research article short-term power generation...

Research ArticleShort-Term Power Generation Energy Forecasting Model forSmall Hydropower Stations Using GA-SVM

Gang Li1 Yongjun Sun1 Yong He1 Xiufeng Li2 and Qiyu Tu2

1 Institute of Hydropower and Hydroinformatics Dalian University of Technology Dalian 116024 China2 Yunnan Power Dispatching Control Center Kunming 650011 China

Correspondence should be addressed to Gang Li gleedluteducn

Received 12 May 2014 Revised 26 June 2014 Accepted 27 June 2014 Published 17 July 2014

Academic Editor Bin Yu

Copyright copy 2014 Gang Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate and reliable power generation energy forecasting of small hydropower (SHP) is essential for hydropower managementand scheduling Due to nonperson supervision for a long time there are not enough historical power generation records so theforecasting model is difficult to be developed In this paper the support vector machine (SVM) is chosen as a method for short-term power generation energy prediction because it shows many unique advantages in solving small sample nonlinear and highdimensional pattern recognition In order to identify appropriate parameters of the SVM prediction model the genetic algorithm(GA) is performed The GA-SVM prediction model is tested using the short-term observations of power generation energy in theYunlong County and Maguan County in Yunnan province Through the comparison of its performance with those of the ARMAmodel it is demonstrated that GA-SVM model is a very potential candidate for the prediction of short-term power generationenergy of SHP

1 Introduction

Small hydropower (SHP) is a kind of world recognized andconcerned renewable clean energies It widely attracts atten-tion in the whole world as its great significance for mediumand small rivers management strengthening the rural waterconservancy infrastructure construction meets rural energydemand improves the rural energy structure reduces thepollution of the environment responds to climate changepromotes the development of the local economy [1ndash5] and soforth In the past two decades the installed capacity of SHPincreases more than 25GW per year because it has manyadvantages such as small scale mature technology shortconstruction time less investment and near-zero pollutionemissions and generally causes no immigration or landsubmersion

Up to the end of 2012 the installed capacity of SHPin China had exceeded 65GW and annual generation over200 TWh which take about 30 of hydropower installedcapacity and power generation respectively and both rankfirst in the world [6] Different from other countries in theworld SHP plays an important role in Chinarsquos rural electricity

supply as it is widely distributed inmore than 1600mountain-ous counties in China approximately half of the territoriesone-third of counties and a quarter of the total populationare dependent upon SHP for rural electricity supply [7 8]However with the fast development of SHP and large-scaleaccess to power grid its influence on the power grid is becom-ing more and more obvious especially in southwest Chinawhich has rich SHP resource SHP has become amajor factorthat affects the safe operation and development of power gridMost of SHP plants are runoff river plant without regulationability so its power output is obviously intermittent andseasonal because of the uncertainty of rainfall In particularin flood season the rainfall is very big and focused so thatSHP plants may generate much more power output thanother periods At the same time the big hydropower plantalso generated even more power output That can probablylead to water resource wasted and electricity dumped underthe condition of current transmission capacity Therefore itis necessary to master short-term power generation energy(STPGE) of SHP in order to avoid the above situation throughusing regulation ability of big hydropower plants

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 381387 9 pageshttpdxdoiorg1011552014381387

2 Mathematical Problems in Engineering

However SHP plants are generally in the small remoteriver basin with shortage of hydrologic station and themanagement is weak due to nonperson supervision for along time so it is very difficult for forecasting STPGE ofSHP because of lack of necessary runoff data At presenta lot of research activities in short-term forecasting mod-els of hydropower stations have been carried out whichfocus on the forecasting of inflow in reservoirs [9ndash12] ofstream flow [13ndash15] or of precipitation [16] But there arefew research works referring to forecasting the STPGE forSHP stations [17] Since the parameters will greatly affectthe performance of SVM some literatures attempted todetermine the proper parameter values for their problems[18 19] However for large scale or real-time feature practiceapplication the considerable search time cannot be acceptedHeuristic algorithms have been successfully used in manycomplex problems [20ndash22]

This paper presents a novel short-term forecasting model(named GA-SVM) for power generation energy of SHPstations In this study support vector machine (SVM) wasused to identify power generation energy based on structuralrisk minimization principle [18 23ndash26] and its parametersare optimized by genetic algorithm (GA) to get the optimalmodel structure [27 28] Considering dynamically puttinginto operation of SHP plant or hydrounit the installed capac-ity utilization hours of SHP are selected as input and outputvalue of the proposed forecastingmodel since the power gen-eration energy of SHP is not the same at different times Thismethod is applied to forecast STPGE of the small hydropowerstations in Yunlong County and Maguan County Yunnanprovince China Compared with the conventional methodthe proposedGA-SVMmodel exhibits superior performancedemonstrating GA-SVMrsquos effectiveness as an approach toforecast STPGE of SHP

The paper is organized as follows In the next sectionldquoBrief Introduction to SVM and GArdquo SVM and GA algo-rithms are briefly introduced Then the proposed GA-SVMforecasting method is described in the following section Inthe next section this method is applied to Yunnan provinceand the results are compared with those of conventionalmethod The final section concludes the paper

