Risk assessment due to local demand forecast uncertainty in the competitive supply industry

Risk assessment due to local demand forecastuncertainty in the competitive supply industry

K.L. Lo and Y.K. Wu

Abstract: A risk assessment on local demand forecast uncertainty is presented. The aim is tohighlight high-risk periods over different lengths of time and daily value-at-risk (VAR) due to loadforecast errors. A number of load forecasts have been performed, and the load forecast is based onARIMA models and ANN structures. With the residuals from load forecasting, the risk indexesover different time periods and seasons are formed. Moreover, a new methodology using thestandard deviation of load increment on evaluating the risk is proposed. In contrast with thestandard forecasting method that relies on a sophisticated forecast procedure, the new approachprovides a useful and fast method to evaluate the risk due to load forecast uncertainty for a varietyof local demand profiles. Finally, the VAR methodology combined with the NETA system isapplied to a local electricity supplier in the UK.

1 Introduction

The UK electricity market has been completely open tocompetition since the sub-100kW market was deregulatedin September 1998. All commercial and industrial custo-mers, as well as domestic customers, can choose theirelectricity suppliers. Moreover, on 27 March 2001, the NewElectricity Trading Arrangements (NETA) came into force,replacing the Pool in England and Wales, and establishingopportunities for wholesale energy trading [1]. Theimplementation of NETA poses new challenges to thesupply business activities of settlement, trading and riskmanagement. Nowadays, the supply market is an extremelytough, high-risk and low-margin commodity business.The typical supply industry faces different types of risk:

� Risk of load forecast error� Risk of equipment� Risk of transmission constraints� Risk of financial return� Risk within contracts

Among the different risks, a key factor is load forecastuncertainty. A number of papers [2, 3] discussed the risk orimpact due to load forecast uncertainty. However, most ofthem paid attention to the problems of the traditionalpower industry without deregulation, and particularly fromthe aspect of system operators. After deregulation, the roleof the demand side is becoming more important. Under thenew arrangement, each electricity supplier must offer itspredicted loads to the system operator and accept anyimbalance payments or charges at settlement time. There-fore, armed with the information of risk assessment of load

forecast errors, private suppliers can better understand theirrisk exposures in energy contracts over different timesections, identify mechanisms to hedge those risks, andimplement such mechanisms. Different kinds of contractscould be used during different periods.In order to evaluate the risk due to demand forecasting,

short-term electrical load forecast (STLF) has becomeincreasingly important in the rise of the competitive energymarket. Load forecasting is however a difficult task becausethe load series is non-stationary and exhibits several levels ofseasonality. In addition, there are many important exogen-ous variables that must be considered. In the past 40 years,a large number of forecasting models and methods havebeen tried [4–6]. These methods are mainly classified intotwo categories: classical approaches such as auto regressiveintegrated moving average (ARIMA) [7] models andartificial intelligence (AI) based techniques. In this paper,we use ARIMA models and artificial neural network(ANN) techniques to predict electricity demands.In addition to forecasting methods, other important

concerns in this paper are to distinguish the characteristicsof different load profiles from system demands to localdemands. The cumulative system demand curves can beobtained from NETA reports. As for the profiling of localdemands, the Electricity Association in the UK haspublished eight types of load profiling under 100kW [8].Among these typical demand curves, the domestic curve isthe most changeable; that is, the risk of domestic electricitysuppliers due to load forecast uncertainty is higher than therisk of others.This paper investigates the risk index of domestic

suppliers due to load forecast uncertainties in the compe-titive power market using the residuals from STLF. Thepaper also presents an efficient method to evaluate the riskover 48 time sections with the standard deviation of loadincrement obtained from historical load data. It could bevery useful for the electricity supply industry to designshort-term contracts and help domestic end-users choosetheir suppliers wisely as well as manage their loadseffectively. Furthermore, risk measurement is becomingmore important in the electric power industry [9] because itcould help private firms in evaluating their financial riskexposure in the uncertain power market. In the final Section

The authors are with the Power Systems Research Group, Department ofElectronic and Electrical Engineering, University of Strathclyde, Glasgow G11XW, UK

r IEE, 2003

IEE Proceedings online no. 20030641

doi:10.1049/ip-gtd:20030641

Paper first received 23rd May 2002 and in revised form 5th March 2003. Onlinepublishing date: 24 July 2003

IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003 573

of this paper, daily value-at-risk (VAR) analysis isperformed on a local electricity supplier using historicalimbalance settlement data in the NETA system and thevolumes of load forecast residuals.

2 System data and data pre-processing

Under the new NETA arrangements in the UK, 1h prior toeach trading period (the original gate-closure time was3.5h), all significant (over 50MW) generators and suppliersprovide a ‘firm physical notification’ (FPN) outlining theirexpected generation and consumption, which allows thesystem operator (SO) to start planning requirements and toinvoke ancillary service contracts. Accumulating theindividual demand forecasts of suppliers, network opera-tors, and directly connected customers, the total powerdemands in the system will be obtained. With the historicalpower demands, SO will predict the system loads in the nexttrading period to make sure that the power flows on thetransmission system remain within technical limits. In thiswork, the historical system demands [10] from April 2001 toOctober 2001 have been used.An electricity supplier is anyone with the appropriate

licence that may supply customers. Typical electricitysuppliers in the UK are divided into two categories:domestic and business suppliers. In this work, the historicallocal load profiles from December 2000 to October 2001have been used to analyse and predict the domestic loads atthe supply end. However, data in May 2001 were excludedbecause the load record was incomplete during this month.For each month, the load data in the first three weeks wereused for training, and the data in the last week were used fortesting. The local demand samples, recorded every half-hour, of domestic customers have been obtained from anelectricity supplier in the UK.These sample data were limited to a very small load

