Research ArticleIntegrated Machine Learning and Enhanced StatisticalApproach-Based Wind Power Forecasting in AustralianTasmania Wind Farm

Fang Yao 12 Wei Liu1 Xingyong Zhao1 and Li Song1

1School of Electric Power and Architecture Shanxi University Taiyuan 030013 China2School of Electrical and Electronics and Computer Engineering University of Western Australia Perth WA 6009 Australia

Correspondence should be addressed to Fang Yao y98122hotmailcom

Received 19 July 2020 Revised 23 August 2020 Accepted 7 September 2020 Published 16 September 2020

Academic Editor Qiang Chen

Copyright copy 2020 Fang Yao et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

)is paper develops an integrated machine learning and enhanced statistical approach for wind power interval forecasting Atime-series wind power forecasting model is formulated as the theoretical basis of our method )e proposed model takes intoaccount two important characteristics of wind speed the nonlinearity and the time-changing distribution Based on the proposedmodel six machine learning regression algorithms are employed to forecast the prediction interval of the wind power output )esix methods are tested using real wind speed data collected at a wind station in Australia For wind speed forecasting the longshort-term memory (LSTM) network algorithm outperforms other five algorithms In terms of the prediction interval the fivenonlinear algorithms show superior performances )e case studies demonstrate that combined with an appropriate nonlinearmachine learning regression algorithm the proposed methodology is effective in wind power interval forecasting

1 Introduction

Wind power is rapidly expanding its market share aroundthe world However the intermittency and uncertainty ofwind make it a challenge to integrate wind power into thepower system )e wind power forecasting system cangreatly help the integration process since system operatorsrely on accurate wind power forecasts to design operationalplans and assess system security [1 2] Servo mechanism isthe foundation of wind turbines and precise wind powerforecasting can improve the accuracy of parameter esti-mation and control of wind turbine servo systems [3ndash5]Predictions of wind power outputs are traditionally providedin the form of point forecasts )e advantage of pointforecasts is that they can be easily understood )e singlevalue is expected to tell everything about future powergeneration Nowadays the majority of the research effortson wind power forecasting is still focused on point fore-casting )e reviews of the state of the art in wind powerforecasting can be found in [6 7] A book on physical

approaches to short-term wind power forecasting also partlydiscusses the state of the art in wind power forecasting [8]

However even if both meteorological and power con-version processes are well understood and modelled therewill always be inherent and inevitable uncertainty in windpower forecasts )e uncertainty comes from the incompleteknowledge of the physical processes that influence futureevents [9] )e uncertainty of wind power forecasts mainlydepends on the predictability of the current meteorologicalstatus and the level of the predicted wind speed [10] To assistwith the management of the forecasting uncertainty ex-tensive research studies have been conducted to developwind power forecasting methods Different regressionmethods have been introduced in [10ndash12] )ese approachesuse probabilistic forecasts generated by different quantileregression methods to provide the complete information offuture wind production A multiscale reliable wind powerforecasting (WPF) method was developed by Yan et al in[13])is method provides the expected future value and theassociated uncertainty by a multi-to-multi mapping network

HindawiComplexityVolume 2020 Article ID 9250937 12 pageshttpsdoiorg10115520209250937

and stacked denoising autoencode Wang et al developed ashort-term wind prediction method with the convolutionalneural network (CNN) based on information of neigh-bouring wind farms [14] One popular approach is to useensemble-based probabilistic forecasting methodologieswhich enable better wind power management and tradingpurposes [15 16] In [17 18] statistical analysis has beenconducted to study the distribution of wind power fore-casting errors Because wind power is stochastic in natureerrors will always exist in wind power forecasts )ereforebesides predicting the expected value of the future windpower it is also important to estimate its forecasting errors

A key weakness of the above studies lies in that they failto establish proper statistical models for interval forecastingof wind power and also fail to take into account the time-changing effect of the error distribution Generally speakinga prediction interval is a stochastic interval which containsthe true value of wind power with a preassigned probabilityBecause the prediction interval can quantify the uncertaintyof the forecasted wind power it can be employed to evaluatethe risks of the decisions made by market participantsExisting methods discussed above cannot effectively handlewind power interval forecasting since they mainly focus onpredicting the expected point value of wind power

)ere are two main challenges for providing accurate in-terval forecasting of wind power (i) the expected value of windpower should be accurately predicted)is is difficult sincewindpower is a nonlinear time series and is therefore highly volatile)e nonlinear research system has high complexity in thefundamental research and lots of nonlinear control problemsunceasingly emerge in real fact [19ndash23] (ii) the probabilitydistribution of forecasting errors should also be accuratelyestimated)is is evenmore difficult since the error distributioncan be time-changing In this paper a novel approach isproposed to forecast the prediction interval of wind power Astatistical model is first formulated to properly model the timeseries of wind speed Based on the proposedmodel a number ofdifferent machine learning algorithms are introduced to predictthe expected value of wind speed and the parameters offorecasting error distribution Prediction intervals of wind speedare then constructed based on the predicted wind speed valueand error distribution )e wind speed prediction interval isfinally transformed into thewind power prediction interval withthe wind turbine power curve Comprehensive studies areperformed to compare the performances of six machinelearning algorithms in wind power interval forecasting

)e main contributions of this paper are as follows

(1) A comprehensive statistical model is introducedwhich forms the theoretical basis for wind powerinterval forecasting

(2) Different machine learning regression methods areincorporated into the proposed model )e com-parison of different regression algorithms in windpower forecasting is presented

(3) )e proposed integrated statistical machine learningapproach can highlight the essential information ofthe available data

)e rest of the paper is organized as follows in Section 2a statistical model for the wind speed time series is for-mulated We also introduce the Lagrange multiplier (LM)test to verify that the forecasting errors of wind power have atime-changing distribution In Section 3 the basic conceptof machine learning and six machine learning algorithms forwind power forecasting are introduced Afterwards com-prehensive case studies are performed in Section 4 Section 5finally concludes the paper

2 The Statistical Model of the Wind SpeedTime Series

To forecast the power output of a wind turbine a widely usedapproach is to predict the wind speed first and thentransform the predicted wind speed into wind power withthe power curve)erefore in this section a statistical modelof wind speed is first formulated We will also briefly explainhow to integrate the proposed model with nonlinear re-gression techniques to forecast the prediction intervals ofwind speed )e wind speed time series can usually be as-sumed to be generated by the following stochastic process

Yt f Ytminus1 Ytminus2 Xrarr

t1113874 1113875 + εt (1)

where Yt denotes the random wind speed and yt is theobserved value of Yt at time t X

rarrt isin Rm is anm-dimensional

explanatory vector Each element Xti of Xrarr

t represents anexplanatory variable which can influence Yt for examplethe temperature and humidity )e current value of Yt canbe determined by its lagged values Ytminus1 Ytminus2 and theexplanatory vector X

rarrt Note that the mapping f(bull) from

Ytminus1 Ytminus2 Xrarr

t to Yt can be any linear or nonlinearfunction Most existing methods essentially forecast windspeed by estimatingmappingf(bull) the forecasted value 1113954f(bull)

of f(bull) can be called the point forecast of wind speedAccording to (1) the wind speed Yt contains two compo-nents f(bull) is a deterministic component and εt is a randomcomponent which is also known as noise Statistical andengineering models are an approximation to reality notreality so they always have some degree of errors Nowa-days there are lots of research studies about error trackingand control [24ndash29] Precise prediction and reducing theerror are the prerequisite for all further control worksDetailed statistical studies [30] show that εt can be assumedto follow a normal distribution We therefore have

εt sim N μ σ21113872 1113873 (2)

Because f(bull) is a deterministic function we should beable to approximate it with arbitrary accuracy by employinga powerful nonlinear machine learning technique (egneural network) Most existing wind speed forecastingmethods mainly focus on estimating f(bull) and selecting itsestimated value as the predicted wind speed On the con-trary because of the uncertainty introduced by noise εterrors will always exist in wind speed forecasts )ereforeestimating μ and σ2 is essential for estimating the

2 Complexity

uncertainty of Yt In models (1) and (2) parameters μ and σ2are assumed to be constant In practice the model pa-rameters can usually be time-changing We therefore in-troduce the following time-changing distribution model ofwind speed

Yt f Ytminus1 Ytminus2 Xrarr

t1113874 1113875 + εt

εt μt + σt middot vt

vt sim N(0 1)

Xrarr

tprime Xt1 Xt2 Xtm1113872 1113873

ut g εtminus1 εtminus2 X

t1113874 1113875

σt h εtminus1 εtminus2 X

t1113874 1113875

(3)

Similar to f(bull) mappings g(bull) and h(bull) can also beeither linear or nonlinear According to model (3) theuncertainty of wind speed is time-changing )e mean andvariance of noise εt are determined by the previous noisesand the explanatory vector Note that model (3) is a gen-eralization to the traditional ARCH (AutoRegressive Con-ditional Heteroskedasticity) model since by setting ut equiv 0and assuming f(bull) and h(bull) are linear functions model (3)will be identical to the ARCH model To more strictly justifyour model the Lagrange multiplier (LM) test can beemployed to verify that the wind speed has a time-changingdistribution In the case study we will test whether the actualwind speed data of Australia have a time-changing distri-bution by performing the LM test

Based on statistical model (3) of wind speed we canconstruct the prediction interval which contains the truevalue of wind speed with any preassigned probability )edefinition of the prediction interval can be given as follows

Definition 1 Given a time series Yt1113864 1113865 which is generatedwith model (3) an α-level prediction interval (PI) of Yt is astochastic interval [Lt Ut] calculated from Yt1113864 1113865 such thatP(Yt isin [Lt Ut]) 1 minus α

Because noise εt is usually assumed to be normallydistributed the α-level prediction interval can therefore becalculated as

Lt ft(bull) + μt minus z(1minusa)2 times σt (4)

