Fuzzy Timing Petri Net for Fault Diagnosis in Power System

Abstract

A model-based system for fault diagnosis in power system is presented in this paper. It is based on fuzzy timing Petri net (FTPN). The ordinary Petri net (PN) tool is used to model the protective components, relays, and circuit breakers. In addition, fuzzy timing is associated with places (token)/transition to handle the uncertain information of relays and circuits breakers. The received delay time information of relays and breakers is mapped to fuzzy timestamps, π(τ), as initial marking of the backward FTPN. The diagnosis process starts by marking the backward sub-FTPNs. The final marking is found by going through the firing sequence, σ, of each sub-FTPN and updating fuzzy timestamp in each state of σ. The final marking indicates the estimated fault section. This information is then in turn used in forward FTPN to evaluate the fault hypothesis. The FTPN will increase the speed of the inference engine because of the ability of Petri net to describe parallel processing, and the use of time-tag data will cause the inference procedure to be more accurate.

1. Introduction

A rapid and correct fault diagnosis is crucial for power system restoration. However, as the complexity of power system increases, fault diagnosis, especially in complicated faults or incorrect operation of protective devices, becomes a very difficult task in the limited short time. This situation has made it necessary to develop intelligent systems to support operators in their decision making process. Over the last two decades different artificial intelligent (AI) approaches have been proposed for fault diagnosis in power system. Most attempts to date have relied on the use of expert system [1] or neural network [2] technology. Expert-system-based approaches have been the most successful so far, while neural-network-based methods continue to improve their performance. Previous reported expert systems for fault diagnosis use either rule-based or model-based approach [3]. The first approach may work well only in simple fault cases. However, to diagnose a fault in complicated cases, it needs a huge number of rules to describe the complicated protection system behavior. As a result, the acquisition and maintenance of such a system is tedious and difficult [3].

On the other hand, model-based diagnostic (MBD) methods are suitable to network fault diagnosis because the power systems and protective relays can be modeled as discrete event systems. MBD covers a wide range of fault scenarios than heuristic reasoning because it is based on the system behavioral analysis. It can detect malfunctioning equipment in the early stages [4]. Nevertheless, the model-based system requires more inference time. As a result, there is a need to enhance speed and performance of diagnoses system. Parallel inference processing and time sequence information of protective relays and circuit breakers is important factor for reducing fault diagnosis processing time [3]. This is so because parallel processing increases the inference procedure and real-time availability of the relay information allows expert systems to reduce the number of hypotheses [4].

One of the powerful tools for modeling parallel processing is Petri net [5]. There have been some proposed model-based systems using Petri net and colored and timed Petri net for faster inference [6, 7]. In [6] final marking of forward and backward Petri nets model is compared to make a decision for faulted section area. However, timestamp of protective devices has not been considered on that model and the model which is proposed in [7] cannot handle the uncertain and missing data. There have also been works on expert systems that use time-tag information of actuated relays and tripped circuit breakers through sequence event recorder (SER) in fault diagnosis [8].

This paper proposes fuzzy timing Petri net to handle uncertain information of protective device and to overcome the drawbacks of previous works. Petri nets have also been successfully applied in power system for verification of concurrent switching sequences [9] and modeling of transmission line protection relaying scheme [10].

The paper is organized as follows. In the next section Petri net will be introduced. A brief and concise description of the fuzzy timing petri net (FTPN) will be given in Section 3. Diagnosis process is described in Section 4. In Section 5, the proposed FTPN is used for diagnosing fault in a simple and typical line. The application will be presented in Section 7. The final section is conclusion.

2. Petri Nets

Petri nets (PNs), as a graphical and mathematical tool, provide a uniform environment for modeling and design of discrete event systems. It is a particular kind of bipartite directed graphs populated by three objects. These objects are places, transitions, and directed arcs connecting places to transitions and transitions to places. Pictorially, places are depicted by circles and transitions by bars [5].

The ordinary Petri nets do not include any concept of time explicitly. With this class of nets, it is only possible to describe the logical structure of the modeled system, but not its time evolution. Responding to the need for the temporal performance of discrete-event systems and modeling concurrent systems with time constraints, various timed extensions of Petri nets have been proposed by attaching timing constraints to transitions, places, and/or arcs [5].

Later, other researchers introduced fuzzy Petri net for knowledge representation to deal with fuzzy production rules [11] and fuzzy timing Petri net (FTPN) for performance, evaluation, and specification of dynamic concurrent system [12, 13] under uncertainty and imprecision.

