Wind energy statistics for large arrays of wind turbines (New England and Central U.S. Regions)

SularEnergy.Vol.20.pp. 379-386. PergamonPress1978.PrintedinGreatBritain

WIND ENERGY STATISTICS FOR LARGE ARRAYS OF WIND TURBINES (NEW ENGLAND AND CENTRAL U.S. REGIONS)t C. G. JUSTUS School of Aerospace Engineering,Georgia Institute of Technology, Atlanta, GA 30332 U.S.A. (Received 10 December 1976; in revised form 19 June 1977; received for publication 27 September 1977)

Abstract--The performance characteristics have been simulated for large dispersed arrays of 500-1500kW wind turbines producing power and feeding it directly into the New England or Central U.S. utility distribution grids. These studies, based on design power performance curves, indicate that in good wind environments the 500 kW generators can average (on an annual basis) up to 240 kW mean power output, and the 1500kW generators can average up to 350 kW mean power output. Higher mean power output (averaging up to 470 kW) is indicated, however from a hypothetical 1125kW rated power unit designed to operate at wind speeds near those observed throughout the study area, rather than the higher design operating wind speed of the 1500kW unit. The beneficial effect of operating large disperse arrays of wind turbines is that available power output can be increased--if winds are not blowing over one part of the array, chances are they will over some other part of the array. These studies indicate that wind power availability levels of 200 kW per 1125kW generator were 77-93 per cent, depending on season. Reasonably steady high wind power in winter and high afternoon peak wind power in summer (corresponding to peak air conditioning load) means that significantpeak load displacement can be achieved without the use of storage.

1. INTRODUCTION This paper reports on the evaluation and analysis of wind energy output statistics of simulated arrays of wind turbines in the New England and Middle Atlantic Federal Power Commission (FPC) Regions of the U.S. (Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, New Jersey and Pennsylvania) and in portions of the West North Central and West South Central FPC Regions (namely Nebraska, Kansas, Missouri, Oklahoma and Texas). For this s)mulation, U.S. National Weather Service tape data on wind speed (1 rain average) at 3 hr intervals were obtained from 53 sites within the two study areas for the 5 yr 1965-69 (New England Area) or 1969-73 (Central U.S. Area). These time series wind data were extrapolated to a uniform wind turbine hub height of 43m (140ft), by methods described in the Appendix. Linear interpolation was used to fill in one or two observation gaps in the data. Sites with more than two consecutive observation gaps were rejected for the month during which the gap occurred. The measured one minute average winds, adjusted to wind turbine hub height were used in power output curves, illustrated by Fig. 1 and described in the Appendix to compute "instantaneous" power output from the simulated wind turbines. Power output from 3 different simulated wind turbine designs were evaluated and reported here: 500 kW, and 1500 kW (Mod 1) designs and a hypotherical 1125 kW rated power design. The power output curves for these wind turbines were determined from wind turbine characteristic parameters given in Table 1. All of these wind turbine designs are, of course, somewhat hypothetical since none of them represent 1"Presented at the 1976 ISES International Solar Energy Conference. Winnipeg.Canada, 15-20 August 1976.

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Wind Speed, mph

~4

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/ Rated Pow t Rated Wind Speed

I

//

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o

'

4

Cut-In

8

12'

v2o'''

Wind Speed, m/s

24

Fig, 1. Assumed power output curve for the 500kW power turbine, power vs hub height wind speed. actual available hardware. Hence there are no guarantees that actual power output from any of these designs, were they to be built, would correspond to the computed outputs presented here. It should also be noted that the 1500 kW (Mod I) wind turbine was designed for sites with higher mean wind speeds then the airport locations used in this study. Therefore, comparative power performance among the machines studied would be different in different wind regimes. Simultaneous values of power output from a collection of National Weather Service sites were combined at each time to simulate the power output of a widely dispersed array of wind turbines. All array power statistics are expressed as power per array generator. Hence, the simulated array can be considered as made up of wind energy "farms" of several wind turbines per site with all generators at a given site being considered 100 per cent correlated.

