Location prediction model of zero value insulator based on PNN

Zero insulators directly reduce the electrical performance of insulator strings, affecting the safe and reliable operation of transmission lines. The grounding current of the insulator string contains the characteristic information of insulator electrical performance. Extracting the characteristic information of grounding current can realize the detection of zero value insulator, which is of great significance to ensure the safe operation of transmission lines. In this paper, the composite insulator used on ultra-high-voltage (UHV) lines is studied to analyze the influence of zero insulators on the electric field distribution. Furthermore, the corresponding characteristics of the zero insulators at different locations are extracted. The fitting relationship between the characteristic quantity and the zero insulator position is analyzed. The effective characteristics of grounding current are selected as training sample to establish the zero insulator position prediction model based on probabilistic neural network (PNN). The research result is meaningful for the detection of zero insulators.


Introduction
As an important component of ultra-high-voltage (UHV) overhead transmission lines, the electrical performance of insulators directly affects the safe and reliable operation of transmission lines [1][2][3]. Insulators crack in the long-term operation because of manufacturing, transportation, aging and deterioration. Due to the overvoltage, the electrical performance of the deteriorated insulators seriously declines and deteriorates into zero insulators [4,5]. The zero insulator, which assumes zero voltage, leads to a more non-uniform voltage distribution of the insulator string [6][7][8].
The electric field near the zero insulator is distorted, resulting in corona discharge and flashover. More seriously, it causes serious accidents such as insulator damage, series B Baina He hbn770425@163.com 1 breakage, grounding of transmission lines, and large-scale blackouts [9,10].
A huge number of line insulators are adopted on the lines. The occurrence of zero insulators is ascribed to the limited inspection range, resulting in the delay of discovery and replacement and eventually leading to serious power accidents [11][12][13]. The insulator grounding current comprehensively reflects the deterioration degree of the electrical performance. The effective characteristic of grounding current is analyzed and extracted by signal processing [14,15].
Probabilistic neural networks (PNNs) use linear learning algorithms to complete nonlinear learning algorithms. The high-precision characteristics of the nonlinear algorithm are maintaining meanwhile, which can meet the real-time processing requirements of the online monitoring system [16,17]. This model can be used to monitor insulators in real time and send out replacement information to inspectors in time when zero value insulators appear. Color models can be built based on the unique color characteristics of glass and ceramic insulators for integration into drone-based inspection systems. Therefore, according to the color judgment combined with the characteristics of the insulator, the fault area of the insulator can be identified [18]. However, the method of determining insulator characteristics based on color is not good in real time. Regional convolutional neural networks and feature pyramid networks can be used to localize insulators with complex background images. After filtering, an adaptive threshold algorithm is used for image segmentation and fault detection [19]. However, the accuracy of this scheme needs to be further improved.
To solve the above problems, the composite insulators used in UHV lines are studied, and the influence of zero insulators on electric field distribution is analyzed. A twodimensional simulation model was built in ANSYS to calculate the electric field, and the fitting relationship between the characteristic quantity and the position of zero insulator was analyzed by extracting the corresponding characteristics of zero insulator at different positions. The effective characteristics of ground current selected as the training samples, the classification mechanism and the corresponding structure and function of each level of the probabilistic neural network were analyzed, and the zero insulator position prediction model based on the probabilistic neural network was established. The feasibility and accuracy of the proposed fault diagnosis strategy were verified through the simulation based on MATALB.

Electric field simulation of insulator string
In this paper, the composite insulator for UHV transmission line is studied. A two-dimensional model is established in ANSYS to calculate the electric field. The boundary element type in the air domain is defined as the infinite boundary. Therefore, the bounded domain is transformed into open domain and the electric field distribution of insulators is solved. In ANSYS simulation, the insulator electric field calculation model consists of insulators, air, fiber reinforce plastic (FRP) rod and metal fittings. The relative dielectric constant and resistivity are shown in Table 1.

