Fault Diagnosis of Electric Power Systems Based on Fuzzy Reasoning Spiking Neural P Systems

TL;DR: The results of case studies show that FDSNP is effective in diagnosing faults in power transmission networks for single and multiple fault situations with/without incomplete and uncertain SCADA data, and is superior to four methods reported in the literature in terms of the correctness of diagnosis results.

Abstract: This paper proposes a graphic modeling approach, fault diagnosis method based on fuzzy reasoning spiking neural P systems (FDSNP), for power transmission networks. In FDSNP, fuzzy reasoning spiking neural P systems (FRSN P systems) with trapezoidal fuzzy numbers are used to model candidate faulty sections and an algebraic fuzzy reasoning algorithm is introduced to obtain confidence levels of candidate faulty sections, so as to identify faulty sections. FDSNP offers an intuitive illustration based on a strictly mathematical expression, a good fault-tolerant capacity due to its handling of incomplete and uncertain messages in a parallel manner, a good description for the relationships between protective devices and faults, and an understandable diagnosis model-building process. To test the validity and feasibility of FDSNP, seven cases of a local subsystem in an electrical power system are used. The results of case studies show that FDSNP is effective in diagnosing faults in power transmission networks for single and multiple fault situations with/without incomplete and uncertain SCADA data, and is superior to four methods, reported in the literature, in terms of the correctness of diagnosis results.

Summary

3) Protective relays of transformers

• When the main protective relays of a transformer operate, all CBs connected to the transformer are tripped.
• If transformer fails and MPR fails to operate, FBPR operates to trip and .
• First, the status information is read from the SCADA system.
• Third, a fault diagnosis model for each section in each candidate outage area is built.
• The key ingredients and steps of FDSNP are presented in detail in Section III.

III. FDSNP

• This section presents a graphic modeling approach, FDSNP, for fault diagnosis of power transmission networks based on FRSN P systems with trapezoidal fuzzy numbers.
• Indicate the input neuron set and the output neuron set of , respectively.
• The motivation for the introduction of trapezoidal fuzzy numbers comes from three aspects.
• In addition, the knowledge in practical applications may contain a certain degree of uncertainty.

D. Algorithmic Elaboration of FDSNP

• Step 1) Read operation messages about protective relays and/or CBs in a power transmission network from the SCADA system.
• Find all the other sections linking with each of the closed CBs and put their numbers from into .
• If is not empty, the search process goes to (iii); vi) Find passive networks, i.e., outage areas, from , where is the maximum number of all numbers referring to section subsets.
• According to the relay protections of the section, the authors design fault fuzzy production rules and then determine proposition and rule neurons and create their linking relationship to obtain the FRSN P system.
• According to Tables V and VI, the authors set confidence levels for main protections, first backup pro-tections, second backup protections and their CBs.

IV. CASE STUDIES

• These cases include single and multiple fault situations.
• FDSNP is used to diagnose faults for the seven cases, and the diagnosis results are shown in Table VIII , which contains the faulty sections and their fault confidence levels.
• The diagnosis IX , where "-" means that this case was not considered in the corresponding reference.
• From Table VIII , the authors can see that the fault confidence levels represented by trapezoidal fuzzy numbers provide a quantitative description for the faulty sections which makes these results more reliable.
• For section , its main protective relay operated and tripped its corresponding CBs, , and .

When , we get the results

• Thus, the termination condition is satisfied and the reasoning process ends.
• In other words, the status information about is missing in this case.

V. CONCLUSIONS

• A graphic modeling approach, FDSNP, based on FRSN P systems with trapezoidal fuzzy numbers is presented for fault diagnosis of power transmission networks.
• This approach provides a good accuracy of diagnosis solutions and a rather understandable fault diagnosis process because of its intuitive illustration of graphical models and understandability of diagnosis model-building process.
• In addition, FDSNP can handle incomplete and uncertain messages from a SCADA system by using trapezoidal fuzzy numbers and fuzzy production rules.
• This study proposes FDSNP and tests its validity and feasibility in diagnosing faults in power transmission networks.
• The set of linguistic terms and their corresponding trapezoidal fuzzy numbers are decided in an empirical way.

