short-term power load forecasting method based on improved...

Research ArticleShort-Term Power Load Forecasting Method Based onImproved Exponential Smoothing Grey Model

Jianwei Mi 12 Libin Fan12 Xuechao Duan 12 and Yuanying Qiu 12

1School of Mechano-Electronic Engineering Xidian University Xirsquoan 710071 China2Key Laboratory of Electronic Equipment Structure Design Ministry of Education Xidian UniversityNo 2 South Taibai Road Xirsquoan 710071 China

Correspondence should be addressed to Jianwei Mi jwmixidianeducn

Received 29 August 2017 Accepted 13 February 2018 Published 25 March 2018

Academic Editor Emilio Turco

Copyright copy 2018 Jianwei Mi et al This 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

In order to improve the prediction accuracy this paper proposes a short-termpower load forecastingmethod based on the improvedexponential smoothing greymodel It firstly determines themain factor affecting the power load using the grey correlation analysisIt then conducts power load forecasting using the improved multivariable grey model The improved prediction model firstlycarries out the smoothing processing of the original power load data using the first exponential smoothing method Secondlythe grey prediction model with an optimized background value is established using the smoothed sequence which agrees withthe exponential trend Finally the inverse exponential smoothing method is employed to restore the predicted value The firstexponential smoothing model uses the 0618 method to search for the optimal smooth coefficient The prediction model can takethe effects of the influencing factors on the power load into considerationThe simulated results show that the proposed predictionalgorithm has a satisfactory prediction effect and meets the requirements of short-term power load forecasting This research notonly further improves the accuracy and reliability of short-term power load forecasting but also extends the application scope ofthe grey prediction model and shortens the search interval

1 Introduction

Short-term power load forecasting is a key issue for theoperation and dispatch of power systems in order to preventthe serious consequences of flash and power failures It isa prerequisite for the economic operation of power systemsand the basis of dispatching and making startup-shutdownplans which plays a key role in the automatic control of powersystems [1ndash3] Accurate power load forecasting not only helpsusers choose a more appropriate electricity consumptionscheme and reduces a lot of electric cost expenditure whileimproving equipment utilization thus reducing the produc-tion cost and improving the economic benefit but also isconducive to optimizing the resources of power systemsimproving power supply capability and ultimately achievingthe aim of energy conservation and emission reduction [4ndash6] As the power system is increasingly complicated and thedegree of electricity marketization is further enhanced howto quickly and accurately predict short-term power loads has

become one of the popular topics in the field of power loadforecasting

As a fundamental research power load forecasting hasbeen investigated for a long time Many experts and scholarshave done a lot of research on prediction theory andmethodsand put forward several prediction models and methods [7ndash11] At present the prediction method of power load canbe divided into two categories [12ndash14] One is the classicalprediction method of statistical class such as regressionanalysis time series method and grey prediction methodAnd the other is the novel prediction method of artificialintelligence class such as expert systems and artificial neuralnetworks Because there are many factors affecting the short-term power load and different prediction methods havedifferent applications none of these methods is applicable toall power systems which need to choose different predictionmodels according to different power load conditions [15ndash18]

Grey system theory was proposed in 1982 [19] It is anovel algorithm of coping with the problem of uncertainty

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 3894723 11 pageshttpsdoiorg10115520183894723

2 Mathematical Problems in Engineering

with less data and poor information Its essence is to estimatethe development law of an object containing incompleteinformation based on the principle of grey system analysis[20 21] Compared with other prediction methods the greyprediction model has the characteristics of less data highprediction precision and no prior information Thereforeit is suitable for short-term power load forecasting Chinarsquospower load has both the certainty increased year by yearand the uncertainty affected by external factors which agreeswith the characteristics of ldquosmall sample poor informationrdquoof the grey system so it is rational to use the grey modelfor modeling prediction [22ndash24] However the GM(1 1)which is commonly used in the traditional grey predictionmodel is a biased exponential model In particular when thedata fluctuates its prediction error is too large to meet therequirements of the actual power load forecasting

The traditional GM(1 1) model is only used for themodeling and prediction of single time series to reveal theinherent development law of the single variable But theactual power system often contains multiple factor variablescoupled with each other that is each factor variable in itsdevelopment process is affected by other factors and alsoaffects other factors at the same time In order to get thepredicted value that agrees with the actual situation weshould take the comprehensive influences of various factorson the predicted variables into consideration

The traditional grey predictionmodel hasmany problemsto be solved such as its complex improved methods thefact that it cannot comprehensively consider the effects ofinfluencing factors its limited application scope and itsprediction error failing to meet the requirement Aimedat these problems many scholars have proposed variousimproved methods [25 26] Based on the analysis of theseimproved methods this paper firstly employs the maininfluencing factor from various influencing factors using thegrey correlation analysis And then it establishes an improvedexponential smoothing grey prediction model combiningthe exponential smoothing method and the characteristicsof short-term power load which carries out short-termload forecasting using the historical data of power loadand influencing factors The simulated results show that themethod has a satisfactory prediction effect on the short-term power loadThe validity and feasibility of the predictionmodel are of great significance to solve the problem of theshort-term power load forecasting in the development ofsmart grids in the future

2 The Exponential Smoothing Method andTraditional Grey Prediction Model

21 The Exponential Smoothing Method The exponentialsmoothing method is also a straightforward time seriesprediction method which has the characteristics of simplecalculation and convenient use It is often applied to short-term and ultrashort-term power load forecasting and hashigh precision [27]The prediction for the linearmodel of theexponential smoothing method is shown in

119910119905+119901 = 119860 119905 + 119861119905 sdot 119901 (1)

where 119905 is the current period 119901 is the predicted period inadvance and 119910119905+119901 is the predicted value in 119905 + 119901 period Theparameters 119860 119905 and 119861119905 are determined by

119860 119905 = 21198781015840119905 minus 11987810158401015840119905 119861119905 = 120572 (1198781015840119905 minus 11987810158401015840119905 )(1 minus 120572) 1198781015840119905 = 120572119865119905 + (1 minus 120572) 1198781015840119905minus111987810158401015840119905 = 1205721198781015840119905 + (1 minus 120572) 11987810158401015840119905minus1

