# Automatic Calculation and Simulation of Time-Varying Failure Rate of Digital Relay Protection Device

Authors: Yuyan Yang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Efficiency is an important indicator of risk assessment, but the failure rate changes with time, which makes risk assessment very difficult. Traditional methods often only measure the steady-state and static indicators of relay protection. The traditional method often only measures the steady-state and static indicators of the relay protection, or directly uses the RiskWeibull analysis system to perform reliability analysis on the relevant data. However, this method can only perform quantitative static analysis on the data. Once the system is disturbed, its reliability will be affected. Analysis is not possible. Since the relay protection device has the possibility of malfunction and refusal at the same time, in order to distinguish, the risk is introduced into the reliability evaluation of the relay protection device to achieve the purpose of considering the possibility and consequences of its failure at the same time. Based on the traditional method, this paper proposes a method to calculate the time-varying failure rate of the relay protection device by using the support vector machine model, which improves the influence of hidden risks on the power grid relay protection, and not only realizes the scientific hidden danger evaluation, risk rating. It is of great significance for the development of power grids to evaluate the consequences of failures and to make the transmission lines operate safely and stably.


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## Body

## 1. Introduction

Relay protection is the first line of defense to ensure the safe operation of the power grid, and its reliable operation is of great significance. With the rapid development of power grid technology, the structure and technology of the secondary system of substations are constantly innovating. The digitization and networking of intelligent substations have greatly changed the working mode of relay protection equipment, making some state quantities of relay protection equipment. It becomes an observable indicator, creating the possibility for the development of practical status assessment work. In this paper, the LS-SVM algorithm is introduced, and the collected basic data is verified by LS-SVM. Since some power operation data do not have the conditions for real-time collection, historical data must be used for prediction, and historical data implies time parameters, the algorithm is suitable for small-sample regression, and can improve the fitting accuracy when the sample data are too small. Using the LS-SVM algorithm to fit the parameters of the Weibull distribution solves the disadvantage that the basic data samples are few, and obtains better results. Good results, so this paper uses the time series-based LS-SVM algorithm to process this type of data.


## 2. Related Work

Abad applied the Markov method to analyze the reliability of relay protection, but the model established in this document did not consider the influence of device self-test on reliability [1]. Rabbi also considered the influence of the self-check, refusal, and malfunction of the secondary equipment on the system, so as to re-divide the system state and establish the state space model of the system [2]. On the basis of the above research, Ke et al. discussed and proposed the method of determining the optimal maintenance period of the relay protection device [3]. Geng and Gao studied the recessive faults of relay protection devices and also proposed the idea of using computers to monitor and control recessive faults [4]. Yang et al. several possible reasons for the recessive failure of relay protection devices and proposed a calculation method about the impact of recessive failures of relay protection devices [5]. Masami proposed to use graphs to describe DSAS and its functions and use discrete Markov chain correlation theory to calculate the TMTTF of a function or the entire system. Because of its extremely complex calculation, power systems are usually assumed to be repairable systems, but it is assumed that the system is an unrepairable system in order to simplify the calculation. Domestic scholars have also successively carried out research based on reliability theory. Common secondary equipment calculation methods include Markov method, probability method, and fault tree method. The Markov method is widely used in repairable systems, and most of the secondary equipment of the power system is a repairable system, so most researches are based on the Markov method to carry out the calculation of the secondary equipment of the power system [6]. Guo et al. applied the probability method to establish a probabilistic model of the protection system and discussed the influence of the protection system on the reliability of the combined power generation and transmission system [7]. Zeng et al. applied the fault tree analysis method to establish the failure model of the substation communication system and then realized the reliability analysis of the substation communication system [8]. Senol uses Markov method to realize the reliability analysis of relay protection. Redhu and Hedge [9] used the operating status information, self-checking information, and hidden fault information as the original data, and used the fuzzy comprehensive evaluation method and Markov prediction method to calculate the status of the secondary equipment for the self-checking information and operating status information, respectively. For hidden information, the state calculation is realized by hidden fault judgment, and finally, the DS evidence theory is used to fuse the three evaluation results at the decision level, resulting in poor feasibility of existing calculation methods, low reliability of calculation results, and failure to carry out condition maintenance work [10].Although the new generation of intelligent substation has realized the online monitoring function of secondary equipment, it is still in the preliminary stage of exploration. Although some progress has been made in related research, there are still many deficiencies, and it has not yet reached the practical level.In this paper, through in-depth analysis of the defects and deficiencies of the existing research on the state calculation of relay protection equipment, combined with the support vector machine model, the network structure of the secondary system of the substation and the structure of the secondary circuit of the relay protection at different development stages are compared and analyzed, and the existing state calculation method is improved., to solve its shortcomings such as not distinguishing the deterioration trend.


