# Automatic Implementation of Fuzzy Reasoning Spiking Neural P Systems for Diagnosing Faults in Complex Power Systems

Authors: Haina Rong; Kang Yi; Gexiang Zhang; Jianping Dong; Prithwineel Paul; Zhiwei Huang
Journal: Complexity
 (2019)

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## Abstract

As an important variant of membrane computing models, fuzzy reasoning spiking neural P systems (FRSN P systems) were introduced to build a link between P systems and fault diagnosis applications. An FRSN P system offers an intuitive illustration based on a strictly mathematical expression, a good fault-tolerant capacity, a good description for the relationships between protective devices and faults, and an understandable diagnosis model-building process. However, the implementation of FRSN P systems is still at a manual process, which is a time-consuming and hard labor work, especially impossible to perform on large-scale complex power systems. This manual process seriously limits the use of FRSN P systems to diagnose faults in large-scale complex power systems and has always been a challenging and ongoing task for many years. In this work we develop an automatic implementation method for automatically fulfilling the hard task, named membrane computing fault diagnosis (MCFD) method. This is a very significant attempt in the development of FRSN P systems and even of the membrane computing applications. MCFD is realized by automating input and output, and diagnosis processes consists of network topology analysis, suspicious fault component analysis, construction of FRSN P systems for suspicious fault components, and fuzzy inference. Also, the feasibility of the FRSN P system is verified on the IEEE14, IEEE 39, and IEEE 118 node systems.


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## Body

## 1. Introduction

As a branch of natural computing, membrane computing was introduced by Păun in 1998 [1, 2]. The distributed parallel computational model is called a membrane system or a P system. Membrane computing aims to investigate the computational models and their applications abstracted from the structure and functioning of cells [2–5]. A large number of studies [6–10] show that many variants of P systems are Turing complete [11–14]. Moreover, distribution, maximally parallel, and expansibility [3, 15–18] make P systems suitable for solving a variety of practical problems, like engineering optimization [3, 19], combinatorial optimization [20], and membrane controllers [21–24].With the development of membrane computing, many types of membrane systems were proposed [12, 13, 25, 26], of which spiking neural P systems (SN P systems) are a hot research topic covering language generation [27, 28], computing power [29, 30], fuzzy reasoning [31–33], and NP-hard problems [28, 30, 34]. SN P systems were introduced by Ionescu et al. in 2006 [13]. As a typical application type of SN P systems, fuzzy reasoning spiking neural P systems (FRSN P systems) were introduced to build a bridge between the P systems and fault diagnosis for complex power systems [3, 24]. An FRSN P system offers an intuitive illustration based on a strictly mathematical expression, a good fault-tolerant capacity, a good description for the relationships between protective devices and faults, and an understandable diagnosis model-building process [3, 35]. According to the investigations reported in literature, FRSN P systems have been successfully used to diagnose the faults occurring in transformers [24, 36], power transmission networks [35, 37–39], traction power supply systems of high-speed railways [40], metro traction power systems[41], and fault classification of power transmission lines [39].Until now, the implementation of FRSN P systems is still at a manual process, which seriously limits the use of FRSN P systems to diagnose faults in large-scale complex power systems. For example, in [3, 24, 35–37, 42], only a small-scale power system was considered. Furthermore, it is impossible to perform complexity analysis for FRSN P systems with a manual diagnosis process. These problems result in the difficulty in the process of comparisons of FRSN P systems with other diagnosis methods. Thus, the automatic implementation of FRSN P systems has always been a challenging and ongoing task for many years.In this paper, an automatic implementation method has been developed for automatically fulfilling the task and it is called membrane computing fault diagnosis (MCFD) method. This is a very significant step in this research direction. The method automatizes input, output, and four diagnosis processes: network topology analysis, suspicious fault component analysis, construction of FRSN P system for suspicious fault components, and fuzzy inference.The article is arranged in the following manner: Section2 discusses MCFD, Section 3 discusses the experimental results of the system performed on IEEE14, IEEE 39, and IEEE 118 node system, Section 4 analyzes the complexity of the system, and Section 5 concludes this work.


## 2. MCFD

Membrane computing fault diagnosis (MCFD) method automatizes mainly three components, i.e., input, output, and diagnosis process. The main components of the diagnosis process consist of network topology analysis, suspicious fault component analysis, construction of FRSN P system for suspicious fault components, and fuzzy inference. The input data is composed of topology data of power systems and protection configuration data. The outputs include fault component information, protective relays information, and circuit breakers operation evaluation. The schematic structure of MCFD is shown in Figure1.Figure 1
Schematic structure of MCFD.


### 2.1. Automatized Input

The information source of the fault diagnosis program is the grid static data and switch state data based on fault information system. In this paper we use access database to store network topology information and protection configuration information. The static topology information and protection configuration information of the power network are given as input into the access database to form the topology table and protection configuration table. Therefore, the input data of FRSN P system for fault diagnosis consists of two parts: topology data of a power system and protection configuration data.


#### 2.1.1. Topology Data of Power Systems

In this paper we mainly discuss the fault diagnosis methods in power transmission network. Moreover, this paper improves the traditional line analysis [43] and redefines the components, i.e., transmission lines, busbars, transformers, and generators. The circuit breakers (CBs) work as switches.The “Component” and “Switch” that appear in the following sections are defined in the following manner. A power system is made up of components and switch devices which connect a variety of other equipment. So, the whole electric power system grid network can be represented by the power transmission network topology as shown in Figure2. The components shown in the figure refer to the transmission lines, busbars, transformers, and generators. The switches refer to the circuit breakers with two states: open and closed.Figure 2
Schematic diagram of power transmission network topology.After there is a failure, because of the grid power system components and complex wiring, it is very difficult to find the faults in huge systems. But whenever fault occurs in a power system, the protective relays and circuit breakers will operate to isolate the fault. We investigate the actions of protective relays and tripped circuit breakers in the network and the connection relationship between them. Figure2 shows a simple and clear power transmission network topology of the connection relation between components and circuit breakers. Then the fault component is searched according to the tripped circuit breakers.The topology table (Table1) is constructed from the components and switches of the entire power transmission network topology. The table stores the data of the main components and switches along with their connection relationships and the protection number associated with each component.Table 1
The topology table.
ID number Switches operation Component/switch Type Type number Associated components/switches Associated protective relays 10108 - - B08 Bus 101 CB0807.CB08G2 10110108.21310214


