Temporal Fuzzy Reasoning Spiking Neural P Systems with Real Numbers for Power System Fault Diagnosis

Temporal Fuzzy Reasoning Spiking Neural P Systems with Real Numbers for Power System Fault Diagnosis Kang Huang1, Tao Wang1, Yangyang He1, Gexiang Zhang1⋆and Mario J. P´ erez-Jim´ enez2 1School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, P.R. China email: [email protected], [email protected], [email protected], [email protected] 2Research Group on Natural Computing Department of Computer Science and Artificial Intelligence Universidad de Sevilla, Sevilla, 41012, Spain email: [email protected] Abstract. This paper proposes a temporal fuzzy reasoning spiking neural P system with real numbers (rTFRSN P system) and its corresponding fault diagnosis method called FDTSNP to diagnose faults in a power system. The introduction of the rTFRSN P system is to make full use of the temporal order information of alarm messages so as to model candidate fault sections. The presentation of the reasoning algorithm within the framework of an rTFRSN P system tries to obtain confidence levels of candidate faulty sections. Thus, FDTSNP offers an intuitive illustration based on a strictly mathematical expression and a good ability to handle incomplete and uncertain alarm messages with temporal order information. The effectiveness of FDTSNP is verified in various fault cases including single and multiple fault situations with/without incomplete and uncertain alarm messages. Experimental results show that FDTSNP is better than several methods reported in the literature, in terms of the correctness of diagnosis results. Keywords: Membrane computing, spiking neural P system, fuzzy reasoning spiking neural P system, temporal fuzzy reasoning spiking neural P system with real numbers, fault diagnosis, power system 1 Introduction Membrane computing, formally introduced by Gh. P˘ aun in [1], is an attractive research field of computer science aiming at abstracting computing models, called membrane systems or P systems, from the structures and functioning of living cells, as well as from the way the cells are organized in tissues or higher order structures. Currently, there are three basic types of P systems: cell-like P systems, tissue-like P systems and neural-like P systems. In recent years, the research on neural-like P systems mainly focused on spiking neural P systems (SN P systems), which were introduced in [2]. An SN P system is a ⋆Corresponding author. 2 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez kind of distributed and parallel computing models inspired by the neurophysiological behavior of neurons sending electrical impulses (spikes) along axons from presynaptic neurons to postsynaptic neurons. Recently, SN P systems have become a hot topic in membrane computing [3]-[22]. Until now, only a few of investigations focus on the use of SN P systems to solve engineering problems. In [14], a fuzzy reasoning spiking neural P system with real numbers (rFRSN P system) was presented to fulfill fault diagnosis. In [15], an rFRSN P system was used for fault diagnosis of power systems and examples were provided to verify its effectiveness. In [17], adaptive fuzzy spiking neural P systems were applied in fault diagnosis of power transmission networks. In [18], a fuzzy reasoning spiking neural P system with trapezoidal fuzzy numbers (tFRSN P system) was presented to fulfill diagnosis knowledge representation and reasoning, and FDSNP was proposed for fault diagnosis of power systems. In [20], a weighted fuzzy reasoning spiking neural P system (WFRSN P system) was presented for fulfilling fault diagnosis of traction power supply systems of high-speed railways. These aforementioned different kinds of SN P systems, called FRSN P systems, are effective in diagnosing faults of different power systems with uncertainty and incompleteness. However, the studies [14,15,17,20] handled uncertainty and incompleteness by probability statistics where the values were obtained based on the frequency of occurrences from historical data while the study [18] by trapezoidal fuzzy numbers which were based on expertise. As a matter of fact, it is difficult to obtain and process real-time statistical data from huge power networks and expertise is usually influenced by experts’ levels. Therefore, how to improve FRSN P systems to handle uncertainty and incompleteness in fault diagnosis of power systems is worth discussing. There exists a time limit constraint relationship between protective relays and circuit breakers (CBs) and a time cooperation