A Linear Regression-Based Study for Temperature ... - IEEE Xplore

A Linear Regression-Based Study for Temperature Sensitivity Analysis of Iran Electrical Load S.M.Moghaddas-Tafreshi [email protected]

Mahdi Farhadi [email protected]

K.N.Toosi University of Technology-Electrical Engineering Faculty University of Birjand -Power Engineering Department Abstract-In this paper sensibility of Iran network load to the temperature has been studied by the linear regression method. The linear regression analysis of Iran’s electrical load recognizes that the load pattern is heavily dependent on temperature, and finds a linear function between the load and the network’s temperature. This study shows that temperature has a great effect on Iran’s network load, so that daily electrical load of Iran is function of the minimum, average and maximum temperatures of the forecasted day and the day before forecasted day too. Finally this paper shows that suitable input variables which can consider the temperature effect on Iran forecasted load in the Short Term Load Forecast (STLF) model are minimum, average and maximum temperatures of the forecasted day and the day before forecasted day. This analysis can be extended to all of the other environmental factors such as humidity, wind velocity and weather overlay too. Also this study can be performed for the other entire countries electrical network. It is worthy to say, the thermal model which has been designed based on this study has been tested in extended STLF soft wares of Iran and their relative papers which have been written by the authors , have been accepted in some of the other international conferences. Keywords- load forecasting, neural networks, linear regression, correlation ,similar days

1-INTRODUCTION Electricity demand which equals the electricity load in the absence of blackouts or load shaving is highly inelastic since it is a necessary commodity and has a strong deterministic component due to seasonal effects on daily, weekly, and yearly time scales. The strongest source of variation (after seasonality has been removed) is temperature. The relationship between demand and temperature is nonlinear, with demand increasing for both low and high temperatures. [1] The range of possible approaches to the forecast is wide. Usually the only possibility is to take a macroscopic view of the problem, and try to model the future load as a reflection of previous behavior. This still leaves open space to very different solutions. [2] The range of approaches for generating forecasts includes semi parametric regression[3], [4],[5],time series modeling[6],exponential smoothing[7],Bayesian statistics[8],[9]time-varying splines[10],neural networks[11],[12],de-composition techniques[13],[14],transfer functions[15],grey dynamic models[16],and judgmental forecasting[17]. Diverse methods for short term load forecasting have been tested with different degrees of success. [18] In the case of a large variation in temperature compared to that of the previous year, the load also changes accordingly.

978-1-4244-1706-3/08/$25.00 ©2008 IEEE.

In such a case, there would be a shortage of similar days' data and the task of forecasting the load would become harder. Conventional methods mainly concentrate on the development of efficient methods for the selection of similar days. [19] In general, the load based on several selected similar days is averaged to improve the accuracy of load forecasting. However, if there is a considerable error between the load on a forecasted day and that on similar days, it would be difficult to expect accuracy in prediction. [19] Actually, variable nonliner factors such as weather, periodic daily, weekly and seasonal changes have some effects on short term load forecasting (STLF). So, studying about short term load forecasting has its own difficulties. [20] STLF is a key issue for reliable and economic operation of power systems. STLF usually consists of the prediction of the load demand for one hour up to one week ahead. [28] In recent years, public acceptance of, and demand for, summer air conditioning has introduced a new and volatile factor in load variability. And in many systems, summer air conditioning has resulted in a change from winter to summer annual system peak load. [29] There is a strong correlation between the behavior of power consumption and weather variables such as temperature, humidity, wind speed, and cloud cover. [33] The change of temperature during spring, fall, and winter is small. Therefore, its effect on the load patterns can be passed over. However, during summer, the electrical load demand is significantly increased due to many uses of the air conditioners resulting from the high temperature. [30] It is important to note that the accuracy of the load forecasting during a summer season drops without the consideration of a close relationship between the temperature and the load. This problem can be solved out by analyzing the temperature sensitivities applied to the load forecasting. [30] This paper describes linear regressionbased method for the analysis of temperature effect on daily electrical load of Iran power network. Studying temperature is actually one of the fundamentals for choosing suitable samples in order to train neural networks for short-term forecasting. The method presented for choosing suitable samples according to temperature and other effective factors on Iran’s load have been experimented by specialists and the results were successful. [20,21,22,23,24,25,26,27] Although in the presented paper because of not having the information on humidity, cloud overlay, and wind speed,we have only analyzed the load sensitivity towards temperature which is actually the most effective environmental factor, but the presented method is applicable for all factors. The discussed studies are over a 10 year period from 1373

until 1383 and the results presented in this paper.