Ut ft(bull) + μt + z(1minusa)2 times σt (5)

where ft(bull) represents the value of the deterministiccomponent f(bull) at time t α is the confidence level andz(1minusa)2 is the critical value of the standard normal dis-tribution Based on (4) and (5) to calculate the predictioninterval we should first obtain three quantities the windspeed forecast ft(bull) the mean μ and the variance σ2 of thenoise In practice traditional time-series models such asARIMA and GARCH usually perform poorly on short-term wind speed forecasting since they are linear modelsand therefore cannot handle the complex nonlinearpatterns of wind speed data To give accurate wind speed

forecasts the three mappings f(bull) g(bull) and h(bull) inmodel (3) should be accurately estimated with nonlineartechniques In this paper we introduce six differentmachine learning methods to estimate f(bull) g(bull) andh(bull) To apply machine learning methods to estimate g(bull)

and h(bull) an unsolved problem is how to obtain the es-timates of mean μt and variance σ2t of the noise In thispaper the moving windowmethod is employed Given thenoise series εt1113864 1113865 the estimates of μt and σ2t can be cal-culated as

1113954μt 1

2n + 11113944

t+n

stminusn

εs (6)

1113954σ2t 12n

1113944

t+n

stminusn

εs minus 1113954μs( 11138572 (7)

By combining amachine learningmethod with proposedmodel (3) the main procedure of wind power intervalforecasting is given as follows

(1) Given the historical wind speed data Yt1113864 1113865 and the

explanatory vector data Xrarr

t1113882 1113883 for time period [0 T]

employ a machine learning technique to estimatefunction Yt f(Ytminus1 Ytminus2 X

rarrt) Denote the es-

timate of f(bull) as 1113954f(bull)(2) Calculate the forecasting errors

et Yt minus 1113954f(Ytminus1 Ytminus2 Xrarr

t) for period [0 T]Note that et can be considered as the estimate ofnoise εt

(3) Based on error series et1113864 1113865 calculate the estimates ofμt and σ2t with equations (6) and (7)

(4) Based on error series et1113864 1113865 and mean and varianceestimate series 1113954μt1113864 1113865 and 1113954σ2t1113966 1113967 employ a machinelearning technique to estimate functions1113954μt 1113954g(etminus1 etminus2 X

rarrt) and 1113954σt 1113954h(etminus1 etminus2 X

rarrt) and

use them as the estimates of g(bull) and h(bull)(5) To forecast the wind speed at t first employ 1113954f(bull)

1113954g(bull) and 1113954h(bull) to calculate 1113954ft(bull) 1113954μt and 1113954σ2t thencalculate the wind speed prediction interval withequations (4) and (5)

(6) Transform the wind speed prediction interval intothe wind power prediction interval with the windturbine power curve which will be discussed in thefollowing sections

3 Machine Learning Methods for Wind PowerInterval Forecasting

In this section we first provide a brief introduction tomachine learning which is an important research area inforecasting Six machine learning algorithms used in thispaper are then presented )e power curve for convertingwind speed into wind power is introduced We finallydiscuss how to evaluate the performance of wind powerinterval forecasting methods

Complexity 3

31 Introduction to Machine Learning Machine learning isscience that studies how to use the computer to simulateor realize human learning activities It is one of the mostintelligent and leading-edge research fields in artificial in-telligence Machine learning techniques are essential tothe renewable energy integration such as PV and windpower [31 32]

Machine learning can be divided into supervisedlearning and unsupervised learning [33ndash35] As can be seenfrom Figure 1 supervised learning can be classified intoclassification and regression and unsupervised learning canbe classified into clustering and correlation

Regression [36] is a process to estimate a functionalmapping between a data vector and a target variableRegression aims at determining a continuous targetvariable which is usually named as the dependent vari-able while the data item itself is usually called inde-pendent variables explanatory variables or predictorsFor example in wind speed forecasting the predictors canbe historical wind speed temperature and humiditywhile the independent variable is the future wind speedRegression usually estimates the mapping based on atraining dataset in which the independent variables of alldata items have been given Regression is therefore asupervised learning problem in the sense that the esti-mation of the mapping is supervised by the training dataRegression is also an important research area of statistics)e most important statistical method is linear regressionwhich assumes that the independent variable is deter-mined by a linear function of predictors In recent yearsthe machine learning society has proposed many otherregression methods such as deep learning In this paperwe will introduce six different machine learning regres-sion techniques and integrate them with the proposedstatistical model to perform wind power intervalforecasting

32 Machine Learning Regression Algorithms Employed in0is Paper

321 Linear Regression Linear regression is a traditionaland widely used statistical technique for regression It isselected as the baseline technique in this paper and will becompared with five nonlinear techniques Linear regres-sion models the relationship between the dependentvariable yi and the vector of predictors xi Linear re-gression assumes that the independent variable y is lin-early dependent on the predictors x plus a noise term εi)e model can be written as

yi β1xi1 + middot middot middot + βpxip + εi xiprime βT

+ εi i 1 2 n

(8)

where xiprimeβT is the inner product between vectors xi and β

And these n equations can be written in the vector form as

y βTX + ε (9)

where

y

y1y2⋮yn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

X

x1primex2prime⋮xnprime

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

βT

β1⋮βp

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

ε

ε1ε2⋮εn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(10)

ε is usually assumed to follow a normal distribution witha zero mean and variance σ2 We therefore have

ε sim N 0 σ21113872 1113873 (11)

and β is a p-dimensional parameter vector which specifieshow much each component of X contributes to the output y

[37]

322 Multilayer Perceptron Network A multilayer per-ceptron (MLP) network is a feedforward artificial neuralnetwork model that maps sets of input data onto a set ofappropriate outputs Based on the standard linear percep-tron MLP uses three or more layer nodes with nonlinearactivation functions An MLP network consists of a set ofsource nodes as the input layer one or more hidden layers ofcomputation nodes and an output layer of nodes

Figure 2 shows the signal flow process of a feedforwardneural network A MLP network has two stages a forwardpass and a backward pass )e forward pass includes pre-senting a sample input to the network and letting activationsflow until they reach the output layer [38 39]

323 Long Short-Term Memory (LSTM) Network-BasedDeep Learning Method )e concept of deep learning wasfirst proposed by Hinton et al in 2006 Deep learning is a

Machinelearning

Supervisedlearning

Unsupervisedlearning

Classification

Regression

Clustering

Correlation

Figure 1 Composition structure of machine learning

4 Complexity

branch of machine learning It is essentially a special arti-ficial neural network Deep learning utilizes a multilayernetwork structure and applies appropriate nonlineartransformation functions to each hidden node to achieve thepurpose of high-level abstraction of the data )e traditionalfeedforward artificial neural network usually contains onlyone hidden layer but there are many hidden layer structuresin deep learning )erefore deep learning adopts a trainingmechanism completely different from the traditional arti-ficial neural network in order to solve the problem of thedeep neural network in training [40]

LSTM is a time-cycle neural network which can effec-tively solve the gradient explosion and gradient disap-pearance problems compared with the traditional cycleneural network LSTM is composed of a set of cyclic subnetscalled memory blocks Each memory block is composed ofthe input gate forgetting gate and output gate Figure 3shows the LSTM structure [41]

In general the LSTM recursive neural network iscomposed of the following components input gate it has thecorresponding weight matrix wxi whi wci and bi forgettinggate ft has the corresponding weight matrix whf wcf andbf and output door ot with the corresponding weight matrixwxo who wco and bo )e function of the input gate is to

record the new information to the cell state selectively )efunction of the forget gate is to selectively forget the statusinformation in the cell the function of the output gate is toexport certain information from the cell )e detailedworkflow of LSTM is shown in the following [42]

it σ ωxixt + whihtminus1 + wcictminus1 + bi( 1113857

ft σ wxfxt + whfhtminus1 + wcfctminus1 + bf1113872 1113873

ot σ wxoxt + whohtminus1 + wcoctminus1 + bo( 1113857

ct ftctminus1 + ittanh wxcxt + whihtminus1 + whcctminus1 + bc( 1113857

(12)

where σ is the logistic sigmoid function with the output in [01] and tanh represents the hyperbolic tangent function withthe output in [minus1 1]

324 Lazy IBK Lazy IBK is one of the widely used lazylearning methods Lazy learning methods defer the deci-sion of how to assign the dependent variable until a newquery explanatory vector is inputted When the queryexplanatory vector is received a set of similar data recordsis retrieved from the available training dataset and is used

F

F

F

F

F

sum

sumsum

sumsum

sum

Input layer

Hiddenlayer

Outputlayer

Figure 2 Diagram of a multilayer perceptron network

Output

Input

Input

Input

Input

RecurrentRecurrent

Recurrent

Recurrent

Recurrent

Block output

Block input

LSTM block

Peepholes

Forget gate

f+

+

+

+

+

Cell c

i

z Input gate

Output gate

h

g

σ

σ

σ

y o

Figure 3 LSTM storage unit with door

Complexity 5

to assign the dependent variable to the new instance [43]In order to choose the similar data records lazy methodsemploy a distance measure that will give nearby datarecords higher relevance Lazy methods choose the k datarecords that are nearest to the query instance )e de-pendent variable of the new instance is determined basedon the k-nearest instances

Lazy learning algorithms have three basic steps

(i) Defer lazy learning algorithms store all trainingdata and defer processing until a new query is given

(ii) Reply a local learning approach developed byBottou and Vapnik in 1992 is a popular method todetermine the dependent variables for news queries[44] In the Bottou and Vapnik learning approachinstances are defined as points in the space and asimilarity function is defined on all pairs of theseinstances

(iii) Flush after solving a query the answer and anyintermediate results are discarded

