Application of Fuzzy-Flower Pollination Algorithmfor Peak Load Forecasting on National Holiday

— Application of Type-2 Fuzzy Logic System (T2FLS) has became attention for a short-term load forecasting problems solution. This paper presentsapplication optimization membership function of antecedent (X,Y) and consequent (Z) interval type-2 Fuzzy Logic System using Flower Pollination Algorithm (FPA) for short-term load forecasting on national holiday. This method has being implemented on the historical peak load data during 14 national holidays case study in Jawa-BaliIndonesia electrical power system in 2011. Flower Pollination Algorithm (FPA) will be applied to optimize interval Footprint of Uncertainty (FOU) membership functions of interval type-2 fuzzy logic system. The test result showed Main Absolute Percentage Error (MAPE) is less than type-2 Fuzzy Logic System (FLS) and optimization type-2 FLS-Big Bang Big Crunch Algorithm. Finally, this paper defined Main Absolute Percentage Error (MAPE) 2.040612143% for type-2 FLS, 1.279257143% for optimization type-2 FLS-Big Bang Big Crunch Atgorithm and 1.091543571% for optimization type2 FLS-Flower Pollination Algorithm.


A. Interval Type-2 Fuzzy Set
IntervalType-2 FuzzySet (IT2FS) is denoted . is membership function with ∈ and ∈ ⊆ 0,1 . Characteristicof IT2FS can be recognized on the following equation: Primaryvariable x which has domain X; ∈ , secondary variable, have domain for each ∈ ; is expressed primary membership of . iscombination of all primary membership ( ) which is expressed the Footprint of Uncertainty (FOU) of . The equation can be seen as follows: Jx is interval with the following equation: From equation FOU ( ) can be expressed by the equation:

B. Interval Type-2 Fuzzy Membership Function Operations
Interval type-2fuzzy set operation which is represented by FOUis doneby using two intervalsthat isUpper Membership Function (UMF)andLower Membership Function (LMF). Operation onmembership function fuzzy interval type-2can be seen on figure3:

C.Kernik Mendel Algorithm
On interval type-2 fuzzy, processof searching the centroid can be doneby using Kernik Mendel Method.This searching methodis formulatedas follows: Switch point of L and R are as follows: The searching ofcentroid value is doneby following equation:
is gamma standard function, andthis distributionis appliedto 0 step. Then,local pollinationand flower constancy can be represented as: j andx t k arepollen from different flowersof similar plant species. This rule imitates flower constancy phenomenon in limited environment. Mathematically, ifx t k andx t k come fromsimilar population, then this rule becomesrandom walklocalif we take from uniform distribution [0,1].

IV. PEAK LOAD FORECASTING ON NATIONAL HOLIDAY USING IT2FL-FLOWER POLLINATION ALGORITHM
There are three steps which is done toapply fuzzy type 2-flower onpeak loadforecasting onholidaynationalthat ispre-processing, processing and post-processing [7].

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( 1 2 )   (13) maxSD(i) ispeak load on holidayandmaxWDisthe average of maximum load 4 daysbeforeholiday. After thatcalculate the Typical Load Difference (TLD MAX (i))that isaveragingthe peak load of LD MAX (i) which is similarin previous year.Then looking forVariation Load Differencethat isthe differencebetween Load Difference (LD) fromTypical Load Difference (TLD MAX (i))withfollowingequation: ( 1 4 )  (15) To calculate Max WD and LD max based on (12) and (13) equations can be seen on Table 1and Table 2. The rule of fuzzy IF-THEN is used inthis methodtoforecastpeakloadwhich is declared as follows: IF X is A i AND Y is B i THEN Z is C i X and Y inputs byusing IT2MF Editor infuzzificationdesign, there are 11 membership functionswhich are used [7], that is:

Negative Very Big (UNVB and LNVB) Negative Big (UNB and LNB) Negative Medium (UNM and LNM) Negative Small (UNS and LNS) Negative Very Small (UNVS and LNVS) Zero (UZE and LZE) Positive Very Small (UPVS and LPVS) Positive Small (UPS and LPS) Positive Medium (UPM and LPM) Positive Big (UPB and LPB) Positive Very Big (UPVB and LPVB)
Examples of fuzzy rules can be seen in Table 3.

can be seen as follows: [R1] IF X is NVS AND Y is NVS THEN Z is NVS [R2] IF X is PVS AND Y is PVS THEN Z is PVS [R14] IF X is ZE AND Y is PVS THEN Z is PVS
In choosing fuzzy set using max rule is by taking the biggest valuewhich is appropriate withmembership degree (μ) of input variable (X, Y) and output (Z) on New Year can be seen inTable 4.Valuewhich is madeinto input to X, Y and Z variables areVLDmaxfromholiday data.X isVLDmax (i) fromsimilar holidaybefore forecasting year. Y isVLDmax (i) fromholidaywhich is adjacentin forecasting year. Z is forecast of VLDmax (i). Variablevalue of X,Y and Z is madeasdividerto LMF and UMF parameters.After that, parameter value of LMF and UMF on FOU is optimizedbyusing flower pollination algorithm. X,Y and Z variables can be seeninfigure6,7 and 8.Flowchart of fuzzy type 2-flower pollination algorithm on peak load forecastingon national holidaycan be seen infigure 5.

C. Post-Processing
The next process islooking forforecast load differencevalue which can be declared as follows: ( 1 6 ) Thenpeak load forecastingon national holidaycan be calculated as follows: ( 1 7 ) To find outthe accuracyofproposed methodthenused absolute error equation. The smaller error which isobtainedindicatesthe used methodis better. Absolute error equation as follows:

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( 1 8 ) 100% ( 1 9 )  V. RESULT AND ANALYSIS The calculation results of forecasting error Type-2 Fuzzy Logic-Flower Pollination Algorithm using data from various types of load conditions on holidays where this result is just a case of forecasting in 2008 show in Table 5 and 6. The test results by using IT2FPA method as a proposed method for load forecasting have Mean Absolute Percentage Error (MAPE) is 1.091543571%. By using IT2FL, MAPE is 2.040612143%. By using IT2FLBBBC, MAPE is 1.279257143%.
VI. CONCLUSIONS Interval Fuzzy Logic Type-2 method which is optimized by using Flower Pollination Algorithm proposed in this research can be used to forecast the peak load during some holidays in Jawa-Bali system, Indonesia.The method has MAPE which is less than 2%. The method is very useful for operators to set up different scenarios for forecasting method.
ACKNOWLEDGMENT Authors would like to thank Power System Operation and Control Laboratory, SepuluhNopember Institute of Technology (ITS Surabaya), for supporting this research.