedule of the wind-power availability is not known in advance. However, if the wind speed can be reliably forecasted up to several hours in advance, the generating schedule can efficiently accommodate the wind generation. Alexiadis et al2 have proposed a new technique for forecasting wind speed and power output up to several hours in advance. The technique is based on cross-correlation at neighboring sites and artificial neutral networks. The proposed technique can significantly improve forecasting accuracy compared to the persistence forecasting model. The new proposed method is calibrated at different sites over a one-year period.

### 4.8 Wind Resource Maps

The wind resource of a vast region or a country is mapped in terms of the wind speed, the wind power density in watts per square meter of the rotor swept area, or the wind energy potential in kWh/m2 per year. Often the wind resource is mapped in all three forms. The data is usually represented by the contour curves, as it is the most useful and easily understood mapping technique. Along the contour line, the plotted parameter remains constant. For example, the isovent map plots the contour lines connecting the sites having the same annual wind speed. The equipotential map plots the contour lines connecting the sites having the same annual wind energy capture potential in kWh/m2. The wind resource maps of many countries have been prepared in such contour form. Some of them are presented in the following sections:

The U.S. wind resource is large enough to produce more than 4.4 trillion kWh of electricity each year. This is more than the entire nation will use in the year 2000. Figure 4-17 is the wind speed map of the U.S.A., whereas Figure 4-18 is the wind power density map.3-4 Although most of the country's installed wind capacity is presently in California, the Department of Energy estimates that almost 90 percent of the usable wind resource in the U.S.A.

FIGURE 4-17

Annual average wind-power density in watts/m2 in the U.S.A. at a 50-meter tower height. (Source: DOE/NREL.)

FIGURE 4-17

Annual average wind-power density in watts/m2 in the U.S.A. at a 50-meter tower height. (Source: DOE/NREL.)

Batteile PNL Map of U.S. Wind Resources

Batteile PNL Map of U.S. Wind Resources

FIGURE 4-18

The U.S. wind resource map. (Source: DOE/Battelle Pacific Northwest Laboratory.)

FIGURE 4-18

The U.S. wind resource map. (Source: DOE/Battelle Pacific Northwest Laboratory.)

lies in the wind-belt spanning eleven Great Plains states. These states stretch from Montana, North Dakota and Minnesota in the north, to Texas in the south. The wind resource of this region has remained virtually untapped until recently. However, significant wind-power generating capacity is being added in the wind-belt states as of the late 1990s.

### 4.8.2 Minnesota

Having a large wind-power potential in the southwestern part of the state, Minnesota started the Wind Resource Assessment Program1 in 1985. The wind monitoring stations were installed at 41 sites with high wind potential. Detailed information on hourly average wind speed, standard deviation, direction, and temperature at many sites in Minnesota were recorded. The Northern States Power Company initially recorded this data on cassette tape recorders powered from batteries charged by photovoltaic modules. Later, data loggers were installed by utilities throughout the state.

In 1993, a new study of wind and solar capabilities was funded by the U.S. Department of Energy, the Northern States Power, and the Minnesota Department of Public Services. Figure 4-19 is a 1995 compilation of the Minnesota wind power potentials at various locations.5 As of the late 1990s, many utilities in that region have become active in developing the wind resource (Figure 4-20).

### 4.8.3 The United Kingdom

The isovent map of the United Kingdom is shown in Figure 4-21 in terms of the annual average wind speed in knots at open sites excluding hilltops.6 Scotland and the western shore of Ireland are the high wind zones. The central portion of England has relatively low wind speeds.

The wind energy map in MWh/m2 per year is shown in Figure 4-22.6 The northwestern offshore sites show high energy potential of 5 MWh/m2 per year.

### 4.8.4 Europe

The wind speed and the energy maps of Europe are combined into one that is published by the Rios National Laboratory in Denmark. The map (Figure 4-23) is prepared for a wind tower height of 50 meters above ground with five different terrains. In the map, the darker areas have higher wind energy density.

4.8.5 Mexico

The wind resource map for Mexico has been recently prepared under the Mexico-U.S. Renewable Energy Cooperation Program.1 The data was collected

FIGURE 4-19

Minnesota wind resource map. (Source: Minnesota wind resources assessment program, Department of Public Service Report, 1994.)

FIGURE 4-19

Minnesota wind resource map. (Source: Minnesota wind resources assessment program, Department of Public Service Report, 1994.)

at numerous city and airport sites spread throughout the country as shown in Figure 4-24. The maps, based on the extensive data collected at those locations, are separately reported for the utility-scale power generation and for the stand-alone remote power generation. This distinction is useful because the wind speed needed to make the wind farm economical for rural application is less than that required for the utility scale application.

Figure 4-25 is the utility-scale wind resource map for Mexico. The highest wind potential for grid-connected power plants is in the Zacatecas and the southern Isthmus of Tehuantepec areas. The rural wind resource map in

®® Portland General Electric Co. Puget Sound Power & Light Co, PacifiCorp

I Sacramento Municipal Utility District # Pacific Gas and Electric Co,

Southern California Edison Co.

Central Maine Power Co. I New England Power Service Co. 1

Eastern Wisconsin Utilities Gre™ fountain Power Corp.» ■ 9 Niagara •

• Northern States Power Co. Mohawk •• Marshall Municipal Utilities Power

Waverly Light & Power. Midwest Power Co. Interstate Power Co. fowa Electric Light & Power Co.

PacifiCorp, Tri-State G&T Assn. Inc.. Public Service Co. of Colorado, and Eugene Water & Electric Board i Southwestern Public Service Co.

