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Contract No. DE-AC36-08GO28308

Assessing Long-Term Wind 

Conditions by Combining 

Different Measure-CorrelatePredict Algorithms

Preprint

J. Zhang

National Renewable Energy Laboratory

S. Chowdhury and A. Messac

Syracuse University

B.-M. Hodge

National Renewable Energy Laboratory

To be presented at the ASME 2013 International Design 

Engineering Technical Conferences and 

Computers and Information in Engineering Conference

Portland, Oregon

August 4–7, 2013

Conference Paper

NREL/CP-5500-57647

August 2013 
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DETC2013-12695

ASSESSING LONG-TERM WIND CONDITIONS BY COMBINING DIFFERENT MEASURECORRELATE-PREDICT ALGORITHMS

Jie Zhang*

National Renewable Energy Laboratory

Golden, Colorado 80401

Email: Jie.Zhang@nrel.gov

Souma Chowdhury†

Syracuse University

Syracuse, New York, 13244

Email: sochowdh@syr.edu

Achille Messac‡

Syracuse University

Syracuse, New York, 13244

Email: messac@syr.edu

Bri-Mathias Hodge

National Renewable Energy Laboratory

Golden, Colorado 80401

Email: Bri.Mathias.Hodge@nrel.gov

ABSTRACT

This paper significantly advanced the hybrid measurecorrelate-predict (MCP) methodology, enabling it to account 

for the variations of both wind speed and direction. The 

advanced hybrid MCP method used the recorded data of 

multiple reference stations to estimate the long-term wind 

condition at the target wind plant site with greater accuracy 

than possible with data from a single reference station. The 

wind data was divided into different sectors according to the 

wind direction, and the MCP strategy was implemented for 

each wind sector separately. The applicability of the proposed 

hybrid strategy was investigated using four different MCP 

methods: (i) linear regression; (ii) variance ratio; (iii) artificial 

neural networks; and (iv) support vector regression. To 

implement the advanced hybrid MCP methodology, we used the 

hourly averaged wind data recorded at six stations in North 

Dakota between the years 2008 and 2010. The station Pillsbury 

was selected as the target plant site. The recorded data at the 

other five stations (Dazey, Galesbury, Hillsboro, Mayville, and 

Prosper) was used as reference station data. The best hybrid 

MCP strategy from different MCP algorithms and reference 

stations was investigated and selected from the 1,024 

combinations. The accuracy of the hybrid MCP method was 

found to be highly sensitive to the combination of individual 

MCP algorithms and reference stations used. It was also 

observed that the best combination of MCP algorithms was 

strongly influenced by the length of the correlation period. 

 *

Postdoctoral Researcher, Transmission and Grid Integration Group, 

ASME member, Corresponding author.

†

Research Assistant Professor, Multidisciplinary Design Optimization 

Laboratory (MDOL), ASME member

‡

Distinguished Professor and Department Chair, Department of 

Mechanical and Aerospace Engineering, ASME Fellow.

Keywords: Measure-correlate-predict (MCP), power 

generation, resource assessment, wind distribution, wind energy

INTRODUCTION

Wind resource assessment is the process of estimating the 

power potential of a wind plant site and has been playing an 

important role in a wind energy project. In general, wind 

resource assessment includes (i) onsite wind conditions 

measurement; (ii) correlations between onsite meteorological 

towers to fill in missing data; (iii) correlations between longterm weather stations and short-term onsite meteorological 

towers; (iv) analysis of the wind shear and its variations; (v) 

modeling of the distribution of wind conditions; and (vi) 

prediction of the available energy at the site. MCP algorithms 

are used to predict the long-term wind resource at target sites 

using the short-term (one- or two-year) onsite data, and the cooccurring data at nearby meteorological stations (that also have 

long-term data). The accuracy of long-term predictions 

obtained using MCP methods is subject to (i) the availability of 

a nearby meteorological station; (ii) the uncertainty associated 

with a specific correlation methodology [1]; and (iii) the likely 

dependence of this correlation on physical features such as the 

topography, the distance between the monitoring stations, and 

the type of the local climate regime [2]. 