indicates the proportion of the total variation in y that is explained by the fitted model. An of, say, 0.9 indicates that 90% of the variation in can be explained by the linear regression model. R-square is calculated as :

(1)

2- LINEAR REGRESSION METHOD Linear regression is one of the most commonly used methods for load forecasting. The process is exactly specified by a linear equation: Yi = β 0 + β 1 X i1 + ... + β p X ip + ε i (1) th

where Yi is the output in the i trial with i = 1,..., n, where n denoted as the sample size, the values X i1 , X i 2 ,..., X ij are

j th of p, j = 0,..., p th independent variables associated with the i output , the nonobservable random variables ε 1 , ε 2 ,..., ε n are random error the observed

value of the

term with E {ε i } = 0 and variance

σ 2 {ε i } = σ 2

and

βj

are unknown parameters to be estimated . The process can be modeled by:

Yi = β 0 + β 1 X i1 + ... + β p X ip

SSR = r2 = SST

2

¦ (Y

2

i

i =1 n

(5) i

−Y )

where Yˆi is the estimated value for Yi , i.e., Yˆi = β X i ⋅ r is always between 0 and 1. We used to judge whether the assumption that a linear model could be fitted to the historical data was valid or not. To further assess the quality of the regression model, residuals can be analyzed. Note that the regression model assumes that the measurement errors are independent and Gaussian, and therefore, it is expected that the residuals are normally distributed . [31,32] T

2

3 –TEMPERATURE EFFECTS ON IRAN DAILY ELECTRICAL LOAD

(OLS). By using OLS, the regression coefficient estimations are achieved by expressing the measurements in the matrix form, for convenience, ( p + 1) is written as p ′ .

X12 X13 " X1p º ªβ0 º ªε1 º X 22 X 23 " X 2 p » ««β1 »» «ε 2 » »× + « » (3) # # % # » «# » «# » » « » « » X n2 X n3 " X np ¼» ¬«β p ¼» ¬ε n ¼ (n × p ′) ( p ′ × 1) (n × 1)

The OLS yields to equation (4) , which gives the least squares

The load studies are mostly to find and understand the effective parameters on the load consumption so by this the forecasting model can be closer and more accurate to reality. In the load study it is attempted to attain the necessary information for programming the distribution for the consumer and the whole electricity system by finding and understanding the electricity demand more accurately. Electrical load consumption is noticeably affected by many environmental factors such as temperature, cloud overlay, humidity, and wind speed. Regarding the fact that the mentioned environmental factors change during the year, the level that the load is affected by these factors also changes. Therefore this model which is designed to forecast the load’s behavior should be able to show the effect of these environmental factors. Seasonal Change Effect

estimate βˆ of the parameter set.

Spring

βˆ = ( X T X ) −1 X T Y

( )

expresses the degree to which the The quantity r-square r linear relationship between a set of predictors and a variable 2

( )

can explain the variance in the variable. In other words, r

2

The dates in this paper are based on the official calendar of Iran, meaning the solar calendar. Based on the solar calendar the 12 months of the year are as followed: 1-Farvardin 2- Ordibehesht 3-Khordad : (Spring season) 4-Tir 5-Mordad 6-Shahrivar : (Summer season) 5-Mehr 6-Aban 7-Azar : (Autumn season) 8-Dey 9-Bahman 10-Esfand : (Winter season)

: 82/2/15

Autumn

: 82/9/17

Summer

: 82/5/13

Winter

: 82/11/27

30000 Load (MW)

(4) It is not enough to simply calculate the coefficients of regression; we also need a way to assess the validity of the regression model. We adopted the widely used r-square fit test for this purpose.

