Electrical Power and Energy Systems 137 (2022) 107786
Contents lists available at ScienceDirect
International Journal of Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
The impact of cyber network configuration on the dynamic-thermal failure
of transformers considering distributed generator controller
M. Hamzeh , B. Vahidi *
Department of Electrical Engineering, Amirkabir University of Technology, Tehran 1591634311, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords:
Distribution transformers
Cyber-physical system
Distributed generator
Generator controller
Reliability
Transformers as one of the valuable assets of the power system, have a remarkable role in the power system
stability. Understanding the effective parameters on the transformer’s failure is so vital to reduce the transformer
outages. On the other hand, with improvement and extension of intelligent systems, identifying the effective
parameters on the security of smart networks is of considerable importance. This paper clarifies the relation
between the cyber network configuration (CNC) and the failure probability of transformers due to the distributed
generator controller. Also, a novel method is proposed to determine the effects of various cyber network con­
figurations on the failure probability of transformers and also select the best CNC to maximize the reliability of
the cyber-physical system. Optimized configuration should maximize the data connection between cyber ele­
ments, particularly cyber elements that have cyber-power interdependency with the critical transformers in the
power network. Results indicate that the improper CNCs can increase the failure probability of transformers and
consequently it leads to increment of expected energy not supplied (EENS) of the power system. The proposed
method is implemented on the real pilot power test system.
1. Introduction
Distribution transformers are one of the essential parts and valuable
assets of the power system [1]. Outages of transformers can cause
financial penalties for the power network that it can be remarkably high
[2]. Financial burdens of transformers failure are not only because of
repair or replacement of failed transformers, but also, they contain
revenue loss of expected energy not supplied (EENS) to the consumers.
So the reliability of the power system can be jeopardized by the trans­
former outages. The failure rate of transformers can reach (12%-17%) in
some developing countries such as India and if not reduced it can lead to
significant damages to the power network [3]. Therefore, analyzing the
different parameters can affect the transformer’s failure is so important
in the asset management of the bulk power network.
Winding failure is one of the main reasons for transformer’s outages
[4]. Winding thermal stress can limit the loading capacity of a trans­
former and it is the main reason for a transformer’s aging [5]. Hot spot
temperature (HST) of winding is the main parameter in dynamicthermal aging failure modeling of transformers [6]. When the HST of
transformers increases, especially in overloaded conditions, the insu­
lation deterioration of the transformer accelerates. To control the HST of
transformers, the loading of transformers should be managed according
to dynamic-thermal modeling of transformer [7].
Some papers investigate the approaches to reduce the winding HST
and dynamic-thermal failure of transformers. In [8], the effects of
different penetrations of DG units on the transformer’s dynamic-thermal
failure and the reliability of a power system are investigated. The novel
charging schedule of plug-in hybrid electric vehicles is proposed to
reduce HST-dependent aging failure of distribution transforms [9].
Soleimani et. al describe the effects of uncoordinated charging of electric
vehicles on distribution transformers in the city of College Station,
Texas, USA [10]. This paper illustrates that electric vehicles charging
can cause overload conditions of transformers and consequently it can
jeopardize the life of transformers.
On the other hand, a combination of power system and cyber
network that consist of control, protection, monitoring and communi­
cation infrastructures lead to creating cyber-physical system [11–12].
With the more expansion of intelligent systems and the growing interest
of attackers to infiltrate them, the importance of comprehensive risk
assessment of the cyber-physical system is increased [13–14]. Reliability
of cyber network remarkably affects the reliability of power one so
identifying the interdependency between cyber and power systems is so
* Corresponding author.
E-mail address: vahidi@aut.ac.ir (B. Vahidi).
https://doi.org/10.1016/j.ijepes.2021.107786
Received 14 August 2021; Received in revised form 12 October 2021; Accepted 6 November 2021
Available online 17 November 2021
0142-0615/© 2021 Elsevier Ltd. All rights reserved.
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
Fig. 1. Generator controller from deep see electronic (DSE) manufacture and it’s relation to the gen. breaker and switch of cyber network.
important to evaluate the reliability of the smart system [15]. Cyberpower interdependency (CPI) means that mal- operation in the cyber
network can cause abnormal performance in the power one [16–17]. In
[18–19], the effects of direct cyber-power interdependency (DCPI) and
indirect cyber-power interdependency (ICPI) are studied on the smart
system performances.