325 Regression Tree A regression tree is one of the widelyused decision tree algorithms A decision tree is a data-miningtool designed to extract useful information from large datasetsand use the information to help decision-making processes Aregression tree consists of a set of nodes that can assign thevalue of the dependent variable to an explanatory vectorRegression tree constructs a tree style decision rule set anddivides the training data into the leaf nodes of the decisiontree according to the numerical or categorical values of ex-planatory variables )e regression rules of each leaf node arederived from a mathematical process that minimizes theregression errors of the leaf nodes [45]

326 Decision Table Similar to the regression tree decisiontable also determines the value of the dependent variablewith a set of decision rules [46] However the decision tablearranges decision rules as a table rather than a tree Adecision table usually consists of a number of parallel de-cision rules Similar to the regression tree the training datawill be divided into several groups each of which will berepresented by a decision rule For a given explanatoryvector (input) an appropriate decision rule will be firstselected based on the values of its explanatory variables )edependent variable for this input will be assigned as theaverage of the dependent variables of all training data vectorsin the corresponding group)e dependent variable can alsobe determined by performing linear regression on thecorresponding group of training data Empirical studiesshow that the decision table has a similar performance toregression trees

33 Converting Wind Speed to Wind Power An elementarymethod is used in this paper to convert the predicted windspeed to the predicted wind power output of a wind turbineor wind farm )e predicted wind speed is provided by oneof the six machine learning regression methods discussed

above )e wind speed is then input into the certified windturbine power curve and transformed into the wind power

)e Vestas V90-30MW wind turbine is selected for thecase studies in this paper Vestas V90-30MW is a pitchregulated upwind wind turbine with active yaw and a three-blade rotor It has a rotor diameter of 90m with a generatorrated at 30MW Vestas V90-30MW is widely used inAustralia wind power plants and has a proven highefficiency

)e typical power curve of Vestas V90-30MW 60Hz1067 dB(A) is shown in Figure 4 It can be clearly ob-served that the wind power output p(u) is proportional tou3 for small wind speed u Moreover the power curve issteep for medium wind speeds and flat for large windspeeds )e cut-in speed is 35 ms and the cut-out speedis 25ms [47]

34 Performance Evaluation Before proposing the casestudy results several criteria are introduced for performanceevaluation Given T historical wind power values pt1le tleT of a time series pt1113864 1113865 which are converted from Thistorical wind speed observations and the correspondingforecasted power values plowastt 1le tleT mean absolute per-centage error (MAPE) is defined as

MAPE 1T

1113944

T

t1

pt minus ptlowast1113868111386811138681113868

1113868111386811138681113868

pt

(13)

MAPE is a widely used criterion for time-series fore-casting It will also be employed to evaluate the proposedmethod in the case studies

Another two criteria are presented to evaluate intervalforecasting Given T wind power values pt 1 le t leT of atime series Py1113966 1113967 and the corresponding forecasted α-levelprediction intervals [lt ut] 1 le t leT the empirical confi-dence 1113954α [48] and the absolute coverage error (ACE) aredefined as

1113954α frequency pt isin lt ut1113858 1113859( 1113857

T

ACE |α minus αand|

(14)

where 1113954α is the number of observations which fall into theforecasted prediction interval (PI) divided by the samplesize It should be as close to α as possible

4 Case Studies

410e Setting of Case Studies In the experiments the windpower forecasting model has been evaluated using the windspeed data from the Devonport Airport Wind StationTasmania Australia )e data were provided by the Aus-tralian Bureau of Meteorology )e training and testing datahave the following four numerical features wind speedwind direction humidity and temperature )e trainingdata are from 1st February 2018 to 1st March 2018 while thetesting data are from 1st February 2019 to 1st March 2019

6 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

uncertainty of Yt In models (1) and (2) parameters μ and σ2are assumed to be constant In practice the model pa-rameters can usually be time-changing We therefore in-troduce the following time-changing distribution model ofwind speed

Yt f Ytminus1 Ytminus2 Xrarr

t1113874 1113875 + εt

εt μt + σt middot vt

vt sim N(0 1)

Xrarr

tprime Xt1 Xt2 Xtm1113872 1113873

ut g εtminus1 εtminus2 X

t1113874 1113875

σt h εtminus1 εtminus2 X

t1113874 1113875

(3)

Similar to f(bull) mappings g(bull) and h(bull) can also beeither linear or nonlinear According to model (3) theuncertainty of wind speed is time-changing )e mean andvariance of noise εt are determined by the previous noisesand the explanatory vector Note that model (3) is a gen-eralization to the traditional ARCH (AutoRegressive Con-ditional Heteroskedasticity) model since by setting ut equiv 0and assuming f(bull) and h(bull) are linear functions model (3)will be identical to the ARCH model To more strictly justifyour model the Lagrange multiplier (LM) test can beemployed to verify that the wind speed has a time-changingdistribution In the case study we will test whether the actualwind speed data of Australia have a time-changing distri-bution by performing the LM test

Based on statistical model (3) of wind speed we canconstruct the prediction interval which contains the truevalue of wind speed with any preassigned probability )edefinition of the prediction interval can be given as follows

Definition 1 Given a time series Yt1113864 1113865 which is generatedwith model (3) an α-level prediction interval (PI) of Yt is astochastic interval [Lt Ut] calculated from Yt1113864 1113865 such thatP(Yt isin [Lt Ut]) 1 minus α

Because noise εt is usually assumed to be normallydistributed the α-level prediction interval can therefore becalculated as

Lt ft(bull) + μt minus z(1minusa)2 times σt (4)

Ut ft(bull) + μt + z(1minusa)2 times σt (5)

where ft(bull) represents the value of the deterministiccomponent f(bull) at time t α is the confidence level andz(1minusa)2 is the critical value of the standard normal dis-tribution Based on (4) and (5) to calculate the predictioninterval we should first obtain three quantities the windspeed forecast ft(bull) the mean μ and the variance σ2 of thenoise In practice traditional time-series models such asARIMA and GARCH usually perform poorly on short-term wind speed forecasting since they are linear modelsand therefore cannot handle the complex nonlinearpatterns of wind speed data To give accurate wind speed

forecasts the three mappings f(bull) g(bull) and h(bull) inmodel (3) should be accurately estimated with nonlineartechniques In this paper we introduce six differentmachine learning methods to estimate f(bull) g(bull) andh(bull) To apply machine learning methods to estimate g(bull)

and h(bull) an unsolved problem is how to obtain the es-timates of mean μt and variance σ2t of the noise In thispaper the moving windowmethod is employed Given thenoise series εt1113864 1113865 the estimates of μt and σ2t can be cal-culated as

1113954μt 1

2n + 11113944

t+n

stminusn

εs (6)

1113954σ2t 12n

1113944

t+n

stminusn

εs minus 1113954μs( 11138572 (7)

By combining amachine learningmethod with proposedmodel (3) the main procedure of wind power intervalforecasting is given as follows

(1) Given the historical wind speed data Yt1113864 1113865 and the

explanatory vector data Xrarr

t1113882 1113883 for time period [0 T]

employ a machine learning technique to estimatefunction Yt f(Ytminus1 Ytminus2 X

rarrt) Denote the es-

timate of f(bull) as 1113954f(bull)(2) Calculate the forecasting errors

et Yt minus 1113954f(Ytminus1 Ytminus2 Xrarr

t) for period [0 T]Note that et can be considered as the estimate ofnoise εt

(3) Based on error series et1113864 1113865 calculate the estimates ofμt and σ2t with equations (6) and (7)

(4) Based on error series et1113864 1113865 and mean and varianceestimate series 1113954μt1113864 1113865 and 1113954σ2t1113966 1113967 employ a machinelearning technique to estimate functions1113954μt 1113954g(etminus1 etminus2 X

rarrt) and 1113954σt 1113954h(etminus1 etminus2 X

rarrt) and

use them as the estimates of g(bull) and h(bull)(5) To forecast the wind speed at t first employ 1113954f(bull)

1113954g(bull) and 1113954h(bull) to calculate 1113954ft(bull) 1113954μt and 1113954σ2t thencalculate the wind speed prediction interval withequations (4) and (5)

(6) Transform the wind speed prediction interval intothe wind power prediction interval with the windturbine power curve which will be discussed in thefollowing sections

3 Machine Learning Methods for Wind PowerInterval Forecasting

In this section we first provide a brief introduction tomachine learning which is an important research area inforecasting Six machine learning algorithms used in thispaper are then presented )e power curve for convertingwind speed into wind power is introduced We finallydiscuss how to evaluate the performance of wind powerinterval forecasting methods

Complexity 3

31 Introduction to Machine Learning Machine learning isscience that studies how to use the computer to simulateor realize human learning activities It is one of the mostintelligent and leading-edge research fields in artificial in-telligence Machine learning techniques are essential tothe renewable energy integration such as PV and windpower [31 32]

Machine learning can be divided into supervisedlearning and unsupervised learning [33ndash35] As can be seenfrom Figure 1 supervised learning can be classified intoclassification and regression and unsupervised learning canbe classified into clustering and correlation

Regression [36] is a process to estimate a functionalmapping between a data vector and a target variableRegression aims at determining a continuous targetvariable which is usually named as the dependent vari-able while the data item itself is usually called inde-pendent variables explanatory variables or predictorsFor example in wind speed forecasting the predictors canbe historical wind speed temperature and humiditywhile the independent variable is the future wind speedRegression usually estimates the mapping based on atraining dataset in which the independent variables of alldata items have been given Regression is therefore asupervised learning problem in the sense that the esti-mation of the mapping is supervised by the training dataRegression is also an important research area of statistics)e most important statistical method is linear regressionwhich assumes that the independent variable is deter-mined by a linear function of predictors In recent yearsthe machine learning society has proposed many otherregression methods such as deep learning In this paperwe will introduce six different machine learning regres-sion techniques and integrate them with the proposedstatistical model to perform wind power intervalforecasting

