LONG TERM ENERGY CONSUMPTION FORECASTING USING GENETIC PROGRAMMING

Journal Mathematical and Computational Applications

-Vol. 13, No. 2, pp. 71-80, 2008. Publisher

-Celal Bayar Universitesi Impact factor

- 1.472

Authors Korhan Karabuluta,

-Department of Computer Engineering, Yasar University, Turkey Ahmet Alkanb, Ahmet S. Yilmazb - Department of Electrical and Electronics Engineering- Kahramanmaras Sutcu Imam University, Kahramanmaras, Turkey

Abstract The most important part of electric utility resource

planning is forecasting of the future load demand in the regional or national service area

This is usually achieved by constructing models

on relative information, such as climate and previous load demand data

In this paper, a genetic programming approach is

proposed to forecast long term electrical power consumption in the area covered by a utility situated in the southeast of Turkey. The empirical results demonstrate successful load forecast with a low error rate.

INTRODUCTION Load forecasting is a requirement for successful

load management Makes possible the trustiest planning for future long term load forecasting is guidance for maintenance of electricity installations and construction planning power system engineers and electricity generation/distribution utilities attach importance to load forecasting

Cont.. long term forecasting, forecast time varies

between 1 and 10 years

power system planners require the mid and long

term load forecasts to make decisions about planning the mid and long term maintenance, preparing the future investment schedules and developing the generation , transmission and distribution systems

Cont.. Planning of future investment for the

constructions depends on the accuracy of the long term load forecasting considerably In this paper, present a genetic programming approach on the forecasting of long term electrical power consumption of a moderate city in Turkey Genetic Program usage through symbolic regression using annual data of the previous years.

METHODS OF FORECASTING AN UNKNOWN FUNCTION curve fitting

data and determined Methods for curve fitting -Interpolation =exact fit of the existing data points-regression permitted. =approximate fit can be

A function is decided to fit the coefficient should be

Acceptability of the model Sum of absolute difference

Mean absolute error Absolute percentage error Sum of squares due to error (SSE) Mean squared error Root mean squared errors most widely using = SSE (squares of vertical

distance of the points in a curve)

Genetic Programming and Symbolic Regression Aim is to search a functional representation of a

model GP searches for the model and coefficients of the

model at the same time. GP simultaneously works on a group of possible

solutions instead of a single solution. Since the original function is unknown, GP

searches for an approximate hence, an acceptable solution

Some basics in GP individuals are represented as trees.

Elements of the trees are functions and terminals Fig.1 shows the representation of the simple

expression, x*y+x/2.

Five major preparatory steps(1) Predefined set of terminals, (2) Predefined set of primitive functions, (3) A fitness measure (called a fitness function to specify what needs to be done) (4) The parameters for controlling the run, such as population size, reproduction operators, probabilities of the operator and so on (5) The method for designating a result and the criterion for terminating a run

Algorithm

Cont.. Reproduction: Reproduce an existing individual

by simply copying it into the new population. Crossover: Create two new individuals by

genetically recombining randomly chosen parts of two existing individuals using the crossover operation. Mutation: Create one new individual from one

existing individual by mutating a randomly chosen part of the individual.

Example of crossover operation

example of mutation operation

Input DataYears 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Input Data(MWh) 583,835,150 694,312,077 851,470,138 1,071,627,809 1,212,078,708 1,275,954,531 1,395,583,698 1,440,110,142 1,543,594,161 1,569,570,225 1,585,366,488 1,671,939,175

LOAD FORECASTING USING CURVE FITTING Curve fitting tool of Matlab can be used to fit data

using polynomial and power equation FOR POLYNOMIAL -4th degree polynomial is f(x) = p1*x4+ p2*x3+ p3*x2+ p4*x+p5 -Then can calculate the coefficient (p1,p2,p3,&p4)using the tool -By using resulting equation can predict the next years load and error

Curve Fitting using Polynomial Eqn

Input Vs Model DataYears Input Data(MWh)Output of the polynomial model

Error %

19941995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

583,835,150694,312,077 851,470,138 1,071,627,809 1,212,078,708 1,275,954,531 1,395,583,698 1,440,110,142 1,543,594,161 1,569,570,225 1,585,366,488 1,671,939,175

571,222,169714,291,378 875,475,063 1,036,021,424 1,182,096,795 1,304,785,652 1,400,090,607 1,468,932,413 1,517,149,960 1,555,500,277 1,599,658,531 1,672,180,280

0.02160.0288 0.0282 0.0332 0.0247 0.0226 0.0032 0.0200 0.0171 0.0090 0.0090 0.0010

Cont

p1=2.049, p2=-5.175, p3=3.498,

p4=0.7127,p5=0.4699

SSE value = 0.00608797

Predicted values using polynomial curve fittingYears Output of the polynomial model