#### 2.1.2. Protection Configuration Data

The SCADA system can provide the tripped circuit breakers and operated protective relays information whenever there is a fault in the grid. Moreover, the data of the components, protective relays, and circuit breakers are used to construct the correlation database. The correlation relationships are introduced in [44–46] in the following manner:“Component-Protective” relay means that the protective relays can be divided into the main protective relays of the component and one of the first backup protective relays.“Protective relay – Switch” means that the circuit breaker can trip in principle once the protective relays operation is performed.“Component1 - Component2” relates to the scope of protection of the second backup protective relay of component1 which can protect component2.With these correlations, the protection configuration table can be described as in Table2.Table 2
The protection configuration table.
IDnumber Protectiverelay Relays operation Operatedswitches Protected equipment 10110113 Main_ protective relay 0 010426.10438.10439 B13


### 2.2. Automatized Network Topology Analysis

After the failure in the power system transmission network, the fault component is eventually isolated by tripped circuit breakers. Moreover, the fault component will be isolated in the passive network. We have elaborated in Section2.1 the entire topology database and protective relay database. Also, we have established the corresponding topology table which represents the correlation between the whole transmission network topology structure and protective relays. Whenever a failure occurs in the power system transmission network, at first the information is received from SCADA system by circuit breaker opening and closing state, and then the suspicious fault component is found by using the network topology analysis method [47, 48]. The specific network topology analysis method is as follows:(1)
Set up M and store all component IDs into M.(2)
Set up the subset N. Take a component from the set M and put it in the subset N. Find all closed circuit breakers connected to it. If there is no closed circuit breaker, then turn to step (5).(3)
Identify the components connected to the closed circuit breaker and add the found components to the subset N.(4)
Continue to search for closed circuit breakers that are connected to the components in step (3) (except for circuit breakers used in step (3)). If there is a closed circuit breaker, go to step (3).(5)
Remove all components in the set M that appear in the subset collection N. If the set M is not empty, then transfer to step (2).(6)
List all the subsets N.In fault diagnosis, the network topology analysis method is used to search all subsets, and then the passive networks are found from these subsets. These passive networks are the outage areas. In this way, the diagnosis scope can be reduced and then the suspicious fault component is diagnosed. It also reduces the amount of operations and improves the efficiency of fault diagnosis. The process of the searching of the passive networks is shown in Figure3.Figure 3
Search the outage area flow chart.


### 2.3. Automatized Suspicious Fault Component Analysis

The network topology analysis method is used to find a passive network and the diagnosis of the suspicious fault components in the passive network. The modeling of FRSN P systems is very complex because of the existence of many components in the complex grid network. In order to improve the diagnosis efficiency and accuracy of the algorithm, in this paper, we introduce the concept of suspected fault component logic analysis. At first a logic diagram is constructed in such a manner that the suspected fault component is considered as the starting point. Then it searches and builds towards each connection to protect the component within the scope of the protection of all components and switches. The FRSN P system model is constructed according to the fault production rules of the suspected fault components. Hence the fault area is reduced and the fault component is identified.In the logic diagram the suspicious component along with other system components and switches in the passive network are represented by a node and the edge between the two nodes represents the connection between the components and switches. Moreover, the condition of the path search termination is(1)
The search is complete when all the protective relays and switches that can protect the suspicious fault components are searched on different paths.(2)
If the search path is disconnected from the peripheral device due to normal operations (such as the operation of the blade, etc.), then the search will be terminated.(3)
If the search direction is opposite to the rule, the search path will terminate.(4)
Search for a loop structure or parallel edge structure on the search path, and if it exists then terminate this direction search.The logic diagram of the suspected fault component describes the topological association of the suspected fault components and its associated protection in the power grid. The following example illustrates the method of forming the logic diagram of the suspected component. In Figure4, it is assumed that the suspicious fault component is B3 by the method of network topology analysis. The logic diagram of the suspected fault component is established by bus B3 in three outgoing line paths: B3→CB5→L3→CB2; B3→CB6→L4→CB7; B3→CB9→L5→CB10, respectively. Moreover, the mutual cooperation between the protective relay and circuit breaker will cut off the connection with the whole grid.Figure 4
A local grid.


### 2.4. Automatized Modeling Suspicious Fault Components with FRSNP System

Before performing the reasoning algorithm, we need to build a FRSN P system diagnosis model. A local grid is shown in Figure4 and the network topology analysis subsystem obtains the bus B3 as the suspicious component. Also, the bus B3 and line L4 are used to build the FRSN P system fault diagnosis model.At first, the busB3 in Figure 4 is used to describe the model where the fault confidence level of bus B3 is the value of output of the FRSN P system. Moreover, we discussed the mutual cooperation between the protective relay and circuit breaker by the suspicious fault component logic diagram in Section 2.3. The fault production rules of bus B3 are described as follows:R 1: IF (B3m operates and CB5 trips) OR (L3Ssoperates and CB2 trips) THEN B3faults (CF=ci),R 2: IF (B3m operates and CB6 trips) OR (L4Ss operates and CB7 trips) THEN B3 faults (CF=ci),R 3: IF (B3m operates and CB9 trips) OR (L5Ss operates and CB10 trips) THEN B3 faults (CF=ci).The following fault diagnosis model based on FRSN P system for busB3 is built according to these fault production rules shown in Figure 5(a). The FRSN P system Π is a construct of the form(1)Π=O,σp1,…,σp20,σr1,…,σr10,syn,in,outwhere(1)
O={a} is the singleton alphabet (a is called spike);(2)
σp1,…,σp20 are proposition neurons corresponding to the propositions with fuzzy truth values θ1,θ2,…,θ22;(3)
σr1,…,σr10 are rule neurons, where σr1,…,σr6, and σr10 are and rule neurons and σr7, σr8, and σr9 are or rule neurons. A real number ciϵ[0,1] is used to represent the certainty factor (CF) of the fuzzy production rule associated with σri(1≤i≤10);(4)
syn⊆1,2,…,22×{1,2,…,10} with i≠j for all i,j∈syn,1≤i,j≤22, is a directed graph of synapses between the linked neurons;(5)
in={σp1,…,σp12}, out={σr10}.Figure 5
Suspect fault components FRSN P system model.
(a)
B 3 FRSN P system model (b)
L 4FRSN P system modelThe transmission lineL4 in Figure 4 is used to describe model building of transmission line, where the fault confidence level of transmission line L4 is the value of output of the FRSN P system. The fault production rules of transmission line L4 are described as follows:R 1: IF (L4Sm operates and CB6 trips) OR (L4Spoperates and CB6 trips) OR (second backup protection operates and CB trips) THEN L4 faults (CF=ci),R 2: IF (L4Rm operates and CB7 trips) OR (L4Rs operates and CB7 trips) OR (second backup protection operates and CB trips) THEN L4 faults (CF=ci).Therefore, fault diagnosis model based on FRSN P system for transmission lineL4 is built according to the fault production rules shown in Figure 5(b).In order to make the reasoning reflect the operation of the actual power grid more accurately, the uncertain factors in the protection and the circuit breaker action information are obtained from the power system dispatching center. In this paper, the initial value of the confidence level for operate and nonoperate protective relays and circuit breakers are given in [49], as shown in Tables 3 and 4, respectively. At the same time, considering the uncertainty of the rule credibility, the certainty factor ci of each fuzzy production rule is considered to be 0.95.Table 3
Confidence levels of operate protective devices.
ComponentsName Main First backup Second backup Relays CBs Relays CBs Relays CBs Bus 0.8564 0.9833 - - 0.7 0.75 Line 0.9913 0.9833 0.8 0.85 0.7 0.75Table 4
Confidence levels of nonoperate protective devices.
Components Name Main First backup Second backup Relays CBs Relays CBs Relays CBs Bus 0.2 0.2 - - 0.2 0.2 Line 0.2 0.2 0.2 0.2 0.2 0.2In this paper, a proposition neuron is used for all second backup protective relays and circuit breakers at both ends of the line. If there are multiple second backup protective relays, a factorµ1, µ2 as (2), (3) is applied before the confidence level of the proposition neuron, and the two ends of the line (S end and R end), respectively. (2)μ1=NumberofprotectiverelaysCBforSendoperationNumberofallprotectiverelaysCBsontheSend(3)μ2=NumberofprotectiverelaysCBforRendoperationNumberofallprotectiverelaysCBsontheRendThe automatic generation of the FRSN P system model is shown below.Step 1.
According to the suspected fault component logic diagram, take one path of the suspected fault component logic diagram, and the components and switches involved in the path can be expressed as a fault production rule.Step 2.
Set up two setθ and δ, where θ is the proposition neuron corresponding to the proposition with fuzzy truth values. The initial value setting of the corresponding protective relay and circuit breaker of the first layer of proposition neurons in the FRSN P system model is set by the information of the input from SCADA system.δis the certainty factor which is added to describe the credibility of the fuzzy generated rules of the neuron.Step 3.
Store the values ofθ and δ according to the confidence levels of operate and nonoperate protective relays and circuit breakers in the first path.Step 4.
Repeat the first three steps until all the values ofθ and δ represented by the paths are added corresponding to one branch direction.