As discussed in literature review, the question is that cyber network
has any effect on the transforms failure probability or not. Another
question is that different cyber networks have different effects on the
distribution transformers failure or not. To answer these questions, the
accurate relation between the cyber elements and the distribution
transformers should be identified. This paper tries to answer these
questions precisely and proposed a novel method to reduce the distri­
bution transformers outages in the smart power network.
The remainder of this paper is organized as follows. Section II in­
troduces problem description. The different cyber power in­
terdependencies and transformer dynamic-thermal model are discussed
in section III and IV, respectively. In section V, the proposed optimiza­
tion method is introduced. Finally, the case study and conclusions are
presented in Sections VI and VII, respectively.
3. Cyber-power interdependency
The Cyber network and power one have interdependencies to each
other that means that Mal operation in one network can cause a problem
in the normal operation of another network. If one of the cyber elements
fails, some power elements can be failed because of cyber-power inter­
dependency. The interdependencies between the cyber network and the
power one are divided into four different relations [19]. If the cyber
element failure causes the direct failure in a specific power element, the
direct element-element interdependency (DEEI) is happened. For
example, failure in one generator controller of the cyber network can
bring failure to specific circuit breaker of the power network that has
direct relation to it.
If a failure in the cyber network causes failure in a specific element of
the power network, the direct network element interdependency (DNEI)
is occurred.
Indirect element-element interdependency (IEEI) means that failure
in cyber elements cannot cause direct failure in power elements, but it
gradually makes harmful effects on power element performance.
If a failure in the cyber network cannot directly make failure in
power elements, but it gradually causes adverse effects on power ele­
ments, it is known as indirect network-element interdependency (INEI).
In this paper, it is assumed that generator controller is from a Deep
see electronics (DSE) manufacture. It should be mentioned that the
generator controller could be from any other manufacturer (for
example, CATERPILLAR, CUMMINS, COMAP, WOODWARD, etc.).
Generator controller, is an important element that can deeply control
the generator unit. One of the generator controllers and it’s relation to
generator breaker as power network element and switches as cyber
network element is depicted in Fig. 1. DSE is an intelligent element that
consists of single-set and multi-set generator control solutions, mains
(utility) protection relays, digital automatic voltage regulators (AVR’s),
remote communications devices and expansion modules [20]. Different
ports of DSE such as generator current, generator voltage, fuel, crank, oil
pressure, water temperature, governor, AVR, ECU, inputs and outputs
are demonstrated in Fig. 1. Also, the port of input data from switch (as
one the cyber element), output data to switch and command signal to
generator breaker is shown in this figure.
2. Problem description
This paper concentrates on risk assessment of smart grids individu­
ally considering the dynamic-thermal aging failure of transformers with
taking into account different cyber network configurations. Also this
paper introduced a novel method to select the best configuration of
cyber configuration to reduce the aging failure of transformers and
improve the reliability of cyber-physical system.
Cyber network configuration is one of the major variables on the
reliability of the power system. A reliable cyber network with maximum
data connection entails a more reliable power network. If one generator
controller of a cyber-network fails or the data flow between one
generator controller and servers be disconnected, disconnection com­
mand will be sent to generator breaker by the generator controller. It
causes a failure in specific DG in the power network that directly has CPI
to this generator controller. DG outage raises the loading of transformers
and it gradually increase the failure probability of them. So attention to
some cyber elements that can increase the failure probability of trans­
formers is vital in the aspect of power system reliability.
This paper tries to emphasize the impacts of cyber network on the
transformer failure probability and it proposed a novel method to select
best CNCs to maximize the data flow through the cyber elements espe­
cially in the elements that have directly connected to the critical
transformers. This method can improve the reliability of cyber-physical
system, remarkably.
