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Towards Sustainable Smart Cities: A Secure and
Scalable Trading System for Residential Homes using
Blockchain and Artificial Intelligence
Omaji Samuel1, Nadeem Javaid1,∗, Turki Ali Alghamdi2, Neeraj Kumar3
1Department of Computer Science, COMSATS University Islamabad, Islamabad 44000,
Pakistan
2Department of Computer Science, College of Computer and Information Systems, Umm
Al-Qura University, Makkah 21955, Saudi Arabia
3Computer Science and Engineering Department, Thapar Institute of Engineering and
Technology, Patiala 147001, India
Abstract
This paper proposes a secure blockchain based energy trading system for resi-
dential homes. In the system, a new proof-of-computational closeness (PoCC)
consensus protocol is proposed for the selection of miners and the creation of
blocks. Moreover, an analytical energy pricing policy is designed to solve the
problem of existing energy pricing policies in a distributed trading environment.
A dynamic multi-pseudonym mechanism is developed for the prosumers to pre-
serve their transactional privacy during energy trading. Since it requires extra
storage and computing resources for the blockchain miners to simultaneously
execute both mining process and application intensive tasks, therefore, an im-
proved sparse neural network (ISNN) is proposed for computation offloading to
the cloud servers. In ISNN, a Jaya optimization algorithm is used to accelerate
the error convergence rate while reducing the number of connections between
different layers of neurons. Besides, ISNN optimizes the overall computational
cost of the system. Furthermore, the security of the prosumers is ensured using
∗Corresponding author: www.njavaid.com
Email addresses: omajiman1@gmail.com (Omaji Samuel1), nadeemjavaidqau@gmail.com
(Nadeem Javaid1,), taghamdi@uqu.edu.sa (Turki Ali Alghamdi2), neeraj.kumar@thapar.edu
(Neeraj Kumar3
)
Preprint submitted to Elsevier September 18, 2021
blockchain technology while security analysis shows that the system is robust
against the Sybil attack. The proposed blockchain based peer-to-peer secure
energy trading system is extremely important for sustainable cities and society.
Simulations are conducted to evaluate the effectiveness of the proposed system.
The proposed pricing policy is compared with time-of-use pricing, critical peak
pricing and real-time pricing policies. From the results, it is proved that the
prosumers achieve a higher degree of satisfaction and utility when using the
proposed pricing policy. Moreover, the probability of a successful Sybil at-
tack is zero as the number of attackers’ identities and computational capacities
increases. Under different sizes of data to be uploaded, the proposed ISNN
scheme has the least average computational cost and data transmission time
as compared to deep reinforcement learning combined with genetic algorithm
(DRGO) and sparse evolutionary training and multi-layer perceptron (SET-
MLP) schemes in the literature. Moreover, the proposed system is tested for
scalability by increasing the number of prosumers. Extensive simulations are
performed and the results depict the satisfactory performance of the proposed
system.
Keywords: Computation offloading, energy trading, proof-of-computational
closeness, improved sparse neural network, smart grid
1. Introduction and Literature Review1
In this section, the introduction of the paper and literature review are pre-2
sented. The problem statement extracted after a brief literature review is also3
discussed. Moreover, the contributions and organization of the paper are given4
at the end of the section.5
1.1. Introduction6
Nowadays, the integration of renewable energy sources (RESs) and informa-7
tion and communication technologies is revolutionizing the energy industry all8
over the world. Besides, distributed generation (DG) is getting popular because9
2
electricity is generated from RESs at the consumers’ end (also known as pro-10
sumers). To this end, the existing power grids are not overstressed. However,11
because of the intermittent nature of RESs, some individuals are incapacitated12
to satisfy their energy demands while others have surplus energy [1]. DG enables13
small-scale energy producers to share and store energy in a decentralized fashion14
[2] using an efficient energy trading mechanism. However, the issues of security,15
privacy, trust and energy pricing determination have hindered the success of16
the existing energy trading mechanisms [3]. Today, blockchain is employed as17
a secure and trusted framework for distributed energy trading [4, 5]. It is de-18
fined as a distributed ledger technology that allows data to be recorded over the19
network. It validates the public ledger by providing a non-partisan way of reach-20
ing an agreement on the global state of the network using consensus processes,21
such as proof-of-work, proof-of-stake, and so on. However, privacy leakage and22
high computational cost are the major issues of the blockchain because of the23
transparency of transactions and execution of computationally expensive min-24
ing algorithms. These issues have restricted the implementation of blockchain25
for resource-constrained users, which is against the concept of sustainable cities26
and society. From the above discussion, it is necessary to provide effective and27
efficient solutions for the privacy, security, resource management and price de-28
termination problems of users in the smart grids. The solutions are extremely29
important for sustainable cities and society.30
1.2. Literature Review31
Today, the smart grid made it easy for individuals to trade and store en-32
ergy, which means that there is a high potential for the energy market [6]. An33
ideal energy market is to create a friendly environment where supply and de-34
mand of energy are possible by reducing high production costs of individuals35
or organizations [2]. Because of the distinct energy usages of individuals, some36
individuals may not have sufficient energy to satisfy their energy needs while37
others may have surplus energy. Thus, it is paramount to provide an efficient38
energy trading market for them. Many thanks to the development of peer-to-39
3
peer (P2P) energy transfer technology where energy is exchanged between peers40
residing in the same area [2, 7]. The most feasible approach in a smart grid is41
a centralized technology, which is simple to set up and implement. However,42
the approach faces a variety of concerns, including lack of trust, single point43
of failure, and high operational and maintenance costs. Moreover, in a P2P44
energy trading scenario, trust, privacy and security are plausible challenges for45
the future smart grids. To enhance the security in energy trading and address46
the above-mentioned challenges, blockchain technology has been recently intro-47
duced.48
1.3. Peer-to-Peer Energy Trading49
Recently, the authors in [8] present a survey that discusses the security prob-50
lems and the impact of deploying blockchain in smart cities. The authors in [9]51
suggest a Byzantine blockchain based consensus system for strengthening data52
protection during energy trading for the involved entities. However, the con-53
straints of entities to execute computationally intensive tasks, like blockchain54
mining, are not considered. The authors in [10] propose a blockchain based55
software-defined network (SDN) for securing energy trading between entities in56
an intelligent transportation system. However, the privacy of entities is not57
considered. Notwithstanding the technological advancement in energy trading58
systems, some issues prevent blockchain and P2P energy trading from being59
fully implemented. Firstly, it is quite difficult to develop a distributed energy60
trading market where a fair balance between data privacy and economic ef-61
ficiency can be achieved. Lastly, as the number of storage devices increases,62
there is a need for developing a new P2P market that accounts for their inter-63
temporal dependencies. To this end, the authors in [11] develop a decentralized64
blockchain based P2P energy exchange framework to solve the challenges. In the65
system, a two-layered platform is proposed. The first layer performs short-term66
pool structured auction using the ant colony optimization method, whereas the67
second layer consists of blockchain that provides a high level of security, real-68
time settlement and automation. However, resource management of users is69
4
not considered. Energy trading between entities is a typical vertical market in70
a smart grid, but when processing energy trading decisions locally, there is a71
security problem as well as a rise in transmission delay and network overhead.72
The authors in [12] recommend a blockchain based edge-as-a-service framework73
for securing energy trading in an SDN enabled vehicle-to-grid ecosystem to solve74
the issues. However, the resource management problem of an entity is not re-75
solved as the proposed consensus mechanism is proof-of-work, which is CPU76
intensive. The authors in [4] resolve the high processing and packet overhead of77
users using a routing method for energy trading in a smart grid. In the routing78
method, a packet is routed on the basis of destination public key. The authors79
in [13] present a pseud digital identity mechanism to prevent privacy leakage80
of entities in a sustainable society. Also, a blockchain based incentive demand81
response mechanism is proposed to ensure the credibility of different entities.82
The authors in [14] propose a blockchain based hesitant fuzzy linguistic sys-83
tem and k-mediods clustering algorithm for improving the decision making in84
energy trading. The proposed system serves as a reference model to different85
participants in energy trading, including governments and companies. Also, it86
helps them to critically understand the impact of deploying blockchain tech-87
nology in energy trading. A novel blockchain based load sharing mechanism is88
proposed in [15] for smart microgrids. In the paper, the authors consider the89
industrial Internet of things ideal for distributed control of renewable micro-90
grids. The proposed system has a layered architecture. The upper layer has91
control over system dispatch, whereas the lower layer is responsible to control92
the proceedings of load.93
1.4. Cloud Computing based Computation Offloading94
Cloud computing provides a promising solution that assists users in per-95
forming computationally intensive tasks using the computing resources [16].96
However, cloud computing faces issues of resource management and scheduling,97
which are multi-objective optimization problems [16]. In the literature, meta-98
heuristic optimization techniques have been adopted to solve the problems in99
5
cloud systems [17, 18]. Besides, machine learning methods [19, 20, 16] have100
been used as possible solutions to resolve the problems. However, the solutions101