379

C. G. JUSTUS

380

Table 1. Characteristicsof the wind turbines used in the site array analyses, 500 and 1500kW values adapted from [3] 1125kW values from[4] Rated Power (kW)

500

1500

1125

Rated Wind Speed at Hub Height (m/s)

9.4

13.1

I0.4

(mph)

21.0

29.3

23.3

(m/s)

4.6

6.6

4.2

(mph)

10.3

14.8

9.4

(m/s)

23.2

28.8

26.8

(mph)

51.9

64.4

60.0

(m)

55.8

57.9

80,8

(ft)

183

190

265

42.7

57.0*

140

187"

Cut-ln Speed at Hub Height

Cut-Out Speed at Hub Height

Rotor Swept Diam.

Tower Height

*

(m)

42.7

(ft)

140

.

Design tower height, 42.7 m (140 f t ) used in these studies, for consistency.

The results reported here address the question of the degree to which wind power availability can be increased by the use of large dispersed arrays of wind turbines (without resort to storage) and the approximate amount of storage time required in order to achieve 90-99 per cent availability of various power levels, so that "credited power" can be provided by wind. From available National Weather Service sites, 28 were selected in the New England and middle Atlantic region study area. In addition to the full 28 site array, three sub-groups of sites were considered as smaller arrays: the New England inland array (13 sites), the Middle Atlantic inland array (8 sites) and the Coastal array (7 sites). These array site locations are shown in Fig. 2 and listed in Table 2. In the Central U.S. Region, 25 sites were selected for study and also divided into two sub-groups: the 13 site North Central array, and the 12 site South Central array, as shown in Fig. 3 and listed in Table 3. 2. WIND POWER OUTPUT AND SEASONALVARIATIONS

One minute average winds, adjusted to 43 m (140ft) hub height were used in wind turbine power output curves to compute "instantaneous" output power from the 3 different wind turbine designs studied. These output power values were averaged over one month intervals, and corresponding months were averaged over the 5 yr studied. Figure 4 shows computed seasonal variations in monthly mean output power from the 3 wind

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Fig. 2. Map of New England--MiddleAtlantic area array sites.

turbine designs for the 25 site Central U.S. array. The seasonal variation in output power follows closely the seasonal variation in monthly mean wind speed. The 1500kW (MOd 1) wind turbine is more sensitive to seasonal variations because of the necessity of higher winds for effective operation of this higher rated power machine. Highest mean power output is indicated from the 1' ~ kW wind turbine, which produces higher power levels than the 500 kW machines during good winds, and (because of the relatively low cut-in and rated speeds) is less sensitive to seasonal variations than the 1500kW

Wind energy statistics for large arrays of wind turbines

381

Table 2. Site names for the New England--Middle Atlantic area sites ABE

Allentown, PA

FMH

Falmouth, MA

ACK

Nantucket, MA

]FK

New York (3. F. Kennedy), NY

Atlantic City, N3

ACY

LGA

New York (Laguardia), NY

ALB

Albany, NY

NEL

Lakehurst, N3

BDL

~'indsor Locks, CT

NHZ

Brunswick, ME

BDR

Bridgeport, CT

OLD

Oldtown, ME

BED

Bedford, MA

ORH

Worcester, MA

BGR

Bangor, ME

PIlL

Philadelphia, PA

BOS

Boston, MA

PSM

Portsmouth, NH

BTV

Burlington, VT

PVD

Providence, RI

CAR

Caribou, ME

PWM

Portland, ME

CEF

Chicopee, MA

SWF

Newburgh, NY

CON

Concord, NH

WHN

Westhampton, NY

EWR

Newark, N3

497

New York (.=!oyd Bennett), NY

Table 3. Site names for the Central U.S. area sites ABI

Abilene, TX

I,~F

ACT

Waco, TX

MCI

KansasCity (Intnl.), MD

AMA

Amarillo, TX

OFK

Norfolk, NB

AUS

Austin, TX

OKC

OklahomaCity, OK

BFF

Scottsbluff, rib

OMA

Omaha,NB

CNK

Concordia, KS

RSL

Russell, KS

DAL

Dallas (Love), TX

SAT

San Antonio (Intnl.), TX

DDC

DodgeCity, KS

SJT

San Angel•, TX

GLD

Goodland, KS

SPS

Wichita Falls, TX

GRI

Grand Island, NB

STJ

St. Joseph, MO

ICT

Wichita KS

TOP

Topeka, KS

LBB

Lubbock, TX

TVL

Tulsa (Intnl.), OK

LBF

North Platte, NB

I. . . . .

....

