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Fault Diagnosis Based on Bayesian Petri Nets [Sensors & Transducers (Canada)](Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: This paper provides a kind of Bayesian Petri net model and presents a fault diagnosis method for power grid based on this model. Firstly, the BPN models for each component are established in power cut area separately, according to the fault spread directions. Secondly, the failed component is determined by the application of Petri net reasoning and Bayesian probability calculation. At last, the result is given by fusing all parties' results using mean method. Diagnosis analysis showed that this method had better fault tolerance under the condition of incomplete information and had better adaptability after the change of network topology structure. In the BPN reasoning, calculating the fault probability of component is based on the prior probability from statistics, so the subjectivity of setting related parameters can be avoided. Copyright © 2014 IFSA Publishing, S. L. Keywords: Bayesian Petri nets, Fault diagnosis, Power system, Fault tolerance. (ProQuest: ... denotes formulae omitted.) 1. Introduction With the expansion of the scale of the power systems and the improvement of the level of automation, the complexity of system operation and loses caused by the problems of the power system increase greatly comparing with the previous. It's significant to find out the problems of the systems promptly and accurately for ensuring the power systems running in a safe and stable condition .At present, the more and more technology and methods of the computational intelligence and knowledge engineering are used in the area of fault diagnosis by the researchers [1-3], for example, expert system, artificial neural network, rough set theory, fuzzy set theory, Bayesian network, genetic algorithm and so on. These methods have their own characteristics and have been used to a certain extent, but in some cases they also expose some shortcomings [2], For example, expert system's rule base is difficult to establish; artificial neural network needs much large representative samples for learning before being used; when the method of rough set theory is in use, the decision table is very huge, even sometimes, the problems of the combinatorial explosion may come up; the part of the fuzzy set theory concerning about obtaining the membership function and the method of the fuzzy models for complex systems is not complete; Bayesian network's training is complex and it needs the information of the priori probability; it's a NP hard problem to analysis the complex problems and the large scale system; to the genetic algorithm, it has difficulty in setting up the reasonable fitness function and making the right parameter selection. Some researchers combine a variety of methods, in this way they can avoid the shortage of using a method only. The quantum theory is brought in the training process of the neural network; it can improve the properties [3]. A fault diagnosis method based on rough set theory and Bayesian classifier is proposed to increase the fault tolerance ability with incomplete information [4], Petri net is a kind of mathematical tools for analyzing the behavior of the discrete event dynamic system (DEDS). It has not only a strict mathematical description but also has an intuitive graphical expression [5]. Power system is a typical discrete event dynamic system, so it is reasonable to use the Petri nets to model the fault diagnosis of the power systems. Petri net is applied in power system, including fault diagnosis, fault recovery, network topology analysis [6]. In [7] the authors give the backward reasoning based on Petri net. K. L. Lo and H. S. Ng set up Petri net model and algorithm for fault diagnosis based on coding, and they compare with other methods of fault diagnosis in power systems [8]. According to the time sequence of the protection action, the fault diagnosis model of Petri net is established based on the distribution protective circuit breakers [9]. The main feature of the Petri net method for fault diagnosis in the power systems is that it can make qualitative and quantitative analysis for the evolution process whether these fault occur concurrently or orderly or circularly. But this kind of method has obvious deficiency. In the first, it needs enough knowledge to establish a complete Petri net model, but it will be easy to produce the problem of the state space explosion if the net has too many nodes. Secondly, it is difficult to adapt to the changes of the power system topology. At last, the fault tolerance ability of the model is poor, for example, it is difficult to identify the false alarm information. Therefore, when the scale of the net is large or when complex problems of the system occur, fault diagnosis is difficult based on the Petri net model. According to the complex power grid, a power grid fault diagnosis method based on directional weighted fuzzy Petri net (WFPN) is proposed [10]. And the elements are modeled on every fault spread direction to insure the universality in the condition of topology changes and the fault tolerance of the algorithm with incomplete information. This method can reduce calculation cost .and obtain the rank of suspicious faulty components with incomplete information. However, there is a big subjective in setting the threshold and the weights of WFPN, it is bad adaptable to different samples. 