32 Machine Learning Regression Algorithms Employed in0is Paper

321 Linear Regression Linear regression is a traditionaland widely used statistical technique for regression It isselected as the baseline technique in this paper and will becompared with five nonlinear techniques Linear regres-sion models the relationship between the dependentvariable yi and the vector of predictors xi Linear re-gression assumes that the independent variable y is lin-early dependent on the predictors x plus a noise term εi)e model can be written as

yi β1xi1 + middot middot middot + βpxip + εi xiprime βT

+ εi i 1 2 n

(8)

where xiprimeβT is the inner product between vectors xi and β

And these n equations can be written in the vector form as

y βTX + ε (9)

where

y

y1y2⋮yn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

X

x1primex2prime⋮xnprime

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

βT

β1⋮βp

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

ε

ε1ε2⋮εn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(10)

ε is usually assumed to follow a normal distribution witha zero mean and variance σ2 We therefore have

ε sim N 0 σ21113872 1113873 (11)

and β is a p-dimensional parameter vector which specifieshow much each component of X contributes to the output y

[37]

322 Multilayer Perceptron Network A multilayer per-ceptron (MLP) network is a feedforward artificial neuralnetwork model that maps sets of input data onto a set ofappropriate outputs Based on the standard linear percep-tron MLP uses three or more layer nodes with nonlinearactivation functions An MLP network consists of a set ofsource nodes as the input layer one or more hidden layers ofcomputation nodes and an output layer of nodes

Figure 2 shows the signal flow process of a feedforwardneural network A MLP network has two stages a forwardpass and a backward pass )e forward pass includes pre-senting a sample input to the network and letting activationsflow until they reach the output layer [38 39]

323 Long Short-Term Memory (LSTM) Network-BasedDeep Learning Method )e concept of deep learning wasfirst proposed by Hinton et al in 2006 Deep learning is a

Machinelearning

Supervisedlearning

Unsupervisedlearning

Classification

Regression

Clustering

Correlation

Figure 1 Composition structure of machine learning

4 Complexity

branch of machine learning It is essentially a special arti-ficial neural network Deep learning utilizes a multilayernetwork structure and applies appropriate nonlineartransformation functions to each hidden node to achieve thepurpose of high-level abstraction of the data )e traditionalfeedforward artificial neural network usually contains onlyone hidden layer but there are many hidden layer structuresin deep learning )erefore deep learning adopts a trainingmechanism completely different from the traditional arti-ficial neural network in order to solve the problem of thedeep neural network in training [40]

LSTM is a time-cycle neural network which can effec-tively solve the gradient explosion and gradient disap-pearance problems compared with the traditional cycleneural network LSTM is composed of a set of cyclic subnetscalled memory blocks Each memory block is composed ofthe input gate forgetting gate and output gate Figure 3shows the LSTM structure [41]

In general the LSTM recursive neural network iscomposed of the following components input gate it has thecorresponding weight matrix wxi whi wci and bi forgettinggate ft has the corresponding weight matrix whf wcf andbf and output door ot with the corresponding weight matrixwxo who wco and bo )e function of the input gate is to

record the new information to the cell state selectively )efunction of the forget gate is to selectively forget the statusinformation in the cell the function of the output gate is toexport certain information from the cell )e detailedworkflow of LSTM is shown in the following [42]

it σ ωxixt + whihtminus1 + wcictminus1 + bi( 1113857

ft σ wxfxt + whfhtminus1 + wcfctminus1 + bf1113872 1113873

ot σ wxoxt + whohtminus1 + wcoctminus1 + bo( 1113857

ct ftctminus1 + ittanh wxcxt + whihtminus1 + whcctminus1 + bc( 1113857

(12)

where σ is the logistic sigmoid function with the output in [01] and tanh represents the hyperbolic tangent function withthe output in [minus1 1]

324 Lazy IBK Lazy IBK is one of the widely used lazylearning methods Lazy learning methods defer the deci-sion of how to assign the dependent variable until a newquery explanatory vector is inputted When the queryexplanatory vector is received a set of similar data recordsis retrieved from the available training dataset and is used

F

F

F

F

F

sum

sumsum

sumsum

sum

Input layer

Hiddenlayer

Outputlayer

Figure 2 Diagram of a multilayer perceptron network

Output

Input

Input

Input

Input

RecurrentRecurrent

Recurrent

Recurrent

Recurrent

Block output

Block input

LSTM block

Peepholes

Forget gate

f+

+

+

+

+

Cell c

i

z Input gate

Output gate

h

g

σ

σ

σ

y o

Figure 3 LSTM storage unit with door

Complexity 5

to assign the dependent variable to the new instance [43]In order to choose the similar data records lazy methodsemploy a distance measure that will give nearby datarecords higher relevance Lazy methods choose the k datarecords that are nearest to the query instance )e de-pendent variable of the new instance is determined basedon the k-nearest instances

Lazy learning algorithms have three basic steps

(i) Defer lazy learning algorithms store all trainingdata and defer processing until a new query is given

(ii) Reply a local learning approach developed byBottou and Vapnik in 1992 is a popular method todetermine the dependent variables for news queries[44] In the Bottou and Vapnik learning approachinstances are defined as points in the space and asimilarity function is defined on all pairs of theseinstances

(iii) Flush after solving a query the answer and anyintermediate results are discarded

325 Regression Tree A regression tree is one of the widelyused decision tree algorithms A decision tree is a data-miningtool designed to extract useful information from large datasetsand use the information to help decision-making processes Aregression tree consists of a set of nodes that can assign thevalue of the dependent variable to an explanatory vectorRegression tree constructs a tree style decision rule set anddivides the training data into the leaf nodes of the decisiontree according to the numerical or categorical values of ex-planatory variables )e regression rules of each leaf node arederived from a mathematical process that minimizes theregression errors of the leaf nodes [45]

326 Decision Table Similar to the regression tree decisiontable also determines the value of the dependent variablewith a set of decision rules [46] However the decision tablearranges decision rules as a table rather than a tree Adecision table usually consists of a number of parallel de-cision rules Similar to the regression tree the training datawill be divided into several groups each of which will berepresented by a decision rule For a given explanatoryvector (input) an appropriate decision rule will be firstselected based on the values of its explanatory variables )edependent variable for this input will be assigned as theaverage of the dependent variables of all training data vectorsin the corresponding group)e dependent variable can alsobe determined by performing linear regression on thecorresponding group of training data Empirical studiesshow that the decision table has a similar performance toregression trees

33 Converting Wind Speed to Wind Power An elementarymethod is used in this paper to convert the predicted windspeed to the predicted wind power output of a wind turbineor wind farm )e predicted wind speed is provided by oneof the six machine learning regression methods discussed

above )e wind speed is then input into the certified windturbine power curve and transformed into the wind power

)e Vestas V90-30MW wind turbine is selected for thecase studies in this paper Vestas V90-30MW is a pitchregulated upwind wind turbine with active yaw and a three-blade rotor It has a rotor diameter of 90m with a generatorrated at 30MW Vestas V90-30MW is widely used inAustralia wind power plants and has a proven highefficiency

)e typical power curve of Vestas V90-30MW 60Hz1067 dB(A) is shown in Figure 4 It can be clearly ob-served that the wind power output p(u) is proportional tou3 for small wind speed u Moreover the power curve issteep for medium wind speeds and flat for large windspeeds )e cut-in speed is 35 ms and the cut-out speedis 25ms [47]

34 Performance Evaluation Before proposing the casestudy results several criteria are introduced for performanceevaluation Given T historical wind power values pt1le tleT of a time series pt1113864 1113865 which are converted from Thistorical wind speed observations and the correspondingforecasted power values plowastt 1le tleT mean absolute per-centage error (MAPE) is defined as

MAPE 1T

1113944

T

t1

pt minus ptlowast1113868111386811138681113868

1113868111386811138681113868

pt

(13)

MAPE is a widely used criterion for time-series fore-casting It will also be employed to evaluate the proposedmethod in the case studies

Another two criteria are presented to evaluate intervalforecasting Given T wind power values pt 1 le t leT of atime series Py1113966 1113967 and the corresponding forecasted α-levelprediction intervals [lt ut] 1 le t leT the empirical confi-dence 1113954α [48] and the absolute coverage error (ACE) aredefined as

1113954α frequency pt isin lt ut1113858 1113859( 1113857

T

ACE |α minus αand|

(14)

where 1113954α is the number of observations which fall into theforecasted prediction interval (PI) divided by the samplesize It should be as close to α as possible

4 Case Studies

410e Setting of Case Studies In the experiments the windpower forecasting model has been evaluated using the windspeed data from the Devonport Airport Wind StationTasmania Australia )e data were provided by the Aus-tralian Bureau of Meteorology )e training and testing datahave the following four numerical features wind speedwind direction humidity and temperature )e trainingdata are from 1st February 2018 to 1st March 2018 while thetesting data are from 1st February 2019 to 1st March 2019

6 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

31 Introduction to Machine Learning Machine learning isscience that studies how to use the computer to simulateor realize human learning activities It is one of the mostintelligent and leading-edge research fields in artificial in-telligence Machine learning techniques are essential tothe renewable energy integration such as PV and windpower [31 32]

Machine learning can be divided into supervisedlearning and unsupervised learning [33ndash35] As can be seenfrom Figure 1 supervised learning can be classified intoclassification and regression and unsupervised learning canbe classified into clustering and correlation

Regression [36] is a process to estimate a functionalmapping between a data vector and a target variableRegression aims at determining a continuous targetvariable which is usually named as the dependent vari-able while the data item itself is usually called inde-pendent variables explanatory variables or predictorsFor example in wind speed forecasting the predictors canbe historical wind speed temperature and humiditywhile the independent variable is the future wind speedRegression usually estimates the mapping based on atraining dataset in which the independent variables of alldata items have been given Regression is therefore asupervised learning problem in the sense that the esti-mation of the mapping is supervised by the training dataRegression is also an important research area of statistics)e most important statistical method is linear regressionwhich assumes that the independent variable is deter-mined by a linear function of predictors In recent yearsthe machine learning society has proposed many otherregression methods such as deep learning In this paperwe will introduce six different machine learning regres-sion techniques and integrate them with the proposedstatistical model to perform wind power intervalforecasting

