0 Introduction

The aim of power system fault diagnosis is to timely and effectively identify the fault sections and interpret the received alarms. In the literature, a variety of methods have been proposed for power system fault diagnosis, such as those based on expert system (ES), artificial neural network (ANN), Petri net (PN), analytic model, etc., which have been shown effective for simple fault scenarios. However, when multiple faults, protective device malfunctions, and/or alarm distortions are involved, the fault diagnosis problem becomes much more complicated, and the task more stressful, time-consuming, and less accurate. Moreover, incorrect or slow actions taken by the operators may cause cascading trips, leading to a widespread blackout of power system. Thus, fault diagnosis under complicated circumstances remains challenging and significant for power system security and stability.

Capable of drawing on the expertise of operators and logic based reasoning, ESs are the earliest attempt in artificial intelligence application to power system fault diagnosis [1-5]. However, it is complex to build and maintain a comprehensive high quality knowledge base. Also, ESs cannot deal with ambiguities, and are liable to suffer inaccuracies due to incomplete knowledge base. ANN based methods are advantageous for its strong learning, noise tolerance and generalization capability [6-8], while PN based methods parallel information processing and strong inclusiveness [9-10]. However, they both present difficulties in adapting topological changes and various protection schemes.

As another effective and promising fault diagnosis method, the analytic model mathematically establishes an objective function, so as to search for the true fault hypothesis (FH), i.e., the most plausible one that could well explain the received alarm messages. First, it makes an effort to analytically determine the operating logics of protective relays(PRs) and circuit breakers(CBs). Then diagnostic criteria can be built up accordingly, and applied to transform fault diagnosis into an unconstrained programming problem. After that, an optimization technique, such as genetic algorithm (GA) [11], tabu search (TS) [12-14], differential evolutionary (DE) [15], can be employed to solve the formed problem. The analytic model is straightforward, but the computational efficiency can be lower when the size of problem solving space grows with the expansion of outage areas.

Despite best efforts, the above mentioned methods still encounter difficulties in improving diagnostic accuracy for complicated faults, since they use status information of PRs and CBs as the only input. Any data corruption would lower the fault tolerance, and thus jeopardize the validity of the methods. Running close to the limit diagnosing complicated faults with protective device malfunctions, such methods may completely fail when alarm distortions are also involved. Such dilemma can be resolved by adding extra data sources and enlarging the amount of available information. In doing this, the negative impact of data corruption is partly mitigated, leading to more accurate diagnosis results.

Recently, a higher level of observability has been achieved with the increasing deployment of PMUs in power systems. It facilitates the studies of new methods and strategies for advanced power system monitoring, control and protection [16-21]. Though having been extensively studied, such methods still suffer from technical difficulties for practical application. Specifically, many factors can affect the real-time performance of the methods, including the PMU placement, measurement accuracy, processing delay and communication delay, etc. By contrast, as a post-fault analysis process, the fault diagnosis methods can tolerate more delays, thus featuring higher availability in the prevailing circumstance. After considering other factors, such methods can be implemented quickly and efficiently. Thus, the phasor data from PMUs is introduced as another data source, so as to improve the efficiency and accuracy of fault diagnosis.

When there are false, missing, or delayed breaker status change alarms during the fault clearance, the breadth first search can be initialized at any other reported boundary circuit breakers. Thus, the proposed method can deal with such uncertainties with the enhancement of PMU data, and determine the outage area(s) efficiently.

(1)An enhanced method is proposed for fast outage area identification using real time CB statues information and phasor data. The modified method features higher efficiency and robustness.

(2)The phasor data is introduced as a complement to the traditional input of the analytic model. Three new criteria are built up based on phasor data to improve the fault tolerance and accuracy of the method.

(3)The FH is reformed to facilitate the diagnosis of alarm distortions, and the traditional criteria are refined to adapt to various protection schemes, under the precondition of not harming the diagnosis efficiency.

Compared with the state-of-the-art methods, the proposed method shows stronger fault tolerance capability for complicated fault scenarios, and higher adaptability to topological changes and different protection schemes and bus configurations, without any burden of database maintenance or sample training.

