NOVEL HYBRID ELECTRIC LOAD FORECASTING MODEL USING ARIMA MODEL AND DISCRETE WAVELET TRANSFORM THESIS Submitted in fulfilment of the requirements of the degree of DOCTOR OF PHILOSOPHY By Harveen Kaur 1410931001 Supervised by Dr. Sachin Ahuja Professor & Director | Research Department of Computer Science and Engineering CHITKARA UNIVERSITY CHANDIGARH-PATIALA NATIONAL HIGHWAY RAJPURA (PATIALA) PUNJAB-140401 (INDIA) February 2021
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NOVEL HYBRID ELECTRIC LOAD FORECASTING
MODEL USING ARIMA MODEL AND DISCRETE
WAVELET TRANSFORM
THESIS
Submitted
in fulfilment of the requirements of the degree of
DOCTOR OF PHILOSOPHY
By
Harveen Kaur
1410931001
Supervised by
Dr. Sachin Ahuja
Professor & Director | Research
Department of Computer Science and Engineering
CHITKARA UNIVERSITY
CHANDIGARH-PATIALA NATIONAL HIGHWAY
RAJPURA (PATIALA) PUNJAB-140401 (INDIA)
February 2021
i
DECLARATION BY STUDENT
I hereby certify that the work which is being presented in this thesis entitled
“Novel hybrid electric load forecasting model using ARIMA model and
Discrete Wavelet Transform” is for fulfilment of the requirement for the
award of Degree of Doctor of Philosophy submitted in the Department of
Computer Science and Engineering, Chitkara University, Punjab
The work has not formed the basis for the award of any other degree or
diploma, in this or any other Institution or University. In keeping with the
ethical practice in reporting scientific information, due acknowledgements have
been made wherever the findings of others have been cited.
Harveen Kaur
ii
CERTIFICATE BY SUPERVISOR
This is to certify that the thesis entitled “Novel hybrid electric load
forecasting model using ARIMA model and Discrete Wavelet Transform”
submitted by Harveen Kaur to the Chitkara University, Punjab in fulfilment
for the award of the degree of Doctor of Philosophy is a bona fide record of
research work carried out by her under my supervision. The contents of this
thesis, in full or in parts, have not been submitted to any other Institution or
University for the award of any degree or diploma.
Dr. Sachin Ahuja
Professor & Director | Research
Chitkara University, Punjab
iii
ACKNOWLEDGEMENT
I wish to thank all of those who made contributions in a variety of forms over the prolonged
period of researching and writing this thesis.
It gives me an immense pleasure in expressing my deepest gratitude towards my research
supervisor Dr. Sachin Ahuja, Professor and Director (Research), Chitkara University,
Punjab, India for his warm encouragement and thoughtful guidance. I am thankful to my
supervisor for all his contributions of time and ideas to make my Ph.D experience productive
and stimulating.
I am highly indebted to Mr. Arun Kumar Gupta, E-in-Chief, Planning, PSPCL, Patiala and
his associated staff for arranging and providing me the real energy consumption data of the
Punjab State and providing valuable ideas in undergoing my research work.
My special thanks to the internal and external examiners who provided valuable fresh insight
into the work and helped to make it more conclusive research.
My deepest gratitude goes to my father Mr. Surinder Pal Singh, Executive Engineer, Office
of Chief Electrical Inspector, Punjab Govt., who has been constantly supporting me for
making my research work more effective and my mother Mrs. Palvinder Kaur for her
unflagging love and being the constant source of inspiration and encouragement throughout
my personal journey that is part of this long research process. Ashmeet Kaur, my sister
whose encouragement, and constant support for me to reach this goal has been the greatest
gift.
Above all, I am grateful to God, Almighty who sustains this beautiful world and without
whose grace nobody can ever succeed.
HARVEEN KAUR
iv
ABSTRACT
Energy is the first and foremost part of the socio-economic and political world in which we
live. The most important of the various forms of energy is electricity. There is always a gap
between the supply and demand for the electric energy. To meet the ever increasing demand
of the electricity consumption there is a dire need for an accurate prediction model that can
prove useful. In the present work, electricity consumption forecasting model is designed for
the State of Punjab, India, in which the dynamic relationship among the time series entities is
explored. The time-series data comprises a variety of information in their samples consisting
of both linear and nonlinear data. Based on the type of Time Series Data, models such as
linear and nonlinear can be applied. In this work, the direct model techniques used are Auto-
Regressive Integrated Moving Average (ARIMA), whereas nonlinear model techniques used
are optimization algorithms, i.e., Cuckoo Search (CS), and Artificial Neural Network (ANN).