Introduced assumptions of the simulation model
Based on ANSYS, the finite element simulation software, the transmission line insulator is simulated and modeled. In the modeling process, the electric field calculation is carried out when the insulator string is clean and dry. Under the premise of ensuring the calculation accuracy, the working environment of the insulator is reasonably simplified. The final simplification in the modeling process includes the following aspects: (1) In the modeling process of insulator string, its own electric field distribution is little affected by tower and transmission line, and the electric field distribution is mainly related to its own capacitance. Therefore, this paper focuses on the modeling of insulator string body, that is, the tower and line model is ignored in the modeling process. (2) Ignore the influence of phases. The calculation result of electric field distribution of insulator string has little correlation with the loading type of three-phase or single-phase, so single-phase loading is used in this paper. (3) Calculate the dimension of the model. The load imposed by insulators under normal working conditions is threephase symmetrical load, and the structural characteristics of insulators are axisymmetric. Based on the above conditions, a two-dimensional calculation model can be established to reduce the memory required for calculation on the premise of ensuring the calculation accuracy.
This paper takes XWP-70 line insulators adopted in Huainan-Huxi UHV project as the research object. The actual insulation specifications are shown in Table 2, and the structural dimensions are shown in Fig. 1.

Setting of boundary conditions
When calculating the electric field of the insulator, the boundary conditions must be set. Among the many solutions of electromagnetic field problem, only one is the true solution, and the necessary condition for obtaining the true solution is to solve it under the given boundary conditions. The solution of the constant electromagnetic field is mainly carried out for the boundary value problem. There are three kinds of boundary conditions in the electromagnetic field analysis: Dirichlet boundary conditions (the first kind of boundary conditions), Neumann boundary conditions (the second kind of boundary conditions), and Loping boundary conditions (the third kind of boundary conditions). In this paper, the voltage value of the high-voltage side or low-voltage side of the line insulator string and the zero potential of the air  domain boundary belong to a class of homogeneous boundary conditions. The second type of boundary conditions in ANSYS electric field calculation is automatically satisfied, also known as automatic boundary conditions, without manual setting. The third type of boundary conditions is the linear combination of the first type of boundary conditions and the second type of boundary conditions.

The governing equation of the computational domain
The boundary of the air domain is set as the boundary attribute of infinity. After converting the open domain problem into a finite domain problem by using the finite element method, the electric field distribution calculation results of the insulator can be obtained based on the following calculation.
In the pending domain, where E is the strength of the electric field in the solution domain.
At the interface of different media: where D 1 and D 2 are the electrical displacements in the medium perpendicular to the dielectric interface on both sides of the interface, respectively.n is the normal vector perpendicular to the medium interface. Wire side potential satisfied: where V 1 is the potential value loaded in ANSYS. V 0 is the specific potential value at the wire side, Finite boundary potential satisfied: where V 2 is the finite boundary potential value.

Mesh division of insulator model
The density of the mesh in the field will affect the calculation efficiency. While improving the calculation accuracy as much as possible, the amount of calculation should also be considered [20]. Therefore, mesh division in different regions with different precision must be carried out according to the characteristics of the insulator structure. Mesh profile of insulator string is shown in Figs. 2 and 3.
In the process of mesh generation, the focus area of insulator body is refined to improve the precision of section. Considering the characteristics of insulator shape, in order to fit the triangular shape structure characteristics of twodimensional insulator on the edge of umbrella skirt and the junction of umbrella skirt and iron cap, triangular shape is used for insulator body mesh division. The accuracy of electric field simulation is ensured.

Electric field simulation of insulator
The length of the insulator string is far less than the AC wavelength under power frequency. The electric field is approximately stable at any time, so that the electrostatic field finite element method can be used to simulate and analyze the electric field distribution of insulators. The two-dimensional electrostatic field boundary can be expressed as Eq. (5).
where ϕ is the scalar potential function of the electrostatic field; ρ is the charge density; ε is dielectric constant of materials; U 0 is the known potentials on the boundary;n is unit normal vectors at interfaces of different materials; σ is charge surface density; G is pending field; Γ 1 is upper potential of insulator end fittings; Γ 2 is sectional boundary of twodimensional model; Γ in is interface boundaries of different materials; x, y are two-dimensional model coordinates.
By adopting interpolation in discretization, the variational problem is transformed into the extremum problem of multivariate function correlation. Therefore, Eq. (7) is obtained as: where K is theN order matrix after the boundary condition is applied; ϕ is the N order potential vector; P is the N order load column vectors.
The potential values on the nodes of the finite field are solved by Eq. (7). Based on the results, the electric field intensity of the insulator is shown in Eq. (8).
where E is the electric field intensity value. Figure 4 shows the electric field intensity distribution of UHV composite insulator string under the condition of good electrical performance, which means no zero insulators exist.
As shown in Fig. 4, the electric field distribution around the insulator string is non-uniform, which conforms to [21]. Because the electric field near the insulator wire and corona ring is relatively concentrated, the electric field intensity is as high as 380.48 V/mm. In comparison, the electric field value of insulator string in the middle is relatively low, about 11.544 V/mm. Moreover, the electric field intensity of insulators near the cross arm rises slightly, reflecting in Fig. 1 that the diagram slightly upwards at the rear. When the local electric field is too high, the electrical performance of the insulator tends to decrease, leading to local degradation.
Therefore, according to electric field distribution characteristics under normal working conditions, the 6th and 20th insulators starting from the high-voltage side are taken potentials to couple with freedom degrees. The zero insulators in the actual situation are analyzed to explore the influence of zero insulators on the overall electrical performance. The results are shown in Fig. 5. Figure 5 shows that when zero insulators exist in the insulator string, the electric field intensity of zero insulators decreases sharply while the electric field intensity of the insulator on both sides increases. It can be concluded that the farther away from the zero insulators, the smaller the influence.

