Neural network based approach for short-term load forecasting

Abstract

Short-term load forecast is an essential part of electric power system planning and operation. Forecasted values of system load affect the decisions made for unit commitment and security assessment, which have a direct impact on operational costs and system security. Conventional regression methods are used by most power companies for load forecasting. However, due to the nonlinear relationship between load and factors affecting it, conventional methods are not sufficient enough to provide accurate load forecast or to consider the seasonal variations of load. Conventional ANN-based load forecasting methods deal with 24-hour-ahead load forecasting by using forecasted temperature, which can lead to high forecasting errors in case of rapid temperature changes. This paper presents a new neural network based approach for short-term load forecasting that uses the most correlated weather data for training, validating and testing the neural network. Correlation analysis of weather data determines the input parameters of the neural networks. The suitability of the proposed approach is illustrated through an application to the actual load data of the Egyptian Unified System.

Full text

Page 1

1

Abstract— Short-term load forecast is an essential part of electric
power system planning and operation. Forecasted values of
system load affect the decisions made for unit commitment and
security assessment, which have a direct impact on operational
costs and system security. Conventional regression methods are
used by most power companies for load forecasting. However,
due to the nonlinear relationship between load and factors
affecting it, conventional methods are not sufficient enough to
provide accurate load forecast or to consider the seasonal
variations of load. Conventional ANN-based load forecasting
methods deal with 24-hour-ahead load forecasting by using
forecasted temperature, which can lead to high forecasting errors
in case of rapid temperature changes. This paper presents a new
neural network based approach for short-term load forecasting
that uses the most correlated weather data for training,
validating and testing the neural network. Correlation analysis of
weather data determines the input parameters of the neural
networks. The suitability of the proposed approach is illustrated
through an application to the actual load data of the Egyptian
Unified System.


Index Terms—Load forecasting, neural network, short-term,
correlation analysis.
I. INTRODUCTION
RELIABILITY, secured service and economics are
essential requirements for electricity supply. Utilities are
always faced with the challenge of meeting the growing load
demands while maximizing their short-term and long-term
operational efficiency. To achieve this goal, several
operational tasks such as fuel allocation, unit commitment,
unit dispatch, reserve allocation and maintenance scheduling
must be carried out efficiently to minimize the overall
operating cost.

To meet the fluctuating load, utilities need to ensure sufficient
transmission and generation resources to meet forecasted
demand. Resource procurements should be done economically
to optimize the operational cost. Since the economy of the
operation and control of power systems are greatly affected
by load demand, significant savings can be attained by
increasing the accuracy of load forecast. High forecast error



can lead to either over conservative or unreliable operation.
For example, higher estimation of load can cause unnecessary
startup of additional generation units or excessive energy
purchase. On the other side, low estimation results in
insufficient spinning reserve, which is contrary to safe
operation requirements. Lack of supply due to errors in load
forecast can also lead to near real time procurement, which is
generally at a higher price compared to scheduled transactions
cost. It is evident that improvement in load forecast has a
direct positive impact on system security and also cost of
operation [1].

Currently, power utilities are using various load forecasting
techniques worldwide. Most of the developed methods can be
broadly categorized into three groups, namely parametric,
nonparametric, and artificial intelligence based methods [2].
In the parametric methods, a mathematical or statistical
relationship is developed between the load and the factors
affecting it. Some examples of these models are time
functions, polynomial functions, linear regressions, Fourier
series and Auto Regressive Moving Average (ARMA) models
[3]-[6]. In time-series methods, the load is treated as a time
series signal with known periodicity such as seasonal, weekly,
or daily. Such repetitive cycle gives a rough prediction of the
load at the given season, day of the week, and time of the day.
The difference between the estimated and actual load can be
considered as a stochastic process, which can be then
analyzed using Kalman filter methods [7]. Nonparametric
methods forecast the load directly from historical data. For
example, using nonparametric regression, the load can be
forecasted by calculating an average of historical loads and
then assign weights to different loads using a multivariate
product kernel [8].

Recently, significant interests and efforts have been directed
towards the application of artificial intelligence techniques to
load forecasting. This includes the application of expert
systems to load forecasting [9], [10], and comparing its
performance to traditional methods [1]. It also includes the
use of fuzzy inference [11] and fuzzy-neural models [12],
[13].

However, the models that have received a high share of
efforts and focus are the artificial neural networks (ANNs).
The main advantage of ANNs is their outstanding
performance in data classifications
approximation. ANN is also
and
of
function
detecting capable
Neural Network Based Approach for Short-
Term Load Forecasting
Zainab H. Osman, Mohamed L. Awad and Tawfik K. Mahmoud
978-1-4244-3811-2/09/$25.00 ©2009 IEEE

Page 2

2
dependencies from historical data without the need to develop
a specific regression model. First publications on ANN
application to the load forecasting problem were made in late
1980’s and early 1990’s [14]. Since then ANN have been well
accepted in practice, and are used by many utilities [15]-[16].