(2)

where120572 is the smooth coefficient and119865t is the original value attime 119905 1198781015840119905 and 1198781015840119905minus1 are the first smoothing values at time 119905 andtime 119905 minus 1 respectively 11987810158401015840119905 and 11987810158401015840119905minus1 are the second smoothingvalues at time 119905 and time 119905minus1 respectively as well as 11987810158401 = 119878101584010158401 =1198651 where 11987810158401 and 119878101584010158401 represent the first smoothing value andthe second smoothing value at the initial time respectivelyand 1198651 represents the original value at the initial time

From (2) we can know that the smooth coefficient 120572value directly affects the accuracy of the predicted valueTherefore themost critical step in the exponential smoothingmethod is to determine the smooth coefficient And it canhelp reduce the prediction error by finding out the optimal 120572valueThemethods commonly used to determine the smoothcoefficient are the empirical estimation method trial anderror and others However the common drawback of thetwomethods is that forecasting researchers must perform theiterations and calculations several times to obtain an optimal120572 value which has a tight relationship with the knowledgeprofessional experience and the number of calculations ofthe forecasting researchers What is more the forecastingprocess of this method (which is used to determine thesmooth coefficient by the empirical estimation and trial-and-error methods) needs human intervention and thus has lowautomation and is an inefficient solvingmethod To overcomethe drawback of the above two methods the 0618 method[28] can be used to search for the optimal smooth coefficientHowever the optimum result of the 0618 method dependsmainly on the objective function chosen

22 The Traditional Grey Prediction Model The grey predic-tion model is one of the core contents of the grey systemtheory The most commonly used grey prediction modelin power load forecasting is the GM(1 1) model whoseparameters indicate that the model establishes a first-orderdifferential equation for one predicted variable to make pre-dictions As shown in Figure 1 the traditional grey predictionmodeling process mainly includes accumulated generationgrey parameters calculation solving the differential equationand inverse accumulated generationThe detailed procedurescan be found in [29] The advantage of the traditional greyprediction model is that there is not much demand for thesample and it can get a better prediction effect in the caseof few data samples The disadvantage is that it can onlymake predictions for a single variable and requires that thedata change be gentle and in accordance with the exponential

Mathematical Problems in Engineering 3

Start

Input the original data sequence

Execute the accumulated generation operation

Calculate the grey parameters and establish thedifferential equation

Solve the differential equation and get the predictedsequence of the accumulated sequence

Perform the inverse accumulated generationoperation and get the predicted sequence of the original data sequence

End

Figure 1 The flow diagram of the traditional grey prediction model

change law thus the prediction effect is not satisfactory incase of data fluctuation

3 The Improved ExponentialSmoothing Grey Model

Because the traditional grey GM(1 1) prediction model isonly applicable to the case in which the data change isrelatively gentle it can neither meet the actual forecastingrequirements without an ideal prediction effect nor considerthe effects of influencing factors on it for the case wherethe data sequence has a fast growth rate or large fluctuationAimed at the disadvantage of the GM(1 1) model (ie itcannot be applied to power load forecasting with fluctuationcomplex environment and obvious effects of influencingfactors) an improved exponential smoothing grey predictionmodel is established in this paper using the selected maininfluencing factor variable and power load variable basedon the analysis of short-term power load characteristicscombining the grey correlation analysis the exponentialsmoothing method and the 0618 method By combiningthe influences of the main factors the prediction model canexpand the application scope of the grey prediction modelshorten the search interval when searching for the optimalsmooth coefficient using the 0618 method and furtherimprove the prediction accuracy and reliability

As shown in Figure 2 the concrete processes of theimproved exponential smoothing grey model are as follows

Step 1 Input the real-time data of the original power load andperform the grey correlation analysis to determine the maininfluencing factor of the predicted object

Step 2 Perform the first exponential smoothing processingto weaken its stochastic volatility and make it closer to theexponential trend

Step 3 Make predictions for the smoothed sequence usingthe grey model with an optimized background value

Step 4 The predicted results are restored to the predictedvalues of the original power load data and the data at the nextprediction time through the inverse exponential smoothingprocessing

Step 5 Judge whether the predicted results reach the require-ment of the fitting error If they do then output the predictedresults If they do not then the 0618 method is introducedwhich reselects the subinterval of smoothing coefficient andthe pilot smoothing coefficient and then judges the pilotsmoothing coefficient If it reaches |120572119894 minus 1205721015840119894 | lt 120576 where120572119894 and 1205721015840119894 are the first pilot smoothing coefficient and thesecond pilot smoothing coefficient in the 119894th subintervalrespectively and 120576 is the accuracy requirement then take theoptimal smooth coefficient 120572lowast119894 = (120572119894 +1205721015840119894 )2 and continue thealgorithm If it does not then take the 120572 value with a smallerMAPE (Mean Absolute Percentage Error) value and continuethe algorithm

The key step in the above forecasting process is todynamically update the original power load data The totalamount of the original power load data in the update processkeeps unchanged that is selecting a suitable moving spanWhen moving a span every time it removes the ldquooldestrdquo dataand adds the ldquolatestrdquo data so that each forecasting process


Input the original power load data updated in real time

Single exponential smoothing processing

Grey prediction model with optimized background value

The requirement ofthe fitting errorreached

Output the predicted data

Reselect the subinterval of smoothing coefficient and the pilot

Optimal smooth coefficient

Choose the value with smaller MAPE

Yes

No

No

Yes

Inverse exponentialsmoothing processing

Grey correlation analysis

Start

End

|i minus i | lt

lowasti = (i +

i )2

Figure 2 The flow diagram of the improved exponential smoothing grey model

corresponds to a particular optimal smoothing coefficientwhich can implement the real-time correction of the predic-tionmodel parameter when thememory occupation stays thesame In addition the smoothing processing of the originaldata sequence is similar to that in [30] which can notonly display the data more smoothly but also eliminate therandom errors to a certain degree