To achieve optimum accuracy, instead of using these techniques individually, a hybrid model
has been developed which was further applied on the Time Series Data of electricity
consumption in Punjab. Initially, the data is decomposed into two levels using the Discrete
Wavelet Transform (DWT) method. DWT is used to decompose the Punjab State Power
Corporation Limited (PSPCL) data into two parts based on electricity consumption, which
helps to determine the highest and the lowest electricity consumption. On each decomposed
data ARIMA technique is applied individually to obtain a Time Series Data. Then, Inverse
Discrete Wavelet Transform (IDWT) is applied to combine the data, which is further
optimized using a nature-inspired CSA technique. The Artificial Neural Network (ANN)
algorithm is used to train the designed model by passing the optimized data to its input layers,
which helps for the prediction of electricity consumption in the future. After applying
ARIMA, the accuracy of the forecasting model is 83.53% and ARIMA with DWT technique
there is an increase of 10.23% in accuracy whereas utilizing ARIMA with the hybrid model
of DWT, CSA and ANN there is an increase of 15.33 % in accuracy. So, the performance of
the proposed hybrid strategy, i.e., ARIMA, DWT, CSA and ANN is better than both existing
forecasting models i.e. ARIMA model and ARIMA with DWT model.
v
SUMMARY
This complete research is comprised of 6 chapters, which by large emphasis the working
functionality and gives a complete explanation of the research work and implementation.
Chapter 1: The introduction chapter consists of the basic terminology of research topic by
highlighting the concepts and the process of enhancing the methods of implementation for the
research work on Novel hybrid electric load forecasting model using ARIMA model and
Discrete Wavelet Transform.
Chapter 2: The literature review chapter provides the base of knowledge on the topic and
helps to identify gaps in research and includes the study by the other authors who have done
the work on same areas.
Chapter 3: The methodology chapter provides the proposed hybrid forecasting model. In this
chapter the proposed methodology is designed and developed.
Chapter 4: The Proposed work chapter comprises of the algorithms used to develop the
proposed hybrid forecasting model. The specific objectives are as follows:
1. To model the time series data and forecast future values using ARIMA.
2. To determine how discrete wavelet transform, resolve the difficulties in ARIMA
modeling.
3. To develop a hybrid model of ARIMA and wavelet transform.
4. To analyze the performance and accuracy of the proposed algorithm.
Chapter 5: This chapter discusses about results and the simulation of the research work done
using MATLAB simulator to forecast the electricity consumption by using different
techniques.
Chapter 6: This chapter is about conclusion and future scope. The research focuses on
design and development of a novel intelligent technique, which can be used to study the
behaviour of electricity consumption on the basis of time series data.
vi
TABLE OF CONTENTS
DECLARATION BY STUDENT ............................................................................................ i
CERTIFICATE BY SUPERVISOR ........................................................................................ ii
ACKNOWLEDGEMENT ..................................................................................................... iii
ABSTRACT .............................................................................................................................. iv
SUMMARY ............................................................................................................................... v
TABLE OF CONTENTS ......................................................................................................... vi
LIST OF FIGURES ................................................................................................................... x
LIST OF TABLES ................................................................................................................... xv
ABBREVIATIONS .............................................................................................................. xvii
Cuckoo Search has attracted a lot of attention due to its simplicity and ability to
solve several optimization problems with numerous applications around the world.
The development of cuckoo behavior mainly affects cuckoo Search, i.e. the
placement of colorful patterns that mimic other bird's nests. Every single egg in the
nest is a solution although essentially the cuckoo egg is a new solution. Using new
and better solutions (i.e. cuckoos), algorithm's main emphasis is on modifying the
worst solution within the slots [17].
Based on the above three laws of the cuckoo hunt, the likelihood is that the host bird
will be able to throw the eggs out of the nest or simply dig the particular nest and
then create a completely fresh nest again. An important problem of CS algorithm is
the application of Levy flights to create new solutions,
(1.3)
Here is either taken from the standard normal distribution with respect to zero
mean and the standard aberration for random walks or the Levy distribution for Levy
flights.
Cuckoo egg
Host birds egg
Host birdsnest
X1 X2 Xn-1 Xn
Next solution
14
Figure 1:11 Flow chart of Cuckoo search optimization algorithm [21]
Afterwards, a random population generation can also be associated with the
similarity between the eggs of the cuckoo and the eggs of the host. The phase size
Generation of N host nest and assign the position to
each nest
Evaluation of healthy function for each nest
Bring out Levy flight to get new nests position and
evaluate its fitness
Compare the fitness of new and old nest, and
If <
A fraction of the worst nests are replaced by new
nests randomly
Compare newly searched nest with worst discovered nest and save the best nest
If max iteration reached
Take the best nest as outcome
Yes
No
No
Yes
15
‘s’ then determines the distance a random walker can cover for a given number of
repetitions [18]. Two components i.e. local and global hare consists of the CS
algorithm. The former is designed to improve the best alternative through a guided
random walk, while the latter is intended to maintain population diversity through
Levy flights. The probability of changing ‘Pa’ regulates a balance between the two
stochastic search parts.