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i

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V|

, |

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j LBB

.... "~-

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olCT

,'.='*, J

/

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i,}idland, TX

I r • MAF

o,.CENTRAL

ABI

sl~.....

• •SJT

i

LI

eDAL •ACT

g

• S. CENTRAL

Fig. 3. Map of Central U.S. a r r a y sites.

Mod 1 machine. Similar results (not shown) were found in the New England Region. As mentioned in Section 1, these comparisons might be different for simulated performance in higher wind speed areas than the airport locations used here, i.e. winds corresponding to those for which the Mod 1 1500kW machine was optimized. The new Mod 2 2000 kW wind turbine design, which will have a blade diameter of about 91 m (300 ft) and hub height rated speed near 10.6 m/s (24 mph) would have the high power output per rated kW of the 500 kW or 1125 kW wind turbines studied here, because of its lower rated speed than the Mod 1 1500 kW machine. The general correspondence between monthly mean power and monthly mean wind speed is illustrated for the 500 kW wind turbine, in Fig. 5. Both single site and. array monthly mean power appear to follow approximately the same relationship with monthly mean speed,

382

C.

....

600

E

each time i, where P(V~) is the wind turbine output as a function of the observed wind speed V~ (adjusted to hub height). Frequency distributions of array power were similarly evaluated by counting up array power values in the various power intervals, where at each time i the • array power/3 was evaluated by summing over the n individual sites in the array

2S'SiTt: A'RIIAY ']

/~CENTRAL

'°°( ,,o° •

G. JUSTUS

1125

U.S.

!

i

O. i i i i , , t ~ , , t , ~ I FMAMJ I ASON D

~, = ~ Pj(v,). j=l

:

Month

Fig. 4. Seasonal variation of monthly mean power output in Central U.S. region for 500, 1500 and l125kW rated power machines. although there is more scatter in the case of the individual site data. The dotted line in Fig. 5, which goes from zero power at 0.69 Vo to rated power at 1.27 V~, where Vo and V~ are the cut-in and rated speeds, adequately characterizes the array mean power versus mean wind speed. Similarly constructed linear relationships also work well for the other wind turbines simulated. For comparison purposes Fig. 5 also shows the theoretically available instantaneous output power, 'ffpV3 d2/8, versus instantaneous wind speed V, and the actual power output curve of instantaneous power versus instantaneous wind speed. At low wind speeds, Fig. 5 shows that monthly average output power versus monthly average wind speed exceeds the instantaneous available power at the same value of instantaneous speed. This is due to the effects of the non-linear power output curve on the monthly averaging of power values and wind speeds (i.e. the same reasons that, for example, the mean of V3 is larger than the cube of the mean V). , ~ ~ o , t ~ o o[oSingle Site ~ / -~ ~ [ e A r ray ~-/ a! I , ~ ~ ., , ~ / ¢sg,fF ~ , / - -~

(1)

Figure 6 shows an example 5 yr average January single site and array power output frequency distribution for the Central U.S. Region. These frequency distribution curves can be used to determine the improvement in power output availability which can be achieved by dispersing the wind turbines into arrays. For example, Fig. 6 shows for the 1125 kW turbine that a power output level of 200 kW per generator in the array has 90 per cent availability (10 per cent cumulative probability), whereas the single site power output level of 200 kW per generator has only 62 per cent availability (38 per cent cumulative probability). For a 100kW per generator power level, the array yields 99 per cent availability versus 71 per cent availability for that power level in single site configuration. As shown by the dotted curves for hypothetical zero correlation arrays in Fig. 6, increased power availability could be obtained from arrays which have lower than the observed spatial correlation (observed to average roughly 30 per cent for the Central U.S. Region). Note that the actual (approximately 30 per cent correlated) array output power distribution curve falls between the curves for single site (100 per cent correlation) and the zero correlation array curves. An analytical model has been developed, and will be reported later, which allows the array distribution to be estimated from the single site statistics and the average correlation of the array. Improved array output power availability could be achieved by spreading the array over a larger spatial area or by going to a larger number of sites (since (r,, the

gg

I

...............

