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Haiyang Zheng

Andrew Kusiake-mail: [email protected]

Department of Mechanical and IndustrialEngineering,

3131 Seamans Center,University of Iowa,

Iowa City, IA 52242-1527

Prediction of Wind Farm PowerRamp Rates: A Data-MiningApproachIn this paper, multivariate time series models were built to predict the power ramp ratesof a wind farm. The power changes were predicted at 10 min intervals. Multivariate timeseries models were built with data-mining algorithms. Five different data-mining algo-rithms were tested using data collected at a wind farm. The support vector machineregression algorithm performed best out of the five algorithms studied in this research. Itprovided predictions of the power ramp rate for a time horizon of 10–60 min. Theboosting tree algorithm selects parameters for enhancement of the prediction accuracy ofthe power ramp rate. The data used in this research originated at a wind farm of 100turbines. The test results of multivariate time series models were presented in this paper.Suggestions for future research were provided. �DOI: 10.1115/1.3142727�

Keywords: power ramp rate prediction, wind farm, data-mining algorithms, multivariatetime series model, parameter selection

IntroductionWind power generation is rapidly expanding and is becoming a

oticeable contributor to the electric grid. The fact that most large-cale wind farms were developed in recent years has made studiesf their performance overdue. Given the changing nature of theind regime, wind farm power varies across all time scales.The fluctuating power of wind farms is usually balanced by the

ower produced by the traditional power plants to meet the gridequirements. The change of power output in time is referred to asamping and it is measured with the power ramp rate �PRR�. Therediction of PRR at 10 min intervals is of interest to the windndustry due to the tightening electric grid requirements �1�.hough the power prediction research has a long tradition in theind industry, the interest in prediction of power ramps is emerg-

ng. There is no industry standard for PRR prediction. Power rampate on 10 min intervals is to benefit the gird management andower scheduling in the wind industry.

The literature related to power ramps is discussed next. Svo-oda et al. �2� proposed a Lagrangian relaxation method to solveydrothermal generation scheduling problems. Three PRR con-traints were considered and illustrated with a numerical example.mmels et al. �3� presented a simulation method to evaluate the

ntegration of large-scale wind farm power with the conventionalower generation sources from a cost, reliability, and environmen-al perspective. Based on the PRR constraints for the reserve ac-ivation and generation schedule, the capability of a thermal gen-ration system for balancing a wind power was investigated.otter and Negnevitsky �4� applied an adaptive-neuron-fuzzy in-erence approach to forecast short-term wind speed and direction.orres et al. �5� used transformed data to build the autoregressiveoving average �ARMA� time series model for prediction ofean hourly wind speed of up to 10 h into the future. Sfetsos �6�

resented a novel method for forecasting mean hourly wind speedased on the time series analysis data and showed that the devel-ped model outperformed the conventional forecasting models.ange and Focken �7� presented various models for short-termind power prediction, including physics-based, fuzzy, and neu-

Contributed by the Solar Energy Engineering Division of ASME for publicationn the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received August 10, 2008;nal manuscript received March 6, 2009; published online July 9, 2009. Review
onducted by Spyros Voutsinas.
ournal of Solar Energy Engineering Copyright © 20

ded 02 Sep 2009 to 128.255.53.136. Redistribution subject to ASM

rofuzzy models. Using meteorological data, Barbounis et al. �8�constructed a local recurrent neural network model for long-termwind speed and power forecasting. Hourly wind farm forecasts ofup to 72 h were produced.

Developing power and PRR prediction models for wind farmsis challenging, as power output is known to undergo rapid varia-tions due to changes in the wind speed, e.g., due to gusts. Thepower output strongly depends on the wind conditions and thechanging environment of the wind farm. The stochastic nature ofa wind farm environment calls for new modeling approaches toaccurately predict the power ramp rate.

Data mining is a promising approach for modeling wind farmperformance. Numerous applications of data mining in manufac-turing, marketing, medical informatics, and energy industryproved successful �9–14�.