Pseudocode of Cuckoo Search Algorithm:
Begin Initialize the N number of nests as population. Calculate Nests. While (the Criteria of terminationis not achieved) Generate randomly a novel solution i among the best nests Select nests j from population If quality of i is superior than j, replace it with solution Replace abandon nest with randomly generated nests Calculate nests.
The CS algorithm begins with a random population initialization and random
solutions generated. In comparison to its fitness function, each solution or nest is
assessed appropriately to find the possibly best solution or nest [19].
For an iterative process, the criteria for termination consist primarily of the
predefined number of generations, the maximum time allowed, or inactivity at the
end of the process. The new solution is generated corresponds to every iteration by
arbitrary walking or charging flights to the best solution. If these solutions are
superior to the solutions chosen at random, they will be replaced by the population.
The dumping of the worse solutions or nests and replacing them with the randomly
generated solutions is performed in proportion to the given probability ‘Pa’ . To find
the best alternative, the entire population is reassessed, and this method lasts until
the end requirements are met. The reason for applying CS in the designed electricity
Consumption prediction model for Punjab is because of its high convergence speed
to reach the optimal solution [20].
16
1.3.4 Artificial Neural Networks (ANNs)
Artificial neural networks (ANNs) are flexible in computation and most applied
predictors that are applicable in various time series forecasting issues along with
improved performance. ANNs are used for forecasting in various application areas
related to engineering, social sciences, foreign exchange, stock problems,
economics, and so on. Some characteristics of ANNs that makes it attractive and
valuable in forecasting task are as follows:
(a) model is not based on traditional method
(b) network can be generalized easily means it's possible for ANN to accurately
infer the unseen part of a population even if noisy information is present in data
(c) forecasting model can easily estimate any continuous function to suitable
accuracy, and ANNs are non-linear, unlike the ARIMA model [21].
1.3.4.1 Time Series Data modeling using ANN
The model of ANN is highly influenced through the features of data; the most
suitable of ANN is used for forecasting, and modeling is termed as the single hidden
layer feed-forward network. Usually, the model is categorized through three layers
of network that are linked via acyclic connections [22]. The mathematical
representation of the input, i.e., yt-1,……..,yt-p and output (yt) of this network is
provided as;
, (1.7)
Here, wi,j in which i varies from 0 to p and j varies from 0 to q, is the parameter of
the model, also known as connections weights. The terms p and q show the number
of input and hidden nodes; the activation function is also utilized in different forms.
Activation feature modes are defined by the neuron condition within the network.
The activation function is often not present in the input layer, although the activation
function's job is to move the information to the hidden layer. The most suitable
activation function in the output layer is the linear function since the non-linear
activation induces distortion in the forecast data [23]. The activation functions used
in the hidden layers are logistic and hyperbolic functions that are used to transfer
function as shown in the equation below;
17
(1.8)
(1.9)
So the ANN performs a non-linear functional mapping by using previous data to get
the future value (output).
and the output, (1.10)
The ANN is created from hundreds of units, artificial neurons, also known as
processing elements, which are related to weights, and creates the neural structure
and are arranged in layers [24]. The mathematical model of ANN is shown below in
figure 1.12.
Figure 1:12 Model of ANN [25]
For processing the input data according to the weighted function, the processing unit
is used. It composes a mathematical equation which helps in balancing the input
along with output data. As shown in figure 1.13, which mainly includes the input
signal and weight value, has been multiplied which performs addition operation and
output for that specific neuron. The sigmoid function is the most used activation
function, which used to perform the weighted sum of input neurons [25]. The
obtained result is passed to the transfer function and the layer structure of ANN as
shown in figure 1.13.
W1
X1
Y Outpu
WX2
X
W
Weig
Inpu
18
Figure 1:13 layered architecture of Feedforward network [26]
i. Input layer: The input data like optimized Time Series Data is passed to this
layer. This layer mainly consists of a node that is not involved in the
modification of signal means the nodes only forward data to the next or the
hidden layer.
ii. Hidden layer: Multiple neurons are included in the hidden layer, and the
nodes of this layer modify the signal, so they are called active nodes. Every
active node is involved in an active part of modeling.
iii. Output layer: The modified neurons are obtained at this layer and represents
the achieved output.