31 The Grey Correlation Analysis The grey correlationanalysis is a multivariable statistical analysis method whosebasic idea is to judge whether there is a correlation betweenany two factor variables according to the similarity degree ofthe curvesrsquo geometrical shapes of various factor sequencesThe closer the curve is the closer the correlation between thecorresponding sequences of variables is that is the greater


the correlation degree is and vice versa [31]The specific stepsare as follows

(1) Determine the main behavior factor variable of thesystem x1 (the predicted object) and the influencingfactor variable sequences x119894

x1 = (11990911 11990912 1199091119896) x119894 = (1199091198941 1199091198942 119909119894119896) (119894 = 2 3 119899) (3)

In the expression above 119896 represents the data length ofx1

(2) Normalize each variable sequence and get the initialvalues x1015840119894 as follows

x1015840119894 = x1198941199091198941 = (11990910158401198941 11990910158401198942 1199091015840119894119896) (119894 = 1 2 119899) (4)

(3) Calculate the correlation coefficient between themain behavior sequence and each influencing factorsequence

Let Δ 119894119895 = |11990910158401119895 minus 1199091015840119894119895|(119895 = 1 2 119896) where 1199091015840119894119895 representsthe 119895th initial value of the 119894th variable The differencesequences can be expressed as the following sequence Δi =(Δ 1198941 Δ 1198942 Δ 119894119896) (119894 = 2 3 119899) The maximum difference119872 and the minimum difference 119898 can be calculated by theequations119872 = max119894max119895Δ 119894119895 and 119898 = min119894min119895Δ 119894119895Therefore the correlation coefficient can be calculated by theequation 120585119894119895 = (119898 + 120588119872)(Δ 119894119895 + 120588119872) In the equation theparameter 120588 isin (0 1) and it is generally equal to 05 [32]

(4) Calculate the correlation degree

Based on the correlation coefficients above one can getthe correlation degree 120574119894 = (1119896)sum119896119895=1 120585119894119895 (119894 = 2 3 119899)where 120574 gt 0 And then one can select the main influencingfactor and eliminate the secondary factors according to thecorrelation degree

By performing the grey correlation analysis for eachinfluencing factor and the main behavior variable the resultcan provide the basis for the selection of the variables inthe prediction model and avoid that the unrelated factors orthe factors with small correlation degree affect the predictionefficiency of the whole system and reduce the predictionaccuracy

32 The Improvements of the Traditional Grey PredictionModel The traditional grey prediction model requires thatthe predicted load sequence should conform with the expo-nential trend The improvement of smoothness of the loadsequence helps to improve the prediction accuracy of thegrey model Therefore the improvements of the traditionalgrey prediction model lie mainly in two aspects (1) thetransformation of the original sequence that is to improve itssmoothness whichmakes it closer to the exponential law and(2) the optimization of model parameters that is to optimizeand transform the background value used for solving the grey

parameters The original power load data is amended usingthe first exponential smoothing method of the exponentialsmoothing method in the improved grey prediction modelwhich weakens its stochastic volatility andmakes the originaldata sequence more smoothly close to the exponential lawIt also implements the prediction restoration of the originalpower load data and the data at the next prediction time usingthe inverse exponential smoothing in the final processingAs shown in Figure 3 the improved grey prediction modelincludes the following steps(1) Firstly perform the grey correlation analysis for theinput original data sequence 1199090119894 And then perform the firstexponential smoothing processing for the selected variablesusing (5) to improve the smoothness of the sequence andmake itmeet the requirement of the input data in the grey pre-dictionmodelThe smooth coefficient in the first exponentialsmoothing equation is obtained by the optimization of the0618 method Finally perform the accumulated generationfor the obtained smoothed sequence 1198780119894 As shown in (6)we can obtain the accumulative sequence 1199101119894 where thesuperscript 0 represents the sequence that did not undergoaccumulated generation and the superscript 1 represents thesequence that underwent accumulated generationMoreover119894 = 1 2 119899 119896 = 2 3 119902 where 119899 represents the numberof variables selected by the grey correlation analysis and 119902represents the number of the original power load data

1198780119894 (119896) = 120572lowast1199090119894 (119896) + (1 minus 120572lowast) 1198780119894 (119896 minus 1) (5)

1199101119894 (119896) = 1198780119894 (119896) + 1198780119894 (119896 + 1) (6)

(2) Optimize the background value 119885119894 in the grey pre-diction model according to (7) using the optimal smoothcoefficient 120572lowast used in the first exponential smoothing pro-cessing Calculate the data matrices 119871 and 119877 according tothe optimized background value as shown in (8) and finallyobtain the grey parameters 119862 and 119863 whose equations are asfollows The weight 120573 of the background value 119885119894 in the greyprediction model is taken as the value related to the optimalsmooth coefficient 120572lowast which can avoid the error caused byfixing 120573 to 05 in the traditional grey prediction model andhelp to improve the prediction precision

120573 = 1120572lowast minus 1119890120572lowast minus 1 (7)

119885119894 (119896) = 1205731199101119894 (119896 minus 1) + (1 minus 120573) 1199101119894 (119896) (8)

In (8) the superscript 1 represents the notion that thesequence has been accumulated And 119894 = 1 2 119899 119896 =2 3 119902 where 119899 represents the number of variablesselected by the grey correlation analysis and 119902 represents thenumber of the original power load data

119871 =[[[[[[[

1198851 (2)1198851 (3)1198851 (119902)

1198852 (2)1198852 (3)1198852 (119902)

sdot sdot sdotsdot sdot sdotsdot sdot sdot

119885119899 (2)119885119899 (3)119885119899 (119902)

111

]]]]]]] (9)


Find the optimal smoothPerform the first exponential smoothing processing

Perform the accumulated generation

Start

End

Calculate the data matrices L and R and the greyparameters C and D

Optimize the background value

and perform the grey correlation analysis

accumulated generation

0618 method

Input the original data sequence x0i

S0i (k) = lowastx0i (k) + (1 minus lowast)S0i (k minus 1)

y1i (k) = S0i (k) + S0i (k minus 1)

Obtain the fitted value and the predicted value yp1i of

the sequence y1i and obtain the fitted value and the

predicted value Sp0i of the sequence S0i by the inverse

Obtain the fitted value and the predicted value y0i of the

sequence x0i by inverse exponential smoothing

coefficient lowast using the

= 1lowast minus 1 elowast

minus 1 Zi (k)) = y1i (( k minus 1) + (1 minus )y1

i (k)

