Application of Adaptive Fuzzy Spiking Neural P Systems in Fault Diagnosis of Power Systems

Transcription

1 Chinese Journal of Electronics Vol.23, No.1, Jan Application of Adaptive Fuzzy Spiking Neural P Systems in Fault Diagnosis of Power Systems TU Min 1, WANG Jun 1, PENG Hong 2 and SHI Peng 3,4 (1.School of Electrical and Information Engineering, Xihua University, Chengdu , China) (2.Center for Radio Administration and Technology Development, Xihua University, Chengdu , China) (3.Department of Computing and Mathematical Sciences, University of Glamorgan Pontypridd, CF37 1DL, UK) (4.School of Engineering and Science, Victoria University Melbourne, Vic 8001, Australia) Abstract Adaptive fuzzy spiking neural P systems (AFSN P systems) are a novel kind of computing models with parallel computing and learning ability. Based on our existing works, AFSN P systems are applied to deal with the fault diagnosis problems of power systems and the uncertainty of action messages about protective and breakers, and a new fault diagnosis model of power systems is proposed with simple reasoning process and fast speed with parallel processing capabilities. The effectiveness of the fault diagnosis model is verified by some examples of fault diagnosis. Furthermore, the learning ability of AFSN P systems can be applied to adjust the weights in the fault diagnosis model automatically. Key words Membrane computing, Spiking neural P systems, Fault diagnosis, Power systems. I. Introduction Membrane computing, also known as P systems, is a novel class of distributed parallel computing models, which are inspired by the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs [1].A large number of P systems and variants have been proposed in recent years. According to the structure of membrane, P systems can be classified into three categories: cell-like P systems, tissue-like P systems, neural-like P systems. Spiking neural P systems (SN P systems) [2] is main form of neural-like P systems, which are inspired by the idea that spiking neurons excite pulses under the framework of membrane computing. SN P systems, which can be viewed as a directed graph, excite and transmit pulses to complete computation under the control of firing/spiking rules. In order to deal with the representation of fuzzy knowledge and complete fuzzy reasoning, several extended spiking neural P systems, called Fuzzy spiking neural P systems (FSN P systems), have been proposed by the authors of this paper in recent years [3 5]. These FSN P systems have the following characteristics: (1) parallel computing advantage, (2) high understandability (due to their directed graph structure), (3) dynamic feature (neuron s firing and spiking mechanism makes them suitable to model dynamic behavior of a system), (4) synchronization, (5) non-determination, (6) non-linearity, and so on. Therefore, FSN P systems are suitable to deal with fault diagnosis problems potentially because of these features. However, many real-world systems are usually dynamic, so it is required that the computing models can adjust themselves automatically. Thus, Adaptive fuzzy spiking neural P systems (AFSN P systems) with learning ability were further developed [6]. With the expansion of grid, security and stability of the power grid operation is one of the important goals of power enterprises. When the grid fails, the automation devices installed in the power system will generate a lot of alarm information, which make the fault diagnosis decision difficult for workers. Therefore, it is important to ensure security and stability of grid via the fault diagnosis timely and accurate. The fault diagnosis of power systems is a process of discriminating faulted elements or areas by tripping of protective and circuit breakers. So far, many fault diagnosis methods have been addressed, such as expert systems [7,12], artificial neural networks [8,13], optimization algorithms [9] and fuzzy logic reasoning [10] and so on. Fault diagnosis method based on expert system has a bottleneck of knowledge acquisition, fault tolerance, maintenance difficult and not fast reasoning speed so that it is difficult to meet the needs of large-scale power system fault diagnosis, mainly for offline analysis. Fault diagnosis method based on neural network is mainly used for small-scale power grid with fixed wiring, do not have the capacity of the grid topology, is difficult to directly connect with the SCADA system and cannot good at dealing with heuristic knowledge. Moreover, it is difficult to establish reasonable mathematical models of transmission network using fault diagnosis method based on a variety of optimization algorithm. In the meantime, there is a difficult problem of establishing the right of fuzzy Manuscript Received Dec. 2012; Accepted Mar This work is partially supported by the National Natural Science Foundation of China (No ), the Open Research Fund of Key Laboratory of High Performance Scientific Computing, Xihua University (No.SZJJ ), Research Fund of Sichuan Key Technology Research and Development Program (No.2013GZX0155), and the Innovation Fund of Postgraduate, Xihua University (No.ycjj201364).