32 Machine Learning Regression Algorithms Employed in0is Paper

321 Linear Regression Linear regression is a traditionaland widely used statistical technique for regression It isselected as the baseline technique in this paper and will becompared with five nonlinear techniques Linear regres-sion models the relationship between the dependentvariable yi and the vector of predictors xi Linear re-gression assumes that the independent variable y is lin-early dependent on the predictors x plus a noise term εi)e model can be written as

yi β1xi1 + middot middot middot + βpxip + εi xiprime βT

+ εi i 1 2 n

(8)

where xiprimeβT is the inner product between vectors xi and β

And these n equations can be written in the vector form as

y βTX + ε (9)

where

y

y1y2⋮yn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

X

x1primex2prime⋮xnprime

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

βT

β1⋮βp

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

ε

ε1ε2⋮εn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(10)

ε is usually assumed to follow a normal distribution witha zero mean and variance σ2 We therefore have

ε sim N 0 σ21113872 1113873 (11)

and β is a p-dimensional parameter vector which specifieshow much each component of X contributes to the output y

[37]

322 Multilayer Perceptron Network A multilayer per-ceptron (MLP) network is a feedforward artificial neuralnetwork model that maps sets of input data onto a set ofappropriate outputs Based on the standard linear percep-tron MLP uses three or more layer nodes with nonlinearactivation functions An MLP network consists of a set ofsource nodes as the input layer one or more hidden layers ofcomputation nodes and an output layer of nodes

Figure 2 shows the signal flow process of a feedforwardneural network A MLP network has two stages a forwardpass and a backward pass )e forward pass includes pre-senting a sample input to the network and letting activationsflow until they reach the output layer [38 39]

323 Long Short-Term Memory (LSTM) Network-BasedDeep Learning Method )e concept of deep learning wasfirst proposed by Hinton et al in 2006 Deep learning is a

Machinelearning

Supervisedlearning

Unsupervisedlearning

Classification

Regression

Clustering

Correlation

Figure 1 Composition structure of machine learning

4 Complexity

branch of machine learning It is essentially a special arti-ficial neural network Deep learning utilizes a multilayernetwork structure and applies appropriate nonlineartransformation functions to each hidden node to achieve thepurpose of high-level abstraction of the data )e traditionalfeedforward artificial neural network usually contains onlyone hidden layer but there are many hidden layer structuresin deep learning )erefore deep learning adopts a trainingmechanism completely different from the traditional arti-ficial neural network in order to solve the problem of thedeep neural network in training [40]

LSTM is a time-cycle neural network which can effec-tively solve the gradient explosion and gradient disap-pearance problems compared with the traditional cycleneural network LSTM is composed of a set of cyclic subnetscalled memory blocks Each memory block is composed ofthe input gate forgetting gate and output gate Figure 3shows the LSTM structure [41]

In general the LSTM recursive neural network iscomposed of the following components input gate it has thecorresponding weight matrix wxi whi wci and bi forgettinggate ft has the corresponding weight matrix whf wcf andbf and output door ot with the corresponding weight matrixwxo who wco and bo )e function of the input gate is to

record the new information to the cell state selectively )efunction of the forget gate is to selectively forget the statusinformation in the cell the function of the output gate is toexport certain information from the cell )e detailedworkflow of LSTM is shown in the following [42]

it σ ωxixt + whihtminus1 + wcictminus1 + bi( 1113857

ft σ wxfxt + whfhtminus1 + wcfctminus1 + bf1113872 1113873

ot σ wxoxt + whohtminus1 + wcoctminus1 + bo( 1113857

ct ftctminus1 + ittanh wxcxt + whihtminus1 + whcctminus1 + bc( 1113857

(12)

where σ is the logistic sigmoid function with the output in [01] and tanh represents the hyperbolic tangent function withthe output in [minus1 1]

324 Lazy IBK Lazy IBK is one of the widely used lazylearning methods Lazy learning methods defer the deci-sion of how to assign the dependent variable until a newquery explanatory vector is inputted When the queryexplanatory vector is received a set of similar data recordsis retrieved from the available training dataset and is used

F

F

F

F

F

sum

sumsum

sumsum

sum

Input layer

Hiddenlayer

Outputlayer

Figure 2 Diagram of a multilayer perceptron network

Output

Input

Input

Input

Input

RecurrentRecurrent

Recurrent

Recurrent

Recurrent

Block output

Block input

LSTM block

Peepholes

Forget gate

f+

+

+

+

+

Cell c

i

z Input gate

Output gate

h

g

σ

σ

σ

y o

Figure 3 LSTM storage unit with door

Complexity 5

to assign the dependent variable to the new instance [43]In order to choose the similar data records lazy methodsemploy a distance measure that will give nearby datarecords higher relevance Lazy methods choose the k datarecords that are nearest to the query instance )e de-pendent variable of the new instance is determined basedon the k-nearest instances

Lazy learning algorithms have three basic steps

(i) Defer lazy learning algorithms store all trainingdata and defer processing until a new query is given

(ii) Reply a local learning approach developed byBottou and Vapnik in 1992 is a popular method todetermine the dependent variables for news queries[44] In the Bottou and Vapnik learning approachinstances are defined as points in the space and asimilarity function is defined on all pairs of theseinstances

(iii) Flush after solving a query the answer and anyintermediate results are discarded

325 Regression Tree A regression tree is one of the widelyused decision tree algorithms A decision tree is a data-miningtool designed to extract useful information from large datasetsand use the information to help decision-making processes Aregression tree consists of a set of nodes that can assign thevalue of the dependent variable to an explanatory vectorRegression tree constructs a tree style decision rule set anddivides the training data into the leaf nodes of the decisiontree according to the numerical or categorical values of ex-planatory variables )e regression rules of each leaf node arederived from a mathematical process that minimizes theregression errors of the leaf nodes [45]

326 Decision Table Similar to the regression tree decisiontable also determines the value of the dependent variablewith a set of decision rules [46] However the decision tablearranges decision rules as a table rather than a tree Adecision table usually consists of a number of parallel de-cision rules Similar to the regression tree the training datawill be divided into several groups each of which will berepresented by a decision rule For a given explanatoryvector (input) an appropriate decision rule will be firstselected based on the values of its explanatory variables )edependent variable for this input will be assigned as theaverage of the dependent variables of all training data vectorsin the corresponding group)e dependent variable can alsobe determined by performing linear regression on thecorresponding group of training data Empirical studiesshow that the decision table has a similar performance toregression trees

33 Converting Wind Speed to Wind Power An elementarymethod is used in this paper to convert the predicted windspeed to the predicted wind power output of a wind turbineor wind farm )e predicted wind speed is provided by oneof the six machine learning regression methods discussed

above )e wind speed is then input into the certified windturbine power curve and transformed into the wind power

)e Vestas V90-30MW wind turbine is selected for thecase studies in this paper Vestas V90-30MW is a pitchregulated upwind wind turbine with active yaw and a three-blade rotor It has a rotor diameter of 90m with a generatorrated at 30MW Vestas V90-30MW is widely used inAustralia wind power plants and has a proven highefficiency

)e typical power curve of Vestas V90-30MW 60Hz1067 dB(A) is shown in Figure 4 It can be clearly ob-served that the wind power output p(u) is proportional tou3 for small wind speed u Moreover the power curve issteep for medium wind speeds and flat for large windspeeds )e cut-in speed is 35 ms and the cut-out speedis 25ms [47]

34 Performance Evaluation Before proposing the casestudy results several criteria are introduced for performanceevaluation Given T historical wind power values pt1le tleT of a time series pt1113864 1113865 which are converted from Thistorical wind speed observations and the correspondingforecasted power values plowastt 1le tleT mean absolute per-centage error (MAPE) is defined as

MAPE 1T

1113944

T

t1

pt minus ptlowast1113868111386811138681113868

1113868111386811138681113868

pt

(13)

MAPE is a widely used criterion for time-series fore-casting It will also be employed to evaluate the proposedmethod in the case studies

Another two criteria are presented to evaluate intervalforecasting Given T wind power values pt 1 le t leT of atime series Py1113966 1113967 and the corresponding forecasted α-levelprediction intervals [lt ut] 1 le t leT the empirical confi-dence 1113954α [48] and the absolute coverage error (ACE) aredefined as

1113954α frequency pt isin lt ut1113858 1113859( 1113857

T

ACE |α minus αand|

(14)

where 1113954α is the number of observations which fall into theforecasted prediction interval (PI) divided by the samplesize It should be as close to α as possible

4 Case Studies

410e Setting of Case Studies In the experiments the windpower forecasting model has been evaluated using the windspeed data from the Devonport Airport Wind StationTasmania Australia )e data were provided by the Aus-tralian Bureau of Meteorology )e training and testing datahave the following four numerical features wind speedwind direction humidity and temperature )e trainingdata are from 1st February 2018 to 1st March 2018 while thetesting data are from 1st February 2019 to 1st March 2019

6 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

branch of machine learning It is essentially a special arti-ficial neural network Deep learning utilizes a multilayernetwork structure and applies appropriate nonlineartransformation functions to each hidden node to achieve thepurpose of high-level abstraction of the data )e traditionalfeedforward artificial neural network usually contains onlyone hidden layer but there are many hidden layer structuresin deep learning )erefore deep learning adopts a trainingmechanism completely different from the traditional arti-ficial neural network in order to solve the problem of thedeep neural network in training [40]