(1)

¦ (Yˆ − Y ) i =1

(2)

A variety of methods exist to find the regression coefficient β j , the most popular approach is ordinary least squares

ªY1 º ª1 X11 «Y » «1 X 21 « 2» =« « «# » # # « » « ¬Yn ¼ ¬«1 X n1 (n × 1)

n

25000 20000 15000 10000 1

3

5

7

9

11 13 15 17 19 21 23 25

Time (h)

Fig.1.Comparition of the load curve of four Monday samples from the seasons of spring, summer, autumn and winter

Temperature has a great effect on the hourly energy consumption .This effect first of all causes an average change in the consumption load curve in a way that the curve is higher for a hot summer day than a colder day and vice-versa.

Temperature Effect 82/2/12 Fri

82/2/19 Fri

82/2/26 Fri

Load (MW)

25000

As the temperature has the most effect on the load at noon and also full viewer T.V. programs are less in these hours, 12 o’clock has been selected in the presented paper. The daily load curves of three Fridays in month Ordibehesht in year 1382 have been shown in the Table 1:

20000

TABLE I TEMPERATURE

INFORMATION OF THREE

AGENT OF COLD, MODERATE AND WARM CITIES OF IRAN

15000

10000 1

3

5

7

9

11

13

15

17

19

21

23

25

Tim e (h)

Fig.2. Comparison of the load curve of three Fridays , in the three sequential weeks of the second month of the year 1382.

Second of all temperature leaves a variable effect on the load consumption throughout different hours of the day. The temperature gradient (

ΔL ) is positive during the ΔT

summer and negative during the winter and regarding the limited cooling and heating devices (in places which the load has reached its saturated limit)the gradient is near zero. The other matter is the temperature inertia which is caused by the temperature of previous days’ effect on today’s load consumption. In the time between summer and winter because of the moderate weather, change in temperature doesn’t have such a great effect.

Day 82/2/12 82/2/19 82/2/26

min 9 6 16

Tabriz (cold ) ave Max 15 21 12.7 18 20.8 28

Ahvaz (Warm) min ave 21 28.1 22 29.3 28 34.5

Max 35 37 41

Also in order to minimize the effect of the other factors on the load, only the working days of each month have been selected. We select the load and temperature information of every month’s working day by omitting holidays , Fridays, Saturdays, Thursdays, and the days before and after holidays for studying. Then Correlation between the load and temperature for 12 o’clock has been calculated. At first, correlations between the load of 12 o’clock and temperature of the same time of that day have been calculated separately for each month in the year 1382. In the following figure (Fig.3) the relation between the load and temperature of 12o’clock, noon, in Farvardin of the year 1382 has been shown. Load - Temperature L=15537-1.7*T Correlation : r=0%

4- SENSITIVE ANALYSIS BY REGRESSION METHOD 18000 Load (MW)

The linear regression approach recognizes that the load pattern is heavily dependent on weather variables, and finds a functional relationship between the weather variables and the system load. The load is represented as a linear combination of explanatory variables. The explanatory variables include weather factors. Coefficients of explanatory variables are estimated by least squares fitting or modem regression techniques. [33] In this section the sensibility of Iran’s daily network load to the temperature in the year 1382 has been studied. To examine the relation between load and temperature, correlation coefficients between the load of 12 o’clock and temperature of the same time of that day have been calculated separately for each month in the year 1382. Also correlation coefficients between the load of 12 o’clock and average, maximum and minimum temperature of the same day and the previous day, during one sample month (Tir), have been calculated respectively. It is noteworthy that in the calculations which explained above, temperature of 12 o’clock of Tehran has been considered as the thermal agent city of Iran. Based on the “Iranian National Dispatching Center” studies, the temperature effect is not similar in different regions of Iran so that the temperature of the three cities Tabriz , Tehran and Ahvaz are representatives for cold , moderate and warm areas. But this study has confirmed that “Tehran” can consider as a suitable thermal agent of Iran.

Tehran (Moderate) min ave Max 12 15.9 19 3 15.3 22 19 25 30

16000 14000 12000 10000 0

10 Temperature (c)

20

30

Fig.3. Correlation between load and temperature of the 12 o’clock in Farvardin month

As you see , regarding the fact that the first month of the year in the solar calendar is in the moderate time of the year, and it is not necessary to use cooling or heating appliances, the correlation coefficient and the effect of temperature on the load consumption level is minimum (r=0). In the figure below (Fig.4) the relation between the load and temperature of 12 o’clock in the second month (Ordibehesht) of the year 1382 has been shown . As it shows gradually by the temperature increasing, the load is increasing slowly and the slope of this increase in more than Farvardin’s (r=79.7%). Its reason is that the cooling systems at the end of the month in some warm regions are switched on.