V rti' oli(v • Texas Utilities Co. • Central and South West Services, Inc.

Hawaiian

Electric

FIGURE 4-20

U.S. utilities gaining experience in developing wind power generation projects. (Source: Wind energy program overview, DOE Report No. 10095-071, March 1995.)

Figure 4-26 shows that areas suitable for stand-alone remote wind farms are widespread, and include about one-half of Mexico.

### 4.8.6 India

The wind speed measurement stations in India have been in operation since early 1980 at numerous locations. Sites with high wind speeds are shown in Figure 4-27, and their annual mean speed listed in Table 4-5. The data has been collected at 10-m or 25-m tower heights as indicated.7 It is seen that most of these sites have the annual mean wind speed exceeding 18 km/h, which generally makes the wind power plant economically viable. The states with high wind potentials are Tamilnadu, Gujarat (Figure 4-28) and Andhra Pradesh.

### FIGURE 4-21

Isovent map of the United Kingdom in knots at open sites, excluding hilltops. (Source: Freris, L. L., Wind Energy Conversion Systems, Prentice Hall, London, 1990.)

### FIGURE 4-21

Isovent map of the United Kingdom in knots at open sites, excluding hilltops. (Source: Freris, L. L., Wind Energy Conversion Systems, Prentice Hall, London, 1990.)

### FIGURE 4-22

Wind energy map of the United Kingdom in MWh/m2 per year at open sites, excluding hilltops. (Source: Freris, L. L., Wind Energy Conversion Systems, Prentice Hall, London, 1990.)

### FIGURE 4-22

Wind energy map of the United Kingdom in MWh/m2 per year at open sites, excluding hilltops. (Source: Freris, L. L., Wind Energy Conversion Systems, Prentice Hall, London, 1990.)

FIGURE 4-23

European wind resource map. (Source: Ris0 Laboratory, Denmark.)

FIGURE 4-23

European wind resource map. (Source: Ris0 Laboratory, Denmark.)

### FIGURE 4-24

Locations in Mexico with surface wind data in DATSAV2 data set. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

### FIGURE 4-24

Locations in Mexico with surface wind data in DATSAV2 data set. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

### FIGURE 4-25

Annual average wind resource map of Mexico for utility scale applications. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

### FIGURE 4-25

Annual average wind resource map of Mexico for utility scale applications. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

### FIGURE 4-26

Annual average wind resource map of Mexico for rural power applications. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

### FIGURE 4-26

Annual average wind resource map of Mexico for rural power applications. (Source: Schwartz, M. N. and Elliott, D. L., Mexico wind resource assessment project, DOE/NREL Report No. DE95009202, March 1995.)

FIGURE 4-27

Wind monitoring sites in India. (Source: Tata Energy Research Institute, New Delhi, India.)

FIGURE 4-27

Wind monitoring sites in India. (Source: Tata Energy Research Institute, New Delhi, India.)

TABLE 4-5

Mean Annual Wind Speed at Selected Sites in India

TABLE 4-5

 Site km/h Site km/h Sites with 25-30 km/h wind speed Sites with 15-20 km/h wind speed Ramakalmedu 30.3 Onamkulam* 19.9 Jogmatti 30.0 Nettur* 19.9 B.& H. Hills 27.1 Gude Panchgani 119.8 Dhank-2 25.1 Bhandariya 19.5 Ramagiri-3 19.4 Sites with 20-25 km/h wind speed Poosaripatti* 19.3 Pongalur 19.1 Dhank-1 24.4 Limbara 19.1 Singanamala 23.8 Jamalamadugu-2* 18.7 Edayarpalayam 22.4 Ottapidaram 18.5 Kadavakallu* 22.1 Ponmudi 18.3 Kalyanpur 22.1 Hardenahalli 18.2 Kumarapuram* 22.0 Kheda 18.2 Kethanur 21.1 Jamgodrani 18.0 Navadra 20.8 Jamalamadunga-1* 17.5 Arasampalayam 20.5 Poompuhar 17.2 Bamambore-2 20.3 Minicoy 17.0 Mustikovala 20.2 Kolahalamendu 16.9 Pancjalimedu 20.2 Naduvakkurichi 16.8 Lamda 20.0 Yeradoddi* 15.8 Mirzapur 15.4

* Data at 25-m height, all others at 10-m height

* Data at 25-m height, all others at 10-m height

References

1. Schwartz, M. N. and Elliott, D. L. 1995. "Mexico Wind Resource Assessment Project," DOE/NREL Report No. DE95009202, National Renewable Energy Laboratory, Golden, Colorado, March 1995.

2. Alexiadis, M. C., Dokopoulos, P. S., and Sahsamanogdou, H. S. 1998. "Wind Speed and Power Forecasting Based on Spatial Correlation Models," IEEE Paper No. PE-437-EC-0-04-1998.

3. Elliott, D. L., Holladay, C. G., Barchet, W. R., Foote, H. P., and Sandusky, W. F. 1991. "Wind Energy Resources Atlas of the United States," DOE/Pacific Northwest Laboratory Report No. DE-86004442, April 1991.

4. Elliott, D. L. 1997. "Synthesis of National Wind Assessment," DOE/Pacific Northwest Laboratory, NTIS Report No. BNWL-2220 Wind-S, 1997.

5. Rory, A. 1994. "Minnesota Wind Resources Assessment Program," Minnesota Department of Public Service Report, 1994.

6. Freris, L. L. 1990. "Wind Energy Conversion Systems," London, Prentice Hall, 1990.

7. Gupta, A. K. 1997. "Power Generation from Renewables in India," Ministry of Non-Conventional Energy Sources, New Delhi, India, 1997.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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