1 The Proposed Framework

In this paper, a two-layer fault diagnosis model is proposed for appropriate utilization of fault relevant information under different fault conditions, so as to increase diagnostic efficiency.Typically, a simple fault, as the most common fault type in power systems, involves only one section. Thus, such faults could be easily identified. When a complicated fault occurs, e.g., a multiple-fault or single-fault with protective device malfunction, more than one section would be involved in the outage area(s). The fault identification can become time-consuming and less accurate. In such cases, a fault-tolerant and efficient fault diagnosis method could provide decision-support to the operators, maintaining a secure and reliable operation of the power system. As shown in Fig.1, the diagnosis process is divided into two parts, i.e., outage area identification, and analytic model-based fault diagnosis.

The first layer performs the outage area identification by employing a modified real-time network topology processor. Based on the method in [22], the modified processor uses the status information of CBs from sequence of event (SOE) as input, and phasor data from PMUs for enhancement of tolerance and efficiency. When simple faults occur, the fault section could be directly identified by this layer. If more than one section is involved, the processor could obtain all the suspected fault sections, and relevant PRs and CBs, which, if necessary, could be subdivided into different outage areas. The subdivision could reduce the scale of the optimization problem to be formulated in the stage of the second layer.

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Fig.1 Proposed two-layer mode for fault diagnosis

2)If a fault occurs on a section dα in Z(ri), all CBs in P(ri, dα) are closed, a PR in F(ri, dα) operates, and a CB in O(ri) fails to trip off, then the expected state is consistent with its actual state.

2 Enhanced Outage Area Identification

The traditional topology processor program, which performs the outage area identification, is slow and susceptible to errors. Once initialized, the program must process every CB status before and after the fault occurrence, to determine the new outage area(s). However, the iterative topology analysis of whole network is time-consuming and unnecessary, since there are only a few sections involved in the outage area that should be determined. Moreover, the conventional topology tracking methods operate on the network connectivity data using real time CB status information only. Such information is susceptible to interference, impeding the performance of outage area identification. Assuming that the status change alarm of a CB in the outage area is distorted, missing, or delayed, the conventional method may not be able to correctly determine the outage area. Here, a fast outage area identification method is proposed with the incorporation of phasor data.

2.1 Determination of Boundary Circuit Breakers

Here, a boundary circuit breaker refers to the one indicating the farthest limit of the outage area, with one of its terminal energized while another de-energized. Once the boundary circuit breakers are recognized, the limit of the outage area, and the sections in the area, can be determined. However, status changes indicated by SOE alone are not sufficiently reliable to determine the boundary circuit breaker, due to the uncertainty of breaker tripping and alarm transmission. The PMUs can measure bus voltages and branch currents, and provide accurately time-stamped voltage and current phasors (both magnitude and phase angle). Thus, phasor data from PMUs is introduced to enhance tolerance.

Fig.2 A simple fault

A simple fault is shown in Fig.2. The circuit breaker c1 is used to illustrate how to determine energization of its terminals.

(1)The voltage measurement is utilized for the terminal connected to bus b1. Typically, the bus voltage would drop to zero if it is de-energized. Assume that V1 is the voltage measurement after fault clearance, and Vset is the preset threshold, then the terminal is de-energized if:

|V1|<Vset

(1)

(2)Similarly, the current measurement is utilized for theterminal connected to line l1. Typically, the line current would drop to almost 0 if it is de-energized. Assume that I1 is the current measurement after fault clearance, and Iset is the preset threshold. Then, the terminal is de-energized if:

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|I1|<Iset

(2)

The states of both terminals of a CB could be recognized by applying (1) and (2). A boundary circuit breaker is identified, when one of its terminals is energized and another not.A CB is not considered as a boundary one, when the states are same, even if the status change alarm is reported. In doing this, the outage area identification can proceed normally regardless of missing or false status change alarms.

