Electrical Power and Energy Systems 37 (2012) 95–102

Contents lists available at SciVerse ScienceDirect

Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Daily load profile and monthly power peaks evaluation of the urban substationof the capital of Jordan Amman

Nabeel I. A. TawalbehElectrical Engineering Department, University of Jordan, Amman, Jordan

a r t i c l e i n f o

Article history:Received 14 February 2010Received in revised form 8 November 2011Accepted 5 December 2011Available online 13 January 2012

Keywords:Load estimationSubstation peakDaily load profileDiversity factorConversion factor

0142-0615/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijepes.2011.12.010

E-mail address: ntawalbeh@ju.edu.jo

a b s t r a c t

The hourly recorded power of an urban substation of the National Electric Power Company (NEPCO) inthe capital of Jordan Amman is used to calculate the diversity and conversion factors of the substation.These factors are used to estimate the daily load power profile and the monthly peak power of the sub-station. The results show that the conversion factors are almost independent of the number of feeders inthe substation, while the diversity factors vary in substations that have six feeders or less. The resultsshow a good correlation between the estimated and actual recorded data of the daily load profile withless than 5% percentage error.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The electrical peak demand in Jordan is continuously increasingas shown in Table A.1. In a recent report the growth of the annualpeak demand in Jordan in the last 7 years increased between 9.2%and 15.2% [1]. The National Electric Power Company (NEPCO) hasbeen taking the proper measures and precautions to face such acontinuous growth. In general, load estimation constitutes the ma-jor source of data that is required for future planning of power dis-tribution systems. This includes, but not limited to, transformersizing, capacitor banks and conductor size selection. Accurate loadestimation, an essential requirement procedure for future planningof power networks, can be achieved using different methodologies.In all cases, the operators experience is proved to be not sufficientfor this purpose [2].

Several methods have been utilized, with different degrees ofaccuracy, to analyze the kWh consumption by electric utilities.The maximum diversified demand is estimated as a function ofthe average kWh per customer. The multiplying factors, denotedby ‘‘K Factors’’, are used to estimate the consumed electric energyby each consumer connected to the network [3].

In [4] a method is introduced to estimate a synthesized loadshapes to identify typical daily load curves and to figure out thebest way to represent its model. It shows that using historical data,one may predict both the maximum peak demand and the dailyaccumulated consumed energy. In [5], however, another method

ll rights reserved.

is presented to calculate the electrical power demand and the loadfactors of different class of customers. This method is based onconstructing the load duration curves and predicting the annualpeak load. In [6] a virtual instrument to predict the short, mediumand long term load forecasting is designed using three ArtificialNeural Networks (ANN) models. The ANN model is trained usinghistorical data taking in consideration weather conditions. Anaccurate and a stable method to predict the medium and long termload forecasting method was also introduced using the radial basisfunction neural networks.

Another method to minimize the energy losses in a distributionsystem is presented in [7]. The method is based on selecting dis-patch capacitors based on loop analysis algorithm which deter-mines the optimal setting of capacitors for all operating times[8]. The maximum annual power, Pmax, can be evaluated usingVelanders formula. Annual energy consumption is translated intoa power demand by the aid of certain mathematical methods [9].His formulation assumes that the maximum demands of the partialloads were normally distributed. However, Velander’s model pro-vides no information as to when the maximum demand occurs.However, this model is proved to be quit reliable in medium volt-age networks [10].

A popular method for estimating the maximum load based onsimilar load behavior was also reported by Hsu et al. [11] and Katoand Naito [12]. This method, as described by Eq. (1) for complete-ness, assumes that the maximum demands of the partial loadswere normally distributed

bPmax ¼ K1Wa þ K2

ffiffiffiffiffiffiffiffiWa

pð1Þ

Table 1Maximum number of samples in a group of feeders.

Nfg 1 2 3 4 5 6 7 8 9 10 11 12

Nl,max 12 66 220 495 792 924 792 495 220 286 66 1

96 N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102

where bPmax is the maximum estimated power, K1 and K2 are coeffi-cients related to the level of different consumer energy, while Wa isthe total annual energy consumption [10].

Another method used to estimate the power is based on esti-mating the load currents of network branching nodes. The esti-mated load current at any branching point is given by thefollowing formula [11,12]:

bILoad; i ¼ IFD �SciPNi¼1Sci

ð2Þ

where IFD is the available current feeder, Sci is the sum of ratedcapacities of transformers at a branching point i, N is the numberof branching points that are supplied from the feeder, and bILoad; i isthe estimated feeder current under consideration.