Figures

Fig. 11. Modeling process of Type 4 using one FRSN P system.

TABLE I LINGUISTIC TERMS AND THEIR CORRESPONDING TRAPEZOIDAL FUZZY NUMBERS

Fig. 10. Modeling process of Type 3 using one FRSN P system.

Fig. 9. Modeling process of Type 2 using one FRSN P system.

Fig. 1. Equipments and sections in a power transmission network.

TABLE IX COMPARISONS BETWEEN FDSNP AND FOUR FAULT DIAGNOSIS METHODS

Fig. 12. Fault diagnosis model of bus based on an FRSN P system.

Fig. 4. Flowchart of FDSNP.

Fig. 3. Local sketch map of the protection system of an EPS.

Fig. 2. Schematic illustration of the power transmission network with sections and protective relays considered in this study.

TABLE V CONFIDENCE LEVELS OF THE OPERATED PROTECTIVE DEVICES

TABLE II MEANING OF EACH PROPOSITION IN RULE SET OF L

TABLE VI CONFIDENCE LEVELS OF THE NON-OPERATE PROTECTIVE DEVICES

TABLE IV MEANING OF EACH PROPOSITION IN RULE SET OF T

TABLE III MEANING OF EACH PROPOSITION IN RULE SET OF B

Fig. 5. Trapezoidal fuzzy number.

TABLE VIII FAULT SECTIONS AND THEIR FAULT CONFIDENCE LEVELS OBTAINED BY USING FDSNP

TABLE VII STATUS INFORMATION ABOUT PROTECTIVE RELAYS AND CBS

Fig. 8. Modeling process of Type 1 using one FRSN P system.

Fig. 6. (a) Proposition neuron and (b) its simplified form.

Fig. 7. Rule neurons. (i) A general rule neuron (a) and its simplified form (b); (ii) An and rule neuron (a) and its simplified form (b); (iii) An or rule neuron (a) and its simplified form (b).

