Isolated Area Load Forecasting using Linear Regression Analysis: Practical Approach

doi:10.4236/epe.2011.34067

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Energy and Power En gi neering, 2011, 3, 547-550

doi:10.4236/epe.2011.34067 Published Online September 2011 (http://www.SciRP.org/journal/epe)

Isolated Area Load Forecasting Using Linear Regression

Analysis: Practical Approach

Md. Apel Mahmud

School of Engineering & Information Technology, The University of New South Wales at Australian Defence Force

Academy, Northcott Drive, Campbell, Australia

E-mail: [email protected]

Received August 2, 2011; revised Se pte m ber 4, 2011; accepted Septembe r 18 , 20 1 1

Abstract

This paper presents an analysis to forecast the loads of an isolated area where the history of load is not

available or the history may not represent the realistic demand of electricity. The analysis is done through

linear regression and based on the identification of factors on which electrical load growth depends. To de-

termine the identification factors, areas are selected whose histories of load growth rate known and the load

growth deciding factors are similar to those of the isolated area. The proposed analysis is applied to an iso-

lated area of Bangladesh, called Swandip where a past history of electrical load demand is not available and

also there is no possibility of connecting the area with the main land grid system.

Keywords: Isolated Area, Load Forecasting, Linear Regression Analysis (LRA).

1. Introduction

In generation expansion planning as well as in distribu-

tion planning, load forecasting is an essential step. The

importance of accurate forecast in planning is that it en-

sures the availability of supply of electricity as well as

providing the means of avoiding over and under utilize-

tion of generating capacity and making the best possible

use of capacity. Obviously, errors in forecasting can lead

to bad planning which will be costly. Too high forecast

lead to more plants than are required which will be an

unnecessary capital expenditure. Too low forecast pre-

vents optimum economic growth and lead to the in stalla-

tion of many costly and expensive-to-run generators.

These costs will finally be borne by the consumers.

Different techniques have been implemented by re-

searchers to solve the load forecasting task. However,

two techniques are widely used, namely; regression and

time series. The regression technique as proposed in [1,2]

is based on is based on finding the functional relationship

between weather components and the load demand.

Therefore, the load is affected by the weather compo-

nents that were used in the regression. The time series

technique [3] is also a type of regression which takes a

load pattern as a signal in a time series and forecasts the

future load. In other words, the future load is only a

function of the previous loads. Therefore, it is essential

to know the historic data of the area that will be fore-

casted. In [4], a load forecasting method used fuzzy lo-

gics is proposed where different factors of a day such as

day’s minimum temperature, day’s maximum tempera-

ture, season, day capacity, rain, daylight intensity (cloudy)

are considered as input. But practically, the amount of

electricity consumed by a community depends on several

factors such population, adu lt literacy, per capita inco me,

and so on.

Linear regression technique is widely used in the area

of load forecasting from the very early stage of power

system planning and expansion. A regression analysis

has been used in [5], to show the relationship between

summer weather and summer loads.

In many countries, especially in developing ones, the

major portion of the population live in remote and iso-

lated areas. In term of electrical energy use, isolated ar-

eas are those areas which cannot be connected with the

main electrical grid system due to economical or techni-

cal reasons. The economical and tech nical incapab ility of

connecting isolated areas with the main grid may evolve

from the distance between the grid and the isolated area

or inconvenient connecting zones. The load forecasting

of an isolated area is nicely described in [1-3]. But the

main limitation of these works is that the load histories

are assumed as known which is not practical. Recently,

optimal scheduling of a renewable micro-grid in an iso-

Md. A. MAHMUD

548



lated load area using mixed-integer linear programming

is proposed in [6], where different aspect of generation

scheduling are considered to meet the demand of the

community.

The aim of this paper is to forecast the load of an iso-

lated area where there is no indication about the past

history of loads. The analysis is don e based on the linear

regression method and other identification factors on

which load growth depends. Identifications factors are

calculated from the factors of an area whose load history

is known as well as the selected area has the similar

characteristic to that of an isolated area. This concept is

also practically implemented on an isolated area of

Bangladesh, called, Swandip whose load growth is simi-

lar to that of another area near author’s own village.

The organization of the paper is as follows. Section 2

represents th e methodo logy with all id entification factors

that are considered for load forecasting. Practical imple-

mentations of the theory and results are shown in Section

3. Finally, the paper is concluded with the new findings

and further recommendation in Section 4.