Most of the conventional ANN-based load forecasting
methods deals with 24-hour-ahead load forecasting or next
day peak load forecasting by using forecasted temperature.
The drawback of this method is that when rapid changes in
temperature of the forecasted day occur, load power changes
significantly, which leads to high forecast error[17]. In
addition, conventional neural networks use all similar day’s
data throughout the training process. However, training of the
neural networks using all similar day’s data is a complex task
and it does not suit learning of neural network. To overcome
the problems mentioned above, this paper proposes a one-
hour-ahead load forecasting method using the most significant
weather data. In the proposed forecasting method, weather
data is first analyzed to determine the most correlated factors
to load changes. The most correlated weather data is then
used in training, validating and testing the neural network.
Correlation analysis of weather data is used to determine the
input parameters of the neural networks. The suitability of the
proposed approach is illustrated through an application to the
actual load data of the Egyptian Unified System.
II. LOAD ANALYSIS

The different characteristics of the power system and its load
patterns significantly affect the ANN model selection. In other
words, the ANN model structure is system-dependent and the
characteristics of the target system should be analyzed as a
fundamental step in ANN design for short–term load
forecasting STLF. The first step in designing any load
forecaster is to extract load characteristics such as periodicity
and trends by analyzing previous load records [1].

In this paper, load analysis is performed on load records for
the Egyptian Unified System. Table 1 shows the monthly peak
load variation in MW for the Egyptian Unified System during
the period of 1998/1999 to 2004/2005. The maximum load for
year 2004 was 15,491 MW and it was observed in the second
week of July. The system average demand consumption for
the year 2004 was 10,978 MW.

The total energy consumption for year 2004/2005 was 85,305
GWh. Figure 1 shows the consumption distributions amongst
the main sectors in Egypt during that year, which were 36.8%
for residential supplies, 35.1% for industrial loads, 11.2% for
public utilities and 16.8% for agricultural, government and
sales for resale and reconnection.

Figures 2 illustrate the load characteristics of the first week of
January, July and October 2004 as representative week for the
seasonal load variations. The figures show the load variations
during these weeks against temperature, dew point, humidity
and wind speed.


TABLE 1. MONTHLY PEAK LOAD FOR THE EGYPTIAN UNIFIED SYSTEM DURING
IN 1998/1999 TO 2004/2005
Month/
Year
1999 2000 2001
Jul
10236 11253 11976
Aug
10530 11415 12188
Sept
10614 11315 12261
Oct
10386 11280 11918
Nov
10230 11016 11806
Dec
10436 11309 11749
Jan
10436 11161 11850
Feb
10451 11193 11798
Mar
10345 11146 11913
Apr
10376 11292 11879
May
10568 11621 12275
June
10919 11736 12376
Max.
10919 11736 12376

1998/ 1999/ 2000/2001/
2002
12801
12973
12913
12564
12355
12376
12572
12313
12387
12461
12726
13326
13326
2002/
2003
13997
13882
14401
14062
13260
13211
13092
13244
13131
13251
13701
14321
14401
2003/
2004
14503
14595
14723
14253
13878
13896
13870
13843
13770
14027
14155
14735
14735
2004/
2005
15491
15321
15468
15204
14531
14591
14615
14644
14570
14861
15310
15678
15678

Fig. 1. Egyptian energy consumption distribution for year 2004/2005


Table 2 shows the correlation factors between the load
demand and the four weather paramerts; temperature, dew
point, wind speed and humidity for the first week of January,
April, July and October, respectively.

The effect of a calendar day, such as day of the week, month
of the year, type of the day and type of the hour has proven to
have an impact on daily peak load by previous researches. An
important observation of previous load analysis is related to
load shape of different weekdays [1]. The load patterns are
diverse in the different days of the week. Thursday and
Sunday loads also hold slightly different patterns from other
working days due to their proximity to weekend days.

Page 3

3
First Week of January 2004
0
50
100
150
1
24477093
116139162
Hour
Load
Temperature
Dew Point


First Week of April 2004
0
50
100
150
1
24 477093
116139162
Hour
Load
Temperature
Dew Point


First Week of July 2004
0
50
100
150
200
1
24477093
116139162
Hour
Load
Temperature
Dew Point


First Week of Octobre 2004
0
50
100
150
200
1
23 45 6789
111133155
Hour
Load
Temperature
Dew Point

Fig. 2. Seasonal load variations for Egyptian load vs. weather
parameters in year 2004

First Week of January 2004
0
50
100
150
1
24477093
116139162
Hour
Load
Wind Speed
Humidity


First Week of April 2004
0
50
100
150
1
24477093
116139162
Hour
Load
Wind Speed
Humidity


First Week of July 2004
0
50
100
150
200
1
2345 6789
111 133 155
Hour
Load
Wind Speed
Humidity



First Week of Octobre 2004
0
50
100
150
200
1
25497397
121 145
Hour
Load
Wind Speed
Humidity

Page 4

4
III. ANN STRUCTURE

The formulation of the ANN model requires a number of
decisions related to different model parameters such as model
structure, training algorithm and input variables. This section
describes the significance of these parameters in short-term
load forecast and how they are selected.