~.o

Avg. :. . . . . . .

Fig. 5. Monthly average single site and array output power vs monthly average hub height wind speed for 500kW turbine. Comparison curves show instantaneous power vs instantaneous speed.

3. WINDPOWERAVAILABILITY Frequency distributions of individual site output power were evaluated by direct "counting up" within power intervals of observed single site power P(V,) for

~.

J

~

/// . . . . . . . .

/'

Increase

~ 2'~---620/0 to 90% i ~ , , , ~ * , , ,-71%, , _L~_t° 99%~J J ~] 1 2 5 10 20 40 60 80 90 95 99 99.9 Cumulative Frequency, Percent

Fig. 6. Power output frequency distribution for 1125kW wind turbine. Average power output is 470kW from array or individualsite. 100 per cent correlationindicates individualsite, 30 per cent correlation is observed average correlation of actual array, 0 per cent correlation is theoretical uncorrelatedarmy.

Wind energy statistics for large arrays of wind turbines standard deviation about the mean power for an uncorrelated n site array, decreases as n -~/2 and makes the slope less steep for the zero correlation array curve), Even with non-zero correlation, the increase in number of sites would still improve the power availability to some extent, Availability levels without storage for both individual sites and for the arrays are summarized in Tables 4 and 5. (T= 0 in Tables 4 and 5 indicates the no storage cases). These tables show that the improved statistics of arrays mean that some small amount of power (e.g. 10 kW per generator) is virtually always available with the array configuration,

383

For an approximate analysis of array power availability with storage the statistics of array power return times were evaluated at two power levels (100 and 200 kW per generator). An array power return time (sometimes called run duration) tR(P) for a given return power P is defined as the time required for the array power output to return above the level P after once going below that value. Return powers are expressed as power per generator. Thus, for an array of n generators, the array return power would be n times P. By evaluation of all return times over the duration of a month the monthly mean and probability distribution of return times were evaluated. The averaging was continued over cor-

Table 4. Availability of power levels of 10,100 and 200 kW per generator with and without storage, 7 site coastal arrayor individual site, T is storage time in hours. R is availability (probabilityof available power) in percent T = 0 indicates no storage. Alternately for T# 0, 1 - R is the probability of encountering a power lull of duration T, at the given power requirement of 100 or 200 kW per enerator and no storage JAN kated Power (kW)

APR

500

1500

T hrs.

R %

T hrs.

JUL

500 R %

T hrs.

1500 R %

T hrs.

OCT

500 R %

1500

T hrs.

R %

T hrs.

500 R %

T hrs.

1500 R %

T hrs.

R %

J

8--,

l,~ID.

0

78

0

60

0

80

0

60

0

72

0

44

0

74

0

51

o

ARRAY

0

98

0

91

0

99

0

93

0

99

0

87

0

97

0

87

IND.

0

~ ~

64

0

54

0

66

0

53

0

54

0

36

0

59

0

44

83

0

75

0

83

0

74

0

70

0

56

0

75

0

63

20

90

22

90

13

90

17

90

15

90

22

90

19

90

28

90

27

95

28

95

15

95

19

95

17

95

26

95

27

95

42

95

47

99

44

99

20

99

23

99

22

99

36

99

49

99

82

99

IND.

0

56

0

49

0

59

0

48

0

44

0

31

0

51

0

40

o

65

0

62

0

65

0

62

0

44

0

37

0

53

0

49

~ 5

29

90

28

90

20

90

25

90

29

90

33

90

39

90

38

90

39

95

38

95

25

95

33

95

37

95

49

95

53

95

48

95

99

64

99

37

99

43

99

60

99

110

99

80

99

74

99

Table 5. Reliability of power levels of 10, 100 and 200 kW per generator with and without storage, 25 site full array or individual sites. T is storage in hours, R is availability in percent T = 0 indicates no storage JANUARY Rated [ Power

(kv!