In this paper, a data-mining approach was applied to build amultivariate time series model to predict power ramp rates of awind farm over 10 min intervals. Five different data-mining algo-rithms for the PRR prediction were employed. The boosting treealgorithm was used to reduce the dimensionality of the input andto enhance prediction accuracy. The models were built using his-torical data collected by the supervisory control and data acquisi-tion �SCADA� system installed at a wind farm.

2 Basic Methodologies for PRR Prediction

2.1 Time Series Prediction Modeling. Time series prediction�15� focuses on determining future events based on known obser-vations, measured typically at successive time intervals �often uni-form�. Time series models are generally applicable to monitoringindustrial processes and tracking time-based business metrics.There are two types of time series models: univariate and multi-variate models. The univariate time series model consists of ob-servations of a single parameter recorded sequentially over equaltime increments. In the multivariate time series model, observa-tions are fixed-dimension vectors of different parameter values.

The univariate time series prediction model �15,16� is ex-pressed as follows:

y�t + wT� = f�y�t�,y�t − T�, . . . ,y�t − mT�� 1�

where T is the sampling time �interval�, wT is the prediction ho-rizon �for example, for w=2 and T=10 min, the prediction hori-

ˆ
zon is 20 min�, y�t+wT� is the predicted parameter, y�t� ,y�t
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T� , . . . ,y�t−mT� are the current and past observed parameters,nd m+1 is the number of inputs �predictors� of the model.

The multivariate time series model �15� is formulated as fol-ows:

y�t + wT� = f�y�t�,y�t − T�, . . . ,y�t − mT�;x1�t�,x1�t − T�, . . . ,

x1�t − mT�;x2�t�,x2�t − T�, . . . ,x2�t − mT�; . . . ;

xn�t�,xn�t − T�, . . . ,xn�t − mT�� 2�

here T is the sampling time �interval�, wT is the prediction ho-izon, x1 . . . ,xn ,y and n+1 are the observations of the time seriesorming the n+1 dimensional vector, y�t+wT� is the predictedarameter, y�t� ,y�t−T� , . . . ,y�t−mT� are the current and past ob-erved values of y, x1�t� ,x1�t−T� , . . . ,x1�t−mT� are the currentnd past observed values of parameters x1 , . . . ,xn, and �m+1��n+1� is the number of inputs �predictors� of the model.To obtain an accurate prediction model with the data-mining

pproach, appropriate parameters �predictors� need to be selected.ata mining offers different algorithms to perform this task. For

xample, the boosting tree algorithm �17,18� and the wrapper ap-roach �19,20�, utilizing the genetic or the first best search algo-ithm �13,21� select the important predictors.

The total number of all possible predictors �m+1�� n+1�orms a high-dimensional input to the time series model, andherefore the performance of the resultant model is likely to benferior. To maximize performance of the prediction model, aoosting tree algorithm is employed to select a set of the mostmportant predictors among the �m+1�� n+1� ones in Eq. �2�:

�y�t�,y�t − T�, . . . ,y�t − mT�;x1�t�,x1�t − T�, . . . ,

x1�t − mT�; . . . ;xn�t�,xn�t − T�, . . . ,xn�t − mT��

2.2 Prediction Accuracy Metrics. Two main metrics, theean absolute error �MAE� and the standard deviation �Std� of the

bsolute error �AE�, were used to measure prediction accuracy ofifferent data-mining algorithms. The small value of MAE and Stdmply the superior prediction performance of the models extractedy data-mining algorithms. In fact, MAE and Std based on abso-ute error are widely used in the wind industry. Their definitionsre expressed as

AE = y�t + wT� − y�t + wT� �3�

MAE =

�i=1

N

AE�i�

N�4�

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i=1

N

�AE�i� − MAE�

N − 1�5�

here y�t+wT� is the predicted PRR, y�t+wT� is the observedmeasured� PRR, and N is the number of test data points for therediction model. The data set used by the PRR prediction modelss divided into training and test data sets.