## 3. Reliability Evaluation of Relay Protection Devices

### 3.1. Reliability Evaluation Method of Relay Protection Device

The algorithm of relay protection device can be divided into analytical method, simulation method, and artificial intelligence algorithm [11].The analytical method is relatively simple in principle, and the calculation steps are clear, but with the increase of components, the calculation process is more complicated, and there are many formulas, which make the calculation amount cumbersome. Usually, the matrix needs to be processed in combination with other methods, and the calculation formula is simplified to improve the calculation efficiency. However, this method is not often used in more complex systems and is only suitable for general simple power distribution systems. If there is a nonminimum path, it needs to be converted into the minimum path, and finally analyzed according to the minimum path analysis method; in the case of a large number of system line loops and an increase in line branches, this method can speed up the calculation progress and improve the efficiency; the minimum path cannot be directly found in complex systems, and the fault analysis results are not accurate enough when considering the influence of backup power sources.The simulation method is divided into sequential simulation algorithm and nonsequential simulation algorithm [12]. These two methods can accurately simulate the working time of different states of the system and the transition probability between states by obtaining the timing information of the runtime state. When the influence of external environmental factors is large, this method can be used to establish a probability model for the system. This probability model is more in line with the actual environment. It requires a large amount of memory, and the convergence speed is also insufficient. Although the nonsequential simulation algorithm has been improved, its model establishment is relatively simple, the memory required for the operation is small, and the relative sequential convergence speed is relatively fast, but it still cannot meet the requirements in practical application [13, 14].When the artificial neural network evaluates the reliability of the system, it first uses the historical data to exercise the neural network and adopts the error back propagation algorithm. It has fast operation speed and high precision, which can meet the complex distribution network and actual operation conditions, but it has relatively high-design requirements for the algorithm itself, and how to correctly select nodes in the hidden layer is a big difficulty, which requires repeated research [15].


