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Game Theoretical Demand Response Management and Short-Term Load Forecasting by Knowledge Based Systems on the basis of Priority Index

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Demand Response Management (DRM) is considered one of the crucial aspects of the smart grid as it helps to lessen the production cost of electricity and utility bills. DRM becomes a fascinating research area when numerous utility companies are involved and their announced prices reflect consumer’s behavior. This paper discusses a Stackelberg game plan between consumers and utility companies for efficient energy management. For this purpose, analytical consequences (unique solution) for the Stackelberg equilibrium are derived. Besides this, this paper presents a distributed algorithm which converges for consumers and utilities. Moreover, different power consumption activities on the basis of time series are becoming a basic need for load prediction in smart grid. Load forecasting is taken as the significant concerns in the power systems and energy management with growing technology. The better precision of load forecasting minimizes the operational costs and enhances the scheduling of the power system. The literature has discussed different techniques for demand load forecasting like neural networks, fuzzy methods, Naïve Bayes, and regression based techniques. This paper presents a novel knowledge based system for short-term load forecasting. The algorithms of Affinity Propagation and Binary Firefly Algorithm are integrated in knowledge based system. Besides, the proposed system has minimum operational time as compared to other techniques used in the paper. Moreover, the precision of the proposed model is improved by a different priority index to select similar days. The similarity in climate and date proximity are considered all together in this index. Furthermore, the whole system is distributed in sub-systems (regions) to measure the consequences of temperature. Additionally, the predicted load of the entire system is evaluated by the combination of all predicted outcomes from all regions. The paper employs the proposed knowledge based system on real time data. The proposed scheme is compared with Deep Belief Network and Fuzzy Local Linear Model Tree in terms of accuracy and operational cost. In addition, the presented system outperforms other techniques used in the paper and also decreases the Mean Absolute Percentage Error (MAPE) on a yearly basis. Furthermore, the novel knowledge based system gives more efficient outcomes for demand load forecasting.
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electronics
Article
Game Theoretical Demand Response Management
and Short-Term Load Forecasting by Knowledge
Based Systems on the basis of Priority Index
Mahnoor Khan 1, Nadeem Javaid 1,*, Sajjad 1, Abdullah 2, Adnan Naseem 3, Salman Ahmed 4,
Muhammad Sajid Riaz 5, Mariam Akbar 1and Manzoor Ilahi 1
1Department of Computer Science, COMSATS University Islamabad, Islamabad 44000, Pakistan;
mahnoor.khan2794@gmail.com (M.K.); ciit.sajjad@gmail.com (S.); mariam.akbar@gmail.com (M.A.);
tamimy@comsats.edu.pk (M.I.)
2Department of Electrical Engineering, COMSATS University Islamabad, Islamabad 44000, Pakistan;
abdullahbjr@gmail.com
3Department of Computer Science and Information Technology, Alhamd Islamic University,
Islamabad 44000, Pakistan; adnan.naseem@alhamd.pk
4Department of Computer Science, Islamic International University, Islamabad 44000, Pakistan;
salmanresearchlab@gmail.com
5Department of Computer Science, Air University, Islamabad 44000, Pakistan; riaz.sajid@gmail.com
*Correspondence: nadeemjavaidqau@gmail.com
Received: 15 November 2018; Accepted: 7 December 2018; Published: 12 December 2018
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Abstract:
Demand Response Management (DRM) is considered one of the crucial aspects of the
smart grid as it helps to lessen the production cost of electricity and utility bills. DRM becomes a
fascinating research area when numerous utility companies are involved and their announced prices
reflect consumer’s behavior. This paper discusses a Stackelberg game plan between consumers and
utility companies for efficient energy management. For this purpose, analytical consequences (unique
solution) for the Stackelberg equilibrium are derived. Besides this, this paper presents a distributed
algorithm which converges for consumers and utilities. Moreover, different power consumption
activities on the basis of time series are becoming a basic need for load prediction in smart grid. Load
forecasting is taken as the significant concerns in the power systems and energy management with
growing technology. The better precision of load forecasting minimizes the operational costs and
enhances the scheduling of the power system. The literature has discussed different techniques for
demand load forecasting like neural networks, fuzzy methods, Naïve Bayes, and regression based
techniques. This paper presents a novel knowledge based system for short-term load forecasting.
The algorithms of Affinity Propagation and Binary Firefly Algorithm are integrated in knowledge
based system. Besides, the proposed system has minimum operational time as compared to other
techniques used in the paper. Moreover, the precision of the proposed model is improved by a
different priority index to select similar days. The similarity in climate and date proximity are
considered all together in this index. Furthermore, the whole system is distributed in sub-systems
(regions) to measure the consequences of temperature. Additionally, the predicted load of the entire
system is evaluated by the combination of all predicted outcomes from all regions. The paper employs
the proposed knowledge based system on real time data. The proposed scheme is compared with
Deep Belief Network and Fuzzy Local Linear Model Tree in terms of accuracy and operational cost.
In addition, the presented system outperforms other techniques used in the paper and also decreases
the Mean Absolute Percentage Error (MAPE) on a yearly basis. Furthermore, the novel knowledge
based system gives more efficient outcomes for demand load forecasting.
Electronics 2018,7, 431; doi:10.3390/electronics7120431 www.mdpi.com/journal/electronics
Electronics 2018,7, 431 2 of 34
Keywords:
behavioral analytics; Stackelberg game; demand response; knowledge based systems;
priority index; similar day; date proximity.
1. Introduction
In the modern day world, smart meters offer two way communication between the users and
the utilities. This communication leads towards a prevalent computing environment, which develops
large-scale data with high velocity and veracity [
1
]. The resultant data also give rise to a time series
concept. This phenomenon generally includes power consumption measurements of appliances over a
specific time interval [
2
]. The techniques of big data are proficient enough to utilize resultant huge
volumes data of sequential time series. Moreover, these techniques also assist in data-driven decision
making. Besides, this big data can update utilities to learn power consumption patterns of consumers,
predicting demand and averting blackouts.
The utilities are keen on finding the optimal ways for cost reduction. Moreover, electricity
companies desire to increase their yields by acquainting their consumers with effective programs
like Demand Side Management (DSM) and demand response. Currently, marginal success has
been observed in achievement of goals for these programs. However, viable results still need to
be achieved [
3
]. Furthermore, implementation of DSM and demand response is a challenging task
for utilities. It is difficult to comprehend and conclude the behavior of every individual consumer.
Moreover, it is also challenging to customize strategies that include profit contrary to distress from
varying behavior of consumers on the basis of energy-saving policies introduced by utilities. Besides,
the association between consumer behavior and the constraints that affect power utilization patterns
are non-static, i.e., the activities of consumers keep on changing from time to time [4].
Usually, the behavior of consumers is reliant on weather and seasons, which has a capricious
effect on power utilization decisions. Thus, active participation of consumers in customized power
management is crucial for energy saving schemes. The companies should give timely response on
power consumption and associated costs [
5
]. Consequently, it is challenging to design such models
that are proficient enough to evaluate energy time series from smart meters. Also, it is stimulating to
train the model that predicts power consumption.
The aforementioned discussion helps to study the influence of consumers’ behavior on power
consumption and to forecast the energy utilization patterns. This analysis can assist the utilities to
develop power saving strategies. Moreover, the utilities can design programs to stabilize the demand
and supply of energy ahead of time. For instance, short term forecast is related to daily and weekly
power usage. This type of prediction is best suitable when there is a need to enhance scheduling and
distribution. Alternatively, medium term forecasting is related to weekly and monthly forecasting.
Besides, long term forecasting is about yearly predictions of energy consumption. Medium and long
term predictions are capable of maintaining the equilibrium between the production of smart grid and
strategic scheduling [
6
]. However, such a task is very challenging as it is significant to mine complex
interdependencies between appliance usages where numerous data streams are taking place.
Generally, DRM can be characterized in two extents, which are the utilities and consumers. There
has been substantial quantity of work done in power systems to maintain the balance between supply
and demand [
7
]. However, these studies have laid emphasis on the financial aspects on the planning
and production levels. Moreover, these studies are unable to take both consumer and utility as a
substantial constituent. Contrariwise, the literature on consumer and utility has presented models to
increase user comfort, devoid of taking the cost of power or the profits of the utilities [
8
]. This paper
takes motivation from this phenomenon. Moreover, this paper observes the increased profits for
consumers and utilities.
This paper analyzes the collaborations between several utilities and consumers. Both entities
share mutual objectives, i.e., maximization of their payoffs. The utilities can increase their profits by
Electronics 2018,7, 431 3 of 34
setting a suitable price per unit. Nonetheless, the users select a specified amount of power to purchase
from any utility on the basis of announced prices. Furthermore, the purchasing behavior of consumer
is dependent on the prices settled by the company. Likewise, the behavior of utilities is reliant for the
prices settled by other utilities. Thus, for solving these challenging collaborations between consumers
and utilities, this paper employs a game theoretical framework. This paper presents a Stackelberg
game plan between consumers and utilities. In this game, the utilities play a non-cooperative game
and the users look for their best optimum response.
The systematic and proficient utilization of electrical power is a hot debate topic in today’s
world [
9
]. The optimal power management and maintaining balance between demand and supply are
considered as challenging tasks for modern power systems [
10
]. Moreover, the prediction of uncertain
production of renewable energy resources [
11
] and short-term load forecasting [
12
] are measured as
significant components of the power grid for optimal power scheduling. Besides, short-term load
forecasting has wide applications in the energy market like load scheduling, unit commitment and
power production [
13
]. It has been observed in the literature that error maximization in short-term
load forecasting can result in substantial growth in the utility operating expenses. Thus, enhancing the
accuracy of predicted results is a challenging task and vital issue in power management.
The proximity of choosing a similar day to the target day is very crucial for selecting the similar
day along with temperature, according to previous studies. In this regard, this paper proposes a
different priority indexing technique for selection of similar days by analyzing the date proximity and
temperature similarity. Moreover, the date proximity used in this paper is the total number and nature
of days between selected and similar days. In contrast, the historic power load data is categorized
according to nature of days in demand prediction. Furthermore, this paper also presents four different
day types and two data-sets are presented for utilization of historical power load data. In addition,
the proposed knowledge based short-term load forecasting method employs monthly and weekly data
for two different data-sets. The best optimum results for short-term load forecasting will be achieved
by grouping of prediction results obtained from these two data-sets.
The consideration of exceptional temperature for any region is ineffectual because of variations
in temperatures in a vast topographical zone. A vast topographical zone is separated into three
climate types in [
14
]. Moreover, the temperature of three cities is labeled as cold, moderate, and
warm. The biased integration of these temperatures is presented as the temperature of the huge region.
The temperature is taken in [
15
] and the whole system is distributed in different regions. Besides,
the short-term load has been forecasted by some regression techniques. However, the precedence of
choosing similar days is also unnoticed in previous studies.
This paper divides the entire system in nine regions. Moreover, the climatic conditions of only
one city is chosen from every region. The knowledge based short-term load forecasting is employed to
every region after the consideration of temperature. In addition, the predicted power load of the entire
system is the aggregate of predicted load of particular regions. The impact of temperature is believed
to be much more efficient and result improving when the system is divided.
The proposed system model is employed in Pakistan’s National Power Network (PNPN), which
is taken as a sample system in this paper. In the proposed system model, Affinity Propagation
(AP) [
16
], and Binary Firefly Algorithm (BFFA) are used as hybrid model. The proposed system
model shows a significant decrease in MAPE in comparison with other traditional knowledge based
methods. This paper uses algorithms of Deep Belief Network (DBN) and Fuzzy Local Linear Model
Tree (F-LOLIMOT) for comparison purposes. The experimental results specifies that the proposed
model requires minimum time for computation when associated with DBN and F-LOLIMOT.
The major research contributions of this paper include the proposition of the priority index for
selection of similar days by means of temperature of specified regions and date proximity. Moreover,
the historic power load is separated in two different data-sets in the paper. Subsequently, the data-sets
predict the short-term load and then the final outcome is supposed to be more precise. The final
Electronics 2018,7, 431 4 of 34
outcomes are achieved by the summation of predicted results from two data-sets. Furthermore, the
paper makes the impact of temperature effective by dividing the system in different regions.
The remaining paper is organized in following manner: Section II presents the previous work
done, Section III provides a brief discussion of a Stackelberg game and demonstrates the distinctiveness
and existence of the Stackelberg Equilibrium. Moreover, Section IV discusses the categorization of
knowledge based short-term load forecasting and Section V employs the proposed method on different
topographical regions. Moreover, results and their discussion are presented in Section VI and Section
VII concludes the paper.
2. Related Work
The challenges addressed in Section I are also discussed in the literature through methodologies of
big-data. A brief discussion of behavioral power consumption data to acquire better energy competence
are presented in [
6
]. Likewise, the influence of developmental fluctuations for energy savings was
observed by [
17
]. The study also discussed the contribution of consumers to collaborate with the
utilities and better energy savings were highlighted.
The literature has proposed many novel methods for short-term load forecasting like fuzzy [
18
],
exponential smoothing [
19
], regression based [
20
], neural networks [
21
], and others. Moreover, every
proposed model has incorporated some techniques. For example, regression based processes are
usually comprised of Autoregressive Integrated Moving Average (ARIMA) [
22
], Auto-Regressive
Moving Average (ARMA) [
23
], Support Vector Regression (SVR) [
24
], and Auto-Regressive Moving
Average with Exogenous variable (ARMAX) [
25
]. Nevertheless, it is essential for aforementioned
techniques to learn the process by bulks of preceding data for tuning of various parameters.
Furthermore, the complexities of these techniques, minimum time of computation and memory
essentials of knowledge based model, can initiate a different perspective to knowledge based short-term
load forecasting.
