forecasting monthly peak demand of electricity in india—a critique
TRANSCRIPT
Energy Policy 45 (2012) 516–520
Contents lists available at SciVerse ScienceDirect
Energy Policy
0301-42
doi:10.1
n Corr
E-m
srinivas1 As
journal homepage: www.elsevier.com/locate/enpol
Forecasting monthly peak demand of electricity in India—A critique
Srinivasa Rao Rallapalli a, Sajal Ghosh b,n,1
a School of Energy Studies, Management Development Institute (MDI), Gurgaon, Indiab Management Development Institute (MDI), Room no. C-10, Scholar Building, MDI, Mehrauli Road, Sukhrali, Gurgaon 122001, India
a r t i c l e i n f o
Article history:
Received 11 November 2011
Accepted 25 February 2012Available online 6 April 2012
Keywords:
Peak demand forecasting
MSARIMA
India
15/$ - see front matter & 2012 Elsevier Ltd. A
016/j.enpol.2012.02.064
esponding author. Tel.: þ91 124 4560309; fa
ail addresses: [email protected],
[email protected] (S.R. Rallapalli), sghos
sistant Professor, Economics.
a b s t r a c t
The nature of electricity differs from that of other commodities since electricity is a non-storable good
and there have been significant seasonal and diurnal variations of demand. Under such condition,
precise forecasting of demand for electricity should be an integral part of the planning process as this
enables the policy makers to provide directions on cost-effective investment and on scheduling the
operation of the existing and new power plants so that the supply of electricity can be made adequate
enough to meet the future demand and its variations. Official load forecasting in India done by Central
Electricity Authority (CEA) is often criticized for being overestimated due to inferior techniques used for
forecasting. This paper tries to evaluate monthly peak demand forecasting performance predicted by
CEA using trend method and compare it with those predicted by Multiplicative Seasonal Autoregressive
Integrated Moving Average (MSARIMA) model. It has been found that MSARIMA model outperforms
CEA forecasts both in-sample static and out-of-sample dynamic forecast horizons in all five regional
grids in India. For better load management and grid discipline, this study suggests employing
sophisticated techniques like MSARIMA for peak load forecasting in India.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Electricity is one major ingredient for economic developmentof any nation. Considering the importance of electricity it wouldbe prudent for developing nations and under developed nations toplan their investments in electrical network based on the fore-casts using advanced scientific methods as both under investmentand over investment would create problems. Under investmentwill cause the problems related to electricity shortage while overinvestment will create standard assets and affect the investmentsin other developmental activities as these countries typically facethe scarcity of resources.
Electricity demand has unique characteristics as it is non-storable,and there are seasonal and diurnal variations. Electricity demandforecast is essential for both electricity system planners and opera-tors; the only difference in their requirements is the forecast horizon.In case of planners the focus is on long term horizon while for systemoperators the focus is on medium to short term forecasts.
Electricity demand based on the forecasting horizon can bedivided into three categories: long term, medium term and shortterm. Long term forecast is used for taking policy decisions,system planning and resource allocation. Medium term forecasthelps in planning yearly maintenance activities of power plants
ll rights reserved.
x: þ91 124 2340147.
[email protected] (S. Ghosh).
and monthly peak and energy demand managements while shortterm forecast helps in day to day operation of power plants andelectrical network to manage daily loads effectively.
India has a total installed power capacity of 182,344 MW as ofSeptember 2011. Region wise northern, western, southern, east-ern and north eastern regions contain 48,720; 56,250; 49,400;25,570 and 2330 MW respectively. India is facing huge powershortage both in terms of energy and peak demand.2 As per theCentral Electricity Authority (CEA) published data India experi-enced energy deficit of 8.5% and peak demand shortage of 9.8% forthe financial year 2010–11. Region wise energy and peak demandshortage are provided in Table 1.