4. Transformer dynamic-thermal modeling
Time and temperature are the main parameters of transformer’s
insulation deterioration. Based on IEEE Std C57.12.60–2020 [5], the
dynamic thermal failure of the transformer is affected by hot spot tem­
perature (HST) of the transformer winding. The ultimate top oil tem­
perature rise over ambient temperature in steady state is calculated by
(1). Ki and Ri are the ratio of instantaneous load to nameplate load of
transformer and the ratio of the nominal loss to the no load loss of
2
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
Fig. 2. Calculation procedure for dynamic-thermal failure probability failure transformer.
transformer, respectively. The instantaneous top oil temperature rise
over ambient temperature is computed by (2). θiO(fl) and θiint O are the full
θiu O = θiO(fl)
load and initial top oil temperature rise over ambient temperature,
respectively. τoil is time Constance of top oil temperature. The ultimate
HST rise over top oil temperature is illustrated in (3). θiHST O(fl) is the full
(
)a
Pi(t)
1 + Ki2
; Ki = i
1 + Ri
Pnam
⎛
θiist O (t) = θiu O ⎝1 −
load HST rise over top oil temperature in steady state. Finally, the ab­
solute value of HST is calculated based on (4), where the θa (t) is ambient
temperature [6,7]. Also, a and b are derived components related to θiu O
and θiHST O (t) , respectively.
The real time of simulation is computed by (5) where the parameters
t,y are an hour of simulation and a year of simulation, respectively.
When the transformers are old or over loaded, the time experiencing of
transformers is faster than normal time. So the equivalent operation
time and total equivalent operation time are identified based on (6) and
(7), respectively. Finally, the failure probability of transformer is shown
by (8), where A,B are constant parameters of transformer expected life
[6,7].In all equations, variable i means i-th transformer on the power
network. The calculation procedure of dynamic-thermal failure proba­
bility of transformer is depicted in Fig. 2.
(1)
⎞
e
− τt ⎠
oil
−
t
+ θiint O e τoil
θiHST O (t) = θiHST O(fl) Ki2b
(3)
θiHST (t) = θiist O (t) + θiHST O (t) + θa (t)
(4)
T = (y − 1) × 8760 + t
(5)
(
etit = Δtt × exp
tetit =
T
∑
)
B
B
−
θiistO θihst (t) + 273
etij
j=1
Fig. 3. The effects of thecyber network element (DSE) on the K factor and dynamic-thermal failure probability of transformer.
3
(2)
(6)
(7)
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
kW) so the K factor in disconnection condition (KY)will be greater from
connected condition (KX). According to (1) to (8), when K factor isin­
creased, the hot spot temperature and failure probability of transformer
will increased too. So the mal-operation of cyber network can increase
the dynamic-thermal failure probability of transformer.
5. Proposed optimization method
In this section, the proposed optimization method is introduced to
select the best configuration of cyber network with minimization of
transformers failure probability and maximization of the power system
reliability. When the data flow paths are increased in cyber network
configuration, especially between cyber elements that have interde­
pendency with critical power elements like DGs located in overloaded
transformers, the reliability of cyber-physical system is improved. It
should be mentioned that all kind of distributed generation technologies
can be considered according to this proposed method. To implement the
mathematical analyses on the data flow graph of cyber network, the
cyber configuration should be converted to an adjacency matrix. If the pth element of cyber configuration be connected with q-th element, the
matrix element in p-th row and q-th column is one otherwise is zero.
Fig. 4 shows the adjacency matrix of n-th elements of cyber networks.
Fig. 4. n × n adjacency matrix of a cyber configuration.
⎡⎛
⎢⎜
i
⎜
fTR
(t) = 1 − exp⎢
⎣⎝
⎞β
⎞β ⎤
⎛
tetit+ etit
⎟ ⎜
⎟ ⎥
tetit
⎥
⎜
(
(
)⎟
)⎟
⎠ − ⎝
⎠ ⎦
B
B
A × exp θ0 +273
A × exp θ0 +273
(8)
2
The total number of variables is n 2− n because the elements on main di­
agonal are zero and this matrix is symmetric. The adjacency matrix of nth element cyber configuration should be initialized in first step of
In Fig. 3, the effects of cyber network element, DSE in this figure, is
shown on the dynamic-thermal probability of transformer. DSE has
direct connection with generator circuit breaker (GCB) in the power
network. When DSE be failed, the disconnection command is send to
GCB and consequently distributed generator will be disconnected from
power grid (performance of DSE will explain in later section). Two
different conditions is depicted in Fig. 3. If DSE be in-service, the
distributed generator will be connected to the power grid and it will
supply the load. In this condition, the load will be supplied from the
transformer and the distributed generator. If the DSE be out of service,
distributed generator will be disconnected from the power grid so the
load will be supplied only from transformer. In this condition, the
loading of transformer (Y kW) is greater from the previous condition(X
2
proposed method. The n 2− n variables should be randomly initialized with
zero or one value.