In literature, there are some works cited in knowledge based systems that employ a similar day
method [
26
28
]. Although, there is a lot of room for enhancement in this scenario which can be studied.
The authors in [
29
] proposed a knowledge based system for short-term load demand forecasting.
However, the paper overlooked the consequences of temperature. The change in temperature can
cause fluctuations in the load demand. Consequently, the effect of temperature must be included in
the short-term load forecasting. The different eight day categories are enumerated in [30].
Moreover, average stabilized loads of historic data for every day has been evaluated by means
of least and maximum load per hour. Furthermore, the least and maximum load for 11 days was
forecasted by means of regression techniques. The Mean Absolute Percentage Error (MAPE) of Irish
electrical power system attained was 2.52%. Moreover, the temperature was also incorporated in this
study and was associated with 3.86% by the statistical technique in [31].
The authors in [
32
] calculated the weighted mean load of every hour for three preceding and
similar days for short-term load forecasting. Moreover, the impact of temperature on prediction of
short-term load is also considered by means of exponential association between power demand and
temperature. Likewise, the mean prediction error for a daily peak load of France was attained 2.74%
in [
32
]. Besides, the consequences of temperature, wind pressure and humidity, was scrutinized in [
33
].
The MAPE calculated in this study was 1.43%. The study in [
23
] was almost equivalent to the proposed
model presented in [
22
]. Moreover, the MAPE achieved in this study was between 1.23% to 3.35% in
seven different states of America [34].
The mean prediction error for daily peak load in [
24
] was achieved 4.65% for weekdays and
7.08% for weekends of three different states of Turkey [
35
]. This mean prediction error was achieved
after smoothing the temperature discrepancies throughout the day. The precedence of similar days is
overlooked in previous studies. It is obvious that there are numerous days which are advantageous for
the knowledge based forecasting of load. Nevertheless, the best suitable preference of these same days
has a substantial effect on forecasting results.
Electronics 2018,7, 431 5 of 34
The consequences of temperature are neglected in [
36
] in terms of priority index. Moreover, in [
37
]
a priority index for medium term load prediction was presented. The proposed model was based on
the similarity of temperature for the selected day. The mean error achieved in [
37
] for Western States
of America was 3.25% for summer season. Besides, few values of error were attained that were more
than 6%. Though, the temperature was the only parameter, which was assessed in this study and the
proximity of chosen day to similar day was ignored. It is a well-known fact that same days do not
have alike temperature. Moreover, the similar days must be near to the target days in order to avert
the selection of similar days with similar temperature and different power load.
The work presented in [
38
] used the Bayesian network to forecast activities of different residents
by a particular appliance. However, the model was not efficient enough to be functional towards real
world circumstances. The authors in [
39
] and [
40
] discussed a multi-label and time sequence based
classifier model for a decision tree taking appliance association as a correlation. The basic purpose
of their model was to predict the power consumption of the appliance. Though, the authors merely
observed the past 24 h frame for future forecasting.
The work in [
41
] presented the association rule mining method to classify the interdependence
between power consumption and appliance usage to help power saving, anomaly detection,
and demand response. Nevertheless, this work lacked the proper rule mining process and
appliance-appliance association.
At present, Artificial Neural Network (ANN) and SVM are considered to work efficiently for
non-linear time series sequences. Karatasou et al. [
42
] demonstrated the practical implementation
of ANN in forecasting power expenditure of a building accompanied by statistical study. In [
43
,
44
],
a model is presented which hybrids the Support Vector Regression (SVR) and Immune Algorithm (IA)
to estimate local yearly report and power load in Taiwan.
Zhao et al. [
45
] presented a framework, which employed SVM to predict residential power
utilization in the humid area. Moreover, the study took meteorological conditions of that particular
area. Besides, Xuemei et al. [
46
] suggested Least Square Support Vector Machine (LS-SVM) for
chilling load prediction [
47
] for a residential zone in Singapore. The forecasting was done by hourly
weather information.
Wang et al. [
48
] discussed that the SVM based models have proven to be efficient as compared to
ANN and ARIMA configurations. They employed Differential Evolution (DE) and SVM to predict
the configurations for yearly energy consumption. Conversely, the development of SVM model
is influenced by the category and constraints of the kernel function. Generally, it is discussed in
literature that the tuning constraints of SVM is a challenging task [
49
]. In addition, a number of models
are presented in literature to tune the parameters of SVM by techniques of machine learning and
artificial intelligence.
Ogliari et al. [
50
] proposed a hybrid model using Neural Network and Genetical Swarm
Optimization for energy prediction. The authors in [
51
] combined SVM with algorithms of Simulated
Snnealing to predict yearly load. On the subject of optimization techniques, Jaya Algorithm has
achieved attention in the last few years as a metaheuristic computing technique. The authors in [
52
]
and [
53
] observed that Jaya Algorithm outperforms other optimization techniques. Moreover, Jaya
Algorithm has also been employed for various real work applications.
There is a variety of literature available on the topic of game theory and DRM. In [
54
], the authors
have discussed power utilization and forecasting as a non-cooperative game plan. This basic aim
was to maximize the cost functions. Likewise, the authors in [
55
] have proposed a distributed set-up.
In this set-up, the cost function is demonstrated by its dependence on inclusive load. The consumers
adjusted their behavior for power consumption on the basis of cost function introduced by the utility.
The authors in [
56
] presented a theoretical framework for mutual optimization of investment and
functioning of a smart grid. Moreover, the aspects of power storing, renewable energy integration, and
demand response were taken into consideration. The paper signified the sharing of portfolio decisions,
Electronics 2018,7, 431 6 of 34
day-ahead pricing, and scheduling. They also presented the benefits of integrated renewable energy
and demand response in terms of minimizing the sharing cost.
A robust optimization has been discussed in [
57
] in order to increase the utility of the end-user
by hourly prediction. The study presented in [
58
] laid emphasis on the knowledge and interest of
users to be aware of the announced electricity prices. The study proposed a technique to cope with
preferences of the consumers to increase power competence and consumer satisfaction. Moreover,
a dynamic cost price has been introduced to motivate users for attaining a cumulative load [
59
]. Also,
this load was handled by different utilities and DRM was scrutinized for bi-directional communication
between consumers in the micro-grid. The authors in [
60
] and [
61
] discussed the dynamic pricing in
detail for smart energy model of a smart grid. The discussed model was dependent on renewable
energy sources, which were further integrated with intelligent control that processed information from
a smart metering devices.
The studies discussed above are inadequate to meet the needs, i.e., the electricity firms considered
utility companies as a single firm. This study differs in this context as this incorporates numerous
utilities and consumers. Moreover, the basic aim of both entities is to increase their profits
(remunerations) by game theoretic approach. Besides, there is a broad literature and findings available
on the Stackelberg game on the topics of profits maximization, congestion control, and interactive
communication [62,63].
3. Game Theoretical Problem Formulation
This study takes nconsumers and
UC
utility companies in consideration. Besides, the energy
sources of the utilities include non-renewable and renewable resources. In literature, it is observed
that power generators, which are centered on the energy of fossils utilize a definite amount of energy.
Moreover, the energy of fossils is also supposed to be harmful for the environment. Contrarily,
renewable energy sources are considered environmentally friendly. However, renewable resources
have inherent natural stochastic behavior, which makes it difficult to predict and control. The studies
show that uncertainties are common with renewable resources. Furthermore, Markov chain (discrete
time) has been extensively employed in literature for the generation of power from renewable
resources [64].
This study takes residential type consumers into account. In addition, all users have dissimilar
requirements for power consumption. The study also distinguishes the users based on their financial
plans; i.e., purchasing power of electrical energy. Likewise, this study proposes a utility function for
every consumer. The function shows an increment using the total expanse of power that any consumer
is able to utilize. Moreover, this paper integrates cost parameters for every consumer.
The
UC
and nhave established a two way communication using the advanced metering
infrastructure for pricing swapping and information sharing. Conversely,
UC
can also communicate
with one another. The ncollect the value (cost) facts from the
UC
. In return, the
UC
then provide their
services to n.
Power initiation, dissemination, and expenditure can be divided in three ways [
65
]: Power
generators,
UC
, and n. This paper emphasizes the communication between nand
UC
. Moreover,
this paper assumes that
UC
show a fluctuating behavior at the business level. Inspired from the game
theory models, the
UC
can play a vital part in an economical marketplace. No participant is capable
enough to affect the market price of electricity through his particular activities. Thus, the market price
is such constraint over which
UC
have no control. Moreover, the
UC
need to increase their production
up to the point where the minimal cost is equivalent to the cost of the market. This phenomenon occurs
once the total contributors increase and no contributor is authorized to govern an enormous power
generation quantity. Nonetheless, this study proposes a predetermined figure of
UC
(contributors).
This scenario depicts that every utility will announce its own price according to its generation capacity.
Table 1shows the list of symbols used.
Electronics 2018,7, 431 7 of 34
Table 1. List of Symbols Used.
Symbol Meaning
UC Utility Companies
nAll consumers
n0Consumer
uc0Utility Company
dn0Demand of consumer
γn0Constant for user analysis
τn0Constant for user demand
ln Function for decision making
κuc0Price per unit
Bn0Total budget of consumer
Λn0,1,Λn0,2 ,Λn0,3 Lagrange multipliers
υcons Best condition of first order
Euc0Available power of uc0
ξuc0+1Price of U C other than uc0
MInvertible matrix
|M| Determinant of M
=prod Strategy sets for M
=cons Strategy sets for n0
dGame plan for all n
dκ+Best feedback of all n
d+
n0Proposed best scheme for n
rIteration Number
δuc0Speed modification constraint of uc0
IiInput Vector in SVM
OiTargeted Output in SVM
ETotal data in SVM
WWeight in SVM
tThreshold estimate in SVM
3.1. Analysis of User and Utility Company
The cost for every consumer shows fluctuation when there are various utility firms having diverse
electricity costs. Moreover, the setting of cost is highly reliant on the rates of other
UC
. In this regard,
game theory offers an ordinary pattern to represent the activities of nand
UC
. Consequently, the
UC
settle the cost for each unit of energy and then publicize this to consumers. The users then respond
back to the cost by demanding an optimal amount of power from the
UC
. In this case,
UC
play first.
The consumers then decide on the basis of announced prices. Moreover, both events are in sequence.
The events are that the utilities play primarily and at that time the consumers decide their verdict
based on the cost. Hence, this paper models the communication between the
UC
and nby a Stackelberg
game [
66
]. The proposed game model takes the
UC
as influential (leaders) and users as followers.
Moreover, the proposed model also considers the events as a multiple leaders and followers game.
3.1.1. Analysis of User Side
Assume that
dn0,uc0
is the request of consumer
n0
from a utility
uc0
. Hence, the value of a consumer
n0,Ccons,n0can be expressed as:
Ccons,n0=γn0
uc0∈U C
ln(dn,uc0+τdn0).uc0∈ UC (1)
Here
γn0
and
τn0
are constants. Also, the ln function is extensively employed in literature for user
making decisions [
67
]. The valuable function used for consumer
n0
in Equation (1) is interrelated to
the function γn0ln dn0,uc0.
Electronics 2018,7, 431 8 of 34
The consumer will recompense -
when the valuable function
γn0ln dn0,uc0
is used regarding
uc0
, such that,
dn0,uc0
= 0. When
dn0,uc0
and
τn0
are equivalent to 0, then benefit of
n0
regarding
uc0
begin to be finite. Generally, the representative cost of τn0= 1.
Suppose
κuc0
is the per unit cost given by any utility company
uc0
and
Bn0
0 is the total
expenditure of any consumer
n0
. Each
uc0
has given a distinct price rates of electrical energy
[κ0,κ1,......, κc] when n0n.
Subsequently, the
n0
computes the best demand response through
resolving best optimum solution (OS cons) given in Equation (2).
dn0=max(dn0,uc0)Ccons,n0uc0∈ U C, (2)
where uc0∈UC κcdn0,uc0Bn0,
dn0,uc00uc0∈ UC (3)
OS cons
is a convex optimization problem. Therefore, the obtained solution is distinctive
and optimal.
This paper considers the scrutiny accompanied by
UC
consumers and three
UC
s. Thus, they seek
for best optimum solution in this scenario for a specified uc0can be expressed as follows:
dn0=max(dn01,dn02)γn0
3
uc0=1
ln(dn+τdn0,uc0), (4)
where κcdn0,1+κcdn0,2Bn0and dn0,1+dn0,20.
The paper employs Lagrange multipliers (
Λn0,1
,
Λn0,2
,
Λn0,3
) for the respective
UC
and setting of
parameters as discussed above. Thus, the Equation (4) can be rewritten as:
υcons,n0=γn0
3
uc0=1
ln(dn1 +τdn0,uc0)Λn0,1(
3
uc0=1
κcdn,uc0B1) + Λn0,2dn0,1+Λn0,3 dn0,2. (5)
The values of the Lagrange multipliers are used as strategies for finding the local maximal and
minimal of the function subjected to inequality constraint. Thus, it improves the performance of
Equation (5).
Λn0,1(
3
uc0=1
κcdn,uc0Bn0) = 0. (6)
Moreover, setting
Λn0,2dn0,1
and
Λn0,3dn0,1
generates Equation (6) to 0. Whereas,
Λn0,1 >
0,
Λn0,2,Λn0,3 ,dn0,1, and dn0,20.
The first order optimality condition for linear, best optimum solution and maximization problem
is by setting
υcons =
0. Here,
υcons = (υcons n0n
). All of the nare interconnected by
κc
. Also,
υcons =0 shows that,
(υcons,n0)(dn,uc0)1=0n0n,uc0∈ UC. (7)
Also,
γn0(τn0+dn0,1)(Λn0,1τ1+Λn0,2)(8)
and
γn0(τn0+dn0,2)(Λn0,2τ1+Λn0,3). (9)
Next, this paper has considered four of the cases, which the n0can avail.