. 500 T hrs.

APRIL

1500

1125

R %

T hrs.

R %

T hrs.

500

R %

T hrs.

JULY

1500

R %

T hrs.

R %

OCIOBER

1125 T hrs.

R %

500 hrs' 500TR %

T 1500R

T

hrs.

%

hrs.

]500

11251

1125R %

I T 'hrs.

R %

T hrs.

R %

T hrs.

R %

IND,

0

79

0

53

0

84

0

85

0

64

0

90

0

78

0

49

0

84

0

75

0

48

0

81

ARRAY

0

lO0

0

99

0

I00

0

lO0

0

99

0

lO0

0

100

0

99

0

lO0

0

lO0

0

99

0

lO0

IND.

0

63

O

47

0

71

0

73

0

59

0

79'

0

50

0

41

0

69

0

58

0

42

0

66

t

0

94

0

84

0

99

0

95

0

91

0

99

0

88

0

78

0

97

0

82

0

72

0

95

13

90

17

90

9

90

I0

90

I0

90

5

90

I0

90

II

90

9

90

14

90

19

90

10

9D

IND.

16

95

22

95

I0

95

II

95

]l

95

5

95

II

95

13

95

I0

95

16

95

24

95

II

95

21

99

35

99

12

99

13

99

13

99

6

99

13

99

18

99

12

99

22

99

39

99

13

99

0

53

0

43

0

62

0

64

0

56

0

72

0

48

0

37

0

59

0

47

0

39

0

57

0

59

0

59

0

90

0

77

0

78

0

93

0

53

0

50

0

84

0

53

0

53

0

77

33

90

27

90

13

90

14

90

14

90

lO

90

20

90

25

90

II

90

36

90

38

90

15

90

37

95

34

95

18

95

16

95

16

95

II

95

32

95

36

95

13

95

45

95

49

95

18

95

46

99

54

99

37

99

34

99

21

99

13

99

69

99

58

99

16

99

66

99

78

99

24

99

k

384

C.G. JuSTUS

responding months of the 5 yr record to compute the overall average return times and the average return time probability distribution. If a storage system is designed to provide P kW per generator for T hours (i.e. for n generators, the total storage in kWh is nPT), and if an array power return time te(P) is found to have, say, a 90 per cent cumulative probability then 90 per cent of the time when the array output power goes below nP the available kWh of storage would not be exhausted before the array power returns above nP again (assuming the storage started fully charged with nPT kWh). Thus a 90 per cent cumulative probability for re(P) = T means roughly that the storage time T will provide array power P per array generator with an availability of 90 per cent. For more accurate assessment of power availability achieved by various storage, a time series simulation of the storage status (i.e. amount of kWh available) must be performed. This is because a long period of time when storage is required could begin with the storage already partially exhausted, instead of fully charged. An alternative interpretation of the return time is in terms of the probability of have a no-storage power output lull of time T. Thus, if a return time T is observed to have a cumulative probability R, the probability that a power lull (with no storage), once the lull has begun, will last as long as T hours or longer, is 1-R. Figure 7 shows the observed frequency distribution (cumulative probability) for return times of various durations: From Fig. 7 it can be seen that, by interpolation, the 500 kW wind turbine, for example, would have 90 per cent availability of 200 kW per generator power output if there were a storage system with about 20 h of power storage (i.e. 4000 kWh storage capacity per generator, 200 kW x 20 h). Similarly the 500 kW wind turbine in Fig. 7 would have 95 per cent availability of 200 kW per generator power if about 32 h of storage were available. For 100 kW per generator and 200 kW per generator, Tables 4 and 5 compare availabilities in percent for individual sites and arrays without storage (T = 0), and the storage time, (in hr), required to produce the given

.