In the figure below (Fig.7) the relation between the load and temperature of 12 o’clock in Mordad 1382 has been shown. At this month, by load increasing, the load does not increase any more and the slope of the Load-Temperature line is less than Tir’s, the reason is the same mentioned for the month Tir. (r=46.3%)

Load - Tem perature L=12791+177*T Correlation : r=79.7%

Load (MW)

18500 18000 17500 17000 16500 16000 15500 15000

10 Temperature (c)

20

30

Fig. 4. Correlation between load and temperature of the 12 o’clock in Ordibehesht month

Load (M W)

22500

0

22000 21500 21000 20500

Load - Temperature L=13342+202*T Correlation : r=91.3%

21000 Load (MW)

Load - Tem perature L=18554+91.6*T Correlation : r=46.3%

0

10 20 Temperature (c)

30

40

Fig. 7. Correlation between load and temperature of the 12 o’clock in Mordad month

20000 19000

In the figure below (Fig.8) the relation between the load and temperature of 12 o’clock in Shahrivar 1382 has been shown.

18000 17000 0


30

Load (M W)

In the figure above (Fig.5) the relation between the load and temperature of 12 o’clock in Khordad 1382 has been shown, as it shows by the temperature increasing the load is strongly increasing and the slope of this increase is much more than Ordibehesht (r=91.3%) that it’s reason is that in the moderate and cold regions the cooling systems are switched on. In the figure below (Fig.6) the relation between the load and temperature of 12 o’clock in Tir 1382 has been shown (r=58.4%).As the figure shows the temperature increasing does not increase the load any more and the load has been saturated, the reason is that all of the cooling systems have entered the network and by the increase of the temperature there is not cooling systems any more which enter to the network. Load - Temperature L=15274+176*T Correlation : r=58.4%

0


30

40

Fig. 6. Correlation between load and temperature of the 12 o’clock in Tir month

Load (MW)

Fig. 5. Correlation between load and temperature of the 12 o’clock in Khordad month

22500 22000 21500 21000 20500 20000 19500


40 22000 21500 21000 20500 20000 19500 19000 18500 0


30

40

Fig. 8. Correlation between load and temperature of the 12 o’clock in Shahrivar month

As it shows by temperature increase, the load increases, but the slope of this increase is less than Mordad’s (r=35.6%). The reason is that the used software for correlation calculating , averages the temperatures ascending Therefore ,in fact , the slope is negative and by temperature decrease cooling systems go out of the network in the cold region and load decreases. In the figure below (Fig.9) the relation between the load and temperature of 12 o’clock in Mehr 1382 has been shown .As it shows by temperature decrease , the load decreases slowly (r=13.4%) that is the result of being switched off of cooling systems in the cold, moderate and warm regions.


18000

18500 18000

Load (MW)

Load (MW )

17500

17500

17000

17000

16500

16500 16000

16000 0


0

30

Fig. 9. Correlation between load and temperature of the 12 o’clock in Mehr month

2

4 6 Temperature (c)

8

10

12

Fig. 12. Correlation between load and temperature of the 12 o’clock in Dey month


Load - Temperature L=17437-93.3*T Correlation : r=54.4%

17400 17200 17000 16800 16600 16400 16200 16000

Load (M W )

17000 Load (M W)

16500 16000 15500 15000 0

5


20

25

0

30

Fig. 10. Correlation between load and temperature of the 12 o’clock in Aban month

In the figure above (Fig.10) , the relation between the load and temperature of 12 o’clock in Aban 1382 has been shown (r=23.9%).In this figure by temperature decrease ,the load decreases as a result of switching off cooling systems in the warm region.

Load (MW)

16500 16000 15500 0

5 Temperature (c)

10

15

4 6 Temperature (c)

8

10

12

In the figure above (Fig.13) the relation between the load and temperature of 12 o’clock in Bahman 1382 has been shown (r=54.4%) and show similar state of the Day’s month. Gradually by temperature increase, the load decreases as a result of switching off of heating systems in some warm regions.