Figure 3 The structure diagram of the improved grey prediction model

119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)

In (11)119867 is a matrix with an order of (119899+ 1) times 119899 119862119879 takesthe first 119899 rows of the119867 matrix and 119863119879 takes the last row ofthe119867matrix To respectively transpose the two submatricesone can get the grey parameters119862 and119863 where119862 is a matrixwith the order of 119899 times 119899 and 119863 is a matrix with the order of119899 times 1(3) Obtain the predicted sequence 1199101199011119894 of the sequence1199101119894 according to the grey prediction (see (12)) and obtain thepredicted sequence 1198781199010119894 of the sequence 1198780119894 by the inverseaccumulated generation (see (13))


1199101199011119894 (119896) = 119890119862(119896minus1) (1199101119894 (1) + 119862minus1119863) minus 119862minus1119863 (12)

1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)

(4) Put the predicted sequence 1198781199010119894 obtained by the greyprediction equation into the inverse exponential smoothingmodel as shown in (14) to realize the prediction restorationof the original power load data and the data at the nextprediction time and finally obtain the predicted sequence 1199100119894of the original power load data 1199090119894 and the data at the nextprediction time

1199100119894 (119896) = (1198781199010119894 (119896) minus (1 minus 120572lowast) 1198781199010119894 (119896 minus 1))120572lowast (14)

33The Improvement of the 0618Method It can be seen fromFigure 3 that the accuracy of the smooth coefficient is directlyrelated to the prediction accuracy Generally speaking theMSE (Mean Square Error) or the MAD (Mean AbsoluteDeviation) will be chosen as the objective function in the0618 method to search for the optimal smooth coefficientThe value ofMSE can be expressed as119891MSE and its calculationformula is shown in (15)The value of MAD can be expressedas 119891MAD and its calculation formula is shown in (16) How-ever through the actual calculation one can observe thatchoosing MAPE as the objective function can yield bettereffects The value of MAPE can be expressed as 119891MAPE andits calculation formula is shown in (17)

119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)

In the equations 119902 is the number of the original powerload data 1199100119894 is the predicted sequence of 1199090119894 which is relatedto the smooth coefficient One can see that 119891MAPE actually isa function of smooth coefficient One can observe from (15)that MSE is the average of the sums of squares of the errorsbetween the actual value and the predicted value whichmakes MSE unable to measure the unbiasedness Similarlyone can observe from (16) that MAD is the average of thesums of the absolute deviation between the actual value andthe predicted value but MAD fails to reflect the effect ofthe deviation on the actual value Therefore compared withMSE and MAD it can not only more accurately reflect thedeviation between the predicted value and the actual valuebut also effectively measure the unbiasedness and improvethe reliability of prediction using MAPE as the objectivefunction of the 0618 method

The specific processes of the improved 0618 method canbe divided into five steps as shown in Figure 4(1) Let 120576 = 001 and divide the smooth coefficient 120572 isin(0 1) into 10 equidistant subintervals 1205721 isin (0 01) 1205722 isin

(01 02) 12057210 isin (09 1) Select a subinterval 120572119894 isin (1198860 1198870)(119894 = 1 2 10) where 1198860 and 1198870 represent the left andright endpoints of the 119894th subinterval respectively proceedto the next step Furthermore the smooth coefficient intervalis divided into 10 equidistant subintervals for meeting therequirement that the objective function of the 0618 methodis a unimodal function Because it is difficult to prove thatMAPE is a unimodal function in the whole interval of [0 1]it is possible to distribute the extreme points of MAPE indifferent subintervals by dividing the interval equally so thatMAPE is a unimodal function in each subinterval EventhoughMAPE is not a unimodal function in each subintervalthere is a little impact on searching for the optimal valueThe reason is that the function value at every point in eachsubinterval is close to its minimum and it is sufficient to meetthe precision requirement of 120576 = 001 when the intervallength is small to a certain extent (equal to 01 here)The basicidea of the 0618 method can be found in [33](2) Take the first trial point and let the first pilotsmoothing coefficient 120572119894 = 06181198860 + 03821198870(3) Take the second trial point and let the second pilotsmoothing coefficient 1205721015840119894 = 03821198860 + 06181198870(4) Judge whether |120572119894 minus 1205721015840119894 | lt 120576 holds or not If it holdsthen take the optimal smooth coefficient 120572lowast119894 = (120572119894 + 1205721015840119894 )2and proceed to the subsequent process If it does not thenproceed to step (5)(5) Calculate the MAPE values 1198911(120572119894) and 1198912(1205721015840119894 ) corre-sponding to the two trial points and compare their values If1198911(120572119894) lt 1198912(1205721015840119894 ) 1198860 keeps constant 1198870 = 1205721015840119894 1205721015840119894 = 120572119894 and1198912(1205721015840119894 ) = 1198911(120572119894) and proceed to step (2) If 1198911(120572119894) gt 1198912(1205721015840119894 )1198870 keeps constant 1198860 = 120572119894 120572119894 = 1205721015840119894 and 1198911(120572119894) = 1198912(1205721015840119894 ) andproceed to step (3)4 Simulated Results and Discussion

As shown in Table 1 the electricity consumption of thewhole society and the national economic indicators thatis the influencing factors data in 8 time periods ofFujian Province in [32] are adopted The factors affectingthe electricity consumption 1199091 in the table include theGDP (Gross Domestic Product) 1199092 the total population 1199093and the import and export total 1199094 In order to verify thevalidity of the proposed improved prediction algorithm thispaper realized the power load forecasting algorithm basedon the improved exponential smoothing grey model whichbuilds the model using the electricity consumption data andits influencing factors data in 8 time periods shown in Table 1and predicts the electricity consumption data in the next 2time periods(1) Determine the main factor variable affecting thepower load forecasting using the grey correlation analysis

One can calculate the correlation degree of 3 influencingfactors in Table 1 for the power load and the results are shownin Table 2

One can observe from the calculation results of thecorrelation degree in Table 2 that the correlation degreebetween the import and export total and the electricityconsumption is the largest one that is the influencing factor