Electronics 2018,7, 431 9 of 34
Case 1
If
dn0,1
and
dn0,2
are greater than 0, then
Λn0,2 =Λn0,3 =
0. So, Equations (8) and (9) are
generalized as:
dn,uc0=γn0(τn0κuc0Λn0,1), (10)
where n0nand uc0=1, 2, ..., n. Now, using Equation (6) in Equation (10),
3(γn0Λn0,1)1=Bn0+τn0
3
uc0=1
κuc0. (11)
Thus, Equation (11) becomes Equation (12) after simplification.
3dn,uc0κuc0= (Bn0+τn0
3
uc0=1
κuc0)τn0(12)
Here value of uc0varies; i.e., 1, 2, or 3.
Case 2
If
dn0,1>
0 and
dn0,2
are equivalent to 0, then
τn0= (Bn0+τn03
uc0=1κuc0)/
3
κuc0
. As discussed
above that
Λn0,2dn0,1
corresponds to 0. This paper derives Equation (13) by considering the cost of the
first utility.
dn0,1=γn0τn0Λn0,1κ1. (13)
This paper further expands Equation (6) to include extra parameter and ease simplification. Thus,
Equation (14) is derived.
Λn0,1(γn0κ1Λn0,1 τn0Bn0) = 0. (14)
As Λn0,1 >0 and γn0κ1Λn0,1τn0Bn0=0, which refers to the point that Λn0,1 =γn0/(κ1τn0+
Bn0). Now, evaluating this in Equation (13),
dn0,1=κ1τn0+Bn0τn0κ1. (15)
Equation (15) is now equivalent to Bn0/κ1. Moreover, Equation (15) can also be presented as:
dn0,1=τn0(κ1+κ2) + Bn03κ1τn0, (16)
where dn0,1= ((τn0(κ1+κ2) + Bn0)/3κ1) + ((τn0(κ1+κ2)Bn0)/3κ1).
Case 3
If dn0,1is equivalent to 0 and dn0,2>0, then the identical scrutiny can be valuated as specified in
Case 2. This paper considered the cost of the second utility; thus, the demand of users with respect to
the second utility is given in Equation (17).
dn0,2=τn0(κ1+κ2) + Bn03κ2τn0. (17)
Subsequently, Equation (17) is now equivalent to Bn0/κ2.
Case 4
If
dn0,1
and
dn0,2
both are equivalent to 0, then
Λn0,1
,
Λn0,2
, and
Λn0,3
are real and positive values.
It is noted that Case 4 is assumed as best case which rarely occurs only when
κuc0=
or else
Bn0
0.
This paper has satisfied the power and cost parameters as equalities in Case 1, 2, and 3. However,
this scenario cannot be mapped on Case 4. This study further assumes that there are nconsumers
Electronics 2018,7, 431 10 of 34
in total and
UC
utilities that satisfies the equality conditions in previous cases for a given set of
κuc0
.
So, Equations (12), (16), and (17) can be combined in the above discussed scenario as:
dn0,uc0=τn0
uc0∈U C
κuc0+Bn0κuc0U C τn0. (18)
In Equation (18), dn0,uc00, n0nand uc0∈ UC. As dn0,uc00. So,
τn0(
uc0∈U C
κ$) + Bn0>τn0κuc0(UC − 1). (19)
3.1.2. Analysis of Utility Companies
This study assumes that
Euc0
(
UC ∈ uc0
) depicts the available electrical energy of
UC
. The aim
of every
UC
is to vend the energy to gain maximum profit. For instance, if there is only one
UC
then this firm will settle the price range according to its ease as there is no competition involved.
However, this study takes two basic strategies that decide the cost range of any
UC
. Firstly, it can be
the economical conditions of average consumers and secondly, it could be an aspect of competitiveness
among
UCs
. Furthermore, the
UCs
also take part in choosing the best optimum cost (game) with
another. Additionally, this study expresses the maximum profit Eprod,uc0of any U C as:
Eprod,uc0(κuc0,ξuc0+1) = κuc0
n0n
dn0,uc0. (20)
Here,
ξuc0+1
is cost of
UC
apart from
uc0
. Thus, the best optimum solution for any
UC
can be
related in terms of OP pro d and can be expressed as:
ξ=max(κuc0)Eprod,uc0(ˇuc0,¸uc0+1),uc0∈ U C (21)
where
nn0dn0,uc0≤ Euc0
and
κuc0>
0,
∀U C uc0
. The maximum profit of any
UC
is fluctuating in
relation to energy for a constant
κuc0
. According to Equation (20), this phenomenon leads to parameters
of equality. Every
UC
proffers to vend all its energy to consumers. This paper assumes
υprod,uc0
to
resolve OP prod by:
υprod,uc0=κc
n0n
dn0,uc0ζuc0(
n0n
dn0,uc0Euc0)(22)
The best optimal solution for the U C furthers presents υprod,uc0/κuc0, which is equivalent to 0.
κ2
uc0ρ(U C − 1)ζuc0(ρ
$∈U C,$6=uc0
+Bn0) = 0. (23)
where
ρ=n0nτn0
and B
=nn0Bn0
. Moreover, the conditions used in Equations (21) and (22)
express
UC
equations. Now, solving these three
UC
, this study sets
κ+= [κ+
1
,
κ+
2
, .....,
κ+
U C ]
and
ζ+= [ζ+
1
,
ζ+
2
, .....,
ζ+
U C ]
. Furthermore,
D=d+
n0,uc0
can be evaluated by means of
κ+
. Consequently,
employing Equation (18) for uc0,
κuc0=ρ(κ$$∈U C,$6=uc0) + B
ρ(UC − 1) + Euc0UC . (24)
Now, using the current value of κuc0this study observes that,
ζuc0=ρ(U C − 1)( ρ(κ$$∈U C,$6=uc0) + B
UC(ρ+Euc0). (25)
It can also be deduced from Equation (23) that
ζuc0=ρκuc0(UC −
1
)
. Also,
ρ
and B
0. It refers
to the phenomenon that there is no essential need to play any game when
UC =
1. Therefore, the study
Electronics 2018,7, 431 11 of 34
merely focuses on the circumstances when
UC ≥
3. To handle the discussed scenario, Equation (23)
can now be computed as:
Mκ=S. (26)
Here M=
E1+J−H · · · −H
−H E2+J· · · −H
· · · · · · · · · · · ·
−H −H −H EU C +J
,
κ= [κ1
,
κ2
, .....,
κU C ]
,J
=ρ(UC −
1
)UC1
,
H=ρUC1
, and
S=
B
UC1
. From the above equations,
it can be concluded that Mis an invertible matrix. However, it could be expressed as:
κ=M1S. (27)
This paper considers some cases to achieve closed-form solution of κ.
Case 1
All the
UC
have equivalent amount of energy available and capacity to produce, then
E1=E2=
E3=· · · =EUC . Utilizing Equation (26),
κuc0=S
E+J+H(1− UC)=κ. (28)
Likewise,
κ=B(UCE)1(29)
Also,
E1
κ
. Then the Equation (27) is used in Equation (19), so that the total demand to any
UC
from n0is given as:
Bn0κτn0(UC − 1)κτn0(UC − 1)(30)
Here, Equation (30) indicates that
Bn0
0. This phenomenon indicates that now all
UC
s produce
equivalent amount of power. Moreover, they have settled some pricing scheme that users have
to follow.
Case 2
Contrary to Case 1, this case considers that capacity of power generation is different for all
UC
s. The
M
in Equation (26) has some unique aspects, which relates that a real valued matrix
M= [mi,j,i,j=1, 2, · · · ,U C]∈ RU C is only considered diagonal as shown in Equation (31),
|mi,j| −
j6=i
|mi,j| ≥ 0, (31)
where, i
=
1, 2,
· · ·
,
UC
. According to [
68
], a taut diagonal matrix is always non-singular and
|M|
is
positive. It is observed that
M
is taut and diagonal matrix as
Euc0+
J
− H(U C −
1
) = Euc0+ (ρ(U C −
1)) (ρ(U C − 1)). Consequently, Euc0>0. Thus, Mis invertible.
Theorem 1. The distinctive solution achieved from Mis positive.
Proof of Theorem 1. The solution of Mis deduced by
κuc0=BU CUC−| |M|1
$∈U C,$6=uc0
(E$+ρ). (32)
Since
|M|
is invertible; thus,
|M|
is positive if its eigenvalues are non zeros and show a symmetry
property. Also, the solution presented in Equation (32) depicts that κuc0>0.
Electronics 2018,7, 431 12 of 34
Theorem 2. The cost function discussed in Equation (27) is a best optimum solution for raising profits.
Proof of Theorem 2.
Let the solution gained from Equation (27) be
κuc0
for any
uc0
. Moreover,
this paper assumes that
uc0
has increased the cost from
κuc0
to
κ
uc0
, while
UC
have same cost of
power generation. From Equation 19, suppose that any consumer ndemands power
dn0,uc0>
0 from
any κuc0then the constraint in Equation (33) is satisfied.
κuc0(Bn0+τn0(
uc0∈U C
κ$)τn0(UC 1)1). (33)
Now suppose that
κuc0
and
κ
uc0
fulfil the requirements of Equation (33). In this regard,
the necessities of consumers will show deviating behavior from dn0,uc0to d
n0,uc0as:
d
n0,uc0=(τn0(uc0∈UC κ$+κ
uc0) + Bn0)
κ
uc0U C τn0. (34)
The differentiation among the necessities of any nfrom the firm uc0will now be expressed as:
dn0,uc0d
n0,uc0=κ
uc0κuc0
κ
uc0κuc0
(τn0(uc0∈UC κ$) + Bn0)
UC . (35)
From Equation (35), it is obvious that
dn0,uc0d
n0,uc0>
0. Hence, the consumers are not capable
of demanding the total power generated by any
uc0
, i.e., the consumer will then demand for lesser
energy as required. Moreover, the profit and cost of
uc0
will increase on the basis of consumer total
power demand. Thus, Equation (36) provides the balanced equation of demand and supply.
E
prod,uc0Eprod,uc0=κ
uc0
n0n
d
n0,uc0κuc0
n0n
dn0,uc0(36)
It is observed that in Equation (36),
E
prod,uc0(κ
uc0
,
ξuc0+1)<Eprod,uc0(κuc0
,
ξuc0+1)
. Thus, the
profit gaining of
uc0
leads towards the loss and it is concluded that the price function presented in
Equation (27) is the best optimum function as it will result in financial advantage.
On the subject of range of
κuc0
,
κuc0[κuc0mi n
,
κuc0ma x ]
. As a matter of fact,
κuc0min
is owing to the
cost functions that is generated by
UC
. Moreover, any
uc0
is not capable to lessen the price lower than
κuc0min
. Nonetheless,
κuc0ma x
is the maximum range. According to
κuc0ma x
, the government has to settle
the cost, which consumers have to follow.
3.2. Proposed Stackelberg Game Modeling
All the
UC
s partake to play the non-cooperative game with one another in order to settle the price
that will be further used by consumers. This is a critical point where Nash Equilibrium is required.
In a Stackelberg game, the equilibrium strategy for the followers is defined as any strategy that is
compromised of the best response. The response is optimal as compared to the strategy that is adopted
or announced by the leaders [69].
This study assumes that
=prod,uc0
is the game-plan rectified for any
uc0
and
=cons,n0
is the scheme
planned for
n0
. Subsequently, the game-plan for
UC
will be
=prod ==proda× =prodb× · · · × =prod,U C
and
for
n0
will be
=cons ==consa× =consb× · · · × =cons,UC
. Thus,
κ+
uc0∈ =prod,uc0
is proposed Stackelberg
equilibrium for any uc0if,
Eprod,uc0(κ+,d(κ+)) Eprod,uc0(κuc0,ξ+
uc0+1,d(κuc0,ξ+
uc0+1)). (37)
Electronics 2018,7, 431 13 of 34
Here,
κ+= [κ+
uc0]
,d
= [d1
,
d2
,
· · ·
,
dn]
is the game plan of all consumers n. Moreover, dand
κ+
are
best feedback of all consumers, i.e., d
∈ =cons
. The best feedback of any consumer
n0
for any particular
(κ1,κ2,· · · ,κuc0)(=prod,1 × =pro,2 × · ·· × =prod,U C )is:
κdn0=χcons,n0∈ =cons,n0Econs,n0(κ,χcons,n0)Econs,n0(κ,dn0). (38)
Here,
χcons,n0=d+
n0(κ+)dn0
. Thus,
d+
n0
is supposed to be best optimum scheme for
n0
. Besides,
d+and κ+is a Stackelberg equilibrium achieved for the game concerning the UC and n.
3.3. Distinctiveness of Stackelberg Equilibrium
The
OS cons
has an exclusive maximum range (as discussed above) for
κ
. Whenever the cost
planning game is played between the companies with a distinctive Nash Equilibrium, then the
Stackelberg game plan holds a special equilibrium.
Theorem 3.
An exclusive Nash equilibrium occurs in the cost selection game plan between
UC
. Likewise,
a distinctive Stackelberg equilibrium subsists as well.
Proof of Theorem 3.
There is equilibrium if
κ
is a real value and
⊂ RU C
. Moreover,
κE
prod,uc0
is
constant in
κ
. On the topic of cost choosing of all
UC
in Stackelberg game,
=prod = (=prod,1 × =prod,2 ×
· · · × =prod,U C )
. Here,
κuc0⊂ =prod,U C
. Moreover,
=prod = [κuc0,min
,
κuc0,max]
. Therefore, the game plan
is real value and ⊂ RU C .