provided by the researchers in [16, 18, 19, 20, 21] do not consider a single point102
of failure, security and privacy concerns, and how to efficiently share computing103
resources trustfully in the smart grids. Moreover, the works in [22, 23, 24, 25]104
propose blockchain based cloud systems for solving resource management prob-105
lem. However, privacy concerns of blockchain nodes are not considered in the106
systems. Also, the systems require further improvement to achieve robust re-107
source management.108
In this study, we consider a scenario of residential homes that wish to trade109
energy securely using blockchain technology. The residential homes can become110
miner nodes based on their computing and storage devices. In addition, security111
and privacy concerns are paramount for ensuring a safe energy trading transac-112
tion for residential homes. That is immensely important for sustainable cities113
and society. Furthermore, an efficient energy trading pricing policy is important114
for enhancing energy trading in a P2P fashion. Therefore, this study proposes a115
secure energy trading system using blockchain and artificial intelligence for rural116
residential homes. Table 1 presents the comparative analysis of the proposed117
scheme with other existing schemes in terms of objectives, mechanisms, energy118
trading, privacy, resource management and security analysis.119
Table 1: Comparative analysis of the proposed scheme with existing
schemes
Objectives Mechanisms Energy
trading
Privacy Resource
manage-
ment
Security
analysis
Blockchain enabled
neighboring energy
trading system [2]
Privacy preserving
mechanism using
multi-pseudonym
3 3 7 7
6
Blockchain based dis-
tributed energy trad-
ing system [4]
Pricing negotiation
method
3 3 7 7
Blockchain based
P2P trading for
crowdsourced energy
system [5]
Day ahead schedul-
ing
3 7 7 7
A Byzantine based
blockchain consensus
framework [9]
Analytic pricing pol-
icy
3 3 7 3
Blockchain based se-
cure energy trading
scheme for electric
vehicles [10]
SDN 3 7 7 7
Blockchain based
decentralized P2P
energy trading
platform [11]
Ant colony optimiza-
tion
3 7 7 7
A consensus based
blockchain mech-
anism for secure
energy trading in
SDN enabled vehicle
to grid [12]
Edge-as-a-service for
secure energy trading
method
3 7 7 7
A blockchain based
price incentive de-
mand response [13]
Non cooperative
game and pseud
identity mechanism
3 3 7 7
A blockchain based
energy trading sys-
tem [14]
Hesitant fuzzy
linguistic and k-
mediods
3 7 7 7
Edge cloud assisted
Internet of things [21]
Iterative double
sided auction scheme
3 7 3 7
7
Blockchain empow-
ered mobile edge
computing [22]
Deep reinforcement
learning method
7 7 3 7
Blockchain em-
powered industrial
Internet of things
[23]
A multi-hop cooper-
ative and distributed
computation offload-
ing algorithm
7 7 3 7
Blockchain based
mobile edge comput-
ing [24]
Stochastic geomet-
ric method and an
alternative direction
method of multiplier
algorithm
7 7 3 7
Blockchain based
cryptocurrency for
computation offload-
ing [25]
Incentive scheme and
a reputation mecha-
nism
7 7 3 7
Proposing a
blockchain based
energy trading
system for rural
residential homes
Analytical pricing
policy, ISNN and
multi-pseudonym
3 3 3 3
120
1.5. Problem Statement121
Recently, blockchain based energy trading systems have been proposed for122
energy users in the smart grids [2, 4]. However, existing schemes depend on123
fixed energy trading pricing policies, auctions, and negotiation methods that are124
ineffective in a network of consumers with a diverse set of needs. Besides, com-125
bining blockchain mining and application intensive tasks, like trading, increases126
the computational cost for resource-constrained energy users. Furthermore, the127
privacy problems of the users are not completely addressed. Therefore, it is128
important to provide an efficient energy trading system that ensures a reduced129
8
computational cost, high privacy and security of energy users, which are ex-130
tremely important for sustainable cities and society.131
1.6. Contributions132
This paper addresses the important issues of privacy and energy trading133
for sustainable cities and society. As the technology for deploying RESs in134
residential homes advances and more people are anticipated to be involved,135
these issues are becoming more significant to be considered in the design of such136
technology. So, a blockchain system for the residential homes to trade energy in137
a distributed way is proposed. In this study, the prosumers are residential homes138
that generate and consume energy locally. The contributions of this paper are139
given as follows.140
1. A blockchain based energy trading system is proposed for the smart and141
sustainable cities with the integration of cloud for computation offloading.142
2. To optimize computation offloading cost for the miner nodes, an improved143
sparse neural network (ISNN) is proposed.144
3. Using the concept of resistance distance [26], a new proof-of-computational145
closeness (PoCC) consensus protocol is designed for miner’s selection and146
block creation.147
4. A novel pricing scheme is proposed to enhance the utility and satisfaction148
of the energy prosumers. It encourages the prosumers to participate in149
energy trading.150
5. A privacy preservation mechanism based on multiple pseudonyms is de-151
veloped. It is used to shield the transactional privacy of prosumers during152
energy trading.153
6. The vulnerability of the proposed system to the Sybil attacks is evaluated.154
The results depict that the system is robust against the attacks.155
7. Extensive simulations are performed to check the scalability of the system156
against increasing number of users.157
9
1.7. Paper Organization158
The remaining paper is organized as follows. Section 2 presents the proposed159
system model and the problem formulation is given in Section 3. Section 4160
provides the privacy preservation for prosumers while Section 5 presents the161
security analysis. Moreover, in Section 6, socio-economic aspects of the proposed162
system are discussed. Section 7 gives the discussion of the simulation results163
and Section 8 concludes the paper.164
2. System Model165
As shown in Fig. 1, the proposed architecture consists of rural residen-166
tial homes, miner nodes, smart meters (SMs), cloud system and consortium167
blockchain. All of the homes have installed SMs to efficiently communicate with168
adjacent peers forming the local communities through direct wireless broadband169
communication technology. The homes use SMs to record information about170
their energy consumption and solar panels to harvest energy, which is stored171
in batteries. The energy need of each home is satisfied with the harvested en-172
ergy that is stored in the batteries. Due to the change in temperature and173
solar irradiation on solar panels [3], the energy generation from RESs of a home174
can become less than the demand. To meet the energy demand, such homes175
purchase energy locally from other homes that have surplus energy via P2P176
energy trading [27]. If the homes do not have surplus energy, then the energy177
is purchased from the main grid. The homes, also known as ordinary homes,178
are connected to access points to get services from the cloud system. In this179
study, ordinary homes have low computational resources and low capabilities to180
perform blockchain mining. The miner nodes are similar to ordinary homes but181
have high computational resources and more capabilities for blockchain min-182
ing. These nodes are responsible for performing blockchain mining tasks and183
providing services like price determination to ordinary homes. Determination184
of price is as issue in a P2P energy trading market, which is labeled as L2 in185
Fig. 1. In this study, the cloud system offers enough computational and out-186
10
Full
Battery Home #1
Solar Panel
Smart
Meter
Full
Battery Home #1
Solar Panel
Smart
Meter
Home #N
Empty
Battery
Home #N
Empty
Battery
Limitations
L1: Security and Privacy
L2: Energy Pricing Policy
L3: Resource Management
Limitations to be addressed
L1
: Lack of Security and Privacy
L2
: Inefficient Energy Pricing Policy
L3
Cloud System
: Problem of Resource Management
Offloading
Computation
Outsourced
Storage
Consortium
Blockchain
L1 and L3
L1 and L2
L1 and L2
L3
#1
#2 #K
Virtual
Machine
Figure 1: The proposed architecture consists of rural residential homes that trade energy with
each other within the consortium blockchain network. During energy trading, the limitations
to be addressed are security and privacy, energy pricing policy and resource management,
which are denoted by L1-L3
sourced storage for miner nodes. In the proposed system, the ordinary homes187
and miner nodes are the nodes of the consortium blockchain. To avoid losses188
during energy transmission between nodes and enhance energy trading in terms189
of quick energy delivery, the energy is exchanged between nodes that are present190
in the same proximity. Note that we do not consider the performance of the191
proposed system in terms of data loss, line interruption, noise and delay. They192
will be taken into consideration in the future. In our system, we consider power193
line communication. Both energy and data are transferred between nodes using194
existing power line infrastructure [28]. Hence, there is no extra cost of electrical195
and communication lines for energy and data transfer, respectively, which make196
the system practical for the real world scenario. A consortium blockchain is em-197
ployed in this paper to provide authentication for the nodes before performing198
energy trading in the sustainable society. Also, a multi-pseudonym mechanism199
is proposed to protect the transactional privacy of homes. Besides, blockchain200
resolves the problems of lack of trust and a single point of failure issues which201
are common in a centralized system [3], labeled as L3 in Fig. 1 .202
11
Inspired by the work in [23], this study assumes that every ordinary home203
performs fewer data processing tasks, excluding the mining task within a pre-204
defined deadline. Two important tasks are considered in this study: the energy205
trading task and the blockchain mining task. This study considers the former206
as a normal task and assumes that the task can be locally performed by both207
ordinary homes and miner nodes, whereas the latter can only be performed us-208
ing the cloud system. Two rationalities are considered in this study concerning209
the task processing activity of an ordinary home. The first rationality is that if210
an ordinary home wants to perform both normal and mining tasks, it uploads211
the tasks to a corresponding miner node, as shown in Fig. 2. For the second ra-212
tionality, if an ordinary home only performs the normal task, then it completes213
the task locally.
Cloud Server
#1
#2
#N
... #k
#1
...
