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To improve the reliability of power grid fault diagnosis by enhancing the processing ability of uncertain information and adequately utilizing the alarm information about power grids, a fault diagnosis method using intuitionistic fuzzy Petri Nets based on time series matching is proposed in this paper. First, the alarm hypothesis sequence and the real alarm sequence are constructed using the alarm information and the general grid protection configuration model, and the similarity of the two sequences is used to calculate the timing confidence. Then, an intuitionistic fuzzy Petri Nets fault diagnosis model, with an excellent ability to process uncertain information from intuitionistic fuzzy sets, is constructed, and the initial place value of the model is corrected by the timing confidence. Finally, an application of the fault diagnosis model for the actual grid is established to analyze and verify the diagnostic results of the new method. The results for some test cases show that the new method can improve the accuracy and fault tolerance of fault diagnosis, and, furthermore, the abnormal state of the component can be inferred.

With the development of the power grid, an increasing number of new energy sources, such as solar energy, photovoltaics, and wind energy [

Wang L, Sun J [

The fuzzy Petri Nets fault diagnosis models, mentioned above, take into account the uncertainty of protection and circuit breaker trip information, as well as the calculation and fault tolerance of the model. However, the impact of uncertain and incomplete information [

Petri Nets are directed graph structures with timing constraints, and the temporal logic of the alert information is automatically considered when generating the Petri Nets model in an online application. However, the received alert information may have various conditions, such as rejection, misoperation, and timing disorder, which may reduce the accuracy of the diagnosis results. Against the background of the above research, the intuitionistic fuzzy Petri Nets fault diagnosis model, based on time series matching, is established to process time series information. The timing information is further mined using the method of timing matching, and the sequence difference and time difference at the time of the fault are calculated by the Edit Distance and the Dynamic Time Warping (DTW) Distance, respectively. At the same time, the description of information uncertainty is more precise by the intuitionistic fuzzy set considering the degree of membership and nonaffiliation of the information. This paper mainly does the following work.

(1) To study the timing properties of alert information, the time series confidence is calculated by analyzing the timing constraint relationship between the protection and the circuit breaker to verify and filter the alarm information and correct the confidence value of the initial position.

(2) To establish an intuitionistic fuzzy Petri Nets fault diagnosis model, the intuitionistic fuzzy algorithm is used to deal with the membership degree and nonmembership degree relationship of the alarm information, when the fault occurs, which can improve the model’s ability to deal with uncertain and incomplete alarm information.

(3) To establish a two-layer fault diagnosis model, after the fault occurs, the nonmembership value of the terminal position is modified according to the number of remote backup protection actions of the component, and the membership value is optimized by the hierarchical transition technique and the Gaussian function.

The reasoning process based on matrix operation is given.

The intuitionistic fuzzy set [

Assuming that

(1)

(2) The function pair

(3)

The time series model in the grid is defined on the basis of study [

(1)

(2)

(3) _{i} is indicated as an electrical equipment failure (Busbar, Line, Transformer) or circuit breaker and circuit breaker failure protection simultaneously trip, the time element

The application of time series information in grid fault diagnosis, in [

The Edit Distance is a measure used to calculate the distance between two strings of sequences, which can be expressed as the minimum number of edit operations required to convert a string into another string (editing operations include insert, delete, and replace).

For example, string sequences

In the formula, if

Editing Distance has been already a mature calculation method. However, due to the high uncertainty of information in the grid fault (the loss of, and erroneous, information, as well as timing chaos), it is difficult to make accurate judgments on sequences that are not synchronized. In this paper, the Editing Distance is combined with the Dynamic Time Warping Distance to form a time similarity matching calculation method to increase the processing ability of the asynchronous information. The specific discussion is as follows.

For time series

If

(1)

(2) _{s} for identifying information loss and timing disorder. Since_{s} is a time subsequence of the

(3) _{s};

The confidence calculation method for timing matching is defined in [

Intuitionistic Fuzzy Time Petri Nets (IFTPN) can be defined as a seven-tuple,

(1)

(2)

(3)

(4)

(5)

(6)

(7)

In this paper, the IFTPN grid fault diagnosis model is constructed by the time series similarity matching method, including the intuitionistic fuzzy Petri Nets theory and the time series characteristics of grid component faults. The model focuses on the timing properties of protection∖circuit breaker action, in grid faults, and adopts a layered transition model structure, which can be used to visually describe the logical relationship and timing characteristics of protection and circuit breakers.