2. Bayesian Petri Nets 2.1. Bayesian Probability Reasoning Bayesian network is an information presentation framework which combines the causal knowledge and the probabilistic knowledge [11]. Bayesian network B(G, P) consists of the directed acyclic graph G which has n nodes and the conditional probability table P which is interrelated with every node. The node-set of G is described by the variables in the domain U = {x,,x2,...,x"}, and the directed arcs mean the relationship between variables. The parent node of the node x,. is described by parents(x,.). The relationship between variables is showed by the conditional probability p{xi\ parents{xi)) between the node x, and the parent node parents(x,.). The joint probability distribution of the variables is showed by (1) [11]. ... (1) The random variable x. has m basic events {xn,xí2,...,x¿m}. If the observed result is F = {x"...,xM,xi+1,...,xn}, the conditional probability is showed by (2) [11]. ... (2) The posterior probability of x, = xu can be calculated by the formula (1) and (2) based on the backward reasoning of Bayesian network [11]. ... (3) If the parent node-set of the xa parents^) = 0 in (3), we can conclude that p(xa | parents(xa)) = p(xa). The Bayesian network model can indicate the joint probability of the variables set, and the causal relation of the parent node and the child node can reflect accurately the dependency between them. So we can obtain the effective causal reasoning and diagnosis reasoning by using the Bayesian network. But there are two main shortcomings when the Bayesian inference is applied to fault diagnosis: 1) when analyzing the complex fault and the largescale system, we need more complex training in the network, and the calculation of the conditional probability table P is proved a NP-complete problem [1]; 2) the method of Bayesian reasoning need to rebuild the network structure and recalculate the conditional probability distribution, when the configuration of the component and the protection devices change. 2.2. Definitions of Bayesian Petri Nets This paper defines the Bayesian Petri nets (BPN) taking Bayesian reasoning and Petri nets into consideration based on [10, 11]. Definition 1: Bayesian Petri nets (BPN) structure is a tentuple ZBPN ={S,T,F,I,U,R,SU,PR,B,M0}; where: S = {sl,s2,...,s"} is the finite set of places; T = {Tn,Tb} is the finite set of transitions, TN={tNl,tN2,...,tNm) is the finite set of general transitions, TB = {tBl,tB2,...,tBk} is the finite set of Bayesian transitions; F cz(SxT)u(TxS) is the finite set of arcs; 1 ^SxT js the fmite set of inhibitor arcs, 7nF=0; U = {xi,x2,...,xn} are the finite variable set, the value of the variable xi is {0,1}; RczU, /?(*.) is the reason variables set of xi based on causal relationship; SU:S^>U is the mapping from S to U; PR:£/->[0,1], PR(xp is the priori probability of x,\ B : tb ->[0,l]' , B(tm) is probability distribution vector of tBi * under the condition of »tB. (In this paper, we use the *t indicate the pre-places of t, and the t * indicate the post-places of t ). ... (4) where b(si) =p(si \ *tBi),i = 1,2,..., j ; M0 is the initial marking of Zs/W. Definition 2: Marking sets M of BPN The marking M< is the description of the system dynamic behavior and the set of all marking of the system can be marked as M. The marking is described by M,. = {(s,;r(s))}, in which *(s)e {0,1} shows that whether the token s of the place exists or not. And 1 indicates the token s exists. The component of Mi M.(s) = (s,x(s)) is value of the posterior probability of the physical meaning which the places indicates. If Mk turns up by the fire of Mj straightway, which marked as M.[t > Mk * Definition 3: Fire rules of Y,BPN 1) When tBeTB, if Vse *ís :(s,tB)e I -» x(s) = 0 and 3se *tB :(s,tB)e F ->;r(s) = l , the transition tB is enabled, marked as M\tB > . 2) When tNeTN, if Vse tN :((s,tN)e = 0) A((s,tN)e F -» k(s) = 1), the transition tN is enabled, marked as M,[tN >. 3) When the marking is Mn the new making Mm turns up by the fire of the transition. We can mark it as Mi[t > Mm , and if Vs e t* : n(s) = l ,then ... (5) 3. Fault Analysis and Diagnosis Based on BPN 3.1. Relay Protection Analysis of Fault Component Relay protection of the power system usually includes the main protection, the nearly back-up protection and the remote back-up protection [12]. For example, The Layout diagram in figure 1 consists of three components: 1 bus (Bl) and 2 lines (L1,L2); 13 protection: main protection of bus (Blm), main protection of line (LISm, L2Sm, LIRm, L2Rm), nearly back-up protection of line (LISp, L2Sp, LIRp, L2Rp) and remote back-up protection of line (LISs, L2Ss, LIRs, L2Rs) and 5 breakers (CB1 ~ CB5). If the information received from the monitoring center is the sequential action of Blm-LlSs-L2Ss and the open of breakers CB1-CB3-CB5. According to the protection principle of the power system and the analysis of the three pathways in Fig. 1, we can obtain protection action sequence when the component fails, which is shown in Table 1. 