2. Isolated Area Load Forecasting: Linear

Regression Analysis

In this section, a linear regression analysis is adopted to

develop a method of load forecasting. The method (LRA)

starts with the identification of factors on which load

growth depends. These factors may be different for dif-

ferent types of loads. Usu ally for an isolated area electric

loads are domestic, commercial, industrial and irrigation.

2.1. Domestic Loads

The domestic load may be a function of population and

standard of living of people. The variation of standard of

living is caused by per capita income and adult literacy

rate. All these factors are time varying quantities. The

domestic load, LD may then be expressed as,

 



1,,

Lt fPtLtPt (1)

where, P(t) = Population at time t, LR(t) = Adult literacy

rate at time t, PI(t) = Per capita income at time t.

2.2. Industrial Loads

Industrial load may depend on the per capita income,

inland communication in per unit area of total area, dis-

tance from the local town, literacy rate and agricultural

land in per unit area of total area. This industrial load LI

can be calculated as,

  



2,,,

I ILTL

Lt fPtRtDtAt (2)

where, RL(t) = Inland communication length in per unit

area at time t, DT(t) = Distance from local town, AL(t) =

Agricultural land in percent of total area at time t.

In some isolated areas, instead of inland communica-

tion, communication across the sea may be the major

type of communication. In that case the communication

must be included the sea route length also.

2.3. Commercial Loads

The commercial load mainly depends on per capita in-

come, inland communication in per unit area and dis-

tance from local town. The commercial load, LC may

then be expressed as,













3,,

CILT

Lt fPtRtDt (3)

2.4. Irrigation Loads

The load for irrigation mainly depends on agricultural

land in per unit area of total area and per capita income.

This industrial load LIR can be calculated as,









IRL I

Lt fAtPt (4)

The total electrical load demand, L(t) in an isolated

area is the sum of the above four loads. That is,











 

DICIR

LtLt Lt LtLt



(5)

Therefore, the load of an isolated area can be ex-

pressed as (6)错误！未定义书签。,











  









,,,,,

RIL LT

LtfPtLtPtRtAtDt (6)

Although Equation (6) expresses that the load is a

function of six time dependent variables. However, all

variables will not contribute equally to the generation of

load. Let X1, X2, X3, X4, X5, and X6 represent the weight-

ing factors by which each time varying factor P(t), LR(t),

PI(t), RL(t), AL(t), and DT(t) respectively contributes to-

wards the load growth. The weighting factors, [X] are

also random in nature. They may vary with different ar-

eas. Now the load can be expressed as,







LtX Rt











 







(7)

From Equation (7), the weighted factors [X] can be

calculated as,

Md. A. MAHMUD549





XLt Rt



















































(8)

To calculate, the value of these weighted factor, the

past history of the considered area need to be known.

One more option is that one can consider an area whose

behaviour is similar to that of the isolated area. This is

what, is the main contribution of this work. This will be

clarified through the practical implementation of the pro-

posed method.

3. Practical Implementation and Results

For the purpose of load forecasting, the data is collected

from the isolated area, Swandip and from a known area

whose characteristics is similar to that of Swandip. In the

district of Naogaon, Dhamuirhat Police Station, which is

located on the bank of a river called, Jamuna Branch

whose characteristics is very close to that of Swandip

where most of the people lead their life by catching fish.

The data are collected from the Naogaon Palli Bidhyut

Samity which is an independent co-operative society of

Rural Electrification Board (REB), Bangladesh and from

the office of the Dhamuirhat Police Station under which

the village is located. All other data are directly collected

from the Swandip.

The data collected from the above mentioned sources

can best be shown by Table 1.

Here, POP = Population (1000), LR = Adult Literacy

Rate (%), PI = Per Capita Income (%), AL = Agricultural

Land (% of Total area), RL = Road Length or Inland

communication length in per unit area (km/km2), DT =

Distance from Local Town (km), MD = Maximum De-

Table 1. Collected data.

Factors Known Area Unknown Area

POP(1000) 184 400

LR (%) 64.5 58

PI (TK) 3700 4000

AL (%) 87 60

RL (km/km2) 15 10

DT (km) 48 57

MD (MW) 150 *

AD (MW) 127 *

mand, September, AD = Average Demand, September, *

to be calculated.

Now, the weighted factors need to be calculated for

maximum demand as well as for average demand. The

calculated weighted factors on different months of 2008

for average demand are shown in Table 2.

Again, the calculated weighted factors on different

months of 2008 for maximum demand are shown in Ta-

ble 3.

Tables 2 and 3 show that the weighting factors evalu-

ated for different load decidi ng variables are not the same.

Table 2. Weighting factors X of load growth deciding vari-

ables for average demand.

