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Navigation: Adjust To Mast, Mean Wind Speeds, and Energy Capture

Ratio Relaxation and Ratio Weighting Adjust to Mast

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The analysis of adjusted WRGs has allowed identifying that there is a limitation in the standard method for adjusting WRGs in very complex areas with significant wind rose variations. Due to the fact that the current method is run on “per directional sector” basis, it has been identified that problematic adjustments may be related with sectors having a small probability of occurrence, leading as a consequence to very large and meaningless “directional ratios”. This limitation can show, for example, severe discrepancies when doing cross-predictions between the different masts in a site.

This document presents a new proposed WRG adjustment method. This method is based on the following main hypotheses:

The ratios hold true at the mast locations as they reflect the reality at these locations.

When you move away from the mast, however, those ratios may lose part of their applicability in points in which the wind rose differs from the one at mast location. Following this, the method proposes relaxing these ratios at each modeled location depending on the following parameters:

1.the Direction Deviation (DD) index, described in Brower et al. (2015)2, that evaluates the similarity between the raw wind rose at the mast and the one at any other location.

1.A Replicability Factor (RF) that is associated to each sector aiming to evaluate how much the speed and frequency ratios of that sector are reliable to be applied in other points of the map.

In the worst-case scenario in terms of WRG adjustment, i.e. at locations where the raw wind roses significantly differ with respect to that at the mast (DD close to 1) and for sectors with low replicability factor (RF close to 0), it is proposed to do the following adjustment:

oThe target wind speed is scaled by the mean wind speeds ratio at mast location (two different methods are proposed for wind speed ratios calculation)

oThe target wind frequency is the same of the raw WRG wind frequency.

Example charts of the variation of the wind speed and frequency ratios as a function of DD and RF are shown in Figures 2, 3 and 4.

 

Location

Acronym

Name

Values

Interpretation

Mast location

i

Ri_d

Wind speed ratio at mast location

(0; >1]

It is the ratio between mast and raw WRG wind speeds in sector d.

If Ri_d=1 than the wind speed of the mast is the same of the raw WRG

Fi_d

Frequency ratio at mast location

(0; >1]

It is the ratio between mast and raw WRG frequencies in sector d.

If Fi_d=1 than the frequency of the mast in a certain sector is the same of the raw WRG

FFi_d

Frequency Factor

(0; 1]

Indicates the minimum value of frequency in sector d between mast and raw WRG

FRFi_d

Frequency Ratios Factor

(0; 1]

Indicates how much the Fi_d deviates from 1

RFi_d

Replicability Factor

(0; 1]

Calculated as the product of FFi_d and FRFi_d. Indicates how much we trust on the ratios Ri_d and Fi_d for a certain sector. Higher the RF value, higher is the reliability of those ratios

Other WRG location

y

DDy_i

Direction DeviationError! Bookmark not defined.

[0; 1]

Indicates how much the frequency wind rose in point y differs from the frequency wind rose in point i

Nsect

Number of sectors

12, 16, etc..

Number of direction sectors of the raw WRG

OPENWI~1_img212

Sectorial distance

[0; Nsect/2]

Indicates the distance (in terms of number of direction sectors) between sectors s and d. OPENWI~1_img212 = 0 if s = d

OPENWI~1_img214

[0; 1]

Weight given to the wind speed ratio in a certain sector s in the calculation of the wind speed ratio in sector d. It depends on DDy and the sectorial distance between sectors s and d. For DDy = 0 no importance is given to sectors others than d, as higher the DDy higher will be their importance. See Figure 1.

OPENWI~1_img215

[0; 1)

Weight given to the ratio of mean wind speeds at mast location i  (or to the frequency of the raw WRG at point y) in the calculation of the wind speed ratio Ry_d (and the frequency ratio Fy_d) at point y. Higher DDy_i (and lower the RFi_d) higher will be this weight

 

Table 6: Acronyms List

 

 

 

 

 

 

Standard method

Currently, the wind speed ratio (Ri) and frequency ratio (Fi) for a direction sector d at mast location i are calculated as

 

OPENWI~1_img216

OPENWI~1_img217

Those factors are then applied to another point y of the map in order to scale the wind speed and frequency of the raw WRG:

OPENWI~1_img218

OPENWI~1_img219

However, the direct application of those ratios can create problems in the adjustment: for example if the frequency in a certain sector is really low (e.g. <1%) then the Ri_d and Fi_d obtained in that sector are not really representative and can hardly be applied in another location in which the frequency in that sector is much higher (e.g. > 10%).

In those cases, unrealistic wind speeds or frequencies can be obtained in some areas far from met mast.

 

Ratio Weighting and Ratio Relaxation Methods

The idea is that the wind speed and frequency ratios for each direction sector are weighted by their reliability (evaluated by a factor called Replicability Factor) and the Directional Deviation (DD) in a certain point (with respect to mast location). Thus new ratios are obtained for each sector and at each map location.