2 88 Chinese Journal of Electronics 2014 rules and membership functions in fault diagnosis method based on fuzzy theory. Therefore, AFSN P systems are used to deal with fault diagnosis problems of power systems, and a new fault diagnosis model of power systems based on AFSN P systems is proposed in this paper. The proposed method has simple reasoning process, fast speed with parallel processing capabilities and the learning ability. The practical motivation behind this work is to build a bridge between SN P systems and fault diagnosis of power system and extend the application areas of membrane computing. Furthermore, this strategy is a first attempt at home and abroad, and provides a new idea for fault diagnosis of power system. The rest of this paper is organized as follows. Section II reviews definition of AFSN P systems, and then describes AFSN P systems-based models for weighted fuzzy production rules. Section III describes a fault diagnosis model based on AFSN P systems. A fault diagnosis example is provided in Section IV. Learning of AFSN P systems for fault diagnosis is discussed in Section V, and conclusions are drawn in Section VI. II. AFSN P Systems In this section, we briefly review the definition of AFSN P systems, and then move on to model the weighted fuzzy production rules and fuzzy reasoning based on AFSN P systems. More details about AFSN P systems can be found in Ref.[6]. 1. Definition of AFSN P systems AFSN P systems (of degree m 1) is a construct of the form Π=(A, N p,n r,syn,i,o) where (1) A = {a} is the singleton alphabet (the object a is called spike). (2) N p = {σ p1,σ p2,,σ pm} is called proposition neuron set, where proposition neuron σ pi expresses the ith proposition in a set of weighted fuzzy production rules, 1 i m. σ pi =(α i,ω i,λ i,r i), where (a) α i [0, 1] is the pulse value contained in proposition neuron σ pi. α i is used to express fuzzy truth value of the proposition associated with proposition neuron σ pi. (b) ω i = (ω i1,ω i2,,ω isi ) expresses the output weight vector of neuron σ pi, whereω ij [0, 1] is the weight on jth output synapse of the neuron, 1 j s i,ands i is the number of all output synapses of the neuron. (c) r i is a firing/spiking rule, of the form E/a α a α, α [0, 1]. E = {α λ i} is called the firing condition, i.e., if α λ i, then the firing rule will be enable, where λ i [0, 1] is called the firing threshold. (3) N r = {σ r1,σ r2,,σ rn} is called rule neuron set, whereruleneuronσ ri expresses the ith weighted fuzzy production rule, 1 i n. σ ri =(α i,γ i,τ i,r i), where (a) α i [0, 1] is called the pulse value contained in rule neuron σ ri. (b) γ i [0, 1] is called the certain factor, which represents the strength of belief of the weighted fuzzy production rule associated with rule neuron σ ri. At the same time, γ i is also the weight on output synapse (arc) of the neuron. (c) r i is a firing/spiking rule, of the form E/a α a β, α, β [0, 1]. E = {α τ i} is called the firing condition, i.e., if α τ i, then the firing rule will be enable, where τ i [0, 1] is called the firing threshold. (4) syn (N p N r) (N r N p) indicates synapses between proposition neurons and rule neurons. Note that there are no synapse connections between any two proposition neurons or between any two rule neurons. (5) I, O N p are input neuron set and output neuron set, respectively. 2. AFSN P systems-based models for weighted fuzzy production rules The motivation of proposing AFSN P systems is to model weighted fuzzy production rules. The weighted fuzzy production rules of the following three types are concerned. Type 1: if p 1 then p 2 Type 2: if p 1 and p 2 and and p n then p n+1 Type 3: if p 1 or p 2 or or p n then p n+1 The weighted fuzzy production rules of the three types can be modeled by three AFSN P systems respectively, shown in Fig.1. In Fig.1, each proposition neuron is denoted by a circle, while each rule neuron is denoted by a rectangle. More details can be found in Ref.