Offload the entire normal
and mining tasks
Ordinary Homes
Blockchain
Managers
Figure 2: Resolving mining centralization problem
214
In this study, if all of the ordinary homes offload tasks through the same215
path, then a lower cost is shared; however, this can result in congestion and216
inefficiency. So, for addressing this issue, we define Bto be the set of miner nodes217
that are willing to engage in block mining and set a deadline for performing each218
normal task. A miner node in Bwith the most computing resources is selected219
as the blockchain manager (BM) to manage the energy trading operations of220
12
all ordinary nodes in the network. In this study, BM executes computationally221
intensive tasks, such as blockchain mining and normal tasks of all ordinary222
homes at a given time slot. In subsequent time slots, there is a possibility223
that BM is unable to execute the tasks because of a large number of mining224
requests from many ordinary homes, labeled as L3 in Fig. 1. For addressing the225
aforementioned issue, data outsourcing and computation offloading mechanisms226
to the cloud system are provided to minimize the overall system cost of BM.227
Also, ISNN is applied before shifting the tasks to the cloud system. In ISNN, the228
Jaya optimization algorithm is integrated into the sparse neural network (SNN)229
for reducing the number of connections between different layers of neurons and230
convergence acceleration.231
2.1. The Proposed Blockchain System232
In this study, an elliptic curve encryption algorithm [29] is employed for233
parameter initialization of the system. Each ordinary home registered with the234
system is given a pair of keys (public pknand private skn) and identity IDn
235
for accessing the system. The pair of keys is used for generating the certificate236
cerfn, which is bound to the wallet waI Dnof the ordinary home. BM stores the237
mapping list {IDn, skn, pkn, cerfn, waI Dn}to the account pool. During energy238
trading, each ordinary home submits waIDnto its corresponding BM for making239
payment and getting incentives. In the proposed system, each miner node in B240
manages and maintains the records of transactions of the corresponding ordinary241
home in the blockchain. The following is the description of each component of242
the proposed blockchain.243
1. Transaction: This is an instance of a record that is digitally signed and244
encrypted by an ordinary home, and broadcasted over the network by BM.245
The hash of the previous transaction is a part of the current transaction246
that forms a block. Several blocks are chronologically chained to create the247
blockchain. In this study, transaction information includes IDn, energy248
token of the actual transaction and timestamp of the transaction. The249
13
transaction is secured and digitally signed by the miner node to ensure250
the authenticity.251
2. Data block: The block is made up of a hash of the current transactions,252
timestamp, hash of the previous block and transaction counter.253
3. Block creation: For each energy trading operation, BM collects the trans-254
action record of a predefined period. A new block is created by BM when255
the old pseudonym expires while the authenticity of a block is verified via256
digital signature and encryption.257
3. Problem Formulation258
This section provides the problem formulation in four sub-formulations. Ta-259
ble 2 describes the variables and parameters used throughout the paper.260
Table 2: Descriptions of variables and parameters used in this paper
Notations Description Notations Description
AAdjacent matrix Ed
j,min Minimum deficit energy
λArrival rate of requests Es
i,min Minimum surplus energy
ρBlockchain incentive Π0
z,l,hModified solution
BLBinary mask of layer LMNetwork model
PrG,b Buying price of grid ζRelative hash of the pro-
sumer
CIjCharges imposed on a buyer
for not remitting the agreed
amount of energy token to a
seller
LF (.) Network loss function
Ccr
kCost of purchasing servers’
resources
nL−1Number of neurons in layer
L−1
Cdt
kCost of data transmission
for offloading tasks
nLNumber of neurons in L
cComputational capacity of
node
mNumber of successful Sybil
identities
14
GConnected graph zNumber of decision variables
αConstant value lNumber of solutions
CdCost of deficit energy P rcr
kPurchasing price of VM
ℵiCredit value of the seller ξPruning rate
Ψ Dataset for the experiment r1and r2Random numbers
PrG,s Selling price of grid LkRequired CPU cycles
dtkTotal transmission rate to
the kth server
SFjSatisfaction of the buyer
drkData transmission rate XSet of nodes
βDecay rate nSize of each layer
Φ Decay time |B|Size of miner nodes in G
DDecision of blockchain man-
ager
ΠL
sSparse matrix
µDeparture rate SSparsity level
XLDense matrix X∗
hSolution with the best value
Dia Diagonal matrix of nodes’
degree
X∗∗
hSolution with the worst
value
τDiscount factor T M T +Total amount of mining
tasks that a miner node k
has to perform in the net-
work after the kth trial be-
fore the start of the Sybil at-
tack
σDrop rate T M T −Total amount of mining
tasks the miner nodes k∈
|B|or any of their Sybil
nodes obtained from the net-
work
Es
iEnergy seller with surplus
energy
iSubscript of energy seller
Ed
jEnergy buyer with deficit
energy
jSubscript of energy buyer
15
γEnergy consumed per CPU
cycles
sSuperscript of energy sur-
plus
EX PdExpected date when the
pseudonym will expire
dSuperscript of energy deficit
FFlag cr Superscript of cloud re-
sources
E(.) Function whose output lies
within R+
P r The proposed price
⊕Hadamard product δk1,k1The Moore-Penrose inverse
of LM
Hblk Hash of blockchain hTime slot
HV M Hash of virtual machine TjTime when energy token is
remitted
ωkHash power of nodes xkin G tjTime slot of energy buyer
Π Hyperparameter to control
the sparsity level S
tiTime slot of energy seller
IDnIdentity of a home NTotal number of ordinary
homes that upload task
through BM
−→
MImproved sparse neural net-
work
RTotal reward of the seller
model
kIndex of blockchain man-
agers
ULnTotal size of data to be up-
loaded
IR Interest rate DLnTotal size of data to be
downloaded
LM Laplacian matrix ITotal numbers of energy sell-
ers
LLayer JTotal numbers of energy
buyers
LqLength of the queue Uj(.) Utility function of energy
buyer
YLine joining any two nodes
in G
WtWaiting time
16
Clocal
kLocal computational task tr Warning message
Ed
j,max Maximum deficit energy kΠk0l0norm of Π
Es
i,max Maximum surplus energy kΠsk0l0norm of Πs
261
3.1. Formulating the Cost of Energy Trading262
The increase in the usage of smart appliances in the sustainable society raises263
energy demand, which overburdens the power grids. Therefore, this study allevi-264
ates the burden on the power grids by proposing a new method of decentralized265
and P2P energy trading for the prosumers, as shown in Fig 3.266
(2) Verify and broadcast the request of the buyer
(4) Generate energy price
Buyer Seller
(7) Generate pseudonym for each transaction
(8) Energy token is sent
(9) Energy is delivered
Consortium
blockchain
Blockchain Manager
Figure 3: Process of energy trading
In the figure, the prosumers act either as energy buyers or sellers according
to the current energy state. They act as energy sellers when they have surplus
energy Es
i, whereas when they are energy deficit Ed
j, they act as energy buyers.
The subscripts iand jdenote the indices of seller and buyer, respectively; while
the superscripts sand ddenote surplus and deficit energy, respectively. In step
(1), the buyer sends an energy request to the blockchain while in step (2), BM
verifies the request and once the verification test is passed, it broadcasts the
request over the network. In step (3), sellers that have surplus energy send
17
responses to the blockchain. Based on the quantity of supply and demand of
seller and buyer, the energy price is calculated in step (4) and the lists of sellers
and energy price are sent to the buyer. The buyer in step (5) selects its preferred
seller based on proximity of location while in step (6), the selected seller accepts
the request of the buyer. For each transaction between a seller and a buyer, a
pseudonym is generated in step (7). The buyer uses an energy token for making
payment to the wallet account of the seller in step (8) and in step (9), seller
delivers the agreed amount of energy to the buyer. If the seller can satisfy the
energy demands of the buyer, then it implies that the buyer can achieve full
energy satisfaction. The satisfaction of the buyer is defined as
SFj=αln Es
i
Cd
+Ed
j,min,(1)
where α∈[0,1] is a constant value that normalizes the buyers’ satisfaction
and Cd=Ed
jP r is the cost of deficit energy. P r =α−τ
ρ
Ed
j
Es
iis the proposed
energy price, τis a discount factor, ρis a blockchain incentive and Ed
j,min is
the minimum deficit energy. Moreover, the satisfaction of a buyer depends
on its Ed
j,min,Cdand Es
i. This means that the Cdis proportional to Ed
j,min.
Besides, the satisfaction of a buyer implies that Ed
jis equal to Es
i, if the following
conditions are satisfied [30].
Ed
j,min ≤Ed
j≤Ed
j,max,
Es
i,min ≤Es
i≤Es
i,max,
I
X
i=1
Es
i=
J
X
j=1
Ed
j,
P rG,b ≤P r ≤P rG,s .
(2)
The conditions show that the maximum energy deficit and surplus are Ed
j,max
and Es
i,max, respectively. Whereas, Es
i,min is the minimum surplus energy. P rG,b
and P rG,s are the grid buying and selling prices, respectively. Iand Jare the
total numbers of sellers and buyers, respectively. The conditions imply that
energy trading is possible only if they are fulfilled. If the energy cannot be sold
locally, then the energy is bought from the grid as P r =P rGEd
j
Es
iwhere PrG,b ≤
18
P rG≤P rG,s . The buyers are risk-averse entities in the energy trading domain.
It means that they are exposed to the uncertainty that needs to be minimized,
i.e., instability of demand and supply. Therefore, the utility functions of both
sellers and buyers are required to determine whether energy trading services are
rendered or not. In this study, we consider two assumptions of a buyer: uses the
same energy token twice to pay for energy to be consumed and refuses to pay
for energy already consumed. Based on the assumptions, the utility of a buyer
is calculated. Besides, the utility function Uj(tj) of a buyer at a given time tj
represents its individual satisfaction or appropriate usage of energy, which can
be expressed in terms of SFj,bdj,CIjand Ed
j.