Full text

Fault Diagn
osis of Electric Power Systems Based
on Fuzzy Reasoning Spiking Neural P Systems
Tao Wang, Gexiang Zhang, Member, IEEE, Junbo Zhao, Student Member, IEEE,
Zhengyou He, Senior Member, IEEE, Jun Wang, and Mario J. Pérez-Jiménez
Abstract—This paper proposes a graphic modeling approach,
fault diagnosis method based on fuzzy reasoning spiking neural P
systems (FDSNP), for power transmission networks. In FDSNP,
fuzzy reasoning spiking neural P systems (FRSN P systems) with
trapezoidal fuzzy numbers a
re used to model candidate faulty sec-
tions and an algebraic fuzzy reasoning algorithm is introduced to
obtain confidence levels of candidate faulty sections, so as to iden-
tify faulty sections. FDSNP offers an intuitive illustration based
on a strictly mathematical expression, a good fault-tolerant ca-
pacity due to its handling of incomplete and uncertain messages in
a parallel manner, a good description for the relationships be-
tween protective devices and faults, and an understandable diag-
nosis model-building process. To test the validity and feasibility of
FDSNP, seven cases of a local subsystem in an electrical power
system are used. The results of case studies show that FDSNP is
effective in diagnosing faults in power transmission networks for
single and multiple fault situations with/without incomplete and
uncertain SCADA data, and is superior to four methods, reported
in the literature, in terms of the correctness of diagnosis results.
Index Terms—Electric power system, fault diagnosis, fuzzy pro-
duction rules, fuzzy reasoning, fuzzy reasoning spiking neural P
system, linguistic term, trapezoidal fuzzy number.
I. INTRODUCTION
W
HEN operating electric power syste
ms (EPS), one of
the key objectives is to supply reliable and stable power
to cu
stomers. Impacted by various factors such as disturbances
and equipment failures, interruption of power service or even
blackout may happen in power systems [1], [2]. To reduce the
loss caused by the two latter undesired events, it is essential for
dispatchers to quickly identify the faulty sections in the power
system to restore power supply. When a fault occurs, a large
number of alarm messages from supervisor control and data ac-
quisition (SCADA) systems are poured into dispatchers' con-
soles in a short period of time. These messages are often in-
complete and uncertain [3]–[6]. Thus, it is necessary to develop
This work was supported by the National Natural Science Foundation of
China (61170016, 61373047, 61170030), the Program for New Century
Excellent Talents in Uni-versity (NCET-11-0715) and SWJTU supported
project (SWJTU12CX008). Paper no. TPWRS-01113-2013.
T.Wang,G.Zhang,J.Zhao,andZ.Heare with
the SchoolofElectrical Engineering, Southwest Jiaotong University,
Chengdu 610031, China (e-mail: wangatao2005@163.com;
zhgxdylan@126.com; junbozhao55589@gmail. com; hezy@swjtu.edu.cn).
J. Wang is with the School of Electrical and Information Engineering, Xihua
University, Chengdu 610039, China (e-mail: wangjun@mail.xhu.edu.cn).
M. J. Pérez-Jiménez is with the Research Group on Natural Computing, De-
partment of Computer Science and Artificial Intelligence, University of Sevilla,
Sevilla 41012, Spain (e-mail: marper@us.es).
a good method to help dispatchers evaluate where the faults are
and which sections fail [4].
Fault diagnosis of a power system is a complicated process
because it contains lots of sections such as generators, trans-
mission lines, bus bars and transformers which are protected
by a protective system consisting of protective relays, circuit
breakers (CBs) and communication equipments [5]. In recent
decades, fault diagnosis has been implemented by various ap-
proaches, such as expert systems (ES) [1], [2], fuzzy logic (FL)
[3]–[7], artificial neural networks (ANNs) [8], [9], Petri nets
(PNs) [4], [5], [10], Bayesian networks (BNs) [11], [12], multi-
agent systems (MAS) [13], [14], optimization methods (OM)
[15]–[17], cause-effect networks (CE-Nets) [6], [7], [18], and
information theory (IT) [19], [20]. Each method has its own
merits and demerits.
ES is the earliest artificial intelligence method for power
system fault diagnosis. ES makes full use of experts'
knowl-
edge, but it has a slow inference speed due to its sequential
search nature, and the difficulties of designing and maintaining
a rule-based knowledge system [2], [18]. FL expr
esses impre-
cision and uncertainty, but it needs to be combined with other
methods [18], [20]. ANNs have the advantages of good toler-
ance and strong learning ability, and the di
sadvantages of the
empirical design of network structures and parameters, prema-
ture convergence and the need for numerous samples [18]. The
major features of PN-based methods
are graphical knowledge
representation and parallel information processing, however,
bad tolerance and combinatorial explosion in large power net-
works are their weaknesses [6]
. Fault diagnosis models based
on BNs are intuitive and can find relationships of causality
between data, but it is difficult for these methods to obtain ac-
curate prior probabilit
ies and model complex power grid [12],
[20]. In MAS, several agents corresponding to several methods
cooperate to fulfill fault diagnosis, but how to properly combine
different methods a
nd how these agents cooperate are unsolved
issues [13], [20]. Although OM may obtain globally optimal
solutions of a complex fault diagnosis problem, it is not easy
to construct an
objective function reflecting the discrepancy
between the expected and actual states of protective devices
and to adjust the parameters in the optimization model [16],
[18]. CE-N
ets are a graphical tool for knowledge representation
with easy algebraic reasoning and parallel information pro-
cessing ability, but their fault tolerance needs to be improved
and the
ir forward reasoning strategy makes CE-Nets unable to
visually represent all possible combinations of main, first and
second protections [18], [21]. IT-based methods are a novel
app
roach emerging with the informatization of power systems.
To a certain extent, these methods deal with the uncertainty in