3.2. Modeling of Bayesian Petri Nets In order to reduce the complexity of the modeling and reasoning, first of all, we should construct Bayesian Petri nets models of action sequence of components on every direction. As shown in Fig. 2, we fusion all reasoning results of different directions. The domain U in the model is used to analyze the components and protection devices. U= {B 1 ,L 1 ,L2,Blm,L 1 Sm,L2Sm,L 1 Rm,L2Rm,L 1 Sp, L2Sp,LlRp,L2Rp,LISs,L2Ss,LIRs,L2Rs,CBl,CB2, CB3,CB4,CB5}. In Fig. 2, the places are marked as O, and the places with the same name of element in U represent the state of corresponding components and protection devices. The token in the places represent the posteriori probability of the state, and the place -LISp means that the state of LISp is not arisen. The places -LIRp, ~L2Sp and - L2Rp indicates similar meaning of the place -LISp. The place LISp' means that the action of LISp occurs and abides by the relaying logic. The places LIRp', L2Sp', L2Rp' indicates similar meaning of the place LISp'. The Bayesian transitions are marked as I-1, which indicates the calculation of the neighbor places with the B function, as equation (4). The inhibitor arcs are marked as ° , which means the neighbor transition will not be fired by the pre-places with the token 1. For example, the BPN model in Fig. 2(a) describes two cases: Blm->CB2, Blm->CB2-^LlSs->CBl. It means that we can conclude B1 faulty when the monitoring center receives two signals (Blm,CB2) which indicate the action of Blm and the open of CB2. If the monitoring center receives three signals (Blm,LlSs,CBl) which indicate CB2 refused to operate and CB 1 made to be open by remote backup protection of LISs, we can still conclude B1 faulty. 3.3. The Parameter of Uncertain Information In order to use the B functions and the PR functions of the BPN model to calculate and reason, we need to obtain the prior probability of component fault and the conditional probability of the relay protection, and all these information reflect the uncertainties in process of fault. According to the data of [12], we can calculate the prior probability of component node fault. The prior probability of the line is 0.1629/hk (hundred kilometers); the bus, 0.0058/b (bar); the transformer, 0.0039/u (unit). The probabilities of the relay protection refused operation and faulty operation are followed: the faulty operation of the main protection of the line is 0.23 %/s (set), the refused operation, 0.07 %/s (set); the faulty operation of the main protection of the bus is 0.06 %/s (set), the refused operation, 3.08 %/s (set); the faulty operation of the main protection of the transformer is 0.14 %/s (set), the refused operation, 0.62 %/s (set); the faulty operation of the main protection of the breaker is 0.48 %/s (set), the refused operation, 0.83 %/s ( set). 3.4. The Process of Fault Diagnosis According to the BPN model in Fig. 2, we illustrate the process of fault diagnostic. Case 1 : The information got from the monitoring center is the action of Blm, LISs, L2Ss and the open of CB1, CB3, CB5. The BPN model will be reasoned on every direction of the components. In the model the 1 indicates the action of the protection device, the open of the breaker and the fault state of the components; the 0 indicates the inaction of the protection device, the close of the breaker and the right state of the components. The calculation process is shown in Table 2. The sequence of the transitions firing in the every BPN model is from up to down in the table. When the transition is firing, we can use equation (3) to calculate the probability value of the postplace by the B function and change the past probability. The initial marking M0 of BPN will become the next marking, then the next marking will become the next of the next marking and the same process will go on. When there is no enabled transition, the making M is the last marking. The value of M(s) is the probability value of fault of the component which the place means. As the reasoning of BPN is done respectively on every direction of the components, we can get a set of diagnostic results for every component. Then we make the fusion of the diagnostic results with the mean value method in Table 2 and confirm the fault with the threshold 0.5 by the voting strategy. The final conclusion is that the bus B1 is faulty and the credibility is 0.9679. 3.5. The Analysis of Fault Tolerance Case 2: The monitoring center receives the following information: the action of Blm, LIRm, LISp, L2Ss and the open of CB1, CB3, CB5. The calculation process is showed in Table 3. As the length is limited, we only give the main calculation steps. The final conclusion is: the bus B1 is faulty and the credibility is 0.9679; the line LI is faulty and the credibility is 0.9941. According to Table 1 and example 2, we know that the information received by the monitoring center may have deficiencies. In case 2, the monitoring center receives the information {Blm, LIRm, LISp, L2Ss, CB1, CB3, CB5}, and it is proved that the fault components are the bus B1 and the line LI. According to the analysis of Table 1, we know that the neighbor breakers of Bl will get the main protection signal from Blm and will be open when Bl is faulty. But