Start

Solve the second pilot and let

Take the optimal smooth coefficient

Put it into the first exponential smoothing equation

End

Respectively calculate the

Yes

Yes No

No

10 equidistant subintervals and

Solve the first pilot and let

MAPE values

Let b0 = i

i = i

Let a0 = i i = i

Let = 001 divide isin (0 1) into

let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )

Figure 4 The structure diagram of the improved 0618 method

Table 1 The original electricity consumption and its influencing factors data

Time119905 1199091 (GWh) 1199092 (billion $) 1199093 (million $) 1199094 (million $)1 1870175 18805 3150 10041812 2236449 27928 3183 12189533 2594770 35765 3237 14445694 2799490 42668 3261 15519725 2997313 49575 3282 17952806 3201954 54776 3299 17160657 3533703 59171 3316 17619568 4015149 65335 3410 2122332

ldquothe import and export totalrdquo has the greatest influence onthe electricity consumptionTherefore the import and exporttotal is chosen as the main influencing factor variable(2) Build the improved exponential smoothing greymodel and make predictions

After determining the main factor variable according toTable 2 one can build the multivariable grey model of theelectricity consumption and the import and export total using

the original data in Table 1 The grey parameters can beobtained by (11) Subsequently the corresponding differentialequations are solved The data in the first 8 time periodsare used to fit the model and the fitted results are shownin Table 3 The fitted errors in Table 3 are calculated by(17) such as (|2236449 minus 23037539|2236449) times 100 =301 The data in the last 2 time periods are used toverify the performance of the prediction model and the


Table 2 The correlation degree between each influencing factor and electricity consumption

Influencing factors GDP1199092 Total population1199093 Import and export total1199094Correlation degree 05185 06110 09243

Table 3 Comparison of the actual values and the fitted values of electricity consumption

Time119905 Original data The improved model The model in [32]Fitted data Error Fitted data Error

1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385

Table 4 Comparison of the actual values and the predicted values of electricity consumption

Time Original values The improved model GM(1 1)model GM(1 4)model The model in [32]Predicted values Error Predicted values Error Predicted values Error Predicted values Error

9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156

Average error 126 366 274 130

predicted results are shown in Table 4 The predicted errorsin Table 4 are calculated by (17) such as (|4391860 minus4346589|4391860) times 100 = 103

It can be seen from Table 3 that the fitted effect obtainedby the improved prediction model is better than that in [32]The parameters of the improved prediction model can bemodified and optimized in real time according to the trendof the actual data However because the parameters of themodel in [32] are fixed and the original data is not processedby any smoothing operations the trend of the fitted data willbe somewhat deviated from the trend of the actual data

It can be seen from Table 4 that the predicted effectobtained by the improved prediction model is the best andits predicted average MAPE value is 126 which meetsthe requirement that the average error in short-term powerload forecasting should be around 3 Although the errorof the improved prediction model is only slightly smallerthan that in [32] the electricity consumption difference willbe large when used in an actual application for example50000 times 00126 = 630 (GWh) 50000 times 0013 = 650(GWh) and the electricity consumption difference EC119889 = 20(GWh) If such a large electricity consumption differenceis taken into account it will save a very large economiccost Especially for the large industrial consumers with alarge electricity consumption base it will be conducive toselecting a more reasonable charging mode by accuratelyforecasting the power demand for the next month whichmakes the economic effect more obvious This phenomenonalso illustrates three problems (1) if the influencing factorswere not taken into consideration in the prediction model it

would lead to a poor prediction accuracy such as theGM(1 1)model (2) if other secondary influencing factors besides themain influencing factor were taken into consideration in theprediction model the prediction error would also increasesuch as theGM(1 4)model (3) if the influencing factors wereconsidered in the predictionmodel but themodel parameterswere not optimized it would also lead to an increase inprediction error such as the model adopted in [32] In orderto show the degree of deviation between the actual value andthe predicted value more intuitively the curves of the actualvalue and the predicted value are plotted in Figure 5

It can be seen from Figure 5 that the trend of pre-dicted values of power load is very close to the trend ofactual value and the overall predicted effect is satisfactoryThe simulated results show that the improved exponentialsmoothing grey prediction model is feasible and effectivefor short-term power load forecasting which improves theprediction accuracy of the prediction model Moreover theintroduction of the 0618 method improves the solutionefficiency and the automation andmakes the predicted resultshighly reliable which basically overcomes the shortcomingsof the traditional grey prediction algorithm Besides thealgorithm is straightforward to be realized

5 Conclusion

The traditional grey prediction model has found wide appli-cations in the field of power load forecasting because ofits characteristics of simple principle lower sample data


5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)

Original valuesPredicted values

times104

Pow

er lo

ad (G

Wh)

Figure 5 Comparison curves of the original values and the predict-ed values

requirement and ability to tackle uncertain problems How-ever the disadvantages of the model itself result in itsdefective prediction effect and thus inability to meet theactual forecasting requirement Aiming at the shortcomingsof the above prediction model this paper proposed a short-term power load forecasting method based on the improvedexponential smoothing grey model which not only preservesthe advantages of the traditional grey prediction model fordealing with the poor information but also analyzes thevarious influencing factors affecting power load forecastingusing the grey correlation analysis and determines the maininfluencing factor The improved prediction model reducesthe calculation quantity and improves the prediction effi-ciency because it does not consider too much the secondaryfactors which can reduce the prediction efficiency Someconclusions can be drawn as follows

(1) The first exponential smoothing model is employedto deal with the original power load data in theimproved prediction model which not only weakensthe randomness but also improves the smoothness ofdata The smoothing processing makes it close to theexponential trend which meets the requirement ofthe input data in the grey prediction model and con-tributes to further improving the prediction accuracy

(2) The 0618 method is introduced in the first expo-nential smoothing process and MAPE is chosen asthe objective function to search for the optimalsmooth coefficient which enhances the reliability ofprediction

(3) The background value of the traditional grey predic-tion model is also optimized which can implementthe real-time correction of the prediction modelparameter

Conflicts of Interest

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

Acknowledgments

This work is partially supported by the 111 Project B14042and the National Natural Science Foundation of China underGrants nos 51490660 and 51405362