3. Fuzzy Timing Petri Net and Extended Fuzzy Timing Petri Net

Fuzzy-timing Petri net (FTPN) has been proposed by Zhou and Murata [12] and is defined as follows.

The static structure of FTPN is a five-tuple structure, 𝑁=(𝑃,𝑇,𝐴,𝐷,FT) where 𝑃={𝑝₁,𝑝₂,…,𝑝_𝑛} is a finite set of places, 𝑇={𝑡₁,𝑡₂,…,𝑡_𝑚} is a finite set of transitions, 𝐴⊆(𝑃×𝑇)∪(𝑇×𝑃) is a set of arcs (flow relation), D is a set of all fuzzy delays 𝑑_𝑡𝑝(𝜏) associated with arcs ⊆(𝑇×𝑃),andFT is a set of all fuzzy timestamp, where a fuzzy timestamps, 𝜋(𝜏)∈FT is associated with each token and each place. It is a fuzzy time function or possibility distribution giving the numerical estimate of the possibility that a particular token arrives at time 𝜏 in a particular place.

The extended fuzzy-timing Petri net (EFTPN) model is a FTPN with the default value of 𝑑_𝑡𝑝(𝜏) being (0,0,0,0) and with additional function CT∶𝑇→𝑄⁺×𝑄⁺×(𝑄⁺∪∞), which is a mapping from transition 𝑇 to firing intervals with possibility 𝑝, that is, each transition is associated with a firing interval, 𝑝[𝑎,𝑏], (𝑎≤𝑏), where the default interval is 1[0,0] (a transition definitely fires as soon as it is enabled) (possibility 𝑝∈[0,1]). 𝑃 is 1 if transition t is not in conflict with any other transition. When different chances are to be assigned to transitions in structural conflict, 𝑃 can be less than 1.𝑄⁺ is set of positive rational numbers.

The dynamic evolution of marking in an FTPN is the same as that of an ordinary PN except that fuzzy timestamps 𝜋(𝜏), fuzzy enabling times 𝑒(𝜏), and fuzzy occurrence time 𝑜(𝜏) need to be computed and updated each time when a transition firing (atomic action) occurs. Fuzzy enabling time 𝑒_𝑡(𝜏) of transition t is the possibility distribution of latest arrival time among the arrival times of all tokens in input places of t that are necessary to enable the transition t in the untimed case and is given by 𝑒_𝑡(𝜏)=latest𝜋_𝑖(𝜏),𝑖=1,2,…,𝑛. (3.1)

Fuzzy occurrence time 𝑂_𝑡(𝜏) of transition t is the possibility distribution of the time at which the transition t starts firing and is given by 𝑂_𝑡(𝜏)=min𝑒_𝑡(𝜏),earlies𝑡𝑒_𝑖(𝜏),𝑖=1,2,…𝑚. (3.2)

The fuzzy timestamp 𝜋_𝑡𝑝(𝜏), the possibility distribution of the time at which a token arrives in an output place of 𝑡, is given by the extended addition of 𝑂_𝑡(𝜏) and 𝑑_𝑡𝑝(𝜏) or 𝜋_𝑡𝑝(𝜏)=𝑂_𝑡(𝜏)⊕𝑑_𝑡𝑝(𝜏). (3.3)

Here 𝜋_𝑡𝑝(𝜏) is updated fuzzy timestamps in an FTPN. When there are 𝑚 transitions in conflict enabled with their fuzzy enabling times, 𝑒_𝑖(𝜏),𝑖=1,2,….𝑚, and CT(𝑡_𝑖)=𝑝_𝑖[𝑎_𝑖,𝑏_𝑖], then fuzzy occurrence time 𝑂_𝑡(𝜏) of transition t is computed as follows: 𝑂_𝑡(𝜏)=min𝑒_𝑡(𝜏)⊕𝑝_𝑡𝑎_𝑡,𝑎_𝑡,𝑏_𝑡,𝑏_𝑡,earliest𝑒_𝑖(𝜏)⊕𝑝_𝑖𝑎_𝑖,𝑎_𝑖,𝑏_𝑖,𝑏_𝑖,𝑖=1,2,𝑚. (3.4)