According to the relay protection setting rules, the components in the power grid are equipped with corresponding primary protection and backup protection, and different protections are provided for different components. For example, the protection of the Busbar is composed of primary protection and remote backup protection. The protection of the line and the transformer provides corresponding primary protection, near backup protection, and far backup protection at the sending end and the receiving end.

The IFTPN model is built according to the above rules. When the grid fails, the protection and circuit breakers act in a sequence (main protection, main protection corresponding to the circuit breaker, near backup protection, near backup protection corresponding to the circuit breaker, far backup protection, and remote backup protection corresponding to the circuit breaker) to stop the action until the problem is resolved.

The time stamp of the first piece of alarm information received is used as a reference point. The alarm hypothesis time series is generated according to the component action delay: main protection (10 ms, 20 ms), near backup protection (485 ms, 545 ms), far backup protection (960 ms, 1070 ms), and circuit breaker trip delay (20 ms, 40 ms).

The components in the grid of this paper adopt the modeling method of hierarchical transition. For the Busbar, the first layer of the model is a submodel of the sending end and receiving end, including two layers of transitions, and the integrated model has one layer of transitions in the second layer. For the line, the first layer of the model includes two transitions in each direction, and the second layer of the model has one transition. When the topology changes, the architecture and operation matrix of the improved model are less adjusted, and the model is more versatile, because it does not need to make any modifications to the model but only update the values of the initial library in the first layer model.

The IFTPN fault diagnosis model for Busbars, transformers, and lines is established, according to the actual grid model, shown in Figure _{1} and double Busbar B_{2}, respectively, and Figure _{2}. The model structures of the transformer and line are the same; only the protection and circuit breaker components are different. This information is not included here.

Actual grid model.

To facilitate the description of the algorithm and simplify the reasoning process, the operator is defined as follows:

Suppose

(1) Direct multiplication operator

(2) Comparison operator

(3) Multiplication operator

(4) Addition operator

The reasoning process of the algorithm described in [

The deterministic value of the interlayer confidence is processed by the Gaussian function, which is applied to the matrix deduction process.

The application of this function can make the calculation results more in line with the characteristics of the fault diagnosis and make the probability of failure more of an ideal value within (0, 1). Assuming that Figure _{1} represents the line main protection, and place P_{2} is the protection corresponding to the circuit breaker, if the uploaded protection and circuit breaker action information satisfy the time constraint, the deterministic value of place P_{1} is set to 0.8564, and the deterministic value of place P_{2} is set to 0.8333. The accumulative determinant value of transition input is 0.8564×0.5+0.8333×0.5=0.8448. After processing using the Gaussian function, the certainty value of place P_{5} is

Basic structure diagram of IFTPN.

For a faulty component in the system, when the primary protection of the component and the corresponding circuit breaker are rejected, the backup protection of the component will act. The higher the number of protection and circuit breaker actions in the fault propagation direction, the greater the fault probability of the component, and the lower the uncertainty of the corresponding component actions. According to the above situation, the uncertainty value of the terminal place in the direction of the fault propagation is corrected by formula (

The uncertainty of the terminal place in the component failure propagation direction is set to

The algorithm for the entire confidence is described as

The improved algorithm includes the cumulative calculation of transition input values, threshold comparisons, and vector calculations for the terminal place. The specific confidence reasoning process is as follows.

(1) The initial state is set to

(2) The threshold of the transition is compared with the input intuitionistic fuzzy value of the transition, and then the transition set

(3) The input intuitionistic fuzzy value

(4) The discriminant value

(5) If

This paper uses the statistical probability data of long-term actual operation, provided by study [

Definition

The parameter

(1) The initial value of the initial component place and virtual place is (0, 1).

(2) The input arc weight is

(3) Learning from study [

The metric function of the probability of failure of the device is

According to the fault alarm information, received by the power dispatching center, the fault area of the system is searched, the suspected fault component set is obtained, and the IFTPN fault diagnosis model is established. The fault diagnosis process is shown in Figure

Fault diagnosis model frame structure.