Independence tests of the reference FEM-based model and mesh
In order to verify the accuracy of the finite element model, a simulation test is carried out on the influence of a single piece of deteriorated insulator on the whole potential of insulator string, and the corresponding numerical calculation is carried out. The path 10 mm away from the central axis of the insulator string is taken as the measuring line, and the potential value is mapped to obtain the potential distribution curve of the insulator string when deterioration occurred. The potential distribution is compared with that of the insulator string with good insulation performance, as shown in Fig. 5. According to Fig. 5, after the deterioration of the 2nd insulator on the wire side, the potential value of the 1st insulator rises from 847.72 kV under normal working condition to 897.72 kV, increasing by 5.89%. The potential of the 3rd, 4th and 5th insulators increased from 758.97 kV, 707.56 kV and 630.28 kV to 874.3 kV, 808.54 kV and 687.26 kV by 15.19%, 14.27% and 9.05%, respectively. The pressure difference borne by the 20th insulator was close to 0, but the potential value borne by the 19th insulator and the 21st insulator increased from 92.786 kV and 71.736 kV to 101.75 kV and 76.465 kV, which increased by 9.67% and 6.59%, respectively. After the deterioration of the 50th insulator on the grounding side, the potential value of the 49th insulator and the 51st insulator increased from 1.8022 kV and 1.288 kV to 8.523 kV and 6.54 kV, respectively, increasing by 372.92% and 407.76%. Therefore, when a single insulator deteriorates, its voltage drop is close to 0, its insulation performance is lost, and the potential value of adjacent insulators rises Fig. 6. On the basis of the potential distribution around the deteriorated insulator, the field distortion is calculated. Set the 2nd, 20th and 50th insulation deteriorate, and the field intensity distribution is shown in Fig. 7.
According to Fig. 7, after insulation deterioration occurs at different positions of insulator string, its own field strength is always close to 0 kV/mm due to electrostatic shielding. The color of the degraded part is deepened, indicating that the field strength decreases and the field strength of the insulator near it increases. Under normal circumstances, the equiele of insulators gradually sparse with the increase in the distance from the wire side, indicating that the electric field intensity decreases. However, when deterioration occurs, the distribution of allelic lines near the insulator is no longer evenly distributed, and the allelic lines are densely distributed around the deteriorated insulator. The spot strength value is  further close to the critical value, and the partial discharge is more likely to cause insulation aging and electrical performance decline. The field strength distribution of deteriorated insulators is obtained by taking the 10 mm path of the central axis of the central of the insulator string as the measuring line, and the field strength distribution is compared with the insulator string with normal insulation performance, as shown in Table 3. According to Table 3, compared with normal conditions, the electric field distribution will be distorted, and the closer the deteriorated insulator is to the high-voltage end, the more obvious the electric field distortion will be. Taking the conductor side of the insulator string as the starting point, after the deterioration of the 2nd insulator, the field strength of the 1st insulator increases from the normal 2.110 kV/mm to 2.410 kV/mm, increasing by 14.22%. After the deterioration of the 20th insulator in the middle section, the field strength of its adjacent insulator increases from 0.056 kV/mm to 0.069 kV/mm, an increase of 23.21%. At the end, the insulation deteriorates and the distortion rate of field intensity is close to 40%. According to the general criteria for the determination of deteriorated insulators, that is, if the distortion degree of the electric field value of the insulator surface caused by the deteriorated insulator is greater than 10%, the region can be identified as having deteriorated. Therefore, the established finite element model and mesh are reliable, and the judgment and prediction of zero value insulator are further carried out.
The zero insulators are analyzed at different positions from the conductor side. The corresponding grounding current waveforms are extracted, and part of the results is shown in Fig. 8. Figure 8 shows the grounding current waveform when the 6th and 20th are zero value insulators. Grounding current with zero insulators at different positions shows that the grounding current varies in sinusoidal and amplitude fluctuates in a certain range. Therefore, it is difficult to detect the zero insulators only by observing the change of the grounding current waveform. It is necessary to excavate the internal feature information and transform the subtle differences between the waveforms into physical features which can be easily distinguished.
The analysis of waveform signals includes time-domain analysis and frequency domain analysis. Time-domain signal parameters are the statistical information of grounding current waveform, including extreme value, standard deviation, kurtosis and others. Because the time-domain signal analysis has a distinctive advantage on real time, the time domain is used to optimize feature information and achieve the zero insulator position judgment. The four-dimensional characteristic indexes and the six dimensionless characteristic indexes are shown in Table 4.
The characteristic quantities in Table 4 are obtained according to the following Eqs. (9)-(10). In the time domain, the relationship between the ten characteristic indicators and the position of the degraded insulator can be obtained. Based on this characteristic quantity, the database is established to provide data support for the PNN-based fault diagnosis model.
where x(n) is leakage current waveform signal and Ns is the sampling number.
In the time domain, the relationship between the ten characteristic indicators and the position of the degraded insulator can be obtained. Based on this characteristic quantity, the database is established to provide data support for the PNNbased fault diagnosis model.