2.3 Data Description. The data used in this research wereenerated at a wind farm with 100 turbines. Though the data wereampled at high frequency, e.g., 2 s, it was averaged and stored at0 min intervals �referred to as the 10 min average data�. The datased in this research were collected over a period of 1 month forll turbines of the wind farm. Some data contained many missingalues or abnormal values outside of the normal physical range,nd thus 89 turbines were selected for the study. For example, theCADA recorded wind speed should be in the range 0–20 m/s, and
he power should be in the range 0–1600 kW. As the rated power
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of each turbine is 1.5 MW, the capacity of the wind farm is 133.5MW.

The power ramp rate used in this paper is defined as the rate ofchange of wind farm power during a 10 min interval �the standardtime interval in wind energy industry� and is expressed in kW/min:

PRR =P�t + 10� − P�t�

10�6�

where P�t+10� is the wind farm power at time t+10 �time t plus10 min� and P�t� is the wind farm power at time t.

The power ramp rate expresses the rate of change of the windfarm power due to the stochastic nature of the wind. Figure 1�a�illustrates the power produced by a wind farm over 10 min inter-vals. Figure 1�b� shows the power ramp rate corresponding to thepower presented in Fig. 1�a�. Figure 1�c� shows the wind speedfor the time period considered in Figs. 1�b� and 1�c�. Ignoring thepower consumed by the wind farm, the power produced is alwayspositive �Fig. 1�a��; however, the PRR can be positive or negative.The positive PRR indicates increasing power over time, while the

Fig. 1 Typical power, power ramp rate, and wind speed plots:„a… wind farm power, „b… power ramp rate, and „c… wind speed

negative PRR value means that the wind farm power is decreas-

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ng. The larger the absolute value of PRR, the faster the powerurge �or drop�.

The wind speeds of 89 turbines, the wind speed statistics, andhe power collected by the SCADA system were used in data min-ng. In this paper, six different parameters were used to build the

ultivariate time series model. The mean, Std, max, min, andower are the first five parameters x1 , . . . ,x5 and the PRR is theixth parameter y of model �2�. Table 1 lists all the parameterssed in this paper. The number of parameters is limited by the datavailable in this research. The model accuracy could be enhancedf more data were available.

The six parameters recorded at 10 min intervals resulted in455 instances �data set 1 in Table 2�, beginning from “1/1/07 at:40 a.m.” and continuing to “1/31/07 at 11:50 p.m.” During thisime period, the overall wind farm performance was considered toe normal. Data set 1 was divided into two subsets: data set 2 andata set 3. Data set 2 contains 3568 data points and were used toevelop a prediction model with data-mining algorithms. Data set

Table 1 List of parameters

arameter Description Unit

ean Mean wind speed of a turbine m/std Standard deviation of the wind speed of a turbine m/sax Maximum wind speed of a turbine m/sin Minimum wind speed of a turbine m/s

ower Wind farm power kWRR Power ramp rate of the wind farm kW/min

Table 2 The data set description

ata set Start time stamp End time stamp Description

1 1/1/07 1:40 a.m. 1/31/07 11:50 p.m. Total data set; 4455observations

2 1/1/07 1:40 a.m. 1/25/07 8:00 p.m. Training data set; 3568observations

3 1/25/07 8:10 p.m. 1/31/07 11:50 p.m. Test data set; 887observations

Fig. 2 The importance of predictors generated by

ournal of Solar Energy Engineering


3 includes 887 data points and were used to test the predictionperformance of the model extracted from data set 2. For the testdata set, the MAE �Eq. �4�� and Std �Eq. �5�� were the metrics usedto evaluate the data-mining algorithms applied to learn multivari-ate time series model of Sec. 2.1.