Power shortage particularly peak load shortages have anadverse effect on the overall economy. According to a study in2009 by the Manufacturers’ Association for Information Technol-ogy (MAIT) and Emerson Network Power, Indian industry hassuffered a loss of $8.64 billion on account of power downturn inthe year 2008–09.
India has skewed distribution of primary energy resources. Forexample, most of our coal and lignite resources are located ineastern and southern regions while hydroelectric resources arepredominantly in the North and North Eastern regions. At thesame time, major load centers are concentered in the northernand western regions. Considering the regional disparities in terms
2 Energy demand (in MWh) is the area under the load curve whereas peak
demand (in MW) is the maximum demand on the load curve at a given time.
Table 1Energy and peak shortages.
Region Energy deficit(million units)
Peak shortage(MW)
Northern 10.9 11.9
Western 11.0 10.9
Southern 10.5 14.5
Eastern 7.7 11.6
North-Eastern 0.3 5.9
3 In our case it is assumed that the trend includes the cyclical component. So,
trend and seasonal components are the permanent components whereas random
component captures all idiosyncratic nature of the series.
S.R. Rallapalli, S. Ghosh / Energy Policy 45 (2012) 516–520 517
of resource availability and power requirements it becomesincreasingly important to forecast the region wise peak loadrequirements with greater precision so that the construction ofpower plants’ schedule and electricity network can be adequatelyplanned. Further with the introduction of national wide Powerexchange it would be extremely beneficial for the merchantpower plant owners to identify the plant sites and also to plantheir yearly activities.
In India periodic electricity demand forecast is carried out byCentral Electricity Authority (CEA), a statutory body under theMinistry of Power. CEA publishes Electric Power Survey of Indiaevery five years (long term forecasts). Using partial end-usemethod it forecasts the yearly demand for the next five yearsand uses trend exploration method for forecasting demand at theend of the subsequent two five-year plans.
In addition CEA also publishes every year a Load GenerationBalance Report (LGBR) which provides the region wise monthlyforecast for the next financial year. The latest report is released forthe financial year 2010–11 which contains the monthly regionwise energy (MU) and peak demand (MW) from April 2011 toMarch 2012. As per the report CEA uses trend method forforecasting monthly energy and peak demand.
One of the criticisms raised against the trend method is thatthough the method has the advantage of its simplicity andproviding quick preliminary estimate of the forecasted value ofthe variable, it ignores the impacts of uncertainty, randomness,seasonality and non-stationarity, which are inherent featuresassociated with power demand data. Application of simplisticmethod like trend analysis makes it difficult for the distributioncompanies to take appropriate business decisions resulting inhuge monetary losses.
Rao (2002) and Chattopadhyay (2004) opine that electricitydemand in India has seldom been scientifically estimated. Fore-casts made by the CEA have found to have overestimated demand.
Considering the importance of electricity demand forecastingin India and criticisms faced by CEA on forecasting an attempt hasbeen made to assess the performance of the CEA’s region wisemonthly peak demand forecast using the performance parameterslike Root Mean Square Error (RMSE), Mean Absolute Error (MAE)and Mean Absolute Percent Error (MAPE).
The study also finds opportunities for improving the monthlyregion wise peak demand forecast. There is an array of methodsthat are available today for demand forecasting. An appropriatemethod is chosen based on the frequency of the data and thedesired nature of the forecasts. The study specifically deploysMultiplicative Seasonal Auto-regressive Integrated Moving Aver-age (MSARIMA), a univariate time series technique, for monthlypeak demand forecasts.
The theoretical study of medium to short-term demand forecast-ing of electric power systems began in 1980s, and a series ofunivariate forecasting methods, such as autoregressive (AR) algo-rithm, moving average (MA) algorithm, general exponential smooth-ing algorithm, autoregressive-moving average (ARMA) algorithm, and
autoregressive integrated moving average (ARIMA) algorithm havebeen developed and employed in electricity demand forecasting.
