An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc.

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1 [Type text] [Type text] [Type text] ISSN : Voume 10 Issue 16 BioTechnoogy 014 An Indian Journa FULL PAPER BTAIJ, 10(16), 014 [ ] Study on prediction of type- fuzzy ogic power system based on reconstruction phase space ABSTRACT Juan Zhao *, Lihui Jiang Department of Mathematics and Physics, Hefei University, Hefei Anhui, 30601, (CHINA) Power oad forecasting is the foundation of power system in fu consideration of the characteristics and the natura, socia conditions, using the effective method, based on historica data to determine the technoogy in the future when the oad vaue. Short term power oad forecast is the sun, wee oad. As an important basis for ensuring networ security, economic operation, power short-term oad forecasting accuracy is arranged on, the pan (incuding the units start and stop, hydro therma coordination, tie ine power, economic oad distribution, reservoir operation and equipment maintenance etc.) the premise and the foundation, can improve the eectric power enterprise economic, socia benefits. According to the power oad is difficut to predict accuratey the probem, this paper introduces the interva type- fuzzy ogic method to reduce the prediction error, presents an interva type- fuzzy ogic mode for the time series of one hour of power oad forecasting, and adopted the first modeing process mode structure, and then use bac propagation agorithm to adjust the mode parameters are determined by simuation. The resuts show that, the mode has higher prediction accuracy and practica vaue to a certain extent, the performance is better than that of the corresponding type fuzzy ogic mode, proved more efficient processing idea uncertainty of type- fuzzy ogic method. KEYWORDS Type- fuzzy sets; Prediction; Reconstruction; Forecasting. Trade Science Inc.

2 9300 Study on prediction of type- fuzzy ogic power system based on reconstruction phase space BTAIJ, 10(16) 014 INTRODUCTION The power oad is an unsteady stochastic process, affected by many natura, socia factors, difficut to accuratey predict [1]. The cassica forecasting methods such as consumption, trend extrapoation method, eastic coefficient method, the method of inear regression and time series prediction method has many shortcomings, it is often difficut to get an idea prediction effect []. Therefore, peope give their attention to the gray system, artificia neura networ, waveet theory and fuzzy ogic in artificia inteigence methods, incuding type- fuzzy ogic has the extraordinary abiity of deaing with uncertainty, in the time series prediction has advantage over the artificia neura networ method, and provides a new idea for forecasting of power oad. Power oad forecasting is based on historica oad data as a basis for determining a series of wor in the future when the oad vaue [3]. As an important basis for the reasonabe panning and economic operation of power system, accurate power oad forecasting can improve the eectric power enterprise economic benefit and socia benefit, pays an important roe in promoting the heathy deveopment of the eectric power industry [4]. Power oad forecasting is based on historica oad data as a basis for determining a series of wor in the future when the oad vaue [5]. As an important basis for the reasonabe panning and economic operation of power system, accurate power oad forecasting can improve the eectric power enterprise economic benefit and socia benefit, pays an important roe in promoting the heathy deveopment of the eectric power industry [6]. Power the oad fuctuation has strong noninear characteristics, can be regarded as an unsteady stochastic process, the accurate prediction of the difficuty is very big. The prediction method of the cassica (such as inear regression method, the state space method and time series method) have many shortcomings, it is often difficut to get an idea prediction effect [7]. Therefore, peope oo into some artificia inteigence methods (such as artificia neura networ, genetic agorithm, fuzzy ogic), of which two type fuzzy ogic can effectivey for uncertainty modeing, the origina data with time-varying, uncertain noise can directy used to train the parameters of the system, capacity is better than the artificia neura networ method for the prediction in time series, therefore it is suitabe for eectric power oad forecasting [8,9]. The main disadvantage of fuzzy ogic is the existence of redundancy probem of fuzzy rue base. For a fuzzy system, have proposed a variety of rue base simpification methods, but most of these methods can ony remove the redundant fuzzy rues, and can not effectivey remove the redundant fuzzy sets, fuzzy simiarity in this respect shows unique advantages. Streamine probem type- fuzzy system rue base is few. Liang and Men-de first proposed to optimum seeing methods of interva type- fuzzy rues with the SVD method, obtained better resut, but aso can effectivey eiminate the redundancy in the adverse effect of fuzzy set. In order to improve the accuracy of power oad forecasting, this paper introduced the interva type- fuzzy ogic, the estabishment of interva type two non singe vaued two type Mamdani fuzzy mode is appied to the time series of short-term power oad forecasting, and proposed a ind of SVD-SM-BP hybrid iterative agorithm, can effectivey simpify the redundant fuzzy sets and fuzzy rues, in order to eiminate its adverse effects, to improve the prediction accuracy of the mode, mae up the shortage of SVD method. RELATED THEORY Logic theory of type- fuzzy sets A type of fuzzy set compared with traditiona, capabiity of type- fuzzy sets processing has more uncertainty, but its structure is aso more compex [10]. Defined on a continuous domain on X type- fuzzy set A can be expressed as: A μ ( xu, )/( xu, ) = x X u Jx A (1) In the formua: μ ( xu, ) [0,1] is the membership function; u J A x is the main membership vaues; Jx Union caed the uncertainty of the trace; FOU, the corresponding ower imit set, membership function; formua in the discrete domain, to repace the formua by Σ. A = 1/( xu, ) x X u J x () μ ( xu, ) = 1, so the interva type- fuzzy sets, pay, and fi operations are greaty simpified. Interva type two A interva vaued fuzzy sets of type- fuzzy ogic is the mainstream appication based on [11]. Fuzzy simiarity is the measure of fuzziness of a very wide range of appications, represents a fuzzy set and another fuzzy set simiarity. This paper adopts axiomatic definition of the foowing interva type- fuzzy simiarity, and puts forward the cacuation formua based on the. { μa μb } { μ μ } 1 min ( x), ( x) dx x X N( A, B) = max A( x), B( x) dx x X (3)