2.4 Parameter Selection. Due to the high-dimensionality ofthe input vector of predictors of the multivariate time seriesmodel, the number of inputs was reduced. The quality of the mod-

Table 3 The importance index of predictors generated by theboosting tree algorithm for t+10 model

Predictor Variable rank Importance

PRR-1 100 1.00PRR-2 100 1.00PRR-3 66 0.66PRR-4 53 0.53PRR-5 71 0.71Mean-1 44 0.44Mean-2 49 0.49Mean-3 38 0.38Mean-4 41 0.41Mean-5 37 0.37Min-1 67 0.67Min-2 52 0.52Min-3 49 0.49Min-4 44 0.44Min-5 42 0.42Max-1 45 0.45Max-2 48 0.48Max-3 37 0.37Max-4 42 0.42Max-5 40 0.40Std-1 43 0.43Std-2 51 0.51Std-3 45 0.45Std-4 43 0.43Std-5 36 0.36Power-1 40 0.40Power-2 54 0.54Power-3 48 0.48Power-4 41 0.41Power-5 39 0.39

the boosting tree algorithm for the t+10 model

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ls learned from high- and reduced-dimensionality data were com-ared in Secs. 3.1 and 3.2. The most significant predictors wereetermined by the boosting tree algorithm �17,18�. The same ap-roach was shown to be successful in a previous research �14�.he basic idea of the boosting tree algorithm is to build a numberf trees �e.g., binary trees� splitting the data set and to approxi-ate the underlying function. The importance of each predictor iseasured by its contribution to the prediction accuracy of the

raining data set.To build a multivariate t+10 time series model �for 10 min

head predictions�, the value of m=5 used in the multivariateodel is selected, which means that four values observed in the

ast and one current value of each parameter are considered. Inotal, six different parameters of the multivariate model were con-idered and thus it contains �5�6�=30 predictors. The 30-imensional input is reduced by the boosting tree algorithm. Tableshows the importance index of 30 predictors computed by the

oosting tree algorithm based on data set 2 of Table 2. The index-1” in Table 3 indicates the observation sampled 10 min earlier,-2” indicates the observation sampled 20 min earlier, and “-3, -4,nd -5” indicate the observations sampled 30 min, 40 min, and 50in earlier, respectively. Note that all the parameter values used in

his paper were all average values over the 10 min interval.Figure 2 shows the importance of all 30 predictors for the t

10 min models ranked from the largest to the smallest one.To maximize prediction accuracy it is important to select im-

ortant predictors among the ones on the list

�y�t�,y�t − T�, . . . ,y�t − mT�;x1�t�,x1�t − T�, . . . ,

x1�t − mT�; . . . ;xn�t�,xn�t − T�, . . . ,xn�t − mT��A threshold value of 0.50 was established heuristically to select

he predictors for the time series models. The predictors selectedy the boosting tree algorithm for the t+10 min PRR are PPR-1,PR-2, PPR-5, Min-1, PPR-3, Power-2, PRR-4, Min-2, and Std-2.he number of predictors was reduced from 30 to 9.The threshold value of 0.50 used in the computation produced

ood quality results. A lower threshold value would lead to more

able 4 Prediction error of the t+10 models without parameterelection generated by the five different algorithms

bsolute errorkW/min� MAE Std Maximum Minimum

LP 340.66 448.19 5119.73 0.03VM 298.94 323.32 2512.34 0.15andom forest 360.19 407.56 2657.89 0.15&R tree 396.62 396.62 4236.02 0.38ace regression 312.44 342.33 3516.80 0.03

ig. 3 Illustration of the multiperiod multivariate time seriesrediction model: „a… the t+10 min PRR prediction and „b… the+20 min PRR prediction

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predictors that could degrade performance of the models due tothe “curse of dimensionality” principle �19,22�, which means thathigh-dimension input could negatively impact performance of themodel built by the data-mining algorithm.

2.5 Multiperiod Predictions With a Multivariate Time Se-ries Model. The t+10 min prediction model is not sufficient forintegration of the wind farm with the power grid. Six differentmultivariate time series models are needed to predict the PRR att+10– t+60 min intervals. For t+10 interval prediction, data set 2in Table 2 is used for parameter selection and building time seriesmodels with data-mining algorithms, and the test data �data set 3in Table 2� were used to validate performance of the models. Fort+20– t+60 predictions, the training data set remains the same;however, the test data set containing 887 points is reduced by onefor each of the next 10 min period predictions.