### 2.5. Automatized Fuzzy Inference

After obtaining the confidence level of the proposition expressed by the proposition neuron and the certainty factor value of the rule neuron, the next step is to carry out the reasoning operation. By executing the following reasoning algorithm, the fuzzy values of the propositions are represented by the output proposition neurons which can be obtained quickly and simply. Specific algorithm steps [35] are as follows (where s represents the number of proposition neurons, t represents the number of rule neurons and s+t=m).Step 1.
Set the initial state tog=0. Set the termination condition to 01=(0,…,0)1×tT. The initial values of θ and δ are set to θg=(θ1g,θ2g,…,θsg)T and δg=(δ1g,δ2g…,δtg)T, respectively.Step 2.
g is increased by one.Step 3.
The firing condition of each input neurong=1 or each proposition neuron (g>1) is evaluated. If the condition is satisfied and there is a presynaptic rule neuron, the neuron fires and transmits a spike to the next rule neuron. Compute the fuzzy truth value vector δg according to (4):(4)δg=D1T⊗θg-1+D2T⊕θg-1+D3T⊙θg-1Step 4.
Ifδg=01, then the algorithm stops and output the reasoning results. Otherwise, the algorithm continues.Step 5.
Evaluate the firing condition of each rule neuron. If the condition is satisfied, then the rule neuron fires and transmits a spike to the next proposition neuron. Next, compute the fuzzy truth value vectorθg according to (5). Then, the algorithm goes to Step 2:(5)δg=ET⊙C⊗δg
Parameter vectors and matrices are described in the following manner:(1)
θ=(θ1,θ2,…,θs)T is a real truth value vector of s proposition neurons. θi(1≤i≤s) is a real number in [0,1] and represents the potential value contained in the ith proposition neuron. If there is no spike in a proposition neuron, its potential value is 0.(2)
δ=(δ1,δ2…,δt)T is a real truth value vector of t rule neurons. δt(1≤j≤t) is a real number in [0,1] and represents the potential value contained in the jth rule neuron. If there is no spike in a rule neuron, its potential value is 0.(3)
C=diag(c1,c2,…,ct) is a diagonal matrix, where ct(1≤j≤t) is a real number in [0,1] representing the certainty factor of the jth fuzzy production rule.(4)
D1=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to general rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to thegeneral rule neuron σj, dij=1; otherwise, dij=0.(5)
D2=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to and rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to theand rule neuron σj, dij=1; otherwise, dij=0.(6)
D3=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to and rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to theor rule neuron σj, dij=1; otherwise, dij=0.(7)
E=(eji)t×s is a synaptic matrix representing the directed connection between rule neurons and proposition rule neurons. If there is a directed arc (synapse) from the rule neuron σj to the proposition neuron σi, eji=1; otherwise, eji=0.
Subsequently, we introduce the following three multiplication operations:(1)
DT⊗θ=(d¯1,d¯2,…,d¯t)T, where d¯j=d1j∗θ1+d2j∗θ2+⋯+dsj∗θs, j=1,2,…,t.(2)
DT⊕θ=(d¯1,d¯2,…,d¯t)T, where d¯j=min⁡(d1j∗θ1,d2j∗θ2,…,dsj∗θs), j=1,2,…,t.(3)
DT⊙θ=(d¯1,d¯2,…,d¯t)T, where d¯j=max⁡(d1j∗θ1,d2j∗θ2,…,dsj∗θs), j=1,2,…,t.


### 2.6. Automatized Output

The outputs include fault component information, protective relays information, and circuit breakers operation evaluation. After the fuzzy value of the output proposition neuron is obtained according to the fault threshold, the suspected fault components can be determined if a failure has occurred. If it is a faulty component, the system outputs the fault component information and fault credibility value and goes to the reasoning process to estimate whether the protection and circuit breaker has the situation of misoperation and misoperation or not. If it is a normal component, the output appears normal.Thus, the network topology analysis algorithm to find the passive region and the diagnosis of the suspected fault components in the passive region are repeated. At first, the suspicious fault component analysis subsystem is called to form the logic diagram of the suspicious fault components, and then the FRSN P system diagnosis model is performed by using the query protection configuration data. Finally, by calling FRSN P system inference algorithm, the fault confidence levels of the suspected fault components are obtained and the fault of the components is determined to realize the whole diagnosis process.


## 2.1. Automatized Input

The information source of the fault diagnosis program is the grid static data and switch state data based on fault information system. In this paper we use access database to store network topology information and protection configuration information. The static topology information and protection configuration information of the power network are given as input into the access database to form the topology table and protection configuration table. Therefore, the input data of FRSN P system for fault diagnosis consists of two parts: topology data of a power system and protection configuration data.


