A Parameter based New Approach for Short Term Load Forecasting using Curve-fitting and Regression line method

A Parameter based New Approach for Short Term Load Forecasting using Curve-fitting and Regression line method

A Parameter based New Approach for Short Term Load Forecasting using Curve-fitting and Regression line method

Manoj Kumar Nigam, Reader in Electrical Engineering Department at

1. Babita Jain is Professor and Dean at Rungta Engineering College, Raipur, CG, India

   RITEE Raipur (C.G.), India

   Prem Chand Tiwari, is M.E. Student at RITEE Raipur (C.G.) India,

   .

   AbstractShort term load forecasting in this paper is done by considering the sensibility of the network load to the temperature, humidity, day type parameters (THD) and previous load and also ensuring that forecasting the load with these parameters can best be done by the regression line and curve fitting methods .The analysis of the load data recognize that the load pattern is not only dependent on temperature but also dependent on humidity and day type. A new norm has been developed using the regression line concept with inclusion of special constants which hold the effect of the history data and THD parameters on the load forecast and it is used for the STLF of the test dataset of the used data set. A unique norm with a, b, c and d constants based on the history data has been proposed for the STLF using the concept of curve fitting technique. The algorithms implementing this forecasting technique have been programmed using MATLAB. The input data of each day average power, average temperature , average humidity and day type are used for prediction of power, in the case of the regression line method and the forecast previous month data and the similar month data of the previous year is used for the curve fitting method. The simulation results show the robustness and suitability of the proposed norm for the STLF as the forecasting accuracies are very good and less than 3% for almost all the day types and all the seasons. Results also indicate the curve fitting method out passes the regression technique w.r.t forecasting accuracy and hence it the best suitable method for accurate short term loads forecasting.

   Index Terms– Short term load forecasting, THD (tempreture, humidity, day type), curve fitting, regression line.

   1. INTRODUCTION

      Load forecasting is an important component for power system energy management system. Precise load forecasting helps the electric utility to make unit commitment decisions, reduce spinning reserve capacity and schedule device maintenance plan properly. Besides playing a key role in reducing the generation cost, it is also essential to the reliability of power systems. The system operators use the load forecasting result as a basis of off-line network analysis to determine if the system might be vulnerable. If so, corrective actions should be prepared, such as load shedding, power purchases and bringing peaking units on line.

      With the recent trend of deregulation of electricity markets, STLF has gained more importance and greater challenges. In the market environment, precise forecasting is the basis of electrical energy trade and spot price establishment for the system to gain the minimum electricity

      purchasing cost. In the real-time dispatch operation, forecasting error causes more purchasing electricity cost or breaking-contract penalty cost to keep the electricity supply and consumption balance. There are also some modifications of STLF models due to this implementation of the electricity market. Weather is defined as the atmospheric condition existing over a short period in a particular location. It is often difficult to predict and it can vary significantly even over a short period. Climate also varies with time: seasonally, annually and on a decades basis [1]. The relationship between demand and temperature is non linear with the demand increasing for both low and high temperature [2]. The range of the possible approaches to the forecast is to take a microscopic view of the problem and try to model the future load as a reflection of previous [3]. In the case of large variation in the temperature compared to that of the previous year, the load also changes accordingly. In such cases there would be the shortage of similar days data and the task of the forecasting load is very difficult [4].

   2. DATA ANALYSIS

      1. LOAD CURVES

         For the analysis and implementation of load forecasting, data is taken from EUNITE network that was provided to participants for a competition many years ago (see acknowledgement). In the data analysis part we are going to analyze load variation with respect to day type, weather condition such as seasonal variation of load with temperature and humidity. Analyzing the monthly and yearly load curves given in Fig.1 and Fig.2 and also load variation with respect to temperature and humidity given in Fig.3 and Fig.4 the following observations are made:

         The load curve patters of two consecutive years is similar

         The load curves of similar months of two consecutive years is also similar

         The load curves are having different pattern in weekdays and weekend days in the month.

         The load curves on the weekends are similar.

         Taking in consideration the above observations the days of the week are classified based on the following categories:

         20000

         15000

         10000

         1. Normal week days (Tuesday – Friday)

         2. Monday

         3. Sunday

         4. Saturday

            100

            90

            80

            70

            Monday is accounted to be different to weekdays so as to take care for the difference in the load because of the previous day to be weekend.