[6]. According to dynamic firing mechanism of AFSN P systems, the fuzzy reasoning process of weighted fuzzy production rules of the three types can be described as follows. { αi γ, if α 1 τ Type 1: α 2 = 0, if α 1 <τ ( n ) ( n ) α i ω i γ, if α i ω i τ i=1 i=1 Type 2: α n+1 = ( n ) 0, if α i ω i <τ { i=1 MAX(αj γ j), α j τ j,j J Type 3: α n+1 = 0, if α j <τ j,j =1, 2,,n Fig. 1. AFSN P systems for weighted fuzzy production rules: (a) Type1;(b) Type2;(c) Type3 III. Fault Diagnosis Model Based on AFSN P Systems The process of fault diagnosis is to use action messages of protective and breakers to diagnose faulted elements. As the power systems may have incorrect operation or rejecting act, the fault diagnosis should consider the backup protection. In China, the power system adopts three-step protection devices including the main protective, first backup protective and second backup protective. In this paper, three types of fault diagnosis are mainly considered: line, bus and transformer. Here, AFSN P systems are used to build the three types of fault diagnosis models. Symbol conventions are as follows: B,L,CB and T represents bus, line, circuit breaker

3 Application of Adaptive Fuzzy Spiking Neural P Systems in Fault Diagnosis of Power Systems 89 and transformer respectively. As to L xy, its first subscript s and r represents the sending and receiving terminals respectively, and the second subscript m, p and s represents main, first backup and second backup protective respectively. (1) The protective relay system of line consists of main protective of sending terminal, first backup protective of sending terminal, second backup protective of sending terminal, main protective of receiving terminal, first backup protective of receiving terminal and second backup protective of receiving terminal. Therefore, the line fault diagnosis model based on AFSN P systems is shown in Fig.2(a), where L xy denotes the protective of line (x {s, r},y {m, p, s}), and CB 1 CB 6 denote the corresponding circuit breakers, and the rule neuron σ r1x represents the operation of L sm that leading to CB 1 trip and any other five states, and the rule neuron σ r2x represents the operation of L sm and L rm that leading to CB 1 and CB 3 trip and any other eight states. (2) The protective relay system of bus is composed of the operation of main protective that leading to corresponding circuit breakers trip and operation of second backup protective that leading to corresponding circuit breakers trip. Therefore, the bus fault diagnosis model based on AFSN P systems is shown in Fig.2(b), where R 1 denotes main protective of bus, and R 2 denotes second backup protective of bus, and CB 1 and CB 2 denote corresponding circuit breakers, and the rule neuron σ r1 represents the operation of main protective that leading to corresponding circuit breakers trip, and the rule neuron σ r2 represents the operation of backup protective that leading to corresponding circuit breakers trip while the main protective can not operate. (3) The protective relay system of transformer has three types. First type is the operation of main protective that leading to corresponding circuit breakers trip. Second type is the operation of first backup protective that leading to corresponding circuit breakers trip while the main protective doesn t operate. Third type is the operation of second backup protective that leading to corresponding circuit breakers trip while the main and first backup protective don t operate. Therefore, the transformer fault diagnosis model based on AFSN P systems is shown in Fig.2(c), where R 1 R 3 denote the protective of transformer, and CB 1 CB 3 denote corresponding circuit breakers, and the rule neuron σ r1 represents the operation of main protective that leading to corresponding circuit breakers trip, and the rule neuron σ r2 represents the operation of first backup protective that leading to corresponding circuit breakers trip while the main protective doesn t operate, and the rule neuron σ r3 represents the operation of second backup protective that leading to corresponding circuit breakers trip while the main and first backup protective don t operate. In the above mentioned three fault diagnosis models based on AFSN P systems, the certain factors of operated protective and