Uj(tj) = SFjEd
j(tj)−CIjEd
i(tj)bdj,(3)
bdj=
0,if a buyer remits an energy token to the seller,
1,otherwise,
(4)
where the charge imposed CIjon a buyer for not remitting the agreed amount
of energy token to a seller is calculated as follows.
CIj= (Tj−tj)I R, (5)
where Tjis the time when energy token is remitted to the seller and IR is
the interest rate. From Eq. 3, if a buyer’s decision bdj= 0, the cost of not
remitting the said amount of energy token to the seller is zero; otherwise, the
cost is calculated. In this study, an energy token is used instead of conventional
currency. Moreover, two assumptions of a seller are considered in this paper.
The first assumption is that the seller fails to deliver the said amount of energy
on time to the buyer while the second assumption is that the same energy is
sold to more than one buyer. Based on the assumptions, the utility function Ui
of a seller at a given time tiis calculated as follows.
Ui(ti) = RIREs
i(ti)−P rE s
i(ti)+ (1 −R)CIiEs
i(ti)sdi,(6)
19
sdi=
0,if a seller delivers energy on time to the buyer,
1,otherwise,
(7)
where the total number of rewards Ris given as PI
i=1 ℵiΦ, ℵi∈[0,1] is the
credit value of the seller and the time decay is calculated as Φ = exp−β(ζ−j).
β > 0 is the decay rate and ζ=HV M
Hblk [22] is the relative hash of the BM. HV M
and Hblk are the number of hashes of virtual machine (VM) and blockchain,
respectively. Note that Rdiminishes with time until the seller delivers the
said amount of energy to the buyer. The charge imposed CIion a seller for
not delivering the agreed amount of energy to a buyer on time is calculated as
follows.
CIi= (Ti−ti)I R, (8)
where Tiis the time when the agreed energy is not delivered to the buyer within267
the specified time. From Eq. 6, if the seller’s decision is sdj= 0, the cost of not268
delivering the said amount of energy to the buyer is zero; otherwise, the cost is269
calculated.270
3.2. Formulating the Cost of Offloading Task271
In the proposed system, the computational tasks involve blockchain mining
and trading management. In this study, the overall system cost is minimized
by the proposed ISNN. BM performs computational tasks locally if it has the
required computing resources to execute the above mentioned tasks; otherwise,
it offloads them to a cloud server. The decision Dof BM is given as follows [23].
If D= 0, then BM performs computations locally, which means that BM has
the required resources; otherwise, BM purchases resources from the server and
offloads tasks to it. In this study, the cost of computational task is measured in
terms of energy tokens to unify units [22]. The total cost of the computational
task is defined as follows.
C=
Clocal
k,if D= 0,
Ccr
k,if D= 1.
(9)
20
In Eq. (9), the cost of local computational task is defined as [23]
Clocal
k=γP r Lk,(10)
where kis the index of BM. γis the energy consumed per CPU cycles for using
BM’s resources to compute the normal task and Lkis the number of required
CPU cycles of the normal task. In a situation where BM cannot handle the
computational tasks, it requires the assistance of cloud servers to achieve better
performance. In such a situation, a certain price is paid to purchase the servers’
resources and it is defined as [22]
Ccr
k=P rcr
kLk,(11)
where P rcr
kis the purchasing price of VM in token per Gcycle and the superscript
cr denotes cloud resources. After Ccr
kis calculated, the transmission rate that
ordinary nodes can get when they upload tasks to BM is calculated as drk=dtk
N
[23] where dtkis the total transmission rate and Nis the total number of
ordinary homes that upload tasks through BM. The total cost of offloading
tasks is defined as [22]
Cdt
k=Ccr
k+Pn∈N(ULn+DLn)
drk
,(12)
where ULnand DLnare the data sizes for uploading and downloading, respec-272
tively.273
3.3. Formulating the Cost of Mining Task274
In this study, a connected graph G= (B, Y ) with Bvertex and Yedge is
defined. Where B={bm1, bm2, . . . , bmk}is the set of miner nodes and Yis
the line joining any two nodes in G. In PoCC, a miner node having the highest
computing resources is selected as BM, i.e., from a list of sorted miner nodes with
high computational resources such that bm1< bm2<· · · < bmk. Moreover, if
two miner nodes have the same highest computing resources, the calculation of
computational closeness between the miner nodes and any adjacent miner node
is considered. The miner node that has the smallest computational closeness is
21
selected as the new BM. Let ωkbe the hash power of nodes bmkin G, which is
calculated as number of correct nonce
elapsed time . We calculate the Laplacian matrix as LM =
Dia−Awhere Dia is the diagonal matrix of nodes’ degree and Ais the adjacent
matrix such that A= [b{bm1,bm2}]. It implies that if there is a communication
between bm1and bm2, then b{bm1,bm2}= 1; otherwise, b{bm1,bm2}= 0. The
Moore-Penrose inverse [31] of LM is calculated as δbm1,bm1=LM +1
|B|ωk
where |B|is the size of miner nodes in G. Thus, the computational closeness is
defined as
Ccl
k=δbm1,bm1+δbm2,bm2−2δbm1,bm2.(13)
In this study, we observe that the proposed solution is still centralized in the275
sense that it depends on BM, which is known as a mining task centralization276
problem (see Fig. 2). To address the problem, we increase the number of miner277
nodes in the network, which is achieved by offering incentives to any ordinary278
node who is ready to increase its computing resources. Also, a deadline is279
defined for each mining task. Setting a deadline by BM aims at lowering the280
transmission load on mining nodes while keeping it within a reasonable range281
[23].282
The overall system cost is given as Csys
k=Clocal
k+Ccr
k+Cdt
k+Ccl
k.283
3.4. Formulation of the Proposed ISNN284
Fig. 4 shows the framework of the proposed ISNN, which comprises of the285
two most important components: SNN and Jaya optimization algorithm.286
3.4.1. Initializing ISNN287
Motivated by the work in [33], the network model is represented as M=
f(Csys
k,Π) and is parameterized by Π, which is broken down into the dense
matrix ΠL∈RnL−1nL.nL−1and nLrepresent the number of neurons in layers
L−1 and L, respectively. The network is minimized by a loss function, which
is defined as
X
k1,k2∈k
LF f(Csys
k1,Π), Csy s
k2.(14)
22
Set the Algorithm Parameters
Compute the Objective Function
Evaluate Objective Function and Trim
Solution to Get the Best and Worst
Solutions
Accept and Replace
the Previous Solution
Is
the Termination Criterion Met?
Keep the Previous
Solution
Is
the Latter Objective Better than
the Former Objective ?
Yes No
Yes
No
Get the Optimized System Cost
Dense Network
Sparse Network
Obtain Dataset as the Overall System
Cost
Jaya
Optimization
Algorithm
Sparse
Neural
Network
Set the Algorithm Parameters
Compute the Objective Function
Evaluate Objective Function and Trim
Solution to Get the Best and Worst
Solutions
Accept and Replace
the Previous Solution
Is
the Termination Criterion Met?
Keep the Previous
Solution
Is
the Latter Objective Better than
the Former Objective ?
Yes No
Yes
No
Get the Optimized System Cost
Dense Network
Sparse Network
Obtain Dataset as the Overall System
Cost
Jaya
Optimization
Algorithm
Sparse
Neural
Network
Figure 4: The proposed ISNN consists of SNN and Jaya algorithm for minimizing the overall
system cost
ISNN model aims to re-parameterize the dense artificial neural networks (ANNs)
using only a small number of parameters Πs[33]. Πsis broken down into the
sparse matrix ΠL
s∈RnL−1nL, which is a connection between the two consecutive
layers L−1 and L. ISNN model is represented as −→
M=fs(Csys
k,Πs). The
sparsity of network is defined as S= 1 −kΠsk0
kΠk0where kΠk0and kΠsk0are the
l0norm of Π and Πs, respectively [33]. The network is initialized as ΠL
s=
ΠL⊕BLwhere ⊕is the Hadamard product and BLis the binary mask. The
objective function, which is minimized using the Jaya optimization algorithm
[34] is defined as
Π = min E(nL+nL−1)
nL+nL−1,(15)
where Eis a function whose output lies within R+. The probabilistic Π is a
hyperparameter to control the sparsity level S, i.e., when nL≥nL−1a lower
sparsity is obtained; otherwise, a higher sparsity is achieved. The non-essential
connections in each Lare pruned after training and the remaining connections
are described as Πs⊕(BL−−→
BL). Where the binary matrix size of −→
BL=BL, i.e.,
−→
BL⊆BL.||−→
BL||0=ξ||BL||0are the non-zero elements of BLthat correspond
to the largest negative weights and the smallest positive weights of ΠL
s.ξis
the pruning rate. Subsequently, the same number of connections with −→
BLare
23
randomly added to each layer and are defined as ΠL
s+ΠL
r. Where ΠL
r∈RnL−1nL
has the same non-zero values of −→
BL. The non-zero ΠL
rvalues are derived using
a Gaussian noise. Finally, BLis updated using Eq. (16) [33].
BL=
1,if ΠL
s= 0
0,otherwise.
