modelling of electrical energy consumption in delhi

Energy 24 (1999) 351–361

Modelling of electrical energy consumption in Delhi

Manish Ranjan, V.K. Jain*

School of Environmental Science, Jawaharlal Nehru University, New Delhi 110067, India

Received 4 December 1997

Abstract

The consumption pattern of electrical energy in Delhi during the period 1984–93 has been analysed asa function of population and weather sensitive parameters. Linear multiple regression models of energyconsumption for different seasons have been developed. The models account for consumption variationsduring the winter, summer and postmonsoon seasons. 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction

For future estimations of power requirements, we require energy consumption patterns as func-tions of the weather. A large number of studies have been published [1–9] on energy consumptionmodels using regression, time-series and linear programming techniques.

India’s energy consumption needs like those of many developing countries have grown mani-fold during past several decades. The gap between energy supply and demand is widening inmost of its urban areas and particularly in metropolitan cities. For example, the total electricityrequirement and availability in Delhi were some 12.27 million units/day in 1984–85 and were30.02 and 29.76 million units/day respectively in 1993–94. The average rate of growth of require-ment has been 10.47% per annum during 1984–94 [10]. Moreover, the consumption varies sig-nificantly according to seasons. In view of the above, an attempt has been made in this paper tomodel the electrical energy consumption as a function of population and weather sensitive para-meters viz., sunshine hours, temperature, rainfall, relative humidity. The modelling technique isdescribed in Section 2 and the results are discussed in Section 3.

* Corresponding author. Tel:1 91-011-610-7676; Fax:1 91-011-686-5886; E-mail: [email protected]

0360-5442/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved.PII: S0360-5442(98)00087-5

352 M. Ranjan, V.K. Jain/Energy 24 (1999) 351–361

2. Description of the modelling technique

Delhi is situated between latitudes 28°259 and 28°539 N and longitudes 76°509 to 77°229 E.The area is 1483 km2. According to a 1991 census, the population was 9.37 million [11]. It bordersthe states of Utter Pradesh, Haryana and Rajasthan. The climate is semi-arid. Meteorological data[12] are available for the winter (December through February), the premonsoonal season (March–May), the summer (June–August), and the postmonsoonal season (September–November). Thevariation in the population data [11] over the study period is approximately linear and can beexpressed by the simple regression equation, population (millions)5 6.65831 0.3259t, wheret( 5 1, 2, 3,....) represents the year number starting from 1984.

To investigate the variation in the electrical energy consumption as a function of populationand weather sensitive parameters, a multiple regression model is considered in the present study.The model equation is

Y 5 a 1 O5i 5 1

biXi (1)

where Y represents the electrical energy consumption. The explanatory variablesXi denotemonthly average values of population (POP), temperature (T), relative humidity (RH), sunshineduration (SD) and rainfall (RAIN) respectively.a is the intercept andbi are regression coefficients.

3. Results and discussion

The data on electrical energy consumption, the population and weather sensitive parametersare used for estimating the regression coefficients in Eq. (1). Since there is drastic variation inthe weather over the year, a season-wise regression analysis has been attempted. Model resultsfor winter, summer, premonsoonal and postmonsoonal seasons are as follows:

3.1. Winter season

The regression results for winter season are shown in Table 1. The model consists of only thepopulation and temperature as explanatory variables. The positive and the negative signs of theregression coefficients of population and the temperature respectively, are in anticipated directions.The significance level of other meteorological variables were found to be very poor, hence they

Table 1Regression results for the winter season

Independent variables Coefficients Standard t-value Significance

Constant 2 25.4682 2.3881 2 10.6645 0.0000Population 5.9647 0.2001 29.8062 0.0000Temperature 2 0.3389 0.1136 2 2.9814 0.0065