The specific steps are as follows.

(1) After the grid fault occurs, according to the data information uploaded to the system, the fault area is first searched, then the suspected fault component is searched, and finally the suspicious fault component set is constructed.

(2) According to the principle of relay protection setting, a protection model is constructed for the protection device of the suspected faulty component to form a set of alarm hypothesis time series.

(3) The distance (Edit Distance and DTW Distance) between each time subsequence in the alarm hypothesis time series set and the alarm information sequence, received by the system center, are calculated by timing matching.

(4) The confidence level of the component protection action value is obtained by timing matching, and the state of the protection device that does not meet the time series matching is evaluated, including the action state of the protection and circuit breaker (rejection, misoperation, and information loss) and the time-scale accuracy of the alarm information (time-scale deviation and timing chaos).

(5) The IFTPN grid fault diagnosis model is established. The probability value of the initial library is corrected by the confidence of the protection and circuit breaker action. The inference algorithm is formed according to the intuitionistic fuzzy Petri Nets model, and the forward deduction is performed in the form of a matrix. Then, the fault probability value of the component is obtained.

In order to describe the entire reasoning process, the number of pieces of fault information is shown in Table

(1) Lines L_{2}, L_{5}, and Busbar B_{3} search for the fault area according to the alarm information sequence to determine possible faulty elements.

(2) Since the information cannot be uploaded when the line, Busbar, and circuit breaker are faulty, the corresponding time-scale information is defined as a fuzzy item. According to the general model of the protection configuration, the time series inference rules and the time series of the alarm information, a time series hypothesis set for the failed component, and the values of a and b are both 5. The fault set of Busbar B_{3} and lines L_{2}, L_{5} is shown in Table

(3) In the case of complex faults, the protection and circuit breaker only act in response to one faulty component. In this case, the fault set of line L_{2} covers the fault set of line L_{5} and Busbar B_{3}, and then the fault analysis of line L_{2} is prioritized. The initial place reliability of the circuit breakers of the line L_{5} protection configuration, of the protection of the Busbar B_{3}, and of the circuit breakers corresponding to the Busbar B_{3} protection is corrected to (0.19666, 0.03147), (0.17128, 0.0579), and (0.16666, 0.04825), respectively.

(4) Taking line L_{2} as an example, the time series confidence of the faulty component is calculated, as shown in Table _{12} is refused. The maximum six propagation directions for the fault of line L_{2} are (B_{3}, CB_{13}), (T_{3}, CB_{14}), (T_{4}, CB_{15}), (L_{5}, CB_{32}), (B_{2}, CB_{6}), and (L_{4}, CB_{27}).

According to the alarm information, four determined fault propagation directions are obtained and modeled separately. The intuitive fuzzy Petri Nets fault diagnosis model for line L_{2} is shown in Figure _{2} as an example in the direction of L_{5} propagation, matrix reasoning is performed on the fault confidence of line L_{2}.

Derived by algorithm,

When M_{3} = M_{2}, the inference calculation ends. The value of the fuzzy confidence of line L_{2} in the direction in which line L_{5} propagates is (0.7454, 0.008351); that is, the degree of certainty of line L_{2} in the direction in which line L_{5} propagates is 0.7454, and the degree of uncertainty is 0.008351. According to the metric function formula, the fault probability of line L_{2} is

A comparison curve, before and after data optimization, is shown in Figure

Data optimization comparison curve.

Single bus B_{1} fault diagnosis model.

Universal subnet diagnostic model

Comprehensive diagnostic model

Double bus B_{1} fault diagnosis model.

Subnet diagnostic model of B_{1}

B_{1} comprehensive diagnosis model

Line L_{2} fault comprehensive diagnosis model.

Line L_{2} receiving end single direction diagnostic model

Line L_{2} sending end single direction diagnostic model

Second layer diagnostic model

Figure _{2} is

In summary, the final failure probability value of line L_{2} is _{2} is the faulty item.

In order to describe the entire reasoning process, the number of pieces of fault information is shown in Table

(1) Searching for the fault area, based on the alarm information received after the fault occurs, the suspect faulty component is determined as line L_{8}, Busbar B_{7}, and line L_{6}.