### 2.1.1. Topology Data of Power Systems

In this paper we mainly discuss the fault diagnosis methods in power transmission network. Moreover, this paper improves the traditional line analysis [43] and redefines the components, i.e., transmission lines, busbars, transformers, and generators. The circuit breakers (CBs) work as switches.The “Component” and “Switch” that appear in the following sections are defined in the following manner. A power system is made up of components and switch devices which connect a variety of other equipment. So, the whole electric power system grid network can be represented by the power transmission network topology as shown in Figure2. The components shown in the figure refer to the transmission lines, busbars, transformers, and generators. The switches refer to the circuit breakers with two states: open and closed.Figure 2
Schematic diagram of power transmission network topology.After there is a failure, because of the grid power system components and complex wiring, it is very difficult to find the faults in huge systems. But whenever fault occurs in a power system, the protective relays and circuit breakers will operate to isolate the fault. We investigate the actions of protective relays and tripped circuit breakers in the network and the connection relationship between them. Figure2 shows a simple and clear power transmission network topology of the connection relation between components and circuit breakers. Then the fault component is searched according to the tripped circuit breakers.The topology table (Table1) is constructed from the components and switches of the entire power transmission network topology. The table stores the data of the main components and switches along with their connection relationships and the protection number associated with each component.Table 1
The topology table.
ID number Switches operation Component/switch Type Type number Associated components/switches Associated protective relays 10108 - - B08 Bus 101 CB0807.CB08G2 10110108.21310214


### 2.1.2. Protection Configuration Data

The SCADA system can provide the tripped circuit breakers and operated protective relays information whenever there is a fault in the grid. Moreover, the data of the components, protective relays, and circuit breakers are used to construct the correlation database. The correlation relationships are introduced in [44–46] in the following manner:“Component-Protective” relay means that the protective relays can be divided into the main protective relays of the component and one of the first backup protective relays.“Protective relay – Switch” means that the circuit breaker can trip in principle once the protective relays operation is performed.“Component1 - Component2” relates to the scope of protection of the second backup protective relay of component1 which can protect component2.With these correlations, the protection configuration table can be described as in Table2.Table 2
The protection configuration table.
IDnumber Protectiverelay Relays operation Operatedswitches Protected equipment 10110113 Main_ protective relay 0 010426.10438.10439 B13


## 2.1.1. Topology Data of Power Systems

In this paper we mainly discuss the fault diagnosis methods in power transmission network. Moreover, this paper improves the traditional line analysis [43] and redefines the components, i.e., transmission lines, busbars, transformers, and generators. The circuit breakers (CBs) work as switches.The “Component” and “Switch” that appear in the following sections are defined in the following manner. A power system is made up of components and switch devices which connect a variety of other equipment. So, the whole electric power system grid network can be represented by the power transmission network topology as shown in Figure2. The components shown in the figure refer to the transmission lines, busbars, transformers, and generators. The switches refer to the circuit breakers with two states: open and closed.Figure 2
Schematic diagram of power transmission network topology.After there is a failure, because of the grid power system components and complex wiring, it is very difficult to find the faults in huge systems. But whenever fault occurs in a power system, the protective relays and circuit breakers will operate to isolate the fault. We investigate the actions of protective relays and tripped circuit breakers in the network and the connection relationship between them. Figure2 shows a simple and clear power transmission network topology of the connection relation between components and circuit breakers. Then the fault component is searched according to the tripped circuit breakers.The topology table (Table1) is constructed from the components and switches of the entire power transmission network topology. The table stores the data of the main components and switches along with their connection relationships and the protection number associated with each component.Table 1
The topology table.
ID number Switches operation Component/switch Type Type number Associated components/switches Associated protective relays 10108 - - B08 Bus 101 CB0807.CB08G2 10110108.21310214


## 2.1.2. Protection Configuration Data

The SCADA system can provide the tripped circuit breakers and operated protective relays information whenever there is a fault in the grid. Moreover, the data of the components, protective relays, and circuit breakers are used to construct the correlation database. The correlation relationships are introduced in [44–46] in the following manner:“Component-Protective” relay means that the protective relays can be divided into the main protective relays of the component and one of the first backup protective relays.“Protective relay – Switch” means that the circuit breaker can trip in principle once the protective relays operation is performed.“Component1 - Component2” relates to the scope of protection of the second backup protective relay of component1 which can protect component2.With these correlations, the protection configuration table can be described as in Table2.Table 2
The protection configuration table.
IDnumber Protectiverelay Relays operation Operatedswitches Protected equipment 10110113 Main_ protective relay 0 010426.10438.10439 B13


## 2.2. Automatized Network Topology Analysis

After the failure in the power system transmission network, the fault component is eventually isolated by tripped circuit breakers. Moreover, the fault component will be isolated in the passive network. We have elaborated in Section2.1 the entire topology database and protective relay database. Also, we have established the corresponding topology table which represents the correlation between the whole transmission network topology structure and protective relays. Whenever a failure occurs in the power system transmission network, at first the information is received from SCADA system by circuit breaker opening and closing state, and then the suspicious fault component is found by using the network topology analysis method [47, 48]. The specific network topology analysis method is as follows:(1)
Set up M and store all component IDs into M.(2)
Set up the subset N. Take a component from the set M and put it in the subset N. Find all closed circuit breakers connected to it. If there is no closed circuit breaker, then turn to step (5).(3)
Identify the components connected to the closed circuit breaker and add the found components to the subset N.(4)
Continue to search for closed circuit breakers that are connected to the components in step (3) (except for circuit breakers used in step (3)). If there is a closed circuit breaker, go to step (3).(5)
Remove all components in the set M that appear in the subset collection N. If the set M is not empty, then transfer to step (2).(6)
List all the subsets N.In fault diagnosis, the network topology analysis method is used to search all subsets, and then the passive networks are found from these subsets. These passive networks are the outage areas. In this way, the diagnosis scope can be reduced and then the suspicious fault component is diagnosed. It also reduces the amount of operations and improves the efficiency of fault diagnosis. The process of the searching of the passive networks is shown in Figure3.Figure 3
Search the outage area flow chart.