4. Diagnosis Process

In the following discussion it is assumed that the protective devices have arrived in their final status. The general philosophy of diagnosis task is based on model-based reasoning: the comparison between the observed and predicted behaviors of the system [14–16]. Diagnosis is performed in two-step reasoning process. The first step is based on forward reasoning (data driven). Having the final status of protective devices, the initial marking of the backward FTPN is performed by assigning fuzzy time function 𝜋(𝜏) to relevant places. That is to say, timestamps information of relays and breakers is used as the initial fuzzy timestamps 𝜋₀(𝜏). In other words, 𝜋₀(𝜏) is the numerical estimate of possibility that a particular protective device has been operated. Processing the FTPN as a forward reasoning to get final marking would get the fault hypotheses. Indeed in the first step of diagnosis, both the candidates of faulted section and estimated time that fault has been cleared by protective devices are derived.

Fault simulation process takes place in the second step of diagnosis task and is based on backward reasoning (goal driven). The predicate behavior of protective devices, in the case of occurring fault, is modeled by the forward FTPN. The fuzzy timestamp of token arriving at the final place of backward FTPN is compared with fuzzy timestamp of token in the final state of forward FTPN.

A default threshold value, 𝜆, is used to validate the discrepancy of two fuzzy timestamps. If discrepancy of two fuzzy timestamps is larger than threshold value, then the fault candidate is assumed to be correct. Otherwise the simulation process is repeated again by executing the forward FTPN by assuming the malfunction of appropriate relay. For instance, by exchanging the possibility of transition 𝑡₂ and 𝑡₃ in Figure 2 the malfunction of relay 𝑅₁ is simulated.

5. Example

For illustration purposes, consider a simple and typical transmission line depicted in Figure 1. Suppose a fault has occurred on point 𝐹. Furthermore, assume that signals have been received and recorded with precise time tags or in a chronological order and available through SER.

Figure 1 

A simple and typical transmission line.

Figure 2 

Forward FTPN model for fault at 𝐹 point in Figure 1. 𝜎1: 𝑀0[𝑡1⟩𝑀1 [𝑡3⟩𝑀2[𝑡4⟩𝑀3[𝑡5⟩𝑀4,𝜎2:     𝑀0[𝑡1⟩𝑀5[𝑡2⟩𝑀6 [𝑡6𝑡9⟩𝑀7 [𝑡7𝑡10⟩𝑀8[𝑡8𝑡11⟩𝑀9,      𝑀0=(𝑃1𝑃5𝑃9𝑃13), 𝑀1=𝑀5(𝑃2𝑃5𝑃6𝑃9𝑃10𝑃13),     𝑀2=(𝑃3𝑃4𝑃6𝑃9𝑃10𝑃13),     𝑀3=(𝑃4𝑃6𝑃9𝑃10𝑃13𝑃14𝑃15𝑃16), 𝑀4=(𝑃5𝑃6𝑃9𝑃10𝑃13𝑃14𝑃15𝑃16),     𝑀6=(𝑃5𝑃6𝑃9𝑃10𝑃13), 𝑀7=(𝑃5𝑃7𝑃8𝑃11𝑃12),𝑀8=(𝑃5𝑃8𝑃12𝑃17𝑃18), 𝑀9=(𝑃5𝑃9𝑃13𝑃17𝑃18), 𝑃5=𝑅2,𝑃9=𝑅1,𝑃13=𝑅4,𝑃16=CB2, 𝑃17=CB1, 𝑃18=CB4.𝜎1 and 𝜎2 are the firing sequences, in the case of correct actuated and nonactuated of relay 𝑅2, respectively, 𝑀0 to 𝑀9 are marking states of the FPTN.

The forward and backward FTPN models with main protection (CB₂) and primary backup protection (CB₁,CB₄) for this point are shown in Figure 2 and Figure 4, respectively.

In Figure 2, the token in place 𝑃₁ shows absence of the fault, 𝐹, and 𝑃₅, 𝑃₉, and 𝑃₁₃ represent readiness of the relays 𝑅₂, 𝑅₁, and 𝑅₄, respectively, Places 𝑃₁₆, 𝑃₁₇, and 𝑃₁₈ correspond to circuit breakers CB₂, CB₁, and CB₄, respectively, The occurrence of 𝐹 is represented by the transition 𝑡₁, which deposits a token in places 𝑃₂, 𝑃₆, and 𝑃₁₀ to indicate that the fault is present.

