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Regresyon analizi ve yapay sinir ağı yöntemleri ile uzun dönem yük tahmini

Long term load forecasting using multiple regression analysis and artificial neural network

  1. Tez No: 100993
  2. Yazar: FATİH AKSEL
  3. Danışmanlar: DOÇ.DR. BELGİN EMRE TÜRKAY
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2000
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 93

Özet

ÖZET Elektrik enerjisi üretim, iletim ve dağıtım sistemleri planlamalanndaki amaç, tüketicilere kaliteli ve ucuz elektrik enerjisi sağlamaktır. Enerji sistemi planlamasının ilk adımım da yük tahmini oluşturur. Gerektiğinden düşük yük tahminine dayalı planlamalar, elektrik enerjisinin güvenilirliğini ve kalitesini düşürür ve tüketiciye sunulan enerji arzının kısıtlanmasına neden olur. Bununla birlikte, gereğinden fazla yük tahminine dayalı planlamalar da düşük kapasiteli ve ekonomik olamayan işletme koşullarına neden olacaktır. Enerji sektörüne yapılan gereksiz büyük yatırımlar mali sıkıntılara yol açacaktır. Genel olarak, yük tahminleri, kısa, orta, uzun dönem yük tahminleri şeklinde üçe ayrılır. Tezde yedi yıllık bir süreyi kapsayan uzun dönem yük tahmini çalışması yapılmış, Türkiye ve İstanbul' un 2001, 2003, 2005 yıllan puant yük ve enerji tüketimi tahminleri yapılmıştır. Bu tahminler için çok değişkenli regresyon analizi, geriye yayınım algoritmalı yapay sinir ağı uygulaması kullanılmış, bu iki yöntemin sonuçlan birleştirme yöntemlerinden biri olan ağırlıklı ortalama yöntemiyle tek sonuca dönüştürülmüştür. Türkiye için, 1980-1998 yıllan arası nüfus, kişi başına düşen gayri safi milli hasıla, büyüme hızı, sanayi üretim endeksi ve petrol varil fiyatı değerleri, İstanbul için 1989-1998 yıllan arası nüfus, kişi basma düşen gayri safi milli hasıla, petrol varil fiyatı ve elektrik enerjisi birim fiyatı değerleri ile bu yıllara ait puant yük ve enerji tüketimi değerleri arasında ilişki kurulmuştur. Daha sonra 2001, 2003, 2005 yıllarında yukandaki girişlerin alacağı değerlere göre puant yük ve enerji tüketimi değerleri tahmin edilmiştir. Maksimum hata, ortalama hata ve ortalama mutlak hata değerleri her yöntem için hesaplanmış ve karşılaştınlmıştır. Üç yöntem için tüm işlemlerde MATLAB 5.0 kullanılmış, yöntemlere ait m- dosyalan yazılmıştır. vuUygulanan yöntemler sonucunda Türkiye ve İstanbul tahminleri aşağıda verilmiştir. Tablo 1 : Türkiye tahmini sonuçlan. Tablo 2 : İstanbul tahmini sonuçlan. via

Özet (Çeviri)