## 2.3. Automatized Suspicious Fault Component Analysis

The network topology analysis method is used to find a passive network and the diagnosis of the suspicious fault components in the passive network. The modeling of FRSN P systems is very complex because of the existence of many components in the complex grid network. In order to improve the diagnosis efficiency and accuracy of the algorithm, in this paper, we introduce the concept of suspected fault component logic analysis. At first a logic diagram is constructed in such a manner that the suspected fault component is considered as the starting point. Then it searches and builds towards each connection to protect the component within the scope of the protection of all components and switches. The FRSN P system model is constructed according to the fault production rules of the suspected fault components. Hence the fault area is reduced and the fault component is identified.In the logic diagram the suspicious component along with other system components and switches in the passive network are represented by a node and the edge between the two nodes represents the connection between the components and switches. Moreover, the condition of the path search termination is(1)
The search is complete when all the protective relays and switches that can protect the suspicious fault components are searched on different paths.(2)
If the search path is disconnected from the peripheral device due to normal operations (such as the operation of the blade, etc.), then the search will be terminated.(3)
If the search direction is opposite to the rule, the search path will terminate.(4)
Search for a loop structure or parallel edge structure on the search path, and if it exists then terminate this direction search.The logic diagram of the suspected fault component describes the topological association of the suspected fault components and its associated protection in the power grid. The following example illustrates the method of forming the logic diagram of the suspected component. In Figure4, it is assumed that the suspicious fault component is B3 by the method of network topology analysis. The logic diagram of the suspected fault component is established by bus B3 in three outgoing line paths: B3→CB5→L3→CB2; B3→CB6→L4→CB7; B3→CB9→L5→CB10, respectively. Moreover, the mutual cooperation between the protective relay and circuit breaker will cut off the connection with the whole grid.Figure 4
A local grid.


## 2.4. Automatized Modeling Suspicious Fault Components with FRSNP System

Before performing the reasoning algorithm, we need to build a FRSN P system diagnosis model. A local grid is shown in Figure4 and the network topology analysis subsystem obtains the bus B3 as the suspicious component. Also, the bus B3 and line L4 are used to build the FRSN P system fault diagnosis model.At first, the busB3 in Figure 4 is used to describe the model where the fault confidence level of bus B3 is the value of output of the FRSN P system. Moreover, we discussed the mutual cooperation between the protective relay and circuit breaker by the suspicious fault component logic diagram in Section 2.3. The fault production rules of bus B3 are described as follows:R 1: IF (B3m operates and CB5 trips) OR (L3Ssoperates and CB2 trips) THEN B3faults (CF=ci),R 2: IF (B3m operates and CB6 trips) OR (L4Ss operates and CB7 trips) THEN B3 faults (CF=ci),R 3: IF (B3m operates and CB9 trips) OR (L5Ss operates and CB10 trips) THEN B3 faults (CF=ci).The following fault diagnosis model based on FRSN P system for busB3 is built according to these fault production rules shown in Figure 5(a). The FRSN P system Π is a construct of the form(1)Π=O,σp1,…,σp20,σr1,…,σr10,syn,in,outwhere(1)
O={a} is the singleton alphabet (a is called spike);(2)
σp1,…,σp20 are proposition neurons corresponding to the propositions with fuzzy truth values θ1,θ2,…,θ22;(3)
σr1,…,σr10 are rule neurons, where σr1,…,σr6, and σr10 are and rule neurons and σr7, σr8, and σr9 are or rule neurons. A real number ciϵ[0,1] is used to represent the certainty factor (CF) of the fuzzy production rule associated with σri(1≤i≤10);(4)
syn⊆1,2,…,22×{1,2,…,10} with i≠j for all i,j∈syn,1≤i,j≤22, is a directed graph of synapses between the linked neurons;(5)
in={σp1,…,σp12}, out={σr10}.Figure 5
Suspect fault components FRSN P system model.
(a)
B 3 FRSN P system model (b)
L 4FRSN P system modelThe transmission lineL4 in Figure 4 is used to describe model building of transmission line, where the fault confidence level of transmission line L4 is the value of output of the FRSN P system. The fault production rules of transmission line L4 are described as follows:R 1: IF (L4Sm operates and CB6 trips) OR (L4Spoperates and CB6 trips) OR (second backup protection operates and CB trips) THEN L4 faults (CF=ci),R 2: IF (L4Rm operates and CB7 trips) OR (L4Rs operates and CB7 trips) OR (second backup protection operates and CB trips) THEN L4 faults (CF=ci).Therefore, fault diagnosis model based on FRSN P system for transmission lineL4 is built according to the fault production rules shown in Figure 5(b).In order to make the reasoning reflect the operation of the actual power grid more accurately, the uncertain factors in the protection and the circuit breaker action information are obtained from the power system dispatching center. In this paper, the initial value of the confidence level for operate and nonoperate protective relays and circuit breakers are given in [49], as shown in Tables 3 and 4, respectively. At the same time, considering the uncertainty of the rule credibility, the certainty factor ci of each fuzzy production rule is considered to be 0.95.Table 3
Confidence levels of operate protective devices.
ComponentsName Main First backup Second backup Relays CBs Relays CBs Relays CBs Bus 0.8564 0.9833 - - 0.7 0.75 Line 0.9913 0.9833 0.8 0.85 0.7 0.75Table 4
Confidence levels of nonoperate protective devices.
Components Name Main First backup Second backup Relays CBs Relays CBs Relays CBs Bus 0.2 0.2 - - 0.2 0.2 Line 0.2 0.2 0.2 0.2 0.2 0.2In this paper, a proposition neuron is used for all second backup protective relays and circuit breakers at both ends of the line. If there are multiple second backup protective relays, a factorµ1, µ2 as (2), (3) is applied before the confidence level of the proposition neuron, and the two ends of the line (S end and R end), respectively. (2)μ1=NumberofprotectiverelaysCBforSendoperationNumberofallprotectiverelaysCBsontheSend(3)μ2=NumberofprotectiverelaysCBforRendoperationNumberofallprotectiverelaysCBsontheRendThe automatic generation of the FRSN P system model is shown below.Step 1.
According to the suspected fault component logic diagram, take one path of the suspected fault component logic diagram, and the components and switches involved in the path can be expressed as a fault production rule.Step 2.
Set up two setθ and δ, where θ is the proposition neuron corresponding to the proposition with fuzzy truth values. The initial value setting of the corresponding protective relay and circuit breaker of the first layer of proposition neurons in the FRSN P system model is set by the information of the input from SCADA system.δis the certainty factor which is added to describe the credibility of the fuzzy generated rules of the neuron.Step 3.
Store the values ofθ and δ according to the confidence levels of operate and nonoperate protective relays and circuit breakers in the first path.Step 4.
Repeat the first three steps until all the values ofθ and δ represented by the paths are added corresponding to one branch direction.