A. Input Variables

Selection of the kind and number of input variables is an
important issue encountered in the design of the ANN. In case
of STLF, the performance of the forecast depends largely on
the proper selection of the load affecting variables. In STLF,
the key variables are time, forecasted weather variables, and
historical load [1]. Therefore, it is vital to identify the input
variables, which have significant impacts on the system load.
This is particularly important since inclusion of irrelevant
inputs or inputs with no significant impact on the target
outputs can distort the forecast performance, increase the
training time, increase network complexity and reduce the
network execution time. One approach to identify the most
affecting input variables is by evaluating the statistical
correlation between such input variables and the target output.
In this paper, the linear correlation coefficient index is
calculated between each input variable and the output target.
Correlation coefficient with absolute values near 1 implies a
high influence of a particular input variable to the target
output.

Table 2 shows the correlation factors between the following
parameters and the next hour load forecast for the Egyptian
Unified System,

•
P (d, t-1), P(d,t-2), P(d,t-3): the load values of the
previous 1, 2 and 3 hours respectively
•
P (d-1,t), P (d-1,t-1), P (d-1,t-2), P (d-1,t-3): the load
values of the day preceding the forecasted day at same
hour, and previous 1, 2 and 3 hours respectively,
•
T (d,t), T (d,t-1), T(d,t-2), T(d,t-3): the hourly
temperature of the same day at same hour and previous 1,
2 and 3 hours respectively,
•
W(d,t), W(d,t-1), W(d,t-2), W(d,t-3): the average wind
speed of the same day at same hour and previous 1, 2 and
3 hours respectively,
•
H(d,t), H(d,t-1), H(d,t-2), H(d,t-3): the relative humidity
of the same day at same hour and previous 1, 2 and 3
hours respectively,
•
D(d,t), D(d,t-1), D(d,t-2), D(d,t-3): the dew point of the
same day at same hour and previous 1, 2 and 3 hours
respectively.





TABLE 2. CORRELATION COEFFICIENTS FOR DIFFERENT
PARAMETERS WITH EGYPTIAN UMIFIED NETWORK LOAD DATA
Entire
Year
P(d, t-1)
0.9194
Winter
Season
0.9006
P(d, t-2)
P(d, t-3)
P(d-1, t)
P(d-1, t-1)
P(d-1, t-2)
P(d-1, t-3)
T(d, t)
T(d, t-1)
T(d, t-2)
T(d, t-3)
W (d, t)
W (d, t-1)
W (d, t-2)
W (d, t-3)
H(d, t)
H(d, t-1)
H(d, t-2)
H(d, t-3)
D(d, t)
D(d, t-1)
D(d, t-2)
D(d, t-3)
0.7658
0.5911
0.9604
0.8866
0.7358
0.5630
0.0179
0.0415
0.0794
0.1287
-0.2816
-0.2531
-0.2060
-0.1474
0.3962
0.3644
0.3067
0.2332
0.4094
0.4023
0.3920
0.3804
0.7228
0.5223
0.9514
0.8633
0.6899
0.4930
0.1025
0.2182
0.3229
0.4090
-0.0562
-0.040
0.0387
0.0251
-0.0274
-0.1072
-0.1848
-0.2539
0.0670
0.0699
0.0591
0.0414

Spring
Season
0.8911
Summer
Season
0.9038
Fall
Season
0.9185
P(d, t-1)
P(d, t-2)
P(d, t-3)
P(d-1, t)
P(d-1, t-1)
P(d-1, t-2)
P(d-1, t-3)
T(d, t)
T(d, t-1)
T(d, t-2)
T(d, t-3)
W (d, t)
W (d, t-1)
W (d, t-2)
W (d, t-3)
H(d, t)
H(d, t-1)
H(d, t-2)
H(d, t-3)
D(d, t)
D(d, t-1)
D(d, t-2)
D(d, t-3)
0.6872
0.4595
0.9512
0.8559
0.6550
0.4285
-0.1914
-0.1002
-0.0054
- 0.0926
-0.2037
-0.1046
-0.00061
0.1032
0.2900
0.1862
0.0755
-0.0381
0.1560
0.1408
0.1221
0.1024
0.7220
0.5219
0.9317
0.8414
0.6628
0.4648
0.5025
0.4209
0.3084
0.1770
-0.4457
-0.3699
-0.2620
-0.1409
0.6225
0.5473
0.4288
0.2956
0.4729
0.4345
0.3841
0.3309
0.7596
0.5713
0.9618
0.8841
0.7277
0.5417
0.3106
0.3507
0.3547
0.3273
-0.3794
-0.4198
-0.4221
-0.3932
0.6054
0.6474
0.6426
0.6057
0.3038
0.3053
0.3022
0.2969