The ways neurons are linked with each other have an impact on the operation of
ANN. The neurons received excitatory input or inhibitory input; it does not matter
neurons may be real or artificial. In the computation of addition operation, excitatory
input neuron is useful, and for the subtraction operation, inhibitory neurons are used
[26]. These three processes are the feedback mechanism having the connection
through a path from the output layers going back to the input layer, and the
Feedback architecture is shown in figure 1.14.
X1
X2
X3
X4
Y1
Y2
Input layer Hidden layer
Output layer
19
Figure 1:14 Feedback network [26]
1.3.4.2 Estimation of the model parameter
To evaluate the parameters of the prediction model, it's not necessary to include only
an individual to optimize and compute the parameters in ANN, using nonlinear
equations. Therefore, the parameter assessment is done through training algorithms
by considering a sequence of data or training data that are fed as input data to ANN.
ANN can tell what will be the output in the future, and the ANN has been trained
based on the data at which the generated error is minimum. The minimization of the
error is performed by changing the Mean squared error (MSE). The weights and bias
values continue to change during the training period until the Time Series Data
values are improved.
1.3.4.3 Model validation and prediction
The ANN training is performed in an iterative manner, which means as the number
of iteration increases, the amount of the MSE values gets reduced. Once the error of
validation have been calculated and validation of the model is completed, this model
is used for Time Series Data prediction [27].
1.4 DECOMPOSITION BASED PREDICTION MODELS
In Time Series Data prediction, pre-processing technique becomes helpful in
improving the efficiency of forecasting. There are several kinds of pre-processing
methods available, among them, the best suitable technology to decompose has been
X1
X2
X3
X4
Y1
Y2
Input layer Hidden layer Output layer
20
applied here. The term decomposition means the process of decomposing the
original Time Series Data data into multiple components. The splitting can be done
based on some behavior of each decomposition in which filtering is the most used
approach [28]. Here in this research work, MA filter based decomposition along
with the wavelet-based decomposition have been applied, which is described below.
1.4.1 Decomposition based on Moving average (MA)
Considering a non-seasonal time series data upon which decomposition is done
based on Moving average (MA), it could be categorized into averaged or smoothed
components known as the trend and noise or residual component known as a
detrended component.
Time Series Data
Decomposition criterion met?
Fix MA Filter of length m
Trend Component Residual Component
Subtractor
no
Yes
Decomposition using MA filter
Figure 1:15 Time Series decomposition using MA Filter [29]
This technique is represented in figure 1.15. The trend component , and noise
component as expressed in given below equation (1.11) and (1.12) correspondingly.
21
The length of the MA filter could be selected to satisfy a certain decomposition
scheme for a specific work [31].
(1.11)
(1.12)
1.4.2 Discrete Wavelet Transform (DWT)
DWT is the most commonly used decomposition tool that helps researchers to get
meaningful information in terms of time and frequency about the deep signal. Using
this approach, the issues of localization, which exist in the Fourier transform has
been resolved. It is a scientific tool that transmits the input to a different field for
signal processing and analysis. The data in terms of time and frequency domain is
appropriate for predicting time-unstable autocorrelation function and unstable
processes. The data related to weather or finance are both unstable as their values
changes over time [30]. To predict such kind of data DWT is an appropriate tool and
the wavelet function considered for a single entity is written in equation 1.13.
(1.13)
In Equation 1.13, ‘c’ denotes the scaling factor that calculates the minimum value of
the given data. The ‘d’ functions are known as the translation parameter and are used
to evaluate the location of the wave time series. The wave is compressed while the
condition | c | <1, is satisfied. The wave is a compressed version that is connected to
higher frequencies (multiple time cycles). On the other hand, if | c |> 1, means that
the signal width of the generated signal is larger than (t), which is directly related
to the low frequencies _ (c, d) (t). Therefore, DWT is an essential tool, utilized to
evaluate the time series based on the wavelet information similar to discrete. It is
mainly depending upon the coded sub bands and compute data in less time. The
process of using the DWT technique is a simple and easier process. The scaling
parameters like ‘c’ has been implied in terms of 2-p as well as other parameters such
22
as l2-p, where, L I for the original dataset (Ap) [31]. The DWT function can be
signified by equation (1.14).
(1.14)
1.4.3 Trend-ARIMA model
A composite method having the decomposition based approach on MA filter is
utilized to process data to remove artifacts so that the ARIMA model can easily
execute data. Some important points included in this model are given below:
Decomposition: The decomposition technique based on MA filtration is used on the
datasets. The trend component (st), and the noise component (rt) has been obtained,
and the yt = st + rt is the original Time Series Data.
ARIMA modeling: After getting the decomposition trend and noise, this model is
applied on the decomposed data. It is not necessary for this model to have same
values in both the cases i.e. trend components and the noise component.