The establishment of PNN neural network training samples
Due to the correlation or redundancy between features, excessive feature inputs increase the burden of PNN, affecting the accuracy of the classification and weakening the robustness of the network. To obtain more accurate input data, the principal component analysis method can be used to reduce the dimensions of the parameters. Therefore, sensitive features A 1 -A 4 and B 1 are selected as the input of the neural network. According to [22], when the number main elements is 5, the selection contribution rate is close to 90%, successfully achieving dimensionality reduction. In order to verify that the characteristic value of the grounding current is closely related to the zero insulator position, the characteristic information obtained by MATLAB is used to establish an image model with the zero insulator position. The image model is shown in Fig. 9. As shown in Fig. 9, monotone function relationships are established between the average rectifier value, standard deviation and zero insulator position, respectively. The average value of the grounding current reflects the deterioration of the insulator electrical performance. The standard deviation reflects the deviation between the sampling value and the average value of the grounding current from another hand. The larger the standard deviation, the more the pulse content in the grounding current. The two quantities transform the physical location information of zero insulator into digital information, realizing the more accurate position detection of zero insulator. Therefore, the average current and standard deviation of insulator grounding current are used as input layer training samples to establish PNN.

Prediction model of zero value insulator location based on PNN
The probabilistic neural network is a branch of the radial basis function network [23]. It has the advantages of simple learning process, fast training speed, more accurate classification, and good fault tolerance [24]. In essence, it belongs to a supervised network classifier based on Bayes minimum risk criterion. Probabilistic neural networks generally have four levels: input layer, mode layer, summation layer and output layer. The input layer is responsible for introducing feature vectors into the network, and the number of input layers depends on sample features. The input is rectified average and standard deviation of root-mean-square insulator. These two characteristic quantities are correspondingly set to vector mode [X 1 , X 2 ]. The value of "Spread" affects the accuracy of classification and recognition of probabilistic neural network, so different values of Spread are used to explore the relationship between the Spread value and the decision accuracy of neural network, so as to determine the best value and achieve the best accuracy of network classification and recognition. A total of 36 groups are selected from the whole sample as training samples. Spread is the expansion coefficient of the radial basis function, and the default value is 1.0. A reasonable Spread value can make radial base neurons respond to all the intervals covered by the input vector. In the process of determining its value, the trial-and-error method is generally used. Therefore, the Spread value is set as 0.1, 0.3, 0.5, 0.7, 1.0 and 1.2, respectively. By observing the neural network to determine the fault region and the actual fault region, the best Spread value can be determined. PNN verifies that different Spread values have different impacts on fault diagnosis performance. When Spread value is 0.1, the fault location diagnosis results reach the best accuracy and can meet the requirements for fault location diagnosis of insulator string.
In addition, the fault location diagnosis of insulators is divided into two stages: the training stage and the diagnosis stage. The main steps are as follows: (1) In order to facilitate the solution of probabilistic neural network data and improve the solving speed of the network, before the establishment of probabilistic neural Fig. 9 The characteristic value of grounding current under different zero value insulator position network, it is necessary to adopt the normalized data processing method for training samples and test samples, so as to generate a complete training and test sample set. (2) Once the sample data have been determined by test or simulation, the sample number and dimension have been determined, and the Spread value is the only adjustable parameter in the probabilistic neural network. By setting the Spread value, the classification error of the probabilistic neural network can be minimized and the best fault classification and diagnosis performance of the network can be achieved. In this way, the highest accuracy of fault region determination can be improved.