A wide variety of MCP techniques have been reported in 

the literature, such as: (1) linear regression [3, 4]; (2) variance 

ratio [4, 5]; (3) Weibull scale [5]; (4) artificial neural networks 

(ANNs) [2, 3, 6]; (5) support vector regression (SVR) [7, 8]; 

(6) Mortimer [2]; and (7) wind index MCP [9]. MCP methods 

were first used to estimate the long-term annual mean wind 

speed [10, 11]. Linear regression [12] was presented to 
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characterize the relationship between the reference and target 

site wind speeds. Rogers et al. [13] compared four MCP 

algorithms: (i) a linear regression model; (ii) a model using 

distributions of ratios of wind speeds at the two sites; (iii) a 

vector regression method; and (iv) a method based on the ratio 

of the standard deviations of the two data sets. Perea et al. [4]

proposed and evaluated three MCP methods based on 

concurrent wind speed time series for two sites: (i) linear 

regression derived from bivariate normal joint distribution; (ii) 

Weibull regression; and (iii) approaches based on conditional 

probability density functions.

Given the unavoidable practical constraints, the overall 

reliability of the predicted long-term wind distribution remains 

highly sensitive to the one-year distribution of recorded on-site 

data. Quantifying and modeling the uncertainty in the MCP 

methods would provide more credibility to wind resource 

assessment and wind plant performance estimation. Kwon [14]

and Lackner et al. [15] presented different frameworks to 

analyze uncertainty in MCP-based wind resource assessment. 

The wind resource-based uncertainty models proposed by

Messac et al. [16] can be applied also to the long-term data 

recorded at meteorological stations when MCP methods are 

used.

Research Objectives and Motivation

The hybrid MCP method recently developed by Zhang et 

al. [17] combines the component MCP algorithms by 

characterizing the distance and elevation difference between 

reference stations and the target wind plant site. The overall 

objective of this paper is to significantly advance the original 

hybrid MCP methodology by:

1. Considering both the wind speed and direction as the 

components of the hybrid MCP methodology; and

2. Investigating the best combination of different MCP 

methods and reference stations.

The advancements to the hybrid MCP method are

presented in the next section. The application of the advanced 

hybrid MCP method and the corresponding results and 

discussion are presented in Section III. Section IV presents the 

concluding remarks of this research.

ADVANCING THE HYBRID MCP METHOD

A brief overview of the original hybrid MCP methodology is 

first presented, followed by the description of the advancements 

introduced in this paper.

Overview of the Original Hybrid MCP Method

The hybrid MCP method developed by Zhang et al. [17]

correlates the wind data at the targeted wind plant site with that 

at multiple reference stations. The strategy accounts for the 

local climate and the topography information. In the original 

hybrid MCP method, all component MCP estimations between 

the targeted wind plant site and each reference station use a 

single MCP method (e.g., linear regression, variance ratio, 

Weibull scale, or neural networks).

The weight of each reference station in the hybrid strategy 

is determined based on: (i) the distance and (ii) the elevation 

differences between the target wind plant site and each 

reference station. The hypothesis here is that the weight of a 

reference station is larger when the reference station is closer 

(shorter distance and smaller elevation difference) to the target 

wind plant site. The weight of each reference station, wi, is 

determined by

wi = 1

2(nrrr − 1)

�

∑ ∆dj

nref

j=1,j≠i

∑ ∆dj

nref

j=1

+

∑ ∆hj

nref

j=1,j≠i

∑ ∆hj

nref

j=1

� (1)

where nrrr is the number of reference stations; and ∆dj and 

∆hj represent the distance and the elevation difference between 

the target plant site and jth reference station, respectively.

In the following subsections, we briefly discuss how this 

paper advances the key components of the original hybrid MCP 

method. These advanced features provide helpful flexibility to 

the hybrid MCP method, and extends its applicability to 

designing full-scale commercial wind plants.

Modeling the Impact of Wind Direction on the Hybrid 

MCP Performance

Each wind data point was allocated to a bin according to 

the wind direction sector measurement at the target wind plant 

site. In this paper, we investigated four cases by choosing to bin 

into different number of sectors: (i) 4 sectors; (ii) 8 sectors; (iii) 

16 sectors; and (iv) 32 sectors. At the multiple reference 

stations, the concurrent wind speed and direction measurement 

was allocated to the corresponding bin. Within each sector, the 

long-term wind speed was predicted by applying the hybrid 

MCP strategy based on the concurrent short-term wind speed 

data within that sector. A wind rose is a graphical tool used by 

meteorologists to provide a succinct illustration of how wind 

speed and wind direction are distributed at a location. Figure 1

shows a wind rose diagram with 16 direction sectors.