## 2.5. Automatized Fuzzy Inference

After obtaining the confidence level of the proposition expressed by the proposition neuron and the certainty factor value of the rule neuron, the next step is to carry out the reasoning operation. By executing the following reasoning algorithm, the fuzzy values of the propositions are represented by the output proposition neurons which can be obtained quickly and simply. Specific algorithm steps [35] are as follows (where s represents the number of proposition neurons, t represents the number of rule neurons and s+t=m).Step 1.
Set the initial state tog=0. Set the termination condition to 01=(0,…,0)1×tT. The initial values of θ and δ are set to θg=(θ1g,θ2g,…,θsg)T and δg=(δ1g,δ2g…,δtg)T, respectively.Step 2.
g is increased by one.Step 3.
The firing condition of each input neurong=1 or each proposition neuron (g>1) is evaluated. If the condition is satisfied and there is a presynaptic rule neuron, the neuron fires and transmits a spike to the next rule neuron. Compute the fuzzy truth value vector δg according to (4):(4)δg=D1T⊗θg-1+D2T⊕θg-1+D3T⊙θg-1Step 4.
Ifδg=01, then the algorithm stops and output the reasoning results. Otherwise, the algorithm continues.Step 5.
Evaluate the firing condition of each rule neuron. If the condition is satisfied, then the rule neuron fires and transmits a spike to the next proposition neuron. Next, compute the fuzzy truth value vectorθg according to (5). Then, the algorithm goes to Step 2:(5)δg=ET⊙C⊗δg
Parameter vectors and matrices are described in the following manner:(1)
θ=(θ1,θ2,…,θs)T is a real truth value vector of s proposition neurons. θi(1≤i≤s) is a real number in [0,1] and represents the potential value contained in the ith proposition neuron. If there is no spike in a proposition neuron, its potential value is 0.(2)
δ=(δ1,δ2…,δt)T is a real truth value vector of t rule neurons. δt(1≤j≤t) is a real number in [0,1] and represents the potential value contained in the jth rule neuron. If there is no spike in a rule neuron, its potential value is 0.(3)
C=diag(c1,c2,…,ct) is a diagonal matrix, where ct(1≤j≤t) is a real number in [0,1] representing the certainty factor of the jth fuzzy production rule.(4)
D1=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to general rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to thegeneral rule neuron σj, dij=1; otherwise, dij=0.(5)
D2=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to and rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to theand rule neuron σj, dij=1; otherwise, dij=0.(6)
D3=(dij)s×t is a synaptic matrix representing the directed connection from proposition neurons to and rule neurons. If there is a directed arc (synapse) from the proposition neuron σi to theor rule neuron σj, dij=1; otherwise, dij=0.(7)
E=(eji)t×s is a synaptic matrix representing the directed connection between rule neurons and proposition rule neurons. If there is a directed arc (synapse) from the rule neuron σj to the proposition neuron σi, eji=1; otherwise, eji=0.
Subsequently, we introduce the following three multiplication operations:(1)
DT⊗θ=(d¯1,d¯2,…,d¯t)T, where d¯j=d1j∗θ1+d2j∗θ2+⋯+dsj∗θs, j=1,2,…,t.(2)
DT⊕θ=(d¯1,d¯2,…,d¯t)T, where d¯j=min⁡(d1j∗θ1,d2j∗θ2,…,dsj∗θs), j=1,2,…,t.(3)
DT⊙θ=(d¯1,d¯2,…,d¯t)T, where d¯j=max⁡(d1j∗θ1,d2j∗θ2,…,dsj∗θs), j=1,2,…,t.


## 2.6. Automatized Output

The outputs include fault component information, protective relays information, and circuit breakers operation evaluation. After the fuzzy value of the output proposition neuron is obtained according to the fault threshold, the suspected fault components can be determined if a failure has occurred. If it is a faulty component, the system outputs the fault component information and fault credibility value and goes to the reasoning process to estimate whether the protection and circuit breaker has the situation of misoperation and misoperation or not. If it is a normal component, the output appears normal.Thus, the network topology analysis algorithm to find the passive region and the diagnosis of the suspected fault components in the passive region are repeated. At first, the suspicious fault component analysis subsystem is called to form the logic diagram of the suspicious fault components, and then the FRSN P system diagnosis model is performed by using the query protection configuration data. Finally, by calling FRSN P system inference algorithm, the fault confidence levels of the suspected fault components are obtained and the fault of the components is determined to realize the whole diagnosis process.