In this case, transitions 𝑡₃, 𝑡₆, and 𝑡₉ are enabled and can fire within their interval time. This corresponds to sensing the fault by relay 𝑅₂, 𝑅₁, and 𝑅₄. However, transitions 𝑡₇ and 𝑡₁₀ will be fired after transition 𝑡₃ because their firing interval is later than 𝑡₃. The static default of firing interval of transition 𝑡₃ is [0,0]. Firing transitions 𝑡₃, 𝑡₆, and 𝑡₉ correspond to sending trip signals and transitions 𝑡₄, 𝑡₇, and 𝑡₁₀ correspond to opening the circuit breakers CB₂, CB₁, and CB₄, respectively.

A fuzzy delay 𝑑_𝑡𝑝(𝜏) is associated with arcs (𝑡,𝑝) from transitions 𝑡₄, 𝑡₇, and 𝑡₁₀ to places 𝑃₁₆, 𝑃₁₇, and 𝑃₁₈, respectively, to map the operating time of CB𝑠. The 𝑑_𝑡𝑝(𝜏) of other arcs are set to (0,0,0,0), which means that transitions connected to these arcs fire and the token will be available to their corresponding output place immediately. The sink transitions 𝑡₂ is fired in the case of malfunction of relay 𝑅₂. Since backup relays send trip signal after main relays, the firing transitions of the FTPN corresponding to these relays should be in correct sequence.

To do this, a static time interval 1[𝑎,𝑏](𝑎≤𝑏) is assigned to the transitions 𝑡₆ and 𝑡₉ to ensure that these transitions will be fired after transitions 𝑡₃ and 𝑡₄. Moreover, in the case of malfunction of CB₂, places 𝑃₁₄ and 𝑃₁₅ will not get tokens. Therefore, transitions 𝑡₆ and 𝑡₉ can fire within their firing intervals. The firing sequences and its marking of the forward FTPN are shown in the bottom of Figure 2.

The backward FTPN consists of three sub-FTPN modules (see Figure 4). Each of the sub-FTPNs corresponds to one CB and its corresponding relay protection module. There are three kinds of places in this FTPN: those which get marking in the case of receiving signals (shown with a circle), the second type that get token in the case of nonreceiving signals from CBs and relays (shown with two circles), and the third one which are used as auxiliary places (shown also with a circle).

In Figure 2, places 𝑃₁, 𝑃₄, 𝑃₉, 𝑃₁₂, 𝑃₁₇, and 𝑃₂₀ correspond to CB₁, 𝑅₁, CB₂, 𝑅₂, CB₄, and 𝑅₄, respectively. In the case of non-receiving signal from relay or CB, the places indicated by two circles get tokens.

As previously mentioned, suppose a fault has occurred at point 𝐹 and information received from relays and breakers with their time delay is 𝑅₂(0.2𝑠) and CB₂(0.3𝑠). Diagnosing process starts by marking appropriate places of the backward sub-FTPN (Figure 4) and assigning each token with fuzzy time function. The goal is to find the fuzzy time function of final state of the backward FTPN in its firing sequences.

To do this, first fuzzy enabling time of transition 𝑡₁₁ is calculated by (3.1). Then the fuzzy occurrence time of 𝑡₁₁ is found by (3.2). The next step is to compute fuzzy timestamp of place 𝑃₁₁. It is calculated by (3.3). The same procedure is done for the next transitions/places in the firing sequences 𝜎₁ (shown at the bottom of Figure 4(a)) to reach the place 𝐹.

At this stage of diagnosis, the fuzzy timestamps at the place 𝐹 are compared with the simulation, result of Figure 2. If discrepancy of two fuzzy timestamps is larger than threshold value and receiving data is compatible with simulation, then the fault candidate is assumed to be correct. Otherwise the simulation process is repeated. In the second round of execution of forward FTPN, transition 𝑡₂ is first fired to simulate the malfunction of relay 𝑅₂ and the result is compared to backward FTPN. The marking of the backward sub-FTPN2 can be shown by vector 𝑀=(𝑃₉𝑃₁₀𝑃₁₁𝑃₁₂𝑃₁₃𝑃₁₄𝑃₁₅𝑃₁₆𝑃₂₅), the last place is the fault section estimation and designated by 𝐹 in place 𝑃₂₅. Therefore, with receiving information from 𝑅₂ and CB₂, the initial marking is 𝑀₀=(100100000)^𝑇, number 1 indicates that places 𝑃₉ and 𝑃₁₂ both get token and zero means otherwise. With this marking only transition 𝑡₁₁ is enabled and can fire. Transition 𝑡₁₂ is not enabled because the place with inhibitory arc connected to it is marked. Firing transition 𝑡₁₁ removes token from places 𝑃₉ and 𝑃₁₂ and deposites one token in the places 𝑃₁₁ and 𝑃₁₂. After firing this transition the new marking is 𝑀₁=(00110000)^𝑇. Having token in places 𝑃₁₁ and 𝑃₁₂ the transition 𝑡₁₄ is now enabled and can fire. Firing 𝑡₁₄ makes the new marking state as 𝑀₂=(00010010)^𝑇. The final marking of this sub-FTPN will be 𝑀₄=(00010001)^𝑇. The broken line in Figure 6 shows the traverse of token in sub-FTPN2. Having delay time of 𝑅₂ and CB₂, the initial fuzzy timestamps would be as in Figure 3.