Predictions: After applying the ARIMA model to fit on the trend component,
prediction has been obtained. It could be represented as st,pre. The obtained noise
components after utilizing this model are represented as rt,pre. Finally, the prediction
was done by adding the obtained value corresponding to trend and noise prediction.
This obtained prediction acquires higher efficiency as compared to the basic
ARIMA model [32].
pre (1.15)
1.4.4 Wavelet-ARIMA model
This model is also utilized as a composite prediction model, in which the
decomposition technique is applied based on wavelet. After that it is used for pre-
processing by which it becomes the best fit in the ARIMA model and gets more
accurate forecasting. Apart from the moving average (MA) filter, the available
wavelet filters are HAAR, db1, db2, db3, db4 and db5. At last, the obtained data is
decomposed into detailed components. More than one level of decomposition is
23
available, as shown in figure 1.16 at the initial level; the Time Series Data is filtered
by applying any one of the discussed wavelet filters [33].
Figure 1:16 Wavelet decomposition [33]
As shown in Figure 1.16, the low and high frequency components are represented by
ya1 and yd1 respectively. The main components are again split into low and high
frequency components are represented by yd1 and yd2 respectively. After doing
these two levels of decomposition, the final obtained parts are ya2, yd1 and yd2.
From these, the final approximate components are represented by ya2, yd1 and yd2.
This decomposition could be further decomposed into further levels according to the
types of Time Series Data [34]. Based on these, Wavelet based ARIMA model
some essential points are discussed below:
Decomposition: By using the wavelet-based decomposition, the dataset is
decomposed into the required number of levels based on input Time Series Data
data.
ARIMA modeling: ARIMA modeling has been applied on every decomposed
output data i.e. ya1, yd1 and yd2 so that best fit value can be obtained.
Prediction: The prediction of the original data was calculated by adding the
projections of all the fragmented components given in the following equation, and
the performance was increased relative to the basic ARIMA model.
+ (1.16)
This form of decomposition is the expanded version of the pattern dependent
ARIMA; here the details on patterns and objects are collected during the
decomposition of the usable dataset which represents a low-frequency portion of a
24
data collection, so noise data is consistent with high-frequency components. Trend
and residual data are close to the first stage of separation, and pattern decomposition
may be further applied to boost the precision of the methods [35].
1.5 CLASSIFICATION TECHNIQUES
There are vast amounts of data, which are being collected and stored in the databases
across the globe. The classification is the technique used for finding the classes of
unknown data. The classification algorithms follow three different learning
In table 5.12, the actual electricity consumption values for the year 2013 is provided.
The corresponding expected values for the electricity consumption is also provided.
It is clear from the obtained expected values; the predicted values and the actual
values are approximately close to each other. However, the actual electricity
consumed by users was about 3063315451. Consumers using the proposed hybrid
model are expected to consume approximately 3064788707 electricity. The original
and predicted value falls into the same range with a small difference.
127
Figure 5:61 Actual and Predicted values of electricity consumption using Proposed Hybrid Model for the Year 2013.
The graphical representation of actual electricity consumption by consumers for the
year 2013 is given in figure 5.61. Blue and red curves in the graph represents actual
and predicted consumption of electricity by using the hybrid proposed model. There
is very little difference in actual and predicted consumed electricity, so the actual
curve is overlapping the predicted electricity value. The graph represents the
consumed electricity in KWh and year along vertical and horizontal axis.
Table 5.12 Original and predicted electricity consumption using Proposed Hybrid Model for the year 2014
Base year 2014 Actual Electricity Consumption
Predicted Electricity Consumption
Jan-14 2406670480 2406632260
Feb-14 2543659240 2543624804
Mar-14 2262755935 2236279532
Apr-14 2229496325 2272945793
May-14 2663094360 2663776436
Jun-14 4135881561 4135897042
Jul-14 5048078068 5048008640
Aug-14 5150618207 5150087643
Sep-14 4184285964 4184295425
Oct-14 3525215760 3525243579
Nov-14 2914127320 2914325679
Dec-14 2691580750 2691535689
128
Table 5.13 depicts the actual as well as predicted consumed electricity for the year
2014. The average of actual consumed electricity is 3312976254. The average of
consumed predicted electricity value is 3314387710. There is insignificant variation
between the actual and predicted value of electricity.
Figure 5.62 represents the consumption of original as well as the predicted
electricity value. Along Y-axis and X-axis correspondingly represent the electricity
consumption and the year 2014 from January to December. The Blue and Red-
colored curves in the graph show the actual and predicted value of electricity.
Figure 5:62 Actual and Predicted values of electricity consumption using Proposed Hybrid Model for the Year 2014.