2 Brief Introduction to SVM and GA

21 Support Vector Machines (SVM) The SVM developedby Vapnik [29] is based on statistical learning theory andimplements the structural risk minimization principle ratherthan the empirical risk minimization principle implementedby most traditional ANN models It seeks to minimize anupper bound to the generalization error instead of minimiz-ing the training error and can achieve an optimum networkstructure Many researchers have used SVM to implementforecasting model in every field which mainly focuses onforecasting rainfall Dibike et al demonstrated the capabilityof the SVM in hydrological prediction such as modelingthe rainfall runoff process [30] There are other scholarswho have used the SVM for rainfall forecast ranging from1-2 days ahead to 1 h ahead [31] In this paper the SVM

model is used to forecast STPGE of SHP And the radialbasis function (RBF) is employed as kernel function whichhas shown to simplify the use of a mapping because theRBF is more compact in comparison with other kernels andis able to shorten the computational training process andimprove the generalization performance [30]TheRBF is alsocomputationally simpler than a polynomial kernel which hasmore parameters [32] The equation for RBF is of the form

119896 (119909119894 119909) = exp

minus1003817100381710038171003817119909 minus 11990911989410038171003817100381710038172

21205902 (1)

22 Genetic Algorithm (GA) GA is a global optimal algo-rithm based on ldquosurvival of the fittestrdquo in Darwinrsquos theoryof evolution and provides an efficient and robust optimizedsearching method in complex space This is an excellentsearch algorithm adapted to the global probability GA oper-ates iteratively on a population of structures each of whichrepresents a candidate solution to the problem encoded asa string of symbols (chromosome) and uses randomizedtechnical guidance to effectively search a coded parameterspace GA makes use of coding technology to transform thesolved space of problem into chromosome space and alsoconvert the decisive variable into a certain structure of indi-vidual chromosomes During the iteration of the algorithmaccording to the rules set by the fitness function these groupsmade up of individuals generated next generation throughselection crossover and mutation Fitness factor which isbeneficial to the population will be inherited while factorsthat reduce fitness will be eliminated with the operationof mutation and crossover in iterations After continuousevolutions the optimal individuals survive which can beapproximate optimal solution of the problem

3 Short-Term Forecasting Model for PowerGeneration Energy Using GA-SVM

31 Forecasting Object Generally the daily power generationenergy is directly selected as forecasting object for STPGEof SHP But considering dynamically putting into operationsmall hydropower plant or hydrounit in some region thereis a difference of installed capacity of SHP between oneday and another day Since the power output of SHP plantis almost close to installed capacity in flood season thepower generation energy is also very different due to theincrease in installed capacity of SHP The model predictionperformance will be affected if power generation energy ofSHP is only used as input and output values of the modelTherefore the installed capacity utilization hour representspower generation energy of SHP in region That could notonly accurately reflect the characteristics of small hydropowerplant without regulation ability but also alleviate short-termfluctuations in power generation curveThe installed capacityutilization hour was

Hour119889=

Energy119889

Capacity119889

(2)

Mathematical Problems in Engineering 3

Input population (t)

mutation

Calculate the fitness

Initialize the population size ofGA and specify the termination

conditions of evolution

t = t + 1

N

Y

Satisfy the termination condition

Output the optimum parameters

Begin

Normalize data

Trainingdata

Testingdata

Build SVM model

Input the testing data

Output the forecast result

Evaluate model performanceby accuracy rate

End

Optimize the parameters of SVM model by GA

Initialize the range of

generate initial population

Divide training data and train

Forecast by optimized SVM modeland evaluate the model performance

parameters (C 120590 and 120576) and

parameters (C 120590 and 120576)

Selection crossover and

Antinormalize data

(C 120590 and 120576)

Figure 1 The flow chart of optimizing SVM by GA

where Hour119889is installed capacity utilization hour in region at

day 119889 Energy119889is power generation energy in region at day 119889

Capacity119889is the install capacity of all small hydropower plants

in region at day 119889

32 Short-Term ForecastingModel of SHPUsing GA-SVM Toapply SVMmodel to forecast STPGE of SHP plants in regionwe need to know the three vital parameters RBF kernels119862 120576 and 120590 which respectively denote positive constantinsensitive loss function andGaussian noise level of standarddeviation Different values of 119862 120576 and 120590 can lead to largedifferences in the forecasting result The parameters 119862 120576and 120590 control the complicacy of the model and error of theapproximation thus reflecting the difficulty of the trainingand the forecasting accuracy In order to improve the fore-casting accuracy we should confirm the three parameters Inrecent years several methods such as the genetic algorithm[33 34] and shuffled complex evolution algorithm [35ndash37]have been developed for model parameter calibration In thispaper GA is used to optimize parameters of SVM kernelfunction This approach requires no a priori knowledge andis of high stability and accuracy Figure 1 illustrates the flowchart of optimizing the three parameters of SVM model by

GAThe GA is used to seek a better combination of the threeparameters in the SVM so that a bigger forecasting accuracyis obtained in each iteration

In this study the input and output variables are normal-ized in the range from 0 to 1 by (3) That can minimizedeformation error range and guarantee the unity of themodeldata in order to improve prediction accuracy Consider

Hour119889=

Hour119889minusHourmin

Hourmax minusHourmin (3)

where Hour119889is the normalization value at day 119889 Hour

119889is

the original value at day 119889 Hourmax and Hourmin are themaximum and minimum of sample data sets respectively

After training and testing the GA-SVM model the fore-cast value of power generation energy is calculated by

Hour119889= Hour

119889times (Hourmax minusHourmin) +Hourmin

Energy119889= Hour

119889times Capacity

119889

(4)

33 Model Performance Estimation A lot of goodness-of-fit measurements have been applied to evaluate model per-formance Appropriate evaluation criteria should be chosen