Furthermore,
Eprod,uc0
is constant in
κuc0
as discussed in Equation (20). Subsequently, the
f00(Eprod,uc0)according to κuc0is,
2Eprod,uc0
κ2
uc0
=0. (39)
3.4. Distributed Algorithm
The users are now proficient enough to compute their optimum demands on the basis of the cost
function provided by the utility companies as discussed in the preceding section. However, the different
utilities show the significant response to policies announced by other companies. Moreover, it is
essential to calculate the price per unit. For this purpose,
uc0
should know the production capacity of
other utilities. Contrary to this, this paper proposes a distributed algorithm that further proves the
Stackelberg equilibrium of the game. The equilibrium is established in such a way that utilities are not
able to identify the constraints of each other.
The
uc0
establishes a subjective cost and then conduct their cost statistics to the users.
This communication is done efficiently by setting an interactive environment for utilities and
consumers. As a consequence, the consumers choose specific amount of electricity they need to
purchase from uc0.
All the
UC
acquire these demanding conditions from consumers. At that moment,
uc0
will analyze
the contrast among the available electrical energy and the entire energy needed by consumers from the
company. The U C will upgrade its price per unit with the help of Equation (40).
κuc0,r+1=dn0,uc0,r
n0n
Euc0+δuc0κuc0,r. (40)
In Equation (40), ris the repetition number and
δuc0
is the rate modification constraint of
uc0
.
Whenever a
uc0
updates its cost function, it sends this information to
n0
. Furthermore, the
n0
update
the demands and send this information back to
uc0
. Subsequently, the
UC
s will also update their
cost functions sequentially. Thus, the procedure lasts until the cost function shows convergence.
Algorithm 1supposes that n0=1 specifies the first consumer.
Electronics 2018,7, 431 14 of 34
Theorem 4. Given that n0n, uc0∈ UC,r=1, 2, 3, · · · and
δuc0κuc0,r(Euc0U Cτn0)τn0$∈UC$6=uc0κ$,rBn0
UCκ2
uc0,r
(41)
Algorithm 1meets the best optimum solution for all
UC
and nas the particular game plans are upgraded in a
specified order.
Proof of Theorem 4.
The feedback of a consumer as specified in Equation (18) is best optimum solution
for a particular κuc0.
Whenever, the cost per unit shows a converging behavior then the demand of every consumer
will coincides towards an established set. Therefore, it is necessary to discuss the converging behavior
of cost in order to demonstrate the changing performance of Algorithm 1.
Algorithm 1will only show the diverging behavior whenever the
κuc0,r
will be negative in
Equation (41).
Algorithm 1: Distributed Algorithm
1Randomly select κuc0,1 for r=1uc0∈ U C
2Consumer uc0=1, 2, 3, · · · ,n
3Calculate Equations (2)–(4) for κrby Equation (18)
4Send dn0,uc0,rto respective uc0
5Any uc0, which has not upgraded its value for r+1
6Evaluate κuc0,r+1by way of Equation (40)
7if κuc0,r+1κuc0,1 =0then
8return Price value is not changed by uc0
9Jump to 8
10 else
11 Transmit the updated cost to n
12 Jump to 3
13 end
14 if κuc0,r+1κuc0then
15 Terminate
16 else
17 Jump to 2
18 end
In Equation (40), if
dn0,uc0,rn0nEuc0
0 then the significant constraint for
κuc0,r+1
for
not gaining a negative amount is
|dn0,uc0,rnn0Euc0|(δuc0)1
. Furthermore, the condition that is
discussed above can be revised as δuc0(Euc0(dn0,uc0,rn0n)(κuc0,r)1).
Equation (40) suggests that the cost
κuc0
amplifies only if
dn0,uc0,rn0nEuc0
gives positive
results and vice versa. However, in Equation (40), when
dn0,uc0,rn0nEuc0=
0 the price value is not
changed. This particular condition is the established stage to which Algorithm 1shows converging
behavior. This stage is the Nash Equilibrium of the game plan (Stackelberg game between nand
UC
).
Afterwards, the UC will not show any fluctuating behavior.
4. Knowledge Based Short-Term Load Forecasting
Knowledge based systems and computational intelligence are considered as major tools of artificial
intelligence. The knowledge based systems employs categorical representations of knowledge like
symbols and words [
70
]. The knowledge based systems are efficient and simple as the categorical
Electronics 2018,7, 431 15 of 34
representation makes the knowledge readable and implicit for a human as compared to numerical
derived models in computational intelligence. The techniques of knowledge based systems incorporate
case based, model based, and rule based systems.
The major difference between a traditional program and knowledge based system is in their
structure [
71
]. The knowledge of the domain is closely associated with software for monitoring the
performance of that particular knowledge in a traditional program. However, the roles are clearly
divided in knowledge based systems. Moreover, there are two basic components of knowledge based
systems, which are knowledge base and inference engine. Nonetheless, some interface proficiencies
are also compulsory for a real-world system, as presented in Figure 1.
Knowledge Base Inference Engine
Interface
DataHumans and Experts Hardware and Software
Figure 1. Principle components of knowledge based system.
The paper categorizes knowledge based short-term load forecasting as classic and proposed.
The explanation of each is given below.
4.1. Classic Knowledge Based Short Term Load Forecasting
All categories of days are quantified initially in a classic knowledge based forecasting on the
basis of annual and weekly load curves. Moreover, this type of categorization of days is usually
associated with the user consumption behavior of a particular state. Besides, the annual growth rate in
load demand also plays a significant role in typical knowledge based forecasting as historical load
data are also required. The annual growth in load demand is mostly reliant on different aspects like
growing economy or population. Consequently, normalization and stabilization of load data are
considered crucial in order to lessen the consequences of annual growth rate. Likewise, normalization
of data is also beneficial to determine similarities in load curves more precisely [
72
]. The hourly data
normalization of load demand is attained by distribution of load on hourly basis [
73
], which is shown
in Equation (42).
Γ0
Sd,H=ΓSd,H
¯
X(ΓSd,H−1,ΓSd,H−2,· · · ,ΓSd,H−n). (42)
In Equation (42),
Γ0
Sd,H
is the load demand,
ΓSd,H
is the normalized value of data at any hour
H
of a similar day
Sd
, and
¯
X
is the mean of npreceding days. In addition,
H=
1, 2, 3,
· · ·
, 24. The load
Electronics 2018,7, 431 16 of 34
demand at any hour
H
of a target day can be obtained by normalization of load demand data of chosen
similar days and average load of npreceding hours, which is presented as:
Γtar,H=1
Dγ
ׯ
X(Γtar,H1,Γtar,H−2,· · · ,Γt ar,H−n). (43)
In Equation (42), tar indicates the target variable, which is predicted by the model for a specified
day. Moreover,
Γtar,H
is the predicted demand load for any hour
H
,
γ
is set of identical days, and
Dγ
is
total number of days chosen, which are similar. The minimum value of
Dγ
reduces the utilized historic
data and inadequate similar days, which are selected. Contrarily, the maximum value of
Dγ
indicate
that
γ
is comprised of vast historic data. Besides, a few number of days may have not sustainable
correlation with selected day according to this scenario.
4.2. Proposed Knowledge Based Short-Term Load Forecasting
The paper proposes a novel hybrid data mining technique in order to predict the load demand
by knowledge based systems. The proposed algorithm basically consists of two parts. The clustering
technique AP is used initially. The AP is employed in this scenario as it looks for noise in data and
then removes this noise from data, thus, decreases the instances of data. Subsequently, BFFA is used in
the next step for feature selection and classification. Furthermore, Support Vector Regression (SVR) is
used as classifier model in this proposed hybrid model. This proposed hybrid model chooses the most
relevant target variables and increases the accuracy of the system. Moreover, the proposed knowledge
based system is able to minimize the operational cost and maximizes the process of data mining for
selection of similar days.
The proposed knowledge based short-term load forecasting is categorized in three parts, which
are explained as follows.
4.2.1. Distribution of Historic Load Data
The selection of similar days from historic days is considered as crucial for knowledge based
forecasting. Moreover, the selection of similar months and days also have a significant impact on the
results of short-term load forecasting. Therefore, this paper presents two historic data-sets, which are
well-defined for every type of days. The first data-set is comprised of similar days from preceding
month along with the selected date. Furthermore, the second data-set incorporates same days from
seven days earlier and subsequent to the target day of the week. The target year and similar days are
also chosen from all preceding years in both data-sets. Besides, the data-sets are specified by scrutiny
of annual load demand and meteorological conditions of Pakistan.
It is a well-known fact that temperature and load demand have a direct relationship with each
other. For example, usage of air conditioners and other cooling devices increases in summers especially.
This phenomenon shows variations in load curve and peak hour of the entire system. Moreover,
the impact of climatic conditions on the load demand in summers is usually more than other time of
year [74].
Figure 2illustrates the load curves for Thursday as an example. Moreover, this load curve is for
Pakistan and depicts all four seasons. It is obvious from Figure 2that the load level and hourly peaks
by day and nights shows a significant fluctuation in different spells. Therefore, it can be determined
that by maximization of the measured time, the range of both data-sets may affect the selection of
similar days with similar temperature. However, this phenomenon is not suitable for load curves
because changes in climate also affect load consumption behavior.
In the first data-set, the same days are chosen from days that have equivalent month along with
the target day. Moreover, this paper has assumed that the selected day can also be similar to its month
or preceding month. Contrary to this, load curves from seven days earlier and subsequent to the
target day is more comparable to the target day when associated to load bends of the preceding month.
Consequently, the other data-set specifies the consideration of these days in a data-set. Moreover,
Electronics 2018,7, 431 17 of 34
this paper assumes that this data-set must have a maximum weightage factor, in contrast to the first
data-set. The priority index for both data-sets can be evaluated by Equation (43). The paper valuates
the final results from the combination of results achieved from both data-sets as:
Γtar,H=W1×Γds1
tar,H+W2×Γds2
tar,H. (44)
In Equation (44),
Γds1
tar,H
and
Γds2
tar,H
are forecasted power load demand specified for each hour
H
and targeted day tar. Moreover,
W1
and
W2
are weights assigned to each data-set. Thus,
Γtar,H
is the
final forecasting achieved by system for each hour Hand targeted day tar.
The proposed methodology for knowledge based forecasting is comprised of two main
constituents, which are
W1
and
Dγ
. Furthermore, the proposed method must also execute for training
data-set in order to choose the best optimum values of
W1
and
Dγ
. Subsequently, the proposed method
should be proficient enough to select the execution, which gives the least prediction error. Besides,
the values of
W1
and
Dγ
are then selected as the optimal ones in order to predict the target day.
Moreover, this paper also assumes that the next 24 h are forecasted by preceding load demand data
and predicted loads of the day. This load demand data is achieved after prediction of the first hour of
tar day by preceding load demand data.
2.0
2.5
3.0
3.5
4.0
0 5 10 15 20 25
Hour (h)
System Load (MW)
Winter Autumn Spring Summer
Figure 2.
Variations in load behavior of sample Thursday during 2015 of Pakistan’s National Power
Network (PNPN).
4.2.2. Priority Index for Same Day
In knowledge based short-term load forecasting, temperature has a significant role. The fluctuating
behavior of climate and weather throughout a week or month shows a significant effect on load curves.
Therefore, it is a vital part in choosing similar days for target year. Conversely, there can be different
motives that are the cause of divergence for load curves. For instance, the power evaluating strategies
and variations in utilization behaviors of Pakistan alter the levels of load demand. Thus, the selection
of similar days along with date proximity is effective to choose for knowledge based forecasting.
The paper determines a priority index of similar days as:
PISd
reg.= [temp,reg.×
C∈κr eg.
(tem pSd
Ctem ptar
C)2+1,reg.×(ηre g.)2]1
2. (45)
In Equation (45),
PISd
reg.
is the priority index of
Sd
in specific region,
tem pSd
C
and
tem ptar
C
are
the average temperatures of a specified city
C
on the daily basis for a similar day
Sd
and tar days,
correspondingly. Furthermore,
ηreg.
is total number of days between tar days and
Sd
days,
κreg.
are the
chosen cities from every region. This paper separates the system in seven different regions and from
every region only one city is selected.
Electronics 2018,7, 431 18 of 34
In this paper,
tem p,reg.
is considered as weighting factor of temperature, while
W1,reg.
is taken as
weighting factor of ηreg.. They are calculated as follows:
tem p,reg.=Dγ
Sdγreg.
×(tem pSd
Ctem ptar
C)2
Dcity
×
C∈κr eg.
(46)
and
W1,reg.=Dγ
Sdγreg.
×1
η2
reg
. (47)
In Equation (46),
Dcity
is total number of chosen cities from regions. Furthermore,
γreg.
are similar
days in a specified region in Equation (47).
This paper assumes that if variance of temperatures among tar and
Sd
is more than a determined
value
tem pds
, then this day is overlooked in
Sd
. Moreover, two days having huge differences in
temperature can depict different curve shapes of load demand. Likewise, this difference can cause
critical impact on knowledge based short-term load forecasting. In addition, this paper also employs
the priority index to the historical data and thus, specifies similar days. Equations (44) and (45) have
significant worth in this paper. The impact of temperature can be measured in an efficient way from
these equations by dividing the PNPN. The next section specifies this phenomenon.
4.2.3. Distribution of PNPN
The selection of exclusive temperature for huge topographical states usually affects the results
in short-term load forecasting. Therefore, an exclusive temperature could not be given to a huge
topographical state or zone in order to attain satisfactory forecasted outcomes. However, it is practical
to give an exclusive temperature to every region when the entire region is distributed. The distribution
of vast topographical zones has been observed in [
75
,
76
]. Nevertheless, these studies overlooked
priority index for similar day selection.