LONG TERM LOAD FORECASTING USING MULTIPLE REGRESSION ANALYSIS AND ARTIFICIAL NEURAL NETWORK SUMMARY The aim of power generation, transmission and distribution is providing consumers, high quality and cheap energy. Power system planning, based on load forecasting which is less than necessary causes reduce in reliabilty, quality and putting under restraint of energy demand. However, the planning based on load forecasting which is much than necessary causes low capacity and uneconomic operation of power systems. Therefore, big investments cause financial problems. In general, load forecasting can be divided into three categories. Short-term load forecasting covers the scale of half-hour to one month. Daily demand charecteristics are determined on-line. The most important data is weather conditions. Medium-term load forecasting ranges from one month to seven years. It involves scheduling fuel deliveries and maintenance operations, operating plants, financial planning and tariff setting. Transmission, distribution systems and small generation (cumbussion- turbine) and mobil power plants that can be accomplished in near future are planned. Finally, long-term load forecasting covers from seven years up to thirty years ahead. It involves generation, transmission and distribution planning. It is concerned with macroeconomic aims, politics, and social chance of regions, country or world. A lot of methods are used for long-term load forecasting. In this paper, multiple regression analysis and artificial neural network are applied for Turkey and Istanbul. Maximum load and energy demand for the years of 2001, 2003 and 2005 are forecasted. The values of population, GNP per capita, growth rate, production index of industry and crude oil price are used as inputs between 1980 and 1998 for Turkey. The values of population, GNP per capita, crude oil price and electrical energy sales IXprice are used as inputs between 1989 and 1998 for Istanbul. Weighted averages method is applied as combining technique to obtain one forecast from two. Maximum error, mean error and mean absulate error are compared. MATLAB 5.0 is used for three forecasting methods and m-files are written. The matrix aproach of multiple regression analysis is used. In regression analysis, the eguality, T=X*B (1) between input and output is obtained where X=[l P]. P is the input matrix, called independed variables, consisting of population, per capita GNP, growh rate etc. T is the output matrix, called depended variables consisting of maximum load and energy demand. The aim is obtain matrix B that ensures relation between input and output. But, there is always an error term represented by s, therefore equality (1) must be written as, T = X*B+s (2) In matrix form, Tn Tu. T21 T22. i TV,T, yl ly2-.T".Ta 1 P11 P12 Pip 1 P21 P22 Pip Pyl Py2- yp Bu B12 Bu B21 B22 Bît Bfix-tti Bi (p+l)l D(p+i)2...D(p+l)t Bf, Sll En E,t 62i E22 S2t Byl 6y2 Eyt (3) In formula (3), Bn, B2i, 3 which are in fist column of B matrix are called intercepts, others are called slope coefficients. If we consider W as W = XT*X (4) B matrix is obtained below,B = W~1*XT*T (5) If we take Tf as error ignored output, s = T-Tf = T- X*B (6) The coefficient of determination (R2) and t coefficients are obtained also. Four layer(two hidden layer) feed forward neural network is used for backpropagation algorithm(BP). BP is designed to adjust weights and biases to minimize the mean squared error between the output and actual values. In general four layer neural network is given below, Output i Input i Input 2 Input 3 Input p Target 1 Target 2 Target 3 Outputt I Targett 2.Hidden Layer Output Layer Input :l2,q Input : ^ Output : «t^q Output : «P^ knodes tnodes Comparison Figure 1 : Four layer neural network. A big problem of constructing a neural network is to determine the number of neurons(nodes) in hidden layers. For this problem, a formula is given. For first bidden layer, SI = ncolsP+ncolsT+1 (7) XIS2 = ncolsT+3 (8) where ncolsP is the column numbers of P matrix and ncolsT is the column numbers of T matrix. Logistic function is used as transfer function that has a relation between input and output is 0=1./(l+e^*0) (9) where a is the slope constant. Scale command is used for normalization inputs and outputs and to range them between 0. 1 and 0.9 in MATLAB. Weighted averages method is the one of combining techniques. According to this method, if there are k forecasting method, x.(1), Xt(2), »x.**, combined forecast is obtained from formula given below. xt = 2>i*xt(i) (10) where Xt(,) is the forecast for the period t from frocasting method i and Wi is the weight assigned to method i. Some methods are given by Newbold and Granger to find optimal weights. One of them is t-l k t-1 wi= [ItfV0)2 )] /IE(r>W ] (ii) s=l j=l s=l where y > 1 and if x is taken as the actual values et(i) =(x-xt®)/x (12) Fortius method, y is taken as 1.0, 1.5 and 2.0. xuTurkey's forecasts for the years of 2001, 2003 and 2005 are given below. Table 1 : Forecasting results of Turkey In regression analysis, the coefficient of determination and t coefficients are found. R2= 0.9921 0.9932 t = [-1.0646 0.0228 -0.3000 -1.6328 -0.1872 -0.3603 -4.3109 -5.2711 7.5769 9.5991 3.0591 3.2219] R2 is quite near to 1.0, therefore error is small. According to t distribution, production index of industry is the most effective to find output especially for energy demand and GNP for capita is the most ineffective. In backpropagation algorithm, smaller errors are obtained compared with regression analysis. Desired output is reached in 17402 epochs. In combination method, maximum load and energy demand are found for y - 1.5 where mean absolute value is smallest between results of y = 1.0, 1.5 and 2.0. Results of Turkey are shown in figure 3 for three methods. xmx ıgfc: Actual Value.: Regression >: Neural Network +:Combination 1980 1S Tim e(Y ears) 2005 Figure 2 : Forecasting results of three methods for Turkey. Istanbul1 s forecasts for the years of 2001, 2003 and 2005 are given below. Table 2 : Forecasting results of Istanbul. In regression analysis, the coefficient of determination and t coefficients are found. XIVR2 is quite near to 1.0 but not as much as Turkey application. According to t distribution, population is the most effective to find output especially for maximum load and crude oil price is the most ineffective. In backpropagation algorithm, smaller errors are obtained compared with regression analysis like Turkey application. Desired output is reached in 7581 epochs. In combination method, maximum load and energy demand are found for y = 1.0 where mean absolute value is smallest between results of y =1.0, 1.5 and 2.0. Results of Istanbul are shown in figure 3 for three methods. x 10ti'. Actual Value ^Regression >:Neural Network +:Combinatton 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 Tim e(Y ears) Figure 3 : Forecasting results of three methods for Istanbul. First step of forecasting is to determine inputs. Then, the relation between inputs and outputs are found by some methods and errors are minimized as much as possible. It is consider that less error means better forecasting. But, this is not always correct idea. Uncertainty increases depending on time scale of forecast. Inputs of future are also forecasts. Therefore, results must be scrutinized by the time depending on change of inputs. In weighted averages method, aim is to minimize error. Therefore, the graph of combination method results tends to artificial neural network's graph which has less errors compared with regression analysis's results. XV

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