References

[1] Y He Q Xu J Wan and S Yang ldquoShort-term power loadprobability density forecasting based on quantile regressionneural network and triangle kernel functionrdquo Energy vol 114pp 498ndash512 2016

[2] Z Zhang and W Gong ldquoShort-term load forecasting modelbased on quantum elman neural networksrdquo MathematicalProblems in Engineering vol 2016 Article ID 7910971 2016

[3] X Wang and Y Wang ldquoA Hybrid Model of EMD and PSO-SVR for Short-Term Load Forecasting in Residential QuartersrdquoMathematical Problems in Engineering vol 2016 Article ID9895639 2016

[4] RHu SWen Z Zeng and THuang ldquoA short-termpower loadforecasting model based on the generalized regression neuralnetwork with decreasing step fruit fly optimization algorithmrdquoNeurocomputing vol 221 pp 24ndash31 2017

[5] H Li L Cui and S Guo ldquoA hybrid short-term power loadforecasting model based on the singular spectrum analysis andautoregressive modelrdquo Advances in Electrical Engineering vol2014 Article ID 424781 7 pages 2014

[6] H Yuansheng H Shenhai and S Jiayin ldquoA novel hybridmethod for short-term power load forecastingrdquo Journal ofElectrical and Computer Engineering vol 2016 Article ID2165324 2016

[7] Y He R Liu H Li S Wang and X Lu ldquoShort-term powerload probability density forecasting method using kernel-basedsupport vector quantile regression and Copula theoryrdquo AppliedEnergy vol 185 pp 254ndash266 2017

[8] M Capuno J-S Kim and H Song ldquoVery short-term loadforecasting using hybrid algebraic prediction and supportvector regressionrdquo Mathematical Problems in Engineering vol2017 Article ID 8298531 2017

[9] H J Sadaei F G Guimaraes C Silva M H Lee and T EslamildquoShort-term load forecasting method based on fuzzy timeseries seasonality and long memory processrdquo InternationalJournal of Approximate Reasoning vol 83 pp 196ndash217 2017

[10] A Laouafi M Mordjaoui S Haddad T E Boukelia and AGanouche ldquoOnline electricity demand forecasting based onan effective forecast combination methodologyrdquo Electric PowerSystems Research vol 148 pp 35ndash47 2017

[11] Y Chen P Xu Y Chu et al ldquoShort-term electrical loadforecasting using the Support Vector Regression (SVR) modelto calculate the demand response baseline for office buildingsrdquoApplied Energy vol 195 pp 659ndash670 2017

[12] B Wang D Wang and S Zhang ldquoShort-term DistributedPower Load Forecasting Algorithm Based on Spark andIPPSO LSSVMrdquo Electric Power Automation Equipment vol 36no 1 pp 117ndash122 2016


[13] S Brodowski A Bielecki and M Filocha ldquoA hybrid systemfor forecasting 24-h power load profile for Polish electric gridrdquoApplied Soft Computing vol 58 pp 527ndash539 2017

[14] M B Germi M Mirjavadi A S S Namin and A Baziar ldquoAhybrid model for daily peak load power forecasting based onSAMBA and neural networkrdquo Journal of Intelligent amp FuzzySystems Applications in Engineering and Technology vol 27 no2 pp 913ndash920 2014

[15] L Xiao W Shao C Wang K Zhang and H Lu ldquoResearchand application of a hybrid model based on multi-objectiveoptimization for electrical load forecastingrdquoApplied Energy vol180 pp 213ndash233 2016

[16] S Zhang R Shi L Zhang B Yan H Zhang and P HeldquoImprovement of chaotic forecasting model and its applicationin power daily load forecastingrdquo Chinese Journal of ScientificInstrument vol 37 no 1 pp 208ndash214 2016

[17] L Xiao W Shao T Liang and C Wang ldquoA combined modelbased on multiple seasonal patterns and modified firefly algo-rithm for electrical load forecastingrdquo Applied Energy vol 167pp 135ndash153 2016

[18] K G Boroojeni M H Amini S Bahrami S S Iyengar A ISarwat and O Karabasoglu ldquoA novel multi-time-scale mod-eling for electric power demand forecasting From short-termto medium-term horizonrdquo Electric Power Systems Research vol142 pp 58ndash73 2017

[19] N Xie and S Liu ldquoInterval grey number sequence prediction byusing non-homogenous exponential discrete grey forecastingmodelrdquo Journal of Systems Engineering and Electronics vol 26no 1 pp 96ndash102 2015

[20] N Xu Y Dang andYGong ldquoNovel grey predictionmodel withnonlinear optimized time response method for forecasting ofelectricity consumption in Chinardquo Energy vol 118 pp 473ndash4802017

[21] L Jian-Kai C Cattani and S Wan-Qing ldquoPower load predic-tion based on fractal theoryrdquoAdvances inMathematical Physicsvol 2015 Article ID 827238 2015

[22] B Zeng andC Li ldquoForecasting the natural gas demand inChinausing a self-adapting intelligent greymodelrdquoEnergy vol 112 pp810ndash825 2016

[23] S Liu and L-X Tian ldquoThe study of long-term electricityload forecasting based on improved grey prediction modelrdquoin Proceedings of the 12th International Conference on MachineLearning and Cybernetics ICMLC 2013 pp 653ndash657 China July2013

[24] J Massana C Pous L Burgas J Melendez and J ColomerldquoShort-term load forecasting for non-residential buildings con-trasting artificial occupancy attributesrdquo Energy and Buildingsvol 130 pp 519ndash531 2016

[25] H Zhao and S Guo ldquoAn optimized grey model for annualpower load forecastingrdquo Energy vol 107 pp 272ndash286 2016

[26] M Y Tong X H Zhou and B Zeng ldquoThe background valueoptimization method in grey NGM (11 k) modelrdquo Control andDecision vol 32 no 3 2017

[27] P Ji D Xiong P Wang and J Chen ldquoA study on exponentialsmoothing model for load forecastingrdquo in Proceedings of the2012 Asia-Pacific Power and Energy Engineering ConferenceAPPEEC 2012 China March 2012