By putting the wind speed data in each sector together, we 

obtained the set of long-term wind data at the target wind plant 

site. The quality of the predicted long-term wind data was 

evaluated using the performance metrics described in the 

following subsection.

Figure 1. WIND ROSE DIAGRAM WITH 16 SECTORS
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Performance Metrics for Evaluating the MCP Method

Three sets of performance metrics were proposed to 

evaluate the performance of the MCP methods: (i) statistical 

metrics; (ii) wind distribution metrics; and (iii) wind plant 

performance: power generation and capacity factor metrics.

Statistical Metrics Mean long-term wind speed is often 

used to characterize the potential of a wind plant site. It is an 

important measure of wind power potential. Four metrics were 

evaluated based on the estimated wind speeds by MCP methods 

and the reference wind speeds: (i) the ratio of mean wind 

speeds [14]; (ii) the ratio of wind speed variances; (iii) root 

mean squared error (RMSE); and (iv) maximum absolute error 

(MAE).

The ratio of mean wind speeds, Rμ, is expressed as

Rμ = 1/nt ∑ v�(tk) nt

i=1

1/nt ∑ v(tk) nt

i=1

(2)

where v(tk) represents the measured hourly averaged wind 

speed at time tk at the targeted wind plant site, v�(tk) is the 

corresponding estimated wind speed value, and nt is the total 

number of paired data points used in the analysis.

The ratio of wind speed variances, Rσ2, is expressed as

Rσ2 = 1/nt ∑ [v�(tk) − μ�] nt 2 i=1

1/nt ∑ [v(tk) − μ] nt 2 i=1

(3)

where μ� and μ represent the mean of the estimated and 

measured wind speeds of all test paired data points.

The RMSE is given by

RMSE = � 1

nt

�[v(tk) − v�(tk)]2

nt

k=1

(4)

The MAE is expressed as

MAE = max

k |v(tk) − v�(tk)| (5)

Wind Distribution Metrics Wind speed distributions are 

necessary to quantify the available energy (power density) at a 

site and to design optimal wind plant configurations. The 

Multivariate and Multimodal Wind Distribution (MMWD) 

model [19, 20] can capture the joint variation of wind speed, 

wind direction, and air density, and also allows representation 

of multimodally distributed data.

The MMWD model was developed based on kernel density 

estimation (KDE) [19, 20]. For a d-variate random sample 

U U Un , , , 1 2  drawn from a density f, the multivariate KDE is 

defined as

∑=

= −

n

i

H Ui K u

n

f x H

1

( ) 1 ( ; ) ˆ (6)

where T u u u ud ( , , , ) = 1 2  and T Ui Ui Ui Uid ( , , , ) = 1 2  ,

i =1,2,,n . Here, K(u) is the kernel that is a symmetric 

probability density function; H is the bandwidth matrix, which 

is symmetric and positive-definite; and 

( ) ( ) 1/ 2 1/ 2K u H K H u H

− − = . The choice of K is not crucial to the 

accuracy of kernel density estimators [21]. In this paper, 

K u ( u u) d T ( ) (2 ) exp 1/ 2 / 2 = − − p is considered the standard normal 

throughout. In contrast, the choice of H is crucial in 

determining the performance of f

ˆ [22]. In the MMWD model, 

an optimality criterion, the asymptotic mean integrated squared 

error [22], is used to select the bandwidth matrix. The details of 

the MMWD model can be found in Ref. [19].

Wind Plant Performance Metrics This power 

generation model was adopted from Chowdhury et al. [23, 24]. 

The power generated by a wind plant is an intricate function of 

the configuration and location of the individual wind turbines. 

The flow pattern inside a wind plant is complex, primarily 

because of the wake effects and the highly turbulent flow. The 

power generated by a wind plant (Pplant) consisting of N wind 

turbines is evaluated as a sum of the powers generated by the 

individual turbines, which is expressed as [23]

Pplant = �Pj

N

j=1

(7)

Accordingly, the wind plant efficiency can be expressed as

ηplant = Pplant

∑ P0j

N

j=1

(8)

where P0j is the power that turbine-j would generate if 

operating as a stand-alone entity for the given incoming wind 

velocity. Detailed formulation of the power generation model 

can be found in the papers [23, 24].