(2) According to the general protection configuration model and the timing matching rule, the alarm hypothesis time series is generated for the protection of each suspicious component and the corresponding circuit breaker. The components related to line L_{8} are L_{8} sending end main protection, CB_{30} circuit breaker, and CB_{40} circuit breaker. The components related to Busbar B_{7} are B_{7} main protection, CB_{34} circuit breaker, CB_{35} circuit breaker, CB_{33} circuit breaker, L_{6} transmission end remote backup protection, and CB_{20} circuit breaker. The components related to line L_{6} are L_{6} sending end remote backup protection and CB_{20} circuit breaker. The hypothetical time series of the corresponding suspicious elements can be constructed according to the fault set in Table

(3) The distance between the hypothesis time and the actual alarm time series of all fault sets of line L_{6}, line L_{8}, and Busbar B_{7} are calculated and then converted into timing confidence, wherein the default value of parameters

(4) The time series confidence is calculated according to (_{8} transmitter is matched with the CB_{30} circuit breaker. The B_{7} main protection is matched with the CB_{34} circuit breaker, CB_{35} circuit breaker, and CB_{33} circuit breaker and is matched with the line L_{6} sending end backup protection and CB_{20} circuit breaker. The terminal primary protection information of line L_{8} is missing, because the CB_{40} circuit breaker trip does not satisfy the time-scale matching of the fault set of Busbar B_{7} but matches the time-scale of the line L_{8} receiving end main protection. Therefore, it is determined that the information of the primary protection of the receiving end of L_{8} is lost. The circuit breaker CB_{31} of the main protection of Busbar B_{7} refuses to operate, and the far-end backup operation of line L_{6} causes the CB_{20} circuit breaker to trip, which satisfies the timing matching of Busbar B_{7} in the line L_{6} fault propagation direction.

The circuit breaker CB_{29} has no relevant components to form a sequence with it, and the difference between the time stamps of other components is large, so CB_{29} is judged to be malfunctioning.

The CB_{40} circuit breaker exists in both the fault set of line L_{8} and the fault set of Busbar B_{7}. Since CB_{40} satisfies the protection action time sequence of line L_{8} and operates accurately, the CB_{40} circuit breaker should be within the fault set of line L_{8}. According to the fault sets of Busbar B_{7}, the CB_{35} circuit breaker should act on the fault of Busbar B_{7}, and the circuit breaker CB_{35} also does not satisfy the fault sets of other components. Thus, the error of the CB_{35} circuit breaker time mark in the Busbar B_{7} fault sets can be judged. Therefore, the weights of the time distances of the CB_{40} circuit breaker and the CB_{35} circuit breaker in the Busbar B_{7} fault sets should be corrected. In (

Line L_{6} does not satisfy the timing matching, and the failure probability can be directly considered as time series confidence P (L_{6}) =0.1.

(5) According to the IFTPN model inference algorithm, the confidence degree of the final line can be obtained. The fault of line L_{8} is P (L_{8}) =0.96723, and the probability of the failure of Busbar B_{7} is P (B_{7}) =0.9975.

The obtained data results are compared with study [

Comparison of the fault degree of the two methods in study [

Component | Transmission line L_{8} | Busbar B_{7} | Transmission line L_{6} |
---|---|---|---|

Weighted fuzzy Petri nets | 0.76745 | 0.82152 | 0.51649 |

| |||

Time-series weighted fuzzy Petri nets | 0.76745 | 0.79695 | 0.2 |

| |||

This article | 0.96723 | 0.9975 | 0.1 |

According to the reasoning process and the comparison in Table

The fault diagnosis results, obtained by the method presented in this paper, through line L_{0407} in study [

Comparison of the diagnostic results under the same conditions.

Number | Alarm information | Suspected Faulty device | Fault probability | |||
---|---|---|---|---|---|---|

The method of [ | The method of [ | The method of [ | The method of this paper | |||

1 | _{0407}; CB_{0704} act | L_{0407} | 0.99 | 0.8910 | 0.9968 | 0.9673 |

| ||||||

2 | _{0407}; CB_{0807}; CB_{0907} act | L_{0407} | 0.8798 | 0.8178 | 0.9601 | 0.9640 |

| ||||||

3 | _{0704} act | L_{0407} | 0.5705 | 0.7143 | 0.9506 | 0.9553 |

| ||||||

4 | _{0407}; CB_{0704}; act | L_{0407} | 0..6016 | 0.7125 | 0.9503 | 0.9550 |

| ||||||

5 | _{0807}; CB_{0907} act | L_{0407} | 0.5012 | 0.6411 | 0.9385 | 0.9412 |

| ||||||

6 | | L_{0407} | 0.4286 | 0.2688 | 0.1341 | 0 |

Comparison of the proposed method and three existing methods for grid fault diagnosis.