The proposed process for ratios calculations follows a 4-steps calculation:

At Mast location (i):

1. Calculate the Ri and Fi for each sector such as in current calculation

 

2. Evaluate the replicability of these ratios: an index called Replicability Factor (RF) is assigned to each sector. This factor depends on the probability of that sector (higher the frequencies of one sector more reliable are the ratios) and on the frequency ratio of that sector (more that ratio deviates from 1, lower will be the reliability of the ratios). Thus, RF can be calculated as the product between the probability of that sector (Frequency Factor – FF, calculated as the minimum value between Pi_d and Pi_d_RawWrg) and on how much Fi_d deviates from 1 (Frequency Ratio Factor - FRF).

OPENWI~1_img220

Where:

OPENWI~1_img221

and

OPENWI~1_img222

OPENWI~1_img223

 

The factor RF is also an indicator of how good the raw WRG catch the wind rose at mast location, in comparison with mast data.

 

At another WRG point (y):

In the proposed method, the ratios of wind speed and direction frequency vary across the map, thus the adjusted WRG wind speed and frequency in a certain point y are calculated as

OPENWI~1_img224

OPENWI~1_img225

The calculation of wind speed and frequency ratios in point y (Ry_d and Fy_d respectively) are reported in the following (steps 3 and 4).

 

3.Calculate the wind speed ratios to be applied

 

For the calculation of wind speed ratios Ry we propose the following two methods.

 

Ratios Weighting Method. Wind speed ratios Ry_d, depend on

1.Wind speed ratio in sector d (Ri_d)

2.Replicability factor (RFi_d)

3.Direction Deviation of the point y with respect to mast location i (DDy_i)

4.Wind speed ratios in closer sectors (Ri_d1) where d1d

OPENWI~1_img226

Using this formula, for calculating the wind speed ratio in a certain sector d, a weight is given to the ratios of each sector as function of the Replicability Factor (RF) of that sector and a parameter OPENWI~1_img227 that depends on the distance to the analyzed sector d and the Direction Deviation of point y:

OPENWI~1_img228

Where:

OPENWI~1_img229 is a normal distribution centered in d with standard deviation = OPENWI~1_img230. See Figure 184.

Nsect is the number of sectors of the WRG (12, 16, etc.)

 

Matteo1

 

Figure 184: OPENWI~1_img232 variation as a function of sectorial distanceOPENWI~1_img233. In d OPENWI~1_img233 = 0

 

 

Figure 185 shows the variation of Ry_d for a sector d with Ri_d = 0.935, while the mean value of the Ri_d weighted for their RFi_d is 0.845. It should be noted that a closer sector s as a high replicability Factor and an Ri_s = 0.77. Analyzing the curve for RFi_d = 0.01 we can see that:

For null DDy_i, Ry_d is equal to Ri_d,

For low DDy_i values (but higher than 0), the effect of the closer sector is prevailing

When DDy_i tends to 1, Ry_d tends to equal the mean values of the ratios at mast location weighted by their replicability factors.

These trends are smoother when RFi_d is higher (greed and red curves).

 

Matteo2

Figure 185:   Example of the variation of Ry_d (calculated using the first method) as a function of DDy_i and RFi_d

 

Ratios Relaxation Method. Wind speed ratios Ry_d, depend on

1.Wind speed ratio in sector d (Ri_d)

2.Replicability factor (RFi_d)

3.Direction Deviation of the point y with respect to mast location i (DDy_i)

OPENWI~1_img235

Where

OPENWI~1_img236 is the ratio between mast and raw WRG mean wind speeds at point i

Figure 186 shows the variation of Ry_d for the same sector previously described (Figure 2). It should be noted that the ratio between mean wind speeds at mast location is OPENWI~1_img2370.87.

Analyzing the curve for RFi_d = 0.01 we can see that:

For null DDy_i, Ry_d is equal to Ri_d,

As DDy_i, increases, Ry_d tends to equal the ratio between mean wind speeds at mast location

These trends are smoother when RFi_d is higher (greed and red curves).

 

OPENWI~1_img238

Figure 186: Example of the variation of Ry_d (calculated using the ratio relaxation method) as a function of DDy_i and RFi_d  

 

4.Calculate the frequency ratios to be applied

Frequency ratio Fy_d, as a function of

a. Replicability factor (RFy_d)

b. Direction Deviation of the point y with respect to mast location i (DDy_i)

OPENWI~1_img239

Figure 187 shows the variation of Fy_d for the same sector previously described, in which Fi_d = 0.78. Analyzing the curve for RFi_d = 0.01 we can see that:

For null DDy_i, Fy_d is equal to Fi_d,

As DDy_i increases, Fy_d tends to 1

These trends are smoother when RFi_d is higher (greed and red curves).

 

OPENWI~1_img240

Figure 187:   Example of the variation of Fy_d as a function of DDy_i and RFi_d

 

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