Tserkezos (1992) employed ARIMA models for forecastinghousehold electricity consumption in Greece using monthly as wellas quarterly data covering the period from January 1975 to January1989. Chavez et al. (1999) used ARIMA univariate time-seriesanalysis for modeling and forecasting future energy productionand consumption in Asturias by using monthly data from 1980 to1996. Saab et al. (2001) employed three different univariate modelsnamely, AR, ARIMA and combining an AR(1) with a high pass filterto forecast monthly electric energy consumption in Lebanon. It hasbeen observed that multiplicative double-seasonal ARIMA andexponential smoothing (ES) models outperform ANN forecasts ofelectricity demand for lead times up to a day ahead for the state ofRio de Janeiro in Brazil and for England and Wales (Taylor et al.,2006). Ediger and Akar (2007) forecasted primary energy demand ofTurkey from 2005 to 2020 using ARIMA and seasonal ARIMAmodels. Erdogdu (2007) estimated short and long run price andincome elasticities of electricity demand in Turkey using co-integra-tion technique and, forecasted future growth in electricity demandusing ARIMA modeling.
As regards to univariate electricity demand forecasting inIndia, Ghosh and Das (2002) forecast monthly maximum elec-tricity demand for the state Maharashtra, India, using MSARIMAmethod for monthly data spanning from April 1980 to June 1999.Ghosh (2008, 2009) forecasts monthly peak and hourly demandsin the northern gird of India and compares those forecasts withHolt–Winters multiplicative exponential smoothing (ES) fore-casts. It has been observed that MSARIMA forecasts outperformES forecasts in both the cases.
2. Univariate time-series forecasting models
A time series usually contains secular trends, seasonal varia-tions, cyclical movements and irregular components. Cyclicalcomponent, which is basically related to the business cyclemovement, causes change considerably over a period of 10–15years. Hence for a short span of time it becomes really difficult todistinguish between the trend and cyclical components in aseries.3
The term ‘univariate time-series’ refers to a time-series thatconsists of single (scalar) observations recorded sequentially overequal time increments. Univariate time-series analysis incorpo-rates making use of historical data of the concerned variable toconstruct a model that describes the behavior of this variable(time-series). This model can, subsequently, be used for forecast-ing purpose. Univariate models are the norm for load forecastingfor lead times up to about 6 h ahead, and, due to the lack ofreadily available weather forecasts, they are sometimes used forlonger lead times (Taylor et al., 2006).
2.1. ARIMA model
A linear non-stationary stochastic process is said to be homo-geneous of degree d when upon differentiating the originalprocess by d times, the resulting transformed process becomescovariance-stationary. If the original series Xt is homogeneous ofdegree d, then
DdXt ¼ ð1�LÞdXt ¼ Zt , t¼ 1,2,3,. . .,T ð1Þ
is covariance-stationary. Here, L is the backward shift operator.
Fig. 1. Monthly peak demand in MW.
S.R. Rallapalli, S. Ghosh / Energy Policy 45 (2012) 516–520518
An integrated process Xt is designed as an ARIMA (p, d, q), if takingdifferences of order d, a stationary process Zt of the type ARMA (p,q) is obtained.
The ARIMA (p, d, q) model is expressed by the function
Zt ¼f1Zt�1þf2Zt�2þ � � � þfpZt�pþut�y1ut21�y2ut22� � � ��yqut2q
or fðLÞð12LÞdXt ¼ yðLÞut
ð2Þ
2.1.1. Non-stationary homogeneous models with seasonal
variations, ARIMA (P, D, Q)s
In most of the monthly electricity time series data, seasonalvariation is one of the main sources of non-stationarity. Toremove seasonal non-stationarity of such series where season-ality is daily, one can proceed with seasonal differencing by s¼24times. The seasonal models ARIMA (P, D, Q) which are notstationary but homogenous of degree D can be expressed as
Zt ¼F1Zt�sþF2Zt�2sþ � � � þFpZt�psþdþut�Y1ut�s�Y2ut�2s� � � �
or FpðLsÞð12Ls
ÞDXt ¼ dþFQ ðL
sÞut ð3Þ
where F and Y are fixed seasonal autoregressive (AR) and movingaverage (MA) parameters.