because it can be expensive to retrieve large amounts of dataeach day through domestic load profile meters. This is thereason that research into the load profile in the UK isbooming instead of the installation of load profile meters ina large supply area. In addition, there are obviousdifficulties in obtaining complete load data in the commer-cially sensitive deregulated power market. However, thesample data still can offer us some useful information.Under NETA, large suppliers have benefited relative tosmall suppliers because their load profiles are more stableand are closer to the system load profile. By contrast, smallsuppliers have faced strict challenges because of loadforecast uncertainty. This impact was derived from theswitching behaviour of customers and the unstable correla-tion between load and weather variables. In other words,small suppliers have suffered from higher risk than largesuppliers. Therefore, the sample data in our work could beregarded as the worst case as it has the most random loadprofile, and presents the highest risk in load forecastuncertainty. If a larger block of load is considered, a highercorrelation between load and other exogenous variablesmay appear, such as weather, social activity, geographicalcharacteristics, economic structure, culture, and the life-styleof the customer. This demonstrates the need to perform anumber of correlation analyses to find some importantexogenous variables to assist in load forecasting. Inaddition, an optimal forecast method and parameterestimate technique would be more successful in thetraditionally larger block of load, because the regularcharacteristics of the larger block would enable moreadvanced forecasting techniques to be created, thus givingbetter results.

To predict power demands precisely, most papers takeinto account the factor of weather [11, 12]. In this work,daily and half-hourly weather data have been used toanalyse the relationship between them and loads bystatistical measures. These data have been obtained fromFair Isle Weather Station and Reading University in theUK.Before the load or weather data are ready to be used

as inputs of statistical measurement and forecastingmodels, they are classified into weekday and weekendprofiles. This is to differentiate the variation of dynamicload by the effect of calendar date or weather. Furthermore,in a competitive market, the significance of each timesection during one day is the same. All the results ofthe load forecast or the relationship between loads andweather will be considered on a basis of half-hour units inthis paper.

3 Description of the proposed forecast models

Two kinds of forecast method have been used, namelyARIMA and ANN. The principle of the ARIMA model isto forecast the current value of a variable by means of alinear combination of previous values of the variable andprevious values of noise. Although it is a complex techniquethat requires a great deal of experience to identify the orderof models, the ARIMA model is still the most popularlinear model. The basic description of the ARIMAmodel isillustrated by (1):

fpðBÞFðBsÞrdrDs Yt ¼ yqðBÞYðBsÞat ð1Þ

where fp, F;yq, Y are autoregressive and seasonal-moving-average parameters of the ARIMA model; rd and rD

s aretrend and seasonal difference equations, and B is a back-shift operator that defines Y(t�1)¼BY(t). By the differenceequations and both ACF and PACF plots, the significanthistorical data in certain time lags were chosen as inputvariables. For example, the input-output relationship of thepredicted function for the January local demand at theweekend is described by

ð1þ f1B2 þ f2B

24Þð1� B1Þð1� B24ÞY ðtÞ¼ ð1þ y1B2 þ y2B24ÞaðtÞ

ð2Þ

Thus, the time series forecasting function can be expressedas

Y ðtÞ ¼b1Y ðt � 1Þ þ b2Y ðt � 2Þ þ b3Y ðt � 3Þþ b4Y ðt � 24Þ þ b5Y ðt � 25Þ þ b6Y ðt � 26Þþ b7Y ðt � 27Þ þ b8Y ðt � 48Þ þ b9Y ðt � 49Þþ b10aðt � 2Þ þ b11aðt � 24Þ þ aðtÞ

ð3Þ

where the parameters bi(i¼ 0B11) are estimated with theleast squares method in this work. The same procedure isrepeated for the other nine months. Details of theforecasting function for each month are given in Section12.1. On the basis of forecast experience on most load timeseries, the most important time lags depend on the nearestavailable historical data and data which are close to one andtwo periods ahead. In addition, the forecasting functions forweekends are more complicated than those for weekdaysbecause the historical data at weekends are fewer. However,certain time series present other important time lags or acombination of them. Therefore, non-linear time seriesmodels or ANN techniques would be more suitable for usein these time series.

574 IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

ANN techniques have been used widely on the loadforecast problem in recent times. They are mathematicaltools originally inspired by the way the human brainprocesses information. The ANN may be seen as amultivariate, non-linear and non-parametric method, andit should be expected to model complex non-linearrelationships much better than traditional linear models.Moreover, it is not necessary for the researcher to postulatetentative models because it is able to automatically map therelationship between input and output data with continuous‘training’ of the network. In this paper, the feed-forwardback-propagation network inside the MATLAB neuralnetwork toolbox has been used as the training algorithm[13]. In addition, the method for identification of ANNinput variables utilised the PACF correlation analysistechnique. These neural networks are constructed withone input layer, one hidden layer, and one output layer withone node. The number of input and hidden nodes is notfixed. The input nodes depend on the PACF plot, and thehidden nodes and iteration numbers have been determinedby heuristics.In general, the accuracy of STLF depends on five major

factors:

1. The optimal forecast technique chosen for different loadprofiles

2. The optimal parameter estimate algorithm for a suitableforecast model

3. The inclusion of important exogenous variables that havea high level of correlation with load

4. The character of the load profile, such as the variance ofload increment

5. The lead time of the forecast

In our work, various forecast techniques [14, 15] and othernon-linear forecast models, such as bilinear and thresholdAR models, have been used. However, the deviation in thelocal demand forecast is still limited to 5%B8% in themean average percentage error (MAPE) which indicatesthat the forecast for small-range demand depends mainlyon the fluctuation of load profiles, because most forecasttechniques cannot trace violent changes through historicaldata. Therefore, the forecast results of single ARIMAmodels and ANN procedures are shown individually inthis paper. Our research is aimed at the correlationcomparison of forecast residuals between different forecastmethods, instead of the improvement of forecast accuracy.Then, a regular rule for detecting the risk index in eachtime period can be defined. The details are described inSections 6 and 7.The lead-time of load forecasting plays an important role

in the forecast accuracy. The gate-closure time of NETAhas reduced from 3.5h to 1h from 2 July 2002, which willreduce extra unnecessary balancing mechanism costs due toload forecast uncertainty. In contrast with one-hour-aheadload forecasting, a four-hour-ahead forecasting moduleconsists of 48 forecasting models in each forecasting period,and each model is used for one particular settlement periodin one day. Under four-hour-ahead load forecasting, thetime series would be reconstructed by selecting historicalload data every eight-settlement period; there are only sixhistorical load data within one day available to be used topredict the load in the next time section, which wouldincrease the forecasting errors. In this work, one-hour-ahead load forecasting has been implemented because theresults are of direct relevance to the newNETA gate-closuretime.