Method | Processing of timing information | Consider uncertainty | Modeling form | Performance |
---|---|---|---|---|

Study [ | Using time series matching method, making full use of time-scale information | No | Timing matching model | The calculation speed is fast but only considers the timing factor; too singular |

| ||||

Study [ | Timing not considered | No | Fuzzy Petri nets model | High diagnostic efficiency; good fault tolerance; did not consider the impact of timing |

| ||||

Study [ | Timing not considered | Yes | Intuitionistic Fuzzy Petri Nets Model | Full consideration of the impact of uncertain, incomplete information but does not take timing into account |

| ||||

The method of this paper | Using the time series matching method, making full use of time-scale information | Yes | Intuitionistic Fuzzy Petri Nets Model Based on Time Series Matching | Fully consider the timing information, and uncertain and incomplete information; better fault tolerance; precise fault diagnosis |

The code of alarm information.

Number | Fault type |
---|---|

a_{1} | L_{2} sending end main protection action |

| |

a_{2} | L_{2} receiving end main protection action |

| |

a_{3} | CB_{8} trip |

| |

a_{4} | CB_{12} trip |

| |

a_{5} | Failure protection B_{3} action |

| |

a_{6} | CB_{13} trip |

| |

a_{7} | T_{3} far backup protection action |

| |

a_{8} | T_{4} far backup protection action |

| |

a_{9} | L_{5} far backup protection action |

| |

a_{10} | CB_{15} trip |

| |

a_{11} | CB_{14} trip |

| |

a_{12} | CB_{32} trip |

Actual alarm information.

Time series set | Alert message content | Time series number |
---|---|---|

((a_{1}, 0,1), 435) | L_{2} sending end main protection action | _{1} |

| ||

((a_{2}, 0,1), 436) | L_{2} receiving end main protection action | _{2} |

| ||

((a_{3}, 0,1), 460) | CB_{8} trip | _{3} |

| ||

((a_{5}, 0,1), 740) | Failure protection B_{3} action | _{4} |

| ||

((a_{6}, 0,1), 766) | CB_{13} trip | _{5} |

| ||

((a_{7}, 0,1), 936) | T_{3} far backup protection action | _{6} |

| ||

((a_{8}, 0,1), 937) | T_{4} far backup protection action | _{7} |

| ||

((a_{9}, 0,1), 938) | L_{5} far backup protection action | _{8} |

| ||

((a_{10}, 0,1), 961) | CB_{15} trip | _{9} |

| ||

((a_{11}, 0,1), 963) | CB_{14} trip | _{10} |

| ||

((a_{12}, 0,1), 973) | CB_{32} trip | _{11} |

Failure collection.

Transmission line L_{2} | |

| |

Transmission line L_{5} | |

| |

Busbar B_{3} | |

The calculation of time series confidence.

Alarm hypothesis time series | ED | TD | TOD | TSC |
---|---|---|---|---|

| 0 | 0 | 0 | 1 |

| ||||

| 1 | 0 | 5 | 0.2 |

| ||||

| 0 | 0 | 0 | 1 |

| ||||

| 0 | 0 | 0 | 1 |

| ||||

_{4}, 10,0), 461), ((a_{5}, 10,1), 740), ((a_{8}, 10,1), 937), ((a_{10}, 0,1), | 0 | 0 | 0 | 1 |

| ||||

_{4}, 10,0), 461), ((a_{5}, 10,1), 691), ((a_{9}, 10,1), 938), ((a_{12}, 10,1), | 0 | 0 | 0 | 1 |

ED: Edit Distance; TD: DTW Distance; TOD: total distance;

TSC: time series confidence.

The code of alarm information.