2.2 Fast Outage Area Identification

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Assume that a group of CB status change alarms, denoted as C={c1, c2, …, cn}, having been received at the control center during the fault clearance. After initialized, the processor picks out the first boundary circuit breaker in C, and run the breadth first search. It indicates that there are more than one outage area, when the breadth first search is performed more than once. All the sections found during the search are recorded as suspicious fault sections for further diagnosis, and grouped by outage areas, if necessary. The identification algorithm is as follows:

Thealgorithmforoutageareaidentification1whilethereisanundiscovered... boundarycircuitbreakercinC2letCxandAREAxbequeues3Cx.enqueue(c)4 labelcasdiscovered5 whileCxisnotempty6 c←Cx.dequeue()7 foralltinTOPO.terminals(c)do8 iftisde-energized9 forallsinTOPO.adjacentSections(t)do10 ifsisnotlabeledasdiscovered11 AREAx.enqueue(s)12 labelsasdiscovered13 forallbinTOPO.adjacentBreakers(t)do14 ifbisnotaboundarycircuitbreaker…andnotlabeledasdiscovered15 Cx.enqueue(b)16 labelbasdiscovered

Based on the work presented in [11-15], an analytic model enhanced with wide area measurements is proposed for power system fault diagnosis, with protective device malfunctions and alarm distortions taken into account. The fault diagnosis process is formed as an integer programming problem, and then solved by the well-developed GA method. The main contribution of this paper includes the following three aspects.

3 Enhanced Analytic Model with Phasor Data

Generally using status information as the only input, the existing analytic model is simple, useful and efficient. However,the lack of enough diagnostic information is likely to render ambiguous results, even false ones, when protective device malfunctions and alarm distortions are involved. Here, phasor data from PMUs is introduced as a complementary information source, so as to improve fault-tolerance. The diagram of the developed analytic model based fault diagnosis procedure is shown in Fig. 3.

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In this section, three phasor data based criteria are defined first, followed by the description of the fault hypothesis and the objective function. Then, it presents the determination of expected states of criteria, so as to calculate the objective function.

Fig.3 Proposed analytic-model-based fault diagnosis procedure

3.1 The Phasor Data Based Criteria

Based on phasor data, the following criteria are proposed for the analytic model.

First, three operators are defined:⊗, ⊕ and- represent logic multiplication, addition and negation, respectively.

3.1.1 m-criterion

The positive sequence fault additional network of the aforementioned simple fault is shown in Fig. 4, as

Fig.4 The positive sequence fault additional network

the current leaving bus is assumed positive. According to the superposition principle, the resultant currents and voltages in the network during fault are the sum of those existed before the fault and the changes due to the fault, i.e., the fault components. The theory of symmetrical components enables the transformation of the fault components into three sets, including positive-, negative- and zero-sequence fault components. Since the positive-sequence fault component is the only one existing in all types of faults, it is used for building up the m-criterion. The phase angle between the positive-sequence voltage and current fault components satisfy:

(3)

where ΔI1andΔU1are the positive-sequence current and voltage fault components measured at bus b1, respectively; arg() returns the phase difference between two phasors; α is a simulated impedance angle, and is set as 12° [23].

According to (3), the m-criterion of line l1 at b1 terminal is defined as:

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(4)

The m-criterion indicates the fault direction referring to the location of measuring point, and is applicable to all terminals of the line. Its value set to be 1 indicates that a fault is occurring in the forward direction.

3.1.2 s-criterion

When an internal fault occurs, that phase angles of the current measurements at both terminals of a line satisfy:

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(5)

where I1 and I2 are the current of the faulted phase measured at respective terminals of the line.

According to (5), the s-criterion can be defined as:

s=sA⊕sB⊕sC

(6)

(7)

where I1X and I2X are the current of phase X measured at terminal-1 and terminal-2, respectively.

Its value set to be 1 indicates that an internal fault occurs.

3.1.3 -criterion

According to Kirchhoff's current law (KCL), the sum of all currents meeting at a bus through the connected branches is equal to zero when there is no fault on the bus. Thus, the v-criterion can be defined as:

v=vA⊕vB⊕vC

(8)

5)O(ri) is the set of CBs that ri should trip off.

(9)

whereIkA, IkB, and IkC are the current measurements of the kth branch connected to the bus; n is the total number of the branches; vset is the preset threshold.

If the value of v is 1, then an internal fault occurs.