circuit breakers are as the input of the corresponding proposition neurons, the probability of fault denoted by the fuzzy truth value of conclusion proposition neurons is acquired through using the fuzzy reasoning algorithm. Fig. 2. The fault diagnosis models based on AFSN P systems: (a) Line;(b) Bus;(c) Transformer IV. Application Example In this section, a relatively complex example of fault diagnosis of power systems is provided, and the exploited fault diagnosis models is adopted to deal with the fault diagnosis problems. The sketch map of protective relay system of power system [9] is shown in Fig.3, in which 28 system elements, 84 protective and 40 circuit breakers are included. Fig. 3. A sketch map of protective relay system of power system

4 90 Chinese Journal of Electronics 2014 We assume that firing threshold of every proposition neuron is λ = 0 and firing threshold of every rule neuron is τ = 0.2. In the meantime, the influence degree of tripped protective and circuit breakers for rule neurons is set to the same, that is ω =0.5. When the rule neurons are related to second backup protective, γ =0.9, in other cases, γ =0.95. It is fault element if the fuzzy truth of element value is over 0.5. In this paper, the certain value of the operated protective and tripped circuit breakers is as same as Ref.[11]. They are shown in Table 1 and Table 2. Table 1. The certain value of the operated protective and tripped circuit breakers Main protective First backup Second backup protective protective Element Protec- Circuit Protec- Circuit Protec- Circuit tive tive tive breakers breakers breakers Line Bus Transformer Table 2. The certain value of the not operated protective and tripped circuit breakers Main protective First backup Second backup protective protective Element Protec- Circuit Protec- Circuit Protec- Circuit tive tive tive breakers breakers breakers Line Bus Transformer Four kinds of detected information of protective and circuit breakers are used to verify the validity of the proposed method. Case 1 Simple fault analysis: only main protective operate and circuit breakers tripped correctly. Operated protective B 1m, and tripped circuit breakers CB 4, CB 5, CB 6, CB 7, CB 9 are detected. (1) The passive region {2} is searched using the method of wiring analysis [11]. (2) The fault diagnosis model based on AFSN P systems of B 1 is given shown as Fig.2(b). (3) When α R1 = and α CB1 =0.9833, the fuzzy reasoning algorithm is adopted to get α σr1 = and α B1 = Therefore, B 1 is judged to be faulted and the fuzzy truth value is Case 2 Complex fault analysis: single one element fault with the incorrect operation of protective and circuit breakers. Operated protective B 1m, L 2rs, L 4rs, andtripped circuit breakers CB 4, CB 5, CB 7, CB 9, CB 12 and CB 27 are detected. (1) The passive region {2, 3, 16, 20} is found by the method of wiring analysis. (2) α B1 = , α B2 = , α L2 = and α L4 = are obtained by adopting the above method. Therefore, B 1 is judged to be faulted and the fuzzy truth value is , and faults are expanded because of the rejecting action of CB 6. Case 3 Multi-element fault analysis: multiple elements fault. Operated protective B 1m, L 1sp, L 1rm, andtripped circuit breakers CB 4, CB 5, CB 6, CB 7, CB 9, CB 11 are detected. (1) The passive region {2}, {15} are found by the method of wiring analysis. (2) α B1 = and α L1 = are obtained by adopting above method. Therefore, B 1 and L 1 are judged to be faulted and the fuzzy truth values are and respectively. Case 4 Incomplete information fault analysis: the information offered by SCADA system is incomplete. For instance, in the Case 2, if the protective relay B 1m is not detected, that is operated protective L 2rs, L 4rs and tripped circuit breakers CB 4, CB 5, CB 7, CB 9, CB 12, CB 27 are detected. (1) The passive region {2, 3, 16, 20} is found by the method of wiring analysis. (2) α B1 = , α B2 = , α L2 = , and α L4 = are obtained by adopting above method. Therefore, B 1 is judged to be faulted and the fuzzy truth value is Seen from above four cases, the fault diagnosis models based on AFSN P systems can deal with the