[28] J A Koupaei S Hosseini and F M Ghaini ldquoA new optimiza-tion algorithmbased on chaoticmaps and golden section searchmethodrdquo Engineering Applications of Artificial Intelligence vol50 pp 201ndash214 2016

[29] Y Yang and D Xue ldquoContinuous fractional-order grey modeland electricity prediction research based on the observationerror feedbackrdquo Energy vol 115 pp 722ndash733 2016

[30] E Cadenas O A Jaramillo and W Rivera ldquoAnalysis andforecasting ofwind velocity in chetumal quintana roo using thesingle exponential smoothing methodrdquo Journal of RenewableEnergy vol 35 no 5 pp 925ndash930 2010

[31] X Xia Y Sun K Wu and Q Jiang ldquoOptimization of astraw ring-die briquetting process combined analytic hierarchyprocess and grey correlation analysis methodrdquo Fuel ProcessingTechnology vol 152 pp 303ndash309 2016

[32] Y P Wang D X Huang H Q Xiong and Y L Niu ldquoUsingrelational analysis and multi-variable grey model for electricitydemand forecasting in smart grid environmentrdquo Power SystemProtection and Control vol 40 no 1 pp 96ndash100 2012

[33] Y X Yuan and W Y Sun Optimization theory and methodScience Press Beijing China 1997 96ndash99

Hindawiwwwhindawicom Volume 2018

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Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


with less data and poor information Its essence is to estimatethe development law of an object containing incompleteinformation based on the principle of grey system analysis[20 21] Compared with other prediction methods the greyprediction model has the characteristics of less data highprediction precision and no prior information Thereforeit is suitable for short-term power load forecasting Chinarsquospower load has both the certainty increased year by yearand the uncertainty affected by external factors which agreeswith the characteristics of ldquosmall sample poor informationrdquoof the grey system so it is rational to use the grey modelfor modeling prediction [22ndash24] However the GM(1 1)which is commonly used in the traditional grey predictionmodel is a biased exponential model In particular when thedata fluctuates its prediction error is too large to meet therequirements of the actual power load forecasting

The traditional GM(1 1) model is only used for themodeling and prediction of single time series to reveal theinherent development law of the single variable But theactual power system often contains multiple factor variablescoupled with each other that is each factor variable in itsdevelopment process is affected by other factors and alsoaffects other factors at the same time In order to get thepredicted value that agrees with the actual situation weshould take the comprehensive influences of various factorson the predicted variables into consideration

The traditional grey predictionmodel hasmany problemsto be solved such as its complex improved methods thefact that it cannot comprehensively consider the effects ofinfluencing factors its limited application scope and itsprediction error failing to meet the requirement Aimedat these problems many scholars have proposed variousimproved methods [25 26] Based on the analysis of theseimproved methods this paper firstly employs the maininfluencing factor from various influencing factors using thegrey correlation analysis And then it establishes an improvedexponential smoothing grey prediction model combiningthe exponential smoothing method and the characteristicsof short-term power load which carries out short-termload forecasting using the historical data of power loadand influencing factors The simulated results show that themethod has a satisfactory prediction effect on the short-term power loadThe validity and feasibility of the predictionmodel are of great significance to solve the problem of theshort-term power load forecasting in the development ofsmart grids in the future

2 The Exponential Smoothing Method andTraditional Grey Prediction Model

21 The Exponential Smoothing Method The exponentialsmoothing method is also a straightforward time seriesprediction method which has the characteristics of simplecalculation and convenient use It is often applied to short-term and ultrashort-term power load forecasting and hashigh precision [27]The prediction for the linearmodel of theexponential smoothing method is shown in

119910119905+119901 = 119860 119905 + 119861119905 sdot 119901 (1)

where 119905 is the current period 119901 is the predicted period inadvance and 119910119905+119901 is the predicted value in 119905 + 119901 period Theparameters 119860 119905 and 119861119905 are determined by

119860 119905 = 21198781015840119905 minus 11987810158401015840119905 119861119905 = 120572 (1198781015840119905 minus 11987810158401015840119905 )(1 minus 120572) 1198781015840119905 = 120572119865119905 + (1 minus 120572) 1198781015840119905minus111987810158401015840119905 = 1205721198781015840119905 + (1 minus 120572) 11987810158401015840119905minus1

(2)

where120572 is the smooth coefficient and119865t is the original value attime 119905 1198781015840119905 and 1198781015840119905minus1 are the first smoothing values at time 119905 andtime 119905 minus 1 respectively 11987810158401015840119905 and 11987810158401015840119905minus1 are the second smoothingvalues at time 119905 and time 119905minus1 respectively as well as 11987810158401 = 119878101584010158401 =1198651 where 11987810158401 and 119878101584010158401 represent the first smoothing value andthe second smoothing value at the initial time respectivelyand 1198651 represents the original value at the initial time

From (2) we can know that the smooth coefficient 120572value directly affects the accuracy of the predicted valueTherefore themost critical step in the exponential smoothingmethod is to determine the smooth coefficient And it canhelp reduce the prediction error by finding out the optimal 120572valueThemethods commonly used to determine the smoothcoefficient are the empirical estimation method trial anderror and others However the common drawback of thetwomethods is that forecasting researchers must perform theiterations and calculations several times to obtain an optimal120572 value which has a tight relationship with the knowledgeprofessional experience and the number of calculations ofthe forecasting researchers What is more the forecastingprocess of this method (which is used to determine thesmooth coefficient by the empirical estimation and trial-and-error methods) needs human intervention and thus has lowautomation and is an inefficient solvingmethod To overcomethe drawback of the above two methods the 0618 method[28] can be used to search for the optimal smooth coefficientHowever the optimum result of the 0618 method dependsmainly on the objective function chosen

22 The Traditional Grey Prediction Model The grey predic-tion model is one of the core contents of the grey systemtheory The most commonly used grey prediction modelin power load forecasting is the GM(1 1) model whoseparameters indicate that the model establishes a first-orderdifferential equation for one predicted variable to make pre-dictions As shown in Figure 1 the traditional grey predictionmodeling process mainly includes accumulated generationgrey parameters calculation solving the differential equationand inverse accumulated generationThe detailed procedurescan be found in [29] The advantage of the traditional greyprediction model is that there is not much demand for thesample and it can get a better prediction effect in the caseof few data samples The disadvantage is that it can onlymake predictions for a single variable and requires that thedata change be gentle and in accordance with the exponential