            18000

            17000

            16000

            AVERAGE LOAD (MW)

            15000

            14000

            13000

            12000

            11000

            10000

            9000

            LOAD Vs DAYS

            power(marcp996

            )

            14500

            AVERAGE LOAD (MW)

            1

            16

            31

            46

            61

            76

            91

            106

            121

            136

            151

            166

            181

            196

            211

            226

            241

            256

            271

            286

            301

            316

            331

            346

            361

            Fig.1 Yearly Load variation of 1996 and 1997

            (power)199

            6

            power(1997

            )

            Fig.3 Monthly Load variation with Temperature

            C. Variation of Load with Humidity

            Fig 4 shows the plot between the average humidity versus average demand. From the graph it can be seen that there exists a positive correlation between load and humidity i.e. demand increases as the humidity increases.

            20000

            18000

            16000

            14000

            12000

            15000

            LOAD Vs DAYS

            1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

            14000

            13500

            13000

            12500

            12000

            11500

            11000

            10500

            10000

            Fig. 2 Monthly Load variation of Mar96 and Mar97

      2. Variation of Load with Temperature

      The variation of the temperature variable results in a significant variation in the load. Fig 3 shows a plot between the maximum temperatures versus average demand. In Fig. 3 the dots represent the actual values and the solid line is the best fitted curve. The graph shows a positive correlation between the load and temperature i.e. demand increases as the temperature increases.

      Fig.4 Monthly Load variation with Humidity

      73

      71

      69

      67

      65

      D. Autocorrelation of Load

      It is seen from the plots that the load pattern of the present year is similar to the load pattern of previous year and also the load curve of a gven month is similar to the load curve of the previous years same month. Hence it can be considered that the load of similar month of previous year can greatly help in load forecasting along with the THD parameters.

   3. SHORT TERM LOAD FORECASTING USING REGRESSION

      LINE

      This section deals with the details of the concept and implementation of regression line method and its implementation to STLF. The relation between load and the THD parameters is defined as they have direct impact on the load as seen in the earlier section. Regression is the study of the relationship among variables, a principle purpose of which is to predict, or estimate the value of the one variable from known or assumed values of other variables related to it .For electric load forecasting regression methods are usually used to model the relationship of load consumption and other factors such as weather and day type [4]-[10].

      As it is clear from the data analysis that the load is totally dependent on the temperature, humidity and day type parameters, hence regression is used to obtain the relationship between load and these parameters. The method is basically divided into three parts as follows:

      Load variation with respect to temperature

      Load variation with respect to temperature and humidity

      Load variation with respect to temperature, humidity and day type.

      Since it is clear from data analysis that all the three THD parameters affect the load forecast the regression line method is used to find the relation between load and all these three parameters.

      Regression line (THD): The regression line equation for load forecast dependent on the temperature, humidity and day type parameters is given as follows:

      (1)

      Where = forecaste day power

      = Previous year average power .

      R = coefficient of co relation of load power with temperature and humidity of previous year .

      Tavg,Havg, Davg = average temperature ,humidity and day type previous year.

      p, T H D = standard deviation of power, temperature

      ,humidity and day type of previous year

      ALGORITHM:-

      Step:-1.Calculation of previous year Pforecasted Tavg, Havg, and Davg

      Step:-2. calculation of coefficient of co relation R R= ( (2)

      Step:-6. For next day load forecasting go step 1 to step 5. Step:-7.Result analysis.

      Step:-8. End

      From the above algorithm we are easily calculating the load power. This method using the previous year load data including the temperature, humidity and the day type .It finding the variation of the load with respect to the parameters which is mention above.

   4. SHORT TERM LOAD FORECASTING USING CURVE FITTING

      The methodology that is developed for the short term load forecasting of load using the curve fitting method would mainly focus on the variation of power with the three main parameters we have already mentioned i.e. Temperature, Humidity and the particular Day Type[11]-[14].

      The first two parameters, quite evidently come under the weather changing phenomenon, but considering the time dependent variation of the load, the data that is available could not only be classified into a particular day type but it also follows a similar month pattern which implies that, for example, if we take the data of January of one particular year, there are steep chances that it is almost identical to the one we had in the same month of its previous year under a similar working environment. As from previous method similarly we are using the all three factors for the forecasting the power .It is explain in the algorithm.

      Algorithm (THD)

      Step1.Write the equestions between power and its parameters using curvefitting .

      (3)

      (4)

      (5)

      (6)

      (7)

      Where the value of

      Step:-3. Taken the value of the forecast day temperature, humidity and day type.