failure processes with fast diagnosis speed, but it is difficult
to dynamically describe the fault information needed [20].
Therefore, much attention should be paid to the improvements
of the aforementioned methods and the exploration of new ones
to solve fault diagnosis problems.
This paper discusses a novel fault diagnosis approach for
power systems by using membrane systems or P systems, which
are theoretical computing devices in the area of membrane
computing. As a newly attractive research field of computer
science, membrane computing, formally introduced by Păun
[22], aims at abstracting computing models from the structure
and the functioning of living cells, as well as from the way that
cells are organized in tissues or higher order structures. A spiking
neural P system (SN P system) is the type of P system inspired by
the neurophysiological behavior of neurons sending electrical
impulses (spikes) along axons from presynaptic neurons to post-
synaptic neurons in a distributed and parallel manner [23]. An SN
P system can be considered as a set of nodes representing neurons
in a directed graph whose arcs express synaptic connections
among neurons. The contents of each neuron are composed of
several copies of a single object type. Likewise, each neuron has a
finite set of firing (spiking) and forgetting rules. Firing rules send
information between neurons in the form of spikes and forgetting
rules remove spikes from neurons. The rules associated with each
neuron are used in a sequentialmanner, but neurons communicate
with each other in parallel. Recently, SN P systems have become a
hot topic in membrane computing [24]–[30].
SN P systems are a class of distributed and parallel computing
models with good understandability and dynamics [28], [29]. The
fault occurrence in power systems is a discrete and dynamical
process [4]–[6]. Thus, SN P systems can be used for diagnosing
faultsin power systems. Inthe preliminary work, we discussedthe
knowledge representation ability of FRSN P systems [26], [27].
To successfully fulfill diagnosis knowledge representation and
reasoning, an FRSN P system with real numbers was presented
in [28], where only one transformer was considered. In these sys-
tems, the potential value that a spike can take within a neuron
and the truth value of a fuzzy proposition (or confidence factor
of a production rule) are represented by real numbers in [0, 1]. In
[21], an approach based on the FRSN P system, presented in [28],
for fault diagnosis of power systems was discussed and three dif-
ferent applications were used to verify its effectiveness. How to
handle the incompleteness and uncertainty of the alarm informa-
tion indifferentpower systems is worth further discussing.
To handle
incompleteness and uncertainty in power transmis-
sion network fault diagnosis in electric power systems, a method
based on FRSN P systems, FDSNP, is developed in this paper.
In FDS
NP, an FRSN P system with trapezoidal fuzzy numbers is
introduced to model candidate faulty sections and an algebraic
fuzzy reasoning algorithm of the FRSN P system is presented
f
or matrix-based fault reasoning to obtain confidence levels of
candidate faulty sections and identify faulty sections. In order to
make the process of building diagnosis models based on FRSN
P systems easily understandable, fault fuzzy production rule sets
to obtain the relationships between protective devices and faults
are presented.
The main contribution of this work is summarized as follows.
This study provides a fault diagnosis method based on FRSN
Fig. 1. Equipments and sections in a power transmission network.
P systems with trapezoidal fuzzy numbers for power transmis-
sion networks. The main ideas of this method include the in-
troduction of trapezoidal fuzzy numbers into FRSN P systems,
the fuzzy reasoning algorithm within the framework of FRSN
P systems with trapezoidal fuzzy numbers and the fault fuzzy
production rule sets based on syntactical ingredients of FRSN P
systems with trapezoidal fuzzy numbers. The use of trapezoidal
fuzzy numbers is helpful to express potential values of spikes
contained in neurons and the fuzzy truth values of the neurons
and consequently allows us to handle incompleteness and un-
certainty in power systems. The presented reasoning algorithm
uses an easily understandable description and has various kinds
of synaptic matrices to describe relationships among faulty sec-
tions, protective relays and their CBs more flexible and effec-
tive. The fault fuzzy production rule sets for main sections in-
cluding transmission lines, buses and transformers in transmis-
sion networks can offer the causality between the faults and the
statuses of protective relays and their corresponding CBs in an
intuitive and visual way.
The remainder of this paper is organized as follows.
Section II states the problem to solve. Section III presents
FDSNP. Following, seven case studies are provided in
Section IV. Conclusions are finally drawn in Section V.
II. P
ROBLEM DESCRIPTION
Strictly speaking, fault diagnosis includes fault detection,
fault section identification, fault type estimation, failure iso-
lation and recovery [17]. Among the five processes, fault
section identification is especially important [4], [5]. A power
transmission network is composed of transmission equipments
and converting equipments, as each of which consists of
many kinds of sections as shown in Fig. 1. In this paper, we
focus on the fault diagnosis of a power transmission network
because it is one of the major networks in power systems. In
this study, the faults of lines, buses and transformers in power
transmission networks are diagnosed by using the statuses of
protective relays and circuit breakers (CBs) because they are
normally read from a power SCADA system. The protective
relays consist of main protective relays (MPRs), first backup
protective relays (FBPRs) and second backup protective relays
(SBPRs). It is worth pointing out that there is not any FBPR for
buses. Fig. 2 shows a schematic illustration of the transmission
network with sections and protective relays considered in this
study.
Protective relays of transmission lines are of two types:
sending end protective relays and receiving end protective
relays. To illustrate the operational rules of different

