Estimates of the Capacity Factor of Farms in the United States

T.C. Larsen and P. Rez* Department of Physics, Arizona State University, Tempe AZ 85287-1504

Received August 30, 2017; Accepted October 27, 2017

Abstract: The capacity factor of wind farms in different regions of the United States has been calculated from hourly wind data and the power curves of the wind turbines. In places with constant high like the Texas panhandle, capacity factors of 40% are possible. However the capacity factors in less favorable locations in or New York are below 20%. Reliable capacity factor estimates are important since displacing efficient combined cycle gas turbines from baseload generation by intermittent could lead to an increase in carbon dioxide emissions. Before a site is considered capacity factors should be calculated from the power curve of the proposed and measured wind data throughout the year, preferably at hub height.

Keywords: , Wind Turbine, Capacity Factor, Carbon Dioxide Emission

1 Introduction The growth in the number of wind turbines installed in both Northern Europe and The United States since 2005 has been spectacular. In 2005 there was 11.603 GW of wind power [1] in the US and 48.122 GW in Europe, and in 2015 the installed power was 74.472 GW in the US and 141.575 GW in Europe [2, 3]. These are “name- plate” capacities, the peak output from the wind turbines. We are really interested in the electrical energy that the wind turbine produces, not just the peak power. Most wind turbines [4] do not produce their rated power until the wind speed reaches about 12 m/sec (20kts ,25 mph). Clearly, to maximize the benefits the wind turbines should be placed in locations with constant high winds. The National Climatic Data Center [5] makes available data for wind at any given hour of the year averaged over a period of 30 years. On the basis of interpo- lation of NCDC data, Archer and Jacobson [6] divided the winds at 80m, a typical

*Corresponding author: [email protected] DOI: 10.7569/JSEE.2017.629514

194 J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms hub height for wind turbines, into a number of classes on the basis of average wind speeds. From this analysis they concluded that one quarter of the US is suit- able for providing electrical power competitive with or [7]. In a subsequent paper Archer and Jacobson [8] extended this analysis worldwide and concluded that wind power could meet all the world’s energy needs. Hoojwijk et al claimed that onshore wind energy would provide 6-7 times the 2001 electrical energy consumption [9]. The real measure of how much energy can be obtained from wind power comes from the capacity factor, defined as the energy actually produced by the wind tur- bine divided by the energy that would have been produced if the unit had been operating at its rated nameplate power 24hrs a day, 365 days a year. Over the range of wind speeds observed in most locations the power output as a function of wind speed v can be represented as a continuous function, P(v), characteristic of the specific wind turbine. The simplest theory would suggest that

Pv( ) ∝ v3 (1) but this only works well at low wind speeds. In practice the power curves of the turbines from the various manufacturers [4] are very similar. The definition of a capacity factor is

1 T CF = ∫Pv()(td) t (2) TP× rated 0 where the time period T extends over many years to average over annual fluctuations. If we have N years of hourly averaged measured wind speeds v(y,h) where y refers to the year and h refers to the hour the capacity factor, CF, would be

11N 8760 CF = Pvyh, × (3) 1 ∑∑ hy == 1 ()( ) N 8760 × Prated

Capacity factors of 30–40% have often been assumed in evaluating the potential of wind power [10, 11] and average capacity factors of 30–40% have been claimed for wind farms in Hungary [12] and Iran [13]. However the measured outputs for the Iranian wind farms are still lower than those estimated from the power curves of the wind turbines [13]. The authors attributed this discrepancy to a need to take into account the probability distribution of wind speeds over short time intervals. In a detailed analysis concentrating on European wind farms Boccard [14] ques- tioned whether capacity factors of 30–35% are realized in practice. He concluded that the average capacity factor for European wind farms was 21%. In a study of

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J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 195 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms the embodied energy of three US wind farms White [15] gave capacity factors of between 20% and 28%. Using data from the Energy Information Agency [16] and the Global Wind Energy Council [3] the average capacity factors for all wind energy between 2004 and 2010 is 25% for the US, 17% for Germany, and 23% for the UK and Denmark. Although using measured wind speed is clearly preferable, in practice they are not readily available at hub height, and in many cases capacity factors have been calculated from theoretical wind speed distributions, such as how the Weibull dis- tribution and power law fits to the manufacturer’s power curve. The parameters defining the Weibull distribution

kk−1 k  v   v  pv( ) =   exp −    (4) c  c   c  c and k can be related to the mean and standard deviation of the wind speed distri- bution [17]. The Rayleigh distribution corresponds to the special case when k = 2. A comparison of these different approaches was given by Ditkovich. [18]. Rather than use wind speed classes in this work we have used the actual hourly measured average wind speeds throughout the year in conjunction with the pub- lished power curves to calculate a capacity factor for various wind farms in differ- ent locations across the United States. A key assumption is that wind speeds vary with height above the ground. Typical turbine hub heights are 80m, while winds speeds in the NCDC database are measured at a standard height of 10m. Two models are used to relate wind speeds at different heights above ground. One model relates the wind speed at height hz to that at a reference height h0 by a power law.