Figure 3 illustrates the concept of a multiperiod prediction forPRR over 10 min intervals. In this model, the sampling time pe-riod T is 10 min. Using the 10 min average measured values�including mean, Std, max, min, power, and PRR in Table 1� at theintervals �t=−50, t=−40� , . . . , �t=−10, t=0−�, the average PRRvalue at the subsequent interval t+10 is predicted �Fig. 3�a��. In

Table 5 Prediction error of the t+10 model with selected pa-rameters generated by five different algorithms

Absolute error�kW/min� MAE Std Maximum Minimum

MLP 280.13 309.38 3248.12 0.16SVM 243.14 276.39 2817.77 0.03Random forest 307.97 335.56 3860.94 0.61C&R tree 356.79 323.92 3516.65 0.15Pace regression 290.57 318.37 3270.62 0.03

Fig. 4 Prediction results produced by the t+10 model withoutparameter selection: „a… prediction performance of the five dif-ferent algorithms for the test data set of Table 2 and „b… theobserved and predicted PPRs by the SVM algorithm



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ig. 3�b�, based on the measured values �including mean, Std,ax, min, power, and PRR in Table 1� at the intervals �t=−50, t−40� , . . . , �t=−10, t=0�, the average PRR value at the subse-uent interval t+20 is predicted. Similarly, with the same inputnd different models, the 10 min average PRR values at intervals+30, t+40, and t+50 are predicted.

Industrial Case Study

3.1 The t+10 min PRR Prediction Without Parameterelection. To compare the accuracy of models built before andfter parameters selection, the original 30 predictors were used asnputs to construct a multivariate time series model. Five differentata-mining algorithms were applied to build PRR prediction

ig. 5 The prediction results of the t+10 model with parameterelection: „a… prediction performance of the five algorithms forhe test data set of Table 2 and „b… observed and predictedRRs by the SVM algorithm

Fig. 6 The importance of predictors com



models for a wind farm based on data set 2 of Table 2. Thesealgorithms include the multilayer perceptron algorithm �MLP��23,24�, the support vector machine �SVM� regression �25,26�, therandom forest �27,28�, the classification and regression �C&R� tree�13,29�, and the pace regression algorithm �13,30�.

The five algorithms used in this research are representative ofdifferent classes of data-mining algorithms. The MLP algorithm isusually used in nonlinear regression and classification modeling.The SVM is a supervised learning algorithm used in classificationand regression. It constructs a linear discriminant function thatseparates instances as widely as possible. The C&R tree builds adecision tree to predict either classes �classification� or Gaussians�regression�. The random forest algorithm grows many classifica-tion trees to classify a new object from an input vector. Each tree

Table 6 The importance index of predictors generated by theboosting tree algorithm for t+20 model

Predictor Variable rank Importance

Mean-1 54 0.54Mean-2 50 0.50Mean-3 41 0.41Mean-4 39 0.39Mean-5 31 0.31Std-1 40 0.40Std-2 46 0.46Std-3 48 0.48Std-4 46 0.46Std-5 32 0.32Max-1 68 0.68Max-2 61 0.61Max-3 42 0.42Max-4 47 0.47Max-5 36 0.36Min-1 33 0.33Min-2 46 0.38Min-3 31 0.31Min-4 32 0.32Min-5 28 0.28PRR-1 100 1.00PRR-2 72 0.72PRR-3 26 0.26PRR-4 49 0.52PRR-5 38 0.38Power-1 68 0.68Power-2 57 0.57Power-3 46 0.50Power-4 47 0.51Power-5 40 0.40

puted by the boosting tree algorithm

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otes for every class, and finally the forest chooses the classifica-ion having the most votes over all the trees in the forest. The paceegression algorithm consists of a group of estimators that areither optimal overall or optimal under certain conditions. It is aew approach to fitting linear models in high-dimensional spaces.

