ESTIMATING WIND SPEED AS A FUNCTION OF HEIGHT …

SAND84-2530

Unlimited Release

Printed

1985

ESTIMATING WIND SPEED AS A FUNCTION OF HEIGHT ABOVE GROUND: AN ANALYSIS OF DATA OBTAINED AT THE

SOUTHWEST RESIDENTIAL EXPERIMENT STATION, LAS CRUCES, NEW MEXICO

D. F. Menicucci and I. J. Hall Sandia National Laboratories Albuquerque, New Mexico 87185

Abstract

Thermal modelling of photovoltaic arrays requires accurate estimates of wind speed at the level of the arrays. Wind speed data are normally recorded by an anemometer at the 30-foot level. To estimate the relationship between wind speed and height, wind speed data were acquired at various heights in the range of 10 to 30 feet and a nonlinear regression analysis was performed. This analysis shows that, over the range of conditions covered by the present data, the predictive relationship given by the Mechanical Engineer~s Handbook3 is quite accurate; wind velocity can generally be estimated to within! 1.5 mph.

ESTIMATING WIND SPEED AS A FUNCTION OF HEIGHT ABOVE GROUND: AN ANALYSIS OF DATA OBTAINED AT THE

SOUTHWEST RESIDENTIAL EXPERIMENT STATION, LAS CRUCES, NEW MEXICO

Introduction

Sandia National Laboratories, Albuquerque (SNLA), New Mexico, and the Jet Propulsion Laboratory (JPL), Pasadena, California, use data collected at various field sites to study the thermal behavior of photovoltaic (PV) arrays. Because the conversion efficiency of a PV cell decreases as the cell temperature increases and because the temperature of the cell is strongly affected by wind speed, it is important that the wind speed be accurately determined. At most sites, the wind speed is measured by an anemometer fixed to a tower at a standard height of 30 feet above the ground. The surfaces of the PV arrays are between 5 and 10 feet. In the past, the estimation of wind speed at the array has been based upon the assumption that wind speed is proportional to the 1/7 power of the height. Results obtained from thermal modelling, using this assumption, indicated that wind speed was not being accurately estimated. Therefore, an experiment was run at the Southwest Residential Experiment Station to investigate the relationship between wind speed and height. An analysis of the data indicated that the 1/7 power assumption is not accurate for predicting wind speeds. An alternate mathematical model was derived. The results of the analysis of the experimental data and a description of the alternate model are reported in this document.

Data Co11 ecti I)n

In the experiment, wind speed and direction were recorded at 6-minute intervals from two anemometers. One anemometer was fixed at the 30-foot level of the tower; the other anemometer was placed for periods of 4 to 6 days at heights ranging from 5 to 30 feet. The placement schedule is shown

Table 1 Schedule for Placement of Anemometer Heights

Anemometer Heights (ft)

30 vs. 30 30 vs. 25 30 vs. 20 30 vs. 15 30 vs. 10 30 vs. 5

Date (1983)

Sept. 1-6 Sept. 8-12 Sept. 14-19 Sept. 21-27 Sept. 29-0ct. 5 Oct. 7-12

The records acquired during the test (experiment) consisted of the wind speed and direction measurements as sensed by both anemometers at 6-minute intervals. The entire data record was reviewed to detect and eliminate those records that showed obvi ous incorrect measuY'ements. Some errors occurred from faulty computer processing of the wind direction data and others from faulty sensors. The data affected by these errors--about 4% of the total-were deleted from the data record.

Wind speeds were predominantly light during this sampling period. There were many days with wind speeds no greater than 8 mph. Only a few hours had wind speeds faster than 12 mph at the 30-foot level. The frequency distribution of wind velocity recorded at the 30-foot level is shown in Figure 1.

-2-

85 80

70

60 g>, 50

ell

~

c:r

ell

Lt 40

30

20

10

o 2 4 6 8 10 12 14 16

20

Wind velocity at 30-ft level, mi/h

Fi gure 1. Frequency distribution of the wind velocity at the 30-ft level.

-3-

Our analysis did not use all the data associated with Figure 1. An examination of the entire data record showed many instances in which the wind velocity at height H(YH) was greater than the wind velocity at height 30 feet (Y30). In all these instances, Y30 was less than 5 mph. This anomaly was interpreted as turbulence resulting from thermal gradients. To avoid trying to model "noise" of this type, we deleted data points that had V30 < 5 mph. The resulting data set is listed in the Appendix, Table A1.

Data Analysis

The following nomenclature will be used:

H = Height in feet at which wind speed is measured

VH = Wind speed 1n miles per hour (mph) at height H. An established relationshi p1,2 for "effective" wind speed as a function of height for computing wind loads on buildin9s is:

(1)

where

VH = effective wind speed at H ft above ground V30 = reference wind speed at 30 feet above ground

and the values of the parameters 8 and HG are selected according to the terrain characteristics

Terrain

Open

7

900 ft

Suburb

4.5

1200 ft

City

3

1500 ft

-4-

The parameter HG is the gradient height, above which the obstructions on the surface (e.g., suburban dwellings, city buildings) no longer affect the wind velocity. For the terrain categories "suburb" and "city", the effective wind speed yielded by Equation 1 for heights less than 30 feet is not equivalent to the actual wind speed and is not suitable for use in analysing the SWRES data.

Another relationship, given in the Mechanical Engineer~s Handbook3, is

(2)

where S = 7, for V30 > 35

S = 5, for: 5..; V30 ..; 35 S = 2, for: V30 < 5

Note that Equations 1 and 2 are identical if the requirements for open terrain and for V30 greater than 35 mph are both satisfied.

Using Equations 1 and 2 as models, the following equation was selected as the basis for a regression analysis:

(3)

where m = lis and e denotes a random deviation from the expected

relationship. Equation 3 has the same form as Equations 1 and 2. The unknown parame-

ters A and mmust be estimated from the data. A nonlinear least-squares computer routine from the SAS library was used to obtain the estimates. The results are given in Table 2. Statisticians refer to this table as an Analysis

-5-

of Variance Table (see e.g., p. 20 of reference (4?. Table 2 also contains estimates of A and m and the standard errors of these estimates.

Table 2 Statistical Results for Fitting Expression (3).

Analysis of Variance

Source Model Resi dual

Degrees of Freedom

2 265

Sum of Squares 11762.6 122.4

Mean Square

5881.3

.46

Parameter

A m

Estimate .963 .184

Std. Error of Estimate

.008

.011

A

The estima,te of VH, say VH, given values of Hand V30, is thus: (4)

A model that has more intuitive appeal than (3) is (2)

(5)

where m = liS. This model has the property that VH = V30 when H = 30, as

one would like. The above-mentioned nonlinear routine gives the results in Table 3.

-6-

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

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download