Fig. 2. Schematic illustration of the power transmission network with sections
and protective relays considered in this study.
Fig. 3. Local sketch map of the protection system of an EPS.
types of protections, a local sketch map of the protection
system of an EPS is chosen from [4], [17] and shown in
Fig. 3, which includes 28 system sections, 40 CBs and 84
protective relays. For the convenience of description, some
notations are described as follows. A single bus, double
bus, transformer and line are represented by
, , ,
and
, respectively. and represent the sending and
receiving ends of the line
, respectively. , ,and
denote the main protection, the first backup protection
and the second backup protection, respectively.
The 28 sections
are labeled as
and the 40 CBs
are labeled as .
The 84 protective relays are composed
of 36 main ones,
represented by
,and denoted as
.
The operational rules of the protective relays for the three
kinds of sections, lines, buses and transformers, are described
in [17] as follows.
1) Protective relays of l ines
Both ends of a line have their own main, first and second
protections. When the main protective relays of a line op-
erate, CBs connected to the line are tripped. For example,
if line
fails, MPRs and are operate to trip
and , respectively. Likewise, when the main
protections of a line fail to operate, the first backup protec-
tive relays operate to trip CBs connected to the line. For
example, if line
fails and main protection relay (MPR)
fails to operate, first backup protective relay (FBPR)
Fig. 4. Flowchart of FDSNP.
operates to trip .Ifline fails and MPR
fails to operate, FBPR operates to trip .When
the adjacent regions of a line fail and their protections fail
to operate, the second backup protections operate to protect
the line. For example, if section
fails and fails to
trip off, second backup protective relay (SBPR)
op-
erates to trip
. If section fails and fails to
trip off, SBPR
operates to trip .
2) Protective relays of buses
When the main protective relays of a bus operate, all CBs
direct connected to the bus will be tripped. For example, if
bus
fails, MPR operates to trip , ,and
. Similarly, if bus fails, MPR operates to trip
, ,and .
3) Protective relays of transformers
When the main protective relays of a transformer operate,
all CBs connected to the transformer are tripped. For ex-
ample, if transformer
fails, MPR operates to trip
and . Likewise, when the main protections of
a transformer fail to operate, the first backup protective re-
lays operates to trip CBs connected to the transformer. For
example, if transformer
fails and MPR fails to op-
erate, FBPR
operates to trip and .When
the adjacent regions of the transformer fail and their protec-
tions fail to operate, the second backup protections operate
to protect the transformer. For example, if bus
fails and
fails to trip off, SBPR operates to trip to
protect
.
In this study, FDSNP is used to fulfill fault diagnosis of main
sections, transmission lines, buses and transformers, in power
transmission networks when some incomplete and uncertain
status information about protective relays and CBs is detected.
TheflowchartofFDSNPisshowninFig.4.First,thestatus
information is read from the SCADA system. Second, outage
areas are identified to obtain the suspected fault sections using
network topology analysis method [10], [31]. Third, a fault
diagnosis model for each section in each candidate outage area
is built. Then, each fault diagnosis model performs a fuzzy rea-
soning algorithm to obtain fault confidence levels of suspicious
fault sections. Finally, faulty sections are determined according
to their fault confidence levels. The key ingredients and steps
of FDSNP are presented in detail in Section III.