2.1.2. General multiplicative seasonal models,
ARIMA (p, d, q) (P, D, Q)s
These models take into account the effect of trend andseasonal fluctuations of a time series and are expressed as
FpðLsÞfpðLÞð12Ls
ÞDð12LÞdXt ¼YQ ðL
sÞyqðLÞut ð4Þ
2.2. ARIMA model building
For a given time series, it is important to know which ARIMAmodel is capable of generating the underlying series. In otherwords, which model adequately represents the behavior of theconcerned Time Series so that the forecasts of the series understudy can be done precisely. Box-Jenkins considers model build-ing as an iterative process which can be divided into four stages:identification, estimation, diagnostic checking and forecasting.
2.2.1. Identification
This stage basically tries to identify an appropriate ARIMAmodel for the underlying stationary time series on the basis ofSample Autocorrelation Function (ACF) and Partial Autocorrela-tion Function (PACF). If the series is nonstationary it is firsttransformed to covariance-stationary and then one can easilyidentify the possible values of the regular part of the model i.e.autoregressive order p and moving average order q in an uni-variate ARMA model along with the seasonal part.
2.2.2. Estimation
In the estimation stage, point estimates of the coefficients canbe obtained by the method of maximum likelihood. Associatedstandard errors are also provided, suggesting which coefficientscould be dropped.
2.2.3. Diagnostic checking
In this stage, additional autoregressive and moving averagevariables can be added and their statistical significance can beexamined. One should also examine whether the residues of themodel appear to be white noise process. After the model has beenre-specified, it will be re-estimated and diagnostic checks will beapplied again until the coefficients are reasonably statisticallysignificant and the residuals are random.
2.2.4. Forecasting
After the diagnostic checking, comes the fundamental aim of themethodology, i.e., the forecasts of the future values of the time series.
3. Data description and statistical analysis
Region wise unrestricted Peak Demand (MW) for the periodApril 2005–March 2011 for the five regions namely north, west,east, south and south-east is collected from Central ElectricityAuthority (CEA) graphical representations of which is given inFig. 1, while statistical properties of these series are provided inTable 2.
The sample autocorrelation function (ACF) and partial auto-correlation function (PACF) have been used to identify thestationarity of the series and possible values of the regular partof the model, that is, autoregressive order p and moving averageorder q in a univariate ARMA model along with the seasonal part,which has then been estimated by maximum likelihood. Theresiduals are then inspected for any remaining autocorrelation ofthe residual series.
The estimated parameters with their standard error, t statisticsand probability values of the best fitted model in terms ofsmallest Akaike information criterion (AIC) and root mean squareerror (RMSE) criterion to explain the monthly peak demand (MW)of electricity from January 2005 to March 2011 for all the fiveregions of India are shown in Table 3. As shown in the tables,coefficients of all AR, MA, SAR and SMA terms are statisticallysignificant at 5% level. The stationarity and invertibility conditionsfor respective seasonal and non-seasonal AR and MA terms arealso satisfied. In all the cases, the residual series appear to bepurely white noise as shown in Table 4.
4. Comparison of CEA and MSARIMA model forecasts
In sample static forecasting is carried out using MSARIMAmodels for the period April 2010–March 2011 for individualregions in order to access the performance of the model. MSAR-IMA forecasts and forecasts made by CEA using trend method arethen evaluated using standard performance factors such as RootMean Square Error (RMSE), Mean Absolute Error (MAE) and MeanAbsolute Percentage Error (MAPE). As shown in Table 5, MSAR-IMA forecasting errors are much smaller than that of CEA errors.Additionally, present study also made an attempt to performdynamic out of sample forecasts for the period April 2011–July2011 and compares it with CEA forecasts after actual peakdemand data got published. Table 6 indicates that MSARIMA
Table 2Statistical properties of the data series.