Months of

2008 X1 X2 X3 X4 X5 X6

Jan 0.690196.8990.034 145.98 8.4672.646

Feb 0.679193.7980.033 143.68 8.3332.604

Mar 0.679193.7980.033 143.68 8.3332.604

Apr 0.684195.3490.034 144.83 8.4002.625

May 0.679193.7980.033 143.68 8.3332.604

June 0.674192.2480.034 142.53 8.2672.583

July 0.668190.6970.033 141.38 8.2002.563

Aug 0.668190.6970.033 141.38 8.2002.563

Sep 0.663189.1470.033 140.23 8.1332.541

Oct 0.668190.6970.033 141.38 8.2002.563

Nov 0.663189.1470.033 140.23 8.1332.541

Dec 0.666190.0470.033 140.90 8.1722.554

Table 3. Weighting factors X of load growth deciding vari-

ables for maximum demand.

Months of

2008 X1 X2 X3 X4 X5 X6

Jan 0.820232.560.040 172.40 10.03.13

Feb 0.800229.460.040 170.11 9.873.08

Mar 0.800229.460.040 170.11 9.873.08

Apr 0.810231.000.040 171.26 9.933.10

May 0.790227.900.040 168.96 9.803.06

June 0.790226.360.039 167.81 9.733.04

July 0.788224.800.039 166.67 9.673.02

Aug 0.788224.800.039 166.67 9.673.02

Sep 0.780223.260.038 165.51 9.603.00

Oct 0.788224.800.039 166.67 9.673.02

Nov 0.780223.260.038 165.51 9.603.00

Dec 0.770221.700.038 164.37 9.532.98

Md. A. MAHMUD

550

Figures 1 and 2 show the different amount of fore-

casted demand of the considered area for different month

of the year, 2008.

This clearly indicates that the load growths do not de-

pend equally on all factors. This is, because some fac-

tors are very sensitive to the development of maximum

demand or average demand while the others are not. 4. Conclusions

Again, by using the values of weighting factors, the

value of maximum demand and average demand can be

calculated. For this, the value of average demand and

maximum demand for different months of a year is Fig-

ures 1 and 2, respectively.

This work mainly focuses the load forecasting only for

an isolated area Swandip in Bangladesh which helps an

electric utility to make important decisions including

decisions on purchasing and generating electric power,

load switching, and infrastructure development. But this

mathematical model is valid for all area to forecast elec-

trical load. The further work will include the application

of the proposed method to any area.

800

810

820

830

840

850

860

123456789101112

850.65

837.25

843.95

837.25

830.56

823.86

817.16

823.86

817.16

821.05

Average

demand

( MW)

Months

5. References

[1] D. Park, M. Al-Sharkawi, R. Marks, A. Atlas and M.

Damborg, “Electric Load Forecasting Using an Artificial

Neural Network,” IEEE Transactions on Power Systems,

Vol. 6, No. 2, 1991, pp. 442-449. doi:10.1109/59.76685

[2] A. D. Papalxopoulos and T. C. Hiterbeg, “A Regression-

Based Approach to Short-Term Load Forecasting,” IEEE

Transactions on Power Systems, Vol. 5, No. 4, 1990, pp.

1535-1547. doi:10.1109/59.99410

Figure 1. Forecasted average demand (MW) of an isolated

area, Swandip. [3] G. Gross and F. D. Galianan, “Short-Term Load Fore-

casting,” Proceedings of the IEEE, Vol. 75, No. 12, 1987,

pp. 1558-1572. doi:10.1109/PROC.1987.13927

[4] S. Sachdeva and C. M. Verma, “Load Forecasting Using

Fuzzy Methods,” Proceeding of Joint International Con-

ference on Power System Technology and IEEE Power

India Conference, New Delhi, 12-15 October 2008, pp.

1-4.

[5] G. T. Heinemann, D. A. Nordman and E. C. Plant, “The

Relationship between Summer Weather and Summer

Loads,” IEEE Transactions on Power Apparatus and Sys-

tems, Vol. PAS-85, No. 11, 1966, pp. 1144-1154.

doi:10.1109/TPAS.1966.291535

[6] H. Morais, P. K. P. Faria, Z. A. Vale and H. M. Khodr,

“Optimal Scheduling of a Renewable Micro-Grid in an

Isolated Load Area Using Mixed-Integer Linear Pro-

gramming,” Renewable Energy, Vol. 35, No. 1, 2010, pp.

151-156. doi:10.1016/j.renene.2009.02.031

Figure 2. Forecasted maximum demand (MW) of an iso-

lated area, Swandip.