3.2 The Fault Hypothesis

An elaborate FH should have an exact dimension that could clearly represent “what happened triggers the received alarms”. The FH consistent with actual fault situation is deemed true. Meanwhile, the form of FH should facilitate establishment of diagnostic criteria. The FH reformed here involves “the states of sections in the outage area (faulted or healthy)”, and “the actual states of protective devices (including PRs and CBs, similarly hereinafter)”,i.e.,

H = [D, R, C]

(10)

where

D[d1, d2, …, dns], and dk represents the state of the kth section in the outage area, with dk =1 and 0 corresponding to its faulted and normal state, respectively;

R[r1, r2, …, rnr], and ri represents the actual state of the ith PR. If it operates, ri = 1, otherwise, ri = 0;

1)If a fault occurs on a section dα in Z(ri), all CBs in P(ri, dα) are closed, and all PRs in F(ri, dα) fail to operate, then ri should operate;

3.3 The Objective Function

The objective function E(H) reflects the credibility of H defined in (10). A smaller E(H) suggests a higher credibility of H. With phasor data based criteria taken into account, the modified objective function is obtained as:

(11)

where mx, sy, and vz are the actual states of the xth m-, yth s-, and zth v-criterion, respectively; ri。and cj。 are the reported states of ri, and cj, respectively; mx*(H), sy*(H), vz*(H), ri*(H), and cj*(H) correspond to the expected states of mx, sy, vz, ri, and cj, respectively.

The value of E(H) can be calculated once the expected states, the actual states and the reported states are known. The reported states of PRs and CBs are indicated by received alarms; the actual states of phasor data base criteria can be obtained by processing the phasor data, while those of PRs and CBs are directly given in FH; the determination of the expected states is described as follows.

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3.4 The Expected States of Criteria

The phasor data based criteria are first proposed, and their expected states are defined as follows:

3.4.1 Phasor Data based Criteria

(1) m-criterion.

The expected state of mx depends on where the fault is referring to the location of mx. If a fault occurs in the backward direction, and the its actual state is 0, then the expected state is set to be 0; otherwise, if a fault occurs in the forward direction, the expected state is set to be 1. The logic is mathematically described as:

Outage areas are surrounded by boundary circuit breakers. Thus, a fast outage area identification can be carried out by initiating a breadth first search at a boundary circuit breaker in the de-energized direction ending at other boundary circuit breakers. The breadth first search starts at the tree root, and explores the neighbor nodes first, before moving to the next level neighbors. It will terminate after all available neighbor nodes are discovered. In doing this, the modified mothed bypasses the iterative topology analysis of whole network, thus improving identification efficiency.

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⊗⊗

(12)

where SBackward(mx) and SForward(mx) are the sets of suspected fault sections in the backward and forward direction of mx, respectively.

(2) s-criterion.

Assume that sy corresponds to the line dy in the outage area, and its expected state is associated with the state of the line, i.e.,

(13)

(3) v-criterion.

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Assume that vz corresponds to the bus dz in the outage area, and its expected state is associated with the state of the bus, i.e.,

(14)

Then the expected states of the traditional criteria are refined to adapt to different protection schemes and bus configurations. Specifically, the operating logics of the primary backup protection (PBP) and the secondary backup protection (SBP) are mathematically refined, and unified into one for backup protection (BP), so as to coordinate different protection schemes; that of the breaker failure protection (BFP) are reformed, with different bus configurations taken into account. For the convenience of presentation, several sets are defined as follows:

1)Z(ri) is the set of sections in the protection zone of ri, or is the set of CBs that ri backs up, depending on whether ri is a BFP.

2)F(ri, dk) is the set of PRs that locate at the same location as ri but operate faster than ri to clear the fault on dk in Z(ri).

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3)P(ri, dk) denotes the set of CBs on the acyclic electrical path from the location of ri to the section dk in Z(ri). The detailed definition of P(ri, dk) is described in [13].

4)I(ri) is the set of PRs that can initiate the timer of ri.

6)T(cj) is the set of PRs that can trip cj off.

The modified traditional criteria are described as follows.

3.4.2 Modified Traditional Criteria

(1) Main protection.

Suppose that ri is the MP of dk. The operating logic of ri is: if a fault occurs on dk, ri should operate, i.e.,

(15)

(2) Backup protection.

Suppose that ri is the BP of dk. The operating logic of ri is as follows.