(a)

(b)

Figure 3 

Two typical fuzzy time functions (a) for delay time of relay 𝑅2 and (b) for delay time of breaker CB2.

(a)

(b)

Figure 4 

The backward FTPN model of Figure 1 for fault at point 𝐹 (shown by place 𝑃25). CB2 and 𝑅2 correspond to the main protection, and CB1, 𝑅1, CB4, and 𝑅4 correspond to the backup protection. (a) Information received from 𝑅2 and CB2. 𝜎1 is the firing sequence of sub-FTPN2. 𝜎1=𝑀0[𝑡11⟩𝑀1[𝑡14⟩𝑀2[𝑡17⟩𝑀3[𝑡18⟩𝑀4, 𝑀0=(𝑃9𝑃12), 𝑀1=(𝑃11𝑃12), 𝑀2=(𝑃12𝑃15), 𝑀3=(𝑃12𝑃16), 𝑀4=(𝑃12𝑃25). (b) Information received from CB2, CB1, 𝑅1, CB4, and 𝑅4. 𝜎1, 𝜎2, and 𝜎3 are firing sequence of sub-FTPN1, sub-FTPN2, and sub-FTPN3, respectively, 𝜎1=𝑀0[𝑡2⟩𝑀1[𝑡5⟩𝑀2[𝑡8⟩𝑀3[𝑡9⟩𝑀4,𝜎2=𝑀5[𝑡12⟩𝑀6[𝑡15⟩𝑀7[𝑡17⟩𝑀8[𝑡18⟩ 𝑀9, 𝜎3=𝑀10[𝑡20⟩𝑀11[𝑡23⟩𝑀12[𝑡26⟩𝑀13[𝑡27⟩𝑀14, 𝑀0=(𝑃1𝑃4),𝑀1=(𝑃3𝑃4), 𝑀2=(𝑃4𝑃7), 𝑀3=(𝑃4𝑃8), 𝑀4=(𝑃4𝑃25), 𝑀5=(𝑃9), 𝑀6=(𝑃9𝑃13), 𝑀7=(𝑃9𝑃15), 𝑀8=(𝑃9𝑃16), 𝑀9=(𝑃9𝑃25), 𝑀10=(𝑃17𝑃20), 𝑀11=(𝑃19𝑃20), 𝑀12=(𝑃20𝑃23), 𝑀13=(𝑃20𝑃24), 𝑀14=(𝑃20𝑃25).

With these fuzzy timestamps at the places 𝑃₉ and 𝑃₁₂, first fuzzy enabling time of transition 𝑡₁₁ should be found.

𝑒₁₁(𝜏)=latest{𝜋_𝑟(𝜏),𝜋_𝑏(𝜏)}=latest{(0.1,0.2,0.2,0.3), (0.2,0.3,0.3,0.4)}=(0.2,0.3,0.3,0.4). Then, fuzzy occurrence time of 𝑡₁₁ is computed (see (3.2)): 𝑜₁₁(𝜏)=min{(0.2,0.3,0.3,0.4), earliest{(0.2,0.3,0.3,0.4)}}=(0.2,0.3,0.3,0.4). Next fuzzy timestamp of place 𝑃₁₁ is calculated (3.3) as 𝜋₁₁(𝜏)=𝑜₁₁(𝜏)⊕𝑑₁₁(𝜏)=(0.2,0.3,0.3,0.4)⊕(0,0,0,0)=(0.2,0.3,0.3,0.4). Here it is assumed that the fuzzy delay time 𝑑₁₁(𝜏) is (0,0,0,0).