relationship between each grade of protective relays and their corresponding CBs. The temporal order information of alarm messages obtained based on global positioning systems (GPS) can record action sequences of these protective relays and CBs by milliseconds (ms). For each fault in a power system, the temporal order information of alarm messages is obtained immediately and objectively from monitoring equipments. The temporal order information can be used to correct redundant information error by using the temporal order information consistency constraint relationship to filter out wrong alarm messages. Thus, more reliable alarm messages are obtained after the information error correction and can overcome the uncertainty caused by maloperation and operation failure of protection devices. So it is a good way to use the temporal order information of alarm messages to handle uncertainty and incompleteness in fault diagnosis of power systems. In this study, to make full use of the temporal order information of alarm messages from supervisory control and data acquisition (SCADA) systems, a temporal fuzzy reasoning spiking neural P system with real numbers (rTFRSN P system) is proposed and a fault diagnosis method based on rTFRSN P systems for power systems (FDTSNP, for short) is developed for fault diagnosis of power systems. In FDTSNP, an rTFRSN P systems is introduced to model candidate fault sections, a reasoning algorithm of the rT- FRSN P system is presented for fault reasoning to obtain confidence levels of candidate faulty sections and temporal order information consistency constraint relationship is Fault Diagnosis of Power systems Based on rTFRSNPS 3 used to handle temporal order information of alarm messages as well as judge its validity. To make the rTFRSN P system models quickly be revised when topology structure of power networks have changes, sub-rTFRSN P system models of each sections are considered. Case studies show that FDTSNP is effective in fault diagnosis of power systems in different types of fault cases. This paper is structured as follows: Section 2 states the problem to solve. The models and reasoning algorithms of rTFRSN P systems are presented in Section 3. Section 4 introduces fault diagnosis method based on P systems (FDTSNP). In Section 5, case studies on fault diagnosis are used to test the effectiveness of FDTSNP. Finally, conclusions are drawn in Section 6. 2 Reasoning Model-based Methods Considering Temporal Order Information When a fault occurs in a power system, electrical quantities change firstly and then protective devices including protective relays and circuit breakers (CBs) operate to isolate this fault. The protective relays consist of main protective relays, first backup protective relays and second backup protective relays. It is worth pointing out that there is not any first backup protective relay for buses [18]. These different kinds of protective relays and their corresponding CBs operate to protect a power system based on certain rules. For details about the operating rules, please see [18]. Thus when a fault occurs, a large number of alarm messages form SCADA systems are poured into dispatchers’ consoles in a short period of time. These messages are often incomplete and uncertain due to reasons such as maloperation and refuse operation of protective devices and distortion of communication channel. One way to deal with the uncertainty is to correct the alarm information in the first step of fault diagnosis. So, we improve the framework of fault diagnosis in power systems using reasoning modelbased method in [20] and show it in Fig. 1. In this study, temporal order information consistency constraint relationship is used to correct the alarm information and then judge the validity of alarm messages. In order to illustrate temporal order information consistency constraint relationship, we first introduce some temporal order concepts as follows. (1) Time point constraints T(t)[23] An interval T(t) = [t−, t+]is defined as a constraint of time point, where t− and t+are lower and upper bounds of T(t), respectively. T(t)is used to describe the uncertainty of temporal order information of alarm messages. Usually, t−and t+are set as 95% and 105%, respectively, i.e., T(t) = [0.95t, 1.05t]. (2) Time distance constraints T(ti, tj)[23] Time distance d(ti, tj) = tj−tirepresents the time distance between two different alarm messages, where, tiand tjare time points of the messages. An interval T(ti, tj)=[t− ij, t+ ij]is defined as a constraint of time distance, where t− ij and t+ ij are the lower and upper bounds of T(ti, tj), respectively. T(ti, tj)is used to describe the uncertainty of time distance of alarm messages. According to the principle of relay protection, the time distance intervals about different kinds of protective relays and their corresponding CBs are T(Pm, CBs)=[40, 60], T(Pp, CBs)=[20, 40], 4 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez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ig. 1. Power system fault diagnosis framework of reasoning model-based methods considered temporal order information. T(Ps, CBs)=[40, 100], where Pm, Pp, Ps represent main protective relays, first backup protective relays and second backup protective relays, respectively. Next, we describe temporal order information consistency constraint relationship as follows. Temporal order information of alarm messages about related protective devices must satisfy the consistency constraint, as shown in (1) [24]. T(tA) + T(tA, tB)∩T(tB)=∅(1) where alarm A and alarm B are alarm messages with logical causality; T(tA)and T(tB) are operational time point constraints of alarm A and alarm B, respectively; T(tA, tB) is a time distance constraints between alarm A and alarm B; the symbol ‘+’ is an operation of a time point and a time distance, and means the additions of the two lower time limits and the two upper time limits of T(tA)and T(tA, tB), respectively. If temporal order information of alarm A and alarm B fails to satisfy the relationship in (1), then A and B also fails to satisfy the consistency constraint relationship, which means that alarm messages A and alarm B are invalid. Besides, we need to illustrate what is corresponding protection set which will be used in the following sections. Fig. 2 is used as a simple example to describe the causality between protective relays and CBs. According to the principle of relay protection, we know that circuit breakers CBij and CBji on line Lij has causal relationship with protective relays. In this study, these protective relays are put into two sets, i.e., Cij and Fault Diagnosis of Power systems Based on rTFRSNPS 5 ! "# ! "#! Fig. 2. A sketch map of protective relays and CBs. Cji, where Cij and Cji represent protective relays corresponding to CBij and CBji, respectively. Cij ={Bim, LijSm, LijSp, LijSs}(2) Cji ={Bjm, LijRm, LijRp, LijRs}(3) 3 rTFRSN P Systems 3.1 Definitions Definition 1: An rTFRSN P system of m≥1is a tuple Π= (O, σ1, . . . , σm, syn, in, out), where: (1) O={a}is a singleton alphabet (ais called spike); (2) σ1, . . . , σmare neurons. For proposition neurons, they are with the form σi= (θi, ti, ri),1≤i≤s; for rule neurons, they are with the form σi= (δi, ci, ri),1≤ i≤t,s+t=m, where: (a) θiis a real number in [0, 1] representing the potential value of spikes (i.e. value of electrical impulses) contained in proposition neuron σi; (b) tiis a real number either 0 or 1 representing the state of proposition neuron σi. If ti= 1, then the alarm message associated with σiis valid; otherwise, the alarm message associated with σiis invalid; (c) δiis a real number in [0, 1] representing the potential value of spikes (i.e. value of electrical impulses) contained in rule neuron σi; (d) ciis a real number in [0, 1] representing the truth value associated with rule neuron σiand is identical with the certainty factor of the fuzzy production rules corresponding to rule neuron σi; (e) For both proposition neurons and rule neurons, rirepresents a firing (spiking) rule contained in neuron σiwith the form E/aθ→aβ, where θand βare real numbers in [0, 1], E={an}is the firing condition. The firing condition means that if and only if neuron σireceives at least nspikes, then the firing rule contained in the neuron can be applied, otherwise, the firing rule cannot be applied; (3) syn ⊆ {1,2, . . . , m}×{1,2, . . . , m}with i=jfor all (i, j)∈syn, 1≤i, j ≤m, is a directed graph of synapses between the linked neurons; (4) in, out ⊆ {1,2, . . . , m}indicate the input neuron set and the output neuron set of Π, respectively. 