A method for identifying the operating state of deteriorated insulators based on partial discharge signal reconstruction algorithm and spatial electric field distribution law

In order to improve the accuracy of identifying the working status of degraded insulators and thereby contribute to preventive maintenance and repair, this proposes a method for identifying the operating status of deteriorated insulators based on a partial discharge signal reconstruction algorithm and spatial electric field distribution law. Firstly, the partial discharge signal of the deteriorated insulator is obtained through capacitive sensor technology and clustering analysis algorithm. Then, the mapping features between the partial discharge signal and the electric field distribution are extracted using the SN-EMD algorithm to determine the spatial electric field distribution on the surface of the insulator. Finally, a state recognition model is established based on the hidden Markov model to identify the operating status of deteriorated insulators. The experimental results show that the method designed in this paper has superior performance in terms of accuracy.


Introduction
The operation and maintenance department of the power company needs to conduct testing of porcelain insulators during the annual power outage maintenance period.Through testing, it was found that some insulators have low or zero value states, indicating that these deteriorated insulators may have potential operational hazards [1].These deteriorated insulators reduce the lightning protection, pollution prevention, and ice prevention capabilities of the line, which may lead to line failures and other events, posing a serious threat to the safe operation of the power grid.
At present, the performance of porcelain insulators cannot be determined by appearance and needs to be confirmed through live or power outage testing.However, traditional manual detection methods have some problems, such as high labor intensity, insufficient safety and efficiency, and susceptibility to environmental factors that can lead to false or missed detections [2].Currently, the commonly used methods for detecting insulator degradation at home and abroad mainly include the voltage distribution method and corona pulse current method for contact measurement, as well as the infrared imaging method, acoustic and ultrasonic method, and ultraviolet imaging method for non-contact measurement.However, these methods each have certain limitations and drawbacks.
In [3], a detection method based on autonomous vision is proposed, which uses a four-rotor aircraft to collect images of transmission towers and utilizes deep learning for insulator defect detection.To address the issue of insufficient training data, a medium-sized insulator dataset was created.The experimental results show that the proposed deep learning algorithm has efficient and accurate detection performance.In [4], scholars propose to measure the impact of pollution and other factors on the leakage current of porcelain insulators through experiments and extract time-frequency information of current characteristics.Besides, six indicators are proposed to evaluate the health status of insulators.By using naive Bayesian techniques for health classification and prediction, and establishing a confusion matrix to determine the appropriateness of each indicator, this method can effectively predict the flashover risk of porcelain insulators and ensure the stable operation of the power system.
However, the above methods may be affected by factors such as image quality, lighting conditions, aircraft positioning accuracy, or require direct contact with transmission towers and insulators, which may cause damage to equipment and may be affected by environmental conditions, thereby affecting the accuracy of detection results.
In order to solve these problems, this paper aims to study the changes and distribution patterns of the electric field of deteriorated insulators and to determine the deterioration status of insulators by analyzing the changes in the distribution of electric field strength around the insulators.This method can effectively detect deteriorated insulators without power outages, thereby reducing labor intensity and improving detection efficiency.It does not require direct contact with transmission towers and insulators, and will not cause damage to equipment.It can be applied to different types of insulators and degradation levels and has broad application prospects.

Partial discharge signal acquisition
Partial discharge (PD) is a specific discharge phenomenon generated by deteriorated insulators.By monitoring and analyzing partial discharge signals, the operational status information of deteriorated insulators can be obtained to assist in status recognition.Using capacitive sensors to obtain partial discharge signals of deteriorated insulators.Capacitive sensors can determine whether there is a partial discharge phenomenon by measuring the electric field distribution around the deteriorated insulator [5].
Capacitive sensors typically consist of two electrodes, one fixed to the surface of the insulator and the other connected to the ground potential.When partial discharge occurs on the surface of the insulator, the charge generated by partial discharge will change the capacitance value between capacitive sensors.By measuring the variation of this capacitance value, the partial discharge signal of the deteriorated insulator can be indirectly obtained.Capacitive sensors can adopt a parallel plate structure, which is composed of two metal parallel plates filled with insulating media between them.One plate serves as the detection electrode, fixed on the surface of the deteriorated insulator, and the other plate serves as the reference electrode, connected to the ground potential.The capacitance value of a capacitive sensor is related to the distance between its two electrodes and the dielectric constant of the medium.When partial discharge occurs on the surface of deteriorated insulators, the charges generated by partial discharge can cause changes in capacitance values.By measuring the variation of capacitance value, the partial discharge signal of deteriorated insulators can be indirectly obtained.The capacitance sensor transmits the measured capacitance value to the data acquisition center for processing and analysis through a signal connection line.The data acquisition center can use analogto-digital conversion (ADC) technology to convert analog signals into digital signals [6].
In order to achieve accurate identification of discharge signals, this paper uses a clustering analysis algorithm to identify the partial discharge signals of deteriorated insulators.Based on the analysis of the above digital signals, assuming that there are n characterization categories for the partial discharge signal, the data vector of the partial discharge signal is: where Y is the characterization vector of the partial discharge signal; where () TY is the clustering center of the partial discharge signal characterization vector; ij y is the jth clustering category of the i-th characterization data; ij s is the jth cluster center vector of the i-th representation vector.Based on the clustering center, the partial discharge signal is identified using the following calculation formula: where () VT is the membership function for initializing the classification based on the number of clusters; () XV is the result of partial discharge signal category recognition; k x is a random clustering function; i y is the i-th characterization category; i v is the voltage signal that is not penetrated in the deteriorated insulator.By utilizing the capacitance sensor technology and clustering analysis algorithm mentioned above, the partial discharge signals of deteriorated insulators can be effectively obtained.This method has non-contact, high accuracy, and low interference performance, and is suitable for monitoring and analyzing partial discharge phenomena on the surface of insulators.