Table 5.13 Actual and predicted electricity consumption using Proposed Hybrid Model for the year 2015
Base year 2015
Actual Electricity Consumption
Predicted Electricity Consumption
Jan-15 2425671683 2425635790
Feb-15 2705001417 2700245689
Mar-15 2387522949 2308754670
Apr-15 2253062900 2253035678
May-15 2884345926 2884309875
Jun-15 3461754270 3461733256
Jul-15 4895975328 4859345678
Aug-15 5076894389 5007646789
Sep-15 4867004448 4867009865
Oct-15 3787014752 3770567899
129
Nov-15 2804034438 2804056789
Dec-15 2719630627 2719634567
In table 5.14 the actual and predicted values for consumption of electricity for the
2015 are shown. The average actual electricity consumption is 3355659427. The
obtained average predicted electricity consumption is 3338498054. Hence there is
no significant amount of difference among these actual and predicted values of
electricity consumption.
Figure 5:63 Electricity consumption Actual and Predicted using Proposed Hybrid Model for the Year 2015
The actual consumed electricity by the consumer for the year 2015 is provided in
figure 5.63. A blue-colored curve denotes the actual value of consumed electricity,
and the expected value is depicted through the red-colored curve. In the graph, the
actual value is overlapped with the expected values of consumed electricity because
of very little difference among these values.
130
Table 5.14 Actual and predicted electricity consumption using Proposed Hybrid Model for the year 2016
Base year 2016
Actual Electricity Consumption
Predicted Electricity Consumption
Jan-16 2567913778 2567945678
Feb-16 2740311321 2740310963
Mar-16 2942162298 2904213480
Apr-16 2522244918 2522123456
May-16 3253239971 3253234568
Jun-16 4500446696 4500412997
Jul-16 5018252044 5020932568
Aug-16 4999539492 4999500532
Sep-16 5404195697 5400412340
Oct-16 3958725442 3905872349
Nov-16 3130248433 3103020975
Dec-16 2921627225 2921606532
Table 5.15 represents the actual and predicted value of consumed electricity for the
year 2016.. The average value corresponding to actual electricity consumption is
3663242276 and for predicted consumption of electricity the average value is
3672383639.
Figure 5:64 Electricity consumption Actual and Predicted using Proposed Hybrid Model for the Year 2016
The graphical representation for the year 2016 is given in figure 5.64. The electricity
consumption (KWh) is plotted along Y-axis against the years 2016 corresponds to
131
X-axis. While blue color is representing the consumed electricity and the red color
curve corresponds to the expected consumed electricity value.
Table 5.15 Actual and predicted electricity consumption using Proposed Hybrid Model for the year 2017
Base year 2017
Actual Electricity Consumption
Predicted Electricity Consumption
Jan-17 2902848056 2902832345
Feb-17 2958390111 2905898637
Mar-17 3209855845 3218576445
Apr-17 2782373785 2723987754
May-17 3705371880 3705344790
Jun-17 4450434098 4404334578
Jul-17 5810138389 5801010875
Aug-17 5645879830 5645898752
Sep-17 5273395962 5273897987
Oct-17 4196118613 4196889768
Nov-17 3191950404 3109112390
Dec-17 3030487191 3004009043
Table 5.16 represents the actual and predicted consumed electricity that corresponds
to the year 2017.
Figure 5:65 Electricity consumption original and Predicted using Proposed Hybrid Model of the Year 2017
132
The obtained average value for actual electricity, as well as predicted electricity
consumption is 3929753864 and 3907684235. The consumption of electricity value
of actual and predicted value is represented graphically in figure 5.65. The blue
colored curve depicts the original consumed electricity value and a red-colored
curve represents the predicted consumed electricity value.
Figure 5:66 Overall comparison of electricity consumption prediction of ARIMA
+DWT, Hybrid proposed model with the original dataset
Figure 5.66 depicts the trend between the actual and predicted electricity
consumption which follows the same trend. The is no much difference depicted
between the original and predicted consumption. The graph clearly shows that both
graphs follow the same trend. However, prediction using the ARIMA and DWT
provides better results than the ARIMA only. The average computed value of the
ARIMA, ARIMA with DWT and proposed hybrid model is 3464988567,
3557198158, and 3455724556. Thus, the average difference between the original
and by using ARIMA with the DWT model is 3%, and that of the proposed model is
0.39%. Thus, our proposed hybrid model using ARIMA, CSA, DWT and ANN
provides better results as compared to both only ARIMA and ARIMA with DWT
approach.