LSTM is a time-cycle neural network which can effec-tively solve the gradient explosion and gradient disap-pearance problems compared with the traditional cycleneural network LSTM is composed of a set of cyclic subnetscalled memory blocks Each memory block is composed ofthe input gate forgetting gate and output gate Figure 3shows the LSTM structure [41]

In general the LSTM recursive neural network iscomposed of the following components input gate it has thecorresponding weight matrix wxi whi wci and bi forgettinggate ft has the corresponding weight matrix whf wcf andbf and output door ot with the corresponding weight matrixwxo who wco and bo )e function of the input gate is to

record the new information to the cell state selectively )efunction of the forget gate is to selectively forget the statusinformation in the cell the function of the output gate is toexport certain information from the cell )e detailedworkflow of LSTM is shown in the following [42]

it σ ωxixt + whihtminus1 + wcictminus1 + bi( 1113857

ft σ wxfxt + whfhtminus1 + wcfctminus1 + bf1113872 1113873

ot σ wxoxt + whohtminus1 + wcoctminus1 + bo( 1113857

ct ftctminus1 + ittanh wxcxt + whihtminus1 + whcctminus1 + bc( 1113857

(12)

where σ is the logistic sigmoid function with the output in [01] and tanh represents the hyperbolic tangent function withthe output in [minus1 1]

324 Lazy IBK Lazy IBK is one of the widely used lazylearning methods Lazy learning methods defer the deci-sion of how to assign the dependent variable until a newquery explanatory vector is inputted When the queryexplanatory vector is received a set of similar data recordsis retrieved from the available training dataset and is used

F

F

F

F

F

sum

sumsum

sumsum

sum

Input layer

Hiddenlayer

Outputlayer

Figure 2 Diagram of a multilayer perceptron network

Output

Input

Input

Input

Input

RecurrentRecurrent

Recurrent

Recurrent

Recurrent

Block output

Block input

LSTM block

Peepholes

Forget gate

f+

+

+

+

+

Cell c

i

z Input gate

Output gate

h

g

σ

σ

σ

y o

Figure 3 LSTM storage unit with door

Complexity 5

to assign the dependent variable to the new instance [43]In order to choose the similar data records lazy methodsemploy a distance measure that will give nearby datarecords higher relevance Lazy methods choose the k datarecords that are nearest to the query instance )e de-pendent variable of the new instance is determined basedon the k-nearest instances

Lazy learning algorithms have three basic steps

(i) Defer lazy learning algorithms store all trainingdata and defer processing until a new query is given

(ii) Reply a local learning approach developed byBottou and Vapnik in 1992 is a popular method todetermine the dependent variables for news queries[44] In the Bottou and Vapnik learning approachinstances are defined as points in the space and asimilarity function is defined on all pairs of theseinstances

(iii) Flush after solving a query the answer and anyintermediate results are discarded

325 Regression Tree A regression tree is one of the widelyused decision tree algorithms A decision tree is a data-miningtool designed to extract useful information from large datasetsand use the information to help decision-making processes Aregression tree consists of a set of nodes that can assign thevalue of the dependent variable to an explanatory vectorRegression tree constructs a tree style decision rule set anddivides the training data into the leaf nodes of the decisiontree according to the numerical or categorical values of ex-planatory variables )e regression rules of each leaf node arederived from a mathematical process that minimizes theregression errors of the leaf nodes [45]

326 Decision Table Similar to the regression tree decisiontable also determines the value of the dependent variablewith a set of decision rules [46] However the decision tablearranges decision rules as a table rather than a tree Adecision table usually consists of a number of parallel de-cision rules Similar to the regression tree the training datawill be divided into several groups each of which will berepresented by a decision rule For a given explanatoryvector (input) an appropriate decision rule will be firstselected based on the values of its explanatory variables )edependent variable for this input will be assigned as theaverage of the dependent variables of all training data vectorsin the corresponding group)e dependent variable can alsobe determined by performing linear regression on thecorresponding group of training data Empirical studiesshow that the decision table has a similar performance toregression trees

33 Converting Wind Speed to Wind Power An elementarymethod is used in this paper to convert the predicted windspeed to the predicted wind power output of a wind turbineor wind farm )e predicted wind speed is provided by oneof the six machine learning regression methods discussed

above )e wind speed is then input into the certified windturbine power curve and transformed into the wind power

)e Vestas V90-30MW wind turbine is selected for thecase studies in this paper Vestas V90-30MW is a pitchregulated upwind wind turbine with active yaw and a three-blade rotor It has a rotor diameter of 90m with a generatorrated at 30MW Vestas V90-30MW is widely used inAustralia wind power plants and has a proven highefficiency

)e typical power curve of Vestas V90-30MW 60Hz1067 dB(A) is shown in Figure 4 It can be clearly ob-served that the wind power output p(u) is proportional tou3 for small wind speed u Moreover the power curve issteep for medium wind speeds and flat for large windspeeds )e cut-in speed is 35 ms and the cut-out speedis 25ms [47]

34 Performance Evaluation Before proposing the casestudy results several criteria are introduced for performanceevaluation Given T historical wind power values pt1le tleT of a time series pt1113864 1113865 which are converted from Thistorical wind speed observations and the correspondingforecasted power values plowastt 1le tleT mean absolute per-centage error (MAPE) is defined as

MAPE 1T

1113944

T

t1

pt minus ptlowast1113868111386811138681113868

1113868111386811138681113868

pt

(13)

MAPE is a widely used criterion for time-series fore-casting It will also be employed to evaluate the proposedmethod in the case studies

Another two criteria are presented to evaluate intervalforecasting Given T wind power values pt 1 le t leT of atime series Py1113966 1113967 and the corresponding forecasted α-levelprediction intervals [lt ut] 1 le t leT the empirical confi-dence 1113954α [48] and the absolute coverage error (ACE) aredefined as

1113954α frequency pt isin lt ut1113858 1113859( 1113857

T

ACE |α minus αand|

(14)

where 1113954α is the number of observations which fall into theforecasted prediction interval (PI) divided by the samplesize It should be as close to α as possible

4 Case Studies

410e Setting of Case Studies In the experiments the windpower forecasting model has been evaluated using the windspeed data from the Devonport Airport Wind StationTasmania Australia )e data were provided by the Aus-tralian Bureau of Meteorology )e training and testing datahave the following four numerical features wind speedwind direction humidity and temperature )e trainingdata are from 1st February 2018 to 1st March 2018 while thetesting data are from 1st February 2019 to 1st March 2019

6 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

to assign the dependent variable to the new instance [43]In order to choose the similar data records lazy methodsemploy a distance measure that will give nearby datarecords higher relevance Lazy methods choose the k datarecords that are nearest to the query instance )e de-pendent variable of the new instance is determined basedon the k-nearest instances

Lazy learning algorithms have three basic steps

(i) Defer lazy learning algorithms store all trainingdata and defer processing until a new query is given

(ii) Reply a local learning approach developed byBottou and Vapnik in 1992 is a popular method todetermine the dependent variables for news queries[44] In the Bottou and Vapnik learning approachinstances are defined as points in the space and asimilarity function is defined on all pairs of theseinstances

(iii) Flush after solving a query the answer and anyintermediate results are discarded

325 Regression Tree A regression tree is one of the widelyused decision tree algorithms A decision tree is a data-miningtool designed to extract useful information from large datasetsand use the information to help decision-making processes Aregression tree consists of a set of nodes that can assign thevalue of the dependent variable to an explanatory vectorRegression tree constructs a tree style decision rule set anddivides the training data into the leaf nodes of the decisiontree according to the numerical or categorical values of ex-planatory variables )e regression rules of each leaf node arederived from a mathematical process that minimizes theregression errors of the leaf nodes [45]

326 Decision Table Similar to the regression tree decisiontable also determines the value of the dependent variablewith a set of decision rules [46] However the decision tablearranges decision rules as a table rather than a tree Adecision table usually consists of a number of parallel de-cision rules Similar to the regression tree the training datawill be divided into several groups each of which will berepresented by a decision rule For a given explanatoryvector (input) an appropriate decision rule will be firstselected based on the values of its explanatory variables )edependent variable for this input will be assigned as theaverage of the dependent variables of all training data vectorsin the corresponding group)e dependent variable can alsobe determined by performing linear regression on thecorresponding group of training data Empirical studiesshow that the decision table has a similar performance toregression trees

33 Converting Wind Speed to Wind Power An elementarymethod is used in this paper to convert the predicted windspeed to the predicted wind power output of a wind turbineor wind farm )e predicted wind speed is provided by oneof the six machine learning regression methods discussed

above )e wind speed is then input into the certified windturbine power curve and transformed into the wind power

)e Vestas V90-30MW wind turbine is selected for thecase studies in this paper Vestas V90-30MW is a pitchregulated upwind wind turbine with active yaw and a three-blade rotor It has a rotor diameter of 90m with a generatorrated at 30MW Vestas V90-30MW is widely used inAustralia wind power plants and has a proven highefficiency

)e typical power curve of Vestas V90-30MW 60Hz1067 dB(A) is shown in Figure 4 It can be clearly ob-served that the wind power output p(u) is proportional tou3 for small wind speed u Moreover the power curve issteep for medium wind speeds and flat for large windspeeds )e cut-in speed is 35 ms and the cut-out speedis 25ms [47]

34 Performance Evaluation Before proposing the casestudy results several criteria are introduced for performanceevaluation Given T historical wind power values pt1le tleT of a time series pt1113864 1113865 which are converted from Thistorical wind speed observations and the correspondingforecasted power values plowastt 1le tleT mean absolute per-centage error (MAPE) is defined as

MAPE 1T

1113944

T

t1

pt minus ptlowast1113868111386811138681113868

1113868111386811138681113868

pt

(13)

MAPE is a widely used criterion for time-series fore-casting It will also be employed to evaluate the proposedmethod in the case studies