a  hz  VVz = 0   (5)  h0 

1 where a is often assumed to be . 7 An alternative model, the log law, relates wind speeds at different heights to surface roughness n h ln z VV= n (6) z 0 h ln 0 n

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196 J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms

In practice the differences in wind speeds between 10m and 80m predicted by these models is quite small. A surface roughness of 2.5 cm is equivalent to the power law exponent of 1/7 when comparing wind speeds at 10m and 80m. The exponent, α, in the power law model varies considerably from one place to another and even changes with time of day [19, 20]. Lackner et al [21] shows a variation from close to zero to 0.4, and Rehman and Al-Abaddi [20] show differ- ences in exponent for winds measured on two sides of the same wind tower in Saudi Arabia. They also show how different values can be derived from measure- ments at different heights above ground. Values of wind exponents of 0.45 have been claimed for sites in Hungary [12] and Malta [22] though these are implausi- bly large. That would imply a wind shear of 25 kts between 10m and 80m when the wind at 10m is 20kts. A typical airliner flying a standard approach would then very likely crash on landing approach. For a single site in Italy, Gualtieri and Secci [19] found a wind shear exponent of 0.3, though this is probably strongly influenced by the local topography. For completeness we have chosen to give 1 capacity factor estimates both with an exponent of and with the 10m wind 7 speed. Our analysis shows that capacity factors vary greatly according to location. In the Texas panhandle and Oklahoma, where there are more or less constant high winds, it is possible for capacity factors to reach 40%. In other locations such as Illinois, where high winds just coincide with the passage of weather systems, capacity factors are only 10-15%. It’s not enough to look at average wind speeds; before installing a wind turbine, it’s essential to do an estimate of the expected capacity factor from the measured wind speeds (preferably at hub height) in the actual location.

2 Method To investigate how capacity factor might vary with location, wind farms in differ- ent regions of the United States were selected. As can be seen from Figure 1, a map showing the location of the wind farms, two were in Texas, 1 each in Colorado and North Dakota, 2 in Illinois and 1 in New York. Data for all wind speeds were obtained from the National Climatic Data Center (NCDC) website. NCDC makes available data for wind at any given hour of the year averaged over a 30 year period from 1981 to 2010 [5]. If v(y,h) represents the wind speed at hour h of year y the NCDC compilation is

1 N vhNCDC ( ) = vy( , h) (7) N ∑ y=1 For any particular NCDC location this means there are 8760 values which ­represent an average wind speed for a particular hour of the year.

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J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 197 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms

Figure 1 Map of US wind farms where capacity factors were determined.

There is a 90% correlation between winds at sites spaced closer than 50 km [11, 23]. The NCDC reporting location closest to each of the wind farms was selected. Table 1 shows the wind farms considered in our study, the wind turbines used at that wind farm, the NCDC location for the wind speeds, and the distance from the wind farm. The power curve information was found from the table published by Carillo et al [4]. In practice the performance of turbines from the different manufac- turers is very similar when scaled according to output and wind speed to deliver rated power, as shown in Figure 2 The output power for a given wind speed corresponding to the NCDC data points were calculated by interpolation using a cubic spline. This gives a better fit to the power curve than the polynomials used by Archer and Jacobson [6]. The capacity factor was then found according to the expression given as equation 8.

8760 1 CF = Pv h × NCDC ∑ h=1 ()NCDC ( ) (8) 8760 × Prated

This analysis is similar to that used for the UK by Sinden [11] though we have extrapolated the 80 m wind speed from the 10 m wind speed using a power law

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Table 1 Wind Farms and NCDC sites. The distance is the distance between the wind farm and the airport site where the winds were measured. Wind farm NCDC site Distance (km) Turbine type Bison Wind Farm Bismarck Municipal 65 Siemens SWT-2.3-101 Airport Siemens SWT-3.0-101 Siemens SWT-3.2-113 Black Hills Wind Farm Pueblo Memorial 77 V100 1.8 MW Airport Wildorado Wind Ranch Amarillo International 40 Siemens SWT-2.3-93 Airport (Mk II) Trent Wind Farm Abilene Regional 48 GE 1.5 MW Airport Rail Splitter Wind Farm Peoria International 47 GE sle 1.5 MW Airport Twin Groves Wind Farm Peoria International 71 Vestas V82 1.65 MW Airport Wethersfield Wind Park Greater Rochester 48 GE sle 1.5 MW International Airport

Vesta V82 GE sle Vesta V100 SWT-2.3-93 Power curve comparison 1

0.8 r we

0.6

tion of rated po 0.4 opor Pr 0.2

0 0510 15 20 25 30 35 Wind Speed (mph)

Figure 2 Comparison of power curves used to find capacity factors.

