Modeling of Fault Diagnosis in Power Systems using Petri Nets

The modern power system is vitally significant for daily life. It is a large scale dynamic system. Fault diagnosis in power systems targets at identifying the faulted components in power systems based on the information of the current status of protective relays and circuit breakers available from Supervisory Control and Data Acquisition (SCADA) systems. It is known that online automatic fault diagnosis is vital to the restorative control and as a result of tremendous significance in declining power supply interruption and enhancing service reliability, particularly for the large size power system with large numbers of Intelligent Electronic Devices (IED) [1]. Fault diagnosis ought to be executed quickly and exactly so as to isolate the faulted components from the healthy part of the system and in order to take appropriate countermeasures to recover normal power supply. Until present, there are many methods, such as Artificial Neural Network (ANN)[2], Expert System (ES), Fuzzy Set Theory (FST)[3], Stochastic Optimization Techniques (SOT)[4], Genetic Algorithms (GAs)[5] and Logic Reasoning (LR)[6], etc., which have been applied to fault diagnosis of power system. Petri Nets (PNs), which have the characteristics of parallel information processing and concurrent operating role, is a very convenient and useful modeling tool. However fault diagnosis in power systems still stays unsolved owing to the high speed and accuracy required. The problem is much more difficult in cases of malfunctions of relays and circuit breakers, or multiple faults. In this paper, a method based on PNs models is proposed on the basis of previous work [7, 8]. The Petri Net (PN) model in [7, 8] regards as both high speed and back-up protections. Nevertheless it has to notice the fault diagnosis and relays’ behavior evaluation with the help of a template or conclude rules summarized based on the rule of thumb, which might not make the operators understand the results clearly and slow down the diagnosis speed as well. In addition, when there are false operations of relays or circuit breakers, the diagnosis results might be false. The proposed PN models can spot the fault components fast and exactly, and constitutes reliable and impressive diagnosis results automatically. It can be applied in the power system for not only simple fault, but also multiple faults or the violent faults are made up of the protective devices false operation. This system is good for the fault diagnosis of power system.


Introduction
The modern power system is vitally significant for daily life.It is a large scale dynamic system.Fault diagnosis in power systems targets at identifying the faulted components in power systems based on the information of the current status of protective relays and circuit breakers available from Supervisory Control and Data Acquisition (SCADA) systems.It is known that online automatic fault diagnosis is vital to the restorative control and as a result of tremendous significance in declining power supply interruption and enhancing service reliability, particularly for the large size power system with large numbers of Intelligent Electronic Devices (IED) [1].Fault diagnosis ought to be executed quickly and exactly so as to isolate the faulted components from the healthy part of the system and in order to take appropriate countermeasures to recover normal power supply.
Until present, there are many methods, such as Artificial Neural Network (ANN) [2], Expert System (ES), Fuzzy Set Theory (FST) [3], Stochastic Optimization Techniques (SOT) [4], Genetic Algorithms (GAs) [5] and Logic Reasoning (LR) [6], etc., which have been applied to fault diagnosis of power system.Petri Nets (PNs), which have the characteristics of parallel information processing and concurrent operating role, is a very convenient and useful modeling tool.However fault diagnosis in power systems still stays unsolved owing to the high speed and accuracy required.The problem is much more difficult in cases of malfunctions of relays and circuit breakers, or multiple faults.In this paper, a method based on PNs models is proposed on the basis of previous work [7,8].The Petri Net (PN) model in [7,8] regards as both high speed and back-up protections.Nevertheless it has to notice the fault diagnosis and relays' behavior evaluation with the help of a template or conclude rules summarized based on the rule of thumb, which might not make the operators understand the results clearly and slow down the diagnosis speed as well.
In addition, when there are false operations of relays or circuit breakers, the diagnosis results might be false.The proposed PN models can spot the fault components fast and exactly, and constitutes reliable and impressive diagnosis results automatically.It can be applied in the power system for not only simple fault, but also multiple faults or the violent faults are made up of the protective devices false operation.This system is good for the fault diagnosis of power system.

Petri net theory
So as to understand the importance of fault diagnosis models easily, the definition and structure of PN are introduced in this section shortly.PN theory was originally developed by the German mathematician Carl Adam Petri in 1960-1962 [7] and is based on the concept that the relationships between the components of a system, which shows asynchronous and concurrent activities, can be represented by a net.

Structure of the petri net
PNs are basically developed for describing and analyzing information flow and they are excellent tools for modeling asynchronous concurrent systems such as computer systems and manufacturing systems, as well as power protection systems.The main structure of a PN is made up of five elements, namely S = (P, T, N, a, ), where P and T are finite nonempty sets of places and transition respectively; N is the token set in the place, and a and  are the directed arcs between P and T [8].
A simple PN model is shown in Fig. 1.Where p 1 , p 2 , p 3 , p 4 are place nodes and t 1 , t 2 are transition nodes.The black point in place p 2 is the token.The structure of PN is static, and its dynamic properties are defined by transitions firing as well as transition of the tokens.The firing will move the tokens from the transitions' input places to its output places.