Another two criteria are presented to evaluate intervalforecasting Given T wind power values pt 1 le t leT of atime series Py1113966 1113967 and the corresponding forecasted α-levelprediction intervals [lt ut] 1 le t leT the empirical confi-dence 1113954α [48] and the absolute coverage error (ACE) aredefined as

1113954α frequency pt isin lt ut1113858 1113859( 1113857

T

ACE |α minus αand|

(14)

where 1113954α is the number of observations which fall into theforecasted prediction interval (PI) divided by the samplesize It should be as close to α as possible

4 Case Studies

410e Setting of Case Studies In the experiments the windpower forecasting model has been evaluated using the windspeed data from the Devonport Airport Wind StationTasmania Australia )e data were provided by the Aus-tralian Bureau of Meteorology )e training and testing datahave the following four numerical features wind speedwind direction humidity and temperature )e trainingdata are from 1st February 2018 to 1st March 2018 while thetesting data are from 1st February 2019 to 1st March 2019

6 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

To empirically prove the validity of our model we willfirst verify that the wind speed data exhibit time-changingdistribution effect by performing the Lagrange multipliertest [49 50] )e results of the LM test with 95 significancelevel on the data from 1st February 2019 to 1st March 2019are given in Table 1

As illustrated in Table 1 setting the significance level as005 P value of the LM test is zero in all six cases Moreoverthe LM statistics are significantly greater than the criticalvalue of the LM test in all occasions )ese two facts stronglyindicate that the wind speed data have strong effect of time-changing distribution In the test an order of 10 means thatthe variance σ2t is correlated with its lagged values up to atleast σ2tminus10 In other words the wind speed at 10 time unitsbefore time t can still influence the uncertainty of the windspeed at time t

42 Results of Wind Speed Forecasting Wind speed fore-casting is the first step of wind power forecasting Six re-gression methods are first employed to perform one-hour-ahead wind speed forecasting in this paper )e perfor-mances of six algorithms are shown in Table 2

As illustrated in Table 2 the MAPEs of LSTM and lazyIBK are smaller than other methodsMoreover theMAPE ofLSTM is under 10 which is sufficiently good consideringthe very high volatility of wind speed )e results indicatethat these two nonlinear machine learning regressionmethods perform well in wind speed forecasting

)e forecasting errors of three methods are graphicallyshown in Figure 5 In Figure 5 the visual inspection suggeststhat the forecasting errors of the three algorithms have anormal distribution It is very important to know the type ofthe error distribution to ensure that the proposed statistical

model has a valid assumption To empirically prove that thewind speed forecasting errors are normally distributed theforecasting errors of all six methods are checked for nor-mality by performing the KolmogorovndashSmirnov normalitytest )e test results also show that all the six forecastingmethods have normally distributed errors )ese resultsagain verify the validity of the assumptions of our model

43 Results of Wind Power Interval Forecasting )e windspeed forecasts given by the six machine learning regressionalgorithms are then converted into wind power forecasts asdiscussed in Section 3 Similarly mean absolute percentageerror (MAPE) is used to evaluate the performances of dif-ferent methods From Table 3 it is observed that for windpower forecasting the MAPE of LSTM is still lower thanother five algorithms

Based on Tables 2 and 3 the LSTMmethod is selected asthe wind speed point forecasting method (the estimator off(bull)) )e procedure discussed in Section 2 is thenemployed to give the prediction intervals of wind power Wewill employ all six regression methods to estimate g(bull) andh(bull) and then compare their performances in wind powerinterval forecasting

0 3 4 5 6 7 8 9 10 11 12Wind speed (ms)

13 14 15 16 17 18 19 20 21 22 23 24 250

500

1000

1500

2000

2500

3000

3500

Pow

er (k

W)

Power curve V90-30MW air density 1225

Figure 4 Power curve for Vestas V90-30MW 60Hz 1067

Table 1 )e results of the Lagrange multiplier test

Dataset Order P value LM statistics Critical valueFeb 2008 to Mar 2008 1 0 19136 38415Feb 2008 to Mar 2008 5 0 19646 110705Feb 2008 to Mar 2008 10 0 19693 18307Feb 2009 to Mar 2009 1 0 28989 38415Feb 2009 to Mar 2009 5 0 30572 110705Feb 2009 to Mar 2009 10 0 3077 18307

Table 2 Prediction errors of different methods

Regression methods MAPELinear regression 1281Multilayer perceptron 1232LSTM 810Lazy IBK 1046Decision table 1510Regression tree 1126

Complexity 7

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

In Table 4 for 95 and 99 confidence levels the ACEsof different regression methods are presented As seen inTable 4 the ACEs of five nonlinear methods are similarregardless of the confidence level On the contrary all thefive nonlinear regression algorithms outperform linear re-gression )is is a clear proof that strong nonlinearity existsin the wind power data

)e 95 level and 99 level prediction intervals givenby different methods are illustrated in Figures 6 and 7 Asillustrated the prediction intervals given by all the fivenonlinear machine learning algorithms perfectly containthe true values of wind power )ese results clearly provethe effectiveness of the proposed statistical modelMoreover the results also show that nonlinear machinelearning regression methods are suitable candidates inwind power interval forecasting Compared with othermachine learning methods LSTM performed best in windpower interval forecasting LSTM is a deep learning neuralnetwork algorithm )e improvement of the structurelevel of the deep learning neural network will make theinformation abstraction ability of the deep learning modelstronger )erefore its ability to extract and learn com-plex information from large amounts of data is alsostronger )e accuracy of wind power interval forecastingwill be improved accordingly Multilayer perceptron(MLP) can be categorized as the feedforward neuralnetwork In the traditional feedforward neural networksuch as MLP the input layer the hidden layer and theoutput layer in the network are fully connected but thenodes within each layer are disconnected )is structureresults in the inability of the traditional feedforward

neural network to deal with the problem of correlationbetween inputs Compared with the feedforward neuralnetwork circular neural network introduces directionalcirculation At this point the nodes between hidden layersin the network are no longer disconnected but connectedAnd the input of the hidden layer includes not only theoutput of the input layer but also the output of the hidden

Table 3 )e MAPE of different methods for wind powerforecasting

Regression methods MAPE ()Linear regression 3762Multilayer perceptron 4248LSTM 1924Lazy IBK 2809Decision table 3558Regression tree 3005

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(a)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(b)

Dist

ribut

ion

of er

rors

()

0

200

400

600

800

1000

1200

1400

ndash10 0 10 20ndash20Errors (ms)

(c)

Figure 5 Distributions of the errors of (a) linear regression (b) LSTM and (c) regression tree

Table 4 Performances of different methods on wind power in-terval forecasting

Regression methods ACE for 95confidence ACE for 99 confidence

Linear regression 537 334Multilayer perceptron 319 039LSTM 302 016Lazy IBK 316 038Decision table 316 043Regression tree 32 039

8 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of linear regression

(a)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of multilayer perceptron

(b)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of LSTM

(c)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of lazy IBK

(d)

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of decision table

(e)

Observed wind powerLower bound of PIUpper bound of PI

480 500 520 540 560 580 600460Time (5 mins)

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

350095 PI of regression tree

(f )

Figure 6 95 level prediction intervals forecasted by six machine learning regression methods

Complexity 9

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

Win

d po

wer

(MW

)99 PI of linear regression

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

0

500

1000

1500

2000

2500

3000

3500

(a)

99 PI of multilayer perceptron

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(b)

99 PI of LSTM

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(c)

99 PI of Lazy IBK

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(d)

99 PI of decision table

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(e)

99 PI of regression tree

480 500 520 540 560 580 600460Time (5 mins)

Observed wind powerLower bound of PIUpper bound of PI

Win

d po

wer

(MW

)

0

500

1000

1500

2000

2500

3000

3500

(f )

Figure 7 99 level prediction intervals forecasted by six machine learning regression methods

10 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

layer at the last moment As a conclusion LSTM canperform better than MLP

5 Conclusion

)is research work develops a novel comprehensive inte-grated statistical machine learning strategy for wind powerforecasting in Australian wind farm including explorationof the statistical characteristics of the data by statistical toolsand developing the forecasting model by different statisticalmachine learning methods Accurate wind power intervalforecasting is essential for efficient planning and operation ofpower systems Wind energy is characterised by its non-linearity and intermittency which pose significant chal-lenges for wind power forecasting Traditional linear time-series models cannot appropriately handle these challengesand therefore cannot achieve satisfactory performances Inthis paper we propose a machine learning-based statisticalapproach which can handle nonlinear time series with time-changing distributions thus is suitable for wind power in-terval forecasting

Compared with other relevant references this researchwork shows that classical regression techniques are notsuitable for complicated applications such as wind powerinterval forecasting It is inappropriate simply to use linearassumptions for these problems In addition other researchworks only using complicated machine learning approachesfailed to balance the important information of the historicaldata Experimental results show that LSTM is the mostsuited candidate for wind power forecasting Moreover theeffectiveness and accuracy of the proposed model in windpower interval forecasting are also proven with the casestudies

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] L Chen Z Li and Y Zhang ldquoMultiperiod-ahead wind speedforecasting using deep neural architecture and ensemblelearningrdquo Mathematical Problems in Engineering vol 2019Article ID 9240317 14 pages 2019

[2] Q Wang Y Lei and H Cao ldquoWind power prediction basedon nonlinear partial least squarerdquo Mathematical Problems inEngineering vol 2019 Article ID 6829274 9 pages 2019

[3] S Wang J Na and Y Xing ldquoAdaptive optimal parameterestimation and control of servo mechanisms theory andexperimentrdquo IEEE Transactions on Industrial ElectronicsEarly Access p 1 2020

[4] S Wang and J Na ldquoParameter estimation and adaptivecontrol for servo mechanisms with friction compensationrdquoIEEE Transactions on Industrial Informatics Early Accessvol 16 2020