The paper distributes the region separately and then predicts the short-term load by consideration
of the proposed priority index for
Sd
selection. Furthermore, the forecasting of short-term load for
the entire system can be achieved by summation of predicted results from all regions. Besides, this
technique takes the temperature for
Sd
selection knowledge based load forecasting in an efficient way.
4.2.4. Proposed Strategy
The similar days are computed by Equation (45) for every respective region. Subsequently,
Γds1
tar,H
and
Γds2
tar,H
are computed. Moreover,
Γtar,H
is attained as ultimate forecasting for every region by
selected similar days, according to Equation (44). The results obtained from all regions are combined
to achieve final forecasted load for the entire system.
5. Application of Proposed Method on Vast Topographical Zone
This paper employs the knowledge based short-term load forecasting model on a vast
topographical region. Moreover, this paper has selected regions of Pakistan for implementation
of the proposed model. Pakistan has four seasons and different climates with significant discrepancies
throughout the year. PNPN is a huge topographical system, which is distributed in nine regions that
are equivalent to regional electric utilities. The primary objective of PNPN in this study is to forecast
the demand load for every region. In addition, Figure 3presents the different colored portions along
with the mean of regions having high temperature throughout the year.
A city is selected from every region that is supposed to be the representative of the region.
Moreover, a city also specifies the temperature of that particular region. There is no restriction on any
system to distribute into specified number of regions. However, the system can be divided according
Electronics 2018,7, 431 19 of 34
to the requirement of the system and fluctuating behavior of weather. Figure 4depicts the changing
behavior of temperature for Lahore city as a sample.
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
2004
2005
1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31 1 10 20 31
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Day
Hour Commencing
−10 0 10 20 30
Hourly Temperature (° C)
Figure 3. Heatmap and yearly weather conditions of sample region.
Date
0
5
10
15
2007−01 2007−07 2008−01 2008−07 2009−01 2009−07 2010−01
Wind speed (mph)
40
60
80
100 Humidity (%)
0
5
10
Rainfall (mm/day, averaged over a week)
960
980
1000
1020
1040 Air pressure (mb)
0
5
10
15
20
25 Outside temperature (°C)
Raw Data Smoothed Curve Median Value
Figure 4. Variations of temperature for average mid-day weather of Lahore.
Electronics 2018,7, 431 20 of 34
The investigation of PNPN demands more scrutiny of Pakistan’s user consumption behavioral
analytics. Monday is the first working day of the week while Sunday is the last one. Moreover,
the seven days of the week are categorized into four types in Pakistan. The first category of the day is
Monday, which is the first working day in Pakistan. Monday has different power demand provisions,
especially in early morning (peak-hours). Furthermore, the days from Tuesday to Friday that are also
considered week-days in Pakistan, show the same load curve. The difference between Monday and
other days of the week is illustrated in Figure 5.
5000
6000
7000
8000
0 5 10 15 20 25
Hour (h)
P (MW)
Monday Tuesday
Figure 5.
Fluctuating Behavior of Load Curve in Pakistan and Difference of Monday and a
Sample Week-day.
Subsequently, another category of day is Friday and Saturday. In this category of days, the
operational hours of most workplaces and factories show a fluctuating behavior in contradiction to
other week-days. Moreover, Sunday is supposed to be the rest day in Pakistan and is the last category
of day. The load curve and load demand depict an entire variating behavior from other categories of
day. Figure 6shows the fluctuating behavior of load curve for a successive week.
−20 0 20 40 60
Hour (h)
P (MW)
Mon Tues Wed Thurs Fri Sat Sun
Figure 6. Fluctuating behavior of load curve in Pakistan of a particular week.
Electronics 2018,7, 431 21 of 34
The paper scrutinizes hourly load for nine regions of PNPN. In this regard, the data form the
duration of June 2015 to May 2017 is used as historic data for short-term load forecasting. Besides,
the paper predicts the load demand for the duration of June 2017 to May 2018. A city is chosen from
every region as a representative of that particular region. It is observed in the literature that there is no
concept of splitting the data-set into training and test data in knowledge based systems. Moreover,
the knowledge based systems use the entire historic data for choosing the best optimum results and
similar days as discussed in Section II. However, the data-sets are divided into training and test data
in DBN and F-LOLIMOT. This paper labels 77% of the data as training data and the remaining 23% of
the data as test data.
This paper performs sensitivity analysis on the PNPN and concludes that the optimal values
achieved for
Dγ
,
W1
, and
W2
are 8, 0.4, and 0.6, respectively. The sensitivity analysis is performed
by means of historic data for the duration of June 2015 to May 2018 in order to get the best optimum
parameter values. Moreover, the data for the duration of June 2017 to May 2018 is not utilized to get
the best optimum parameter values. The load demand for the specified time period of previous data
like from the duration of June 2016 to May 2017 is supposed to be the vital goal of prediction by the
load information and earlier than that period. This helps in selecting the best optimum parameter
values. The best optimal value is achieved when it has least prediction error for the specified period as
discussed above. The value of W1is changing from 0 to 1. Therefore, it is now obvious that the value
of W2will be calculated by W2=1W1.
In addition, the best optimum values of
W1
and
W2
are evaluated by the scrutiny of the historic
data. Besides, data for the duration of June 2017 to May 2018 is not used in this analysis as this data is
for prediction purposes. Likewise, the value of
Dγ
is also attained from this method. This constraint
shows a fluctuating behavior to achieve the least predicting error for a particular time spell. Table 2
presents the prediction error for every execution. In this table, the values of
W1
and
W2
show a variance
between 0 and 1. Nonetheless, the value of
Dγ
lies between 5 and 15. The best optimum values for
Dγ
,
W1and W2are 8, 0.4, and 0.6, respectively.
Table 2. Mean Absolute Percentage Error (MAPE) for every pair of Dγand W1for training data.
DγW1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
51.430 1.722 1.322 1.517 1.113 1.321 1.612 1.421 1.117 1.220 1.312
61.128 1.787 1.316 1.501 1.119 1.313 1.611 1.417 1.113 1.216 1.307
71.418 1.712 1.312 1.509 1.102 1.325 1.609 1.415 1.111 1.215 1.305
81.418 1.711 1.321 1.507 1.100 1.303 1.615 1.420 1.119 1.217 1.311
91.418 1.713 1.217 1.599 1.102 1.307 1.617 1.425 1.123 1.206 1.315
10 1.419 1.715 1.311 1.503 1.105 1.311 1.621 1.430 1.125 1.213 1.321
11 1.431 1.715 1.311 1.505 1.106 1.312 1.622 1.433 1.130 1.219 1.320
12 1.491 1.710 1.331 1.501 1.107 1.315 1.625 1.432 1.132 1.220 1.320
13 1.431 1.713 1.360 1.599 1.108 1.324 1.629 1.435 1.131 1.223 1.319
14 1.472 1.721 1.366 1.502 1.109 1.327 1.630 1.440 1.131 1.227 1.326
15 1.414 1.789 1.363 1.503 1.111 1.328 1.631 1.441 1.134 1.228 1.329
This paper further assumes that the proposed methodology employs the similar day load demand
data in the preceding years for the distinct days like public and religious holidays. This is done because
there is an inadequacy in the historic data. Therefore, the technique of priority index is not applicable
for distinct days. Consequently, it is one of the major reasons to observe the effect of temperature in
the priority index for normal days instead of distinct days.
The paper only lays emphasis on the short-term forecasting for normal days. Moreover, the
distinct days are overlooked from record for selection of similar day. Besides, the paper explains the
knowledge based short-term forecasting for Tuesday, 28 June 2016.
Electronics 2018,7, 431 22 of 34
1.
At first, the days having a similar category of day are chosen on the basis of categorization of
target day. In this scenario, Tuesday is included in the second category of day classification as
discussed above. Moreover, all the days between Tuesday to Friday are selected. However, all the
distinct days is overlooked for analytical purposes. Subsequently, these days are distributed in
two data-sets, as discussed in Section II.
2.
The priority index of every region is evaluated by Equation (45), for all chosen days. Table 3
presents the priority index of selected days for a sample region Islamabad as an example of
30 June 2015. Moreover, in this scenario the value of
tem p,reg.
is 0.03 and
1,reg.
is 1.5
×
10
5
.
All the values and Table 3are associated with the second data-set of Islamabad for the specified
date. Every region and every data-set are different from one another.
Table 3. Selection of similar days on the basis of priority index values for 28 June 2016.
Date Day Difference of Temperature Proximity of Date Index Value
4 June 2015 Thursday 1 371 0.1393
7 June 2015 Sunday 0 366 0.1282
10 June 2015 Wednesday 2 337 0.2859
11 June 2015 Thursday 1 332 0.2747
15 June 2015 Monday 2 266 0.1549
16 June 2015 Tuesday 5 265 0.3295
17 June 2015 Wednesday 3 264 0.3791
19 June 2015 Friday 4 263 0.3795
24 June 2016 Friday 1 4 0.0212
25 June 2016 Saturday 3 7 0.5701
26 June 2016 Sunday 2 6 0.1210
27 June 2016 Monday 0 5 0.0021
3.
The priority index and short-term load forecasting of every region is evaluated by Equations (42)
and (43) as discussed in Section II. In this scenario,
Dγ
and final best suitable chosen similar days
are 25 June 2016, 26 June 2016, 27 June 2016, 4 June 2015, and 7 June 2015 in Islamabad. Moreover,
Table 3depicts that few same days show less difference in temperature rather than choosing same
days. However, they are overlooked in this paper as along with the difference in temperature,
the proximity of date has also significant worth. For instance, 10 June 2015 and 11 June 2015
will have less difference in temperature as compared to 15 June 2015. However, such days are
neglected because they have maximum values of date proximity. Therefore, this paper can choose
a similar day that has maximum difference in temperature in the proposed methodology because
of proximities in date. Moreover, this phenomenon can produce more similar load curve shapes.
Besides, the same chosen days in Islamabad and other regions can cause a discrepancy in selecting
the same days from Islamabad for prediction of 28 June 2016.
4.
The predicted demand load of the entire system is combined load that is obtained from all regions
after short-term load forecasting is done for every respective region.
5.1. Deep Belief Network
In [
77
], the basis of DBN is presented briefly. Moreover, the auto-correlation of load demand
data has been depicted in Figures 710 for the previous data. It is obvious from the auto-correlation
plots that the preceding data is more auto-correlated to experimental data, to some extent. This paper
performs Ljung Box [
78
] analysis of null supposition to check this assumption more quantitively.
The suppositions are as follows:
S0
: The preceding data are disseminated autonomously, i.e., the correlation is 0 in the preceding
data from where the sample is chosen. Therefore, any experimental correlations in the preceding
data are the resultant from the unpredictability of the test group.
S1
: The preceding data are not disseminated autonomously, i.e., the data show serial correlation.
Electronics 2018,7, 431 23 of 34
The auto-correlations tests are performed whose outcomes are shown in Table 4.
0 10 20 30 40
0.00 0.01 0.02 0.03 0.04 0.05
Original data: (0,1)
Figure 7.
Auto-correlation of preceding demand load data for day lags in deep belief network (DBN)
for original data (0, 1).
0 10 20 30 40
0.00 0.01 0.02 0.03 0.04 0.05
Resampled data: (0,1)
Figure 8.
Auto-correlation of preceding demand load data for day lags in DBN for original data (0, 1).
0 10 20 30 40
0.00 0.01 0.02 0.03 0.04 0.05
Original data: (1,2)
Figure 9.
Auto-correlation of preceding demand load data for day lags in DBN for original data (1, 2).
Electronics 2018,7, 431 24 of 34
0 10 20 30 40
0.00 0.01 0.02 0.03 0.04 0.05
Resampled data: (1,2)
Figure 10.
Auto-correlation of preceding demand load data for day lags in DBN for resampled
data (1,2).
Table 4. ρValues of the Ljung Box auto-correlation test with different region values.
Original Data Experimental Data Region Size
(0, 1) 1.00 ×1070.5510981 8175
(0, 2) 6.75×1040.6528330 14,798
(1, 1) 0.00×1000.4384530 16,856
(1, 2) 0.00×1000.7561250 15,087
The outcomes show that the preceding data is much more auto-correlated as compared to the
experimental data. It is often observed in literature that numerous testing process reject the
S0
for the
preceding data. However,
S0
is not rejected by experimental data. Therefore, there subsists a spatial
correlation in preceding data. Moreover, if sampling techniques are applied on the historic data then
this correlation can be disintegrated. The paper also performs sensitivity analysis and the structure of
DBN used for this paper includes one hidden layer with five neurons. Moreover, there are 25 neurons
are in input layer and 20 neurons in the output layer in the proposed architecture. These neurons
generate the prediction of load demand for the target day (24 h). On the topic of architecture of this
network, the input layer is comprised of two constraints for mean and maximum temperature for
selected day. Moreover, one constraint is for categorization of the forecasted day while the remaining
22 input constraints are associated with the preceding load demand data, which are as follows:
$τ=Γτ
mΓτ
n
Γτ
n
. (48)
In Equation (48),
$τ
represents the total load demand data,
Γτ
m
and
Γτ
n
are demand load for
τth
hour (
τ=
1, 2, 3,
· · ·
, 24) preceding to selected day. This paper assumes that
Γτ
m
and
Γτ
n
represents the
τ
and
τ
-1 hours in Equation (48). Moreover, there are 20 neurons in the output (
OS τ
) layer of DBN
that signifies the difference of load demand on the hourly basis for preceding and selected days,
OS τ=Γτ
tar Γτ
n
Γτ
n
. (49)
The categorization of days in DBN are entirely divergent from knowledge based system.