4. DIURNALVARIATIONSOF WIND POWER OUTPUT

Although, in the wind power studies reported above, wind power output was not separately evaluated by time of day, some interesting and encouraging preliminary results have been obtained by a simplified diurnal analysis. Figure 8 shows the January and July 5 yr mean power outputs, estimated from wind speed values by time of day for Boston, projected to a hub height of 43 m (140ft). This figure shows that wintertime (January) estimated powers are high, with little diurnal variations, while summertime (July) estimated powers although lower on the average, have a significant afternoon peak which corresponds roughly with the afternoon air conditioning load. This correspondence of summertime available wind power to the air conditioning demand, means that the availability of wind power to provide "peaking power" in summer months is even better than the data of Tables 4 and 5 would indicate. I

i

i

[

i

JAN 6

g4 ~2

~o o 6

*

•

1500

o

500

8

100 f

:f

array power levels with 90, 95 and 99 per cent availability. The data in Tables 4 and 5 can alternately be interpreted in terms of probability of a power lull lasting (once started) as long as time T if no storage is available (with 10, 5 and 1 per cent lull probabilities corresponding respectively to the 90, 95 and 99 per cent R values).

t'2 t~

io JULY

12

1~

20 24

Time of Day, hrs

o

1500

/~/

Fig. 8. Mean power output for 500 and 1500 kW wind turbines versus time of day in Boston, estimated from hub height projected mean wind speeds.

lU

20

JULY

5. CONCLUSIONS -

2

5 10 20 40 60 80 90 95 99 99.9 Cumulative Frequency (Availability), %

Fig. 7. Frequency distribution (availability) for various return times (amount of storage), for 500, 1500 and l125kW wind turbines in the central U.S. region in July.

Simulation of performance of arrays of wind turbines in the New England, Middle Atlantic and Central U.S. areas indicates annual average output and seasonal maximums (Winter) and minimums (Summer) as shown in Table 6. This table, indicates annual average capacity factors (fraction of rated power) of about 40-50 per cent for the 500 kW, about 15-25 per cent for the 1500kW, and about 30--40 per cent for the l125kW machine. Seasonal variations are more pronounced for the

Wind energy statistics for large arrays of wind turbines Table 6. Annual average and seasonal maximum and minimum output power for three wind turbines. Range of values include variations from moderate winds (inland arrays) to good winds (coastal array) in New England and good winds in Central U.S. Wind Turbine

Seasonal Maximum Power

Annual Average Power

Seasonal Minimum Power

(kW)

(kW)

(kW)

V2 x Zh Z~ a p (r,

385

hub height cut-out speed of wind turbine number of generators at each array site hub height of wind turbines anemometer height exponent in height variation of "instantaneous" wind ambient air density standard deviation of array power about its average

REFERENCES

~Z..~ ~_~

500

2Q.0- 290

190 - 2t~0

1°,0 - [90

1500

3.50 - /490

2#0 - 3t40

130 - 190

.500

310 - 3#0

2#0

tt~0 - 160

Z L:J

.,a •(

. ~

,,,.)

1500

.5#0

1125

630 - 690

-

610

320

-

330

t~60 - #70

II0

-

1.50

250 - 290

1500 kW (ranging in N e w England from a summertime low of about 50 per cent of the annual average to a wintertime high of about 1.4 times the annual average). Seasonal variations for the 500 and l 1 2 5 k W units are less severe (ranging seasonally from 0.75 to 1.2 times the annual average). Availability of power outputs of 100-200kW per generator can be significantly improved by dispersing the wind turbines in large arrays. Much better availability can be achieved by the addition of 24-48 hrs of storage capacity. However, preliminary diurnal analysis indicates strong summertime afternoon peak wind power levels which correspond with afternoon air conditioning loads. This, combined with reasonably steady high wintertime wind power, may mean that significant "peak load displacement" can be achieved without resort to power storage systems.

I. C. G. Justus and Amir Mikhail, Height variations of wind speed and wind distribution statistics. Geophys. Res. Lett. 3, 261-264 (1976). 2. R. P. Zimmer, C. G. Justus, R. M. Mason, S. L. Robinette, P. G. Sassone and W. A. Schalter, Benefit-cost methodology study with example application of the use of wind generators. Re f. NASA CR-134864 (1975). 3. General Electric, Final presentation-wind turbine generator study contract. Re[. NAS-319403 (17 July 1975). 4. W. Wiesner and A. Kisovec, Design characteristics and cost of advanced technology wind turbine generator for Minnesota wind spectra. Boeing Vertol Rep. D210-11051-2 (Mar. 1976).