Table 1 The119883mean 119878119909 119862119904119883min and119883max of the data set of Yunlong County and Maguan County

County Data set 119883mean 119878119909

119862119904

119883min 119883max

YunlongTraining 8008 3926 06 2002 23662Testing 11741 1548 minus12 7006 13696Entire 8257 3924 05 2002 23662

MaguanTraining 24404 11212 04 4406 48051Testing 34021 7099 04 23365 47663Entire 25046 11243 03 4406 48051

when usingmulticriteria to validatemodel performance [38]In this paper the following two statistical measures whichare usually used in other researches are chosen as evaluationcriteria for model performance

RMSE = radic 1119899

119899

sum

119889=1

(Energy119889minus Energylowast

119889)2

MAPE = 1119899

119899

sum

119889=1

100381610038161003816100381610038161003816100381610038161003816

Energylowast119889minus Energy

119889

Energylowast119889

100381610038161003816100381610038161003816100381610038161003816

times 100

(5)

where 119899 is the total amount of observed data Energylowast119889and

Energy119889are respective observed and forecasted value at day

119889The root mean squared error (RMSE) is an arbitrary

positive value and will indicate a good performance when itis close to zero The mean absolute percentage error (MAPE)is a relative index of absolute model error and can expressaccuracy as a percentage [39 40] The smaller the value ofMAPE is the better performance the model shows

4 Numerical Results

41 Study Areas and Data There is extremely rich hydro-power resource in Yunnan province whose potential capacityranks third in China The hydropower resources of everyregion are extremely uneven and mainly distributed in thewest and north followed by the east and south By the end ofOctober 2012 the SHP plants in Yunnan had reached 1587with 3417 units and 845305MW of the installed capacitywhich accounts for more than 27 and 12 of hydropowercapacity in Yunnan province and SHP capacity in Chinarespectively [41] The two typical counties Yunlong Countyand Maguan County are in Dali region and Wenshan regionin Yunnan province respectively and are selected as studyareas in this paper The location of the two counties is shownin Figure 2

YunlongCounty is located in thewest of Yunnan provincewith a total area of 440095 km2 And the annual average tem-perature and annual average rainfall are 159∘C and 7295mmrespectively By the end of 2013 there are 10 small hydropowerplants with installed capacity 1115MW Maguan County islocated in the southeast of Yunnan province with a totalarea of 2676 km2 And the annual average temperature andannual average rainfall are 169∘C and 1345mm respectively

WN

ES

Maguan

Yunlong

NujiangJinshajiang

river

riverNujiang

riverJinshajiangriver

Jinshajiang

river

riverNujiang

Lancang Jiang

Lancang Jiang

Lancang Jiang

Figure 2 Location of the study area

By the end of 2013 there are 22 small hydropower plants withinstalled capacity of 21389MW

The data derived from the two counties are both 915 dayslong with the period between May 1 2011 and October 312013 for which 854 days of the power generation energydata from May 1 2011 to August 31 2013 are used forcalibration and the remaining 61 days from September 12013 to October 31 2013 are used for validation The dailystatistical parameters of calibration and validation and theentire data set for the two counties are shown in Table 1 In thetable119883mean 119878119909119862119904119883min and119883max stand formean standarddeviation skewness coefficient minimum and maximumrespectively The table indicates that the training data fullyincludes validation data In addition it can be easily foundthat power generation energy for the two counties both varyover a wide range and are concentrated in the flood seasonmuch bigger than other seasons So the data from Septemberto October in flood season is selected for model testing andother data for model training In addition the dispatchingpersonnel of power grid are more concerned about powergeneration energy of SHP in flood season

42 Results and Discussion In this study the GA is employedas parameter search scheme In order to get better parametersof SVM the maximum iterative time of GA is set as 50 andthe population size is set to 30 50 80 100 120 and 150


Table 2 The performance statistics of GA-SVMmodels for Yunlong County

Population size Optimal parameters(C 120576 and 120590)

Calibration Validation

RMSE MAPE RMSE MAPE

(i) 30 (40754 01989 00078) 11388 852 8108 515(ii) 50 (55762 02275 00073) 11366 849 7731 502(iii) 80 (187495 0105 00103) 11398 853 8042 508(iv) 100 (103452 01464 00077) 11387 851 8086 511(v) 120 (244174 00528 00064) 11446 858 8185 519(vi) 150 (94141 00348 00025) 11511 862 8053 507

Table 3 The performance statistics of GA-SVMmodels for Maguan County



RMSE MAPE RMSE MAPE

(i) 30 (23792 06749 00058) 25225 754 23367 437(ii) 50 (73517 0056 00197) 25495 792 23436 438(iii) 80 (10808 00799 00192) 25429 790 23375 440(iv) 100 (84248 00538 00156) 25518 792 23354 436(v) 120 (140828 00758 00191) 25428 789 23392 440(vi) 150 (11421 0058 00063) 25587 783 23302 432

Table 4 AIC value and performance indices of alternative ARMAmodels for Yunlong County

(119901 119902) AIC Calibration ValidationRMSE MAPE RMSE MAPE

(3 12) 95266 11430 870 8207 558(4 8) 95270 11484 887 8340 524(5 13) 95153 11317 898 7849 506(6 12) 95281 11398 891 7854 504(7 12) 95276 11380 890 7788 499(8 8) 95265 11366 885 8018 522

respectively And the optimal scope of three parameters (119862120576 and 120590) of SVM model are [2minus5 25] [0 2] and [2minus13 2minus1]respectively The performance statistics of SVM models aregiven in Tables 2 and 3 for the two counties