The power generated by a wind plant with nine turbines 

was evaluated in this paper. Two types of wind turbines were 

selected: (i) the GE 1.5-MW XLE [25] and (ii) the GE 2.5-MW 

XL [26].

CASE STUDY: ASSESSING THE WIND RESOURCE 

POTENTIAL AT A WIND PLANT SITE

To implement the advanced hybrid MCP methodology, we used 

the hourly averaged wind data recorded at six stations in North 

Dakota between 2008 and 2010. The station Pillsbury was 

selected as the target wind plant site. The recorded data at the 

other five stations (Dazey, Galesbury, Hillsboro, Mayville, and 

Prosper) was used as reference station data. The station 
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locations were shown in Fig. 2; the six stations inside the outer 

rectangle were used in this paper.

The wind data is obtained from the North Dakota

Agricultural Weather Network (NDAWN) [27]. Table 1 shows 

the geographical coordinates and elevation of each station. The 

measurement information is listed as follows.

1. Wind speed is measured at 3 meters above the soil surface 

with an anemometer.

2. Wind direction is the direction from which wind is blowing 

(degrees clockwise from north) measured at 3 m above the 

soil surface (N = 0o

; NE = 45o; E = 90o; SE = 135o; S = 

180o

; SW = 225o; W = 270o; NW = 315o; etc.) with a wind 

vane. The value is the average of all measured wind 

directions for a 24-hour period from midnight to midnight. 

Figure 2. NDAWN STATION LOCATIONS [27] 

Table 1. DETAILS OF NDAWN STATIONS [27]

Station Latitude Longitude Elevation (m)

Dazey 47.183 -98.138 439

Galesburg 47.210 -97.431 331

Hillsboro 47.353 -96.922 270

Mayville 47.498 -97.262 290

Pillsbury 47.225 -97.791 392

Prosper 47.002 -97.115 284

Component MCP Methods

In this research, four MCP methods were investigated: (i) 

linear regression; (ii) variance ratio; (iii) ANNs; and (iv) SVR. 

It is helpful to note that other MCP methods can also be used in 

conjunction with the hybrid strategy, because the weights 

determination strategy is independent with the MCP method.

The Linear Regression Method Linear regression is a 

common method to characterize the relationship between the 

reference and target site wind speeds. The prediction equation 

is given as

y� = ax + b (9)

where y� is the predicted wind speed at the target site; x is the 

observed wind speed at the reference site; and a and b are the 

estimated intercept and slope of the linear relationship, 

respectively. 

The Variance Ratio Method When using linear 

regression, the predicted mean wind speed at the target site will 

be close in value to the measured mean during the training 

interval. However, the predicted variance at the target site will 

be less than the measured variance. This can result in biased 

predictions of wind speed distributions.

The variance ratio method was proposed in response to the 

above limitations of linear regression. It involves forcing the 

variance of the predicted wind speed at the target site to be 

equal to the measured variance at the target site. The prediction 

equation is express as

y� = μy − σy

σx

μx +

σy

σx

x (10)

where μx, μy, σx and σy are the means and standard deviations 

of the two concurrent data sets.

The ANNs Method ANNs have been used to correlate 

and predict wind conditions because of their ability to 

recognize patterns in noisy or otherwise complex data. A neural 

network generally contains an input layer, one or more hidden 

layers, and an output layer. An ANN is developed by defining 

the following parameters:

1. The interconnection pattern between different layers of 

neurons;

2. The learning process for updating the weights of the 

interconnections; and

3. The activation function that converts a neuron’s weighted 

input to its output activation.

The SVR Method SVR has gained popularity both within 

the statistical learning community [28, 29] and within the 

engineering optimization community [30-32]. The SVR 

approach provides a unique way to construct smooth, nonlinear, 

regression approximations by formulating the surrogate model 

construction problem as a quadratic programming problem. The 

SVR approach can be expressed as [33]

f̃(x) = 〈w, ∅(x)〉 + b (11)

where 〈∙,∙〉 denotes the dot product; w is a set of coefficients to 

be determined; and ∅(x) is a map from the input space to the 

feature space. To solve the coefficients, we can allow a 

predefined maximum tolerated error ε (with respect to the 

actual function value) at each data point, given by [33]