20062007 2008

1,792,690,2121,997,504,667 2,320,009,115

20092010

2,800,469,4153,484,069,565

Curve fitting using power equation FOR POWER EQUATION

- f(x) = a(x)^b+c

-After determining coefficient can form the model with prediction error

Curve Fitting using power Eqn

Input Vs Model DataYears Input Data(MWh)Output of the power Eqn model

Error %

19941995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

583,835,150694,312,077 851,470,138 1,071,627,809 1,212,078,708 1,275,954,531 1,395,583,698 1,440,110,142 1,543,594,161 1,569,570,225 1,585,366,488 1,671,939,175

529,963,176762,699,648 926,630,360 1,057,477,084 1,168,185,943 1,265,107,087 1,351,886,289 1,430,833,849 1,503,517,209 1,571,054,560 1,634,274,951 1,693,812,141

0.09230.0985 0.0883 0.0132 0.0362 0.0085 0.0313 0.0064 0.0260 0.0009 0.0308 0.0131

Cont. a=1.914, b=0.3409, c=-0.3431. SSE value = 0.02194693

Predicted values using power Eqn curve fittingYears 2006 2007 2008 2009 2010 Output of the power Equation model 1,750,162,789 1,803,724,223 1,854,819,876 1,903,716,971 1,950,639,142

APPLICATION OF GENETIC PROGRAMMING TO LOAD FORECASTING GPLAB Toolbox in Matlab used for getting the

symbollic Model of the Data Identify the set of terminals. T = {X}. identify the set of functions . F = {+, -, *, %, SIN,

COS, EXP, RLOG}. The combinacin funcional set will identified by

using the genetic algorithm (slide No 14)

Parameters used in the genetic programming applicationParameters Genetic operators Selection method Tournament size Operators Fitness function Value Crossover and mutation Tournament 25 rand, plus, minus, times, mydivide, mypower, sin, cos, log Sum of absolute difference between the expected output value and the value returned by the individual

Number of generations 200 Population size 200

Function model using symbolic Regression The creation of this initial random population of functions is

a blind random search of the search space of the problem Example (+ (* 0.234 Z) (- X 0.789)), (* (* Z Y) (+ Y (* 0.314 Z))). Each individual computer program in the population is

measured in terms of how well it performs in the particular problem environment. This measure is called the fitnessn measure. In our problem every function is evaluated using the year ,

The difference between evaluated value and given value gives the error,By using these error can calculate the SSE

Cont.. If the termination criteria didnt met (here it is 200

generation),the next population will create using the following operations Reproduction

-The best fitted function directly transferred to the next generation

Cont. Crossover

- Assign some probability based on fitness to the previous population for the occurrence of crossover -two parental function selected based on probability -select a part on each function randomly -interchange each part and produces two new offspring Example Parents (+ (* 0.234 Z) (- X 0.789)) & (* (* Z Y) (+ Y (* 0.314 Z))).

Cont.. Suppose that the crossover points are the * in the

first parent and the + in the second parent (+ (* 0.234 Z) (- X 0.789)) & (* (* Z Y) (+ Y (* 0.314 Z))) The resulting offsprings are

(+ (+ Y (* 0.314 Z)) (- X 0.789)) & (* (* Z Y) (* 0.234 Z))

Cont. Mutation

-Here the selection of parent is same as mentioned in the cross over operation -After selecting one parent ,randomly chose a part in the function -The selected part should change with an part which is randomly selected

Cont. Example

parent Offspring

Cont..

By using the newly generated population the

process (fitness measure & new generation population)should be repeated until the termination criterion would met

Input Vs Model DataYears Input Data(MWh) Output of the GPmodel

Error %

1994 19951996 1997 1998 1999 2000 2001 2002 2003 2004 2005

583,835,150 694,312,077851,470,138 1,071,627,809 1,212,078,708 1,275,954,531 1,395,583,698 1,440,110,142 1,543,594,161 1,569,570,225 1,585,366,488 1,671,939,175

582,237,085 730,416,316849,058,233 1,074,374,233 1,209,824,362 1,312,746,495 1,395,695,795 1,465,610,216 1,540,809,210 1,540,302,306 1,604,301,096 1,675,694,099

0,0027 0,04940,0028 0,0026 0,0019 0,0280 0,0001 0,0174 0,0018 0,0190 0,0118 0,0022

Genetic programming fitting of data

Predicted values using genetic programming modelYears2006 2007 2008 2009

Output of the genetic programming model1,767,946,313 1,888,205,855 2,036,490,833 2,205,872,493

2010

2,384,744,357

Comparison of three methods

SSE values of the three methods

Comparison of forecasts produced by three methods

CONCLUSION Long term power consumption forecasting can

provide important information for power distribution centers. As seen from the data, power consumption is in this city is rapidly growing, therefore accurate forecasts can help authorities to make reliable plans. The goodness of the fit produced by the genetic programming method is evaluated using SSE method, which is better than the other two methods of regression.