3 BTAIJ, 10(16) 014 Juan Zhao and Lihui Jiang 9301 Interva type- fuzzy ogic A definition in the X domain of the two type fuzzy set is as foows: A% = [ μ ( x)] / x = x X u J x [ f (u) / u] / x x X u J x A% x (4) Where: u is the eement of the X main membership vaues, Fx (U) is a membership vaue, the range of Jx u and the uncertainty of a trace (FOU), FOU, respectivey, ower imit of the corresponding membership function. Visibe, two types of fuzzy membership function is three-dimensiona, more than one type of fuzzy membership function of fuzzy set mutipe one-dimensiona, degree of enhancement, but aso increase the compexity of the set and its compement, intersection, so the computationa compexity. The time interva of type- fuzzy set membership vaues are 1, as shown in the foowing formua: A % [ 1/ u ]/ x = x X u J x (5) The fuzzy set of interva type two is a simpified version of the type- fuzzy sets, avoids the choice of membership functions, and the pay, compensation, and cacuation are greaty simpified, so it has practica vaue. The shortcomings of the existing type- fuzzy theory Starting from the ate ninety's, peope graduay reaized the imitations of a type of fuzzy set in the description of mutipe fuzzy uncertainty, maes some students study a type of fuzzy sets have turned to type- fuzzy sets. The J. M. Mende, et a America University of Southern Caifornia professor of type- fuzzy sets are vigorousy promote the improvement and appication of the theoreticay, and the two type fuzzy system has been successfuy used in the noninear and time varying channe homogenization. Since then, two types of fuzzy set theory in the communication, bioogy, finance, automation contro and many other fieds have been successfuy appied. The successfu appication refects with noninear fuzzy uncertainty information of compex giant system modeing and anaysis of appication potentia [1]. For type- fuzzy sets high computation compexity of the probem, Mende et a. Further put forward the concept of interva type- fuzzy sets, namey the type- fuzzy set of two order membership function is defined as the degree of membership for the "1" of the interva vaued fuzzy sets. This concept was proposed to simpify operation type- fuzzy sets, to enhance the abiity of type- fuzzy systems for rea-time appications in engineering, to promote appication of type- fuzzy sets theory. Since then, most appications of type- fuzzy sets theory based on the interva type- fuzzy sets. SHORT TERM POWER LOAD FORECASTING BASED ON INTERVAL Interva type- fuzzy forecasting mode The interva SVD-SM-BP hybrid iterative agorithm of two non singe vaued Mamdani type- fuzzy prediction mode is estabished based on the process is: first to identify the mode input and rues, the number of pieces before after coection of shapes and rues, then use BP agorithm to adjust the parameters of the mode, and then use the interva type- fuzzy simiarity to streamine the redundant rues in the ibrary coection, and finay to the seection of rue by SVD method. (a) Fuzzy controer Fuzzy controer wi enter the exact vaues into intervas of type- fuzzy set, in order to fuy process the oad has a strong uncertainty. Interva two main membership function of fuzzy set seection variance of uncertainty the Gauss function, membership function, as shown in the foowing formua. The mode has 3 input, 1 output, that is, with the first 3 moments of the oad vaues to predict vaues after a moment. * 1 x x μx ( x ) exp = μx σ * 1 x x ( x) = exp σ (6) =3. Where: x* is the exact input vaues, [, ] σ σ is variation range of variance; K =1,... p, is the input dimension, p (b) The rue ibrary In this mode, the form of the rue is as foows. Rue before, after parts are seected interva type- fuzzy sets, membership function is the main function of mean Gauss, uncertain, membership functions such as type (7), type (8) are shown. Each of the front parts of the input space consists of three sets, so the rue base containing M compete =3 * 3 * 3 =7