The results of Table 2 show that the historical load
information are the most correlated parameters to the
forecasted load. The results also show that summer and fall
load forecasts are highly related to the temperature especially
when compared to the correlation between winter and spring
loads to weather parameters. Out of the different weather
parameters, temperature and humidity seem to be the most

Page 5

5
affecting weather parameters on summer and fall loads. In
winter and fall, wind speed effect is almost negligible on the
load.

Table 2 also shows that the effect of forecasted hour weather
information is close to that of the previous hour weather
information. For example the correlation between forecasted
load and forecasted temperature for the summer season is
0.5025, which is close to correlation between forecasted load
and previous hour temperature, which is 0.4209.

In this approach, the forecast time interval is taken to be one
hour i.e. forecast is done for each hour. Therefore, it is
assumed that the hourly values of the weather parameters can
capture the most conservative conditions that may happen
during this hour.


B. Training Data

Training is the process by which ANN determines the
different network parameters such as weights and biases. In
general, the training data set should cover a wide range of
input patterns sufficient enough to train the network to
recognize and predict the relationship between input variables
and target output.

Typically, ANNs are trained following a supervised pattern,
i.e. the desired output is given for each input and the training
process then adjusts the weights and biases to match the
desired output [18]. A new method for selecting the training
vector is presented in this paper. In this method, the minimum
distance between the forecasted input variable and its desired
outcome is calculated for the entire historical database. This
method is applied by assuming a specific condition and then
filtering the data that does not achieve this condition such
that,

| P (d, t)-P^ (d, t) |<ai,

where P(d,t) is the actual load, P^ (d, t) is its forecasted value
and ai is the assumed threshold.

This approach helps in cancelling any odd data or load
patterns, which are related to special events such as holidays.
It also helps in eliminating the effect of sudden load changes
due to drastic changes in the weather conditions. The new
search strategy demonstrates an improved accuracy over other
methods when tested using one year data.
The load pattern is divided into seven patterns (subsets)
corresponding to the seven days of the week. According to
similar days approach, load curve is forecasted by using
information of the days that are similar to weather condition
of the forecast day. Additionally, since the load and
temperature vary year-round, a different training vector is
developed for each of the four different seasons, i.e. summer,
winter, spring, and fall.

The Levenberg-Marquardt algorithms is used to train the
developed network since it provides a good compromise
between fast convergence and a low computation cost
[1],[18].
The network is updated for each new input vector added. To
get best generalized performance and overcome over fitted
issue, the data is divided into training data and validation data.
The data of two months is divided into two groups; one hour
for training and next hour for validation. Next month data is
used for testing the performance of the network for
forecasting. In these model 50% of the total data are used for
training and 50% for validation. The data is scaled first and
then divided into four seasons (winter, spring, summer, and
fall), with weekend and public holidays data excluded. For
each season past 60 days of data (approximately 1440 points )
is used for training, and the following month data is used for
testing.

C. Network Topology

In this paper, a three-layer feed forward neural network is
used to construct the STLF model. In theory, a three-layer
feed forward network can be used for predictions [14]. For the
number of neurons in each layer, the number of units in the
input and output layers are fixed by the number of inputs and
the number of outputs, respectively. Since the target output is
the forecasted hourly load, the model has one output
representing the forecasted load of the target hour. Due to
seasonal load variations, four case studies, related to the
different four seasons are performed. The number of inputs
for each case is dependent on the number of the effective
parameters as determined by the correlation analysis as
previously discussed in the Load Analysis Section.

One of the challenges in the design of ANN is the proper
selection of the number of neurons in the hidden layer, which
affects the learning capability and varies by the complexity of
the problem. In general, a tradeoff between accuracy and
generalization ability can be achieved by selecting the proper
number of hidden units. While, there is no rigorous set of
rules to determine the optimal number of hidden units, the
fundamental rule is to select the minimum number of hidden
neurons just enough to ensure the complexity of the problem,
but not too many to cause over fitting of the training set and
losing generalization ability. The approach presented in [13]
is also adopted here. The method starts by setting the
estimated optimal number of hidden neurons as the square
root of the product of the number of inputs times the number
of the outputs. Then the number of hidden neurons is
gradually incremented by one. Each time, the model is trained
and the forecast error from the test set is recorded for
comparison.

D. Seasonal Models