uncertainty of action messages about protective and breakers. Furthermore, fault element is diagnosed properly while the information is incomplete because of the well fault tolerance. Therefore, this method is effective in fault diagnosis. V. Learning Ability of AFSN P Systems It can be seen from the above reasoning, that the AFSN P systems can model weighted fuzzy production rules and carry out fuzzy reasoning, and then get the results of fault diagnosis. More importantly, AFSN P systems also have the ability to adjust automatically, which is the learning ability. The previous weights and thresholds in AFSN P systems are acquired by experience, so that the results are affected seriously by human factors. In this paper, the weights are adjusted via the learning algorithm of AFSN P systems so that the results are more in line with the actual situation. Taken example of the AFSN P systems model of bus shown in Fig.4, the learning weights process is as follows. Fig. 4. The fault diagnosis model of bus Firstly, the training data which consist of input data of antecedent proposition neuron and output data of consequence proposition neuron should be certain. The input data is corresponding to the certain value of operated protective and tripped circuit breakers, and the initial output data is

5 Application of Adaptive Fuzzy Spiking Neural P Systems in Fault Diagnosis of Power Systems 91 Fig. 5. The learning results: (a) ω 1 ;(b) ω 2 ;(c) error corresponding to the results that got via weighted fuzzy reasoning algorithm. Furthermore, the initial output data is also corresponding to the probability of faulted bus, and the ideal output data is determined artificially. All training data is shownintable3. Table 3. Training data Initial Ideal Num- Input sample output output ber sample sample The differentials between current output and ideal output should be computed, and the weights will be modified by LMS algorithm constantly until the differentials meet requirements. The weight updating representations of LMS algorithm is as follows. W (t +1)=W (t)+2δe(t)x(t) (1) e(t) =y (t) y(t) (2) where t is iteration number, W (t) is weight while iteration number is t, δ is learning rate, X(t) is input sample, e(t) is differentials, y (t) is ideal output sample, y(t) is current output while iteration number is t. Fig.5 shows that the two weights converge to ω 1 =0.739, ω 2 = when the iteration is around Lastly, e(t) = From the example, we can see that the fuzzy reasoning algorithm and the learning algorithm of AFSN P systems are very effective. VI. Conclusion A novel fault diagnosis model based on AFSN P systems is proposed in this paper. The feasibility and validity of the method are verified by the analysis results of fault diagnosis. Comparing with the existing fault diagnosis models, the proposed method is not only simple and faster, but also can represent the probability of the different fault element through the fuzzy truth value of fault diagnosis, which make the incorrect operation and false alarm can be judged easily. Furthermore, the diagnosis results can be more ideal because of the learning ability of the AFSN P system. However, there are only part of weights in bus fault model are adjusted in this paper. Therefore, our future works include learning more weights in line and transformer fault models. References [1] Gh. Paun, G. Rozenberg, A. Salomaa, The Oxford Handbook of Membrane Computing, Oxford Unversity Press, New York, USA, [2] M. Ionescu, Gh. Paun, T. Yokomori, Spiking neural P systems, Fundameta Informaticae, Vol.71, No.2-3, pp , [3] J. Wang, L. Zhou, H. Peng, G.X. Zhang, An extended spiking neural P system for fuzzy knowledge representation, International Journal of Innovative Computing, Information and Control, Vol.7, No.7A, pp , [4] H. Peng, J. Wang, M.J. Pérez-Jiménez, H. Wang, J. Shao, T. Wang, Fuzzy reasoning spiking neural P system for fault diagnosis, Information Sciences, Vol.235, No.20, pp , [5] J. Wang, P. Shi, H. Peng, M.J. Pérez-Jiménez, T. Wang, Weighted fuzzy spiking neural P systems, IEEE Transactions on Fuzzy Systems, Vol.21, No.2, pp , [6] J. Wang, H. Peng, Adaptive