This process is performed for firing sequence 𝜎₁ until the final state of sub-FTPN2 (i.e., place 𝑃₂₅(𝐹)). In this case, the fuzzy time function of place 𝐹 will be 𝜋_𝐹(𝜏)=(0.2,0.3,0.3,0.4).

Having fuzzy timestamps of fault hypothesis in the backward FTPN, the fuzzy timestamps of final marking in the forward FTPN (see Figure 2) are to be computed. The following are assumed:  𝜋₁(𝜏)=(0,0,0,0), means that token in place 𝑃₁ is immediately available. 𝜋₅(𝜏)=(0.1,0.2,0.2,0.3) and 𝜋₉(𝜏)=𝜋₁₁(𝜏)=(0.3,0.4,0.4,0.5).

Having token in place 𝑃₂, the fuzzy enabling time of transition 𝑡₃ is 𝑒₃(𝜏)=latest𝜋₀(𝜏),𝜋₅(𝜏)=(0.1,0.2,0.2,0.3). (5.1)

To compute fuzzy occurrence time of transition 𝑡₃, the earliest enabling time of 𝑡₂ and 𝑡₃ is found first as follows.  earliest{𝑒₃(𝜏)⊕0.9(0.01,0.01,0.03,0.03),𝑒₂(𝜏)⊕0.1(0.25,0.25,0.4,0.4)}=earlies𝑡{0.1,0.2,0.2,0.3)⊕0.9(0.01,0.01,0.03,0.03),(0,0,0,0)⊕0.1(0.25,0.25,0.4,0.4)}=max(0.9,0.1),min(0.11,0.25),min(0.21,0.25), min(0.21,0.4),min(0.31,0.4)}=0.9(0.11,0.21,0.21,0.31). Therefore, the fuzzy occurrence of 𝑡₃ is computed as follows:  𝑜₃(𝜏) = min{𝑒₃(𝜏)⊕ 0.9(0.01, 0.01, 0.03, 0.03), earliest{𝑒₃(τ) ⊕ 0.9(0.01, 0.01, 0.03, 0.03), 𝑒₂(τ) ⊕ 0.1(0.25, 0.25, 0.4, 0.4}} = min{(0.1, 0.2, 0.2, 0.3) ⊕ 0.9(0.01, 0.01, 0.03, 0.03), earliest{𝑒₃(τ) ⊕ 0.9(0.01, 0.01, 0.03, 0.03), 𝑒₂(τ) ⊕ 0.1(0.25, 0.25, 0.4, 0.4}} = min{0.9(0.11, 0.21, 0.21, 0.31), 0.9(0.11, 0.21, 0.21, 0.31)} = 0.9(0.11, 0.21, 0.21, 0.31). Now fuzzy timestamp of place 𝑃₃ is found as follows:  𝜋₃(𝜏)=𝑜₃(𝜏)⊕𝑑₃(𝜏), where 𝑑₃(𝜏) is fuzzy delay time from transition 𝑡₃ to place 𝑃₃.  𝜋₃(𝜏)=0.9(0.11,0.21,0.21,0.31)⊕(0,0,0,0)=0.9(0.11,0.21,0.21,0.31). Then the fuzzy occurrence transition 𝑡₄ would be as follows: 𝑜₄(𝜏)=𝑒₄(𝜏)=𝜋₃(𝜏)(),𝜋=0.90.11,0.21,0.21,0.31₁₆(𝜏)=𝑜₄(𝜏)⊕𝑑₄(𝜏)()⊕()().=0.90.11,0.21,0.21,0.310.1,0.1,0.1,0.1=0.90.21,0.31,0,31,0,41 (5.2)

6. Comparison of Two Fuzzy Timestamps

At this stage of diagnosis the comparison of two fuzzy timestamps 𝜋_𝐹 and 𝜋₁₆ derived from forward and backward FTPN is to be evaluated. Refer to [13]. The possibility of 𝜋_𝐹=𝜋₁₆ may be found as follows (see Figure 5): 𝜋_𝐹=𝜋₁₆=min𝜋_𝐹≤𝜋₁₆𝜋₁₆≤𝜋_𝐹=min(0.9,1)=0.9. (6.1) If the threshold value, 𝜆, is assumed to be 𝜆=0.8, therefore it is concluded that a fault has occurred at point 𝐹 and relay 𝑅₂ and breaker CB₂ have operated correctly.