�f̃(xi) − f(xi)� ≤ ε (12)

where f(x) is the actual function to be approximated. The 

flatness of the approximated function can be characterized by 
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w. By including slack variables ξ to the constraint and a cost 

function, the coefficient w can be obtained by solving a 

quadratic programming problem given by [33]

min

w,ξ,ξ∗

1

2

‖w‖2 + C�(ξi + ξi

∗

)

np

i=1

subject to f(xi) − f̃(xi) ≤ ε + ξi

f(xi) − f̃(xi) ≤ ε + ξi

∗

ξi, ξi

∗ ≥ 0

(13)

where np is the number of sample points. The parameter C > 0 

is user-specified and represents the trade-off between flatness 

and the amount up to which errors larger than ε are tolerated. 

The above formulation is the primal form of the quadratic 

programming problem. In most cases, the dual form with fewer 

constraints is easier to solve, and is widely used to define the 

final form of the approximation. It can be shown that the dual 

form is convex and therefore has a unique minimum. Typical 

allowed mapping functions are radial basis functions, such as 

the Gaussian function.

Selection of Parameters

The MATLAB Neural Network Toolbox [34] was used in 

this paper. The Levenberg-Marquardt algorithm was selected 

for neural network training. Eighty percent data points were 

randomly selected as training points; and 20 percent points 

were used to validate the network. The MSE metric was used to 

evaluate the performance of the developed neural network. For 

the SVR method, we used an efficient SVM package, LIBSVM 

(A Library for Support Vector Machines), developed by Chang 

and Lin [35].

Results and Discussion

Two scenarios were analyzed in the case study. In the first, 

the hybrid MCP strategy was implemented without binning 

wind data points to different sectors. The objective of the first 

scenario was to investigate the performance of the hybrid MCP 

method with mixing combinations of MCP algorithms and 

reference stations. In the second scenario, we evaluated the 

hybrid MCP performance, including consideration of both wind 

speed and direction. However, this paper discussed wind 

direction primarily related to the prediction of wind speed. The 

prediction of the long-term wind direction at the target wind 

plant site was not within the scope of this paper.

Scenario I: Hybrid MCP Methods with Mixing 

Combinations A preliminary comparison of the hybrid MCP 

method (using multiple reference stations) with the individual 

MCP method (using one reference station) was investigated in 

the paper by Zhang et al. [17]. However, the hybrid MCP 

methods discussed in Ref. [17] used a single MCP technique 

for all five reference stations, which might not be optimal. Each 

reference station has the flexibility to use any of the available 

MCP techniques. In this case study, the same five stations were 

selected as reference stations. In addition, each station can be 

combined into the hybrid MCP method with one of the four 

following MCP algorithms: (i) linear regression; (ii) variance 

ratio; (iii) neural network; and (iv) SVR. Therefore, a total of 

1,024 (which is equal to 45

) combinations were investigated to 

formulate the hybrid MCP strategy.

Figs. 3-5 illustrate the three sets of performance metrics. 

Each line in the figures represents one specific combination of 

stations and MCP algorithms. It was observed that the 

performance of the hybrid MCP technique varied significantly. 

For instance, the average value of RMSE during the length of 

correlation period (Fig. 3(c)) varied 4.91% during the 1,024 

hybrid MCP models.

The smaller the RMSE value, the more accurate the 

estimated wind pattern. Based on the RMSE values, we found 

the best combination of MCP algorithms and reference stations, 

shown in Table 2. In the table, “Ratio,” “Linear,” “ANN,” and 

“SVR” represent variance ratio, linear regression, artificial 

neural networks, and support vector regression, respectively. 

Four combinations were observed based on the length of the 

correlation period. It was shown from Table 2 that: (i) the 

variance ratio algorithm was chosen at the Dazey, Mayville, 

and Prosper reference stations for all four correlation periods; 

(ii) the SVR algorithm was selected at the Galesbury reference 

station when the correlation period was between 3,500-11,500 

hours; and (iii) at the Hillsboro reference station, different MCP 

algorithms were selected based on the length of the correlation 

period.