III. FDSNP
This section presents a graphic modeling approach, FDSNP,
for fault diagnosis of power transmission networks based on
FRSN P systems with trapezoidal fuzzy numbers. We first give
the definition of an FRSN P system with trapezoidal fuzzy num-
bers and then describe its algebraic fuzzy reasoning algorithm.
Subsequently, the fault fuzzy production rule sets for main sec-
tions including transmission lines, buses and transformers in
power transmission networks are presented. Finally, FDSNP is
algorithmically illustrated.
A. FRSN P Systems With Trapezoidal Fu zzy Numbers
Definition 1: An FRSN P system with trapezoidal fuzzy num-
bers (with degree
) is a construct
where
1)
is a singleton alphabet ( is called spike);
2)
are neurons of the form
,where
a)
is a trapezoidal fuzzy number in [0, 1] representing
the potential value of spikes (i.e., the value of elec-
trical impulses) contained in neuron
;
b)
is a trapezoidal fuzzy number in [0, 1] representing
the fuzzy truth value correspondingtoneuron
;
c)
represents a firing (spiking) rule associated with
neuron
of the form ,where is a
regular expression, and
and are trapezoidal fuzzy
numbers in [0, 1].
3)
with for all
, is a directed graph of synapses
between the linked neurons;
4)
indicate the input neuron set and
the output neuron set of
, respectively.
In an FRSN P system, the pulse value contained in each
neuron is not the number of spikes represented by a real
number, but a trapezoidal fuzzy number in [0, 1], which can
be interpreted as the potential value of spikes contained in
neuron
. The motivation for the introduction of trapezoidal
fuzzy numbers comes from three aspects. First of all, due to
experts' subjectivity, professional knowledge acquisition has
various uncertainties. Subsequently, human knowledge in the
real world, such as knowledge in fault diagnosis process, is
usually expressed by using linguistic terms with a certain
degree of uncertainty. For example, we often use fuzzy con-
cepts (ab so lutely-false, very-low, low, medium-low, medium,
medium-high, high, very-high, absolu tely-high) to describe a
degree of uncertainty. In addition, the knowledge in practical
applications may contain a certain degree of uncertainty. For
instance, the operation process of protective devices in fault
diagnosis usually includes uncertainly protective messages
such as maloperation and misinformation.
The trapezoidal fuzzy number in Definition 1 can be param-
eterized by a 4-tuple
, as shown in Fig. 5,
where
and are real numbers such that
Fig. 5. Trapezoidal fuzzy number.
, which are the four horizontal axis values of the trape-
zoid. The membership function
of the trapezoidal fuzzy
number
is defined as follows:
(1)
Let
and be two trapezoidal fuzzy numbers,
and . The arithmetic
operations of the trapezoidal fuzzy numbers
and are listed
as follows. More operations can be seen in [6] and [32].
1) Addition
:
;
2) Multiplication
:
.
We define four logic operations as follows, where
and
are trapezoidal fuzzy numbers, and , are real numbers.
1) Minimum operator
: ;
2) Maximum operator
: ;
3) and
:
;
4) or
:
.
We also define a scalar multiplication operation as follows,
where
is a trapezoidal fuzzy number and is a real number.
1) Scalar Multiplication:
.
With regard to the pulse value
,if ,neuron
contains a spike with value , otherwise, the neuron contains
no spike. The firing condition
means that the spiking
rule associated with neuron
can be applied if and only if the
number of spikes that neuron
receives at any computational
step equals
, otherwise, the firing rule cannot be applied. If the
number of spikes that neuron
receives is less than ,neuron
performs the operation or on the potential values carried
by these spikes to update its pulse value.
According to their usage, in an FRSN P system the neurons
are divided into two categories: proposition neurons and rule
neurons. Each neuron
corresponds to either a proposition or
a fuzzy production rule, which will be described later in this sec-
tion. Thus, the trapezoidal fuzzy number
can be understood
as either the fuzzy truth value of a proposition or the certainty
factor of a fuzzy production rule.