17500 17000

2

Fig. 13. Correlation between load and temperature of the 12 o’clock in Bahman month

Load - Tem perature L=16853-40.4*T Correlation : r=32.2%

18000 Load (MW)

Load - Tem perature L=17574-89.8*T Correlation : r=54.5%

Load - Tem pe rature L=17273-9.3*T Correlation : r=23.2%

18000 17800 17600 17400 17200 17000 16800 16600 16400 0

5


20

25

Fig. 11. Correlation between load and temperature of the 12 o’clock in Azar month

Fig. 14. Correlation between load and temperature of the 12 o’clock in Esfand month

In the figure above (Fig.11) the relation between the load and temperature of 12 o’clock in Azar 1382 has been shown (r=32.2%). By temperature decrease, the load increases as a result of switching on of heating systems in the moderate and cold regions. In the figure below (Fig.12) , the relation between the load and temperature of 12 o’clock in Dey 1382 has been shown (r=54.5%).As the figure shows , by temperature decrease , the load increases as a result of switching on heating systems until the end of Azar in all of the country.

In the figure above (Fig.14) the relation between the load and temperature of 12 o’clock in Esfand 1382 has been shown (r=23.2%).As the figure show , by temperature decrease ,the load increases very slowly that is the result of being switched off of heating systems in warm region. Further in the paper, correlation between the load of 12 o’clock and the average, maximum and minimum temperatures of that same day in sample month (Tir) are shown in figures 15, 16 and 17.


22500

22000

22000

21500

21500

Load (MW)

Load (MW)

22500

21000 20500

21000 20500

20000

20000

19500

19500

-

10.0 20.0 Temperature (c)


30.0

0

40.0

10

20 Temperature (c)

30

40

Fig.15. Correlation between the load of 12 o’clock and average temperature of that day in Tir month

Fig. 18. Correlation between the load of 12 o’clock and average temperature of previous day in Tir month



22500

22500 22000 Load (MW)

Load (MW)

22000 21500 21000 20500 20000

21000 20500 20000 19500

19500 0

10


40

0

50

Fig. 16. Correlation between the load of 12 o’clock and maximum temperature of that day in Tir month


30

40

Fig. 19. Correlation between the load of 12 o’clock and maximum temperature of previous day in Tir month


22500


22500 22000 Load (MW)

22000 Load (MW)

21500

21500 21000 20500 20000

21500 21000 20500 20000 19500

19500 0


30

40

Fig.17 .Correlation between the load of 12 o’clock and minimum temperature of that day in Tir month

As the figures show, the load consumption for each day of Iran’s electrical network is affected much by the average , maximum and minimum temperatures of that same day with correlation coefficients as below : r=76.7% , r=72.9% and r=74.9% Therefore temperature effect for the forecasted day should be accounted for. Also during the correlation between the load of 12 o’clock and the average, maximum and minimum temperatures of that previous day in sample month (Tir) are shown in figures 18, 19 and 20.

0

10

20 Temperature (c)

30

40

Fig.20. Correlation between the load of 12 o’clock and minimum temperature of previous day in Tir month

As the figures show, the load consumption level for each day of Iran’s electrical network is affected by the average, maximum , and minimum temperatures of the previous day with correlation coefficients of

r=68.8%

, r=49.6%

and

r=73.9%

Of course according the fact that the level the load is affected by the temperature of one days ago less than that of the day itself, but usually the temperatures of day before forecasting and the day of forecasting are used in the forecasting model.

5- RESULTS Electrical load consumption in a complicated and non-linear way is a function of many parameters including weather conditions especially temperature. In this paper the linear regression analysis of Iran’s electrical load recognizes that the load pattern is heavily dependent on temperature, and finds a linear function between the load and the network’s temperature. This study shows that temperature has a great effect on Iran’s network load, so that daily electrical load of Iran is function of the minimum, average and maximum temperatures of the forecasted day and the day before forecasted day too. According to this study, suitable input variables which can consider the temperature effect on Iran forecasted load in the Short Term Load Forecast (STLF) model are minimum, average and maximum temperatures of the forecasted day and the day before forecasted day. This analysis can be extended to all of the other environmental factors such as humidity, wind velocity and weather overlay too. Also this study can be performed for the other entire countries electrical network.