4 Different character of system and local demand(supplier demand)

In Fig. 1, temperature, weekday system demand and localdemand from 23 June to16 July 2001 are shown. From thisFigure, the following two points are noticed:(a) At first, it is observed that the profiles of local demand

are more complex than the curves of system demand nomatter what the shapes, vertical or horizontal deviation,especially in a small range of local demand. To illustrate thedifferences, a comparison of day-by-day demand curvesbetween local and system demands is shown in Fig. 2.System demands present a regular change over a whole day,but the local demands alter very irregularly from 7:00 AMto 9:00 PM even though they are likely to be at the sametemperature and time section, but on different days. Thereis no doubt that the forecast of local demands is a difficulttask, and similarly, it is evident that the risk due to loadforecast uncertainty for the supply industry is likely to behigh.(b) As expected, it is difficult to estimate the correlation

between temperature and loads from continuous time seriessuch as in Fig. 1 and Fig. 2. However, we divided load datainto 48 periods within one day and made an analysis ofsimilarity individually by using correlation coefficients. ThePearson correlation [16] in (4) has been used to measure thecorrelation coefficient in this paper between power demandsand temperature:

r ¼Xni¼1

ðxi � xavgÞðyi � yavgÞSxSyðn� 1Þ

ð4Þ

where n is the sample size, xavg is the mean of x, yavg is themean of y, Sx is the standard deviation of x and Sy is thestandard deviation of y.

The value of the correlation coefficient betweentwo kinds of demand and temperature is shown inFig. 3. From this Figure, it is observed that the relationshipbetween system demand and temperature has a higherand more stable correlation than the relationship betweenlocal demand and temperature. For example, from thecorrelation analysis in Fig. 3, the temperature rise inthe summer will introduce significant increase of

loca

l loa

ds, k

W 100

50

800700600500

h

40030020010005

syst

em lo

ads,

MW

(×1

04 )

4.0

3.5

3.0

2.5

80070060050040030020010002.0

tem

pera

ture

, °C 25

20

15

10

80070060050040030020010005

Fig. 1 Typical curves for temperature, system demands and localdemands


power consumption for the system demands, especiallyduring the time from 8:30 AM to 2:30 PM. By performingregression analysis, the system demands during theabove time periods can be solved as function of temperature

in (5):

PnðTnÞ ¼ 0:93036þ 0:083228Tn � 0:012758T 2n ð5Þ

where Tn¼T/Tmean is the normalised temperature andPn¼P/Pmean is the normalised power consumption.By performing the first order derivative of (5), the

temperature sensitivity (TS) of the system power consump-tion can be obtained, and the percentage of powerconsumption change for a 1% temperature increase canbe calculated. TS is a very useful coefficient to correct thepredictive values of system demands after completingtraditional load forecast procedures.In contrast, the correlation between local demands and

temperature is highly unstable. It is difficult to establish anyrule to trace or predict the effect of temperature on localdemands. To investigate comprehensively the correlationbetween local demand and temperature not only in thesummer but also in all other seasons, Fig. 4 gives a

summary of the statistical results during the four seasons in2001. From the statistical analysis, it is observed that thereis no definite positive or negative correlation between localdemand and temperature because the relationship betweenthem consists of a variety of factors, such as the life styles oflocal domestic consumers, social programmes [17], and thetypes of heaters that consumers use. For example, owing tolonger daylight in the summer, people are likely to beoutdoors and participate in social programmes at weekends,especially during hot days, which will lead to the decrease ofdomestic power consumption. Therefore, a negative corre-lation between temperature and local demand duringsummer weekends can be seen in Fig. 4b. Another exampleis that some domestic heating systems use gas instead ofelectricity; consequently the strong negative correlationbetween local demands and temperature does not exist inwinter. Instead, there may be positive correlation duringwinter weekends, which symbolises other domesticactivities.In this Section, the correlation between temperature and

load has been examined with sample data from a localelectricity supplier. However, different local demand profileswould lead to diverse relationships between load andtemperature. This is the reason that research on localdemand profile is growing in most power markets.

2.00 5 10 15 20 25 30 35 40 45 50

2.2

2.4

2.6

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3.0

3.2

3.4

3.6

3.8

4.0

pow

er d

eman

d, M

W (

×104 )

time, periods

100 5 10 15 20 25 30 35 40 45 50

20

30

40

50

60

70

80

90

100

110

pow

er d

eman

d, k

W

time, periods

a

b

Fig. 2 Comparison between system and local demand profilesa System demand profilesb Local demand profiles

−0.8

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−0.4

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time, half-hour periods in one day