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J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 199 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms with a fixed 1/7 exponent while he derived a relationship between 80 m and 10m wind speeds by fixing the average capacity factor at 30%. Calculating the capac- ity factor using wind speeds for a given hour averaged over a period of 30 years might not be the same as calculating the 30 year average of the capacity factors as given by equation 2. To test the effect of the averaging procedure we used hourly wind speed data recorded at Mogollon Airpark, AZ, over a 5 year period. We compared the capac- ity factor for a GE 2.5xl turbine sited at Mogollon with the capacity factor for the same wind turbine estimated from the 30 year average winds from the NCDC data set for Winslow, 71.5 km away. Both these sites are in the favorable band for outlined by Acker et al [24]. Since the anemometer at Mogollon is at a height of 3m, the wind speeds were corrected to those appropriate for a hub height of 80 m using equation 5.

2.1 Results and Discussion The use of wind speeds for a given hour averaged over many years to calculate capacity factor was tested by comparing with a capacity factor calculated from the hour-by-hour wind speeds measured at Mogollon Airpark over a 6 year period. The capacity factor for the GE 2.5xl sited at Mogollon Airpark was 20%, very close to the estimate from the estimate of 20.4% from the averaged NCDC data for the same turbine sited at Winslow. The averaging of the wind speed at a given hour over 30 years gives a useful picture of the range of possible wind speeds at any given time of the year. A plot showing the measured NCDC wind speed for Dallas and Rochester is shown as Figure 3 (a) and (b). The width of the band is a good measure of the distribution of wind speeds and is a good measure of the intermittency. At any given time a range of wind speeds is possible. The wind speeds at a hub height of 80m were estimated from equation 5 and are shown in Figure 3c and 3d. The estimated wind speeds at 80m in conjunction with the power curves gives a band of possible power outputs. The variation as a fraction of rated power throughout the year is shown for Rochester as Figure 4a and Dallas in Figure 4b. The width of the band corresponds to between 0.2 and 0.7 the rated power for Dallas, with seasonal peaks of 0.9 rated power in April, and 0.6 rated power in December. For Rochester the band again corresponds to 0.2 rated power. The seasonal peaks, again in April and December, are much lower corresponding to about 0.4 rated power. The capacity factors for the wind farms listed in Table 1 are given as Table 2. Equation 5 was used to estimate the wind speed at hub height from the wind speed at the nearest NCDC site. It is of interest to see the effect of the wind shear correction, so Table 3 gives what the capacity factors calculated would have been using the NCDC reported wind speeds 10m above the ground.

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Wind speed (mph) Wind speed (mph) Cut in speed Cut in speed Rochester 10m winds Lubbock 10m winds 20 25

15 20

15 10

10 Wind speed (mph) Wind Wind speeds (mph) Wind 5 5

0 0 Jan MarMay Jul SepNov Jan Mar May Jul SepNov (a)(Month b) Month

Adjusted wind speed (mph) Adjsuted wind speed (mph) Cut in speed Cut in speed

Rochester 80m winds Lubbock 80m winds 20 25

20 15

15 10

10 nd speed (mph) Wind speed (mph) Wind Wi 5 5

0 Jan MarMay Jul SepNov 0 Jan MarMay JulSep Nov (c)(Month d) Month

Figure 3 NCDC wind averaged wind speeds throughout the year for (a) Rochester NY measured at 10m and (b) Lubbock TX measured at 10m, (c) Rochester NY corrected using equation 5 to give winds at 80m (d) Lubbock TX corrected to using equation 5 to give winds at 80m.

The main effect of the wind shear correction is on the lower wind speeds. Figure 5 shows the change in the wind speed distributions for Rochester. Without the wind shear correction lower velocity winds are less than the cut in speed and make no contribution to the power output. The increase in wind speed at 80 m shifts the wind speed distribution so that the peak is above the cut-in velocity and

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Fraction of Fraction of Rated power rated power 1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 Jan MarMay Jul SepNov JanMar MayJul SepNov (a)(b)

Figure 4 The band showing the fraction of rated power throughout the year for a wind farm at (a) Rochester NY and (b) Lubbock TX derived from the NCDC wind speeds corrected by equation 5 to give wind speeds at a hub height of 80m and the relevant turbine power curves.