The results from Table 2 clearly indicate that the popu-lation size (ii) for SVM models with the optimal parameters(119862 120576 120590) = (55762 02275 00073) can be selected as forecastmodel for Yunlong County

For Maguan County it can be seen from Table 3 that thetwo statistical measures of population size (i) in calibrationstage are clearly better than others since those are slightlybetter or worse in validation stage So the optimal parameters(119862 120576 120590) = (23792 06749 00058) were selected throughcomprehensive comparison

In order to get a better comprehension of the GA-SVMmodel performance the ARMA model was employed as acomparative purpose The basic components to an ARMAmodel is autoregression (AR) and moving-average (MA) Toobtain a suitable ARMA (119901 119902) model the two integers 119901

and 119902 have to be determined respectively by the numberof autoregressive orders and the number of moving-averageorders of the ARMA model In this paper the AIC (Akaikeinformation criterion) value of ARMA models for 119901 and 119902ranging from 1 to 13 is calculated

For Yunlong County the models ARMA (3 12) (4 8) (513) (7 12) (6 12) and (8 8) which have relatively smallerAICvalues are selected as the candidatemodels Table 4 shows theAIC value and the performance of selectedARMAmodels Bycomparing analysis the ARMA (7 12) model was chosen asthe final ARMAmodel for Yunlong County

For Maguan County the models ARMA (1 2) (2 1) (22) (2 3) (2 4) and (3 1) which have relatively smaller AICvalues are selected as the candidatemodels Table 5 shows theAIC value and the performance of selected ARMA modelsBy comparing analysis the ARMA (2 4) model was chosenas the final ARMAmodel for Maguan County

In this study the same training and verification sets areused for the two models in order to have the same basis


Table 5 AIC value and performance indices of alternative ARMAmodels for Maguan County


(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460

Table 6Model statistics of the calibration and validation period forYunlong County

ModelCalibration Validation

RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499

of comparison Meanwhile in order to evaluate the modelperformance for forecasting STPGE of SHP the time seriesdata are derived from two study sites in different regionAnd the two statistical measures are employed to evaluate themodel performance

For YunlongCounty themodelrsquos RMSE andMAPE statis-tics of the calibration and validation period are summarizedin Table 6 With the results shown in Table 6 the analysiscan be executed crisply The results reveal that the GA-SVM model outperformed ARMA with respect to the twomeasures in the calibration period In this stage theGA-SVMmodel improved the ARMA model of about 024 in RMSEvalue and 041 in MAPE value For the comparison betweenGA-SVMandARMAmodel in the validation period theGA-SVM obtains better RMSE value than the ARMA while theMAPE value of the twomodels are nearly equal to each otherFigure 3 shows the comparison of forecasted versus observeddischarge using GA-SVM and ARMA model for YunlongCounty It can be seen from the residuals that the GA-SVMmodel performs better than ARMA Furthermore it can beconcluded from Table 4 and Figure 3 that GA-SVM modelobtains slightly better forecast precision than ARMA

For Maguan County the modelrsquos RMSE and MAPEstatistics of the calibration and validation period are sum-marized in Table 7 Table 7 demonstrates that the GA-SVMmodel is clearly superior to ARMA in the calibration andvalidation period of the two measures In the validationperiod the GA-SVM model improved the ARMA model ofabout 789 and 041 in RMSE and MAPE values respectivelyFor the comparison between GA-SVM and SVM model inthe validation period the GA-SVM model obtains slightlybetter MAPE value and worse RMSE value than the ARMAFigure 4 shows the comparison of forecasted versus observedpower generation energy using GA-SVM and ARMAmodelsfor the Maguan County As can be seen from the residuals

Table 7 Model statistics of the calibration and validation period forMaguan County


RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447

the GA-SVM model performs better than ARMA except fora few peaks Furthermore it can be concluded from Table 5and Figure 4 that the GA-SVMmodel overall performs betterthan the ARMAmodel

5 Conclusion

In the present study the GA-SVM prediction model com-prising support vector machine with genetic algorithm hasbeen developed for forecasting short-term power genera-tion energy of small hydropower in region The historicalobserved data derived from Yunlong County and MaguanCounty in Yunnan province in China were employed toinvestigate the modeling potentiality of GA-SVM Data fromMay 1 2011 to August 31 2013 and from September 1 2013to October 31 2013 are used for training and validationrespectively in short-term power generation energy predic-tion Due to the lack of small hydropower operation dataSVM is chosen as forecasting model because of its ability insolving small sample The three parameters of SVM modelare not known a priori and optimized by GA in order to getappropriate parameters for improving forecasting accuracyIn order to get a better comprehension of the GA-SVMmodel performance the ARMA model was employed asa comparative purpose The two models were constructedand their performances were compared crisply The resultsindicated that the GA-SVM model can give slightly betterprediction performance than the other model

For the less data of small hydropower in region theGA-SVM model proposed in this paper is an effectivemethod for improving short-term forecasting accuracy Thatis useful for fully absorbing small hydropower resources andavoiding water resource wasted and electricity dumped inflood season


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)

Figure 3 Comparison of forecasted versus observed power generation energy using GA-SVM and ARMAmodel for Yunlong County

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210

minus1minus2minus3minus4

(c)

Figure 4 Comparison of forecasted versus observed power generation energy using GA-SVM and ARMAmodel for Maguan County