Load estimation using Eq. (2) is inaccurate since the loads of thedistribution system do not have similar profile. For example, thepeak load of a certain industrial customer may appear in the after-noon, while that of a commercial one may take place in theevening.

An approach based on fuzzy set theory is proposed [13] to esti-mate the loads in the distribution system. This approach benefitsfrom the operators’ experience and the knowledge of experts.The load patterns are characterized using fuzzy set to reflect theactual behavior of a power substation. The load nodes within thesame category of customers are assumed to have similar hourlyload pattern per day. However, this approach can only be consid-ered as an approximate one due to the fact that the exact historicalrecords of the branching nodes usually do not exist. A fuzzy modelreported in [14] is applied to express the correlation between theactive peak load of a certain substation and the supplied activeload of a certain customer in the electric power distribution net-work. Neural Network and Fuzzy set were later applied to estimatethe load for the active demand in radial networks [15]. The loadcurve was generated based on the energy consumption of certainclasses of customers.

The conversion and diversity factors for the main substation inthe north of Jordan were evaluated to estimate the daily profile andthe monthly peak demands [17]. A similar approach is applied toan urban substation in the capital of Jordan Amman to analyzeits load profiles. The conversion and diversity factors are evaluatedand the daily load profile is also estimated. The methodology pre-sented in [16,17] was adopted for this purpose. The impact of thevariations of the number of feeders on the load diversity factorsin the substation under investigation is thoroughly investigated.The monthly peak MW demand of the system and the daily loadprofile were also calculated. The estimated daily load profile usingthese factors is then compared with the actual measured load forthe considered group of feeders for validation purposes.

This paper is organized as follows: Section 2 outlines the meth-od to calculate the monthly based diversity factor. Section 3 intro-duces a method to evaluate the conversion factor. The monthlypeak and daily load profiles are presented in Section 4. An estima-tion algorithm and nemrical simulation is summarized in Section5. Finally, Section 6 presents concluding remarks.

2. Monthly based diversity factor

Diversity factor in a distribution network is the ratio of thesum of the peak demands of the individual customers to the peak

demand of the network. This will be determined by the type ofservice, i.e., residential, commercial, industrial or a combinationof these loads [18,19]. These factors model the peak demand ofgroups of customers, which does not characterize the aggregateof individual customer peak demands [18]. The diversity factor,DF, is greater than unity and defined by the following formula:

DF ¼Pn

j¼1Pj

Pgð3Þ

where Pj is the maximum demand of load j, disregarding time ofoccurrence, Pg is the maximum demand of group of n loads, and jis the index of the individual feeder.

In order to estimate the diversity factor for the substation underconsideration, the number of feeders in the substation, the combi-nation of these feeders, and the maximum number of samples in agroup of feeders must be identified. Hence, let Nf, Nfg, Nl,max be thenumber of feeders in the substation, the combination feeders in agroup of feeders, and the maximum number of samples in thesame group of feeders, respectively, while the order of samplegroups is assumed to be l.

For the substation under consideration, Nf = 12, Nfg = 1,2, . . . , 12, while the number of sample groups l takes the valuesl = 1, 2, . . . , Nl,max, where Nl,max is given by:

Nl;max ¼Nf

Nfg

� �¼ Nf !

Nfg !ðNf � NfgÞ!ð4Þ

The values of Nl,max for different substation feeders are pre-sented in Table 1.

The hourly measured power data can then be analyzed accord-ing to the type of day, defined by the d, where d takes two differentvalues according to the type of day; i.e.,

d ¼1 for working days2 for holidays and weekenddays

�ð5Þ

The hourly consumption of peak power for a given feeder, j, in agiven type of day, d, during a certain month, m, is calculated by:

Pj;maxðm;dÞ ¼maxh;d

Pjðm;D; hÞ ð6Þ

where D represents the day of the month the peak occurs. Clearly,the days of the month in which D = 1, 2, . . . 28, 30, or 31 dependingon the month are classified as weekdays and weekends. Hence, thepeak recording is classified accordingly as Eq. (5) shows.