North South West East North-East
Mean 30675.92 26113.27 34081.83 11201.8 1528.4
Median 30857 26054 34969 11284 1566
Maximum 37431 33256 40798 13767 1913
Minimum 23180 20900 25308 8480 1176
Std. dev. 3249.516 3222.359 3726.112 1513.353 182.179
Skewness �0.10407 0.208397 �0.25745 �0.16297 �0.14048
Kurtosis 2.516908 2.16481 2.112191 1.846494 1.897837
Jarque-Bera stat. 0.864689 (0.64) 2.722685 (0.25) 3.29167 (0.19) 4.490019 (0.10) 4.042827 (0.13)
Figures in brackets are probability values.
Table 3Estimated parameters of ARIMA model to explain monthly region wise peak
demand.
Variable Coefficient Std. error t-Statistic Prob.
Northern region
AR(1) 0.417808 0.113194 3.691068 0.0005
AR(2) 0.512017 0.111587 4.588511 0
MA(12) �0.86371 0.03697 �23.3625 0
Western region
C 1218.865 296.6055 4.109381 0.0001
AR(1) 0.679991 0.093961 7.236922 0
MA(12) �0.906684 0.044546 �20.35388 0
Southern region
MA(1) �0.900144 0.06862 �13.11774 0
SMA(12) �0.811421 0.067238 �12.0679 0
Eastern region
MA(1) �0.65175 0.094781 �6.876352 0
SMA(12) �0.836799 0.036006 �23.24055 0
North Eastern region
AR(12) �0.389596 0.135724 �2.870515 0.0061
MA(1) �0.300375 0.138288 �2.1721 0.0349
SMA(12) �0.873933 0.045944 �19.02169 0
Table 4Diagnostic checking of estimated ARIMA model.
Lags Region
North West South East North East
Probability of Ljung–Box Q-statistics
4 0.232 0.042 0.115 0.151 0.101
5 0.486 0.049 0.082 0.271 0.251
6 0.695 0.089 0.128 0.387 0.200
7 0.791 0.150 0.210 0.499 0.326
8 0.676 0.219 0.277 0.587 0.434
9 0.632 0.253 0.372 0.524 0.535
10 0.616 0.256 0.385 0.615 0.478
11 0.696 0.316 0.208 0.707 0.519
12 0.761 0.385 0.271 0.786 0.610
13 0.833 0.334 0.317 0.781 0.700
14 0.814 0.335 0.356 0.800 0.759
15 0.753 0.375 0.241 0.787 0.740
16 0.807 0.419 0.298 0.774 0.793
17 0.851 0.472 0.178 0.781 0.833
18 0.866 0.528 0.222 0.833 0.816
19 0.874 0.588 0.266 0.876 0.663
20 0.896 0.491 0.244 0.673 0.453
21 0.911 0.523 0.197 0.728 0.216
22 0.937 0.470 0.204 0.635 0.211
23 0.947 0.500 0.248 0.690 0.250
24 0.888 0.199 0.231 0.671 0.218
25 0.893 0.239 0.255 0.706 0.251
26 0.898 0.273 0.160 0.737 0.267
27 0.923 0.267 0.196 0.766 0.245
28 0.943 0.302 0.172 0.750 0.289
Note: Q-statistic at lag is ‘K’ is a test statistic for the null hypothesis that there is
no autocorrelation up to order ‘K’.
S.R. Rallapalli, S. Ghosh / Energy Policy 45 (2012) 516–520 519
model again outperforms CEA forecasts. Considering superiorperformance of MSARIMA model one should argue that there isa good opportunity for CEA to improve its forecasts.
Table 5In-sample forecasting performance (from April 2010 to March 2011).