6 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez An rTFRSN P system is an extension of SN P systems. (1) The definition of neurons are extended. The rTFRSN P systems consist of two kinds of neurons: proposition neurons and rule neurons, where rule neurons contain two subcategories: and and or. (2) The pulse value θicontained in each proposition neuron or the pulse value δicontained in each rule neuron is a real number in [0, 1] representing potential value of spikes contained in this neuron instead of the number of spikes in SN P systems. (3) Each neuron σiis associated with either a proposition or a fuzzy production rule. For a proposition neuron σi, the real number tirepresents the state of this proposition neuron and is used to determine whether proposition neuron σiis valid or not. If ti= 1, then the alarm message associated with σiis valid and this means that the protective device associated with this alarm message operates correctly; otherwise, the alarm message associated with σiis invalid and this means that the protective device associated with this alarm message maloperates. For a rule neuron σi, the real number ti∈[0,1] represents the certainty factor (CF) of the fuzzy production rule associated with σi. (4) Each neuron contains only one firing (spiking) rule of the form E/aθ→aβ. When the firing condition of one neuron is satisfied, the firing rule is applied, which means that the potential value θis consumed and then this neuron produces a new spike with potential value of β. These different types of neurons aforementioned handle the potential values θand βin different ways. In this study, tiis used to determine whether proposition neuron σiis valid and the value of tiitself is not used in a computing process. Therefore, the definitions of neurons (and and or rule neurons) and ways of handling potential values θand βare the same with those in [14]. Thus, we will not describe them again here (see [14] for more details). If the firing condition of one neuron is satisfied, then the potential value of the spikes received by this neuron is updated via logical and or or operators. (5) Time delay is ignored in rTFRSN P systems, thus all neurons are always open. 3.2 Reasoning algorithm In order to present a reasoning algorithm for rTFRSN P systems, we first introduce some parameter vectors and matrices as follows. (1) θ= (θ1, . . . , θs)Tis a real truth value vector of the sproposition neurons, where θi(1≤i≤s) is a real number in [0, 1] representing the potential value contained in the ith proposition neuron. If there is not any spike contained in a proposition neuron, its potential value is 0. (2) δ= (δ1, . . . , δt)Tis a real truth value vector of the trule neurons, where δj (1≤j≤t) is a real number [0, 1] representing the potential value contained in the jth rule neuron. If there is not any spike contained in a rule neuron, its potential value is 0. (3) C=diag(c1, . . . , ct)is a diagonal matrix, where cj(1≤j≤t) is a real number in [0, 1] representing the certainty factor of the jth fuzzy production rule. 4) D1= (dij)s×tis 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 σito the general rule neuron σj, then dij = 1, otherwise, dij = 0. 5) D2= (dij)s×tis 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 σito the and rule neuron σj, then dij = 1, otherwise, dij = 0. Fault Diagnosis of Power systems Based on rTFRSNPS 7 6) D3= (dij)s×tis a synaptic matrix representing the directed connection from proposition neurons to or rule neurons. If there is a directed arc (synapse) from the proposition neuron σito the or rule neuron σj, then dij = 1, otherwise, dij = 0. 7) E= (eji)t×sis a synaptic matrix representing the directed connection from rule neurons to proposition neurons. If there is a directed arc (synapse) from the rule neuron σjto the proposition neuron σi, then eji = 1, otherwise, eji = 0. Subsequently, we introduce some multiplication operations as follows. (1) ⊗:DT⊗θ= ( ¯ d1, . . . , ¯ dt)T, where ¯ dj=d1j∗θ1+. . . +dsj ∗θs,for j= 1, . . . , t. (2) ⊕:DT⊕θ= ( ¯ d1,..., ¯ dt)T, where ¯ dj=min{d1j∗θ1, . . . , dsj ∗θs},for j= 1, . . . , t. (3) ⊙:DT⊙θ= ( ¯ d1, . . . , ¯ dt)T, where ¯ dj=max{d1j∗θ1, . . . , dsj ∗θs},for j= 1, . . . , t. Next, we list the pseudocode of reasoning algorithm for rTFRSN P systems. INPUT: The fuzzy truth values of the propositions corresponding to the input proposition neurons. OUTPUT: The fuzzy truth values of the propositions corresponding to the output proposition neurons. Step 1): Let g= 0 be the reasoning step; Step 2): Set initial values of D1,D2,D3,E,Cand the termination condition 01= (unknown, (t) . . ., unknown)T. The initial values of θand δare set to θg= (θ1g, θ2g, . . . , θsg)and δg= (δ1g, δ2g, . . . , δtg), respectively; Step 3): gis increased by one; Step 4): The firing condition of each input neuron (g= 1) or each proposition neuron (g > 1) is evaluated. If the condition E=asis satisfied and there is a postsynaptic rule neuron, the neuron fires and transmits a spike to the next rule neuron; Step 5): Compute the fuzzy truth value vector δgaccording to (4); δg= (DT 1⊗θg−1) + (DT 