Start






End





















Yes

No

No

Yes



Start

End

|i minus i | lt

lowasti = (i +

i )2







x1 = (11990911 11990912 1199091119896) x119894 = (1199091198941 1199091198942 119909119894119896) (119894 = 2 3 119899) (3)



x1015840119894 = x1198941199091198941 = (11990910158401198941 11990910158401198942 1199091015840119894119896) (119894 = 1 2 119899) (4)









1199101119894 (119896) = 1198780119894 (119896) + 1198780119894 (119896 + 1) (6)



119885119894 (119896) = 1205731199101119894 (119896 minus 1) + (1 minus 120573) 1199101119894 (119896) (8)


119871 =[[[[[[[

1198851 (2)1198851 (3)1198851 (119902)

1198852 (2)1198852 (3)1198852 (119902)


119885119899 (2)119885119899 (3)119885119899 (119902)

111

]]]]]]] (9)




Start

End





0618 method












i (k)


119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)




1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









Start






End





















Yes

No

No

Yes



Start

End

|i minus i | lt

lowasti = (i +

i )2







x1 = (11990911 11990912 1199091119896) x119894 = (1199091198941 1199091198942 119909119894119896) (119894 = 2 3 119899) (3)



x1015840119894 = x1198941199091198941 = (11990910158401198941 11990910158401198942 1199091015840119894119896) (119894 = 1 2 119899) (4)









1199101119894 (119896) = 1198780119894 (119896) + 1198780119894 (119896 + 1) (6)



119885119894 (119896) = 1205731199101119894 (119896 minus 1) + (1 minus 120573) 1199101119894 (119896) (8)


119871 =[[[[[[[

1198851 (2)1198851 (3)1198851 (119902)

1198852 (2)1198852 (3)1198852 (119902)


119885119899 (2)119885119899 (3)119885119899 (119902)

111

]]]]]]] (9)




Start

End





0618 method












i (k)


119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)




1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018

















Yes

No

No

Yes



Start

End

|i minus i | lt

lowasti = (i +

i )2







x1 = (11990911 11990912 1199091119896) x119894 = (1199091198941 1199091198942 119909119894119896) (119894 = 2 3 119899) (3)



x1015840119894 = x1198941199091198941 = (11990910158401198941 11990910158401198942 1199091015840119894119896) (119894 = 1 2 119899) (4)









1199101119894 (119896) = 1198780119894 (119896) + 1198780119894 (119896 + 1) (6)



119885119894 (119896) = 1205731199101119894 (119896 minus 1) + (1 minus 120573) 1199101119894 (119896) (8)


119871 =[[[[[[[

1198851 (2)1198851 (3)1198851 (119902)

1198852 (2)1198852 (3)1198852 (119902)


119885119899 (2)119885119899 (3)119885119899 (119902)

111

]]]]]]] (9)




Start

End





0618 method












i (k)


119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)




1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018











x1 = (11990911 11990912 1199091119896) x119894 = (1199091198941 1199091198942 119909119894119896) (119894 = 2 3 119899) (3)



x1015840119894 = x1198941199091198941 = (11990910158401198941 11990910158401198942 1199091015840119894119896) (119894 = 1 2 119899) (4)









1199101119894 (119896) = 1198780119894 (119896) + 1198780119894 (119896 + 1) (6)



119885119894 (119896) = 1205731199101119894 (119896 minus 1) + (1 minus 120573) 1199101119894 (119896) (8)


119871 =[[[[[[[

1198851 (2)1198851 (3)1198851 (119902)

1198852 (2)1198852 (3)1198852 (119902)


119885119899 (2)119885119899 (3)119885119899 (119902)

111

]]]]]]] (9)




Start

End





0618 method












i (k)


119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)




1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018











Start

End





0618 method












i (k)


119877 =[[[[[[[[[

11987801 (2)11987801 (3)11987801 (119902)

11987802 (2)11987802 (3)11987802 (119902)


1198780119899 (2)1198780119899 (3)

1198780119899 (119902)

]]]]]]]]] (10)

[119862119879119863119879] = 119867 = (119871119879119871)minus1 119871119879119877 (11)




1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018










1198781199010119894 (119896) = 1199101199011119894 (119896) minus 1199101199011119894 (119896 minus 1) (13)




119891MSE = sum119902119894=1 (1199090119894 minus 1199100119894 )2119902 (15)

119891MAD = sum119902119894=1 100381610038161003816100381610038161199090119894 minus 1199100119894 10038161003816100381610038161003816119902 (16)

119891MAPE = 100119902119902sum119894=1

1003816100381610038161003816100381610038161003816100381610038161199090119894 minus 11991001198941199090119894

100381610038161003816100381610038161003816100381610038161003816 (17)








Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









Start




End


Yes

Yes No

No



MAPE values

Let b0 = i

i = i

Let a0 = i i = i


let i isin (a0 b0)

i = 0618a0 + 0382b0

i = 0382a0 + 0618b0

lowasti = (i +

i )2

|i minus i | lt

f2(i ) = f1(i)

f1(i) = f2(i )

f1(i) lt f2(i )

f1(i) Ｈ＞ f2(i )












1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018













1 1870175 1870175 0 1870175 02 2236449 23037539 301 2289198 2363 2594770 2488468 41 2472449 4714 2799490 26963009 369 2674738 4465 2997313 29326489 216 2899909 3256 3201954 3204651 008 3153190 1527 3533703 35218013 034 3441807 2608 4015149 38967811 295 4169584 385



9 4391860 4346589 103 4301738 205 4296327 218 4346589 10310 4968287 4894073 149 4706522 527 4804423 330 4890730 156







5 Conclusion



5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









5

45

4

35

3

25

2

151 2 3 4 5 6 7 8 9 10

Time (month)


times104

Pow

er lo

ad (G

Wh)








Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018





































Journal of












Journal of







Volume 2018






Volume 2018








short-term power load forecasting method based on improved...

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