Region MSARIMA forecasts CEA forecasts
RMSE MAE MAPE RMSE MAE MAPE
North 806.465 660.818 1.923 2266.080 2059.083 6.103
West 658.246 597.737 1.599 1729.621 1174.333 4.280
South 718.237 537.856 1.771 1143.750 1221.797 3.770
East 315.402 250.651 1.912 1815.844 1714.333 13.100
North-East 44.415 35.144 2.054 170.164 149.167 8.910
5. Conclusion
The uncertainty, randomness, seasonality and non-stationarityrelated to electricity market sometimes make it difficult to takeappropriate business decisions. Electricity demand forecasting isvery important for a country like India which suffers from severepower shortages and regional imbalances. In addition, withgrowing competitive power market in India sophisticated loadforecasting is the need of the hour.
At present, the load forecasting tools used in India are archaicin nature and are not in line with the market requirements. Thereare a number of latest forecasting tools which can help us toforecast demand with better precision. Some of the promisingtools include MSARIMA, ARIMA-EGARCH, Exponential Smoothing,Vector Auto Regression, Neural Networks, etc.
The present study has attempted to forecast the region-wisemonthly peak demand using MSARIMR technique. In addition tothat, forecasting performance of the MSARIMA is compared withthat of CEA forecast based on trend method. It has been observedthat MSARIMA model outperform the CEA’s forecasts to a large
extent both in-sample and out-of-sample. Hence opportunityexists to improve the performance of CEA forecasts. This willhelp to achieve superior load management and grid discipline in apower-starved country like India.
Table 6Out of sample forecast (from April 2011 to July 2011).
Region MSARIMA forecasts CEA forecasts
RMSE MAE MAPE RMSE MAE MAPE
North 945.426 481.420 3.160 1647.641 922.250 7.640
West 833.676 353.604 2.820 1111.577 587.750 5.590
South 208.693 100.013 0.930 515.764 236.833 3.180
East 431.381 234.743 3.940 733.242 383.833 8.230
North-East 44.454 19.442 3.160 119.117 64.333 10.750
S.R. Rallapalli, S. Ghosh / Energy Policy 45 (2012) 516–520520
References
Chattopadhyay, P., 2004. Cross-subsidy in electricity tariffs: evidence from India.Energy Policy 32 (5), 673–684.
Chavez, S.G., Bernat, J.X., Colla, H.L., 1999. Forecasting of energy production andconsumption in Asturias. Energy 24, 183–198.
Erdogdu, E., 2007. Electricity demand analysis using cointegration and ARIMA
modelling: a case study of Turkey. Energy Policy 35, 1129–1146.Ediger, V.S., Akar, S., 2007. ARIMA forecasting of primary energy demand by fuel in
Turkey. Energy Policy 35 (3), 1701–1708.Ghosh, S., Das, A., 2002. Short-run electricity demand forecasts in Maharashtra.
Applied Economics 34 (8), 1055–1059.Ghosh, S., 2008. Univariate time series forecasting of monthly peak demand of
electricity in northern India. International Journal of Indian Culture and
Business Management 1 (4), 466–474.Ghosh, S., 2009. Univariate forecasting of day-ahead hourly electricity demand in
the northern grid of India. International Journal of Indian Culture and Business
Management 2 (6), 625–637.Rao, S.L., 2002. The political economy of power. Economic and Political Weekly.Saab, S., Badr, E., Nasr, G., 2001. Univariate modeling and forecasting of energy
consumption: the case of electricity in Lebanon. Energy 26 (1), 1–14.Taylor, J.W., de Menezes, L.M., McSharry, P.E., 2006. A comparison of univariate
methods for forecasting electricity demand up to a day ahead. International
Journal of Forecasting 22 (1), 1–16.Tserkezos, E.D., 1992. Forecasting residential electricity consumption in Greece
using monthly and quarterly data. Energy Economics 14 (3), 226–231.