The power consumption of each group of l samples in the sub-station is calculated by:

Pglðm;D;h;NfgÞ ¼XNfg

j¼1

Pjðm;D; hÞ ð7Þ

Similarly, the hourly consumption of peak power Pgl,max, for acertain group of feeders is given by:

Pgl;maxðm;d;NfgÞ ¼maxh;d

Pglðm;D; h;NfgÞ ð8Þ

Substituting (6) and (8) into (3) yields the following diversityfactor for the group of l samples:

DFlðm; d;NfgÞ ¼PNfg

j¼1Pj;maxðm;dÞ

Pgl;maxðm; d;NfgÞð9Þ

x 10−3

N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102 97

and its average value is calculated by:

DFlðm;d;NfgÞ ¼PNl;max

l¼1 DFðm; d;NfgÞNl;max

ð10Þ

Clearly, from (10), the monthly average diversity factor dependson the index of the month, m, the type of day, d, and on the numberof feeders in the substation, Nfg.

Fig. 1a and b shows the calculated monthly diversity factors forthe substation under consideration.

The monthly diversity factors shown in Fig. 1a and b depict sim-ilar behavior of a first-order system. Observe that when the num-ber of feeders exceeds six, most of diversity factors approach asteady-state value. In January for example, the response of thediversity factor for the working days can be approximated by thefollowing equation:

DF ¼ 1þ 0:226ð1� e�0:2857ðNfg�1ÞÞ

where Nfg is the number of feeders.Similar formulas can be obtained for all months during week-

days and weekends and holidays.Fig. 1 shows the variations of the average diversity factor DF

versus the number of feeders for the working days (i.e, d = 1). Threedistinct groups of months are realized. Clearly, the highest diver-sity factors occur in the months of June and January, while Febru-ary, May, July and August present the lowest diversity factor of theyear. The remaining months are gathered to form the third groupof medium average diversity factors. For the weekend and holi-days, however, Fig. 1 shows that in the month of January the loadbehavior exhibits a persistent increase diversity in both weekdays

1 2 3 4 5 6 7 8 9 10 11 12

Aver

age

dive

rsity

fact

or, D

F

Jun.Jan.Oct.Mar.Apr.Sep.Nov.Dec.May.Feb.Jul.Aug.

(a)

1 2 3 4 5 6 7 8 9 10 11 12

Aver

age

dive

rsity

fact

or, D

F

Jan.Aug.Oct.Mar.Sep.Apr.MayJul.Feb.Jun.Dec.Nov.

11.025

1.051.075

1.11.125

1.151.175

1.21.225

1.251.275

1.3

Number of feeders in a group, Nfg

1

1.025

1.05

1.075

1.1

1.125

1.15

1.175

1.2

1.225

1.25

1.275

1.3

(b)Number of feeders in a group, Nfg

Fig. 1. Average diversity factors for (a) working days, and (b) weekend andholidays.

and weekends. This is due to the nonhomogeneous power con-sumption during the coldest month of the year and the beginningof the midyear school holidays.

3. Conversion factor

The conversion factor is a measure used along with the diversityfactor to estimate the peak power of a certain group of feeders. Theconversion factor, CF, is defined as the sum of all individual cus-tomer peaks of a certain group divided by the total energy usagefor the same group over a given period [3]; i.e.,

CF ¼P

Individual peaksGroup energy

ð11Þ

The conversion factor, CF, depends only on the month, m, thetype of day, d, and does not depend on the number of feeders[20,21]. To calculate the conversion factors for a certain group, asample, l, of a group of feeders are chosen until l reaches its max-imum value, Nl,max, (i.e., l = 1, 2,, . . . , Nl,max), where Nl,max is given by(4), and the individual peak power of a feeder j is given by (6).

The daily energy use of the same feeder every hour is calculatedusing the following equation:

Ejðm;dÞ ¼X24

h¼1

Pðm;D; hÞð1 hÞ ð12Þ

Combining (6) and (12), the conversion factor CF for sample l isthen given by:

1 2 3 4 5 6 7 8 9 10 11 12

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8Jun.Sep.Jan.Oct.May.Jul.Aug.Feb.Mar.Apr.Dec.Nov.

1 2 3 4 5 6 7 8 9 10 11 126.66.8

77.27.47.67.8

88.28.48.68.8

99.29.49.69.810 x 10−3

Jul.Dec.Sep.Jun.Mar.Apr.Feb.Jan.Oct.Aug.Nov.May.

Con

vers

ion

fact

or, C

F

(a)

Number of feeders, Nfg

Con

vers

ion

fact

or, C

F

(b)

Number of feeders, Nfg

Fig. 2. Conversion factors for (a) working days, (b) weekend and holidays.