30 35 40 45 50

0.4

0.6

0.8

1.0

corr

elat

ion

coef

ficie

nt

system demandslocal demands

Fig. 3 Correlation comparison between temperature and system,local demands

weekendsweekdays

weekendsweekdays

weekendsweekdays

weekendsweekdays

dc

ba

time, half-hour sections5040302010

corr

elat

ion

coef

ficie

nt

1.0

0.5

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−0.5

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1.0

0.5

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−0.5

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1.0

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0

−0.5

−1.0


corr

elat

ion

coef

ficie

nt

1.0

0.5

0

−0.5

−1.0

Fig. 4 Correlation coefficient between temperature and localdemand over one year


5 Numerical results of load forecasting

From the discussion in Sections 2 and 3, the STLF modelsfor weekdays and weekends in each month are different.Therefore, local demand data in each month are dividedinto two parts and we make use of ARIMA and ANNmodels to predict both weekday and weekend demands ineach month. As a result, there are 40 STLF models (2methods/period� 2 periods/month� 10 months) requiredfor load forecast because local demand data over tenmonths are used in this work. A single variable, historicalload data, is chosen for predicting future load profilesbecause there are no other available variables that arecorrelated with the sample local demands.To compare the forecast errors between system and local

demands, the historical load data on local and systemweekday demands from 2 to 20 July 2001 are used topredict the power demands from 23 to 27 July 2001.Obtained forecasting results from ARIMA models andANN are presented in Table 1 and Fig. 5 respectively. InTable 1, the mean absolute percentage error (MAPE) hasbeen used as the method to calculate forecast errors. Itsdefinition is given as:

MAPE ¼ 1N

XNi¼1

jpi � aij=ai ð6Þ

where p is the predicted value, a is the actual value, andN isthe number in each time section.As expected, the achieved accuracy from load forecast

depends on the variation of load profiles. For the forecastson system demands, the MAPE lies in a range of 0.41-0.48%, but for the forecasts on local demands, the rangeexpands to 5.5-5.9 %. The results have shown that the localdemands are difficult to predict owing to the uncertainty ofload profiles. Except for the load forecast with the July loaddata, the load data from December 2000 to October 2001except May 2001 have been used to analyse and forecastmonthly. Taking December 2000 as an example, bothforecast residuals from the ARIMA model and ANN areshown in Fig. 6. From this Figure, it is evident that thereare strong correlations between the forecast results ofARIMA models and ANN procedures. As a result, higherforecast errors are likely to appear in some specific periodsduring a whole day no matter which model is used. Forexample, it is observed that the 18th and 38th period havepeak forecast errors that are higher than errors in otherperiods with both forecasting methods. Similarly, a strongcorrelation between the results of the two types of forecastmethod has appeared in other months as well. Usingstatistical analysis as described above, we could observe thatsome high-risk peaks due to load forecast errors existedduring 48 eight periods in a whole day, and both linear andnon-linear forecast models point to the same time sections.All programs of the ARIMA models and ANN

structures have been written in MATLAB language. On aPentium-III personal computer, the response time of theARIMA model and ANN method for all test cases,including weekday and weekend loads, is less than oneminute, which makes them feasible for online application.

6 Analysis of risk values on load forecasting errors

From 40 STLF programs, residuals from load forecast havebeen calculated for a total of ten months. The residuals ofload forecast play a crucial role in the risk assessment due toforecasting uncertainty. It is worth noting that the residualsare calculated in kW instead of the MAPE values because