APPENDIX

Analysis methods Wind data. Wind speeds used in the study were the routinely measured (manual observation) 1 rain average wind speeds at National Weather Service Airport locations. The 1 rain average winds are read once per hr, on the hour. Only every third observation is digitized onto tape at most sites, however. Thus the input data are 1 rain average wind speeds spaced once per 3 hr (8 observations per day). For purposes of most statistics, the sample interval of 8 per day can be considered a quasi-random sampling method which provides approximately 240 samples per month per site, i.e. there is no significant loss of statistical information by the use of one l-rain sample every 3 hr. Wind speeds were measured at anemometer heights which varied from station to station and, in some cases, changed during the 5 yr period of study at a given site. In order to put all of the wind data on a common basis which would be most applicable to the wind power study, winds were projected from anemometer height Z~ to a common hub height Zh by the relation Vh = Va(ZhIZ~) ~

Acknowledgements--This work was supported by NSF Contract AER75-00647 and by ERDA Contract EY-76-54)6-2439.

a A b B C d n P /~ /~ Pj P, R T 'R V V~ Vc Vh V~ I/o Vj

NOMENCLATURE coefficient in height variation of exponent coefficient in power output variation between Vo and V~ coefficient in height variation of exponent coefficient in power output variation between Vo and V~ coefficient in power output variation between Vo and V~ rotor swept diameter number of separate array sites output power from wind turbine array average output power array average output power at time index i individual site output power for site j rated power of wind turbine availability of a power level amount of wind power storage time array wind power return time (time after array power goes below power P per generator until it returns above P) "instantaneous" (one minute average) wind speed measured wind speed at anamometer height average of cut-in and rated speed (Vo+ V,)12 extrapolated wind speed at hub height "instantaneous" wind speed at time index i (at site ]) hub height cut-in speed of wind turbine hub height rated speed of wind turbine

(A1)

where, from methods developed by Justus and Mikhail[l], the exponent a was considered to be variable with the measured wind speed Va at the anemometer height, through the relationship a = a + b In V~

(A2)

where the coefficients a and b are given by a = 0.37/[1 - 0.088 In (ZJl0)] b = - 0.088/[1 - 0.088 In (ZJl0)].

(A3)

For values of constants as given in eqns (A2)-(A4) the speed Va must be in m/s and the anemometer height Zo must be in meters. Wind turbine power output statistics. Prelimillary designs for 500-1500kW rated power turbine systems were used in the simulations of this study. Each wind turbine was assumed to have a power output curve similar to the one illustrated for the 500 kW wind turbine shown in Fig. 1. This curve is assumed to start at zero output power at the hub height cut-in speed Vo, increase to rated power at the rated speed V~, then remain constant at rated power up to the hub height cut-out speed V2, at which point the system is shut down for safety at high winds. At a given time the one minute average wind speed V, adjusted to 42.7m (140ft) hub height, is used as the argument of an analytical expression P(V) to determine output power for a given wind turbine. The analytical expression P(V) for the given

386

C.G. JuSTUS

generator is given by

up the array. n

0

P(V)=

A+BV+CV2 P, 0

V<-Vo V°
V,
P = ~ P(V,)/n (AS)

V > V2

where V,, is the hub height cut-in speed, V, is the hub height rated speed, V2 is the hub height cut-out speed, P, is the rated power and the coefficients A, B, and C are determined by solution of the following set of simultaneous conditions A+BVo+CVo2=O A + BV, + CVI 2 = P, A + BVc + CVc2 = P,(VclV,) ~