98 N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102

CFlðm;d;NfgÞ ¼PNfg

j¼1Pj;maxðm;dÞPNfg

j¼1Ejðm; dÞð13Þ

The numerator and denominator of Eq. (13) must be calculatedfor a group of feeders that has more than one feeder. Hence, theaverage value of the conversion factor for a group of feeders is gi-ven by:

CFðm;d;NfgÞ ¼PNl;max

l¼1 CFlðm;dÞNl;max

ð14Þ

The average conversion factors of the substation under consid-eration for the working and weekend days are shown in Fig. 2a andb.

Fig. 2 shows the monthly calculated conversion factors for bothweekends and working days. The rate of increase of the conversionfactor during weekends is almost equal to the decline in the rate ofenergy consumption over the 2 days. Obviously, the values of themonthly conversion factors are constants and do not have any cor-relation with the number of feeders. The months of June, Septem-ber, and January reflects higher values of conversion factors duringweekdays than the rest of the year. This is obviously due to the in-crease in the number of tourists and visitors in the beginning of thesummer time in Jordan. This is emphasized by the value of the con-version factor during the weekends in the month of July where thenightlife in Amman is longer than any other month of the year.

The start of a new academic year which occurs in September re-quires higher power demands and that is reflected in the high val-ues of the conversion factors for all days. That is also applicable tothe months of January and December where residence tends to usemore electric power for heating. It is interesting to realize that theconversion factor during weekends is clustered in almost allmonths of the year except in July. This is probably reflects theway of life during weekends in the Amman.

4. Monthly peaks and daily load profile estimation

In order to estimate the monthly peaks and daily load profilesfor a certain group of feeders, the total number of feeders of thesubstation under consideration is divided into two groups asshown in Table 2; these are the Test and the Control groups. Thediversity factor of the test group is determined and used to calcu-late its conversion factor CF. The conversion factor of the test groupis then used to estimate peak for the control group.

Let Nf,t and Nf,c be the number of the Test and the Control groupsrespectively, as shown in Table 2. The power consumed by the Testgroup for each hour in the month m, Pf,tg, is evaluated by the sum-mation of the individual feeder power consumption as follows:

Pf ;tðm;D;h;Nf ;tÞ ¼XNf ;t

n¼1

Pnðm;D; hÞ ð15Þ

The consumed peak power of a certain group, Pf,t,max, is thenfound by the analysis of all hourly measured data during the days.The maximum hourly power that match the type of the day is gi-ven by:

Table 2Groups of feeders.

Test group Control group

Abdoon 2 Abdoon 1Amman Main2 Amman Main1Salt Road1 Salt Road2Lewibdeh1 3rd Round1Wadisair1 3rd Round2Lewibdeh2 Wadisiar1

Pf ;t;maxðm;d;Nf ;tÞ ¼maxh;d

Pf ;tðm;D;h;Nf ;tÞ ð16Þ

The day of the month with the maximum peak denoted by Dp iswill be used to estimate the daily load profile. The total energy thatis consumed by the Test group is then calculated by means of:

Ef ;tðm;Nf ;tÞ ¼X24

h¼1

XDmax

D¼1

Pf ;tðm;D; h;Nf ;tÞð1 hÞ ð17Þ

where Dmax is the maximum number of weekdays or weekend days;i.e., depending on the month, Dmax = 202,223 for weekdays andDmax = 8 weekend days.

From (15) and (16), the normalized consumed power for thepeak day of the month, Dp, of the test group is given by:

Pnormðm;d;hÞ ¼Pf ;tðm;Dp;h;Nf ;tÞPf ;t;maxðm; d;Nf ;tÞ

ð18Þ

The next step is to estimate the daily power profile for the con-trol group all 12 months using the calculated DF and CF factors ofthe Test group.

A similar procedure is then applied for the remaining feeders ofthe substation (i.e., the feeders of the Control group listed in Table2), which yields:

Pf ;c;maxðm;d;Nf ;cÞ ¼maxh;d

Pf ;cðm;D;h;Nf ;cÞ ð19Þ

and

Ef ;cðm;Nf ;cÞ ¼X24

h¼1

XDmax

D¼1

Pf ;cðm;D;h;Nf ;cÞð1 hÞ ð20Þ

The peak power for the Control group is estimated by means ofthe expression:

bPf ;c;maxðm; dÞ ¼ Ef ;cðm;Nf ;cÞCFðm;dÞ

DFðm; d;Nf ;cÞð21Þ

Finally, using (18) and (21), the load shape of the control groupis estimated by:

bPf ;cðm; dÞ ¼ bPf ;c;maxðm;dÞ � Pnormðm;d;hÞÞ ð22Þ

The actual and estimated load profiles are shown in Figs. 3 and4. Fig. 3 shows the load profiles of the working days. Two peaks canbe realized for almost all months of the year, one for the day timeand another one for the night time. The day time peaks have highermaximum power values over most of the months. Unlike theremaining months of October, November and December wheretheir peaks occurs over the night time of the day.