Table 1: Comparison between the forecast errors fromsystem and local demands

Time section Forecasting errors forsystem demand

Forecasting errors forlocal demand

ARIMA,%

ANN, % ARIMA,%

ANN, %

00:00B00:30 2.1586 2.6412 7.3565 7.3973

00:30B01:00 0.1771 0.4344 1.4965 2.7940

01:00B01:30 0.5220 0.5220 2.5324 4.4494

01:30B02:00 0.4430 0.3814 2.0577 2.0108

02:00B02:30 0.4714 0.5576 2.1597 3.2852

02:30B03:00 0.1493 0.2746 1.8687 3.0695

03:00B03:30 0.2479 0.2722 1.3222 2.4555

03:30B04:00 0.2739 0.3068 3.1368 3.6773

04:00B04:30 0.1795 0.2324 7.2519 9.3368

04:30B05:00 0.4126 0.2296 2.6698 4.9132

05:00B05:30 0.0826 0.2080 6.5489 5.0220

05:30B06:00 0.2942 0.4847 5.7657 5.0880

06:00B06:30 0.5469 0.5646 6.9059 4.9094

06:30B07:00 0.5664 0.6287 7.4786 9.3551

07:00B07:30 1.0272 0.3326 6.9846 6.5780

07:30B08:00 0.3769 0.3713 6.4660 4.0853

08:00B08:30 0.7615 0.5629 4.3608 9.9133

08:30B09:00 0.9777 0.3968 9.7961 7.0822

09:00B09:30 0.4724 0.3518 8.8582 8.9851

09:30B10:00 0.2846 0.2645 7.1400 5.9087

10:00B10:30 0.1284 0.0868 3.4762 3.5522

10:30B11:00 0.2694 0.2289 5.2383 5.0239

11:00B11:30 0.1795 0.1743 7.4345 6.2084

11:30B12:00 0.1513 0.2129 4.4230 4.2024

12:00B12:30 0.1297 0.1615 3.4465 4.4226

12:30B13:00 0.3960 0.2646 8.9812 9.4512

13:00B13:30 0.4621 0.3639 7.3624 6.2688

13:30B14:00 0.3026 0.2025 4.8268 6.0720

14:00B14:30 0.2421 0.1996 3.1399 2.8138

14:30B15:00 0.2316 0.1279 7.4745 6.0933

15:00B15:30 0.3295 0.2339 4.4942 5.2318

15:30B16:00 0.4791 0.3784 4.2991 5.6182

16:00B16:30 0.2594 0.2012 2.5938 1.5938

16:30B17:00 0.3098 0.2880 4.6597 4.3236

17:00B17:30 0.1814 0.1793 2.6448 4.1299

17:30B18:00 0.3139 0.4100 2.5008 3.2076

18:00B18:30 0.3912 0.3807 2.0183 1.2050

18:30B19:00 0.2933 0.2627 2.2493 2.2593

19:00B19:30 0.6559 0.4882 1.1321 2.6289

19:30B20:00 0.4559 0.4888 10.4359 10.1367

20:00B20:30 0.4469 0.2647 10.3808 11.6035

20:30B21:00 0.8148 0.7623 15.2836 19.2352

21:00B21:30 0.6302 0.5417 9.5374 14.0050

21:30B22:00 1.5011 0.8584 11.4621 8.1653

22:00B22:30 0.6413 0.3646 5.1290 6.1437

22:30B23:00 0.4970 0.4242 6.1049 4.8002

23:00B23:30 0.9395 0.6999 7.8324 12.9718

23:30B24:00 0.8313 0.4960 3.4840 2.9214

Average 0.4769 0.41 5.5042 5.93


the actual load volumes are more meaningful in acompetitive power market. For risk assessment, theresiduals from all load forecasts have been transferred tothe risk index in per unit values and the base value is themaximum value of forecast residuals during the 48 time

sections. In this paper, the risk index is separated among 48half-hour periods as indicated in Fig. 7 and Fig. 8 forweekdays and weekends respectively. Additionally, the riskindex is also separated into seasons, as indicated in Fig. 9.The risk index in these Figures is concluded from all

2.0700 750 800 850

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actual demand curvesforecasting demand curves

actual demand curvesforecasting demand curves

Fig. 5 Forecasting results for 23-27 July 2001 between systemdemands and local demandsa System demand profilesb Local demand profiles

00 5 10 15 20 25 30 35 40 45 50

2

4

6

8

load

fore

cast

err

ors,

kW

10

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time, sections during one day

ARIMA modelANN model

Fig. 6 Comparisons of load forecast errors by ARIMA and ANNfor December 2000

00 5 10 15 20 25 30 35 40 45 50

0.1

0.2

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pu

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Fig. 7 Risk index of load forecast errors on weekdays

00 5 10 15 20 25 30 35 40 45 50

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risk,

pu

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Fig. 8 Risk index of load forecast errors at weekends

summerwinter

1.0

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risk,

pu

0.4

0.3

0.2

0.1

4weekend

3weekday

2weekend

1weekday

0

Fig. 9 Risk index of load forecast errors in different seasons


forecasting residuals. From the risk index of Fig. 7 andFig. 8, it can be seen that more irregular peaks appeared atweekends because it is more difficult to predict the weekenddemand profiles precisely. However, the values of risk indexon weekdays as indicated in Fig. 7 are still higher than thoseat weekends as indicated in Fig. 8. Furthermore, Fig. 9 alsoshows that the risk index in the winter months is high due tohuge volume of demand.

7 Proposed method for evaluating the risk due toSTLF uncertainty

In this paper, the actual local demand data from anelectricity supplier have been used. With the residualsderived from both ARIMA and ANN load forecasts, therisk indexes under different time sections or seasons can beobtained. However, different load profiles, characters andpower consumptions are likely to exist in different areas.Moreover, customer-switching behaviour needs to be takeninto account. Therefore, the risk index over 48 time sectionsis likely to change according to areas and dates. The indexthen needs to be automatically updated once a day.Furthermore, the risk index of load forecast uncertaintydepends mainly on the load profiles and characters. Hence,we propose a new procedure to evaluate the risk indexwithout using the residuals from STLF, but using thestandard deviation of load increment as the risk index. Inour proposed method, the risk index in the kth time periodcan be formulated as (7):

Rk ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xni¼1

ðXki � XkiÞ2

sð7Þ

where Xki means half-an-hour increment in load, which isdefined as Xki¼Lki�L(k�1)i; when k is equal to one, the riskindex in the first time section is calculated as: X1¼L1�L48.In addition, Xki is a mean value of Xki, and n is the numberof specified successive days. Details with a worked exampleof the proposed algorithm for the risk index is given in theAppendix, Section 12.2.Based on this algorithm, the weekday local demands

from December 2000 to October 2001 except May 2001have been analysed totally to evaluate the risk indexes over48 periods. The obtained result is shown in Fig. 10. It isevident that there is a high correlation between two kinds ofrisk index that are shown in Fig. 7 and Fig. 10 respectively.Fig. 11 indicates the relationship between two kinds of riskindex derived from STLF and the proposed method. From

this Figure, the risk index 1 (R1) is the risk measurementusing the standard deviation of load increment by Fig. 10,and the risk index 2 (R2) is obtained from the residuals of allSTLFs by Fig. 7. All forecasting results are used to analysethe correlation between the two indexes. It is evident thatthere is a linear correlation between the two kinds of riskindex, as described in Fig. 11. The linear regressionequations on weekdays and weekends are listed below:

Weekday :R1 ¼ 0:895R2 þ 0:049 ð8Þ

Weekend :R1 ¼ 0:887R2 þ 0:082 ð9ÞThe strength of the proposed method lies in its ability toidentify the risk index accordingly from historical load data,and avoid using complex STLF procedures. With a simplelinear transformation, the risk index R1 in each half-hourperiod provides a compact evaluation of the risk index R2resulting from actual forecasting errors.