Definition 2: A proposition neuron,asshowninFig.6,cor-
responds to a proposition in the fuzzy production rules. Such a
neuron is represented by the symbol
.
The fuzzy truth value of a proposition neuron equals to
the fuzzy truth value of the proposition corresponding to this
neuron. If such a proposition neuron receives one spike, i.e.,
, it will fire and emit a spike. The parameter of the
firing rule contained in such a proposition neuron is identical
to
. If a proposition neuron is an input, then its pulse value
equals to the fuzzy truth value of this neuron. Otherwise, if
there is only one presynaptic rule neuron, then
equals to the
pulse value transmitted from this neuron. In any other case,
equals to the result of the operation on all pulse values
received from its presynaptic rule neurons.
There are three types of rule n eurons: general, and and or,
which are represented by the three symbols
, and ,re-
spectively. We use
to denote a rule neuron. If the number of
spikes a rule neuron receives equals the number of its presy-
napses, it will fire and emit a spike. In what follows we define
each type of rule neurons.
Definition 3: A general rule neuron
, as shown in Fig. 7 (i),
corresponds to a fuzzy production rule which has only one
proposition in the antecedent part of the rule. The consequent
part of the fuzzy production rule may contain one or more
propositions.
A general rule neuron has only one presynaptic proposition
neuron and one or more postsynaptic proposition neurons. The
fuzzy truth value of a general rule neuron equals to the certainty
factor of the fuzzy production rule corresponding to its neuron.
If a general rule neuron receives a spike with potential value
and its firing condition is satisfied, then the neuron fires and
produces a new spike with potential value
.
Definition 4: An and rule neuron
, as shown in Fig. 7 (ii),
corresponds to the fuzzy production rule which has more than
one proposition with an and relationship in the antecedent part
of the rule. The consequent part of the fuzzy production rule
contains only one proposition.
An and rule neuron has more than one presynaptic proposi-
tion neuron and only one postsynaptic proposition neuron. The
fuzzy truth value of an and rule neuron equals to the certainty
factor of the fuzzy production rule corresponding to its neuron.
If an and rule neuron receives
spikes with potential values
, respectively, and its firing condition is satisfied,
then the neuron fires and produces a new spike with the poten-
tial value
.
Definition 5: An or rule neuron
,asshowninFig.7(iii),
corresponds to the fuzzy production rule which has more than
one proposition with an or relationship in the antecedent part
of the rule. The consequent part of the fuzzy production rule
contains only one proposition.
An or rule neuron has more than one presynaptic proposi-
tion neurons and only one postsynaptic proposition neuron. The
fuzzy truth value of an or rule neuron equals to the certainty
factor of the fuzzy production rule corresponding to its neuron.
If an or rule neuron receives
spikes with potential values
, respectively, and its firing condition is satisfied,
then the neuron fires and produces a new spike with the poten-
tial value
.
Fig. 6. (a) Proposition neuron and (b) its simplified form.
Fig. 7. Rule neurons. (i) A general rule neuron (a) and its simplified form (b);
(ii) An and rule neuron (a) and its simplified form (b); (iii) An or rule neuron
(a) and its simplified form (b).
Fig. 8. Modeling process of Type 1 using one FRSN P system.
In what follows, we use FRSN P systems to model these
fuzzy production rules, which will be used to model fault
diagnosis in power systems. We consider four types of fuzzy
production rules. An FRSN P system is used to model one
or more fuzzy production rules. In the following description,
is the th fuzzy production rule, repre-
sents the number of fuzzy production rules,
is a trapezoidal
fuzzy number in [0, 1] representing the certainty factor of
, is the th proposition appearing in the
antecedent or consequent part of
, represents the number
of proportions, and
is a trapezoidal fuzzy number in [0, 1]
representing the fuzzy truth value of proposition
.
Type 1:
.The
modeling process of this rule type by using one FRSN P system
is shown in Fig. 8, where (a), (b), and (c) represent spike
being
transmitted from input neuron
to output neuron . The fuzzy
truth value of the proposition
is .