Feature extraction of mapping between partial discharge signals and electric field distribution
The mapping features between partial discharge signals and electric field distribution are extracted with the SN-EMD (Sifting Natural Orthogonal Mode Function Empirical Mode Decomposition) algorithm to determine the electric field distribution on the surface of insulators [7].The specific steps for extracting mapped features are as follows: (1) Initialize the modal operation order m to 0 and the remaining signal component ( ) (2) Determine whether the remaining signal component ( ) m rt contains high-frequency electric field distribution mapping components; (3) When it contains high-frequency electric field distribution mapping components, we estimate the local envelope mean of signal component added for the i th time, as follows: where m  refers to the mapping range control coefficient.
We calculate the residual of the +1 m nd order partial discharge signal using the following formula:  , obtaining the residual partial discharge signal at this time [8].The specific formula is as follows: , It is necessary to jump to Step (2) and continue the calculation until the decomposition stops when the stop criteria are reached; (6) Save all the modal components of the electric field distribution mapping in the above steps to obtain the mapping features between the partial discharge signal and the electric field distribution.

Establishment of State Identification Model
A state recognition model is established based on the hidden Markov model, and the operating status of deteriorated insulators is identified by analyzing the mapped electric field distribution characteristics [9].The identification process is shown in Figure 1.The hidden Markov model calculates the probability of the occurrence of electric field distribution features in the insulator electric field distribution feature graph library to determine which type of operating state it belongs to [10].The probability calculation formula is as follows: The probability between the electric field distribution features and which electric field distribution feature library feature is the highest, and the electric field distribution feature belongs to which state of the insulator.Thus, the identification of the operating status of deteriorated insulators is completed.

Experimental Results and Analysis
Using XSY 2002 model insulators.
Partial discharge detection instruments are used to collect signals from insulators to obtain partial discharge signals.A simulated high-voltage transmission line environment is built on the MATLAB simulation platform, including live conductors, pillars, and deteriorated insulators.Under experimental conditions, we apply the corresponding electric field at the observation position based on the rated voltage of the insulator of 660 V.The experimental environment temperature is set at 25°C and consistent experimental conditions are maintained by controlling the humidity to 50%.Based on the method presented in this paper, the collected partial discharge signals are reconstructed to extract effective features, analyze the distribution of spatial electric fields around insulators, identify the operating status of deteriorated insulators, and provide results.
Using literature [3] and literature [4] as comparative methods, the accuracy of different methods in identifying the operating status of deteriorated insulators was verified.The results are shown in Table 1 1 shows that the method proposed in this paper can effectively achieve the output of identification results for the operating status of deteriorated insulators, with a high accuracy rate of 96.28% on average, while other methods have lower identification accuracy rates of 91.9% and 90.86% on average, respectively.This means that the method presented in this paper can provide more reliable results and provide effective support for maintenance and management work.
It further verifies the timeliness of the operational state recognition of the method proposed in this paper, and records the recognition time of different methods.The less time it takes, the stronger the timeliness of this method is.Otherwise, it indicates that the timeliness of the method is weaker.Based on the above five groups, the identification time was recorded, and the results are shown in Table 2 2, it can be seen that the running state recognition time of this method is within 0.65 seconds, while the recognition time of other methods is more than 1 second, far exceeding the time consumption of this method.This indicates that the method proposed has better performance in terms of timeliness.
Based on the above experimental results, it is shown that the degraded insulator operation status recognition method based on the partial discharge signal reconstruction algorithm and spatial electric field distribution law has more accurate and efficient performance in application.

Conclusion
The detection technology for deteriorated insulators based on the changes and distribution patterns of electric fields studied in this paper greatly improves the efficiency of channel operation and maintenance, reduces maintenance costs, and ultimately enhances the safety operation guarantee ability of the large power grid.Therefore, it has high social and economic benefits. where

 4 )
refers to the average partial discharge signal of( ) ( ) i rt  .And the +1m rd mode is calculated, with the specific formula as follows: When it does not contain high-frequency electric field distribution mapping components, the EMD algorithm is used to decompose and obtain the +1 m
of electric field distribution characteristics; o represents the observation sequence;  represents the HMM model; ( ) at i represents the forward probability of each hidden state at the initial time.

Table 1 .
: Accuracy of Operating State Identification by Different Methods/%.

Table 2 .
: Timeliness of Operating State Identification for Different Methods/s.