8 Daily value-at-risk analysis for the supplybusiness

In addition to the risk index, risk measurement, especially infinancial risk measurement, is a very significant topic of riskassessment for load forecast uncertainty. Recently, anumber of financial tools in risk measurement have beenapplied to the electric power industry. One of the mostpopular methods is value-at-risk (VAR) measurement [18],which is an estimated methodology for quantifying the levelof risk exposure to which a portfolio of holdings issubjected. Its definition is the largest likely loss from marketrisk that an asset will suffer over a time interval and with adegree of certainty selected by the decision-maker. The goalof this section is to apply VAR analysis to the daily financialrisk of local supplies due to load forecast errors.Due to those forecast errors, electricity suppliers may

purchase more or less energy than they could sell. In theNETA imbalance settlement system, two spot prices arecalculated for each half hour of the day. One price, thesystem sell price (SSP), is paid to trade parties who have anet surplus of imbalance energy, and the other, the systembuy price (SBP), is paid by trade parties who have a netdeficit of imbalance energy. For example, if a supplierunderestimates the demand, it would have to pay the SBPfor the difference between the notified contract volume andthe actual metered consumption. If a supplier overestimatesthe demand, it would be paid the SSP. However, thesupplier would also have to pay additional costs to the other

00 5 10 15 20 25 30 35 40 45 50

0.1

0.2

0.3

0.4

risk,

pu

0.5

0.6

0.7

0.8

0.9

1.0

time, periods

Fig. 10 The risk index from the proposed method

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.1

0.2

0.3

0.4

risk

inde

x 2,

res

idua

ls fr

om S

TLF

0.5

0.6

0.7

0.8

0.9

1.0

risk index 1, standard deviation of load increment

Fig. 11 Relationship between two kinds of risk index


party for surplus energy on the basis of the bilateralcontracts. As a result, electricity suppliers may sufferfinancial loss because of load forecast errors. The relation-ship between load forecast errors and the loss of finance foreach half-hour is shown below:

Ploss;under ¼ SBPðVr � Vf Þ if Vr4Vf ð10Þ

Ploss;over ¼ ðPc � SSPÞðVf � VrÞ if Vf4Vr ð11Þwhere Vr, Vf mean real and forecast demand volumesrespectively. Pc is the contract price between bilateraltraders. The daily financial losses caused by load forecasterrors are calculated using (10) and (11). However, contractprices depend on traders’ strategies and may vary duringdifferent time sections, and they are confidential to traders.Therefore, it is impossible to obtain these data in our work.The first step in calculating VAR for this paper is to assumethat Pc is equal to zero. This assumption gives the minimumloss for a power supplier. Hence, we could obtain dailydeficit and surplus energy financial risks, which are shownin Fig. 12 with the elements in ascending order. In thisFigure, the positive side indicates the financial risk fordeficit energy, and the negative side indicates the financialrisk for surplus energy without considering contract prices.Once contract prices increase from zero to a specific value,the negative side could decrease and could even accumulateto be positive. In this way total financial risk wouldincrease. For example, if it is assumed that Pc is twice SSPat any time, then the financial risk for surplus and deficitenergy is shown in Fig. 13. This Figure consists of twosegments: the dark segments are deficit financial risks andthe light segments are surplus financial risks. From thehistorical data set, one can calculate the expected maximumfinancial loss with a certain confidence level. The historicalVAR method is presented in the Appendix Section 12.3.

Based on the historical VAR method, the daily VAR ofthe supply’s trading is 774.7 pounds sterling at 95%confidence level and 572.1 pounds sterling at 90%confidence level for serving a 10MW local demand, whichis shown in Fig. 12. In other words, under a normal market,there is the probability of only five percent uncertainty thatthe daily loss will exceed 774.7 pounds sterling. In order tocheck whether these threshold VARs are adequate, thispaper verifies the actual daily losses from 21 October 2001to 31 October 2001 and counts the number of outlets with

threshold VARs. The procedure is critical for VARevaluation because the ‘looking forward’ step can verifywhether historical VAR numbers can accurately describefuture actual risk exposure. Table 2 lists the number oftimes that the losses exceed the 95% and 90% thresholdsrespectively. It is clear that the estimated VARs areadequate because no losses appear outside the VARthresholds. However, it can be seen that the historicalVAR is high because it is sensitive to extreme values. Thehistorical VAR method is more conservative than otherVAR methods, such as Monte Carlo simulation and theRiskMetrics approach [18].

In this paper, the number of historical data, such as SBPsand SSPs, is small because NETA has only been launchedsince April 2001. However, the above procedure on VARmeasurement is feasible and convenient. It could provideelectricity supply companies with the ability to take a dailysnapshot of their holdings and understand the largest likelyloss in the future. Furthermore, because SBP is much higherthan SSP, most suppliers could have therefore responded toNETA imbalance prices by over-contracting to reduceexposure to SBP. The cost of over-contracting can beviewed as an insurance premium that reduces exposure tohigh risks. This paper suggests that suppliers may make theoptimal over-contracting strategy by referring tothe product of the risk index of load forecast errors andthe value of SBP in the 48 trading periods. That is, supplierscould manage risk more cost-effectively by reducing over-contracting outside certain trading periods and increasingcontracts over other trading periods.

9 Conclusions

The importance of risk assessment on local demand forecastuncertainty has been stated. According to the statistical

−2000 5 10 15 20 25 30 35 40 45

0

200

400

600

hist

oric

al fi

nanc

ial l

osse

s di

strib

utio

n

800

1000

1200

1400

day

VAR = 774.7 95% confidence level

VAR = 572.1 90% confidence level

Fig. 12 The historical data of daily financial losses due to loadforecast errors for local supplier (from June 2001 to September2001)

0 5 10 15 20 25 30 35 40 450

500

finan

cial

ris

k du

e to

load

fore

cast

ing

erro

rs, p

ound

s

1000

1500

day

deficit financial risk

surplus financial risk

Fig. 13 The financial risk for deficit and surplus energy (fromJune 2001 to September 2001)

Table 2: Threshold for VAR and number of times thresholdexceeded

Confidencelevel

ThresholdVAR, pounds

Number of times thresholdVAR exceeded, days

95% limit 774.7 0

90% limit 572.1 0


analysis, there appeared to be no strong correlation betweenlocal demand and weather for the sample of data analysed.Furthermore, the forecast of local demands is more difficultthan the forecast of system demands, especially in a smallarea range. Load forecast has been performed on the basisof traditional ARIMA models and ANN procedures. Withthe residuals from load forecast, the risk indexes overdifferent time periods or seasons have been presented.Moreover, a method for risk assessment has been proposed.It is based on calculating the standard deviation of loadincrement as the risk index of load forecast uncertainty. Theobject of the proposed methodology is to provide anuncomplicated and convenient procedure for risk assess-ment due to load forecast uncertainty. Finally, we havepresented daily value-at-risk evaluation for a supplybusiness using a historical simulation method that incorpo-rates residuals of load forecast and imbalance settlementdata in NETA. The contribution of risk measurement is toprovide local electricity suppliers with an opportunity toeasily quantify their risk exposure and make optimaltrading strategies in the competitive electricity market.