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National High Technol-ogy Research and Development of China 863 Program


(2012AA050205) and the Fundamental Research Funds forthe Central Universities (DUT13JN05)

References

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[2] S Dudhani A K Sinha and S S Inamdar ldquoAssessment of smallhydropower potential using remote sensing data for sustainabledevelopment in Indiardquo Energy Policy vol 34 no 17 pp 3195ndash3205 2006

[3] T Haakon Bakken H Sundt A Ruud et al ldquoDevelopmentof small versus large hydropower in Norway comparison ofenvironmental impactsrdquo Energy Procedia vol 20 pp P185ndashP199 2012

[4] T Boslashckman S Fleten E Juliussen H J Langhammer andI Revdal ldquoInvestment timing and optimal capacity choice forsmall hydropower projectsrdquo European Journal of OperationalResearch vol 190 no 1 pp 255ndash267 2008

[5] L Kosnik ldquoThe potential for small scale hydropower develop-ment in the USrdquo Energy Policy vol 38 no 10 pp 5512ndash55192010

[6] J-K Li ldquoResearch on prospect and problem for hydropowerdevelopment of Chinardquo Procedia Engineering vol 28 pp P677ndashP682 2012

[7] S Zhou X Zhang and J Liu ldquoThe trend of small hydropowerdevelopment in Chinardquo Renewable Energy vol 34 no 4 pp1078ndash1083 2009

[8] H Ma L Oxley and J Gibson ldquoChinarsquos energy situation in thenew millenniumrdquo Renewable and Sustainable Energy Reviewsvol 13 no 8 pp 1781ndash1799 2009

[9] V Nikam and K Gupta ldquoSVM-based model for short-termrainf all forecasts at a local scale in the Mumbai Urban areaIndiardquo Journal of Hydrologic Engineering vol 19 pp P1048ndashP1052 2014

[10] RGolob T Stokelj andDGrgic ldquoNeural-network-basedwaterinflow forecastingrdquo Control Engineering Practice vol 6 no 5pp P593ndashP600 1998

[11] P Coulibaly F Anctil and B Bobee ldquoDaily reservoir inflowforecasting using artificial neural networks with stopped train-ing approachrdquo Journal of Hydrology vol 230 no 3-4 pp 244ndash257 2000

[12] D Paravan T Stokelj and R Golob ldquoImprovements to thewater management of a run-of-river HPP reservoir method-ology and case studyrdquo Control Engineering Practice vol 12 no4 pp 377ndash385 2004

[13] D Dutta W D Welsh J Vaze S S H Kim and D NichollsldquoA comparative evaluation of short-term streamflow forecastingusing time series analysis and Rainfall-Runoffmodels in ewatersourcerdquoWater Resources Management vol 26 no 15 pp 4397ndash4415 2012

[14] M Vafakhah ldquoApplication of artificial neural networks andadaptive neuro-fuzzy inference system models to short-termstreamflow forecastingrdquo Canadian Journal of Civil Engineeringvol 39 no 4 pp 402ndash414 2012

[15] C M Zealand D H Burn and S P Simonovic ldquoShort termstreamflow forecasting using artificial neural networksrdquo Journalof Hydrology vol 214 no 1ndash4 pp 32ndash48 1999

[16] R J Kuligowski and A P Barros ldquoExperiments in short-term precipitation forecasting using artificial neural networksrdquoMonthly Weather Review vol 126 no 2 pp 470ndash482 1998

[17] C Monteiro I J Ramirez-Rosado and L A Fernandez-Jimenez ldquoShort-term forecasting model for electric powerproduction of small-hydro power plantsrdquo Renewable Energyvol 50 pp 387ndash394 2013

[18] B Yao C Yang J Yao and J Sun ldquoTunnel surroundingrock displacement prediction using support vector machinerdquoInternational Journal of Computational Intelligence Systems vol3 no 6 pp 843ndash852 2010

[19] B Z Yao P Hu M H Zhang and M Q Jin ldquoA support vectormachine with the Tabu search algorithm for freeway incidentdetectionrdquo International Journal of Applied Mathematics andComputer Science vol 24 no 2 pp 397ndash404 2014

[20] B Z Yao P Hu M H Zhang and X M Tian ldquoImprovedant colony optimization for seafood product delivery routingproblemrdquo PrometmdashTrafficampTransportation vol 26 no 1 pp 1ndash10 2014

[21] B Yao P Hu M Zhang and S Wang ldquoArtificial bee colonyalgorithm with scanning strategy for the periodic vehiclerouting problemrdquo Simulation vol 89 no 6 pp 762ndash770 2013

[22] B Yao C Yang J Hu J Yao and J Sun ldquoAn improved antcolony optimization for flexible job shop scheduling problemsrdquoAdvanced Science Letters vol 4 no 6-7 pp 2127ndash2131 2011

[23] B Z Yao P Hu X H Lu J J Gao and M H Zhang ldquoTransitnetwork design based on travel time reliabilityrdquo TransportationResearch C vol 43 pp 233ndash248 2014

[24] B YuWHK Lam andM L Tam ldquoBus arrival time predictionat bus stopwithmultiple routesrdquoTransportation Research C vol19 no 6 pp 1157ndash1170 2011

[25] B Yu S Wu B Yao Z Yang and J Sun ldquoDynamic vehicle dis-patching at a transfer station in public transportation systemrdquoJournal of Transportation Engineering vol 138 no 2 pp 191ndash2012012