Number | Fault type |
---|---|

a_{1} | L_{8} sending end main protection action |

| |

a_{2} | CB_{30} trip |

| |

a_{3} | CB_{40} trip |

| |

a_{4} | B_{7} main protection action |

| |

a_{5} | CB_{34} trip |

| |

a_{6} | CB_{35} trip |

| |

a_{7} | CB_{33} trip |

| |

a_{8} | L_{6} send end far backup action |

| |

a_{9} | CB_{20} trip |

| |

a_{10} | CB_{29} trip |

| |

a_{11} | L_{8} receiving end main protection |

| |

a_{12} | CB_{31} trip |

Actual alarm information.

Time series set | Alert message content | Time series number |
---|---|---|

((a_{1}, 0,1), 05: 315) | L_{8} sending end main protection action | _{1} |

| ||

((a_{2}, 0,1), 05:344) | CB_{30} trip | _{2} |

| ||

((a_{3}, 0,1), 05:345) | CB_{40} trip | _{3} |

| ||

((a_{4}, 0,1), 06:315) | B_{7} main protection action | _{4} |

| ||

((a_{5}, 0,1), 06:343) | CB_{34} trip | _{5} |

| ||

((a_{6}, 0,1), 05:327) | CB_{35} trip | _{6} |

| ||

((a_{7}, 0,1), 06:352) | CB_{33} trip | _{7} |

| ||

((a_{8}, 0,1), 06:824) | L_{6} send end far backup action | _{8} |

| ||

((a_{9}, 0,1), 06:846) | CB_{20} trip | _{9} |

| ||

((a_{10}, 0,1), 08:100) | CB_{29} trip | _{10} |

Failure collection.

Transmission line L_{8} | |

| |

Busbar B_{7} | _{4} |

| |

Transmission line L_{6} | |

The calculation of time series confidence.

Alarm hypothesis time series | ED | TD | TOD | TSC | |
---|---|---|---|---|---|

| L_{8} | 0 | 0 | 0 | 1 |

| 1 | 0 | 5 | 0.2 | |

| |||||

| B_{7} | 0 | 0 | 0 | 1 |

| 0 | 1 | 1 | 1 | |

| 0 | 0 | 0 | 1 | |

| 0 | 1 | 1 | 1 | |

| 1 | 0 | 5 | 0.2 | |

| 0 | 0 | 0 | 1 | |

| |||||

| L_{6} | 1 | 1 | 10 | 0.1 |

ED: Edit Distance; TD: DTW Distance; TOD: total distance;

TSC: time series confidence.

(1) For uncertain and incomplete information in power grids, we propose the IFTPN fault diagnosis model in this paper. The influence of the combination of the intuitionistic fuzzy algorithm and Petri Nets on the fault diagnosis results is explored. The results show that the model can still make a rapid and effective diagnosis of power system faults, when the information is incomplete.

(2) In order to make full use of the alarm information, we introduce the concept of timing matching into the intuitionistic fuzzy Petri Nets for grid fault diagnosis. The initial place data are corrected by timing confidence, and the case deduction shows that the diagnosis results are more accurate.

(3) In this paper, the degrees of certainty and uncertainty in the intuitionistic fuzzy algorithm are separately optimized in the calculation process. The optimization curve shows that the method improves the accuracy and reliability of fault diagnosis. In future work, we will research the electrical quantity itself and the effect of the time-constrained relationship between electrical quantity and component action on the diagnostic results.

(1) The IFTPN fault diagnosis model of the single Busbar A_{1} is shown in Figure _{1}, _{1}); (_{2}, _{2}); (_{3},

(2) IFTPN fault diagnosis model of double Busbar B_{1} is shown in Figure _{4}, _{4}); (_{5}, _{5}); (_{6}, _{12}); (_{6}, _{27}); (_{7}, _{11}); (_{9}, _{28}).

(3) The IFTPN fault diagnosis model of line L2 is shown in Figure _{8}, _{12},

See Tables

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest.

The Project was supported by the National Natural Science Foundation of China Program (no. 61503224), Shandong Natural Science Foundation of China (no. ZR2017MF048), Major Research Development Program of Shandong province of China (no. 2016GSF117009), and Qingdao Minsheng Science and Technology Plan Project (no. 17-3-3-88-Nash).