the breakers CB2 and CB4 refuse to operate, then the remote backup protection LISs and L2Ss can make the breakers CB1 and CB3 to be open after receiving the protection signals. When LI is faulty, the main line protection LISm and LIRm will make the breakers on the both sides to be open. But the breaker CB1 refuses to operation. The nearly backup protection LISp tries making the breaker CB1 to be open again. At last the breaker CB1 is open. In the above processes, the main line protection signal from LISm and the remote backup protection signal from LISs are not received by the monitoring center, but the missing information doesn't have significant influence to the results of fault diagnosis. Therefore, the BPN model provided in this paper has good universality and fault tolerance with incomplete information. 3.6. Adaptability Analysis After Topology Change The fault analysis based the BPN is modeled on every fault spread direction, so the model is only related to the protection and the breaker on this direction. For example, the line L3 is added to power system in Fig. 1, and the topology is changed as shown in Fig. 3(a). If we model this system and reason the fault based on Bayesian method, the Bayesian network for the whole system should be reconstructed and the conditional probability table of the nodes should be recalculated. Based on the proposed BPN model, the influence of the added L3 is just increasing a pathway IV. We only establish the corresponding subnet of the pathway. The existing structure and the results will not be affected. Case 3: On the basis of case 1, L3 is added, the monitoring center receives the following information: the action of Blm, LISs, L2Ss, L3Ss and the open of CB1, CB3, CB5, CB7. The diagnosis result of case 1 is the bus Bl faulty, the structure change for Bl in Fig. 3 (a) means adding a new pathway. Therefore, we can keep the model and the calculation results of the three existing pathways. The BPN model of pathway IV of the Bl is established as shown in Fig. 3(b). The initial marking MO is {(L3Ss,l),(CB7,l), (Blm,l), (CB4,0), (B1,0)}, after the transitions t24 and t25 fire, M2={(L3Ss,l), (CB7,1), (Blm,l), (CB4,0),0.9998}. After combining the results with the results of the original three pathways, we can get final conclusion: the bus Bl is faulty and the credibility is 0.9759. The analysis and calculation process above shows that the method provided in this paper can keep its existing model and calculation results when the topology of the power system changes. It can only model the changed pathway, so we reduce the complexity of the modeling deeply. It shows that the BPN model can adapt to topology change better. 3.7. The Comparison of Methods Compared with the reference [11], this method can reduce calculation cost and obtain the rank of suspicious faulty components with incomplete information. In addition, because the diagnostic process is modeled on a single component, and the failure probability of multiple fault spread direction is separately calculated, so the modeling complexity is lower than the analysis in reference [10]. 4. Conclusions 1) The Bayesian Petri nets combines the advantage of the Petri nets in the description and analysis of the discrete event dynamic system and the characteristic that Bayesian probability method is good at dealing with uncertain knowledge expression and reasoning. Based on this model, we can model the fault of the power system effectively and can deal with the incomplete information. 2) The calculation of B function in the Bayesian Petri nets is actually Bayesian probability calculation, and we use the statistical prior probability to calculate the probability of component fault. So the results have high credibility. And we can avoid the subjectivity from setting calculation parameters directly that the modeling is based on the common Petri nets reasoning method. 3) The BPN model is established based on the analysis method which is used respectively on every fault spread direction of the relay protection. It can effectively reduce the complexity of the calculation and simplify the model. The process of diagnosis analysis shows that the model with incomplete information has better ability of fault tolerance and has better adaptability of the topology change. Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant No. 61170223 and No. U1204610, the Key Scientific and Technological Research Project of Science and Technology Department of Henan Province of China No. 122102210004, and the National Key Technology R&D Program of the Ministry of Science and Technology of China No. 2013BAH23F01. Thanks for the help. References [1]. Wang Jialin, Xia Li And Wu Zhengguo, State of arts of fault diagnosis of power systems, Power System Protection and Control, Vol. 38, Issue 18, 2010, pp. 210-216. [2]. C. Angeli, Online expert systems for fault diagnosis in technical processes, Expert Systems, Vol. 25, Issue 2,2008, pp. 115-132. [3]. 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Yonghui Yi XJ Electric Company Limited, Xuchang 461000, China Tel: +86-0374-3211919, fax: +86-0374-3216619 E-mail: [email protected] Received: 7 May 2014 /Accepted: 29 August 2014 /Published: 30 September 2014 (c) 2014 IFSA Publishing, S.L. |