For more clarifying of the proposed method, the following example is
introduced. It is assumed that sample cyber network needs nine DSEs,
nine switches and two servers. The total number of cyber elements and
the total number of adjacency matrix variables are 20 and 190,
respectively. The Fig. 5 demonstrates one of the adjacency matrices of
this cyber network that randomly initialized.
a. Constraints
Two constraints are considered to implement this proposed optimi­
zation method. First constraint confirms that the graph of the initial
adjacency matrix be connected. That means that all of the cyber
Fig. 5. Adjacency matrix of the sample cyber network.
4
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
Fig. 6. The procedure of the constraint one on the adjacency matrix of sample cyber network.
elements are connected to each other. Second constraint emphasized
that each DSE is connected to at least one server of cyber network with a
path consisting at least one switch. These two constraints are the pro­
tocols of cyber network that should be satisfied in each initial adjacency
matrix.
Constraint one:
The connectivity of cyber graph is the main concept in cyber
protocols. The cyber elements, consisting DSEs, servers and switches as
nodes should be connected each other with connectors as edges in each
cyber graph. To implement the first constraint, the below steps should be
considered:
1) Receive the initialized adjacency matrix
Fig. 7. The procedure of constraint two on the adjacency matrix of sample cyber network when DSE six is the origin.
5
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
Fig. 8. The procedure of constraint two on the adjacency matrix of sample cyber network when DSE two is the origin.
2) Select one of the cyber elements randomly then mark the element
and count it
3) Mark and count the elements that are connected directly to the
marked elements
4) Repeat step 3 until the all elements that connected to marked ele­
ments (neighbors) be marked and counted
5) If the number of counted elements be equal to the number of cyber
elements, the first constraint is satisfied other is not.
6) End
7) Select another DSE as origin until all DSEs be selected and go to 3.
8) If steps 2 to 5 be valid for all DSEs, the constraint is satisfied for
adjacency matrix.
9) End.
Fig. 7 and Fig. 8 illustrate this constraint on the sample adjacency
matrix. In Fig. 7, the DSEsix is selected as the origin and servers one and
two are selected as the destinations. According to the constraint steps,
the DSEsix and the elements connected directly to DSEsix (switch six)
are marked. Then the elements connected to marked elements are
marked. At the end of this procedure, server two as one of the destina­
tions is marked. So this constraint is acceptable for DSEsix. This pro­
cedure is repeated for DSE two as origin and server one and two as
destinations based on Fig. 8. After implementation of constraint steps,
none of the destination are marked and this constraint is not acceptable
for DSE two. So this sample adjacency matrix is not appropriated
because constraint two is not acceptable for all DSEs.
If the constraint one and two simultaneously be valid for adjacency
matrix, then the adjacency matrix is appropriate to EENS calculation in
TLBO process.
b. State upgradation and fitness function assessment
In this section, the expected energy not supplied (EENS) as a fitness
function is introduced. Before the reliability evaluation, the state of
cyber-physical system should be upgraded. The steps of this upgradation
are expressed as below:
Step 1: State initializing
Recognition of the in-service and out of service probability of ele­
ments is necessary for reliability assessment. The in-service and out of
service of each power and cyber element can be calculated by using
uptime and downtime variables. The uptime and downtime variables of
each element can be computed based on eq. (9) and eq. (10).
For more clarifying the proposed constraint, the adjacency matrix of
the sample cyber network is used to implement above steps. Fig. 6 shows
the steps of connectivity constraint on the adjacency matrix. As shown in
Fig. 6, switch one is randomly selected as first element and it is marked
and counted. Then the elements connected to switch one (DSE one and
switch two) are marked and counted. This procedure is continued until
all elements that connected to the marked elements be counted and
marked. In the end, the number of counted elements is four while the
number of cyber elements are twenty. So the first constraint is not
satisfied for this adjacency matrix and this matrix is not appropriate.