Figure 5 

Comparison of two possibility distributions 𝜋𝐹 and 𝜋16.

Figure 6 

A simplified protection scheme of Kapar substation.

7. Application

Figure 6 depicts one of the existing Malaysian substations, the so-called Kapar substation. It consists of two breaker and half systems (500 kV and 275 kV), which are connected by autotransformer. Since the complete protection scheme of the substation is complex, only simplified protection version will be used for one of the buses, say 275 kV north bus.

At the 275 kV north bus—at the CB₈ side—the following protective devices are used: 87BN HI: high impedance busbar relay (trips 86N HI), 87BN LI: low impedance busbar relay (trips 86N LI), 50BF: breaker failure (trips 86BF), 86BF: breaker failure lockout relay, 86BN HI: high impedance busbar lockout relay, 86BN LI: low impedance busbar lockout relay.The same protection scheme is at the 500 kV south bus. In addition, the autotransformer is protected by relay 87TB, which is a biased transformer differential relay.

Suppose a fault occurs at 275 kV north bus of the Kapar substation. If the main relay (the busbar differential protection-87BN-HI) senses the fault and operates correctly, it then sends trip to CB₈ and CB₇ to isolate the busbar from fault. This scenario is modeled by the forward and backward FTPN and shown in Figures 7 and 8, respectively. If the main relay fails to operate, the local backup relay (87BN-LI) sends trip signal to the breakers CB₈ and CB₇. In the case of malfunction of circuit breaker CB₈ the breaker failure relay will send trip signal to the circuit breakers CB₇, CB₄, CB₆, and CB₁₀. The broken lines in the forward FTPN models (Figure 7) show the route of FTPN in their firing sequences corresponding to their protection scheme.

Figure 7 

The forward FTPN model of protection scheme for fault at 275 kV north bus bar of Kapar substation. The marking state of FTPN before occurrence of fault. The token in 𝑃1 shows absence of fault, and firing transition 𝑡1 indicates the occurrence of fault. Tokens in places 𝑃3, 𝑃12, and 𝑃18 indicate the readiness of main, local backup, and breaker failure relays, respectively. The broken lines show the FTPN route in its firing sequences (in the case of correct operation of main relay and circuit break).

Figure 8 

The backward FTPN model of Figure 6 for fault at 275 kV north busbar of Kapar substation. The marking state of FTPN indicates the postfault condition. Places 𝑃49, 𝑃23, 𝑃26, and 𝑃13 correspond to main, local backup, remote backup, and breaker-failure relay, respectively. Token in place 𝑃49 indicates that the main relay (87BN HI) has been operated and its signal has been received. Receiving signal from circuit breaker CB8 is shown by a token in places 𝑃17 and 𝑃39. Receiving signal from circuit breaker and CB7 is shown by a token in places 𝑃1, 𝑃19, and 𝑃41. The broken lines are the routes of the FTPN in its firing sequences.In the case of tripping circuit breakers, places designated by trip CB𝑋 get token, and in the case of nonoperation of any CB, places the indicated by Ntrip would get token. OP𝑃49 means that the main relay has operated and NOP𝑃49 means otherwise. Transitions 𝑡12, 𝑡17, and 𝑡23 are sink transitions and would fire if the main relay and breakers CB8 and CB7 have operated, respectively.

In the backward FTPN models the token in place F shows the estimated fault section, which in this case is 275 kV busbar. This estimated fault section hypothesis in turn is compared with its relevant forward FTPN models. The procedure is similar as the one explained in Section 6.

8. Conclusions

A new model-based reasoning for power system fault diagnosis is proposed in this paper. It is based on fuzzy timing Petri net. It is believed that this proposed system could cover drawbacks of the previously reported model-based systems. This is because this proposed system gets the advantages of some powerful tools and concepts for designing real-time systems such as Petri net for modeling parallel processing and power of fuzzy set theory to handle uncertainty and imprecision. This system is able to handle parallel processing, therefore reducing the inference processing time. On the other hand, it uses the timestamps of circuit breakers (CB) and relays, which causes the fault hypotheses to be reduced accordingly. Moreover, the uncertain information from CB𝑠 and relays is handled by this system, therefore causing the diagnosis of the faulted section area to be more precise.

Acknowlegment

The first author would like to thank UTM for providing finacial support for this research.