Matrix description of the petri net
Along with graphical methods, the structure of PNs and the procedure of firing its transitions can be also described and evaluated by matrix operations.The fundamental matrixes are made up of incidence matrix C, the marking vector M and the transition firing vector U.The incidence matrix is used to reveal the topology of a PN.The dimension of this vector is equal toPXTand is defined as [8] ( , ) ( , ) where PandTare the number of elements of P and T sets respectively.w (p,t) is the weight of arc from the place P to the transitions T, and F is the set of arcs.(p,t)F means that there is a relation between p and t.As a consequence, the incidence matrix of the PN as shown in Fig. 1 is given by The marking vector M (PX 1) is used to exhibit the token marking state of the places."1" in this vector indicates the number of tokens in the suitable place and "0" means that there are no tokens in the place.The initial state of marking is expressed by M 0 .For the Fig. 1 M 1 = M 0 + CxU. (3)

Petri net models of the protection scheme
In this section, we firstly present a transmission line model protection relaying scheme, then briefly describe the fault diagnosis model, finally the PN model of the protection scheme is developed.A simple power system is shown in Fig. 2. The PN models of fault diagnosis can be divided into two kinds according to the different coordination logic of the protective devices for a power transmission system.It namely bus model and transmission line model.The generator and transformer can be considered the line or bus elements.

Bus model
In Fig. 2 we take bus B 3 as A simple.The PN model of the bus is given in Fig. 3.In this model, the transitions T 1 , T 2 , T 3 and its input places CB 7 , CB 8 , CB 9 simulate the main protective devices of the bus (B 3 ).Their operating process, while the transitions T 1a , T 2a , T 3a and its input place CB 4 , CB 13 , CB 17 simulate the corresponding back-up protective devices.The place B 3 is used to show the state of the bus.The states K 1 , K 2 , K 3 are virtual nodes, which have no physical meanings.

Transmission line model
In Fig. 2 we take the transmission line L 5 as A simple.The PN model of the transmission line is given in Fig. 4. In this model, the transitions T 1 , T 2 and the place CB 6 , CB 11 simulate the main protective devices of the line (L 5 ).Their operating process, and CB 1 , CB 7 , T 1a , T 1b as well as CB 3 , T 2a simulate the back-up protective devices respectively.The transmission line is simulated by the place L 5 .The places K 1 , K 2 , K 3 as well as K 4 , K 5 are virtual nodes, which have no physical meanings.

Fault diagnosis in the transmission line model
The initial tokens are distributed to the places according to the received alarm signals.When the circuit breaker CB n operates, the place of the breaker CB n is filled with a token and when the initial token marking process has been finished, the transition node gratifying the firing condition will be fired.The firing condition of the transition T 1 and T 2 is described as follows.The main protection device of the transmission line L 5 operates, and a token presents in the input place of the transition.When the back-up protection device of the transmission line L 5 operates, the transition T 1a , T 1b and T 2a will be fired.A token presents in the input place of the transition.
If all the input places of the transition have tokens inside, the transition T 3 , T 4 and T 5 will be fired.After the transitions' firing the tokens will be redistributed in the PN and when there is no transition can be fired the net will achieve its steady state.As a consequence, the faulted components can be identified by the steady PN.If the place L 5 of the steady PN has a token inside, so this transmission line has a fault, otherwise the transmission line is healthy.
A simple power system given in Fig. 2 is still used to illustrate the working process of the suggested PN models.A fault is assumed to happen at line L 5 , and protective devices numbered 6, 11 have operated.Think that circuit breaker CB 11 failed to operate and the fault is cleared by the back-up protective relay at CB 3 and breaker CB 3 .Then, incidence matrix C L5 can be attained by the structure of the PN model L 5 (shown in Fig. 4) according to the formula (1) 5 0 0 0 0 0 0 0 1 Following the above-mentioned rules, the place CB 6 and CB 3 are assigned a token respectively.The initial state of PN model of the transmission line L 5 is given in Fig. 5. .As the transition nodes T 1 and T 2a have met the fire condition, these transitions are fired, which make the tokens transfer from the transitions' input place to output place.This is the first fire and it can be described by the state equation ( 3).M 01 = M 0 + C L5 x U 1.
The firing vector U 1 is given by;   .The PN model which has finished the first fire is given in Fig. 6.The steady PN is given in Fig. 8.The place node L 5 in the steady PN has a token inside.For other transmission lines in the simple power system, their steady PNs can also be attained by the similar modeling.The diagnostic process, from which we can know their place nodes corresponding to the lines have no tokens.So, the fault diagnosis results can be attained directly, that is, the line L 5 is fault and other lines have no faults.We no more go into other transmission lines details here.

Conclusions
In this paper a detailed PN model and a simplified PN model of protection scheme for a simple power system are presented.The marked PN model of the system is described in detail.A new approach based on PNs was suggested for modeling of the power system protection systems.This approach provides the possibility of hierarchically monitoring of power system.In this method, the model of protection systems performance has been formulated using PNs and by deductions of protection system data.The proposed system can be easily adapted to the changes in the electric power system.The proposed method uses information from relays and circuit breakers to evaluate the system condition and to make a diagnosis.Nevertheless in the case of broken breaker operating mechanism, or breaker contact failing to interrupt the fault current, it is possible that the breaker auxiliary switches may open and show the Scada that the breaker is open, but in fact the breaker fails to interrupt the fault, and back-up protection still operates.For this case, it is hard to be identified by the proposed PN models.The deduction procedure can be presented graphically in the form of PNs and implemented by matrix operations.This model is good for the fault diagnosis of power system.It shows that the fault diagnosis system based on the proposed models is practicable and effective.

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vector U (TX 1) exhibits that which transition or transitions among t 1 , t 2 , ....t m have been fired.The transitions firing vectors of the PN for Fig.1areThe dynamic behavior of the PN can be depicted by the following equation[8]

Fig. 4 .
Fig. 4. The fault diagnosis transmission model based on PNs

Fig. 6 .
Fig. 6.The first fire state of PN modelAfter the first fire finished, T4 is the exclusively one in all transitions which can be fired.The firing vector U 2 is given by;