Table 2 Capacity factors of a number of sites in the US calculated from winds at 10m corrected to the appropriate hub height using equation 5. Energy from wind Energy from Capacity speed distribution nameplate factor % (GWh) capacity (GWh) Wethersfield Windparks 149 1100 13.50 (NY) Black Hills Wind Farm (CO) 39.8 252 15.81 Wildorado Wind Ranch (TX) 578 1410 41.03 Twin Groves Wind Farm (IL) 461 3470 13.28 Rail Splitter Wind Farm (IL) 97.0 880 11.02 Bison Wind Farm (ND) 385 2560 15.08 Trent Wind Farm (ND) 319 1310 24.26 these winds can make a contribution to the overall energy generated throughout the year. Although it would appear from the power curve that the contribution would be small, the higher probability of these low velocity winds means that the contribution is significant, increasing the capacity factor from 3-4 % to about 15% for Rochester NY.

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Table 3 Capacity factors using measured wind speeds at 10m height. Energy from wind speed Energy from Capacity distribution (GWh) nameplate factor % capacity (GWh) Wethersfield Windparks 42.3 1100 3.84 (NY) Black Hills Wind Farm 13.6 252 5.38 (CO) Wildorado Wind Ranch 216 1410 15.35 (TX) Twin Groves Wind Farm 112 3470 3.22 (IL) Rail Splitter Wind Farm 26.1 880 2.97 (IL) Bison Wind Farm (ND) 137 2560 5.35 Trent Wind Farm (ND) 103 1310 7.86

Approximated speed Power curve Wind speed Power curve

80m estimated wind speed 10m measured wind speed 2200 1400 2200 1400

1200 1200 1650 1650 1000 1000

800 800 e (kW) e (kW)

1100 1100 unt Count 600 600 Co wer cu rv wer 400 cu rv wer 400 Po 550 Po 550 200 200

0 0 0 0 0510 15 20 25 0510 15 20 25 Range (mph) Range (mph)

Figure 5 Histogram showing frequency relative to cut in speed of a wind turbine at Rochester, NY.

Discussion Capacity factors vary by a large range depending on location and wind speed distributions. Plotting the averaged hour-by-hour wind speeds from the NCDC data set gives a good picture of the range of possible wind speeds for a given time of the year. It’s possible to have capacity factors as high as 40%

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J. Sustainable Energy Eng., Vol. 5, No. 3, December 2017 203 Larsen and Rez: Estimates of the Capacity Factor of Wind Farms for favorable locations such as Wildorado Ranch in the Texas panhandle. Not surprisingly, the North Dakota wind farm has a higher capacity factor than the average but still lower than the Texas wind farm. In most places capacity fac- tors are more likely to be 20% or lower. This is in agreement with the study of White [15]. In the United States there has been a trend to using combined cycle natural gas turbines for baseload . In a combined cycle, the hot exhaust gases from the gas turbine are used to generate steam for a steam turbine. The overall thermal efficiency can be very high, in the range of 50-60%. About one third the total power output comes from the steam cycle and two thirds from the gas turbine operating on its own. [25]. However like all steam cycles it takes time to start and is unable to meet the fluctuating load from renewables. In the absence of extensive storage, wind power can only be combined with the gas turbines operating on their own to cope with the rapid changes in output. If wind, or for that matter solar, makes it impossible to run the combined cycle and achieve the higher thermal efficiency, it is reasonable to ask whether more CO2 is emitted with a combination of the renewable and the gas turbine on its own. Clearly if the gas turbine alone is providing more than 67 % of the energy when matching the peak wind power, and the wind or solar is providing less than 33% of the energy, more CO2 is emitted than if the combined cycle were operating continuously. That means that if wind power is displacing combined cycle natural gas the capacity factor has to be greater than 33% for a net reduction in CO2 emissions. This does not seem to be the case except in the most favorable locations such as the Texas panhandle.

Conclusions We have calculated the capacity factor of wind farms across the United States from NCDC wind data and the manufacturer’s power output curves. In Texas, where high winds, ~ 10m/sec, are frequent, capacity factors of 40% are possible. In other parts of the country where average wind velocities are lower, we estimate capacity factors to be about 15%. The largest uncertainty in our estimate is the wind shear model used to estimate wind velocities at typical hub heights of 80m from wind velocities measured at 10m. To evaluate whether it is worthwhile to build a wind farm at a given site the capacity factor should be calculated from actual measured wind speeds at the hub height. Due to its intermittent nature, wind power has to be combined with fast acting gas turbines to meet a baseload electrical energy requirement. If the wind is substituting for the highly efficient combined cycle gas turbine units, the capacity factor has to be greater than about 33% for there to be a net reduction in CO2 emissions. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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