2⊕θg−1) + (DT 3⊙θg−1)(4) Step 6) If δg=01, the algorithm halts and outputs the reasoning results; Step 7): Evaluate the firing condition of each rule neuron. If the condition E=asis satisfied, the rule neuron fires and transmits a spike to the next proposition neuron; Step 8): Compute the fuzzy truth value vector θgaccording to (5). Go to Step 3. θg=ET⊙(C⊗δg)(5) 4 Fault Diagnosis Method Based on rTFRSN P Systems 4.1 Fault diagnosis models based on rTFRSN P systems In this study, fault diagnosis of faulty sections are considered according to the statuses of protective relays and circuit breakers (CBs) because they are normally read from a power SCADA system. The protective relays consist of main protective relays, first backup protective relays and second backup protective relays, which are represented by m, p, s, respectively. For transmission lines, there are two types of protective relays: 8 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez ! " # $ % "& "' "( "$ #( #% "% ( #' "# ) #& #) ") ' " "" & #$ # "! ) & ' #" ## #! " # % ( $ *# *( *#! *" * *& *) *' *% *$ Fig. 3. Topological diagram of IEEE 10 Generator 39 Bus System. sending end protective relays and receiving end protective relays, which are represented by Sand R, respectively. It is worth pointing out that there is not any first backup protection devices for buses. Fig. 3 shows an IEEE 10 Generator 39 Bus System, which is used to illustrate how to build rTFRSN P system fault diagnosis models. First, bus B04 in Fig. 3 is used to describe model building of buses, where the fault confidence level of bus B04 is the maximal value of outputs of the three sub-rTFRSN P systems. We can see that B04 connects with lines L0304, L0405, L0414. When B04 has a fault, the main protective relay B04mof B04 will act to trip its corresponding CBs, i.e., CB0304,CB0405 and CB0414, to protect this bus. If B04mdoes not operate or its associated CBs do not trip, then first backup protective relays of bus B04 will act to trip their associated CBs. Otherwise, this fault will spread to the adjacent lines of bus B04. For example, if CB0414 does not trip, then second backup protective relay L0304Ss will act to trip CB0403 to isolate the fault section. Likewise, if CB0405 does not trip, then second backup protective relay L0405Rs will act to trip CB0504; if CB0414 does not trip, then second backup protective relay L0414Rs will act to trip CB1404. Thus, the fault production rules of bus B04 are described as follows (let us note that the number of fault fuzzy production rules of a bus is identical with the number of its adjacent lines). R1:IF (B04moperates and CB0414 trips)OR (L0414Rs operates and CB1404 trips while CB0414 does not trip)THEN B04 faults (CF = 0.95) R2:IF (B04moperates and CB0403 trips)OR (L0304Ss operates and CB0304 trips while CB0403 does not trip)THEN B04 faults (CF = 0.95) Fault Diagnosis of Power systems Based on rTFRSNPS 9 R3:IF (B04moperates and CB0405 trips)OR (L0405Rs operates and CB0504 trips while CB0405 does not trip)THEN B04 faults (CF = 0.95) Therefore, fault diagnosis models based on rTFRSN P systems for bus B04 are built according to these three fault production rules shown in Fig. 4. The corresponding rTFRSN P system for bus B04 is defined as follows: Π1= (O, σ1, σ2, . . . , σ10, syn, in, out) where 1) O={a}is the singleton alphabet (ais called spike); 2) σ1, σ2, . . . , σ7are proposition neurons corresponding to the propositions with fuzzy truth values θ1, θ2, . . . , θ7; 3) σ8, σ9, σ10 are rule neurons, where σ8, σ9are and rule neurons, σ10 are or rule neurons; 4) syn ={(1,8) ,(2,8),(2,9),(3,9),(4,9),(5,10),(6,10),(8,5),(9,6),(10,7)}; 5) in ={σ1, σ2, σ3, σ4},out ={σ7}. It is worth pointing out that there are assistant arcs in this figure. For example, in Fig. 4 (a), there is an assistant arc from σ2to σ9. It means that if CB0414 trips, then the operation information about L0414Rs and CB1404 is invalid. Likewise, the meaning of assistant arcs in Fig. 4 (b) and (c) is similar. Then, transmission line L0939 in Fig. 3 is used to describe model building of transmission lines, where the fault confidence level of line L0939 is the maximal value of outputs of the two sub-rTFRSN P systems. Fault fuzzy production rules of transmission line L0939 are described as follows. R1:IF (L0939Sm operates and CB0939 trips)OR (L0939Sp operates and CB0939 trips OR (L0809Ss operates and CB0809 trips)) while CB0939 does not trip) THEN L0939 faults (CF = 0.95) R2:IF (L0939Rm operates and CB0939 trips)OR (L0939Rp operates and CB0939 trips OR (L0139Ss operates