4 930 Study on prediction of type- fuzzy ogic power system based on reconstruction phase space BTAIJ, 10(16) 014 rue. Due to the adoption of Center - of - sets drop type, it can be set after the piece with (interva set) instead, as shown in eq.: 1 x m σ exp, x m, μfξ ( x) = 1, m x m, 1 x m exp, x m, > σ (7) 1 x m m + m exp,, x σ μfξ ( x) = 1 x m m + m exp, x, > σ (8) (c) Reasoning machine For the two type of interva Mamdani fuzzy mode, the reasoning process is as foows, in the cacuation is set, membership function. 1 μ ( y ) y Y G% = * b f μg ( y), f * μg ( y) b (9) Type: * is the t- norm, the minima operator; μ ( y) G, function; f, f are active set, membership function. μ G ( y) is respectivey after piece is set, membership SVD-SM-BP hybrid iterative agorithm For a coection of highy overapping, can be used to identify the fuzzy simiarity, combined to produce a pubic coection, and then use the pubic coection to repace these overapping set. m = λm + (1 λ ) m q q 1 1 m = λ m + (1 λ ) m q q σ = λσ + (1 λ ) σ q q 3 3 (10) (11) (1) If there are two simiar interva type- fuzzy sets, m, m q q = [59,63] respectivey m, m [65,70] =, the q m m q m = + =, the repacement ensembe FOU mean is shown in Figure 1. mean variance respectivey 6 The front piece equivaent if rue in the rue base obtained by means of merger, deete set in, then ony need to eep one, the consequent parameters and determine the retention rues. SVD-SM-BP hybrid iterative agorithm is proposed in this paper taes three threshod α, β, ρ, the fow chart shown in Figure.

5 BTAIJ, 10(16) 014 Juan Zhao and Lihui Jiang 9303 Figure 1: (a) FOUs of interva type two fuzzy sets F % and q F % Figure 1: (b) FOU of Aternative set F % q Figure : The initia mode by BP agorithm to reguate the parameters of the mode

6 9304 Study on prediction of type- fuzzy ogic power system based on reconstruction phase space BTAIJ, 10(16) 014 Figure is the initia mode by BP agorithm to reguate the parameters of the mode. Assume that after parameter adjustment interva type- fuzzy system rue base with M rue R = {R 1,, R M }, α (0, 1) and the β (0, 1). Type- fuzzy ogic system Type- fuzzy ogic system based on type two fuzzy sets, generay incudes the fuzzifier, rue base, the inference engine, drop type device and the defuzzification part five, as shown in Figure 3, a type of fuzzy ogic system of more than one drop type ins. Compared with the first type fuzzy ogic systems, type- fuzzy ogic system in construction and reasoning mode of the system and there is no significant change, but it is to type- fuzzy sets as a basis, the adjustabe parameter increased, increasing the number of degrees of freedom can be adjusted, so as to obtain the better abiity of handing uncertainty. Ordinary the two type of fuzzy ogic system, reaize the difficut and compicated cacuation, appication of interva type- fuzzy ogic system can reduce the amount of cacuation, and simpifies the reasoning process. Figure 3: The inference engine, drop type device and the defuzzification Adjusting the prediction mode parameters According to the way of input-output data to estabish a fuzzy ogic system has inds: one ind is the first by the input and output data to generate fuzzy rues, then seect the fuzzy inference machine, fuzzy controer and fuzzy soution is to construct the system; another is the first to identify the structure of fuzzy ogic system, part or a of the free parameters change in the structure of the system, and then through some parameter earning agorithm (such as the bac-propagation agorithm) to determine these free parameters. In the construction of a fuzzy ogica system, if the seection of the singeton fuzzifier, Max product composition, product definition and highy defuzzifier, can be used to describe the system type: M p y μ ( x ) F M = 1 = 1 ( ) = s( ) = = ( ) M p ϕ = 1 μ ( x ) F = 1 = 1 yx f x y x (13) Visibe, a type of fuzzy ogic system can be seen as the fuzzy basis function expansion, the fuzzy basis function and fuzzy rues are in correspondence. EXPERIMENTAL RESULTS The simuation and verification Seects the city in August 1, 013 to August 31st a houry oad data as time series prediction, a tota of 744 data, of which the first 504 data (1 days before the data) is used to adjust the parameters, 40 months after the data (after 10 days of data) used to test resuts.