(16)
Note that the creation of new connections follows the trimming process of Jaya288
optimization algorithm [34]. We chose Jaya algorithm for sparsity operation289
over existing evolutionary optimization algorithms [33, 35] because it does not290
depend on the algorithm specific control parameters, such as mutation factor291
and crossover rate. However, population size should be determined carefully.292
3.4.2. Jaya based Optimization Algorithm293
At every time slot h, the objective function is to minimize Π. It is assumed
that there are znumber of decision variables and the number of solutions is
denoted by l. Within the solution set, the solution with the best value is defined
as X∗
h, whereas the solution with the worst value is denoted by X∗∗
h. If we obtain
the value Xz,l,hin the lth solution for the zth decision during the hth time slot,
then we present the modified solution as [34]
X
0
z,l,h=Xz,l,h+r1X∗
z,h− |Xz,l,h|−r2X∗∗
z,h− |Xz,l,h|,(17)
where X∗
z,his the value of the zth decision for the best solution and X∗∗
z,his the294
value of the zth decision for the worst solution. X0
z,l,his the modified solution of295
Xz,l,hwhere r1and r2∈[0,1] are random numbers, which maintain the diversity296
from one solution of the population. The term r1(X∗
z,h− |Xz,l,h|) means that297
X0
z,l,happroaches the best solution while the term r2(X∗∗
z,h− |Xz,l,h|) implies298
that X0
z,l,hdeviates from the worst solution. If the best solution is obtained,299
then X0
z,l,his selected. At each time slot, all of the selected function values are300
retained and are used as the inputs for the next time slots.301
24
Start
Energy status
of buyer\
sellers
Buyers’ energy
demands are
broadcasted by
BM
Sellers
respond to the
requests
Pairs are made
for energy
trading
Energy
price is
computed
Check for abnormal
connection
Penalize the
responsible
prosumer
Prosumers’ engages in
mining tasks
Compute
prosumers’
satisfaction
and utility
Calculate
mining cost
of BMs
Check decision of
BMs
Perform
computations
locally
Compute
offloading cost
and threshold
If offloading <
threshold
Existing VM is
used
New VM is
used
End
No
yes
Yes
False
False
No
True
True
Figure 5: Flowchart proposed blockchain based energy trading system
3.4.3. Algorithm Implementation302
Based on the proposed mechanisms in Algorithm 1 and flowchart 5, sellers303
and buyers submit information about their surplus and deficit energy status to304
the blockchain, respectively. Using this information, BM broadcasts the energy305
demands of the buyers over the network. The sellers that meet the energy re-306
quirements respond to the blockchain. Once there is an established connection307
between the buyers and the sellers, BM computes the energy price. Afterward,308
the satisfaction and utility of the prosumers are calculated. If the prosumers309
wish to perform only normal tasks, then the tasks are completed locally. On310
25
the other hand, if the prosumers wish to perform both normal tasks and mining311
tasks, they upload the tasks to the corresponding BM. The BM checks the com-312
putational resources to decide whether to perform computational tasks locally313
or not. If BM has sufficient computational resources, then computations are314
performed locally; otherwise, BM purchases the server’s resources. Before the315
computation offloading process, BM minimizes Csys
kusing the proposed ISNN.316
When an abnormal connection occurs from either buyers or sellers, a warning317
message, denoted as tr, is triggered and the energy trading transaction is initi-318
ated. The prosumers who initiate the abnormal connections are charged with319
some amount of energy tokens as a fine. In the proposed algorithm, two ra-320
tionalities of prosumers are analyzed. First, prosumers can either be buyers321
or sellers and second, they are resource constrained. Therefore, our proposed322
mechanisms enable prosumers to trade energy trustfully in a P2P fashion.323
4. Privacy Preservation for Energy Prosumers324
The proposed system provides privacy to prosumers from the perspectives325
of the cloud and blockchain based systems. Motivated from [2], the privacy326
mechanism is designed.327
4.1. Privacy Preservation based on Blockchain328
The level of anonymity provided to each prosumer in the blockchain system329
depends on the number of pseudonyms that are generated for each transac-330
tion. It implies that the energy trading trends are completely hidden from331
each prosumer. Prosumers broadcast messages using pseudonyms rather than332
their real identities. In this study, a 14 bytes pseudonym, whose format is333
{IDn, Wt, EX Pd}, is designed. The pseudonym format ensures that the pseudonyms334
generated on the present date are different from the pseudonyms generated on335
the previous date. I Dnis a random string of 7 bytes of length and Wtis the336
waiting time that indicates the length of time for which a new pseudonym337
is created. Also, it is the proportion of requests’ arrivals that are served.338
26
Algorithm 1: Algorithm of the proposed energy trading system
Initialize: Set SNN with Llayers, sparsity S, pruning rate ξ, the maximum number of
iterations dmax, decision of BM D,sand rare the indices of Π
Initialize: Set time h←1, flag F: false and trigger tr: true
if tr == true then
An abnormal connection has occurred, pannalize the responsible prosumer
else
while Fand ∼tr do
for h←1 to Tdo
Get prosumers’ demand and supply information and calculate energy trading price
if Prosumers engage in local energy trading then
Calculate prosumers’ satisfaction and utility
tr: false
else
Calculate mining cost and minimize the overall system’s cost
for s←1 to Ldo
Set k←1 and ΠL
s←ΠL⊕BL
Set ΠL←Normalized(ΠL
s)
for r←1 to Ldo
Set ΠL←Πs⊕(BL−−→
BL) and ΠL
s←ΠL
s+ ΠL
r
end for
Get the best and worst solutions
repeat
Set r1, r2∈[0,1] and modify the solution
k←k+ 1
until k > dmax
end for
if ΠL
s←0then
F: true
end if
if D== 0 then
BM performs computations locally
Compute local computational cost
else
Purchase resources from the server
Calculate computation offloading cost
end if
Calculate computation offloading’s threshold
if Computation offloading <threshold then
An existing VM is used
else
A new VM is used
end if
end if
end for
end while
end if
27
EX Pd= (current date + Wt) indicates the expected date when the pseudonym339
will expire. Note that the sizes of Wtand EXPdare 1 byte and 6 bytes, respec-340
tively.341
In this study, we consider the case when there are several requests for new342
pseudonyms in a queue, which is formulated as the queuing problem using Erlang343
[36]. Given the arrival rate of requests λ, the drop rate σand a departure344
rate µ, the length of the queue is defined as Lq=λ−σ
µ. It implies that the345
exponential survival rate of those prosumers whose requests do not drop out346
during the waiting period is defined as µ
λ= exp−Wtµwhere Wt=1
µln λ
µ. The347
present architecture of blockchain does not support transactions’ reversibility as348
there is a limited time to mitigate or address the occurrence of an attack [37].349
Furthermore, transaction reversal may erode confidence in the system’s fairness,350
but a system that allows significant losses due to bug exploitation would lose351
users. This raises the question of how will the system be able to recover the352
identities of the parties if false information (i.e., the wrong amount of energy353
demand or supply) occurs that needs to be traced. For tracing who provided the354
false information, BM uses the timestamp of the transaction that was created355
and the signature of the node who provided the false information. For identifying356
the node, the signature is verified using the pool of public keys in the system.357
The public key that matches the signature, identifies the owner of the false358
information. Based on the consensus of mining nodes, the node that provides359
the false information is penalized by paying a fine.360
4.2. Privacy Preservation based on Cloud System361
The proposed system enables BM to have two options: perform computa-362
tional tasks locally and request the services of a cloud system for computation363
offloading. Multiple VMs are created at the server side to completely shield364
prosumers’ information. The proposed system calculates the computation of-365
floading threshold to determine whether a new VM should be used or not. The366
configuration of the threshold follows a probability distribution. When BM’s367
computation offloading is less than the threshold, the existing VM is used. Oth-368
28
erwise, a new VM is used. To determine the growth of computation offloading,369
the maximum value is estimated and the threshold is obtained using the average370
method.371
The proposed system is secured by preserving the privacy of prosumers and372
authenticating them. Owing to this, the prosumers are authenticated anony-373
mously. In the proposed system, the prosumers generate both pseudonyms and374
digital signatures for all transactions. On successful authentication, the pro-375
sumers are allowed to trade energy. The privacy of prosumers is preserved376
when a pseudonym is generated. The dynamic generation of pseudonyms for all377
transactions protects prosumers from identity based attacks.378
5. Security Analysis379
This study analyzes a scenario where a miner node creates fake pseudonyms380
for getting more incentives [38]. This kind of attack is known as the Sybil attack.381
Definition 5.1 (Sybil Attack).Considering a graph Gwhere Sybil attack is382
applied to B, i.e., B={bm1, bm2, . . . , bmk} ∀383
k∈ |B|and the modification of Gis G−={B−, Y −}. The Sybil attack occurs384
when a miner node in the network creates different pseudonyms and assigns385
mining tasks to them for increasing incentives. This is important for the miner386
node as long as it receives more incentives from the created nodes than the exact387
amount of incentives received from legitimate block mining.388
A successful Sybil attack increases the incentives of the involved miner nodes389
via block mining within the network. The profit of the Sybil attack is defined390
as follows.391
Definition 5.2 (Profit from Sybil Attack).Let rhoibe the Sybil attack on G
for k > 0and the assignment of a unit of mining task be T Mk. Let T MT +
be the total amount of mining tasks that a miner node khas to perform in the
network after the kth trial before the start of the Sybil attack. Let T M T −be
the total amount of mining tasks the miner nodes k∈ |B|or any of their Sybil
29
nodes obtained from the network. The profit of this sequence of a Sybil attack
is defined as [39]
supT M T +
T M T −, k ∈ |B|,if T M T −6= 0,(18)
if supremum sup is ∞, the Sybil attack is highly profitable for an attacker,392
whereas if sup is greater than 1 and finite, the Sybil attack is weakly profitable393
for the attacker. On the other hand, if sup is less than or equal to 1, the Sybil394
attack is not profitable for the attacker. The proposed system is shown to be395
immune to the Sybil attack.396
Theorem 5.1. The Sybil attack is not a problem for the proposed system.397
Proof 5.1. The proof of Theorem 5.1 is as follows. Suppose there are several398
mining tasks to be performed by miner nodes in the network after kth step of the399
Sybil attack and T M T −for an individual unit of mining task that is allocated400
to a miner node kduring the attack, the capacities of some miner nodes in401
k∈ |B|that have contributed to the network must drop by 1 unit of the mining402
task. This implies that maximum one unit of mining task of T M T −can be403
contributed by a miner node in k∈ |B|after the kth step of the attack. Hence404
T M T +< T M T −. This explains that the proposed system is resistant to the405
Sybil attack with a profit of no more than 1.406
In the proposed system, each pseudonym only contains a single identity of the407
node and it expires once mining and normal tasks are completed. Furthermore,408
the number of blocks in the network does not surpass the number of nodes. To409
this end, a collision attack is resolved for concurrent block mining. This study410
also determines the success probability of a legitimate node in the network to411
select one of the Sybil identities created by the attacker. Let πbe a defined412
threshold for accomplishing the Sybil attack while an attacker has to create more413
than πidentities in the network. In this study, π=c∆ where cis the number414
of computational capacities of nodes and ∆ is the defined consensus threshold.415
We denote mto be the number of successful Sybil identities and Nto be the416
number of legitimate node identities in the network. Then the total pool of417
30
identities comprises N+m−1 identities. Let wbe the number of identities418
that are selected from N+m−1 identities created during the initialization419
step. In each trial of the attack, the success probability is defined as a function420
of the number of Sybil identities generated by the attacker, which is dispersed421
among different valid nodes. The attacker fails to execute the Sybil attack if422
the number of Sybil identities generated by the attacker is less than π. The423
probability P[w] of randomly selecting wSybil identities from the whole pool424
of N+m−1 identities in each trial is defined in Theorem 5.2.425
Theorem 5.2 (Analytical Analysis).If an attacker can create mSybil identities
during the kth trial, then the probability of randomly selecting wSybil identities
from the pool of N+m−1is defined as
P[w] = m
wN−1
N−w
N+m−1
N.(19)
Proof 5.2. The proof of Theorem 5.2 is trivial from the fact that wfollows a426
hypergeometric distribution where m
w=m!