and CB0139 trips)) while CB3909 does nottrip) THEN L0939 faults (CF = 0.95) From Fig. 3, we can see that L0939 connects with lines L0139 and L0809. When L0939 has a fault, the main protective relays, L0939Sm and L0939Rm, of L0939 will act to trip L0939 and L3909 to protect this line. If main protective relays do not operate or their associated CBs do not trip, then first backup protective relays, L0939Sp and L0939Rp of line L0939 will act to trip their associated CBs. Otherwise, this fault will spread to adjacent lines. For example, if CB0939 does not trip , then second backup protective relay L0809Ss will act to trip CB0809 to isolate the fault section. Likewise, if CB3909 does not trip, then second backup protective relay L0139Ss will act to trip CB0139. For a transmission line, a fault can spread to its sending terminal and receiving terminal. Thus, the number of fault fuzzy production rules for a line is always equal to two. Therefore, fault diagnosis models based on rTFRSN P systems for transmission line L0939 are built according to two fault fuzzy production rules and are shown in Fig. 5. It is worth pointing out that there are assistant arcs in this figure. For example, in Fig. 16 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez Diagnosis results: line L0414 has a fault, and its fault confidence level is 0.722. We can see that when line L0414 has a fault, its main protective relay L0414Rm rejects to operate while its first backup protective relays L0414Rp operates to trip CB1404 to isolate this fault. Case 4: bus B14 and line L0414 have faults. Status information from the SCADA system: (B14m, 25ms), (L0414Sm, 27ms), (L0414Rm, 32ms), (CB0414, 62ms), (CB1314, 63ms), (CB1404, 75ms), (CB1413, 77ms), (L1415Rs, 675ms), (CB1514, 816ms). Results of handling temporal order information: L={CB1314},H={B14m, L0414Sm, L0414Rm, CB0414, CB1404, CB1413, L1415Rs, CB1514}. Diagnosis resultsbus B14 and Line L0414 have faults, and their fault confidence levels are 0.707 and 0.7671, respectively. We can see that bus B14 and Line L0414 have faults, CB1415 fails to trip while the second backup protective relay L1415Rs operates to trip CB1514 to isolate this fault. Moreover, CB1314 maloperates in this case. Case 5: lines L0318 and L0414 have faults. Status information from the SCADA system: (L0318Sm, 34ms), (L0318Rm, 37ms), (CB0318, 63ms), (CB1817, 132ms), (L0414Sp, 342ms), (L0414Rp, 350ms), (CB0414, 389ms), (CB1404, 391ms), (L1718Rs, 436ms), (L1718Ss, 712ms), (CB1718, 714ms). Results of handing temporal order information: L={CB0318, CB1817},H= {L0318Sm,L0318Rm,L0414Sp,L0414Rp,CB0414,CB1404, L1718Rs, L1718Ss, CB1718}. Diagnosis Results: Lines L0318 and L0414 have faults, and their fault confidence levels are 0.5866 and 0.6769, respectively. We can see that when line L0318 has a fault, CB1803 fails to trip while the second backup protective relay L1718Ss operates to trip CB1718 to isolate the fault. And when line L0414 has a fault, main protections L0414Sm and L0414Rm fail to operate while the first backup protective relays L0414Sp and L0414Rp operate to isolate the fault. More over, L1718Rs and CB1817 maloperate in this case. Table 2 lists the status information (alarm messages) from the SCADA system, candidate faulty sections and diagnosis results of these cases of FDTSNP (faulty sections, fault confidence levels and operation estimation), as well as comparisons between FDTSNP and three fault diagnosis methods, fuzzy Petri net (FPN), time sequence fuzzy Petri net (TSFPN) net and weighted fuzzy Petri net (WFPN), from [25], [26] and [27] respectively. It is worth pointing out that “-” means that this case was not considered in the corresponding reference and the diagnosis results of cases in Table 2 about FPN and TSFPT are listed in appendix C of [27] rather than in [25] and [26]. From Table 2, we can see that diagnosis results of FDTSNP, from case 1 to case 5, are the same as those in [27]. In other words, FDTSNP is effective in fault diagnosis of electrical power systems. Table 2 also shows that in some cases, FDTSNP has superiority to FPN and TSFPN on correctly identifying fault sections. For instance, in case 4, the fault diagnosis results of FDTSNP are different from those of FPN and TSFPN. In this case, for section L1415, only L1415Rs operated. Actually, L1415Rs operated as the second backup protective relay of section B14 because of the operation failure of CB1415. So in fact, L1415 is not a faulty section. Thus, for case 4, the diagnosis results of FDTSNP are better than those of FPN and TSFPN. Likewise, for case 5, the diagnosis results of FDTSNP are better than those of FPN and TSFPN. In cases 1-5, Fault Diagnosis of Power systems Based on rTFRSNPS 17 comparisons of diagnosis results verify that FDTSNP can obtain satisfying results in single and multiple fault situations with/without maloperation or operation failure of protective relays and CBs. Therefore, FDTSNP is effective with a good accuracy used in electrical power system fault diagnosis. 