Constraint two:
In cyber protocols, it is necessary that each DSEs be connected to at
least one server with a path consisting at least one switch. This
constraint should be satisfied because server elements in cyber network
should control the all elements in power one and the DSEs are interface
elements between servers and DGs. Below steps are explained to clarify
the procedure of this constraint.
1) Receive the initialized adjacency matrix
2) Select one of the DSE elements as origin and all the servers as
destination.
3) Mark the origin.
4) Mark the elements that are connected to the marked elements.
5) Repeat step 3 until the all elements that connected to marked ele­
ments be marked (neighbors).
6) If none of the servers as destination be marked, the constraint is not
satisfied and go to 9, else go to 7.
Up timeiinitial,t = − MTTF i × ln(u1 )
(9)
Down timeiinitial,t = − MTTRi × ln(u2 )
(10)
In these equations, meantime to failure (MTTF) and meantime to
6
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
repair (MTTR) are obtained by test system historical data. A uniform
random variables u1 and u2 that distributed on [0–1] are essential to
generate the uptime and downtime variables.
The system state is defined as the availability of whole elements of
the power and the cyber system in each time segment (an hour) of
simulation. The availability of each element indicates that an element is
in service or out of service in each time segment of simulation based on
(11). Where a variable availibilityit demonstrates the i-th element is in-
service or out of service in t-th time segment. If availibilityit be one
means the i-th element is in-service, and if it be zero means the i-th
element is out of service in the t-th time segment. The availability of all
cyber-physical system makes the state of the system based on (12).
NPower and NCyber are the total number of power elements and total
number of cyber elements , respectively. The availability and state of
this upgradation step that are based on the natural failure of each power
and cyber element, is called initial availability and initial state,
respectively.
{
1ift∊Up timei
avialibilityiinitial,t =
(11)
0ift∊Down timei
]
[
NCyber +NPower
Sinitial,t = availibility1initial,t , availibility2initial,t , ⋯, availibilityinitial,t
(12)
Step 2: State upgradation because of direct network-element cyber
power interdependency
In this state upgradation step, the matrix of NEI (network-element
interdependency) with NCyber × NCyber dimension, should be generated.
The element of NEI(i,j) is one, if the failure in i-th cyber element causes
the failure in the j-th cyber element, otherwise it is zero. It should be
mentioned that the NEI matrix is produced based on the topology of
cyber network configuration. This upgradation is formulated based on
eq. (13) and eq. (14).
}
{
∀m, n∊ 1, 2, ⋯, NCyber
{
(13)
avialibiltynt ∩ avialibiltymt ifNEI(m, n) = 1
n
availibiltynew,t =
avialibiltynt ifNEI(m, n) = 0
]
[
NCyber +NPower
Snew,t = availibility1new,t , availibility2new,t , ⋯, availibilitynew,t
(14)
Step 3: State upgradation because of direct element-element cyber
power interdependency
In this state upgradation step, the matrix of EEI (element-element
interdependency) with NCyber × NPower dimension, should be produced.
The element of EEI(i,j) is one, if the failure in i-th cyber element causes
the failure in the j-th power element, otherwise it is zero. Failure in some
cyber elements can cause failure in specific power elements directly.
With using eq. (15) and eq. (16), this step upgradation can be performed.
}
{
∀m∊ 1, 2, ⋯, NCyber ∀n∊{1, 2, ⋯, NPower }
{
(15)
avialibiltynt ∩ avialibiltymt ifEEI(m, n) = 1
availibiltynnew,t =
avialibiltynt ifEEI(m, n) = 0
]
[
NCyber +NPower
Snew,t = availibility1new,t , availibility2new,t , ⋯, availibilitynew,t
Fig. 9. Line diagram of cyber-physical system based on best cyber network
configuration.
Table 1
Characteristics data of the transformers dynamic thermal failure.
(16)
It should be emphasized that failure and availability are opposite
concepts, it means that if the element failure is occurred (one value) the
element availability is zero, otherwise it is one. Finally, with given stats
of cyber-power elements, the reliability indices like EENS can be eval­
uated in each time segment of Monte Carlo simulation. The procedure of
EENS assessment in MCS is explained completely in [8].
N.o.