## 3. Experiments

To verify the effectiveness of the automatic implementation, the IEEE14 node power system network model shown in Figure6 is tested. It is a 14-bus system containing B01~B14 14 buses and L0102~L1314 20 lines. The protective device consists of 134 protective relays and 40 circuit breakers, and B01m,…,B14m are the main protective relays of the buses. Moreover, LXSm and LXRm are the main protective relays on both ends of the line, LXSp and LXRp are the first backup protective relays on both ends of the line, and LXSs and LXRs are the second backup protective relays on both ends of the line (where X represents the ID of the line). Before diagnosing the suspected fault component, the components and switches of the entire power transmission network must adopt the method described in the input data section to construct their respective topology table. The detailed protection configuration of various components, as well as the relationship between the protective relays and the circuit breakers, has been represented by the corresponding database in Tables 5 and 6. Furthermore, the whole diagnosis process is carried out in the MATLAB environment. We give an example to illustrate the steps of MCFD method.Table 5
IEEE14 node power system network topology database.
ID number Switch operation Component/switch Type Type number Associated components/switches Associated protective relays 10101 - - B01 Bus 101 CB01G1.CB0102.CB0105 10110101.22310201.22310202 10102 - - B02 Bus 101 CB0201.CB0203.CB0204.CB0205 10110102.21310201.22310203.22310204.22310205 10103 - - B03 Bus 101 CB0302.CB0304 10110103.21310203.22310206 10104 - - B04 Bus 101 CB0402.CB0403.CB0405.CB0407.CB0409 10110104.21310204.21310206.22310207.22310208.22310209 10105 - - B05 Bus 101 CB0501.CB0502.CB0504.CB0506 10110105.21310202.21310205.21310207.22310210 10106 - - B06 Bus 101 CB0605.CB0611.CB0612.CB0613 10110106.21310210.22310211.22310212.22310213 10107 - - B07 Bus 101 CB0704.CB0708.CB0709 10110107.21310208.22310214.22310215 10108 - - B08 Bus 101 CB0807.CB08G2 10110108.21310214 10109 - - B09 Bus 101 CB0904.CB0907.CB0910.CB0914 10110109.21310209.21310215.22310216.22310217 10110 - - B10 Bus 101 CB1009.CB1011 10110110.21310216.22310218 10111 - - B11 Bus 101 CB1106.CB1110 10110111.21310211.21310218 10112 - - B12 Bus 101 CB1206.CB1213 10110112.21310212.22310219 10113 - - B13 Bus 101 CB1306.CB1312.CB1314 10110113.21310213.21310219.22310220 10114 - - B14 Bus 101 CB1409.CB1413 10110114.21310217.21310220 10201 - - L0102 Line 102 B01.B02 21110201.22110201.21210201.22210201.22310202.22310203.22310204.22310205 10202 - - L0105 Line 102 B01.B05 21110202.22110202.21210202.22210202.21310205.21310207.22310201.22310210 10203 - - L0203 Line 102 B02.B03 21110203.22110203.21210203.22210203.21310201.22310204.22310205.22310206 10204 - - L0204 Line 102 B02.B04 21110204.22110204.21210204.22210204.21310201.21310206.22310203.22310205.22310207.22310208.22310209 10205 - - L0205 Line 102 B02.B05 21110205.22110205.21210205.22210205.21310201.21310202.21310207.22310203.22310204.22310210 10206 - - L0304 Line 102 B03.B04 21110206.22110206.21210206.22210206.21310203.21310204.22310207.22310208.22310209 10207 - - L0405 Line 102 B04.B05 21110207.22110207.21210207.22210207.21310202.21310204.21310205.21310206.22310208.22310209.22310210 10208 - - L0407 Line 102 B04.B07 21110208.22110208.21210208.22210208.21310204.21310206.22310207.22310209.22310214.22310215 10209 - - L0409 Line 102 B04.B09 21110209.22110209.21210209.22210209.21310204.21310206.21310215.22310207.22310208.22310216.22310217 10210 - - L0506 Line 102 B05.B06 21110210.22110210.21210210.22210210.21310202.21310205.21310207.22310211.22310212.22310213 10211 - - L0611 Line 102 B06.B11 21110211.22110211.21210211.22210211.21310210.22310212.22310213 10212 - - L0612 Line 102 B06.B12 21110212.22110212.21210212.22210212.22310211.22310213.22310219 10213 - - L0613 Line 102 B06.B13 21110213.22110213.21210213.22210213.21310210.21310219.22310211.22310212.22310220 10214 - - L0708 Line 102 B07.B08 21110214.22110214.21210214.22210214.21310208.22310215 10215 - - L0709 Line 102 B07.B09 21110215.22110215.21210215.22210215.21310208.21310209.22310214.22310216.22310217 10216 - - L0910 Line 102 B09.B10 21110216.22110216.21210216.22210216.21310209.21310215.22310217.22310218 10217 - - L0914 Line 102 B09.B14 21110217.22110217.21210217.22210217.21310209.21310215.21310220.22310216 10218 - - L1011 Line 102 B10.B11 21110218.22110218.21210218.22210218.21310211.21310216 10219 - - L1213 Line 102 B12.B13 21110219.22110219.21210219.22210219.21310212.21310213.22310220 10220 - - L1314 Line 102 B13.B14 21110220.22110220.21210220.22210220.21310213.21310217.21310219Table 6
IEEE14 node power system network protection configuration database.
ID number Protective relay Relays operation Operated switches Protected equipment 10110101 Main_protective relay 0 10401.10403.10501 B01 10110102 Main_protective relay 0 10402.10405.10407.10409 B02 10110103 Main_protective relay 0 10406.10411. B03 10110104 Main_protective relay 0 10408.10412.10413.10415.10417 B04 10110105 Main_protective relay 0 10404.10410.10414.10419 B05 10110106 Main_protective relay 0 10420.10421.10423.10425 B06 10110107 Main_protective relay 0 10416.10427.10429 B07 10110108 Main_protective relay 0 10428.10442 B08 10110109 Main_protective relay 0 10418.10430.10431.10433 B09 10110110 Main_protective relay 0 10432.10435 B10 10110111 Main_protective relay 0 10422.10436 B11 10110112 Main_protective relay 0 10424.10437 B12 10110113 Main_protective relay 0 10426.10438.10439 B13 10110114 Main_protective relay 0 10434.10440 B14 21110201 Main_protective relay 0 10401 L0102 21110202 Main_protective relay 0 10403 L0105 21110203 Main_protective relay 0 10405 L0203 21110204 Main_protective relay 0 10407 L0204 21110205 Main_protective relay 0 10409 L0205 21110206 Main_protective relay 0 10411 L0304 21110207 Main_protective relay 0 10413 L0405 21110208 Main_protective relay 0 10415 L0407 21110209 Main_protective relay 0 10417 L0409 21110210 Main_protective relay 0 10419 L0506 21110211 Main_protective relay 0 10421 L0611 21110212 Main_protective relay 0 10423 L0612Figure 6
IEEE14 node power system network.Case. Bus B13 has a fault(I)
Operated relays:B13m; tripped circuit breakers: CB1306, CB1312, CB1314.(II)
Call the network topology analysis algorithm to get the passive zone{13}.(III)
To query the topology database of power system, the corresponding logic diagram of suspected fault components is formed, as shown in Figure7.(IV)
According to logic diagram of suspected fault components, query protection configuration database is used to form a FRSN P system model, as shown in Figure8.(V)
The FRSN P system algorithm is invoked to perform inference operations on suspicious fault components.(VI)
The FRSN P system algorithm is invoked to perform inference operations on suspicious fault components.The reasoning process is as follows:
(1)
Parameter initialization:g=0, θ0 and δ0 are set according to the pulse values contained in each neuron; i.e., the pulse values can be set according to the initial confidence level in Tables 3 and 4. Therefore, θ0=(0.9833,0.8564,0.2,0.2,0.9833,0.8564, 0.2,0.2,0.9833,0.8564,0.2,0.2  0,…,0)T, δ0=0,0,0,0,0,0,0,0,0,0T.(2)
g=1, θ1=(0,…,0,0.8136,0.19, 0.8136,0.19, 0.8136, 0.19,0,0,0,0)T, δ1= 0.8564,0.2,0.8564,0.2,0.8564,0.2,0,0,0,0T.(3)
g=2, θ2=(0,…,0,0.7729,0.7729,0.7729)T, δ2=(0,0,0,0,0,0,0.8136,0.8136,0.8136,0)T.(4)
g=3, θ3=(0,…,0,0.7343)T, δ3=(0,0,0,0,0,0,0,0,0,0.7729)T.(5)
g=4,δ4=(0,0,0,0,0,0,0,0,0,0)T=0.The termination condition is satisfied and output is obtained.The fault component confidence level of busB13 is 0.7343, according to the decision rule. Bus B13 is the fault component. The diagnostic results in the form of a graphical user interface have been displayed in Figure 9.(VII)
Protective relays and circuit breakers perform all operations normally.Figure 7
B 13 Logic diagram.Figure 8
B 13 FRSN P system model.Figure 9
IEEE14 node power system fault diagnosis program simulation results (Bi represents the bus, Lij represents the line between the bus Bi and Bj, CBij represents the circuit breaker connecting the Bi bus and the Lj line, and Gi represents the generator).In addition, this method is also applicable to the large-scale power grid. In this paper, the IEEE39 node power system (show as Figure10), and the IEEE118 node power system (show as Figure 11) are tested in the same way, whether there is a single fault or multiple faults, even if the protective relay and circuit breaker information are lost. The faulty component can still be quickly diagnosed.Figure 10
IEEE39 node power system fault diagnosis program simulation results (Bi represents the bus, Lij represents the line between the bus Bi and Bj, CBij represents the circuit breaker connecting the Bi bus and the Lj line, and Gi represents the generator).Figure 11
IEEE118 node power system fault diagnosis program simulation results (Bi represents the bus, Lij represents the line between the bus Bi and Bj, CBij represents the circuit breaker connecting the Bi bus and the Lj line, and Gi represents the generator).