ACKNOWLEDGMENT This work was supported by National Dispatching Center of Iran. REFERENCES [ 1 ] P.E.McSharry, S.Bouwman, and G.Bloemhof, “Probabilistic Forecasts of the Magnitude and Timing of Peak Electricity Demand,” IEEE Trans. vol. 20, No. 2, pp. 1166-1172, May 2006 [ 2 ] C.Tranchita, A.Torres, “Soft Computing Techniques for Short Term Load Forecasting,” IEEE 2004 pp.1-6 [3] P.E.McSharry, S.Bouwman, and G.Bloemhof, “Probabilistic Forecasts of the Magnitude and Timing of Peak Electricity Demand,” IEEE Trans. vol. 20, No. 2,pp. 1166-1172, May 2006 [4]-R.F.Engle,C.W.J.Granger,J.Rice,andA.Weiss,”Semi parametric Estimates of the relation between weather and electricity sales,”J.Amer. Stat.Assoc.,vol.81,no.394,pp.310–320,1986. [5]-D.W.Bunn,”Forecasting loads and prices incompetitive power markets,”Proc.IEEE,vol.88,no.2,pp.163–169,Feb.2000. [6]-N.Amjady,Short-term hourly load forecasting using time-series modeling with peak load estimation capability,IEEE Trans.PowerSyst.,vol.16,no.3,pp.498–505,Aug.2001. [7]-J.W.Taylor,Short-term electricity demand forecasting using double Seasonal exponential smoothing,.Oper.Res.Soc.,vol.54,pp.799–805,2003. [8]-A.P.Douglas,A.M.Breipohl,F.N.Lee,andR.Adapa,heimpacts of temperature forecast uncertainty on Bayesian load forecasting,IEEE Trans.PowerSyst.,vol.13,no.4,pp.1507–1513,Nov.1998. [9]-M.Smith,Modeling and short-term forecasting of new south wales electricity system load,.Intell.Robot.Syst.,vol.18,no.4,pp. 465–478,2000. [ 10 ] T.Kohonen et al., SOM_PAK. The Self-Organizing Map Program Package,User's Guide, Helsinki University of Technology,1995 [ 11 ] K.Fei, Thang, “ MATLAB Implementation of Neural & Neuro-Fuzzy Approaches for Short-Term Electricity Demand Forecasting” ,IEEE POWERCON 2004, Singapore, pp.1213-1218, November 2004 [12]-J.W.Taylor andR.Buizza,Neural network load forecasting with Weather ensemble predictions,IEEE Trans.PowerSyst.,vol.17,no. 3,pp.626–632,Aug.2002. [13]-H.K.Temraz,M.M.A.Salama,andV.H.Quintana,Application of the decomposition technique for forecasting the load of a largeelectric-power network,Proc.Inst.Elect.Eng.Gen.,Transm.,Distrib.,vol.143, no.1,pp.13–18,1996.