### 3.2. Reliability Evaluation of Relay Protection Devices

Relay protection reliability refers to the accumulative probability of correct action of the device under certain time and conditions. Usually, the protection reliability action rate is the main factor, and at the same time, the abnormal action probability is comprehensively investigated, and the normal action characteristics of normal yueren are analyzed to characterize the protection reliability, which is an important indicator in the operation reliability evaluation. In addition, considering that the abnormal state of the relay protection system can be divided into the fault state and the maintenance state, when establishing the relay protection model, different ways can be used to express the reliability. At present, in view of the accelerated marketization process of the power industry, the reliability of relay protection can also be considered from the perspective of value (Figure1).Figure 1
Flow chart of the reliability evaluation system of relay protection.The research on the reliability of relay protection is based on the parameter estimation and probability calculation based on the mathematical model, and the system state and reliability are evaluated through the mathematical model. However, in actual operation, accident consequences and losses are important objective basis for measuring whether the system is safe and reliable. Therefore, evaluating the system quality by probability is too simple and unrealistic and cannot accurately express its reliability. Therefore, considering the risk of relay protection at the same time, taking into account the probability of equipment failure and its consequences, the quality of the relay protection system can be more accurately and comprehensively expressed [16].As the first line of defense of the power grid, the safety and reliability of the relay protection device have always been the top priority in production, and the secondary reliability is an important guarantee to avoid accidents or other impacts, and its importance is evident. Failure rate is an important indicator of risk assessment, but the failure rate will change with time, making risk assessment very difficult. Traditional methods can only perform quantitative static analysis of data. Once the system is disturbed, its reliability analysis will be difficult and cannot be done. Relay protection devices rarely have abnormal actions under normal operating conditions, but if they occur, they will cause serious faults or even accidents. Therefore, the risk can be judged from the operating state, thereby considering the reliability of the equipment. The Institute of Electrical and Electronics Engineers defines risk as a measure of the probability and consequences of an undesired event. Its definition form is generally expressed as the product of consequence and probability, namely,(1)Risk=Pr×I,where Pr is the probability of an accident and I is the consequence.In practice, in view of the difficulty of statistics, the loss of power transmission due to protection failure is often used to represent the consequences of relay protection failure. Based on this, the risk of relay protection can be expressed as follows:(2)Risk=∑Pri×P×Ti,where i is the failure category, Pri is the probability of occurrence of the ith failure, electrical power, Pi is the transmission power lost by the ith failure, and Ti is the expected repair time of the ith failure.


## 3.1. Reliability Evaluation Method of Relay Protection Device

The algorithm of relay protection device can be divided into analytical method, simulation method, and artificial intelligence algorithm [11].The analytical method is relatively simple in principle, and the calculation steps are clear, but with the increase of components, the calculation process is more complicated, and there are many formulas, which make the calculation amount cumbersome. Usually, the matrix needs to be processed in combination with other methods, and the calculation formula is simplified to improve the calculation efficiency. However, this method is not often used in more complex systems and is only suitable for general simple power distribution systems. If there is a nonminimum path, it needs to be converted into the minimum path, and finally analyzed according to the minimum path analysis method; in the case of a large number of system line loops and an increase in line branches, this method can speed up the calculation progress and improve the efficiency; the minimum path cannot be directly found in complex systems, and the fault analysis results are not accurate enough when considering the influence of backup power sources.The simulation method is divided into sequential simulation algorithm and nonsequential simulation algorithm [12]. These two methods can accurately simulate the working time of different states of the system and the transition probability between states by obtaining the timing information of the runtime state. When the influence of external environmental factors is large, this method can be used to establish a probability model for the system. This probability model is more in line with the actual environment. It requires a large amount of memory, and the convergence speed is also insufficient. Although the nonsequential simulation algorithm has been improved, its model establishment is relatively simple, the memory required for the operation is small, and the relative sequential convergence speed is relatively fast, but it still cannot meet the requirements in practical application [13, 14].When the artificial neural network evaluates the reliability of the system, it first uses the historical data to exercise the neural network and adopts the error back propagation algorithm. It has fast operation speed and high precision, which can meet the complex distribution network and actual operation conditions, but it has relatively high-design requirements for the algorithm itself, and how to correctly select nodes in the hidden layer is a big difficulty, which requires repeated research [15].