      Step:-4 writing the relation between load power and the

      parameters

      Step:-5.Calculating MAPE(mean absolute percentage error)of power.

      Step 2: Using privious year data of similar month calculate cofficent of a,b,c &d.

      = .

      =

      Asuming the cofficents

      =

      Step 3: Cofficent subsitution in the equestion(3)

      =

      Step 4: Calculating the forecasting power of each day in present month

      Step 5: Calculating MAPE(mean absulute percentage error)of power.

      Step 6: For next month forecasting of power repeat steps 2 to step 5.

      Step 7: Result analysis Step 8: End.

      From the above algorithm the forecasting of the load power with respect to the parameters are easily calculated .this method is very simple and having less complex as compared to the regression line method .

   5. SUMMARY OF THE METHODTHOLOGY

      In this part we are discussing the summery of the methods which are used in this paper, regression line and the curve fitting are the same steps to follow and hence we draw the methodology in the same flow diagram.

      START

      DATA ANALYSIS

      DATA ANALYSIS

      REGRESSION LINE METHOD CURVEFITTING METHOD

      RELATION BETWEEN POWER AND ITS AFFECTING FACTOES

   6. RESULT ANALYSIS

      The result analysis of the simulation performed on the power variation with respect to its corresponding parameters clearly suggests the dependency of the load power on the main three factors that were considered in this paper, namely Temperature, Humidity and the Day Type. To understand this, we have tabulated the individual variation of power with temperature taken separately, power with temperature and humidity taken together and finally the power variation along with day type also. Based on the tabular data of the readings obtained, we also plotted the individual graphs each showing the variation of power with respect to its parameters separately and also when considered together. In this analysis part separate method results are tabular form shown and the graphical analysis is given below.

      Table: I

      Parameters of the regression line and curve fitting algorithms

      PARAMETERS	VALUES
      PAVERAGE	13053.34
      R	0.0014
      TAVERAGE	48.6190
      HAVERAGE	38.2240
      DAVERAGE	3.1448
      P	13608.54
      T	17.4668
      H	19.3137
      D	1.227
      a	11279.72
      b	3.71783
      c	-29.0868
      d	760.9079

      Table: II

      PAST DATA INPUT

      Comparative STLF of Saturday, Sunday, Monday and Tuesday Load

      PREVIOUS YEAR DATA PREVIOUS YEAR SIMILAR

      MONTH DATA

      DAY TYPE

      SN	DATE	Actual Load	REGRESSION Forecast Load	CURVEFITTING Forecast Load
      1	1/11/97	11674.79167	12250.324	11720.18706
      2	2/11/97	11021.91667	11561.25783	10929.62926
      3	3/11/97	12754.66667	13080.58321	12495.5655
      4	4/11/97	13030.375	13123.7481	13190.33612

      FORECASTING THE POWER

      USE THE PRESENT MONTH

      USE THE PRESENT YEAR

      TEMPERATURE ,HUMIDITY TEMPERATURE HUMIDITY AND

      AND DAY TYPE

      ERROR CALCULATION (MAPE)

      DIFFERENCE BETWEEN ACTUAL DIFFRENCE BETWEEN ACTUAL AND PREDICTED POWER AND PREDICTED POWER

      SEASONAL FORECASTED POWER SEASONAL FORECASTED POWER RESUILT RESUL

      RESULT ANALYSIS

      FIG. 5 SUMMARY OF MATHEDOLOGY.

      REGRESSION LINE AND CURVEFITTING

      REGRESSION LOAD

      CURVEFITTING LOAD

      ACTUAL LOAD

      14000

      13000

      12000

      11000

      10000

      AVERAGE LOAD

      Fig.6 Curve of the load of the Saturday, Sunday, Monday and Tuesday

      Load

      Table: III

      Comparative STLF MAPE Saturday , Sunday , Monday and Tuesday

      Load

      DATE THD(MAPE)

      REGRESSION LINE CURVEFITTING

      1/11/97 4.9297 0.388832548

      2/11/97 4.893351854 0.837308176

      3/11/97 2.555272922 2.031422499

      4/11/97 0.716580306 1.227601821

      Table V

      Comparative STLF MAPE Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday forecasted Load

      DATE	THD(MAPE)
      	REGRESSION LINE	CURVEFITTING
      2/11/97	4.893351854	0.837308176
      3/11/97	2.555272922	2.031422499
      4/11/97	0.716580306	1.227601821
      5/11/97	0.437738972	2.127080421
      6/11/97	0.843095478	1.040767906
      7/11/97	0.380420849	1.63109466
      8/11/97	9.086378284	0.022678997

      Table II,III,IV and V present the day wise load forecast for the selected days obtained by the two different methodology which are Regression line (THD)and the curve fitting (THD).