C[c1, c2, …, cnc], and cj represents the actual state of the jth CB. If it is tripped off, cj = 1, otherwise, cj = 0.

The second layer is called an analytic model-based fault diagnosis method, using both status information and phasor data. Two information sources create a complementary mechanism, ensuring optimal fault-tolerance. The diagnosis results include fault sections, malfunctioned PRs and CBs, as well as the incorrect and missing alarms.

Then,ri* can be determined as

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(16)

(3) Breaker Failure Protection.

The operating logic of BFP is different as the bus configuration varies.

1)For a BFP pertaining to the MP of a bus, suppose that ri is a BFP and cj is a CB in Z(ri). The operating logic of ri is: if a tripping signal is received from rα in the intersection of I(ri) and T(cj), indicating that a fault has occurred on a section in Z(rα) or another CB in Z(rα) has failed to trip off, but cj fails to trip off, then ri should operate, i.e.,

(17)

2)For a dedicated BFP, suppose that ri is the BPF, and cj is the only CB in Z(ri). The operating logic is similar, i.e.,

⊗

(18)

(4) Circuit Breaker.

The operating logic of CBs is: if tripping signals are received from rx in T(cj), then cj should trip off, i.e.,

(19)

3.5 Solution Method

A well-developed GA method is employed to solve the optimization problem formed in the model. GA is a population-based stochastic searching technique. The search and optimization process follow the principle of the survival of the fittest to generate successively better results over generations to finally approach the optimal solution. Different from classical calculus-based optimization techniques, GA is not restricted to specific formulations of the objective function and the constraints, i.e. they are able to solve complex, nonlinear, nondifferentiable and nonconvex problems such as the one proposed in this paper. Details about GA can be found in [24].

4 Case Study

The developed method is tested by simple fault scenarios as well as complicated fault scenarios involving malfunctions and alarm corruptions. Due to space limitation, only two complicated fault scenarios simulated on IEEE 39-bus power system are presented in this section. The first fault scenario is described in detail, so as to facilitate the understanding of the developed model, while only the diagnosis report is presented for the second fault scenario.

4.1 The Fault Scenario 1

The diagram of IEEE 39-bus power system is shown in Fig.5, with the shadow area being the outage area of fault scenario 1. As shown in Fig.5, there occur four faults, resulting in formation of two outage areas involving a total of eight sections. Also, the protective device malfunctions, status change alarm distortions and phasor data errors are taken into account.

Fig.5 IEEE New England 10-machine 39-bus system

For the convenience of presentation, an encoding method is defined as follows. Here,b, l, r and c represent bus, line, PR, and CB, respectively; l0414 represents the line between b04 and b14; r0910m represents the MP of l0910 located at the b09 end, while r1009m the MP located at the other side; r03m represents the MP of b03; r0910p, r0910s and c0910 represent the corresponding PBP, SBP and CB, respectively; r0910bf represents a dedicated BFP of c0910, while r09bf a BFP pertaining to r09m; m, s, v represent m-， s-, v-criterion, respectively, and m0910, s0910, and，v09 can be deduced by analogy.

The fault scenario is detailed as follows.

(1)Faults occurred on l0414, l1213, l2629, and b14;

(2)The MP of l0414 at b14 terminal operated and sent a signal to successfully trip c1404 off, while the MP at b04 terminal failed to operate; then the PBP at b04 terminal operated and tripped c0414 off;

(3)The MP of b14 operated to successfully trip off CBs connected to b14, i.e., c1404, c1413, c1415, and CBs at the remote terminals, i.e., c1514, c1314, c0414;

(4)The MPs of l1213 at both terminals operated, and c1213 was tripped off successfully while c1312 failed. Then the BFP at b13 operated to successfully trip off CBs connected to b13, i.e., c1314, c1310, and CBs at the remote terminals, i.e., c1013, c1413, c1213;

(5)The MP of l2629 at both terminals operated and tripped off c2629 and c2926, respectively;

(6)The following alarms are received: r0414p, r1404m, r14m, r1013s, r1213m, r1312m, r2629m, r2926m, c0414, c1404, c1413, c1415, c1514, c1310, c1314, c1013, c2629, and c2926.

The fault diagnosis procedure by the proposed method is carried out as follows.