w!(m!−w!) is a binomial coefficient.427
Theorem 5.3 (Numerical Analysis).Given that wSybil identities are created
by an attacker have been chosen from mSybil identities after the initialization
step. Then the probability of having atleast wSybil identities in a network is
defined as
P[w] = c
wpw+ (1 −p)c−w,(20)
if m≤π, an attacker is not successful to perform Sybil attack. Hence,428
P[w] = 0. Besides, we consider the limit N, m → ∞ and m
N=pis fixed. For429
the analysis, P(w) is determined for each identity created by attacker in the430
network.431
Proof 5.3. For the proof of Theorem 5.3, given the number of nodes in m,
the capacity of each node and the overall number of chosen identities for atleast
31
π+ 1 Sybil identities will be
P[w] = m
wN−m
c−w
N
c=m!
(m−c)!c!.(N−m)!
(m−c)!(N−m−c+w)!
.c!(N−c)!
N!=c
wm(m−1)(m−2) . . . (m−w+ 1)
N(N−1)(N−2) . . . (N−w+ 1).
(N−m)(N−m−1)
(N−w)(N−w−1) . . . (N−m−(c−w) + 1)
(N−c+ 1)
=m(m−1)(m−2) . . . (m−w+ 1)
N(N−1)(N−2) . . . (N−w+ 1) ≈mw
Nw=pw,
if wis fixed, then mand Ndiverge while cis finite.
=(N−m)(N−m−1) . . . (N−m−(c−w) + 1)
(N−w)(N−w+ 1) . . . (N−c+ 1) ≈
(N−m)c−w
Nc−w= (N−m
N)c−w= (1 −p)c−w,
(21)
considering the binomial distribution, we have
lim
N,m→∞,m
N=pc
wpw(1 −p)c−w,(22)
if the limit holds, Theorem 5.3 is satisfied. Moreover, if w > c, it will be
considered in our future work. Considering the condition w≤c, then P[w+ 1]
is defined as
P[w+ 1] = m
m
X
w=π+1
w
X
m=π+1 m
∆N−1
N−wm
wN−w
c−w
N+m−1
NN
c.(23)
For security analysis, a scenario is considered where a miner node generates fake432
identities to get more tasks in order to increase the incentives. The rest of the433
scenario is the same as mentioned in algorithm 1 and section 3.4.3. Moreover,434
the system is blockchain based, so jamming, hacking, fraud and theft are not435
possible by a single user. As all the nodes use pseudonyms for transactions;436
hence, they cannot cooperate to hack or jam the network. Fraud and theft437
are not possible because the transactional records are saved in a decentralized438
manner in blockchain and each transaction is confirmed by the consensus of439
nodes. Moreover, unauthorized access is prevented by registering each node on440
the network with a unique identity.441
32
6. Socio-economic Impacts442
The proposed system is a blockchain based energy trading system. Blockchain443
is a disruptive technology. It is changing the ways of financial dealing. Using444
blockchain, two parties can exchange anything without knowing each other and445
involving a third party. In short, it is a trustless technology where smart con-446
tracts take care of flawless dealings. The proposed system is considered to have447
a revolutionary impact on sustainable cities and societies. The prominent im-448
pact of the system is on the economy because the transactional cost in the449
blockchain is significantly lower than the traditional transactions. Other socio-450
economic impacts of the proposed blockchain based system include transparency,451
fairness, simplicity and regulation of rules while performing transactions. From452
the economical point of view, it is a decentralized system and leans towards a453
democratic system. Hence, it is a threat to the monopoly of the utility com-454
panies. Moreover, the low transactional cost of both data storage and trading455
between parties results in economic and financial growth. The data stored in456
the blockchain is immutable, which results in data integrity. Therefore, the457
data stored on the blockchain is reliable and consistent. From the social point458
of view, all users or blockchain nodes get fair incentives and are treated equally.459
Moreover, all the transactions are automatic and controlled by smart contracts,460
so there are minimum or no disputes between users. Every legitimate and au-461
thorized user has the freedom of performing transactions and trading with other462
users without any discrimination. Furthermore, the trustless nature of the sys-463
tem makes it suitable and hassle-free for the users.464
It is a known fact that nothing is flawless. Every technology or innovation465
has some limitations. Same is the case with a blockchain based system. In spite466
of all the above discussed advantages and positive socio-economic aspects, the467
proposed system too has some limitations. As mentioned above, the blockchain468
is an immutable technology, which ensures data integrity; however, if a false469
transaction is added or users want to reverse their transactions, the committed470
transactions are irreversible. Moreover, the blockchain is highly dependent on471
33
technology and complex to be deployed. So, its adaptability is also limited.472
One of the major challenges of the blockchain is dispute resolution between473
two parties. Although, rules for known disputes are defined in the system,474
however, solving a unique dispute between two parties is only possible with the475
involvement of a third party.476
7. Simulations and Results477
The numerical results are used to test the performance of the proposed478
mechanisms in this section. The proposed solution is implemented in Python479
3.7, with details about the cloud system taken from [22, 23]. Moreover, the480
simulation setup is described as follows. In our scenario, prosumers within the481
same proximity are considered and they communicate with each other via SMs482
and the total number of seller and buyer prosumers is 200. However, this study483
is not limited to the above mentioned number of prosumers, it can accommodate484
an infinite number of prosumers (Section 7.4). It is assumed that each seller485
has surplus energy between 75 MWh and 220 MWh and each energy deficit486
prosumer requires energy within [20, 60] MWh [41]. Other parameters used for487
the simulations are provided in Table 3 [22] while some are randomly generated488
if not stated. We consider 5 VMs and the initial reward that is given to a489
miner for completing a task is 30 tokens. To design ISNN model, the network490
structure is given as [1,1000,1] with 1 input layer, 1000 dimensions and 1 output491
layer. The pruning rate ξ= 20 is used to control the sparsity of the network492
and the dimension of observations is 203×3312 [33]. For the Jaya optimization493
algorithm 1000, and the maximum and minimum limits of population values are494
1 and 0, respectively.495
7.1. Evaluation Metrics496
The following metrics are used for evaluating the proposed system.497
1. System cost: It is used as a metric to assess the proposed algorithm’s498
performance. A lower system cost means that the system is performing499
well.500
34
Table 3: Simulation parameters
P V P V
α0.7 Lk[20, 40] Gcycles
τ0.3 P rcr
k[1,5] ×10−6tokens/Gcycles
ρ0.7 dtk250 kbps
Tj3ULk[100, 1000] kB
tj2λ0.6
IR 0.5 σ0.2
β[1, 5] µ0.5
R[0, 1] ℵ[1 ×10−6,1×10−5]
HV M [20, 100] MHash/s I200
Hblk [1 ×103, 1 ×105] GHash/s J200
P: Parameters, V: Values.