To test the accuracy of these algorithms, models trained fromata set 2 of Table 2 were tested on data set 3 from Table 2. Tableshows the prediction accuracy of the models generated by the

ve algorithms. Figure 4�a� illustrates the absolute error of differ-nt algorithms. The first 100 observed PPRs and those predictedy the SVM algorithm for data set 3 were shown in Fig. 4�b�. It cane seen from Table 4 and Fig. 4 that the SVM algorithm outper-orms the other four algorithms. The C&R tree algorithm produceshe worst predictions, and the pace regression algorithm performsuite well. The model can be updated to reflect the process changever time. The update frequency could be, e.g., 3 weeks. Alterna-ively, a separate routine could monitor the model performancend refresh the model once its performance would degrade.

3.2 The t+10 min Prediction With Parameter Selection.n this section, the predictors as input for the multivariate timeeries model are selected by the boosting tree algorithm. As de-cribed in Sec. 2.3, 9 out of 30 predictors were selected to buildhe time series model. The nine selected predictors are PPR-1,PR-2, PPR-5, Min-1, PPR-3, Power-2, PRR-4, Min-2, and Std-2.To test the difference between t+10 min prediction models

uilt with and without parameter selection, the five data-mininglgorithms in Sec. 3.1 were used. Multivariate models were re-rained from data set 2 of Table 2 and were tested on data set 3rom Table 2. Table 5 shows the prediction accuracy of the modelsenerated by the five algorithms. Figure 5�a� illustrates the abso-ute error of the five algorithms, while Fig. 5�b� shows the first00 observed PPRs and those predicted by the SVM algorithm forata set 3. The results in Tables 4 and 5, and Figs. 4 and 5 dem-nstrate that the prediction accuracy of all five algorithms wasmproved after parameter selection by the boosting tree algorithm.he SVM algorithm outperformed the other four algorithms in bothcenarios, i.e., with and without parameter selection.

3.3 The t+20 min Prediction With Parameter Selection.o build a multivariate time series model for t+20 min PRR pre-iction, parameter selection is performed by the boosting tree al-orithm. Table 6 shows the importance of 30 predictors computedy the boosting tree algorithm based on data set 2 in Table 2 and+20 prediction horizons. In Table 6, -1 denotes the observationampled 10 min earlier, �2 denotes the observation sampled 20in earlier, and -3, -4, and -5 denote the observations sampled 30in, 40 min, and 50 min in the past, respectively.Figure 6 shows the importance index of the 30 predictors for

+20 PRR predictions ranked from the largest to the smallest one.hen comparing the results in Figs. 6 and 2, and Tables 6 and 3,

he importance of predictors varies for the t+10 and t+20 models.Similar to Sec. 2.4, 0.5 was established as a threshold to select

ignificant predictors for t+20 model. The boosting tree algorithmelected seven predictors and provided the following ranking:

able 7 Prediction error for the t+20 models generated by theve different algorithms

bsolute errorkW/min� MAE Std Maximum Minimum

LP 362.52 360.21 3960.36 1.27VM 301.31 319.48 3635.03 0.10andom forest 364.28 366.12 4067.49 0.88&R tree 336.25 340.41 4473.17 1.34ace regression 336.79 347.08 4023.24 0.65

PR-1, PPR-2, Max-1, Power-1, Max-2, Power-2, and Mean-1.

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Fig. 7 Observed and predicted PRRs from the t+20 modelswith selected parameters: „a… MLP algorithm, „b… SVM algorithm,„c… random forest algorithm, „d… C&R tree algorithm, and „e…
pace regression algorithm


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Table 7 shows the prediction error of the models generated byhe five algorithms �the same as in Sec. 3.2�. Figure 7 shows therst 100 observed and predicted PRR values for data set 3 in Table. The SVM algorithm outperformed the other four; however, theccuracy decreased compared with the t+10 results reported inec. 3.2.

3.4 Multiperiod Prediction With Parameter Selection. Ashe SVM algorithm performed better for both t+10 and t+20 pre-ictions. Therefore, it was selected to build multivariate time se-ies PRR models for t+30– t+60 min intervals. After parameterelection with the same parameter importance threshold of 0.5, the0 predictors were reduced to a seven-dimensional input with theoosting tree algorithm.