10 Acknowledgments

The authors would like to thank Mr. Ken Spiers of theDepartment of Meteorology, University of Reading forproviding the necessary climate data recorded every fiveminutes, and acknowledge the help of NETA and ScottishPower through their Internet helpline.

11 References

1 ‘New Electricity Trading Arrangements (NETA) Programme’(Ofgem publications, January 2001)

2 Douglas, A.P., Breipohl, A.M., Lee, F.N., and Adapa, R.: ‘Risk dueto load forecast uncertainty in short term power system planning’,IEEE Trans. Power Syst., 1998, 13, (4), pp. 1493–1499

3 Valenzuela, J., Mazumdar, M., and Kapoor, A.: ‘Influence oftemperature and load forecast uncertainty on estimates of powergeneration production costs’, IEEE Trans. Power Syst., 2000, 15, (2),pp. 668–674

4 Hippert, H.S., Pedreira, C.E., and Souza, R.C.: ‘Neural networks forshort-term load forecasting: a review and evaluation’, IEEE Trans.Power Syst., 2001, 16, (1), pp. 44–55

5 Amjady, N.: ‘Short-term hourly load forecasting using time-seriesmodeling with peak load estimation capability’, IEEE Trans. PowerSyst., 2001, 16, (3), pp. 498–505

6 Juberias, G., Yunta, R., Garcia Moreno, J., and Mendivil, C.: ‘A newARIMAmodel for hourly load forecasting’. Proc. IEEE Transmissionand distribution Conf., 1999, Vol. 1, pp. 314–319

7 Box, G.E.P., Jenkins, G.M., Reinsel, G.C., and Jenkins, G.: ‘Timeseries analysis: forecasting and control’ (Prentice Hall, 1994, 3rd Edn.)

8 Allera, S.V., and Horsburgh, A.G.: ‘Load profiling for energy tradingand settlements in the UK electricity markets’. Presented byDistribuTECH Europe DA/DSM Conf., London, 27-29 October 1998

9 Dahlgren, R.W., Liu, C.C., and Lawarree, J.: ‘Volatility in theCalifornia power market: source, methodology and recommenda-tions’, IEE Proc., Gener. Transm. Distrib., 2001, 148, (2), pp. 189–193

10 http://www.bmreports.com/bwx_reporting.htm accessed December2001

11 Douglas, A.P., Breipohl, A.M., Lee, F.N., and Adapa, R.: ‘Theimpacts of temperature forecast uncertainty on Bayesian loadforecasting’, IEEE Trans. Power Syst., 1998, 13, (4), pp. 1507–1513

12 Khotanzad, A., Davis, M.H., Abaye, A., andMaratukulam, D.J.: ‘Anartificial neural network hourly temperature forecaster with applica-tions in load forecasting’, IEEE Trans. Power Syst., 1996, 11, (2),pp. 870–876

13 El Desouky, A.A., and Elkateb, M.M.: ‘Hybrid adaptive techniquesfor electric-load forecast using ANN and ARIMA’, IEE Proc., Gener.Transm. Distrib., 2000, 147, (4), pp. 213–217

14 Charytoniuk, W., and CHEN, M.-S.: ‘Very short-term load forecast-ing using artificial neural networks’, IEEE Trans. Power Syst., 2000,15, (1), pp. 263–268

15 Shahidehpour, M., Yamin, H., and Li, Z.: ‘Market operations inelectric power system: forecasting, scheduling, and risk management’(Wiley, New York, 2002)

16 Draper, N.R., and Smith, H.: ‘Applied regression analysis’ (Wiley,New York, 1966)

17 Owayedh, M.S., Al-Bassam, A.A., and Khan, Z.R.: ‘Identification oftemperature and social events effects on weekly demand behavior’.Proc. IEEE Power Engineering Society SummerMeeting 2000, Vol. 4,pp. 2397–2402

18 Alexander, C.: ‘Risk management and analysis, volume 1: Measuringand modelling financial risk’, (Wiley, New York, 1999)

12 Appendix

12.1 Conclusion of local demand forecastingfunctions with time series analysis

Month Weekly data Time series forecasting function

December2000

Weekday y(t)¼ 0.6411y(t�1)+0.7859y(t�24)�0.5225y(t�25)+0.1679y(t�48)�0.0758y(t�49)�0.7656a(t�24)

Weekend y(t)¼ 0.4826y(t�1)�0.0298y(t�2)+0.1692y(t�24)+0.5322y(t�48)�0.1653y(t�49)+0.9576a(t�24)

January2001

Weekday y(t)¼ 0.4997y(t�1)+0.1442y(t�23)+0.6887y(t�24)�0.5009y(t�25)�0.1365y(t�47)+0.2905y(t�48)+0.0154y(t�49)�0.8247a(t�24)

Weekend y(t)¼ 0.9349y(t�1)�0.2152y(t�2)+0.0275y(t�3)+0.6396y(t�24)�0.4479y(t�25)+0.1095y(t�26)�0.0566y(t�27)+0.1101y(t�48)�0.0883y(t�49)�0.3272a(t�2)�0.5652a(t�24)

February2001


Weekend y(t)¼ 0.3859y(t�1)+0.2303y(t�2)+0.4652y(t�23)+0.1671y(t�24)�0.4129y(t�25)+0.05y(t�26)�0.1427y(t�47)+0.2564y(t�48)�0.4933a(t�24)