2. Number of epochs: The proposed algorithm’s convergence rate and com-501
putation complexity are determined by the number of epochs. The algo-502
rithm converges better if the number of epochs is less.503
3. Trading cost: It is used to assess the efficacy of a pricing policy plan. A504
lower trading price corresponds to a more favourable purchasing strategy.505
In this study, the limitations to be addressed are mapped to the proposed506
solutions, which are then validated by simulation results. The mapping of the507
proposed solutions to the limitations to be addressed is presented in Table 4.508
The table shows how the proposed solutions are validated.509
To overcome the limitation L1, blockchain is used to secure the prosumers’510
transactions and also provide trust between them. The privacy of each node’s511
transaction is achieved using the proposed multi-pseudonym mechanism.512
7.2. Evaluation of the Blockchain based Energy Trading System513
In this subsection, validations of the solutions to L2 are presented. To514
evaluate the performance of the proposed pricing policy, other existing pricing515
policies, such as time of use (ToU), critical peak pricing (CPP) and real-time516
35
Table 4: Validating solutions based on identified problems
Limitations to be ad-
dressed
Solutions proposed Validations
L1: Lack of security
and privacy
We have used consor-
tium blockchain and
cloud for achieving
security. Multi-
pseudonym is used for
privacy preservation
We have used multi-
pseudonym, anony-
mous authentication
and blockchain
L2: Inefficient energy
pricing policy
An analytical energy
pricing policy based on
supply and demand ra-
tio is employed
Figs. 6, 7, 8 and
9 show the efficiency
of the proposed energy
pricing policy
L3: Problem of re-
source management
An ISNN with Jaya op-
timization algorithm is
used
Figs. 10, 11, 12, 13, 14
and 15 validate the effi-
ciency of the proposed
ISNN
pricing (RTP) are used [3, 40]. As shown in Fig. 6, the proposed pricing policy
0 5 10 15 20 25
Time (hour)
0
20
40
60
80
100
120
140
Price ($ per MW)
Proposed
ToU
CPP
RTP
Figure 6: Analysis of energy price
517
36
has the minimum price for each hour as compared to its counterpart policies.518
The figure shows that from 11th to 16th interval, the electricity price using519
CPP is highest. The second peak in electricity price is observed in case of RTP.520
However, the peak of RTP during 6 to 10 is lower than CPP and the difference521
is huge. Moreover, the pricing peak of ToU is even lower than RTP. The results522
of the proposed pricing scheme depict that its price is lowest in almost all of the523
intervals. It implies that there is a minimum difference between energy supply524
and demand, which ultimately leads to a stable energy trading market.525
0 5 10 15 20 25
Time (hour)
0.0
0.2
0.4
0.6
0.8
1.0
Average Satisfaction
Proposed ToU CPP RTP
Figure 7: Analysis of prosumer’s satisfaction
Fig. 7 shows the buyers’ average satisfaction for 24 hours. From the figure, it526
is observed that our proposed pricing policy achieves the maximum satisfaction527
of approximately 90% as compared to 58% for ToU, 70% for CPP and 63% for528
RTP. It implies that on reduced energy price, buyers achieve a higher degree of529
satisfaction. However, it is observed from Fig. 6 for CPP that during the hours530
11 to 16, the electricity price is the highest while the satisfaction is relatively531
high in Fig. 7. It means that the cost of energy is low because of moderate532
energy demand. The same is the case with RTP during the hours 7 to 10.533
Moreover, the satisfaction of buyers implies that energy demand is equal to the534
energy supply. It also implies that the buyers’ satisfaction is influenced by the535
ability of the sellers to meet their energy demands with a minimum energy price.536
However, this satisfaction cannot be used as either prosumers’ profit or utility.537
37
Therefore, the prosumers’ utility is analyzed in two cases as follows.
5 10 15 20
Time (hour)
0
200
400
600
800
1000
Buyer Average Utility
Proposed ToU CPP RTP
Figure 8: Evaluation of the utility of sellers
538
In the first case, the buyers’ average utility values are given in Fig. 8. From539
the results, it is observed that our proposed pricing policy achieves high utility540
values as compared to other existing policies. The utility function shows the541
relationship between buyers’ satisfaction and their energy demands. Depending542
on the utility values, buyers decide whether to engage in energy trading with543
sellers or not. Once the buyers are unable to fulfill the energy need from the544
sellers, they purchase the required amount of energy from the main grid. More-545
over, in our case, we have no negative utility values, which implies that there546
are no cost negations. Besides, positive utility values may imply that the utility547
is proportional to satisfaction.548
In the second case, Fig. 9 shows the average utility values of the sellers.549
From the figure, it is observed that our proposed pricing policy achieves better550
and higher utility value as compared to other existing policies due to low energy551
price. Moreover, sellers’ satisfaction is determined by the number of rewards552
they received. Therefore, the utility values of sellers are proportional to their553
rewards. Hence, the proposed pricing policy is effective for energy trading in a554
sustainable society.555
38
5 10 15 20
Time (hour)
0
20
40
60
80
100
Seller Average Utility
Proposed ToU CPP RTP
Figure 9: Evaluation of the utility of buyers
7.3. Evaluation of the Proposed ISNN Model556
In this subsection, validations of the solutions to L3 are presented. The557
proposed ISNN model aims to converge at a minimum number of epochs. Con-558
sidering the proposed mechanisms in Algorithm 1, the convergence of the system559
is important to determine whether the sparsity of the network is achieved or560
not. Moreover, the network is said to achieve convergence when the learning561
curve becomes smooth and flat; therefore, the loss function is plotted against the562
number of epochs. In Fig. 10, the learning curve converges at 1 ×105epoch. It563
implies that the learning curve achieves optimality within an acceptable number564
of epochs.565
Fig. 11 shows the convergence analysis of the computation offloading cost.566
It is observed that the initial cost is 0.957 token per kB. As the number of567
epochs increases, the computation offloading cost increases to a peak of 1.0568
token per kB and then reduces afterwards due to optimization. It implies that569
the proposed system is efficient to minimize the computation offloading cost at570
an acceptable number of epochs.571
To evaluate the performance of the proposed system under different sizes of572
data, i.e., 100-1000 kB, two performance parameters, such as average computa-573
tional cost and data transmission time, are considered. For the comparison with574
the existing schemes, deep reinforcement learning combined with genetic algo-575
39
0 1 2 3 4 5
Number of Epochs 105
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Loss
Figure 10: Convergence analysis of ISNN
0 10 20 30 40 50
Number of Epochs
0.95
0.96
0.97
0.98
0.99
1
Offloading Cost (Token/kB)
Predicted
Target
Figure 11: Convergence analysis of offloading cost
rithm (DRGO) [22], and sparse evolutionary training and multi-layer perceptron576
(SET-MLP) [33] are used.577
It is observed from Fig. 12 that our proposed scheme achieves the lowest578
average computational cost for long term decision making as compared to DRGO579
and SET-MLP schemes due to Jaya optimization algorithm. The figure shows580
that the system’s average computational cost increases with the increase in the581
size of the data to be uploaded.582
Fig. 13 shows the average data transmission time with different sizes of data.583
It is obvious from the result that the average data transmission time increases584
with increase in the sizes of data. The results depict that our scheme performs585
40
100 300 500 700 900
Uploading Data Size (kB)
1.2
1.4
1.6
1.8
2
2.2
2.4
Average Cost (Token)
Proposed
DRGO
SET-MLP
Figure 12: Analysis of average system cost
100 300 500 700 900
Uploading Data Size (kB)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Average Transmission Time (s)
Proposed
DRGO
SET-MLP
Figure 13: Analysis of average transmission time
better than DRGO and SET-MLP schemes based on the following reasons. Both586
DRGO and SET-MLP use genetic algorithm that requires algorithmic specific587
control parameters like mutation factor and crossover rate for tuning. These588
parameters affect the processes of exploitation and exploration. Contrarily, our589
proposed scheme uses Jaya algorithm that does not depend on algorithmic spe-590
cific control parameter; however, it requires information related to population591
size only. Besides, its data transmission time is the lowest as compared to other592
schemes.593
Fig. 14 shows the comparison of average system cost, transmission cost594
and computation offloading cost under different sizes of data to be uploaded.595
41
100 300 500 700 900
Uplaoding Data Size (kB)
0
0.5
1
1.5
2
Average Cost (Token)
System Cost
Offloading Cost
Transmission Cost
Figure 14: Cost evaluation of the proposed system
It is observed from the figure that the average system cost is the highest as596
compared to computation offloading cost and data transmission cost. Besides,597
average system, data transmission and computation offloading costs are affected598
by different sizes of data.599
12345
Number of VMs
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average Cost (Token)
0
2
4
6
8
10
MHash/s
105
Mining Cost
Blockchain Hash
Figure 15: Cost evaluation of blockchain
Fig. 15 shows the average cost for mining process of blockchain and hash600
under different VMs. It is observed that each VM has distinct mining and hash601
cost in tokens. However, VM4 shows the lowest mining and hash cost due to602
the calculation of computational closeness.603
42
Table 5: Cost (Token) comparison of the proposed system for scalability evaluation
Average
data size
(kB)
N=200 N=400 N=600 N=800
100 1.29 2.46 3.76 5.02
200 1.35 2.68 4.05 5.21
300 1.4 2.9 4.2 5.32
400 1.45 2.943 4.31 5.43
500 1.48 3.1 4.35 5.49
600 1.56 3.02 4.68 6.14
700 1.6 3.25 4.8 6.38
800 1.65 3.29 4.94 6.7
900 1.72 3.39 5.08 6.87
1000 1.81 3.64 5.41 7.04
Average 1.499 3.0673 4.558 5.96
7.4. Performance Evaluation in Terms of Scalability604