(A7)

i= l

(A6)

where V, = (V,, + V,)I2. General solutions for A, B and C from (A6) are given by Zimmer et al.[2]. At a given time the array output/5 is computed by averaging over the set of National Weather Service sites assumed to make

where P(VI) is the analytical expression (AS) evaluated at observed speed V~ (adjusted to hub height) at site i, and there are n sites in the array. This output per generator would be the same if one assumed n sites with one generator per site or, more realistically, assumed n sites with a "farm" of x generators at each site (x being the same at all sites). Various statistics such as mean, standard deviation, probability distribution, etc. are computed for the average individual site situation (all values of P(V~) for each site i for all times, i.e. about 240 n values per month) and for array average situation (values of/5 for all time, i.e. about 240 n values per month). Such statistics as probability distributions are evaluated by direct counting of values of P(V~) or/5 within various intervals--no reliance is made on any assumed analytical wind speed distributions. Analyses were performed for each month of a 5 yr time series, then results are reported as 5 yr average by averaging corresponding monthly data over the 5 yearly sets of results.

Resumen--Han sido simuladas las caracteristicas de comportamiento para grandes disposiciones dispersas de 500 a 1500 kW de turbinas de viento de producci6n de energh y alimentando diresctamente a la red de Nueva Inglaterra o del Centro de los Estados Unidos. Estos estudios, basados en las curvas de potencia de diseno, indican queen ambientes de buen viento, los generadores de 500 kW pueden promediar por encima de los 240 kW de salida anual, y los de 1500 kW encima de los 350. El mayor valor medio de salida (promediado encima de los 470 kW) se indica, sin embargo, para una unidad hipot6tica de 1125 kW de potencia nominal disefiada para operar a velocidades de viento cercanas alas observadas en los alrededores del ~ea en estudio en hgar del disefio de mayor velocidad de viento de 1500 kW. El efecto ben6fico de la operaci6n de disposiciones dispersas gTandes de turbinas de viento es que la potencia de salida puede incrementada; si el viento no sopla sobre una parte del sistema existe la chance de que Io haga en otra. Estos estudios indican que la potencia e61ica obtenible estfi en niveles de 200 kW para generador de 1125 kW, donde del 77 al 93% dependen de la estaci6n. En invierno hay un razonable alto nivel regular de viento yen verano un alto pico por la tarde (correspondiente al pico de carga por acondicionamiento de aire) lo que signitica que un significativo desplazamiento del pico de carga puede ser conseguido sin emplear acumulaci6n. R~um6--Les caract6ristiques du fonctionnement ont 6t6 simul6es pour de grandes 6tendues dispers6es de turbines ~, air de 500 k W h 1500 kW fournissant directement le r6seau 61ectrique national de distribution pour l'utilisation en Nouvelle Angleterre ou le centre des Etats Unis. Ces 6tudes, bas6es sur des courbes de performance de la puissance, indiquent que pour des environnements favoris6s pour l'6nergie 6olienne, les g6n6rateurs de 500 kW peuvent aller en moyenne (bas6e sur un an) jusqu'h 240 kW de puissance moyenne de sortie, et que les g6n6rateurs de 1500 kW peuvent aller jusqu'~ une puissance de sortie moyenne de 350 kW. On indique cependent une puissance moyenne de sortie sup~rieure (allant jusqu'~ 470 kW) pour une unit6 de puissance hypoth6tique 6valu6e h 1125 kW, con~ue pour fonctionner h des vitesses de vent proches de ceUes observ6es au-dessus de l'aire d'6tude, plut6t que la vitasse de vent plus 61ev6e dans le fonctionnement du projet de l'unit6 de 1500 kW. Le b6n6fice du fonctionnement avec de grandes 6tendues dispers6es de turbines ~ air est que la puissance de sortie disponible peut 6tre augment6e--si les vents ne soutflent pas au-dessus d'une partie de la surface, il y a des chances qu'ils seront pr6sents au-dessus de quelque autre partie de l'6tendue. Ces 6tudes indiquent que les niveaux disponibles de la puissance 6olienne de 200 kW pour un g6n6rateur de 1125 kW 6taient de 77 h 93 pour cent suivant la saison. Une puissance des vents raisonnablement 61ev6e et r6gull~re en hiver, avec un pic dans l'apr~s-midi en 6t6 (currespondant au pic de charge des besoins en air conditionn6) signifie qu'un d6placement significatif du pic de charge peut 6tre obtenu sans l'alde de stockage.