      REGRESSION LINE & CURVE FITTING

      10

      MAPE

      8

      6

      4

      2 REGRESSION LINE

      REGRESSION LINE AND CURVEFITTING

      0

      6

      4

      2

      0

      MAPE

      2/1/1997

      3/1/1997

      4/1/1997

      5/1/1997

      6/1/1997

      7/1/1997

      8/1/1997

      CURVEFITTING

      REGRESSION

      (MAPE)

      CURVEFITTING

      (MAPE)

      Fig. 7 MAPE of the load MAPE Saturday, Sunday, Monday and Tuesday

      Load

      Table: IV

      Comparative STLF of Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday forecasted Load

      Fig. 9 Comparative MAPE of the entire week forecasted load

      From the above analysis it is clear that both the regression line and the curve fitting methods are quite suitable for the short term load forecasting giving very good forecasting accuracies with MAPEs of most of the cases quite less than 3%. Results also indicate that the curve fitting method is better compared to the regression line method for short term load forecasting. The curve fitting method is simple and robust in

      comparison to the regression line method. The method yields

      DATE

      ACTUAL LOAD

      REGRESSION

      THD

      very good results for days of all types and all around the year as the weekly result values clearly indicate.

      LINE CURVEFITTING

      2/11/97 11021.91667 11561.25783 10929.62926

      3/11/97 12754.66667 13080.58321 12495.5655

      4/11/97 13030.375 13123.7481 13190.33612

      5/11/97 13077.625 13134.87086 13355.7966

      6/11/97 13264.5 13152.6676 13402.55266

      7/11/97 13129.41667 13079.46963 13343.56988

      8/11/97 12054.45833 13149.77202 12057.19216

      REGRESSION LINE & CURVE FITTING

   7. CONCLUSION

      Accurate load forecasting is very important for electric utilities in a competitive environment created by the electric industry deregulation. In this paper, we have presented the regression line and curve fitting methods for short term load forecasting. The following are the conclusions derived from the proposed methods:

      AVERAGE LOAD (MW)

      15000

      14000

      13000

      ACTUAL LOAD

      In this paper, regression and curve fitting methods have strongly proved the impact of THD parameters in the

      12000

      11000

      2/1/1997

      3/1/1997

      4/1/1997

      5/1/1997

      6/1/1997

      7/1/1997

      8/1/1997

      10000

      REGRESSION LINE

      CURVEFITTIN G

      STLF using the relation between input and output variable through the systematic rule. In the regression method input data is previous years data and for the curve fitting method data input is previous years similar months data.

      The simulation results have shown that the both the proposed methodologies are quite good and completely

      Fig. 8 curve of the load of Sunday, Monday, Tuesday, Wednesday,

      Thursday, Friday and Saturday forecasted Load

      suitable for STLF of all types of the days and for all

      months round the year giving the MAPE for most of the cases quite less than 3%.

      Results also indicate that the curve fitting method has an edge over the regression line method. The efficiency of the curve fitting method is due to the consideration of the previous years similar month as the training data set for the calculation of the constants. The data analysis part of Section II indicates the strong impact of the previous year similar month load on the present month. This impact of previous year similar month goes very well with the curve fitting method.

   8. ACKNOWLEDGMENT

      The authors gratefully acknowledge Mr. R. Venkatendra for providing the EUNITE Network load forecasting data, which has been used for simulation study in this paper. Authors information about the source of data is based on the information provided by Mr. R. Venkatendra.

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   10. BIOGRAPHIES

M Babita Jain is PhD student at the International Institute of Information Technology, Hyderabad, India since 2006. The areas of interestinclude IT Applications to Power Systems, Load forecasting and Multi Agent Systems. She has actively involved in establishing IEEE student branch and Women in engineering affinity group

activities.

Manoj Kumar Nigam is Reader in Electrical Engineering Department at RITEE Raipur (C.G.) India. He is completed his ME in Industrial systems & drives from MITS Gwalior, his area of interest is electrical drives & power electronics.

Prem chand Tiwari is the ME student at RITEE Raipur (C.G.) India since 2010. The area of interest is electronic devices and circuits and power electronics.