[26] B Yu Z Z Yang and S Li ldquoReal-time partway deadheadingstrategy based on transit service reliability assessmentrdquo Trans-portationResearchA Policy andPractice vol 46 no 8 pp 1265ndash1279 2012

[27] B Yu Z Yang X Sun B YaoQ Zeng andE Jeppesen ldquoParallelgenetic algorithm in bus route headway optimizationrdquo AppliedSoft Computing Journal vol 11 no 8 pp 5081ndash5091 2011

[28] B Yu H B Zhu W J Cai N Ma and B Z Yao ldquoTwo-phase optimization approach to transit hub locationmdashthe caseof Dalianrdquo Journal of Transport Geography vol 33 pp 62ndash712013

[29] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[30] Y B Dibike S Velickov D Solomatine and M B AbbottldquoModel induction with support vector machines introductionand applicationsrdquo Journal of Computing inCivil Engineering vol15 no 3 pp 208ndash216 2001

[31] W Hong ldquoRainfall forecasting by technological machine learn-ing modelsrdquo Applied Mathematics and Computation vol 200no 1 pp 41ndash57 2008

[32] A Anandhi V V Srinivas R S Nanjundiah and D NageshKumar ldquoDownscaling precipitation to river basin in India forIPCC SRES scenarios using support vector machinerdquo Interna-tional Journal of Climatology vol 28 no 3 pp 401ndash420 2008

[33] P Pai ldquoSystem reliability forecasting by support vectormachines with genetic algorithmsrdquo Mathematical and Com-puter Modelling vol 43 no 3-4 pp 262ndash274 2006

[34] L M Saini S K Aggarwal and A Kumar ldquoParameter opti-misation using genetic algorithm for support vector machine-based price-forecasting model in National electricity marketrdquo


IET Generation Transmission and Distribution vol 4 no 1 pp36ndash49 2010

[35] Q Duan S Sorooshian and V K Gupta ldquoOptimal use of theSCE-UA global optimization method for calibrating watershedmodelsrdquo Journal of Hydrology vol 158 no 3-4 pp 265ndash2841994

[36] S Sorooshian and V Gupta ldquoEffective and efficient globaloptimization for conceptual rainfall-runoff modelsrdquo WaterResources Research vol 28 no 4 pp 1015ndash1031 1992

[37] J Lin C Cheng and K Chau ldquoUsing support vector machinesfor long-term discharge predictionrdquoHydrological Sciences Jour-nal vol 51 no 4 pp 599ndash612 2006

[38] R Modarres ldquoMulti-criteria validation of artificial neural net-work rainfall-runoff modelingrdquo Hydrology and Earth SystemSciences vol 13 no 3 pp 411ndash421 2009

[39] T S Hu K C Lam and S T Ng ldquoRiver flow time series pre-diction with a range-dependent neural networkrdquo HydrologicalSciences Journal vol 46 no 5 pp 729ndash745 2001

[40] W Wang K Chau C Cheng and L Qiu ldquoA comparison ofperformance of several artificial intelligence methods for fore-casting monthly discharge time seriesrdquo Journal of Hydrologyvol 374 no 3-4 pp 294ndash306 2009

[41] L Gang L Benxi L Shanzong C Chuntian and L XiufengldquoAn overview of large-scale small hydropower in yunnan powergrid situations challenges and measuresrdquo in Proceedings of theWorld Environmental and Water Resources Congress pp 2139ndash2145 Cincinnati Ohio USA May 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


However SHP plants are generally in the small remoteriver basin with shortage of hydrologic station and themanagement is weak due to nonperson supervision for along time so it is very difficult for forecasting STPGE ofSHP because of lack of necessary runoff data At presenta lot of research activities in short-term forecasting mod-els of hydropower stations have been carried out whichfocus on the forecasting of inflow in reservoirs [9ndash12] ofstream flow [13ndash15] or of precipitation [16] But there arefew research works referring to forecasting the STPGE forSHP stations [17] Since the parameters will greatly affectthe performance of SVM some literatures attempted todetermine the proper parameter values for their problems[18 19] However for large scale or real-time feature practiceapplication the considerable search time cannot be acceptedHeuristic algorithms have been successfully used in manycomplex problems [20ndash22]

This paper presents a novel short-term forecasting model(named GA-SVM) for power generation energy of SHPstations In this study support vector machine (SVM) wasused to identify power generation energy based on structuralrisk minimization principle [18 23ndash26] and its parametersare optimized by genetic algorithm (GA) to get the optimalmodel structure [27 28] Considering dynamically puttinginto operation of SHP plant or hydrounit the installed capac-ity utilization hours of SHP are selected as input and outputvalue of the proposed forecastingmodel since the power gen-eration energy of SHP is not the same at different times Thismethod is applied to forecast STPGE of the small hydropowerstations in Yunlong County and Maguan County Yunnanprovince China Compared with the conventional methodthe proposedGA-SVMmodel exhibits superior performancedemonstrating GA-SVMrsquos effectiveness as an approach toforecast STPGE of SHP

The paper is organized as follows In the next sectionldquoBrief Introduction to SVM and GArdquo SVM and GA algo-rithms are briefly introduced Then the proposed GA-SVMforecasting method is described in the following section Inthe next section this method is applied to Yunnan provinceand the results are compared with those of conventionalmethod The final section concludes the paper