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Fault diagnosis of electric power systems based on fuzzy reasoning spiking neural p systems" ?

This paper proposes a graphic modeling approach, fault diagnosis method based on fuzzy reasoning spiking neural P systems ( FDSNP ), for power transmission networks. The results of case studies show that FDSNP is effective in diagnosing faults in power transmission networks for single and multiple fault situations with/without incomplete and uncertain SCADA data, and is superior to four methods, reported in the literature, in terms of the correctness of diagnosis results. 

Q2. What future works have the authors mentioned in the paper "Fault diagnosis of electric power systems based on fuzzy reasoning spiking neural p systems" ?

Future work will focus on verifying the performance superiority of FDSNP, compared with other diagnosis methods, by using performance metrics including diagnosis time, fault section misinformation rate, fault section missing rate and computational complexity. The authors would like to thank the Editor-in-Chief, Prof. A. Conejo, the editors, and the anonymous reviewers for their insightful comments and suggestions which greatly helped in improving the quality of this paper. 

Q3. What are the four methods used to perform comparative experiments?

Four diagnosis methods, fuzzy logic (FL) [3], fuzzy Petri nets (FPN) [4], genetic algorithm-tabu search (GATS) [15], and genetic algorithm (GA) [17], are used as benchmarks to perform comparative experiments. 

Q4. Why do the authors use linguistic terms to describe certainty factors?

Due to the uncertainty of the knowledge of experts and senior dispatchers, the authors use linguistic terms to describe certainty factors. 

Q5. Why do the authors suggest network topology analysis?

The authors suggest network topology analysis because it decreases the number of candidate diagnosing areas and reduce the subsequent computational workload [10]. 

Q6. How many scientific papers has he published?

He has published thirteen books in computer science and mathematics, and over 250 scientific papers in international journals (collaborating with researchers worldwide). 

Q7. What is the definition of a FRSN P system with trapezoidal fuzzy numbers?

In an FRSN P system, the pulse value contained in each neuron is not the number of spikes represented by a real number, but a trapezoidal fuzzy number in [0, 1], which can be interpreted as the potential value of spikes contained in neuron . 

Q8. What is the main reason why FDSNP can be used in large-scale power transmission networks?

this method can be used for large-scale power transmission networks because the complexity of the fault diagnosis models based on FRSN P systems does not increase sharply and quickly with the scale of networks. 

Q9. what is the process of this rule type modeled by using one FRSN P system?

The process of this rule type modeled by using one FRSN P system is shown in Fig. 10, where (a), (b), and (c) represent spike being transmitted from input neuron to output neurons.