(1)The first step is to identify the outage area(s) using the enhanced topology processor presented in Section 2, based on the breaker status change alarms and phasor data. The search procedure is shown in Fig. 6, and the outage areas are identified as shadow areas shown in Fig.5. The CBs are searched in the following order: c0414→ c1404→ c1413→ c1415→ c1314→ c1514→ c1312→ c1310→ c1213→ c1013→ c2629→ c2926.

Fig.6 Scheme of searching fault areas

The search result shows that there are two outage areas. One is formed by c2629 and c2926, and involves only one section, i.e., l2629. Hence, it is identified as the fault section. Whether there are any malfunctioned PRs can be determined by applying several if-then rules. Another outage area involves seven sections, i.e., l0414, l1415, l1314, l1013, l1213, b13, b14.

(2)The basic form of a FH is obtained as

H=[d1, …, d7, r1, …, r32, c1, …, c10]

(20)

(3)Determine the basic form of the objective function E(H) as stated in Section 3. According to the received alarms, the reported states of PRs and CBs can be obtained. The actual states of phasor data based criteria can be directly determined using the voltage and current measurements, while the traditional criteria’s are assumed in FH. The key issue lies in the determination of expected states of diagnostic criteria according to method presented in Section 3. For better understanding the operation of the proposed methods, take the determination of and instance.

⊗⊕(r1404m⊗⊗r1404p))

(21)

⊕r1404p⊕r1404s⊕r14m⊕r14bf

(22)

⊕(db14⊕

dl1415⊕dl1314))⊗dl0414

(23)

By now, the value of E(H) can be calculated.

(4)Use the GA method to obtain the optimal solution of the optimization problem. The result is shown in Table 1, which is consistent with those simulated. It is worth noting that the actual state of rl013p is identified as “not clear”, meaning that two different actual states lead to the same objective function value. However, such ambiguity is of no importance in most cases, and can be removed only by thoroughly investigation of the protection system.

Table 1 Fault diagnosis results

Note:X1/X2/X3 corresponds to the expected state/actual state/reported state; the symbol “—” and “*” represent “not applicable” and “not clear”, respectively.

(5)A diagnosis result report can be generated as shown in Table 2, so as to support the operator and the maintenance personnel for troubleshooting the malfunctioned protective devices.

4.2 The Fault Scenario 2

Another typical fault case is also tested on IEEE 39-bus power system, with related power network shown in Fig. 7. The fault scenario is detailed as follows.

(1)Faults occurred on l1516 and l1619;

(2)The MPs of l1516 at both terminals operated to successfully trip off c1516 and c1615, respectively;

(3)The MPs of l1619 at both terminals operated, and c1916 was successfully tripped off while c1619 failed. Then the BFP at b16 operated to successfully trip off CBs connected to b16, i.e., c1615, c1617, c1621 and c1624, and CBs at the remote terminal, i.e., c1516, c1716, c1916, c2116 and c2416;

Table 2 Fault diagnosis result report

(4)The BFP at b17 operated incorrectly. Consequently, the CBs connected to b17 and CBs at remote terminals were tripped off;

(5)The following alarms are received: r1516m, r1615m, r1916m, r16bf, r17bf, c1615, c1916, c1617, c1621, c1624, c1716, c2116, c2416, c1718, c1727, c1817 and c2717.

Fig.7 Power system diagram associated with fault scenario 2

Using the proposed method, the obtained diagnosis results are shown in Table 3. The fault diagnosis results are consistent with those simulated.

Table 3 Diagnosis result report

5 Conclusions

A novel analytic model enhanced with wide area measurement is presented for power system fault diagnosis. Not only does the developed model estimate fault sections, but it also identifies protective device malfunctions and alarm distortions. The introduction of phasor data can accelerate the outage area identification, and ensure the validity of the process against alarm missing. It also enlarges the amount of available information that the fault diagnosis method can utilize, enabling the establishment of new diagnostic criteria, thus making the proposed method more fault tolerant. The FH and the operating logics of PRs and CBs, are elaborately reformed to accommodate to complicated faults, various protection schemes and different bus configurations. It is demonstrated by many simulated fault scenarios that the developed model is correct, and the method efficient.

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