According to Equations (48) and (49), Tuesday must be taken apart from days that range from
Wednesday to Friday. Therefore, in DBN five categories of days are taken for analysis.
Electronics 2018,7, 431 25 of 34
5.2. Fuzzy Local Linear Model Tree Algorithm
The paper employs F-LOLIMOT algorithm for training of the linear fuzzy model. The explanatory
analysis of F-LOLIMOT algorithm has been discussed in detail in [
79
]. Moreover, the F-LOLIMOT
algorithm is capable of predicting the hourly demand load, which is ahead than the current time
by means of climatic and load data. Figure 11 depicts that there are different inputs and outputs of
demand load and climatic data. This is done after sensitivity analysis on the system.
Furthermore, the lags of climate are the climatic condition of the preceding week and target
day. Likewise, the time lags of each hour load demand (inputs) are actually demand load data of
similar hour at preceding 9 and 10 days earlier than selected hour. It is obvious that the initial hour of
target day by utilizing preceding and recognized load data the upcoming hourly load is forecasted by
preceding data.
−1.0
−0.5
0.0
0.5
1.0
0 10 20 30
Day Lag
Autocorrelation
Figure 11.
Auto-correlation of preceding demand load data for day lags in Fuzzy Local Linear Model
Tree (F-LOLIMOT).
6. Results and Discussion
At first, this section presents the evaluational measures that are used in this paper. Subsequently,
the results are discussed.
6.1. Evaluational Measures
In literature, Daily Maximum Error (DME), Maximum Distance Minimum Error (MDME),
and MAPE have been widely used in order to valuate the outcomes, which are achieved from
short-term forecasting. This paper has used MAPE, MDME and DME as:
MAPE =D1
f
H=1
Df
Γtar,HΓν,H
Γν,H
(50)
and
DME =max(Γtar,HΓν,H
Γν,H
). (51)
In Equations (50) and (51),
Df
are the hours that are forecasted and
Γν,H
is the real demand load at
specified hour
H
of tar day. This paper presents 4 implications to indicate the benefits of the proposed
system. The implications are based on the forecasting of load demand for the duration of June 2015 to
June 2016. Moreover, these implications are made by climatic and load data, which lies in the range of
June 2015 to exactly one day before the target day. The paper takes this data as training data in this
scenario. The implications are:
Electronics 2018,7, 431 26 of 34
1. MAPE of short-term load forecasting throughout the year (Df= 9750)
2.
Average of DME throughout the year, which is referred as maximum distance and minimum error
3. Total number of days, which have MAPE higher than 3% (=3)
4. Total number of days, which have maximum error higher than 5% (=5)
The last two implications depict the division of errors, which are achieved from the results of
short-term load forecasting. In this paper, the proposed model minimizes the total number of exceeding
days from a certain limit and also enhances the performance of MAPE and DME.
6.2. Discussion of Results
The paper has evaluated the results on the basis of two assumed evaluations that are discussed
as follows.
6.2.1. Evaluation of Priority Index and Splitting Consequences on Knowledge Based Systems
This paper implements the proposed method on PNPN. In this regard, the following cases are
observed to discuss the consequences, which are associated with distribution of the forecasting results
and taking temperature in priority index.
1.
Case 1: Short-term load forecasting of PNPN without taking temperature and distribution of data
2.
Case 2: Short-term load forecasting of PNPN including consequences of data distribution without
taking the temperature
3.
Case 3: Short-term load forecasting of PNPN including including temperature without taking the
consequences of data distribution
4. Case 4: Short-term load forecasting of PNPN with temperature and distribution of data
The data distribution is overlooked in Case 1. Therefore, a distinctive temperature is not suitable
for the system. Moreover, the priority index is the center of attention in this case along with the date
proximity. Besides, the whole system is distributed in different sections in Case 2. Subsequently,
the prediction is performed for every respective section. The prediction of the entire system is a
combination of predicting outcomes in all sections. Case 2 differs from Case 1 as the data distribution
is carried out in this scenario. Nonetheless, the data distribution is also overlooked in Case 3. However,
the temperature is taken in consideration in terms of subjective average values in relation to the
demand from every region. The consequences of temperature are studied in Case 4. The paper
assumes Case 4 as a comprehensive case as it takes temperature in the priority index for selection of
similar days from every section.
Tables 5and 6presents the outcomes of the aforementioned cases for every category of the day.
It can be observed that MAPE of the entire system is minimum in Case 4 as compared to other cases.
The data distribution is done in Case 2 and Case 1 has overlooked this phenomenon. Thus, it is
proved that distributing the entire system can enhance the prediction outcomes. Moreover, the data
distribution also minimizes the MAPE and maximum distance and minimum error. Besides, the data
distribution among different regions minimizes the total number of days that go beyond acceptable
measures (=3and =5).
Table 5.
Consequences of priority index and data distribution on the forecasting results for
=5
and
=3
.
=5=3
Nature of Days Case 1 Case 2 Case 3 Case 4 Case 1 Case 2 Case 3 Case 4
Weekdays 10 8 7 65 4 6 8
Weekend 3 4 4 31 1 2 1
Yearly Mean 25 26 20 19 20 13 11 12
Electronics 2018,7, 431 27 of 34
Table 6.
Consequences of priority index and data distribution on the forecasting results for Maximum
Distance Minimum Error (MDME) and MAPE.
MDME MAPE
Nature of Days Case 1 Case 2 Case 3 Case 4 Case 1 Case 2 Case 3 Case 4
Weekdays 3.70 3.65 2.95 2.58 1.23 1.33 1.25 1.29
Weekend 2.96 2.92 2.75 2.49 1.19 1.15 1.17 1.01
Yearly Mean 2.70 2.26 2.51 2.24 1.09 1.07 1.03 1.02
The consideration of temperature devoid of distributing the data in different regions is responsible
for reduction in valuation constraints when associated with Case 1 and Case 2. Nevertheless, the MAPE
of Case 4 is enhanced as compared to Case 3. Moreover, Case 4 has minimum days with maximum
error that is larger than 4%. Contrariwise, forecasting results are improved in Case 4 as it distributes
the data in different regions and takes temperature in priority index. The MAPE in Case 4 is 1.02 %
as depicted in Tables 5and 6. This achieved MAPE is approximately 8% improved than Case 2 and
almost 9% enhanced than Case 1. Besides, Case 4 has the total number of optimum days that exceeds
the acceptable criteria. The results achieved for minimum days with maximum error and
=5
are also
enhanced in Case 4 as compared to Case 3. Nonetheless,
=3
has achieved enhanced results in Case 3 in
comparison with Case 4.
Table 7presents
Dγ
and
W1
for target year. The optimum result achieved is for
Dγ
= 7 and
W1
= 0.3. The results achieved for
W1
= 0.3 are approximately near to
W1
= 0.4. Thus, the
achieved parameters from training data can give suitable outcomes and are proven appropriate
for the proposed method.
Table 7. MAPE for every pair of Dγand W1for target data.
DγW1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
51.115 1.161 1.089 1.075 1.096 1.049 1.078 1.088 1.117 1.121 1.125
61.015 1.029 1.021 1.017 1.019 1.022 1.026 1.031 1.040 1.045 1.050
71.043 1.012 1.011 1.009 1.016 1.025 1.043 1.045 1.052 1.105 1.106
81.301 1.318 1.313 1.314 1.321 1.325 1.329 1.342 1.378 1.389 1.391
91.208 1.219 1.217 1.216 1.223 1.234 1.249 1.265 1.290 1.301 1.315
10 1.305 1.315 1.321 1.311 1.326 1.336 1.349 1.367 1.387 1.403 1.421
11 1.308 1.329 1.325 1.326 1.331 1.341 1.352 1.353 1.376 1.391 1.415
12 1.309 1.301 1.327 1.328 1.345 1.347 1.358 1.367 1.395 1.412 1.428
13 1.309 1.302 1.324 1.331 1.337 1.348 1.362 1.381 1.413 1.426 1.443
14 1.403 1.436 1.431 1.435 1.443 1.453 1.466 1.487 1.503 1.529 1.525
15 1.404 1.414 1.416 1.423 1.439 1.465 1.494 1.511 1.534 1.529 1.549
6.2.2. Evaluation of Consequences on knowledge Based Systems from Preceding Data
The preceding data is categorized in two different sets as discussed in Section II. The paper studies
three cases in this subsection to depict the consequences of this type of categorization.
1. Case 1: Load forecasting by collected similar days in initial data-set, Γds1
tar,H
2. Case 2: Load forecasting by collected similar days in last data-set, Γds2
tar,H
3. Case 3: Load forecasting by Γds1
tar,Hand Γds2
tar,H, i.e., Γt ar,H=Equation (44)
Table 8presents the outcomes of Case 1, Case 2, and Case 3 for every category of the day. Table 8
presents the outcomes of Case 1, Case 2, and Case 3 for every category of the day.
Electronics 2018,7, 431 28 of 34
Table 8. Consequences of taking Γds1
tar,Hand Γds2
tar,Hon forecasting.
=5=3MDME MAPE
Nature of Days Case 1 Case 2 Case 3 Case 1 Case 2 Case 3 Case 1 Case 2 Case 3 Case 1 Case 2 Case 3
Weekdays 10 13 78 7 73.21 2.73 2.71 1.81 1.52 1.26
Weekend 5 3 22 1 12.89 2.35 2.35 1.09 1.23 1.17
Yearly Mean 39 16 16 18 14 13 2.68 2.24 2.24 1.31 1.10 1.03
The MAPE of the entire system in Case 1 is maximum as compared to Case 2 and Case 3 in case
of
Γds1
tar,H
. Thus, it can be concluded that taking same days from selected or last month gives maximum
errors in forecasting results. Moreover, the total number of exceeding days from acceptable conditions
is not suitable, particularly
=5
. Nevertheless, integration of
Γds1
tar,H
and
Γds2
tar,H
gives enhanced results for
MAPE and minimum days with maximum error in Case 3. Furthermore, passed days from acceptable
conditions is lessened in Case 3.
Figures 1214 depicts the comparative analysis of traditional and proposed forecasting method.
According to Figures 1214, the days presented are four different days and these days belong to
dissimilar months. The predicted outcomes are then associated with real load demand. Moreover,
the results of the proposed system are much nearer to real load as compared to traditional
forecasting techniques.
2.4
2.7
3.0
3.3
0 5 10 15 20 25
Hour (h)
Load (MW)
Actual.Load Classic.Forecasting Modified.Forecasting
Figure 12.
Comparative analysis and effect of proposed and traditional method for Monday,
19 September 2015.
2.7
3.0
3.3
3.6
3.9
0 5 10 15 20 25
Hour (h)
Load (MW)
Actual.Load Classic.Forecasting Modified.Forecasting
Figure 13.
Comparative analysis and effect of proposed and traditional method for Wednesday,
13 June 2015.
Electronics 2018,7, 431 29 of 34
1.8
2.0
2.2
2.4
0 5 10 15 20 25
Hour (h)
Load (MW)
Actual.Load Classic.Forecasting Modified.Forecasting
Figure 14.
Comparative analysis and effect of proposed and traditional method for Sunday,
4 January 2015.
6.3. Comparative Analysis of Proposed Method, DBN, and F-LOLIMOT
The paper compares the results achieved from proposed knowledge based system with DBN and
F-LOLIMOT. The results are evaluated in terms of precision and operational time. The short-term load
predicting techniques is applied on PNPN to forecast the load demand for the duration of June 2017
to May 2018. Moreover, these predictions are based on temperature and load demand data, which
lies in the range of June 2015 to exactly one day before the target day. The results are presented in
Table 9, which shows that proposed knowledge based system has enhanced MAPE to 1.01. Besides,
the MAPE of
=5
and
=5
is also decreased. The DBN and F-LOLIMOT techniques show MAPE is
approximately higher than 3% for a month and approximately 5% greater in 47–50 days (maximum
error). Nonetheless, the proposed method has MAPE, which is greater than 3% in 15–18 days and 5%
with 23 days (maximum error). The variances discussed are notable enhancements in forecasting.
Table 9.
Comparison of Fuzzy Local Linear Model (F-LOLIMOT), deep belief network (DBN), and
proposed method.
Operational Time (s)
Technique =5=3MDME MAPE Training Time Executing Time
Proposed 17 10 2.83 1.10 15 0.41
DBN 50 42 2.89 1.21 29 0.52
F-LOLIMOT 42 35 3.43 1.50 215 0.81
On the topic of operational cost, the proposed knowledge based method takes minimum time
in training and executing in comparison with DBN and F-LOLIMOT. The proposed knowledge
based system, DBN, and F-LOLIMOT are executed to predict the days on a yearly basis. Besides,
the operational time is distributed to total number of predicted days in order to get the usual operational
time of prediction for a specified day. Moreover, the proposed system, DBN, and F-LOLIMOT are
executed with the same conditions. Besides, the parameters were tuned for every specified day
and forecasted demand load has been achieved for every technique. The paper distributes the day,
according to training and operational time in every technique. The proposed knowledge base systems
have less operational time as it does not require as much training as compared to DBN and F-LOLIMOT.
The proposed method lays emphasis on the selection of similar day and then predicts the load demand
as discussed above.
The forecasting of sample day is presented in Figures 15 and 16 by means of DBN, F-LOLIMOT,
and proposed knowledge based system. It is obvious that MAPE of the proposed method is 0.69
Electronics 2018,7, 431 30 of 34
for a sample day. This MAPE is lesser than MAPEs of DBN and F-LOLIMOT, which are 0.91 and
0.97 respectively. Moreover, the DME is minimized in the presented knowledge based system as
compared to others. The phenomenon of priority index is not suitable for special days (public holidays)
as discussed in earlier sections. Nevertheless, the special days can be forecasted by the presented
knowledge based system devoid of taking a priority index. Besides, the MAPE of the proposed system
is 1.30 for all days, together with special days. Nonetheless, the major aim of this paper is to study the
consequences of the priority index on the knowledge based system. Moreover, the scrutiny of special
days is beyond the scope of this paper.