[14]-E.H.Barakat,J.M.Al-Qassim,and S.A.Al-Rashed,”New model for peak demand forecasting applied to highly complex load characteristics of a fast developing area,”Proc.Inst.Elect.Eng.C,Gen.,Transm.,Distrib.,vol.139,no.2,pp.136– 140,1992. [15]-A.Pardo,V.Meneu,and E.Valor,”Temperature and seasonality influences on Spanish electricity load,”Energy Econ.,vol.24,pp.55–70, 2002. [16]-H.Morita,T.Kase,Y.Tamura,andS.Iwamoto,”Interval prediction of annual maximum demand using grey dynamic model,”Int.J.Elect.PowerEnergySyst.,vol.18,no.7,pp.409–413,1996. [17]-M.S.Kandil,S.M.El-Debeiky,andN.E.Hasanien,”Overview and Comparison of long-term forecasting techniques for a fast developing utility:PartI,”Elect.PowerSyst.Res.,vol.58,no.1,pp.11–17,2001. [18] C.Tranchita, A.Torres, “Soft Computing Techniques for Short Term Load Forecasting,” IEEE 2004 pp.1-6 [ 19 ] T.Senjyu, P.Mandal, K.Uezato, and T.Funabashi, “Next Day Load Curve Forecasting Using Recurrent Neural Network Structure,” IEE Proc.Gener. Transm. Distrib., vol. 151, No.3, pp. 388-394, May 2004 [ 20 ] Farhadi.M , Moghaddas Tafreshi. S.M ,” A Novel Model for ShortTerm Load Forecasting of Iran Power Network by Using Kohonen Neural Network”,IEEE,ISIE 2006, July 9-12 ,2006, Montreal , Quebec,Canada [ 21 ] Farhadi.M , Moghaddas—Tafreshi S.M,”Effective Model for Next Day Load Cureve Forecasting Based Upon Combination of Perceptron and Kohonen ANNs Applied to Iran Power Network”, IEEE , INTELEC 2007, Sep 30 - Oct 4, ,2007, Rome , Italy [ 22 ] Farhadi.M , Moghaddas—Tafreshi S.M,” Daily Electrical Load Forecast of Iran by a New Model of Two Combitional Kohonen Neural Networks” PSC2004, Nov 9-12 ,2004, Tehran , Iran [ 23 ] Moghaddas—Tafreshi S.M , Farhadi.M , ” Development of Iran Daily Load Forecast Software by Kohonen and Perceptron Neural Network Algorithm Based on Thermal Coefficients”, IEEE , IPEC 2007, Dec 3-6 ,2007, Singapore [ 24 ] Moghaddas—Tafreshi S.M , Farhadi.M , ”Improved SOM Based Method for Short Term Load Forecast of Iran Power Network” , IEEE , IPEC 2007, Dec 3-6 ,2007, Singapore [ 25 ] – Moghaddas–Tafreshi S,M, Muller H, Petritsch G., "Clusterung der Tageslastganglinien mittels selbstorganisierendem neuronalem Netzwerk", Researoh report FB 5/1994 of Institute for Electrical Power Systems Of Technical University of Vienna , 1994 [ 26 ] – Moghaddas – Tafreschi S.M. , Muller H. , Petritsch G., "Energieprognose mittels neuronaler Netzwerkkonzepte '' , Paper to International Conference on Operations Research (OR 1994) , Berlin , Aug. / Sep. 1994 in Operations Research Proceedings 1994 , Berlin : Springer – Verlag ,1995 , pp.424-429 [ 27 ] – Moghaddas – Tafreschi S.M. , Muller H. , Petritsch G., " Energy and Load Forecasting by Fuzzy–Neural Networks Proceedings of Eufit–The European Congress on Intelligent Techniques and Soft Computing " Aachen , Germany 1998 / pp. 1925 –1930 " [ 28 ] Amjady.N. ,”Short-Term Bus Load Forecasting of Power System by a New Hybrid Method” , IEEE Transactions on Power Systems “, Vol.22 , NO. 1, pp. ,333-341,February, 2007 [ 29 ] Heinemann.G.T. , Nordman.D.A. , Plant. E.C. , ” The Relationship Between Summer Weather and Summer Loads - A Regression Analysis “ IEEE Transactions on Power Apparatus and Systems “, Vol.PAS , NO.11, pp. ,1144-1154,November, 1966 [ 30 ] Bin Song.K , Kwan Ha.S , Wook Park.J,Jin Kweon.D. , Ho Kim.K. ,”Hybrid Load Forecasting Method With Analysis of Temperature Sensitivities” IEEE Transactions on Power Systems “, Vol.21 , NO.21, pp. ,869-876,May, 2006 [ 31 ] Li Lim.H. ,Brown.R.H. , “Gas Load Forecasting Model Input Factor Identification Using A Genetic Algorithm” IEEE,2001 [ 32 ] Baran.M.E. ,Freeman.L.A.A. , Hanson.F. , Ayers.V. , “Load Estimation for Load Monitoring at Distribution Substations ” , IEEE Transactions on Power Systems “, Vol.20 , NO. 1, pp. ,164-170,February, 2005 [ 33 ] Owayedh.M.S. , Al-Bassam.A.A. , Khan.Z.R. , “ Identification of Temperature and Social Events Effects on Weekly Demand Behavior “ , IEEE ,2000