## 4. Complexity Analysis

It is assumed that there aren busbars, lines, transformer components, and switches in a given power grid. If each of these components and switches is treated as a node, the power grid can be viewed as a topology with n nodes. For a given power grid, the number of outgoing lines of each component is determined by a constant set as k. In this paper, we mainly analyze the complexity of this automatic implementation method with busbar components as an example. For busbar components with k outgoing lines, the protection settings are 1 bus main protection, k backup protection on line components with different outgoing directions, a total of k+1 protections, and the number of circuit breakers involved which is 2∗k. Analysis of each algorithm module is described as follows.In the suspicious fault component analysis algorithm module (as shown in Pseudocode1), according to the protection configuration of bus components, the relation between the number of nodes and the number of outgoing lines in the formed logical graph is 3k+1. At the same time, each node in the logic diagram needs to determine whether it is the component associated with the protection of the suspect fault component. Therefore, (3k+1)∗(k+1) steps need to be performed for the formation of logical diagram of each suspect fault component, and a total of (3k+1)∗(k+1)∗n steps need to be performed for an n-node system.Pseudocode 1:The suspicious fault component analysis algorithm.
Input:Suspicious fault component node set N, Component node-switch node adjacent matrix G Output:Information about each component node and breaker node in the logic diagram 1: Set stop condition: All associated protection of suspicious fault components are accessed, protective_mark=(1,1,…,1)p; 2: Set Initialize state: protective_mark=(0,0,…,0)p, n=0; 3: Add the suspicious fault component node to set Set0; 4: while(all protective_mark≠1) do 5: foreach node i in set Setn  do 6: for each node j in node-switch adjacent matrix Gdo 7: ifnode adjacent matrix G(i,j)==1  then 8: The searched node j are added to set Setn+1; 9: G(i,j)=0; 10: Add the node j to logic diagram; 11: for each associated protection of suspicious fault component k  do 12: ifj is the node of protection k-switch association set then 13: protective_markk=1; 14: end if 15: end for 16:end if 17:end for 18:end for 19:n=n+1; 20: end whileIn the modeling suspicious fault components with FRSN P system algorithm module (as shown inPseudocode2), there are k branches in the logic diagram for the suspect fault component. At the same time, k+1 protections are configured. In these protections, either the main protection action or the backup protection action will cause the related k circuit breakers to trip. Therefore, obtaining the initial value θ0 of FRSN P system diagnostic model from logic diagram need performs a total of (k+1)∗k∗k steps.Pseudocode 2:The modeling suspicious fault components with FRSN P system algorithm.
Input:Suspicious fault component logic diagram adjacent matrix SG, Information about each component node and breaker node in the logic diagram Output: The fuzzy truth values of the input proposition neurons θ0 1: Set stop condition: All outgoing line directions of the suspicious fault component logic diagram are access completed; 2: Set Initialize state: Set initialize access outgoing line direction number k=1, set all outgoing line directions number of suspicious fault component K; 3: while(k≤K)  do 4:foreach associated protection of suspicious fault components i  do 5:ifassociated protection i is the main protection then 6: query the protection database, obtain breaker ID number that should be tripped when protection i is active; 7: for the must trip breaker j when main protection i action do 8: ifj is the breaker in the outgoing line direction k  then 9:According to the operation information of breaker j and protection i set the fuzzy truth value vector θ0; 10:end if 11: end for 12: elseassociated protection i is the backup protection then 13: query the protection database, obtain breaker ID number that should be tripped when protection i is active; 14: forthe must trip breaker j when backup protection i action do 15: ifj is the breaker in the outgoing line direction k  then 16: According to the operation information of breaker j and protection i set the fuzzy truth value vectorθ0; 17: end if 18: end for 19:end if 20:k=k+1; 21:end for 22:end whileIn the fuzzy inference module (as shown in Pseudocode3). In the FRSN P system diagnosis model, there are 7k+1 proposition neurons and 3k+1 rule neurons. In order to obtain the pulse value of the output proposition neuron, the algorithm performs a total of (7k+1)∗(3k+1) steps. Therefore, when the proposed method diagnoses the faulty component, the algorithm performs a total of (3k2)∗n+k2+22k2+10k+1 steps, so the time complexity of the proposed algorithm is O(n), which is very competitive to other power system diagnosis techniques like Petri nets [43–46, 48].Pseudocode 3:The fuzzy inference algorithm.
Input:The fuzzy truth values of the input proposition neurons θ0 Output:The fuzzy truth value of the output proposition neurons θg 1: Set stop condition: 01=(0,0,…,0)sT,01=(0,0,…,0)tT; 2: Set reasoning step: g=1; 3: while(θg≠01orδg≠02) do 4: foreach input neurons (g=1) or proposition neurons (g>1) do 5: ifthe condition of fire E=an is satisfied then 6: Compute the fuzzy value vector δg, δg=D1T⊗θg-1+D2T⊙θg-1+D3T⊛θg-1; 7: ifthis proposition neurons have a postsynaptic neuron then 8: Transmits a spike to the next rule neuron; 9: else 10: this proposition neurons only accumulates spike values; 11: end if 12:end if 13: end for 14: foreach rule neurons do 15: ifthe condition of fire E=an is satisfied then 16: Compute the fuzzy truth value vector θg, θg=ET⊛(C⊗δg); 17: Transmits a spike to the next proposition neuron; 18: end if 19: end for 20: g=g+1; 21: end while


## 5. Conclusions

In this paper, the whole diagnosis process of power system fault diagnosis based on FRSN P systems is realized by an automatic implementation method. The whole diagnostic algorithm includes data structure module, power grid topology analysis algorithm module, suspicious fault component logic analysis algorithm module, and FRSN P system inference algorithm module. IEEE14, IEEE39, and IEEE118 node systems are discussed to verify the diagnosis algorithm program. The diagnosis of the results is consistent with manual calculation results, which verifies the feasibility and reliability of automatic diagnosis algorithm procedures. The FRSN P system is used for fault diagnosis of the entire program diagnostic algorithm and also the speed and complexity of the various modules have been studied. Moreover, this method can be used to improve the automation of fault diagnosis and to explore the superiority of the fault diagnosis method based on FRSN P system in the large-scale grid fault diagnosis with more nodes in comparison with other methods.



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*Source: 2635714-2019-06-19.xml*