Variable
Value
1
2
3
4
5
n
m
R
A
6
7
τoil
1
0.8
4.87
0.56
3.5 h
B
θfu O
θHST O(fl)
28.6 ◦ C
8
6. Case study
1500
36 ◦ C
implement the proposed method of this paper. The aggregated peak load
of the power system is 6 MW. Thirty-seven 20/0.4 kV transformers are
equipped in each load point of the test system. Also five diesel genera­
tions as distributed generation are installed in specified load points as
An actual 20 kV distribution system of Bandarabbas regional electric
company (BREC) of Iran is selected as a pilot smart network to
7
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
the power grid. Total number of cyber elements (n) is 12 so the number
Table 2
Characteristics data of diesel generators.
2
N.o. Distributed generators
Capacity
Cyber controller
DG-1
DG-2
DG-3
DG-4
DG-5
400 kW
400 kW
400 kW
400 kW
400 kW
DSE_1
DSE_2
DSE_3
DSE_4
DSE_5
of optimization variables (n 2− n ) is 66in optimization processes. Teaching
learning-based optimization algorithm (TLBO) that is independent of
optimization parameters, is used to select the best CNC of cyber-physical
network. The description of the TLBO algorithm is explained by R. Rao
et al. in [21–22]. In each iteration of the TLBO algorithm, Monte Carlo
simulation is used to evaluate the EENS of the smart system as a fitness
function of the optimization algorithm.
The best cyber configuration of cyber network with minimum
transformer failure probability and maximum reliability index is
depicted in Fig. 9. Purple dash lines and green dash lines of this figure
expose the relation between each DSE in the cyber network and related
generator breaker of diesel generator in the power one and the relation
between the generator breaker and related diesel generator, respec­
tively. The bi-directional lines in cyber networks show the two-way flow
of information between cyber elements based on Fig. 9. Also, the
depicted in Fig. 9. The characteristics data of the dynamic thermal
model of transformers are demonstrated in Table 1.
The cyber network has five DSEs, five switches and two servers ac­
cording to CPIs with the power test system. Each DSE of this cyber
network controls the conditions of the related diesel generators in the
power network. If the diesel controller fails, the disconnection command
is sent to gen. breaker and the diesel generator will be disconnected from
Table 3
Effects of various CNCs of test system (Bandarabbas regional electric company) on the failure probability of transformers and reliability of test system considering the
proposed method.
EENS
(MW.h/year)
constraint
two
constraint
one
Configuration
–
No
No
1
–
Yes
No
2
–
No
Yes
3
74.31
Yes
Yes
4
67.92
Yes
Yes
5
8
N.O.
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
Fig. 10. Hot spot temperature of transformers in LP16, LP24, LP28, LP33 and LP37 under various scenarios of DSE be in-service and DSE be out of service in each
load point.
characteristics data of diesel generators consist of capacity and cyber
controller are demonstrated in Table 2.
The graph of this cyber network maximize the data connection be­
tween the cyber elements especially in sensitive and important ele­
ments. For example the DSE five has three data connectors because this
DSE has CPI with diesel five that is located in the heavy loaded trans­
former with the high failure of probability. Diesel outages can cause the
outage of TR5 because of critical condition of this transformer. So the
importance of DSE five is more than other DSEs of cyber network based
on reliability concerns.
The characteristics of various cyber graphs of the test system (Ban­
darabbas regional electric company) on the transformer failure proba­
bility and the reliability of the system are presented in Table 3 based on
the proposed method. In this table, the satisfaction of constraints one
and two, EENS value of cyber-physical network are demonstrated. In the
configuration n.o. 1 of this table, the connectivity constraint and path
existence constraint between each DSE and servers are not satisfied so
this configuration is not acceptable for the optimization algorithm. The
constraint two is valid for configuration n.o.2 but the connectivity of this
graph is not satisfied. Although the constraint one is valid for the
configuration n.o. 3 but the constraint two is not satisfied because one of
the DSEs is directly connected to servers without any switches. All
constraints are valid for configurations n.o. 4 as one of the acceptable
configuration and n.o. 5 as the best configuration network. The EENS
ofn.o. 4 and n.o. 5 is 74.31 MW.h and67.92 MWh, respectively. The
configuration n.o. 5 has a minimum value of EENS in comparison with
all acceptable cyber configurations based on the proposed optimization
method and it is selected as the best configuration of the cyber network
for Bandarabbas regional electric company.