At the end, to examine the performance of this research work,Mean Absolute
Percentage Error(MAPE), Mean Average Precision (MAP), and Accuracy (%) are
utilized as an evaluation parameter. Each one of them are explained below:
133
Mean Absolute Percentage Error (MAPE)
MAPE is a measure to compute the amount of dependent series that varies from its
level of the predicted model. This parameter is independent of units and can so it can
be used to compare series with distinct units. MAPE demonstrates the performance
in the percentage of the error, and it can be expressed mathematically as;
, denotes the actual sequence, Forecasted electricity values and P
represents the number of samples.
Mean Average Precision (MAP)
The parameter precision means more than two values of the measurements that are
close to each other. The precision value is different due to the prediction error.
Higher precision depicts the result measurement is constant, and low precision
depicts the varying measurement. But all time is not necessary; the higher precision
produces an enhanced result. The mathematical expression to compute precision is
provided below;
Where, TP = True positive, FP= False Positive
Mean average precision for any collection of electricity consumption datasets is
defined as the mean of the average precision scores for every corresponding data by
applying different techniques. The mathematical expression of MAP by using
average precision is provided below;
134
Where denotes the number of desired samples, is the number of retrieved
samples, corresponds to the average of precision at level .
Accuracy (%)
The ability of the system to measure accurate value means it defines the closeness
for the measured value to a true value. The computation of accuracy can be done by
using the small reading through which the error is reduced. The accuracy can be
defined mathematically as provided below;
5.2.4 Computed parameters
To analyze the prediction performance of various models including the proposed
hybrid model and to prove the effectiveness of the proposed model the results of
predicted electricity consumption has been presented in the table 5.17. The
parameters such as MAP (Mean Average Precision), MAPE (Mean Absolute
Percentage Error) and accuracy has been utilized to analyze the performance.
Table 5.16 Computed MAP for ARIMA, ARIMA with DWT and Proposed Hybrid Model
MODEL MAP
ARIMA 0.4623940
ARIMA with DWT 0.894494
Proposed Hybrid Model 0.94521
Table 5.17 depicts the various techniques used in proposed work along with the
examined MAP values. The graphical representation of the same is shown in Figure
5.67. There is an increase of accuracy by 5.67 % compared to the ARIMA with the
DWT model.
135
Figure 5:67 Computed MAP for ARIMA, ARIMA with DWT and Proposed Hybrid Model
From the graph, it is clearly seen that the maximum MAP of 0.94521 has been
attained using the hybrid approach.
Table 5.17 Computed MAPE for ARIMA, ARIMA with DWT and Proposed Hybrid Model
MODEL MAPE
ARIMA 44.239359
ARIMA with DWT 26.438503
Proposed Hybrid Model 8.944945
Table 5.18 depicts the MAPE corresponding to various techniques used in the
proposed work. The Proposed Hybrid Model shows the lowest Mean Average
Percentage Error when compared with other techniques.
Figure 5:68 Computed MAPE for ARIMA, ARIMA with DWT and Proposed Hybrid Model
136
The graphical representation of the MAPE is shown in figure 5.68. Y-axis is
depicting the obtained MAPE value corresponding to ARIMA, ARIMA with DWT,
and the Proposed Hybrid Model. As per the reduction in MAPE, the performance of
the system has been enhanced. The MAPE of the proposed hybrid model is lowest.
After applying ARIMA with the DWT technique, there is a decrease of 17.800856
as compared to utilizing only ARIMA. Whereas applying Proposed Hybrid Model,
there is a decrease of 17.493558 as a contrast to ARIMA with DWT.
Table 5.18 Computed Accuracy for Different Combinations
Used techniques Accuracy (%)
ARIMA 83.53
ARIMA with DaubechiesWavelet 92.67
ARIMA with HAAR Wavelet 93.76
Proposed Hybrid Model 98.86
Table 5.19 depicts the various techniques used in work. The ARIMA technique
shows the Accuracy of 83.53%, ARIMA with the DaubechiesWavelet shows the
accuracy of 92.67%, ARIMA with HAAR Wavelet the accuracy of 93.76 % and
Proposed Hybrid Model technique shows the Accuracy of 98.86%.
Figure 5:69 Computed Accuracy (%) for ARIMA, ARIMA with DWT, ARIMA with HAAR and Proposed Hybrid Model
137
After applying ARIMA and ARIMA with the DWT technique, there is an increase
of 4.6 % accuracy as shown in figure 5.69. Whereas applying Proposed Hybrid
Model there is an increment in accuracy by 1.15% as compared to ARIMA with
DWT.
Thus there is an increase in the accuracy of the proposed work of 18.35 %, 6.68 %,
and 5.44 % from the ARIMA, ARIMA with Daubechies, and ARIMA with Haar
techniques respectively.
