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
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
I

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,, DR
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,




4, 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,
 






R
I
L
L
T
Pt
Lt
Pt
LtX Rt
A
t
Dt







 







(7)
From Equation (7), the weighted factors [X] can be
calculated as,

Md. A. MAHMUD549








1
R
I
L
L
T
Pt
Lt
Pt
XLt Rt
A
t
Dt

























(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
837.25
843.95
837.25
830.56
823.86
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.