In Fig. 10, hot spot temperatures of five transformers consist of LP16,
LP24, LP28, LP33 and LP37 is demonstrated. HST of each load point is
depicted in two scenarios. The first scenario is related to DSE of load
point be in-service and the second scenario is related DSE of load point
be failed. For example in LP33, when DSE_4 be failed, the maximum HST
of transformer n.o. 33 can be reached to 137C and when DSE_4 be inservice the maximum HST only can be reached to 108C as it is shown
in Fig. 10. This figure demonstrates the cyber network element condition
is one of the factors affecting the hot spot temperature of transformers
and consequently it can impress the failure probability of transformers.
Finally in Table 4, the failure probability of all transformers under
the different cyber configuration consist of configuration n.o. 4 (as one
of the acceptable configurations) and configuration n.o. 5 (as the best
configuration, is demonstrated. As it can be seen from this table, the
failure probability of transformers is decreased with implementing the
optimized cyber configuration that it be achieved from the proposed
method of this paper.
7. Conclusion
This paper introduces a novel method to reveal the effects of various
CNCs on the failure probability of transformers and select best config­
uration of cyber network considering reliability concerns of a cyberphysical system. The connectivity and path existence between DSEs
and switch as optimization constraints are considered to satisfy the
cyber protocols. TLBO algorithm and MCS are used to implement the
proposed optimization method. The results show that the cyber
configuration remarkably affects on the transformers failure probability
especially on the critical ones and it impacts on the reliability of power
system. As illustrated in the results, the optimized configuration of cyber
network that extracted from proposed method maximizes the connec­
tion data between the cyber elements especially the elements that have
interdependency with critical transformers. This paper illustrates the
Table 4
Transformers probability under different cyber configurations.
N.o. of transformers
Configuration n.o. 4 (as one of the
acceptable configuration)
Configuration n.o. 5 (as the best
configuration)
Failure probability of
TR_16 (f/y)
Failure probability of
TR_24 (f/y)
Failure probability of
TR_28 (f/y)
Failure probability of
TR_33 (f/y)
Failure probability of
TR_37 (f/y)
0.0046
0.0042
0.0054
0.0039
0.0044
0.0035
0.0033
0.0046
0.0032
0.0037
9
M. Hamzeh and B. Vahidi
International Journal of Electrical Power and Energy Systems 137 (2022) 107786
importance of proper cyber graph selection in the future conditions of
the power network.
[8] Hamzeh M, Vahidi B, Askarian-Abyaneh H. Reliability evaluation of distribution
transformers with high penetration of distributed generation. International J.
Electrical Power & Energy system Dec. 2015;73(1):163–9.
[9] Hamzeh M, Hashemi-Dezaki H, Askarian Abyaneh H, Gharehpetian GB, Vahidi B.
Risk management of smart grids based on plug-in hybridelectric vehicles’ charging
considering transformers’ hottest spot temperature-dependent aging failures.
Renew. Sustain. Energy 2016;8(3):034102. https://doi.org/10.1063/1.4948929.
[10] M. Soleimani and M. Kezunovic, “Mitigating Transformer Loss of Life and Reducing
the Hazard of Failure by the Smart EV Charging,” in IEEE Transactions on Industry
Applications, vol. 56, no. 5, pp. 5974-5983, Sept.-Oct. 2020, doi: 10.1109/
TIA.2020.2986990.
[11] Tavcar J, Horvath I. A Review of the Principles of Designing Smart Cyber-Physical
Systems for Run-Time Adaptation: Learned Lessons and Open Issues. IEEE Trans.
Systems, Man Cybernetics: Systems 2019;49(1):145–58.
[12] Clark A, Zonouz S. Cyber-Physical Resilience: Definition and Assessment Metric.
IEEE Trans Smart Grid March 2019;10(2):1671–84.
[13] M. Wolf and D. Serpanos, “Safety and Security in Cyber-Physical Systems and
Internet-of-Things Systems,” in Proceedings of the IEEE, vol. 106, no. 1, pp. 9-20,
Jan. 2018.
[14] Wang H, et al. Dynamic Data Injection Attack Detection of Cyber Physical Power
Systems With Uncertainties. IEEE Trans Ind Inf Oct. 2019;15(10):5505–18.