7 BTAIJ, 10(16) 014 Juan Zhao and Lihui Jiang 9305 The prediction accuracy of the two modes with the average reative error is shown in the formua to evauate the absoute vaue: N 1 f x E = N s ( + 1) i= 1 ( ) ( ) s( + 1) (14) Type: s (K + 1) is the actua data, f (x ()) is a mode to predict the data, is the mode input data. The prediction resuts of the two modes are shown in Figure 4. Figure 4: The prediction resuts of the two modes From the modeing process and the prediction resuts can be nown, non singe vaued type Mamdani fuzzy ogic mode with 3*3*3 = 7 rues, a tota of 1*3 + *3* 7 + 1*7 = 19 design parameters, incuding input set variance sigma K, before rue set of mean m and variance sigma L K, consequent of a rue set center of mass Y L, and the error between the true vaue of the predictive vaue of 3.67%. in the same number of rues, interva type non singe vaued design parameters of two type Mamdani fuzzy ogic mode has a tota of *3 + 3* 3*7 + *7 = 303, incuding input set variance sigma K, before rue set M - L K and M - mean L and variance sigma L K, the consequents of the rues set Y - L and Y - the center of mass L, more adjustabe parameters means more adjustabe degree of freedom therefore, the prediction performance is improved, the error decreased to 3.18%. From Figure 4 can be seen, the prediction curves of the two modes are better to trac actua oad curve, and the interva of a non singe vaued type two The prediction vaue of Mamdani fuzzy ogic mode is cose to the actua vaue, especiay has higher precision in near the pea, indicating that the prediction mode has certain practica vaue in the fied of eectric power oad The design of the prediction modevia type- fuzzy ogic We can see from the process of modeing and simuation resuts: a mode with 3 * 3 * 3 = 7 rues, a tota of 1 * 3 + * 3 * * 7 =19 design parameters, incuding input set variance parameter K, before rue set mean parameter m and mean variance parameters sigma L K, gauge after pieces of centroid parameters of YL set, the predictive vaue and the actua vaue of the average reative error between the absoute vaue of 3.44%. With the same number of rues, mode two design parameters than the mode a more, a tota of x 3 +3 x 3 x 7 + x 7 = 303, incuding input set variance parameter K, before rue set mean parameter m and the mean variance parameter L K, rue consequent matter cardiac parameters of Y L set, this means that the mode two has more adjustabe degree of freedom, and thus improve the prediction accuracy, the prediction error is down to 3.16%; the mode three with SVD method in mode two is based on rejecting the bad rues, further improve the prediction accuracy, ony 1 rues, which maes the prediction error is reduced to.98%. The mode of three phase ratio, mode four first maes use of simiarity and eiminates the redundant rues in the ibrary coection in the merger process, redundant set, produced the same rues of the former parts, the merger wi reduce the number of rues, and then on this basis, using the method of SVD seected the most important rues for rue base, further "downsizing", and improve the prediction accuracy, ony with 8 rues, so that the prediction error is reduced to.80%. Figure 5 and Figure 6 in the simuation curve is aso verified the above anaysis, to the 4 mode can be used to trac the actua oad

8 9306 Study on prediction of type- fuzzy ogic power system based on reconstruction phase space BTAIJ, 10(16) 014 curve, but the mode two prediction curve than the mode coser to the actua oad curve fitting, mode three better performance than the mode two, and mode fitting performance of four of the best. Figure 5: The actua vaue of the average reative error vaue of 3.44% Figure 6: The actua vaue of the average reative error vaue of 3.16% CONCLUSIONS Power oad SVD-SM-BP hybrid iterative agorithm based on mode prediction, it has higher forecast precision, better abe to trac the actua oad curve in eectric power oad forecasting, the fied has a good appication prospect. Compared with the SVD-BP hybrid iterative agorithm, SVD-SM-BP hybrid iterative agorithm much streamining the process redundancy of set, so it has the disadvantage of arge amount of cacuation, but it too the ean capacity stronger, not ony reduced the redundancy in the mode set, improve the rues of interpretation, but aso a greater degree of reduced the number of rues, and thus a greater extent reduces the adverse effects of redundancy and improving the accuracy of approximation mode. Fuzzy simiarity is an important measure of the degree of simiarity between two fuzzy sets, using the fuzzy simiarity to simpify fuzzy system rue base, has the advantages of simpe and easy to understand, accord with human thining. In the system modeing, BP agorithm is sensitive to initia vaue, improper initia vaue wi affect the precision of the mode, to get the optima initia vaue is an urgent probem to be soved. ACKNOWLEDGEMENT The wor was supported by the Found of Nationa Natura Science Fund Project ( ), and Anhui Province University Natura Science Fund (KJ013B34)), and Hefei University appied mathematics ey construction discipines (NO.014XK08).

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