6 Conclusions In this study, rTFRSN P systems are applied in fault diagnosis of power systems. A graphic modeling approach called FDTSNP, is presented for fault diagnosis of power systems. In FDTSNP, an rTFRSN P systems which can make use of temporal order information of alarm messages is introduced to model candidate fault sections, a reasoning algorithm of the rTFRSN P system is proposed for fault reasoning to obtain confidence levels of candidate faulty sections and temporal order information consistency constraint relationship is used to handle temporal order information of alarm messages from SCADA systems as well as judge its validity. Case studies show that FDTSNP is effective in fault diagnosis of power systems in different fault cases. The ability of a fault diagnosis method is usually associated with knowledge availability and reasoning process. An rTFRSN P system is a novel graphic model with parallel computing ability for representing fuzzy knowledge and information, and different types of neurons increase the ways of knowledge representation and reasoning compared with traditional fault diagnosis tools. Since FDTSNP considers temporal order information of alarm messages which can correct alarm messages to handle the uncertainty and incompleteness in fault diagnosis without massive historical data collections and dependence on experts’ experience, FDTSNP shows great potential in power system fault diagnosis and especially for complex or large-scale power grids. When a fault occurs in a power system, electrical quantities change firstly and then protective devices operate to isolate this fault. In this study, only alarm messages of protective devices are considered. In the future, we will pay attention to explore superiority of FDTSNP in fault diagnosis of complex or large-scale power systems and how to consider electrical measurements in the framework of FRSN P systems or SN P systems. Moreover, to test the speed and accuracy of rTFRSN P systems in fault diagnosis of power system, our future work will simulate them on MATLAB, P-Lingua and/or MeCoSim. Acknowledgment The work of K. Huang, T. Wang, Y. He and G. Zhang is supported by the National Natural Science Foundation of China (61170016, 61373047). The work of M.J. P´ erez- Jim´ enez is supported by Project TIN2012-37434 of the Ministerio de Econom´ ıa y Competitividad of Spain. References 1. P˘ aun, Gh.: Computing with Membranes. Journal of Computer System Sciences 61(1), 108– 143 (2000) 18 K. Huang, T. Wang, Y. He, G. Zhang and M.J. P´ erez-Jim´ enez Table 2. Status information and comparisons between FDTSNP and three fault diagnosis methods Alarm Candidate FPN WFPN TSFPN diagnosis results of FDTSNP Cases messages faulty sections [25] [26] [27] Faulty Fault Operation sections confidence levels estimation 1 (B14m, 20ms) - - B14 B14 (L0414Ss, 750ms) L1415Rs (L1415Rs, 371ms) B14 0.7671 maloperation (CB1415 , 73ms) L0414 0.1805 CB1404 (CB1413 , 81ms) Operation failure (CB0414 , 87ms) 2 (L0414Sm, 27ms) L0414 L0414 L0414 (L0414Rm, 32ms) (CB0414 , 73ms) B14 0.1805 B14m: (B14m, 91ms) L0414 L0414 0.7671 maloperation (L1415Rs, 712ms) L1415 L1415 0.1805 CB1404: (L1314Ss, 736ms) L1314 0.1805 operation failure (CB1314 , 764ms) (CB1514 , 816ms) 3 (L0414Sm, 21ms) L0414 L0414 L0414 L0414 L0414 0.7671 (CB0414 , 3ms) L0414Rm : (L0414Rp, 367ms) operation failure (CB1404 , 370ms) 4 (B14m, 25ms) (L0414Sm, 27ms) (L0414Rm, 32ms) B14 0.7671 CB1314 : (CB0414 , 62ms) L0414 B14 B14 B14 B14 0.7671 maloperation (CB1314 , 63ms) L1314 L0414 L0414 L0414 L0414 0.1805 CB1415 : (CB1404 , 75ms) L1415 L1415 L1415 0.1805 operation failure (CB1413 , 77ms) (L1415Rs, 675ms) (CB1514 , 816ms) 5 (L0318Sm, 34ms) (L0318Rm, 37ms) (CB0318 , 63ms) (CB1817 , 132ms) B18 B18 0.1805 L1718Rs, (L0414Sp, 342ms) L0318 L0318 B18 L0318 L0318 0.5866 CB1817 (L0414Rp, 350ms) L1718 L1718 L0318 L0414 L0414 0.1805 maloperation (CB0414 , 389ms) L0414 L0414 L0414 0.6769 CB1803 (CB1404 , 391ms) operation failure (L1718Rs, 436ms) (L1718Ss, 712ms) (CB1718 , 714ms) Fault Diagnosis of Power systems Based on rTFRSNPS 19 2. 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