2 Brief Introduction to SVM and GA

21 Support Vector Machines (SVM) The SVM developedby Vapnik [29] is based on statistical learning theory andimplements the structural risk minimization principle ratherthan the empirical risk minimization principle implementedby most traditional ANN models It seeks to minimize anupper bound to the generalization error instead of minimiz-ing the training error and can achieve an optimum networkstructure Many researchers have used SVM to implementforecasting model in every field which mainly focuses onforecasting rainfall Dibike et al demonstrated the capabilityof the SVM in hydrological prediction such as modelingthe rainfall runoff process [30] There are other scholarswho have used the SVM for rainfall forecast ranging from1-2 days ahead to 1 h ahead [31] In this paper the SVM

model is used to forecast STPGE of SHP And the radialbasis function (RBF) is employed as kernel function whichhas shown to simplify the use of a mapping because theRBF is more compact in comparison with other kernels andis able to shorten the computational training process andimprove the generalization performance [30]TheRBF is alsocomputationally simpler than a polynomial kernel which hasmore parameters [32] The equation for RBF is of the form

119896 (119909119894 119909) = exp

minus1003817100381710038171003817119909 minus 11990911989410038171003817100381710038172

21205902 (1)

22 Genetic Algorithm (GA) GA is a global optimal algo-rithm based on ldquosurvival of the fittestrdquo in Darwinrsquos theoryof evolution and provides an efficient and robust optimizedsearching method in complex space This is an excellentsearch algorithm adapted to the global probability GA oper-ates iteratively on a population of structures each of whichrepresents a candidate solution to the problem encoded asa string of symbols (chromosome) and uses randomizedtechnical guidance to effectively search a coded parameterspace GA makes use of coding technology to transform thesolved space of problem into chromosome space and alsoconvert the decisive variable into a certain structure of indi-vidual chromosomes During the iteration of the algorithmaccording to the rules set by the fitness function these groupsmade up of individuals generated next generation throughselection crossover and mutation Fitness factor which isbeneficial to the population will be inherited while factorsthat reduce fitness will be eliminated with the operationof mutation and crossover in iterations After continuousevolutions the optimal individuals survive which can beapproximate optimal solution of the problem

3 Short-Term Forecasting Model for PowerGeneration Energy Using GA-SVM

31 Forecasting Object Generally the daily power generationenergy is directly selected as forecasting object for STPGEof SHP But considering dynamically putting into operationsmall hydropower plant or hydrounit in some region thereis a difference of installed capacity of SHP between oneday and another day Since the power output of SHP plantis almost close to installed capacity in flood season thepower generation energy is also very different due to theincrease in installed capacity of SHP The model predictionperformance will be affected if power generation energy ofSHP is only used as input and output values of the modelTherefore the installed capacity utilization hour representspower generation energy of SHP in region That could notonly accurately reflect the characteristics of small hydropowerplant without regulation ability but also alleviate short-termfluctuations in power generation curveThe installed capacityutilization hour was

Hour119889=

Energy119889

Capacity119889

(2)



mutation




t = t + 1

N

Y



Begin

Normalize data

Trainingdata

Testingdata

Build SVM model




End









Antinormalize data

(C 120590 and 120576)









Hour119889=




119889is



Hour119889= Hour


Energy119889= Hour


119889

(4)





119862119904

119883min 119883max





119899

sum

119889=1


119889)2

MAPE = 1119899

119899

sum

119889=1

100381610038161003816100381610038161003816100381610038161003816


119889

Energylowast119889

100381610038161003816100381610038161003816100381610038161003816

times 100

(5)





4 Numerical Results



WN

ES

Maguan

Yunlong

NujiangJinshajiang

river

riverNujiang


Jinshajiang

river

riverNujiang

Lancang Jiang

Lancang Jiang

Lancang Jiang









RMSE MAPE RMSE MAPE

(i) 30 (40754 01989 00078) 11388 852 8108 515(ii) 50 (55762 02275 00073) 11366 849 7731 502(iii) 80 (187495 0105 00103) 11398 853 8042 508(iv) 100 (103452 01464 00077) 11387 851 8086 511(v) 120 (244174 00528 00064) 11446 858 8185 519(vi) 150 (94141 00348 00025) 11511 862 8053 507




RMSE MAPE RMSE MAPE

(i) 30 (23792 06749 00058) 25225 754 23367 437(ii) 50 (73517 0056 00197) 25495 792 23436 438(iii) 80 (10808 00799 00192) 25429 790 23375 440(iv) 100 (84248 00538 00156) 25518 792 23354 436(v) 120 (140828 00758 00191) 25428 789 23392 440(vi) 150 (11421 0058 00063) 25587 783 23302 432



(3 12) 95266 11430 870 8207 558(4 8) 95270 11484 887 8340 524(5 13) 95153 11317 898 7849 506(6 12) 95281 11398 891 7854 504(7 12) 95276 11380 890 7788 499(8 8) 95265 11366 885 8018 522












(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460



RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499






RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447


5 Conclusion




1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











mutation




t = t + 1

N

Y



Begin

Normalize data

Trainingdata

Testingdata

Build SVM model




End









Antinormalize data

(C 120590 and 120576)









Hour119889=




119889is



Hour119889= Hour


Energy119889= Hour


119889

(4)





119862119904

119883min 119883max





119899

sum

119889=1


119889)2

MAPE = 1119899

119899

sum

119889=1

100381610038161003816100381610038161003816100381610038161003816


119889

Energylowast119889

100381610038161003816100381610038161003816100381610038161003816

times 100

(5)