Similar trends can be observed over the weekend and holidays.However, the night peaks are higher for the winter months (Octo-ber to April).

The relative error in the peaks between the actual and esti-mated daily load profiles is calculated for all 12 months of the year,and for the types of days as shown in Figs. 5 and 6. It is clear lessthan 5% error between the actual and estimated values is notice-able. More specifically, the average percentage error over the yearis evaluated and found to be 3.05% for the working days and 4.92%for the weekend and holidays. This implies that there is a goodagreement between the actual and the estimated results is evident.

5. Estimation algorithm

The following steps summarize the proposed algorithm to esti-mate the daily and monthly power profile for urban substations:

1. Collect raw data each 5 min.2. Smooth data by averaging through every 1 h.

0 4 8 12 16 20 24Time, hours

Pow

er, M

WWorking days of Jan.

ActualEstimated

(a)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Working days of Feb.

ActualEstimated

(b)

0 3 6 9 12 15 18 21 24

15

20

25

30

Time, hours

Pow

er, M

W

Working days of April

ActualEstimated

(d)0 3 6 9 12 15 18 21 24

20

25

30

35

40

45

50

55

60

Time, hours

Pow

er, M

W

Working days of May

ActualEstimated

(e)

0 4 8 12 16 20 2420

25

30

35

40

45

50

55

60

Time, hours

Pow

er, M

W

Working days of July

ActualEstimated

(g)0 4 8 12 16 20 24

2025303540455055606570

Time, hours

Pow

er, M

W

Working days of Aug.

ActualEstimated

(h)

0 4 8 12 16 20 2420

25

30

35

40

45

50

55

Time, hours

Pow

er, M

W

Working days of Oct.

ActualEstimated

(j)0 4 8 12 16 20 24

15

20

25

30

35

40

45

Time, hours

Pow

er, M

W

Working days of Nov.

ActualEstimated

(k)

0 3 6 9 12 15 18 21 2415

20

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Working days of March.

ActualEstimated

(c)

0 4 8 12 16 20 2415

20

25

30

35

40

45

50

55

Time, hours

Pow

er, M

W

Working days of June

ActualEstimated

(f)

0 4 8 12 16 20 2425

30

35

40

45

50

55

60

65

Time, hours

Pow

er, M

W

Working days of Sep.

ActualEstimated

(i)

0 4 8 12 16 20 2415

20

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Working days of Dec.

ActualEstimated

(l)

20

25

30

35

40

45

50

55

Fig. 3. Daily load power profile: (a) January, (b) February, (c) March, (d) April, (e) May, (f) June, (g) July, (h) August, (i) September, (j) October, (k) November, and (l) December.

N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102 99

3. Classify data according to months and type of days.4. Compute the Diversity Factor for all months and type of days

using Eqs. (6)–(10).5. Compute the conversion factor for all months and type of

days using Eqs. (12)–(14).6. Divide the data into test and control groups.7. Identify the peak value and the peak day of the month at

which the peak value occur using Eq. (16) for Test group

and (19) for Control group.8. Calculate the monthly energy using Eq. (17) for Test group

and (20) for Cotrol group.9. Normalize the demand of the peak day using Eq. (18).

10. Calculate the maximum demand for the control groupsusing Eq. (21) with values of DF and CF obtained from points(4) and (5).

11. Compute the estimated peak using Eq. (22).

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

WWeekend & Holidays of Jan.

ActualEstimated

(a)

0 3 6 9 12 15 18 21 24

20

25

30

35

Time, hours

Pow

er, M

W

Weekend & Holidays of April.

ActualEstimated

(d)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Weekend & Holidays of July

ActualEstimated

(g)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Weekend & Holidays of Oct.

ActualEstimated

(j)

0 4 8 12 16 20 2420

25

30

35

40

45

Time, hours

Pow

er, M

W

Weekend & Holidays of Feb.