R2(Adj.) 5 0.9725

353M. Ranjan, V.K. Jain/Energy 24 (1999) 351–361

Table 2Results of analysis of variance for the winter season

Source Sum of squares Degree of Mean square F-ratio P-valuefreedom

Model 671.455 2 335.727 444.584 0.0000Error 18.1236 24 0.755 – –

were excluded from the model. An examination oft-statistics [13] reveals that thet-values forthe constant (a) and the regression coefficients (b1 andb2) are greater than the critical tabulatedvalue of 2.064 forN-3 degrees of freedom whereN 5 27. It may be noted that for the winterseason there are 27 observations over a 9 year period (1984–93). Thus the null hypothesis thatthe individual slope coefficients are zero, is rejected. The results of analysis of variance are shownin Table 2. TheF-value is the ratio of mean sum of squares due to the model and the error. Themean sum of squares are calculated by dividing the explained sum of squares (ESS) and residualsum of squares (RSS) by associated degrees of freedom respectively [13]. The computedF-ratio5 444.589 is very large compared with critical value ofF 5 3.40 for degrees of freedom (2,24)

Fig. 1. Normal probablity plot of residuals for the winter season.


Fig. 2. Observed vs. predicted electric energy consumption for the winter season.

at 5% level of significance. This indicates that the null hypothesis, requiring all slope coefficientsto be simultaneously zero, is rejected. The coefficients of determination adjusted for degrees offreedomR2(Adj.) which is a measure of goodness of fit, is< 0.9715. It implies that 97% ofvariation in electrical energy consumption can be explained by only two variables i.e., populationand temperature. On the basis oft-statistics,F-ratio andR2(Adj.) values, the model fit is foundto be good. The adequacy of the model is further examined by using residual analysis. The normalprobability plot of residuals, a useful tool in this regard, is given in Fig. 1. It may be seen thatthe points in the plot are clustering around a straight line. This indicates that residuals follow anormal distribution i.e. they are uncorrelated. A plot of observed vs. predicted values is given inFig. 2 which also demonstrates the adequacy of the model.

3.2. Summer season

The regression and analysis of variance results for summer months (June, July and August)are given in the Tables 3 and 4. The best model fit is again obtained when population and tempera-ture are the only explanatory variables considered. However, the sign of both the regressioncoefficients is positive. The positive coefficient of temperature indicates higher consumption of


Table 3Regression results for the summer season

Independent variables Coefficients Standard error t-value Significance level

Constant 2 44.2198 2.1386 2 20.6765 0.0000Population 6.9926 0.1206 57.9768 0.0000Temperature 0.2447 0.0618 3.9570 0.0006

R2(Adj.) 5 0.9925

Table 4Results of analysis of variance for the summer season


Model 934.689 2 467.344 1716.94 0.0000Error 6.532 24 0.272 – –

Fig. 3. Normal probablity plot of residuals for the summer season.


Fig. 4. Observed vs. predicted electric energy consumption for the summer season.

electricity as the temperatures rise during the summer. All thet-statistics in Table 3 are signifi-cantly greater than the criticalt-value ( 5 2.064) for 24 degrees of freedom and 5% level ofsignificance. This implies that the regression coefficients are highly significant. The computedF-ratio ( 5 1716.94) in Table 4 is also found to be very much greater than theF(2.24) at 5% levelof significance. The value of coefficient of determinationR2(Adj.) is 0.9925 which indicates that< 99% variation in electric consumption in summer can be explained by population and tempera-ture alone. The normal probability plot given in Fig. 3 shows all the points approximately alonga straight line which indicates that there is no correlation among the residuals. The observed andpredicted values of the energy consumption are compared in Fig. 4 The above results indicatethe suitability of the model obtained in Table 3.

3.3. Premonsoonal season

For the months of March, April and May, the regression and analysis of variance results areshown in Tables 5 and 6. In the initial stages of model building, all the explanatory variableswere considered. Thet-statistics of all the variables except sunshine duration and relative humiditywere found to be insignificant. Hence they were excluded from the model. It may be seen in


Table 5Regression results for the premonsoon season


Constant 43.6125 5.9466 7.3340 0.0000Sunshine duration 2 0.0482 0.0203 2 2.3668 0.0264Relative humidity 2 0.3183 0.0882 2 3.6063 0.0014

R2(Adj.) 5 0.3868

Table 6Results of analysis of variance for the premonsoon season


Model 363.326 2 181.663 9.201 0.0011Error 473.834 24 19.743 – –

Fig. 5. Normal probablity plot of residuals for the premonsoon season.


Fig. 6. Observed vs. predicted electric energy consumption for the premonsoon season.