2.50
2.75
3.00
3.25
3.50
0 5 10 15 20 25
Hour (h)
System Load (MW)
Actual.Load Similar.Day DBN F.LOLIMOT
Figure 15. Short-term load forecasting for a sample day.
0
1
2
3
4
0 5 10 15 20 25
Hour (h)
Error
Similar_Day DBN F_LOLIMOT
Figure 16. Error values for a sample day.
7. Conclusions
This paper presents a novel knowledge based short-term load forecasting method. The entire
system (region) is distributed in nine sub-systems (zones) by consideration of temperature to predict
the demand load more efficiently. The outcomes depict that distribution of huge topographical power
network improves the forecasting results. Moreover, this paper presents a novel priority index in which
climatic conditions and the date proximity of every particular region is observed. The algorithms of
AP and BFFA are hybridized in this paper to achieve better accuracy for a knowledge based system.
The proposed knowledge based system is verified on PNPN. The achieved outcomes depict that
proposed method minimizes the MAPE and other errors of forecasting in comparison with traditional
Electronics 2018,7, 431 31 of 34
forecasting techniques. Furthermore, the obtained results from proposed system are 15–20% improved
as compared to DBN and F-LOLIMOT techniques. Furthermore, this paper defines two standard
measures for error distribution. The outcomes verify that the total amount of exceeded days is reduced
through proposing knowledge based systems from acceptable criteria. This phenomenon specifies
more efficient forecasting results as compared to DBN, F-LOLIMOT, and traditional knowledge
based systems.
Author Contributions:
All authors have contributed to this paper with the same effort in finding available
literature, resources and writing the paper. Moreover, all authors have read and approved the final manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
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... Thus, making institutional, residential, business, etc., environments smart. SEM is one of the constituents of a smart community that efficiently monitors, controls and regulates the energy without affecting the comfort of energy users [6,7,8,9,10,11,12,13]. An example of SEM is Smart Energy Trading (SET), which comprises of energy providers and consumers [14,15,16,17,18]. ...
... 11: The Effects of SDR=1 in the Proposed Pricing Scheme. ...
Thesis
Full-text available
The rapid deployment of Electric Vehicles (EVs) and usage of renewable energy in day-to-day activities of energy consumers have contributed toward the development of a greener smart community. However, load balancing problems, security threats, privacy leakages, and lack of incentive mechanisms remain unresolved in energy systems. Many approaches have been used in the literature to solve the aforementioned challenges. However, these approaches are not sufficient to obtain satisfactory results because of the resource and time-intensiveness of the primitive cryptographic executions on the network devices. In most cases, energy trading systems manage transactions using a centralized approach. This approach increases the risk of a single point of failure and overall system cost. In this study, a blockchain based Local Energy Market (LEM) model considering Home Energy Management (HEM) system and demurrage mechanism is proposed to tackle the issue of a single point of failure in the energy trading system. It allows both the prosumers and consumers to optimize their energy consumption and minimize electricity costs. This model also allows end-users to shift their load to off-peak hours and to use cheap energy from the LEM. On the other hand, users’ privacy leakages are still not solved in blockchain and can limit its usage in many applications. This research also proposes a blockchain based distributed matching and privacy-preservation model that uses a reputation system for both residential homes and EVs to preserve users’ privacy and efficiently allocate energy. A starvation free energy allocation policy is presented in the model. In addition, a charging forecasting scheme for EVs is introduced that allows users to plan and manage their intermittent EVs’ charging. Partial homomorphic encryption based on a reputation system is used to hide the EVs users’ whereabouts. Identity Based Encryption (ID Based encryption) technique is incorporated in the model to preserve the users’ information privacy in the blockchain. Another bottleneck in the energy trading systems is to perform efficient and privacy-preserving transactions. Therefore, an efficient and secure energy trading model leveraging contract theory, consortium blockchain, and a reputation system is proposed. Firstly, a secure energy trading mechanism based on consortium blockchain is developed. Then, an efficient contract theory based incentive mechanism considering the information asymmetry scenario is introduced. Afterwards, a reputation system is integrated to improve x transaction confirmation latency and block creation. Next, a shortest route and distance algorithm is implemented in order to reduce the traveling distance and energy consumption by the EVs during energy trading. Cheating attacks launched by both buyers and sellers are also issues, which are still not resolved. Thus, a mutual-verifiable fairness mechanism during energy trading based on timed commitment is presented. Proof-of-Energy Reputation Generation (PoERG) and Proof-of Energy Reputation Consumption (PoERC) consensus mechanisms are proposed to solve the high computational cost and huge monetary investment issues created by Proof-of-Work (PoW) and Proof-of-Stake (PoS) existing mechanisms. The mechanisms are developed based on reputation where energy trading transactions are audited, validated, and added into blocks of a blockchain. In order to protect the proposed model from impersonation attacks and minimize malicious validators, a two-stage peer-to-peer secure energy trading model based on blockchain is proposed. The proposed model has two layers: a mutual authentication process layer, and a secure and privacy-preserving energy trading layer. Afterwards, an incentive-punishment algorithm is introduced to motivate energy prosumers to contribute more energy in the proposed model. Next, a dynamic contract theory based supply-demand ratio pricing scheme is proposed. The purpose of the proposed pricing scheme is to solve the issues associated with the existing pricing scheme. Also, to preserve the privacy of the actual energy consumption behavior of the trading participants. Furthermore, storage overhead and delay in communication are challenges that need urgent attention, especially in resource constrained devices for sustainable and efficient transactions. Therefore, a consortium blockchain based vehicular system is proposed in this work for secure communication and optimized data storage in Internet of Vehicles (IoV) network. To secure the proposed system from active and passive attacks, an encryption technique and an authentication mechanism are proposed based on public key encryption scheme and hashing algorithm, i.e., Advanced Encryption Standard-256 and Rivest Shamir Adleman (AES-256+RSA), and Keccak-256. It also protects the model from double spending attack. Moreover, a cache memory technique is introduced to reduce service delay and high resource consumption. In the cache memory, the information of frequently used services is stored, which results in the reduction of service delivery delay. Simulation results show that all of the proposed models perform significantly better as compared to the existing schemes.
... Several decisions related to power are made on the basis of the information of future load demand. Similarly, a consumer can use the forecasted values of electricity prices and change its energy consumption pattern accordingly [44,45]. Electricity load and price forecasting gained attention of researchers in this area because these two factors have a great influence on maintaining the stability of the grid [46,47,48,49]. ...
... The buyEnergy function stores this information and passes the buyer's and seller's information to the main smart contract with the market price of electricity. The next two functions (lines if remainder==0 then 35: removeSeller(j) 36: removeBuyer(i) 37 if remainder==0 then 43: removeBuyer(i) 44: removeSeller(j) 45 ...
Thesis
Full-text available
With the advent of the smart grid (SG), the concept of energy management flourished rapidly and it gained the attention of researchers. Forecasting plays an important role in energy management. In this work, a recurrent neural network, long short term memory (LSTM), is used for electricity price and demand forecasting using big data. This model uses multiple variables as input and forecasts the future values of electricity demand and price. Its hyperparameters are tuned using the Jaya optimization algorithm to improve the forecasting ability. It is named as Jaya LSTM (JLSTM). Moreover, the concept of local energy generation using renewable energy sources is also getting popular. In this work, to implement a hybrid peer to peer energy trading market, a blockchain based system is proposed. It is fully decentralized and allows the market members to interact with each other and trade energy without involving a third party. In addition, in vehicle to grid and vehicle to vehicle energy trading environments, local aggregators perform the role of energy brokers and are responsible for validating the energy trading requests. A solution to find accurate distance with required expenses and time to reach the charging destination is also proposed, which effectively guides electric vehicles (EVs) to reach the relevant charging station and encourages energy trading. Moreover, a fair payment mechanism using a smart contract to avoid financial irregularities is proposed. Apart from this, a blockchain based trust management method for agents in a multi-agent system is proposed. In this system, three objectives are achieved: trust, cooperation and privacy. The trust of agents depends on the credibility of trust evaluators, which is verified using the proposed methods of trust distortion, consistency and reliability. To enhance the cooperation between agents, a tit-3-for-tat repeated game strategy is developed. The strategy is more forgiving than the existing tit-for-tat strategy. It encourages cheating agents to re-establish their trust by cooperating for three consecutive rounds of play. Also, a proof-of-cooperation consensus protocol is proposed to improve agents’ cooperation while creating and validating blocks. The privacy of agents is preserved in this work using the publicly verifiable secret sharing mechanism. Additionally, a blockchain based edge and cloud system is proposed to resolve the resource management problem of EVs in a vehicular energy network. Firstly, a min-max optimization problem is formulated to construct the proposed entropy based fairness metric for resource allocation. This metric is used to determine whether users have received a fair share of the system’s resources or not. Secondly, a new deep reinforcement learning based content caching and computation offloading approach is designed for resource management of EVs. Lastly, a proof-of-bargaining consensus mechanism is designed for block’s validation and selection of miners using the concept of iterative negotiation. Besides, a survey of electricity load and price forecasting models is presented. The focus of this survey is on the optimization methods, which are used to tune the hyperparameters of the forecasting models. Moreover, this work provides a systematic literature review of scalability issues of the blockchain by scrutinizing across multiple domains and discusses their solutions. Finally, future research directions for both topics are discussed in detail. To prove the effectiveness of the proposed energy management solutions, simulation are performed. The simulation results show that the energy is efficiently managed while ensuring secure trading between energy prosumers and fair resource allocation.
... Thus, making institutional, residential, business, etc., environments smart. SEM is one of the constituents of a smart community that efficiently monitors, controls and regulates the energy without affecting the comfort of energy users [3][4][5][6][7]. An example of SEM is Smart Energy Trading (SET), which comprises of energy providers and consumers. ...
Research Proposal
Full-text available
The rapid deployment of Electric Vehicles (EVs) and usage of renewable energy in day-to-day activities of energy consumers have contributed toward the development of a greener smart community. However, load balancing problems, security threats, privacy leakages, and lack of incentive mechanisms remain unresolved in energy systems. Many approaches have been used in the literature to solve the aforementioned challenges. However, these approaches are not sufficient to obtain satisfactory results because of the resource and time-intensiveness of the primitive cryptographic executions on the network devices. In most cases, energy trading systems manage transactions using a centralized approach. This approach increases the risk of a single point of failure and overall system cost. In this study, a blockchain based Local Energy Market (LEM) model considering Home Energy Management (HEM) system and demurrage mechanism is proposed to tackle the issue of a single point of failure in the energy trading system. It allows both the prosumers and consumers to optimize their energy consumption and minimize electricity costs. This model also allows end-users to shift their load to off-peak hours and to use cheap energy from the LEM. On the other hand, users’ privacy leakages are still not solved in blockchain and can limit its usage in many applications. This research also proposes a blockchain based distributed matching and privacy-preservation model that uses a reputation system for both residential homes and EVs to preserve users’ privacy and efficiently allocate energy. A starvation free energy allocation policy is presented in the model. In addition, a charging forecasting scheme for EVs is introduced that allows users to plan and manage their intermittent EVs’ charging. Partial homomorphic encryption based on a reputation system is used to hide the EVs users’ whereabouts. Identity Based Encryption (ID Based encryption) technique is incorporated in the model to preserve the users’ information privacy in the blockchain. Another bottleneck in the energy trading systems is to perform efficient and privacy-preserving transactions. Therefore, an efficient and secure energy trading model leveraging contract theory, consortium blockchain, and a reputation system is proposed. Firstly, a secure energy trading mechanism based on consortium blockchain technology is developed. 1 Then, an efficient contract theory based incentive mechanism considering the information asymmetry scenario is introduced. Afterwards, a reputation system is integrated to improve transaction confirmation latency and block creation. Next, a shortest route and distance algorithm is implemented in order to reduce the traveling distance and energy consumption by the EVs during energy trading. Cheating attacks launched by both buyers and sellers are also issues, which are still not resolved. Thus, a mutual-verifiable fairness mechanism during energy trading based on timed commitment is presented. Proof-of-Energy Reputation Generation (PoERG) and Proof-of Energy Reputation Consumption (PoERC) consensus mechanisms are proposed to solve the high computational cost and huge monetary investment issues created by Proof-of- Work (PoW) and Proof-of-Stake (PoS) existing mechanisms. The mechanisms are developed based on reputation where energy trading transactions are audited, validated, and added into blocks of a blockchain. In order to protect the proposed model from impersonation attacks and minimize malicious validators, a two-stage peer-to-peer secure energy trading model based on blockchain is proposed. The proposed model has two layers: a mutual authentication process layer, and a secure and privacy-preserving energy trading layer. Afterwards, an incentivepunishment algorithm is introduced to motivate energy prosumers to contribute more energy in the proposed model. Next, a dynamic contract theory based supply-demand ratio pricing scheme is proposed. The purpose of the proposed pricing scheme is to solve the issues associated with the existing pricing scheme. Also, to preserve the privacy of the actual energy consumption behavior of the trading participants.
... The proposed framework includes PV, WT and ESS; however, MT and electricity market tariff are not considered. To avoid conflict and ensure cooperation between intelligent rational decision making in the microgrid, the concept of game theory is now introduced into the microgrid domain [151]. This concept attempts to look at relationships between distributed energy resources participants and predict optimal decisions. ...