ActualEstimated

(b)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

ActualEstimated

(e)

0 4 8 12 16 20 2425

30

35

40

45

50

55

60

Time, hours

Pow

er, M

W

Weekend & Holidays of Aug.

ActualEstimated

(h)

0 4 8 12 16 20 2415

20

25

30

35

40

45

Time, hours

Pow

er, M

W

Weekend & Holidays of Nov.

ActualEstimated

(k)

Weekend & Holidays days of May

0 3 6 9 12 15 18 21 2415

20

25

30

35

40

45

Time, hours

Pow

er, M

W

Weekend & Holidays of March

ActualEstimated

(c)

0 4 8 12 16 20 2420

25

30

35

40

45

50

55

Time, hours

Pow

er, M

W

Weekend & Holidays of June

ActualEstimated

(f)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Weekend & Holidays of Sep.

ActualEstimated

(i)

0 4 8 12 16 20 2420

25

30

35

40

45

50

Time, hours

Pow

er, M

W

Weekend & Holidays of Dec.

ActualEstimated

(l)Fig. 4. Daily load power profile for the weekend and holidays: (a) January, (b) February, (c) March, (d) April, (e) May, (f) June, (g) July, (h) August, (i) September, (j) October, (k)November, and (l) December.

100 N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102

6. Conclusions

The variations of the diversity and conversion factors of the ur-ban substation of the capital of Jordan Amman are evaluated forboth the working days as well as the weekend and holidays ofthe year 2008.

It has been demonstrated that when the number of feeders inthe substation is higher than a certain number (in our study 6),

the diversity factor becomes almost independent of the numberof feeders. However, this factor is month dependent.

The conversion factor, in the contrary, seems to be independentof the number of feeders in the substation, as it has almost a fixedvalue irrespective of the number of these feeders. The estimatedvariations of the diversity and conversion factors were used to esti-mate the daily load profile and the monthly MW demands of theyear.

0 1 2 3 4 5 6 7 8 9 10 11 12Months

Peak

, MW

actualestimated

0 1 2 3 4 5 6 7 8 9 10 11 12Months

% e

rrors

(a) (b)

0

10

20

30

40

50

60

−5

−4

−3

−2

−1

0

1

2

3

4

Fig. 5. Estimated and actual peaks for the working days: (a) Actual and estimated peaks. (b) Percentage errors.

0 1 2 3 4 5 6 7 8 9 10 11 12Months

Peak

, MVA

r

actualestimated

0 1 2 3 4 5 6 7 8 9 10 11 12Months

% e

rrors

(a) (b)

0

10

20

30

40

50

0

1

2

3

4

5

Fig. 6. Estimated and actual peaks of the weekend and holidays: (a) Actual and estimated peaks. (b) Percentage errors.

N.I.A. Tawalbeh / Electrical Power and Energy Systems 37 (2012) 95–102 101

The estimated results are compared with the actual (measured)profiles and peaks of the substation. The relative error in the peaksof the actual and estimated daily load profiles is calculated for the12 months of the year for validation purposes. For the workingdays as well as the weekend and holidays, a percentage error ofless than 5% is noticeable, implying good correlation is achievedand the estimated results are highly accurate.

This implies that the results of this study can sufficiently be em-ployed for future plan purposes. The daily load profile is found byidentifying the hourly demand for all months, feeders, and type ofdays. The small estimation error is found due to the similarity be-tween the test and the control groups. I expect that if there is a big

Table A.1Jordan system peak loads.

All Jordan Interconnected system

Year Local Imported Exported Total MW Growth (%)

2004 1314 241 – 1555 1515 9.22005 1495 276 20 1751 1710 12.92006 1641 404 144 1901 1860 8.82007 1763 397 – 2160 2130 14.52008 1978 282 – 2260 2230 4.72009 2229 223 132 2320 2300 3.12010 2670 – – 2670 2650 15.2

dispersion, the estimation error would be bigger and this problemis open for further research.

The daily load profile is found by identifying the hourly demandfor all months, feeders, and type of days. The proposed algorithmused to estimate the monthly load profile can also be used to esti-mate the daily load profile. The analysis that is done over an entiremonth can be done over a single day when we record the hourlypeaks which can be treated as daily peaks in the proposed algo-rithm. The small estimation error is found due to the similarity be-tween the test and the control groups. I expect that if there is a bigdispersion, the estimation error would be bigger and this problemis open for further research.

Appendix A

Table A.1.

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