Table 5 thatt values of the coefficients are significant at 5% level of significance. The calculatedF-ratio (9.201) is also greater than the criticalF-value (3.40). However the value ofR2(Adj.) 50.3868 is not so good. It implies that sunshine duration and RH can account for only< 39%variation in electric energy consumption. The results of residual analysis shown in Fig. 5 indicatethat the points are along a straight line. Although, the results oft andF-statistics are reasonablysatisfactory, the overall fitness of the model is not so good as inferred from the plot of observedvs. predicted consumption (Fig. 6). One of the possible reasons for not being able to model theelectric energy consumption in a satisfactory manner could be the frequent power breakdown andloadshedding in the month of May.

3.4. Postmonsoonal season

The results for best model fit given in Tables 7 and 8, are obtained when population, tempera-ture and rainfall are considered as explanatory variables. The signs of all the coefficients arepositive. It may be noted that the magnitude of coefficient of rain is very small which impliesnegligible contribution to the variation in the electricity consumption. Thet-statistics of individualvariables is greater than the criticalt-value (2.069) for 23 degree of freedom and at 5% level ofsignificance. The modelF-ratio ( 5 584.93) shown in Table 8 is significantly higher thanF-value


Table 7Regression results for the postmonsoon season


Constant 2 40.8423 1.8770 2 21.7583 0.0000Population 6.0697 0.1570 38.6442 0.0000Temperature 0.3490 0.0426 8.1883 0.0000Rainfall 0.0055 0.0021 2.6628 0.0139

R2(Adj.) 5 0.9854

Table 8Results of analysis of variance for the postmonsoon season


Model 752.697 3 250.899 584.934 0.0000Error 9.865 23 0.428 – –

Fig. 7. Normal probability plot of residuals for the postmonsoon season.


Fig. 8. Observed vs. predicted electric energy consumption for the postmonsoon season.

for (3,23) degrees of freedom at 5% level of significance. TheR2(Adj.) value is 0.9854. Thenormal probability plot shown in Fig. 7 clearly exhibits a linear behaviour. The comparison ofobserved vs. predicted consumption shown in Fig. 8 also point towards the adequacy of themodel fit.

From the above, it is concluded that linear multiple regression models can account for mostof the variations in the electric energy consumption in winter, summer and postmonsoon monthsexcept during premonsoonal season. Based on the results in Tables 1, 3, 5 and 7, the followingmodel equations are obtained for different seasons:

Winter: Y 5 2 25.4681 5.964(POP)2 0.338(T)

Summer:Y 5 2 44.2191 6.992(POP)1 0.244(T)

Premonsoon:Y 5 43.6122 0.048(SD)2 0.318(RH)

Postmonsoon:Y 5 2 40.8421 6.069(POP)1 0.349(T)1 0.005(RAIN)


The above models are quite different from the model proposed by Al-Garni et al. [9] to explainthe variation in electric energy consumption in the city of Dhahran in eastern Saudi Arabia. Theirmodel equation does not describe the data set of the present study. This may be due to differentgeographical and environmental attributes of Delhi and Dhahran.

Acknowledgements

One of us, Manish Ranjan, would like to thank University Grants Commission for providingfinancial assistance in the form of Junior Research Fellowship during the course of this study.

References

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the International Symposium on Energy and Ecological Modelling sponsored by the International Society forEcological Modelling, April 20–23. Loutsville (KY) 1981.

[6] Luhanga ML, Mwandosya MJ, Lutejanya PR. Energy—The International Journal 1993;18(11):1171.[7] Reddy TA, Claridge DE. Energy and Buildings 1994;21(1):35.[8] Little TA. Wind Engineering 1993;17(1):9.[9] Al-Garni AZ, Zubair SM, Nizami JS. Energy—The International Journal 1994;19(10):1043.

[10] Annual report, Central Electricity Authority, Northern Regional Electricity Board, New Delhi, 1984–1993.[11] Delhi Statistical Handbook, Bureau of Economics and Statistics. Delhi: Delhi Administration, 1991.[12] Meteorological data, Indian Meteorological Department, Lodhi Road, New Delhi, 1984–1993.[13] Gujarati DN. Basic Econometrics. New York: McGraw Hill, 1988.

modelling of electrical energy consumption in delhi

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