The two-parameter Weibull distribution was the most 

widely accepted distribution for wind speed. The shape 

parameter (k) and the scale parameter (c) determine the 

probability distribution. In this research, the ratios of k� (and c̃) 

for the predicted wind speeds to k (and c) for the observed 

targeted wind speeds, Rk and Rc, were evaluated. The values of 

Rk and Rc are given by

Rk = k�

k , a Rc = c̃c

(14)

Figure 4 shows the normalized Weibull k and c

parameters for the total 1,024 combinations. The closer the 

value of the ratio is to one, the more accurate the estimated 

long-term wind condition. The average values of Rk and Rc

varied 1.94% and 15.82%, respectively, throughout the 1,024 

different combinations. The above observation indicates that 

the scale parameter (c) is more sensitive to the MCP strategies 

than the shape parameter (k).

The power generation of the nine-turbine wind plant is 

shown in Fig. 5. Figs. 5(a) and 5(b) show the 1,024 wind power 

generations of wind plants with 1.5-MW and 2.5-MW turbines, 

respectively. It was observed that: (i) the average value of the 

power generation with GE 1.5MW-XLE turbines during the 

length of correlation period (Fig. 5(a)) varied 5.57% during the 

1,024 hybrid MCP models; and (ii) the average value of the 

power generation with GE 2.5MW-XL turbines during the 
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length of correlation period (Fig. 5(b)) varied 4.81% during the 

1,024 hybrid MCP models.

Scenario II: Hybrid MCP Methods Considering 

Wind Speed and Direction Each wind data point was 

allocated to a bin according to the wind direction sector 

measurement at the target plant site (Pillsbury station). In the 

case study, four cases were investigated: (i) 4 sectors; (ii) 8 

sectors; (iii) 16 sectors; and (iv) 32 sectors. For the five 

reference stations (Dazey, Galesbury, Hillsboro, Mayville, and 

Prosper), the concurrent wind speed and direction measurement 

was allocated to the corresponding bin. Within each sector, the 

long-term wind speed was predicted by applying the hybrid 

MCP strategy based on concurrent short-term wind speed data 

within that sector. In Scenario II, the hybrid MCP strategy used 

a single MCP technique for all five reference stations.

Figure 6 shows the ratio of mean wind speeds with the four 

different direction sectors. The closer the value of the ratio is to 

one, the more accurate the estimated wind pattern. It was 

observed that: (i) the hybrid MCP methods performed relatively 

better than the individual MCP algorithms; (ii) the hybrid SVR 

algorithm performed relatively worse than the other three 

hybrid MCP methods; (iii) the hybrid linear regression, the 

hybrid variance ratio, and the hybrid neural network methods 

performed best when the correlation period was between 5,500-

8,500 hours (approx. 8 to 12 months).

Figure 7 shows the wind speed distributions with the four 

different direction sectors. The closer the predicted distribution 

curve is to the actual distribution curve (the black line in the 

figure), the more accurate the estimated wind pattern. It was 

observed that: (i) for 8, 16, and 32 direction sectors, the hybrid 

variance ratio method (solid blue line) agreed more with the 

actual distribution curve (solid black line) than other MCP 

methods; (ii) for 4 direction sectors, the individual variance 

ratio method (dashed blue line) agreed more with the actual 

distribution curve.

Figure 8 shows the wind power generation of the wind 

plant with nine GE 1.5MW-XLE turbines. The closer the 

predicted power generation curve to the actual power

generation curve (the black line in the figure), the more 

accurate the estimated wind pattern. The predicted power 

generation of the wind plant was estimated using the long-term 

wind data predicted by the hybrid MCP method; the actual 

wind plant power generation was estimated using the measured 

long-term wind data. We observed that: (i) the hybrid variance 

ratio method performed best when the correlation period was 

between 2,000-3,500 hours (approximately 2.5 to 5 months) for 

all four direction sectors; (ii) the linear regression and the 

neural network methods had relatively better power generation 

estimations when the correlation period was between 6,000-

9,000 hours (approximately 8.5 to 12.5 months); (iii) the power 

generation was generally overestimated by the neural network, 

hybrid neural network, linear regression, hybrid linear 

regression, and hybrid variance ratio methods; and (iv) the 

power generation was generally under-estimated by the SVR, 

hybrid SVR, and variance ratio methods.