fuzzy spiking neural P systems for fuzzy inference and learning, International Journal of Computer Mathematics, Vol.90, No.4, pp , [7] V.M. Ernesto, L. Oscar, M. Chacon, J. Hector, F. Altuve, An on-line expert system for fault section diagnosis in power systems, IEEE Transactions on Power Systems, Vol.12, No.1, pp , [8] T.S. Bi, Y.X. Ni, F.L. Wu, Q.X. Yang, A novel neural network approach for fault section estimation, Proceedings of the Chinese Society for Electrical Engineering, Vol.22, No.2, pp.73 78, (in Chinese) [9] X.N. Lin, S.H. Ke, Z.T. Li, H.L. Weng, X.H. Han, A fault diagnosis method of power systems based on improved objective function and genetic algorithm-tabu search, IEEE Transactions on Power Delivery, Vol.25, No.3, pp , [10] H.C. Chin, Fault section diagnosis of power system using fuzzy logic, IEEE Transactions on Power Systems, Vol.18, No.1, pp , [11] J.W. Yang, Z.Y. He, T.L. Zang, Power system fault-diagnosis method based on directional weighted fuzzy Petri nets, Proceedings of the Chinese Society for Electrical Engineering, Vol.30, No.34, pp.42 49, (in Chinese) [12] G.J. Cheng, W.M. Li, Expert system based on neural network for ICCAT, Acta Electronica Sinica, Vol.22, No.8, pp.24 28, (in Chinese) [13] D.Q. Zhu, Q.B. Sang, A fault diagnosis algorithm for the pho-

6 92 Chinese Journal of Electronics 2014 tovoltaic radar electronic equipment based on quantum neural networks, Acta Electronica Sinica, Vol.34, No.3, pp , (in Chinese) TU Min was born in Sichuan Province, China, in She is currently a M.S. student of Xihua University. Her research interests include the membrane computing and its application in fault diagnosis and economic load dispatch of power systems. ( haoshenqi@126.com) WANG Jun was born in Sichuan Province, China, She received the B.S. degree and the M.E. degree in industry automation from Chongqing University, China in 1988 and 1991, respectively; the Ph.D. degree in electrical engineering from the Southwest Jiaotong University, China, in She was a lecturer in the Sichuan College of Science and Technology, China ( ) and an associate professor in Xihua University, China ( ). She is currently a professor in the School of Electrical and Information Engineering, Xihua University, China, since Her research interests include electrical automation, intelligent control, and membrane computing. ( junwang66@tom.com) PENG Hong wasborninsichuanprovince,china,1966. HereceivedtheB.S.degreeandtheM.E.degreeinmathematics from Sichuan Normal University, Chengdu, China, in 1987 and 1990, and the Ph.D. degree in signal and information processing from University of Electronic Science and Technology of China, Chengdu, China, in He was a lecturer in the Sichuan College of Science and Technology, China ( ) and an associate professor in Xihua University, China ( ). He was a visiting scholar in Research Group of Natural Computing, University of Seville, Spain ( ). He is currently a professor in the Center for Radio Administration and Technology Development, Xihua University, China, since His research interests include membrane computing, digital watermarking, image processing, signal processing and kernel methods. SHI Peng was born in Heilongjiang Province, China, in He received the B.S. degree in mathematics from Harbin Institute of Technology, China, in 1982; the M.E. degree in systems engineering from Harbin Engineering University, China, in 1985; the Ph.D. degree in electrical engineering from the University of Newcastle, Australia, in 1994; and the Ph.D. degree in mathematics from the University of South Australia in He was awarded the degree of doctor of science by the University of Glamorgan, UK, in Dr Shi was a lecturer in Heilongjiang University, China ( ), in the University of South Australia ( ) and a senior scientist in Defence Science and Technology Organisation, Department of Defence, Australia ( ). He joined in the University of Glamorgan, UK, as a professor in He has been also a professor at Victoria University, Australia, since Dr Shi s research interests include system and control theory, computational and intelligent systems, and operational research.