138
CHAPTER 6: CONCLUSION AND FUTURE SCOPE
6.1 CONCLUSION
This research focuses on design and development of a novel intelligent technique
which can be used to study the future behaviour of electricity consumption on the
basis of Time Series Data. The analysis of future behaviour in relation to very
sudden changes in the time series data of consumed electricity is very complex and
major challenge for the electricity providers and investors as well. However, the
benefits associated with accurate forecasting have prompted researchers to develop
new and advanced models.
Predicting the next values of time series has been a major research problem that
attracts researchers from numerous fields. In this research, short-term forecasting is
studied in one step ahead and many steps ahead modeling and three forecasting
models are compared, namely, ARIMA, ARIMA with DWT and Proposed hybrid
model. Time series from different applications generally consists of both linear and
non linear variations. Linear ARIMA and ARIMA with DWT models cannot
accurately model this data separately. A hybrid model is proposed, which is an
integration of individual models such as ARIMA, DWT, CSA and ANN. By taking
the advantages of all these techniques a novel model is designed with high
prediction accuracy.
The first one or the basic model is ARIMA with DWT, which was proposed in this
research by using the statistical features of ARIMA model. The MA filter has been
utilized to decompose the available time series electricity data into two data sets that
consists of lower and upper level of data, which was later used to forecast the data
obtained using hybrid model. This hybrid model is able to predict electricity
consumption at the earliest. The designed model was applied to simulate Time
Series Data and forecast electricity consumption in Punjab State.
The proposed hybrid model using Discrete Wavelet Transformation (DWT), Cuckoo
Search (CS) algorithm and Artificial Neural network (ANN) was the final one,
139
which is used to estimate and forecast electricity demand/consumption using a
stochastic process. In the proposed electricity forecasting model, the wavelet
transform technique has been applied to reduce the white noise present in the
original dataset taken from PSPCL from 2013 to the 2017 year and hence obtained a
more stable dataset compared to the original dataset. DWT is applied as wavelet
transformation, which decomposes a signal into an essential orthogonal function of
different frequencies. The main feature of DWT is that it is totally lossless
transformation. We can regain our original signal while using reverse DWT. The
electricity data is non-stationary as its consumption varies continuously over time.
Therefore, DWT is the best way to express this type of data. This is done to forecast
highly accurate value by using a simple technique named as ARIMA model. The
work has been performed using two combinations of wavelets that are Daubechies
and HAAR wavelet. After analysis, it has been observed that prediction using the
HAAR wavelet provides better results compared to the Daubechies approach.
Therefore, HAAR has been selected as a wavelet decomposition approach, and then
ARIMA, CS with ANN has been applied to enhance the prediction performance of
the proposed work.
The comparison of predicted energy consumption values as well as the MAP,
MAPE, and Accuracy (%) of the proposed model have been compared with the
traditional approachs. The experimental values show that the predicted values using
the proposed model are highly correlated with the original dataset, which indicates
that the designed model is efficient and highly accurate to predict electricity
consumption. Thus, the increase in the accuracy by proposed model is 10.23 %
when compared with ARIMA, 6.19 % when compared with ARIMA and
Daubechies and 5.1 % with ARIMA and HAAR respectively.
140
6.2 FUTURE SCOPE
In future this work can be extended using other traditional classifiers such as
Support Vector Machine (SVM), Fuzzy Logic, Convolutional Neural Network and
other techniques. Also, for data optimization other techniques such as Genetic
Algorithm (GA), Particle Swarm Optimization (PSO), Firefly algorithms can be
used.
Here, MA filter is used as pre-processing scheme using ARIMA model. Other
existing pre-processing methods that were presented in literature can also be
experimentally validated for better prediction accuracy. An appropriate pre-
processing method can also be properly designed to increase forecast accuracy to
adapt to a well forecasting model.
The model can be applied for other statistical analysis which can be used to predict
various time series data i.e. live-stock product, agricultural yield, health expenditure,
currency exchange rate and many more.
141
RESEARCH PUBLICATIONS
1. Kaur, H. and Ahuja, S., 2017. Time series analysis and prediction of electricity consumption of health care institution using ARIMA model.. Advances in Intelligent Systems and Computing, vol 547.Springer, Singapore
2. Kaur, H. and Ahuja, S. (2019). A Hybrid Arima and Discrete Wavelet Transform Model for Predicting the Electricity Consumption of Punjab. International Journal of Innovative Technology and Exploring Engineering, 8(11), pp.1915-1919
3. Kaur, H. and Ahuja, S. (2019). SARIMA Modelling for Forecasting the Electricity Consumption of a Health Care Building. International Journal of Innovative Technology and Exploring Engineering, 8(12), pp.2795-2799.
142
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