March 2001 Weekday y(t)¼ 0.5918y(t�1)+0.9766y(t�24)�0.5799y(t�25)+0.0196y(t�48)�0.0076y(t�49)�0.7142a(t�24)

Weekend y(t)¼ 0.7674y(t�1)+0.4571y(t�24)�0.2232y(t�25)+0.3484y(t�48)�0.1263y(t�49)�0.1263a(t�24)

April 2001 Weekday y(t)¼ 0.5818y(t�1)+1.0247y(t�24)�0.5531y(t�25)�0.0357y(t�48)�0.0182y(t�49)�0.8415a(t�24)

Weekend y(t)¼ 1.5471y(t�1)�0.5866y(t�2)+0.0363y(t�24)�0.1919y(t�25)+0.1686y(t�26)+0.0539y(t�48)�0.0308y(t�49)�0.3771a(t�1)

June 2001 Weekday y(t)¼ 0.6646y(t�1)+0.8763y(t�24)�0.5669y(t�25)+0.1102y(t�48)�0.0832y(t�49)�0.7325a(t�24)


July 2001 Weekday y(t)¼ 0.64y(t�1)+0.8762y(t�24)�0.5314y(t�25)+0.083y(t�48)�0.068y(t�49)�0.7218a(t�24)


August 2001 Weekday y(t)¼ 0.9941y(t�1)�0.1737y(t�2)�0.0476y(t�24)�0.0062y(t�25)+0.0614y(t�26)+0.5603y(t�48)�0.3908y(t�49)+0.0935a(t�1)


September2001



12.2 Risk index evaluation with the standarddeviation of load incrementTo clarify the proposed method on risk index, an illustrativeexample is presented here. It is assumed that a data setincludes five successive days of local demands, and each dayconsists of six load record periods. The load data are shownin Table 3, and the algorithm is performed in three steps.

Step 1: Calculate the differences between loads of currentand last period in each day. The load increments in eachperiod are listed in Table 4. Clearly, although the values ofload increment are high in each day’s period 6, the standarddeviation of load increments in period 6 is very low. That is,the risk index R6 is low. However, in period 3, the variationof load increments, ranging from 17.4kW to 58.1kW, isvery high. It means that the risk in period 3 is relativelyhigh.

Step 2: Calculate the standard deviation for each period.

The result is shown in Table 5. For example, R2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið4:8�12:6Þ2þð18:2�12:6Þ2þð10:8�12:6Þ2þð10:3�12:6Þ2þð18:9�12:6Þ2

4

q¼

5:299Step 3: Transform the standard deviations to the risk

index into per unit values. The base value is the maximumvalue among standard deviations (Table 6).

12.3 The historical method to estimate value-at-riskStep 1: Calculate the daily financial losses caused by loadforecast errors. For simplifying the calculation, daily VARis calculated on the basis of minimum financial loss in thispaper; that is, it is assumed that contract price is zero. Thenumerical data for a simple sample are given in Table 7. Itconsists of ten-day data for daily financial loss.

Step 2: Determine the probability distribution for dailyfinancial losses. The distribution based on the data inTable 7 is presented in Fig. 14.

Step 3: Obtain the VAR according to the specificconfidence level. For example, if 90% confidence level ischosen, the VAR corresponds to the (100-90)% lower-taillevel. In this case, the cumulative number in the probabilitydistribution is 10; that is, the second highest value 623.6 ischosen as the VAR. Similarly, if 80% confidence level ischosen, the corresponding VAR is 359.5.


October 2001 Weekday y(t)¼ 0.6313y(t�1)+1.0544y(t�24)�0.617y(t�25)�0.0794y(t�48)+0.01y(t�49)�0.7662a(t�24)

Weekend y(t)¼ 0.5397y(t�1)+0.0721y(t�22)�0.1596y(t�23)+0.6293y(t�24)�0.4333y(t�25)�0.0396y(t�46)+0.0461y(t�47)+0.2966y(t�48)+0.0425y(t�49)�0.7754a(t�24)

Table 3: Sample data for local demand within fivesuccessive days

Day Power demand, kW

Period 1 Period 2 Period 3 Period 4 Period 5 Period 6

1 23.5 28.3 86.4 74.8 76.4 32.5

2 26.5 44.7 62.1 64.2 71.6 23.6

3 23.3 34.1 71.6 75.4 72.6 24.2

4 24.3 34.6 61.1 71.8 71.7 24.7

5 23.4 42.3 84.5 74.5 73.1 28.4

Table 4: Load increments in daily periods for sample data

Day Load increment, kW


1 �9 4.8 58.1 �11.6 1.6 �43.9

2 2.9 18.2 17.4 2.1 7.4 �48

3 �0.9 10.8 37.5 3.8 �2.8 �48.4

4 �0.4 10.3 26.5 10.7 �0.1 �47

5 �5 18.9 42.2 �10 �1.4 �44.7

Table 5: The standard deviation of load increments forsample data

Timesection


Standarddeviation

4.114 5.299 13.891 8.519 3.542 1.792

Table 6: Risk index for sample data

Timesection


Risk in-dex

0.296 0.381 1.0 0.613 0.255 0.129

Table 7: Sample data for daily financial loss as a result of load forecast errors

Day 1 2 3 4 5 6 7 8 9 10

Financialloss

89.5 201.5 116.2 95.6 230.9 359.5 623.6 1374.4 170.4 158.5

00 200 400 600 800 1000 1200 1400

0.5

1.0

1.5

prob

abili

ty d

istr

ibut

ion,

num

ber

2.0

2.5

3.0

financial loss, pounds

80%confidence level

90%confidence level

Fig. 14 Probability distribution of financial loss for the sampledata


Documents

Risk assessment due to local demand forecast uncertainty in the competitive supply industry