(3) To achieve the best diagnostic effect of probabilistic neural network, that is, after determining the Spread value, input sample set data for fault location diagnosis. (4) The diagnostic results are obtained after autonomous calculation and classification by probabilistic neural network.
According to the effective feature information extracted in Sect. 3, a two-dimensional vector X = [X 1 , X 2 ] containing the rectified mean and standard deviation is constructed. Insulator strings contain 54 insulators, some of which are set as zero insulators to extract training samples. Thereinto, 36 sets of data are selected as training samples, as shown in Table 5. The other 18 sets of data are used as test samples, as shown in Table 6. The PNN toolbox in Matlab is used to predict the fault location.
First, the toolbox is used to build a probabilistic neural network and training samples. The only adjustable parameter "Spread" is set to 0.1, which minimizes the PNN classification error and achieves the best fault performance of the network. The PNN model for zero insulator location diagnosis contains 36 input samples, each of which has 2dimensional vector. The network is trained by samples to determine the connection weights and thresholds. After training, the process of nonlinear mapping is realized according to a set of symptoms. According to the given sample, the corresponding location can be detected.
As can be seen from Table 6, the accuracy of the predictive model based on probabilistic neural networks can reach 83.33%. Therefore, this method can be applied to the diagnosis of zero value insulator location.
With the development of transmission equipment and artificial intelligence equipment, substations and operation centers have achieved a high degree of intelligence. Therefore, the proposed scheme has extremely high feasibility in engineering applications. Firstly, the required leakage current information of the insulator string is obtained from the substation. Secondly, the principal component analysis method is used to transform the data from the high-dimensional space into a low-dimensional space, extracting the principal component feature quantity. Finally, the fault location is detected by the built-in PNN algorithm of the computer equipment. The proposed scheme is suitable for substations and can assist maintenance personnel in fault locations.
At present, there have been researches on the accurate and fast positioning and status recognition of insulator strings in aerial images of UHV transmission lines. In Ref. [25], an insulator string diagnosis method based on improved YOLOv3 is proposed. Based on the independent establishment of aerial photography insulator string database, the method requires 5000 times of training on the model in the data set of 4000 samples, and the loss curve is always in a state of large oscillation. Due to the influence of time, weather, angle and other factors in the shooting process, the UAV aerial photography image is prone to uneven illumination, fuzzy and other problems, which may affect the practical application of this method. In this paper, the average value of the ground current in order to avoid the problem of sample imbalance and improve the training effect and test accuracy, and standard deviation converts the physical position information of zero insulator into digital information and realizes more accurate position detection of zero insulator. The accuracy of prediction model based on probabilistic neural network can reach 83.33%. Therefore, the proposed method can be better used to diagnose the position of zero value insulators.

Conclusion
The time-domain characteristics of insulator strings grounding current with different zero insulator positions are studied. On this basis, a prediction model of zero insulator position based on probabilistic neural network is established.
(1) When zero insulators appear in composite insulator strings, the closer the distribution of electric potential and electric field around the insulator string is to the high-voltage end, the greater the distortion of electric field and electric potential caused by zero insulator. Because the voltage across zero insulators is almost zero, partial discharge is more likely to occur in the parts adjacent to zero insulators. The phenomenon affects the electrical performance of insulators and shortens the normal service life of insulators. (2) The average value of rectifier, standard deviation and zero insulator position in the grounding current waveform of UHV composite insulator string are monotonic functions, which can be used as effective characteristic quantities to characterize the zero insulator position.