Table 2. BEST COMBINATION OF MCP ALGORITHMS AND REFERENCE STATIONS

Station 2,000–3,500 (hours) 3,500–5,500 (hours) 5,500–8,500 (hours) 8,500–11,500 (hours)

Dazey Ratio Ratio Ratio Ratio

Galesburg Ratio SVR SVR SVR

Hillsboro Linear Linear ANNs SVR

Mayville Ratio Ratio Ratio Ratio

Prosper Ratio Ratio Ratio Ratio

(a) Mean ratio (b) Variance ratio
7

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(c) RMSE (d) MAE

FIGURE 3. STATISTICAL PERFORMANCE METRICS TO EVALUATE THE HYBRID MCP WITH 1,024 COMBINATIONS

(a) Normalized Weibull k parameter (b) Normalized Weibull c parameter

Figure 4. WIND DISTRIBUTION METRICS TO EVALUATE THE HYBRID MCP WITH 1,024 COMBINATIONS

(a) Power generation with GE 1.5-MW XLE turbines (b) Power generation with GE 2.5-MW XL turbines

Figure 5. POWER GENERATION METRICS TO EVALUATE THE HYBRID MCP WITH 1,024 COMBINATIONS
8

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(a) 4 direction sectors (b) 8 direction sectors

(c) 16 direction sectors (d) 32 direction sectors

Figure 6. THE RATIO OF MEAN WIND SPEEDS WITH DIFFERENT DIRECTION SECTORS

CONCLUSION

This paper developed an advanced hybrid MCP 

methodology that accounts for the variations of both wind 

speed and direction. The advanced hybrid MCP method uses 

the recorded data of multiple reference stations to estimate the 

long-term wind condition at a target plant site. Two scenarios 

were analyzed using the hybrid MCP methodology, and 

interesting results were observed and discussed.

Because each reference station has the flexibility to use 

any of the available MCP techniques, the multiple reference 

weather stations were combined into the hybrid MCP strategy 

with the best suitable MCP algorithm for each reference station. 

In the first scenario, each reference weather station used one of 

the following MCP algorithms: (i) linear regression; (ii) 

variance ratio; (iii) neural network; and (iv) support vector 

regression. Therefore, a total of 1,024 (which is equal to 45

) 

combinations were investigated to formulate the hybrid MCP 

strategy. The best hybrid MCP strategy of MCP algorithms and 

reference station combination was determined and analyzed. 

We found that the accuracy of the hybrid MCP method was 

highly sensitive to the combination of individual MCP 

algorithms and reference stations. We also found that the best 

hybrid MCP strategy varied based on the length of the 

correlation period.

In the second scenario, both wind speed and direction were 

considered in the application of the hybrid MCP strategy. We 

found that the hybrid MCP methodology performed best when 

the correlation period was between 5,500-8,500 hours 

(approximately 8 to 12 months) based on the ratio of mean 

wind speeds. For the nine-turbine wind plant, the power 

generation was generally overestimated by the neural network, 

hybrid neural network, linear regression, hybrid linear 

regression, and hybrid variance ratio methods; it was under 

estimated by the support vector regression, hybrid support 

vector regression, and variance ratio methods.

Quantifying and modeling the uncertainty in the MCP 

methods would provide more credibility to wind resource 
9

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assessment and wind plant performance estimation. Modeling 

the propagation of uncertainty through the MCP process would 

allow quantification of the expected uncertainty in on-site wind 

conditions and wind plant power generation. In addition, an 

investigation of how the uncertainties in the annual distribution 

of wind conditions interact with the uncertainties inherent in the 

MCP correlation methodology is also necessary. This 

investigation is an important topic for future research.

(a) 4 direction sectors (b) 8 direction sectors

(c) 16 direction sectors (d) 32 direction sectors

Figure 7. WIND DISTRIBUTION METRICS WITH DIFFERENT DIRECTION SECTORS
10

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at www.nrel.gov/publications.

(a) 4 direction sectors (b) 8 direction sectors

(c) 16 direction sectors (d) 32 direction sectors

Figure 8. POWER GENERATION METRICS TO EVALUATE THE HYBRID MCP WITH DIFFERENT DIRECTION SECTORS 

(GE 1.5MW-XLE)

ACKNOWLEDGMENTS

Support from the National Science Foundation Awards 

CMMI-1100948 and CMMI-0946765 is gratefully 

acknowledged. Any opinions, findings, conclusions, or 

recommendations expressed in this paper are those of the 

authors and do not necessarily reflect the views of the NSF. 

This work was also supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

NREL.

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