Thesis
Full-text available
This thesis examines the privacy preserving energy management issue, taking into account both energy generation units and responsive demand in the smart grids. Firstly, because of the inherent stochastic behavior of the distributed energy resources, an optimal energy management problem is studied. Distributed energy resources are used in the decentralization of energy systems. Large penetration of distributed energy resources without the precise cybersecurity measures, such as privacy, monitoring and trustworthy communication may jeopardize the energy system and cause outages, and reliability problem for consumers. Therefore, a blockchain based decentralized energy system to accelerate electrification by improving service delivery while minimizing the cost of generation and addressing historical antipathy and cybersecurity risk is proposed. A case study of sub-Sahara Africa is considered. Also, a blockchain based energy trading system is proposed, which includes price negotiation and incentive mechanisms to address the imbalance of order. Besides, the Internet of energy makes it possible to integrate distributed energy resources and consumers. However, as the number of users involved in energy transactions increases, some factors are restricting conventional centralized energy trading. These factors include lack of trust, privacy, fixed energy pricing, and demurrage fees dispute. Therefore, additive homomorphic encryption and consortium blockchain are explored in this thesis to provide privacy and trust. Additionally, a dynamic energy pricing model is formulated based on the load demand response ratio of prosumers to address the fixed energy pricing problem. The proposed dynamic pricing model includes demurrage fees, which is a monetary penalty imposed on a prosumer if it failed to deliver energy within the agreed duration. Also, a new threat model is designed and analyzed. Secondly, mobile prosumers, such as electric vehicles offer a wide range of sophisticated services that contribute to the robustness and energy efficiency of the power grid. As the number of vehicles in the smart grid grows, it potentially exposes vehicle owners to a range of location related privacy threats. For example, when making payments, the location of vehicles is typically revealed during the charging process. Also, fixed pricing policy and lack of trust may restrict energy trading between vehicles and charging stations. Therefore, a private blockchain system is proposed to preserve the privacy of vehicle owners from linking based attack while a public blockchain system is established to enhance energy trading. Various parameters are used to formulate a demand based pricing policy for vehicles, such as time of demand, types of vehicles and locations. Using the demand based pricing policy, an optimal scheduling method is designed to maximize the vehicles both social welfare and utility. An improved consensus energy management algorithm is proposed to protect the privacy of vehicle owners by applying differential privacy. The proposed system is robust against temporal and spatial location based privacy related attacks. Thirdly, blockchain is an evolving decentralized data collection technology, which costeffectively exploits residential homes to collate large amounts of data. The problems of blockchain are the inability to withstand malicious nodes, which provide misleading information that destabilize the entire network, lack of privacy for individual node and shared data inaccuracy. Therefore, a secure system for energy users to share their multi-data using the consortium blockchain is proposed. In this system, a credibility based Byzantine fault tolerance algorithm is employed as the blockchain consensus mechanism to achieve the fault tolerance of the system. Also, a recurrent neural network is used by certain honest users with credibility to forecast the energy usage of other honest users. A recurrent neural network operates on the collated data without revealing the private information about honest users and its gradient parameters. Moreover, additive homomorphic encryption is used in the recurrent neural network to secure the collated data and the gradient parameters of the network. Also, a credibility management system is proposed to prevent malicious users from attacking the system and it consists of two layers: upper and lower. The upper layer manages global credibility that reflects the overall readiness of honest users to engage in multi-data sharing. The lower layer performs local credibility that reflects certain feedback of honest users on the accuracy of the forecast data. Lastly, combining blockchain mining and application intensive tasks increases the computational cost for resource constrained energy users. Besides, the anonymity and privacy problems of the users are not completely addressed in the existing literature. Therefore, this thesis proposes an improved sparse neural network to optimize computation offloading cost for resource constrained energy users. Furthermore, a blockchain system based on garlic routing, known as GarliChain, is proposed to solve the problems of anonymity and privacy for energy users during energy trading in the smart grid. Furthermore, a trust method is proposed to enhance the credibility of nodes in the GarliChain network. Simulations evaluate the theoretical results and prove the effectiveness of the proposed solutions. From the simulation results, the performance of the proposed model and the least-cost option varies with the relative energy generation cost of centralized, decentralized and blockchain based decentralized system infrastructure. Case studies of Burkina Faso, Cote d’Ivoire, Gambia, Liberia, Mali, and Senegal illustrate situations that are more suitable for blockchain based decentralized system. For other sub-Sahara Africa countries, the blockchain based decentralized system can cost-effectively service a large population and regions. Additionally, the proposed blockchain based levelized cost of energy reduces energy costs by approximately 95% for battery and 75% for the solar modules. The future blockchain based levelized cost of energy varies across sub-Sahara Africa on an average of about 0.049 USD/kWh as compared to 0.15 USD/kWh of an existing system in the literature. The proposed model achieves low transaction cost, the minimum execution time for block creation, the transactional data privacy of prosumers and dispute resolution of demurrage fees. Moreover, the proposed system reduces the average system overhead cost up to 66.67% as compared to 33.43% for an existing scheme. Additionally, the proposed blockchain proof of authority consensus average hash power is minimized up to 82.75% as compared to 60.34% for proof of stake and 56.89% for proof of work consensus mechanisms. Simulations are also performed to evaluate the efficacy of the proposed demand based pricing policy for mobile prosumers. From the simulation results, the proposed demand based pricing policy is efficient in terms of both low energy price and average cost, high utility and social welfare maximization as compared to existing schemes in the literature. It means that about 89.23% energy price reduction is achieved for the proposed demand based pricing policy as compared to 83.46% for multi-parameter pricing scheme, 73.86% for fixed pricing scheme and 53.07% for the time of use pricing scheme. The vehicles minimize their operating costs up to 81.46% for the proposed demand based pricing policy as compared to 80.48% for multi-parameter pricing scheme, 69.75% for fixed pricing scheme and 68.29% for the time of use pricing scheme. Also, the proposed system outperforms an existing work, known as blockchain based secure incentive scheme in terms of low energy prices and high utility. Furthermore, the proposed system achieves an average block transaction cost of 1.66 USD. Besides, after applying the differential privacy, the risk of privacy loss is minimum as compared to existing schemes. Furthermore, higher privacy protection of vehicles is attained with a lower information loss against multiple background knowledge of an attacker. To analyze the efficiency of the proposed system regarding multi-data sharing, an experimental assessment reveals that about 85% of honest users share their data with stringent privacy measures. The remaining 15% share their data without stringent privacy measures. Moreover, the proposed system operates at a low operating cost while the credibility management system is used to detect malicious users in the system. Security analysis shows that the proposed system is robust against 51% attack, transaction hacking attack, impersonation attack and the double spending attack. To evaluate the proposed system regarding energy management of resource constrained blockchain energy users, a Jaya optimization algorithm is used to accelerate the error convergence rate while reducing the number of connections between different layers of the neurons for the proposed improved sparse neural network. Furthermore, the security of the users is ensured using blockchain technology while security analysis shows that the system is robust against the Sybil attack. Moreover, the probability of a successful Sybil attack is zero as the number of attackers’ identities and computational capacities increases. Under different sizes of data to be uploaded, the proposed improved sparse neural network scheme has the least average computational cost and data transmission time as compared to deep reinforcement learning combined with genetic algorithm, and sparse evolutionary training and multi-layer perceptron schemes in the literature. Simulation results of the proposed GarliChain system show that the system remains stable as the number of path requests increases. Also, the proposed trust method is 50.56% efficient in detecting dishonest behavior of nodes in the network as compared to 49.20% of an existing fuzzy trust model. Under different sizes of the blocks, the computational cost of the forwarding nodes is minimum. Security analysis shows that the system is robust against both passive and active attacks. Malicious nodes are detected using the path selection model. Moreover, a comparative study of the proposed system with existing systems in the literature is provided.
Thesis
Full-text available
Forecasting of electricity load through combining different deep learning and machine learning techniques is most active and hot topic in electrical engineering. The modern grid is known as a Smart Grid (SG) provide affective, reliable and economic energy consumption to users. Accurate electricity load prediction helps in efficient power load management. In the SG, the key issue is to predict accurate electricity load. There still need some better structure for Long-term electricity load forecasting. In our proposed model, we focus on Long-term electricity load forecasting to maximize the accuracy. For this purpose, we will use hybrid feature selector that is consists on XG-boost, Relief-f and Random Forest (RF) in order to choose features. For feature extraction we will use Principal Component Analysis (PCA). For the prediction of electricity load we will use Convolution Neural Network and Long Short-term Memory Network (CNN-LSTM) and Extreme Learning Machine (ELM) as a classifier. CNN-LSTM optimize with Harmony Search Algorithm (HSA) called CNN-LSTM-HSA and the hyper parameters of ELM tuned with Social Learning Optimization (SLO) algorithm called ELM-SLO. Our proposed techniques CNN-LSTM-HSA and ELM-SLO perform 97% and 92% accuracy in predicting the electricity load. The error rate of MAPE, MSE, MAE, RMSE are very low.
Preprint
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Electrical utilities depend on short-term demand forecasting to proactively adjust production and distribution in anticipation of major variations. This systematic review analyzes 240 works published in scholarly journals between 2000 and 2019 that focus on applying Artificial Intelligence (AI), statistical, and hybrid models to short-term load forecasting (STLF). This work represents the most comprehensive review of works on this subject to date. A complete analysis of the literature is conducted to identify the most popular and accurate techniques as well as existing gaps. The findings show that although Artificial Neural Networks (ANN) continue to be the most commonly used standalone technique, researchers have been exceedingly opting for hybrid combinations of different techniques to leverage the combined advantages of individual methods. The review demonstrates that it is commonly possible with these hybrid combinations to achieve prediction accuracy exceeding 99%. The most successful duration for short-term forecasting has been identified as prediction for a duration of one day at an hourly interval. The review has identified a deficiency in access to datasets needed for training of the models. A significant gap has been identified in researching regions other than Asia, Europe, North America, and Australia.
Thesis
Full-text available
The revolution of power grids from traditional grids to Smart Grids (SGs) requires effective Demand Side Management (DSM) and reliable Renewable Energy Sources (RESs) incorporation in order to maintain demand, supply balance and optimize energy in an environment friendly manner. Data analytics provide solutions to the emerging challenges of power systems, such as DSM, environmental pollution (due to carbon emission), fossil fuel dependency mitigation, RESs incorporation, cost curtailment, grid’s stability and security. To efficiently manage electricity and maximize the profit of power utilities several tasks are focused in this thesis, i.e., prediction of electricity load to avoid demand and generation mismatch, wind power forecasting to satisfy energy demand effectively, electricity price forecasting for regulating market operations, carbon emissions forecasting for reducing payment of carbon tax, Electricity Theft Detection (ETD) for recovering power utilities’ revenue loss caused by electricity theft. In addition to that, a wind power forecast based DSM scheme is proposed. Furthermore, impact of RESs integration level on carbon emissions, electricity price and consumption cost is quantified. Both forecasting and classification techniques are utilized for efficient energy management. Forecasting of electricity load, price, wind power and carbon emissions is performed, whereas, classification of fair and fraudulent electricity consumers is performed. To balance electricity demand and supply, electricity load forecasting is required. Three models are proposed for this purpose, i.e., Deep Long Short-Term Memory (DLSTM), Efficient Sparse Autoencoder Nonlinear Autoregressive eXogenous network (ESAENARX) and Differential Evolution Recurrent Extreme Learning Machine (DE-RELM). DLSTM utilizes univariate data and gives single result, whereas, ESAENARX and DE-RELM model multivariate data and predict electricity load and price simultaneously. Due to adaptive and automatic feature learning mechanism, DLSTM achieves accurate results for separate forecasting of electricity load and price. ESAENARX and DE-RELM models are enhanced by newly proposed efficient feature extractor and model’s parameter tuning, respectively. Real-world datasets of ISO-NE, PJM, NYISO are used for load and price forecasting. The purpose of regulating the electricity market operations is achieved by forecasting of electricity load, price, wind power and carbon emissions. Wind power generation is predicted by an efficient model named Efficient Deep Convolution Neural Network (EDCNN). Moreover, a DSM strategy is also proposed based on predicted wind power generation. Power utilities have to pay carbon emissions tax imposed by government. To pay less carbon emissions tax, carbon emissions prediction is required, which helps in encouraging electricity consumers to shift their consumption load to low carbon price time periods of the day. For accomplishing the carbon emissions forecasting task, an efficient model named as Improved Particle Swarm Optimization based Deep Neural Network (IPSO DNN) is proposed. This model is improved by tunning the parameters of DNN by newly proposed improved optimization technique named as IPSO. ISO-NE dataset is used for wind power and carbon emissions forecasting. To reduce the financial loss of power utilities ETD is very important. For this purpose four models are proposed, named as, Differential Evolution Random Under Sampling Boosting (DE-RUSBoost), Jaya-RUSBoost, RUS Ensemble CNN (RUSE-CNN) and anomaly detection based ETD. In DE-RUSBoost and Jaya-RUSBoost, the parameters of RUSBoost classifier are tunned by DE and Jaya optimization techniques, respectively. In RUSE-CNN, RUS data balancing technique is applied along with ensemble CNN to improve ETD performance. DE-RUSBoost, Jaya-RUSBoost and RUSE-CNN are supervised model that work on labeled electricity theft data. Whereas, anomaly detection based ETD model is capable of identifying electricity theft from unlabeled electricity consumption data. Real-world datasets of SGCC, UMass, PRECON, CER, EnerNOC and LCL are used for ETD. Simulation results show that all the proposed models perform significantly better on real-world dataset as compared to their state-of-the-art counterpart models. The improved feature engineering and model hyper-parameter tuning enhance the performance of the proposed models in terms of prediction and classification results.