A system is considered scalable if increasing values of one system parameter605
have a linear or no impact on other parameters. To ensure the scalability of606
the proposed system, the behavior of computational time and cost parameters607
is monitored against different numbers of prosumers: 200, 400, 600 and 800.608
Table 5 shows that under different numbers of prosumers, the increase in system609
cost (tokens) is linear. The first column of the table contains different sizes of610
data that are uploaded and the next four columns show the system cost against611
different numbers of prosumers. The average cost of prosumers is also computed.612
It can be observed from the results that in the case of 200 prosumers, the average613
cost is 1.499 tokens. When the number of prosumers is increased to 400, the614
average system cost also increased up to 3.0673. Furthermore, for N= 600 and615
N= 800, the increments in system cost are 4.558 and 5.96, respectively. The616
experimental values show that there is no abrupt change in the system when617
43
Table 6: Transmission time (s) comparison of the proposed system for scalability evaluation
Average
data size
(kB)
N=200 N=400 N=600 N=800
100 0.01 0.021 0.03 0.039
200 0.03 0.05 0.091 0.11
300 0.045 0.10 0.135 0.178
400 0.05 0.11 0.17 0.21
500 0.1 0.19 0.32 0.4
600 0.12 0.21 0.37 0.50
700 0.15 0.28 0.44 0.61
800 0.2 0.38 0.61 0.78
900 0.23 0.42 0.69 0.90
1000 0.25 0.47 0.76 0.95
Average 0.1185 0.2291 0.3616 0.4677
the number of users is increased. Similarly, Table 6 shows the transmission618
cost of the proposed system against different numbers of prosumers: 200, 400619
and 800. The first column shows the average data size of prosumers and the620
next three columns show different numbers of prosumers. The average data621
transmission time (s) is also computed to demonstrate the effect of the increasing622
number of users. The results depict that the increase in data transmission time623
is linear. The transmission time increases with prosumers because the data to624
be transmitted is also increasing with each prosumer. Hence, the results prove625
that the proposed system is scalable.626
Energy management is important for smart and sustainable cities. With627
increases in computational requests, the energy consumption also increases.628
Moreover, efficient utilization of resources has a great impact on energy con-629
sumption. Table 7 shows the resource utilization in percentage and the corre-630
sponding energy consumption of a processor. It is observed that initially, the631
44
Table 7: Average energy consumption (joules) comparison of the proposed scheme with respect
to resource utilization
Resource utilization Energy consumption
(jouls)
10% 0.07
20% 0.1
30% 0.18
40% 0.2
50% 0.22
60% 0.3
70% 0.4
80% 0.53
90% 0.8
100% 1.4
Table 8: Average energy consumption (joules) comparison of the proposed system for scala-
bility evaluation
Average
data size
(kB)
N=200 N=400 N=600 N=800
200 0.2 0.41 0.59 0.81
250 0.3 0.61 0.88 1.23
300 0.4 0.78 1.25 1.79
350 0.6 1.23 1.99 2.62
400 0.9 1.91 2.79 3.91
450 1.35 2.82 4.38 5.7
500 1.91 3.85 5.88 7.95
Average 0.8086 1.83 2.794 3.529
45
energy consumption shows linear behavior with resource utilization. However,632
when the resource utilization reaches 70%, the increase in energy consumption633
becomes non-linear. The abrupt increasing behavior is observed, which indi-634
cates that when a processor is overburdened, it consumes more energy than635
usual. So, computation offloading has great importance. Similarly, Table 8636
shows the energy consumption of the proposed scheme when the numbers of637
users increase from 200 to 800 with step sizes of 200. The table shows that638
the energy consumption increases non-linearly when data size increases. The639
average is also taken for different numbers of prosumers. On comparing the640
average energy consumption values, it is observed that the change in energy641
consumption is high. The reason is that 200 users are increased on each step,642
so the corresponding requests also increase with the same rate and so does the643
data size. Moreover, the resource utilization also increases, which results in high644
energy consumption. The results depict the trade-off of the proposed system.645
However, as mentioned above, for efficient resource utilization and reduce the646
computational burden from the processor, computation offloading is employed647
in the proposed system. Hence, the scalability of the system is not affected by648
high energy consumption.649
7.5. Security Analysis650
This study evaluates the Sybil attack by performing extensive numerical sim-651
ulations, which are compared with analytical results. The probability of success652
for selecting Sybil identities generated by an attacker is evaluated regarding653
block hash rate. Moreover, the block hash rate is computed as the ratio of the654
hash power of the attacker to the overall hash power of the network. For the655
analysis, the different numbers of Sybil identities (m) are considered. This study656
begins by analyzing the network of N= 14 nodes with a sample of m= 4 nodes657
and the capacity cof 3 nodes. Fig. 16 shows the probability of a successful Sybil658
attack using the aforementioned parameters. It is observed that as the block659
hash rate increases, the analytical and numerical results do not align with each660
other. This occurs as a result of π. Moreover, both numerical and analytical661
46
results satisfy Theorem (5.2) and (5.3).662
0 0.2 0.4 0.6 0.8 1
Adversary Hash Rate
0
0.1
0.2
0.3
0.4
0.5
Probability of Success
Analytical Result
Numerical Result
Figure 16: Sybil attack when N= 14 and m= 4
0 0.2 0.4 0.6 0.8 1
Adversary Hash Rate
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Probability of Success
Analytical Result
Numerical Result
Figure 17: Sybil attack when N= 200 and m= 4
As we increase the number of nodes up to 200 (N= 200) as shown in Fig.663
17, it is obvious that the analytical and numerical results align with each other.664
This means that the proposed analytical results follow the same pattern as nu-665
merical results. Fig. 18 shows the patterns of the probability of a successful666
Sybil attack as the number of samples increases. For this scenario, the capacity667
of nodes in mis c= 100 and different samples m, such as 4, 8 and 10 are consid-668
ered. It is observed that as the number of samples (m) increases, the probability669
of a successful Sybil attack reduces. This means that the proposed system can670
47
0 0.2 0.4 0.6 0.8 1
Adversary Hash Rate
0
0.1
0.2
0.3
0.4
0.5
Probability of Success
m=4
m=8
m=10
Figure 18: Sybil attack when N= 200, and m= 4,8 and 10
tackle Sybil identities that are created by an attacker. In normal cases, when the671
number of Sybil identities increases, it increases the probability of the selection672
of more Sybil identities from the selection pool N+m-1. However, increasing673
the number of identities involves high computational power to complete multi-674
ple tasks in the proposed system. Furthermore, a time limit is also defined for675
task completion. The computational power of the miner nodes is not unlimited.676
Moreover, getting cloud resources involves additional costs. Hence, increasing677
the Sybil identities weakens the attacker’s computational power and the prob-678
ability of success decreases. Fig. 18 proves that the proposed system is robust679
against Sybil attacks.680
8. Conclusion681
This paper proposes a secure energy trading system based on blockchain682
for residential homes. Firstly, an analytical energy pricing policy is designed683
to solve the problem of existing energy pricing policies in a distributed en-684
ergy trading environment. Secondly, the security of prosumers is ensured us-685
ing the consortium blockchain. The privacy of prosumers is preserved in the686
blockchain using the proposed multi-pseudonym mechanism. In this mecha-687
nism, each transaction requires a distinct pseudonym. Thirdly, a strategy is688
proposed that allows prosumers to either compute tasks locally or offload them689
48
to the cloud system. In the strategy, an ISNN is designed to achieve compu-690
tation offloading efficiency. It also integrates the Jaya optimization algorithm,691
which reduces the number of connections between different layers of neurons and692
speeds up the error convergence rate. The strategy ensures the scalability of the693
system.. At last, in the cloud system, a new VM is only used when the com-694
putation offloading task is greater than its defined threshold. Security analysis695
shows that the proposed system prevents Sybil attacks. Simulation results val-696
idate the performance of the proposed scheme. From the results, it is observed697
that the proposed pricing policy shows the least average energy price and the698
highest average maximum utility as compared to ToU, CPP and RTP pricing699
policies. Also, a buyer achieves approximately 90% average satisfaction using700
the proposed pricing policy as compared to 58% with ToU, 70% with CPP and701
63% with RTP. Under different sizes of data, ISNN has the least average compu-702
tational cost and data transmission time as compared to DRGO and SET-MLP703
schemes. Furthermore, the convergence of the proposed scheme is achieved at704
1×105epoch. Besides, extensive simulations are performed to check the scala-705
bility of the system under increasing number of prosumers. The results depict706
that the system is scalable because on increasing the number of prosumers, the707
change in transmission cost and system cost is linear. Contrarily, the increase708
in energy consumption becomes nonlinear after a certain point. It is considered709
as the trade-off of the system. However, the proposed work tackles this issue710
by computation offloading where BM offloads the computational tasks to cloud711
server. Hence, scalability of the system is not affected.712
The robustness of the proposed PoCC will be thoroughly investigated in713
the future to increase network throughput. We also plan to partner with a714
utility operator to incorporate and test our proposed system’s prototype. This715
will allow us to assess its real-world usefulness and scalability more accurately.716
Moreover, the proposed system will be tested in inter-blockchain communication717
scenario where energy will be traded among prosumers of different communities.718
49
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