4 Numerical Results



WN

ES

Maguan

Yunlong

NujiangJinshajiang

river

riverNujiang


Jinshajiang

river

riverNujiang

Lancang Jiang

Lancang Jiang

Lancang Jiang









RMSE MAPE RMSE MAPE

(i) 30 (40754 01989 00078) 11388 852 8108 515(ii) 50 (55762 02275 00073) 11366 849 7731 502(iii) 80 (187495 0105 00103) 11398 853 8042 508(iv) 100 (103452 01464 00077) 11387 851 8086 511(v) 120 (244174 00528 00064) 11446 858 8185 519(vi) 150 (94141 00348 00025) 11511 862 8053 507




RMSE MAPE RMSE MAPE

(i) 30 (23792 06749 00058) 25225 754 23367 437(ii) 50 (73517 0056 00197) 25495 792 23436 438(iii) 80 (10808 00799 00192) 25429 790 23375 440(iv) 100 (84248 00538 00156) 25518 792 23354 436(v) 120 (140828 00758 00191) 25428 789 23392 440(vi) 150 (11421 0058 00063) 25587 783 23302 432



(3 12) 95266 11430 870 8207 558(4 8) 95270 11484 887 8340 524(5 13) 95153 11317 898 7849 506(6 12) 95281 11398 891 7854 504(7 12) 95276 11380 890 7788 499(8 8) 95265 11366 885 8018 522












(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460



RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499






RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447


5 Conclusion




1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119862119904

119883min 119883max





119899

sum

119889=1


119889)2

MAPE = 1119899

119899

sum

119889=1

100381610038161003816100381610038161003816100381610038161003816


119889

Energylowast119889

100381610038161003816100381610038161003816100381610038161003816

times 100

(5)





4 Numerical Results



WN

ES

Maguan

Yunlong

NujiangJinshajiang

river

riverNujiang


Jinshajiang

river

riverNujiang

Lancang Jiang

Lancang Jiang

Lancang Jiang









RMSE MAPE RMSE MAPE

(i) 30 (40754 01989 00078) 11388 852 8108 515(ii) 50 (55762 02275 00073) 11366 849 7731 502(iii) 80 (187495 0105 00103) 11398 853 8042 508(iv) 100 (103452 01464 00077) 11387 851 8086 511(v) 120 (244174 00528 00064) 11446 858 8185 519(vi) 150 (94141 00348 00025) 11511 862 8053 507




RMSE MAPE RMSE MAPE

(i) 30 (23792 06749 00058) 25225 754 23367 437(ii) 50 (73517 0056 00197) 25495 792 23436 438(iii) 80 (10808 00799 00192) 25429 790 23375 440(iv) 100 (84248 00538 00156) 25518 792 23354 436(v) 120 (140828 00758 00191) 25428 789 23392 440(vi) 150 (11421 0058 00063) 25587 783 23302 432



(3 12) 95266 11430 870 8207 558(4 8) 95270 11484 887 8340 524(5 13) 95153 11317 898 7849 506(6 12) 95281 11398 891 7854 504(7 12) 95276 11380 890 7788 499(8 8) 95265 11366 885 8018 522












(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460



RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499






RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447


5 Conclusion




1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













RMSE MAPE RMSE MAPE

(i) 30 (40754 01989 00078) 11388 852 8108 515(ii) 50 (55762 02275 00073) 11366 849 7731 502(iii) 80 (187495 0105 00103) 11398 853 8042 508(iv) 100 (103452 01464 00077) 11387 851 8086 511(v) 120 (244174 00528 00064) 11446 858 8185 519(vi) 150 (94141 00348 00025) 11511 862 8053 507




RMSE MAPE RMSE MAPE

(i) 30 (23792 06749 00058) 25225 754 23367 437(ii) 50 (73517 0056 00197) 25495 792 23436 438(iii) 80 (10808 00799 00192) 25429 790 23375 440(iv) 100 (84248 00538 00156) 25518 792 23354 436(v) 120 (140828 00758 00191) 25428 789 23392 440(vi) 150 (11421 0058 00063) 25587 783 23302 432



(3 12) 95266 11430 870 8207 558(4 8) 95270 11484 887 8340 524(5 13) 95153 11317 898 7849 506(6 12) 95281 11398 891 7854 504(7 12) 95276 11380 890 7788 499(8 8) 95265 11366 885 8018 522












(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460



RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499






RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447


5 Conclusion




1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












(1 2) 111782 26122 794 23476 446(2 1) 111739 26049 795 23348 453(2 2) 111755 26037 796 23482 455(2 3) 111778 26036 796 23413 454(2 4) 111779 26014 795 23224 447(3 3) 111767 26007 796 23495 460



RMSE MAPE RMSE MAPE

GA-SVM 11366 849 7731 502ARMA 11380 890 7788 499






RMSE MAPE RMSE MAPE

GA-SVM 25225 754 23367 437ARMA 26014 795 23224 447


5 Conclusion




1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedGA-SVM

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Pow

er g

ener

atio

nen

ergy

(MW

h) 6

5

4

3

2

1

0

times103

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

8

4

0

minus4

minus8

minus12

times102

Resid

uals

(MW

h)

GA-SVMARMA

(c)


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

ObservedGA-SVM

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

(a)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

times102

16

12

8

4

0Pow

er g

ener

atio

nen

ergy

(MW

h)

ObservedARMA

(b)

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61Day

Resid

uals

(MW

h)

GA-SVMARMA

times102

43210


(c)




Acknowledgments




References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article short-term power generation...

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