[5] S Wang L Tao Q Chen J Na and X Ren ldquoUSDE-basedsliding mode control for servo mechanisms with unknownsystem dynamicsrdquo IEEEASME Transactions onMechatronicsvol 25 no 2 pp 1056ndash1066 2020

[6] M Santhosh and C Venkaiah ldquoCurrent advances and ap-proaches in wind speed and wind power forecasting forimproved renewable energy integration a reviewrdquo Engi-neering Reports vol 2 no 6 pp 1ndash20 2020

[7] G Gregor and K George Renewable Energy Forecasting FromModels to Applications Elsevier Amsterdam Netherlands2017

[8] M Lange and U Focken Physical Approach to Short-TermWind Power Prediction Springer Berlin Germany 2006

[9] Z Zhang Y Chen X Liu et al ldquoTwo-stage robust security-constrained unit commitment model considering time au-tocorrelation of windload prediction error and outagecontingency probability of unitsrdquo IEEE Access vol 7pp 2169ndash3536 2019

[10] Q Hu S Zhang M Yu and Z Xie ldquoShort-term wind speedor power forecasting with Heteroscedastic support vectorregressionrdquo IEEE Transactions on Sustainable Energy vol 7no 1 pp 241ndash249 2016

[11] C Wan J Lin J Wang et al ldquoDirect quantile regression fornonparametric probabilistic forecasting of wind power gen-erationrdquo IEEE Transactions on Power Systems vol 32 no 4pp 2767ndash2778 2016

[12] Y Ren P N Suganthan and N Srikanth ldquoA novel empiricalmode decomposition with support vector regression for windspeed forecastingrdquo IEEE Transactions on Neural Networks andLearning Systems vol 27 no 8 pp 1793ndash1798 2016

[13] J Yan H Zhang Y Liu S Han L Li and Z Lu ldquoForecastingthe high penetration of wind power on multiple scales usingmulti-to-multi mappingrdquo IEEE Transactions on Power Sys-tems vol 33 no 3 pp 3276ndash3284 2018

[14] Z Wang J Zhang Y Zhang C Huang and L Wang ldquoShort-term wind speed forecasting based on information ofneighboring wind farmsrdquo IEEE Access vol 8 pp 16760ndash16770 2020

[15] L Zhang Y Dong and J Wang ldquoWind speed forecastingusing a two-stage forecasting system with an error correctingand nonlinear ensemble strategyrdquo IEEE Access vol 7pp 176000ndash176023 2019

[16] Y-K Wu P-E Su T-Y Wu J-S Hong and M Y HassanldquoProbabilistic wind-power forecasting using weather en-semble modelsrdquo IEEE Transactions on Industry Applicationsvol 54 no 6 pp 5609ndash5620 2018

[17] F Ge Y Ju Z Qi et al ldquoParameter estimation of a Gaussianmixture model for wind power forecasting error by RiemannL-BFGS optimizationrdquo IEEE Transactions on Power Systemsvol 22 no 1 pp 258ndash265 2007

[18] C Wang Q Teng X Liu et al ldquoOptimal sizing of energystorage considering the spatial-temporal correlation of windpower forecast errorsrdquo IET Renewable Power Generationvol 13 no 4 pp 530ndash538 2019

[19] J Na B Wang G Li S Zhan and W He ldquoNonlinearconstrained optimal control of wave energy converters withadaptive dynamic programmingrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 10 pp 7904ndash7915 2019

[20] J Na Y Huang X Wu et al ldquoAdaptive finite-time fuzzycontrol of nonlinear active suspension systems with inputdelayrdquo IEEE Transactions on Cybernetics vol 50 no 6pp 2639ndash2650 2019

[21] J Na A Chen Y Huang et al ldquoAir-fuel ratio control ofinternal combustion engines with unknown dynamics

Complexity 11

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity

estimator theory and experimentsrdquo IEEE Transactions onControl Systems Technology vol 8 p 8 2019

[22] C Wu Y Zhao and M Sun ldquoEnhancing low-speed sen-sorless control of PMSM using phase voltage measurementsand online multiple parameter identificationrdquo IEEE Trans-actions on Power Electronics vol 35 no 10 pp 10700ndash107102020

[23] M Sun ldquoTwo-phase attractors for finite-duration consensusof multiagent systemsrdquo IEEE Transactions on Systems Manand Cybernetics Systems vol 50 no 5 pp 1757ndash1765 2020

[24] Q Chen H Shi and M Sun ldquoEcho state network basedbackstepping adaptive iterative learning control for strict-feedback systems an error-tracking approachrdquo IEEE Trans-actions on Cybernetics Early Access vol 50 no 7 Article ID2931877 2019

[25] Q Chen S Xie M Sun and X He ldquoAdaptive nonsingularfixed-time attitude stabilization of uncertain spacecraftrdquo IEEETransactions on Aerospace and Electronic Systems vol 54no 6 pp 2937ndash2950 2018

[26] M Tao Q Chen X He et al ldquoAdaptive fixed-time fault-tolerant control for rigid spacecraft using a double powerreaching lawrdquo International Journal of Robust and NonlinearControl vol 29 no 12 pp 4022ndash4040 2019

[27] Q Chen X Ren J Na et al ldquoAdaptive robust finite-timeneural control of uncertain PMSM servo system with non-linear dead zonerdquo Neural Computing and Applicationsvol 28 no 12 pp 3725ndash3736 2017

[28] Q Zheng L Shi J Na X Ren and Y Nan ldquoAdaptive echostate network control for a class of pure-feedback systems withinput and output constraintsrdquo Neurocomputing vol 275no 1 pp 1370ndash1382 2018

[29] Q Chen X Yu M Sun et al ldquoAdaptive repetitive learningcontrol of PMSM servo systems with bounded nonparametricuncertainties theory and experimentsrdquo IEEE Transactions onIndustrial Electronics 2020

[30] D Tung and T Le ldquoA statistical analysis of short-term windpower forecasting error distributionrdquo International Journal ofApplied Engineering Research vol 12 no 10 pp 2306ndash23112017

[31] L Wang R Yan F Bai et al ldquoA distributed inter-phasecoordination algorithm for voltage control with unbalancedPV integration in LV systemsrdquo IEEE Transactions on Sus-tainable Energy Early Access Article ID 2970214 2020

[32] L Wang R Yan and T Saha ldquoVoltage regulation challengeswith unbalanced PV integration in low voltage distributionsystems and the corresponding solutionrdquo Applied Energyvol 256 no 1 Article ID 113927 2019

[33] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[34] J Kober J A Bagnell and J Peters ldquoReinforcement learningin robotics a surveyrdquo 0e International Journal of RoboticsResearch vol 32 no 11 pp 1238ndash1274 2013

[35] S J Pan and Q Yang ldquoA survey on transfer learningrdquo IEEETransactions on Knowledge and Data Engineering vol 22no 10 pp 1345ndash1359 2010

[36] R )omas ldquoModern Regression Methodsrdquo John Wiley amp SonsHoboken NJ USA 2009

[37] R Maronna R Martin V Yohai and M S-Barrera RobustStatistics 0eory and Methods Wiley New York NY USA2019

[38] J Keller D Liu and D Fogel ldquoMultilayer Neural Networksand Backpropagation rdquo Wiley Hoboken NJ USA 2016

[39] E Alpaydin ldquoIntroduction to Machine Learning rdquo )e MITPress Cambridge MA USA 2014

[40] E Alpaydin ldquoMachine Learning0e New AIrdquo)eMIT PressCambridge MA USA 2016

[41] S Kok andM Simsek ldquoADeep LearningModel for Air QualityPrediction in Smart Citiesrdquo pp 1983ndash1990 IEEE Internationalconference on Big Data Boston MS USA 2017

[42] P Zhou W Shi and J Tian ldquoAttention-based bidirectionallong short-term memory networks for relation classificationrdquoin Proceedings of the 54th Annual Meeting of the Associationfor Computational Linguistics pp 207ndash212 Berlin Germany2016

[43] Z Hou S Liu and T Tian ldquoLazy-learning-based data-drivenmodel-free adaptive predictive control for a class of discrete-time nonlinear systemsrdquo IEEE Transactions on Neural Net-works and Learning Systems vol 28 no 8 pp 1914ndash19282017

[44] L Merschmann and A Plastino ldquoA lazy data mining ap-proach for protein classificationrdquo IEEE Transactions onNanoBioscience vol 6 no 1 pp 36ndash42 2007

[45] C Zheng V Malbasa andM Kezunovic ldquoRegression tree forstability margin prediction using synchrophasor measure-mentsrdquo IEEE Transactions on Power Systems vol 28 no 2pp 1978ndash1987 2013

[46] M Azad and M Moshkov ldquoMinimization of decision treedepth for multi-label decision tablesrdquo in Proceedings of the2014 IEEE International Conference on Granular Compu-ting(GrC) pp 368ndash377 Noboribetsu Japan October 2014

[47] VESTAS Wind Power Solution Company Webpage httpwwwvestascomAdminPublicDWSDownloadaspxFile

2FFiles2FFiler2FEN2FBrochures2FVestas_V_90-3MW-11-2009-ENpdf

[48] E Mazloumi G Currie and G Rose ldquoStatistical confidenceestimation measures for artificial neural networks applicationin bus travel time predictionrdquo in proceedings of the 2010Transportation Research Board 89th Annual Meeting pp 1ndash13 Washington DC USA 2010

[49] M Wang K Ngan and H Li ldquoLow-delay arte control forconsistent quality using distortion-based lagrange multiplierrdquoIEEE Transactions on Image Processing vol 25 no 7pp 2943ndash2955 2016

[50] Y Lin and A Abur ldquoA new framework for detection andidentification of network parameter errorsrdquo IEEE Transac-tions on Smart Grid vol 9 no 3 pp 1698ndash1706 2018

12 Complexity