For the t+30 min model, the seven predictors were ranked asollows: Min-3, Min-1, Min-2, PRR-2, PRR-3, Max-3, andRR-1. For the t+40 min model, the ranking is PRR-2, PRR-4,RR-1, Max-1, Power-1, PRR-3, and Mean-1. For the t50 min model, the ranking is PRR-1, Max-1, Mean-1, PRR-3,td-1, PRR-4, and Power-5. And for the t+60 min model, theanking is Std-2, PRR-2, Mean-2, Max-2, Power-4, Power-5, and

ax-3. The boosting tree algorithm selects different parametersver different periods of the PRR prediction, i.e., the results de-end on the data set properties.

Using the selected parameters, multiperiod prediction modelsere built by the SVM algorithm. The test data set used for the t10 min model of Sec. 3.2 containing 887 points was reduced byfor each of the next 10 min period predictions. Table 8 shows

he absolute error statistics for the multivariate time series predic-ion over four different 10 min intervals. Figures 8�a�–8�d� showhe first 100 observed and predicted PRRs over t+30 min, t40 min, t+50 min, and t+60 min intervals, respectively. Theean, the standard deviation, and the maximum error all increase

s the prediction horizon lengthens. However, the minimum erroremains relatively stable. The multivariate model provides accu-ate PRR prediction at the t+10 to t+40 intervals; however, theccuracy at the t+50 and t+60 intervals deteriorates. It appearshat for longer horizon predictions, weather forecasting data maye useful.

ConclusionIn this paper, multivariate time series models for power ramp

ate prediction at different time horizons, from 10 min to 60 min,ere constructed. Five different data-mining algorithms were used

o build the PRR prediction models. The boosting tree algorithmelected important predictors. After parameter selection, the origi-al 30-dimensional input was significantly reduced, and thus theccuracy of the multivariate time series model was improved. TheVM algorithm outperformed the other four algorithms studied inhis paper. The multivariate time series model for PRR predictionuilt by the SVM algorithm turned out to be accurate and robust.he models constructed in the paper predicted the power ramp at+10– t+60 min intervals. A comprehensive comparative analysisf the multivariate models built with different data-mining algo-ithms was reported in this paper.

The time series models accurately predicted the power rampate of the wind farm at t+10– t+40 horizons; however, the accu-

Table 8 Absolute error statistics for multiperiod models

Absolute error�kW/min� MAE Std Maximum Minimum

t+30 min prediction 329.83 347.03 4109.27 0.59t+40 min prediction 347.92 418.41 4600.32 1.94t+50 min prediction 387.45 404.92 4566.47 0.02t+60 min prediction 458.70 469.24 4972.20 0.62

acy at t+50 min and t+60 min horizons degrades. The extracted



models are essential in power grid integration and management.The multivariate time series prediction model may become a basisfor predictive control aimed at optimizing the power ramp rate.

The current wind farm power prediction models usually esti-

Fig. 8 Observed and predicted PRRs for different periods forthe first 100 test data points: „a… the t+30 min PRR model, „b…the t+40 min PRR model, „c… the t+50 min PRR model, and „d…the t+60 min PRR model

mate the power at 1 h or 3 h intervals based on weather forecast-

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ng data. These predictions reveal power ramps over long timeorizons. Prediction of power ramp rates at shorter intervals, e.g.,0 min, is of importance to the electric grid. The model built inhis research does not use weather forecasting data, and it pro-ides valuable ramp rate prediction on 10 min intervals. One av-nue to be pursued in future research is the transformation of theime series data, e.g., using wavelets or Kalman filters.

One disadvantage of the proposed approach is that the multi-ariate time series model used different parameters, and thereforepdating the model with most current data is important. As theumber of prediction steps increases, the error increases. Theodels investigated in this research were intended for predicting

he power ramp rate at relatively short horizons. One possibleitigation strategy is to incorporate weather forecasting and addi-

ional off-site observation data, all at additional computationalost. Other research questions, including the seasonal perfor-ance of the proposed approach, could be addressed, provided

hat the appropriate data would be available.

cknowledgmentThe research reported in the paper has been partially supported

y funding from the Iowa Energy Center Grant No. 07-01.

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