[15] K. Marashi, S. S. Sarvestani, A. R. Hurson, K. Marashi, S. S. Sarvestani and A. R.
Hurson, “Consideration of cyber-physical interdependencies in reliability modeling
of smart grids”, IEEE Trans. Sustain. Comput., vol. 3, no. 2, pp. 73-83, Apr.–Jun.
2017.
[16] Liu W, Gong Q, Han H, Wang Z, Wang L. Reliability Modeling and Evaluation of
Active Cyber Physical Distribution System. IEEE Trans Power Syst Nov. 2018;33
(6):7096–108.
[17] Cao Y, Shi X, Li Y, Tan Y, Shahidehpour M, Shi S. A Simplified Co-Simulation
Model for Investigating Impacts of Cyber-Contingency on Power System
Operations. IEEE Trans Smart Grid Sept. 2018;9(5):4893–905.
[18] H. Hashemi-Dezaki, H. Askarian-Abyaneh and H. Haeri-Khiavi, “Impacts of direct
cyber-power interdependencies on smart grid reliability under various penetration
levels of microturbine/wind/solar distributed generations,” in IET Generation,
Transmission & Distribution, vol. 10, no. 4, pp. 928-937, 10 3 2016.
[19] Falahati B, Fu Y. Reliability Assessment of Smart Grids Considering Indirect CyberPower Interdependencies. IEEE Trans Smart Grid July 2014;5(4):1677–85.
[20] “Deep see electronic manual”, Accessed on: Jun. 18, 2021. [Online]. Available:
https://www.deepseaelectronics.com/.
[21] Rao RV, Savsani VJ, Vakharia DP. Teaching–learning-based optimization: an
optimization method for continuous non-linear large scale problems. Inf. Sci. (Ny)
2012;183(1):1–15.
[22] Rao RV. Teaching Learning Based Optimization Algorithm: And Its Engineering
Applications. 1st ed. Incorporated: Springer Publishing Company; 2015.
CRediT authorship contribution statement
M. Hamzeh: Conceptualization, Methodology, Software, Writing –
original draft. B. Vahidi: Supervision, Validation, Writing – review &
editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
References
[1] M. Badar, P. Lu, Q. Wang, T. Boyer, K. P. Chen and P. R. Ohodnicki, “Real-Time
Optical Fiber-Based Distributed Temperature Monitoring of Insulation OilImmersed Commercial Distribution Power Transformer,” in IEEE Sensors Journal,
vol. 21, no. 3, pp. 3013-3019, 1 Feb.1, 2021, doi: 10.1109/JSEN.2020.3024943.
[2] Calitz D, Hennig EG, Gray S, Schweiger E. Power transformers: Mitigate
Environmental Impact and Fire Risk Reduction and be prepared for the
Unexpected. IEEE/PES Transmission Distribution Conference Exposition (T&D)
2020;2020:1–5. https://doi.org/10.1109/TD39804.2020.9299931.
[3] Singh, Jaspreet and S. Singh. “Transformer Failure Analysis:Reasons and Methods.”
International journal of engineering research and technology, 4,15, (2018).
[4] Soleimani M, Faiz J, Nasab PS, Moallem M. Temperature Measuring-Based
Decision-Making Prognostic Approach in Electric Power Transformers Winding
Failures. IEEE Trans Instrum Meas 2020;69(9):6995–7003. https://doi.org/
10.1109/TIM.1910.1109/TIM.2020.2975386.
[5] “IEEE Standard for Thermal Evaluation of Insulation Systems for Dry-Type Power
and Distribution Transformers,” in IEEE Std C57.12.60-2020 (Revision of IEEE Std
C57.12.60-2009) , vol., no., pp.1-61, 3 April 2020, doi: 10.1109/
IEEESTD.2020.9057790.
[6] Cheng L, Yu T, Wang G, Yang B, Zhou L. Hot Spot Temperature and Grey Target
Theory-Based Dynamic Modelling for Reliability Assessment of Transformer OilPaper Insulation Systems: A Practical Case Study. Energies 2018;11:249. https://
doi.org/10.3390/en11010249.
[7] Awadallah SKE, Milanovic JV, Jarman PN. The Influence of Modeling Transformer
Age Related Failures on System Reliability. IEEE Trans Power Syst 2015;30(2):
970–9.
10