## 3.2. Reliability Evaluation of Relay Protection Devices

Relay protection reliability refers to the accumulative probability of correct action of the device under certain time and conditions. Usually, the protection reliability action rate is the main factor, and at the same time, the abnormal action probability is comprehensively investigated, and the normal action characteristics of normal yueren are analyzed to characterize the protection reliability, which is an important indicator in the operation reliability evaluation. In addition, considering that the abnormal state of the relay protection system can be divided into the fault state and the maintenance state, when establishing the relay protection model, different ways can be used to express the reliability. At present, in view of the accelerated marketization process of the power industry, the reliability of relay protection can also be considered from the perspective of value (Figure1).Figure 1
Flow chart of the reliability evaluation system of relay protection.The research on the reliability of relay protection is based on the parameter estimation and probability calculation based on the mathematical model, and the system state and reliability are evaluated through the mathematical model. However, in actual operation, accident consequences and losses are important objective basis for measuring whether the system is safe and reliable. Therefore, evaluating the system quality by probability is too simple and unrealistic and cannot accurately express its reliability. Therefore, considering the risk of relay protection at the same time, taking into account the probability of equipment failure and its consequences, the quality of the relay protection system can be more accurately and comprehensively expressed [16].As the first line of defense of the power grid, the safety and reliability of the relay protection device have always been the top priority in production, and the secondary reliability is an important guarantee to avoid accidents or other impacts, and its importance is evident. Failure rate is an important indicator of risk assessment, but the failure rate will change with time, making risk assessment very difficult. Traditional methods can only perform quantitative static analysis of data. Once the system is disturbed, its reliability analysis will be difficult and cannot be done. Relay protection devices rarely have abnormal actions under normal operating conditions, but if they occur, they will cause serious faults or even accidents. Therefore, the risk can be judged from the operating state, thereby considering the reliability of the equipment. The Institute of Electrical and Electronics Engineers defines risk as a measure of the probability and consequences of an undesired event. Its definition form is generally expressed as the product of consequence and probability, namely,(1)Risk=Pr×I,where Pr is the probability of an accident and I is the consequence.In practice, in view of the difficulty of statistics, the loss of power transmission due to protection failure is often used to represent the consequences of relay protection failure. Based on this, the risk of relay protection can be expressed as follows:(2)Risk=∑Pri×P×Ti,where i is the failure category, Pri is the probability of occurrence of the ith failure, electrical power, Pi is the transmission power lost by the ith failure, and Ti is the expected repair time of the ith failure.


## 4. Calculation of Failure Rate of Relay Protection Device

### 4.1. Brief Introduction to the Principle of Failure Rate of Relay Protection

Failure refers to the loss of the original function of the equipment. The index of failure is usually expressed by the failure rate function, also known as the failure rate, which is denoted asφ(t) to describe the probability of the protection device not failing within the time t of failure per unit time. If X is used to represent the fault-free running time of the device, and Pr is used to represent the probability of occurrence of an event, then the failure rate function is (3)ϕt=limΔt⟶0PrX<t+Δt|X>tΔt.Failure rate is similar to failure frequency and is used to reflect equipment reliability. According to the relevant definition, the reliabilityR(t) is often used to represent the probability that the equipment does not have abnormal conditions at time t, which is related to the failure rate satisfying (4)Rt=e−∫0tϕtdt.Iff(t) and F(t) are used to describe the probability density and distribution function of equipment uptime Z, respectively, the failure rate is (5)ϕt=ftRt=ft1−Ft.


### 4.2. Failure Rate Curve and Estimation Process of Relay Protection Device

The failure rate function is widely used in reliability calculation and risk assessment, which lays a foundation for the hidden danger risk assessment work. From the failure rate formula, it can be seen that the failure rate is related to the timet, so the failure rate of the relay protection device is a graph that follows the time-varying law. Most of the reliability models are determined by the time-varying failure probability. In reality, there are many uncertain factors, resulting in a basin-shaped function graph, as shown in Figure 2.Figure 2
Time-varying curve of failure rate.Generally speaking, failures are divided into accidental failures and aging failures. Among them, the failure caused by accident is called accidental failure, and the failure caused by component aging is called aging failure. Therefore, the failure rate must be calculated from these two aspects. Supposeδ0 is the accidental failure rate, λ1(t) is the aging failure rate, and λ(t) is the total failure rate. The estimation process is shown in Figure 3.Figure 3
Flowchart of total failure rate estimation.The traditional two-parameter Weibull distribution aging phenomenon runs through the entire operation of the equipment, which is inconsistent with reality. The three-parameter Weibull distribution does not appear aging before the critical point, and then begins to appear aging, which perfectly fits the failure rate curve in reality. Therefore, the three-parameter Weibull distribution is used to fit the failure rate.When the three-parameter Weibull distribution is satisfied, the failure distribution and failure rate functions are (6) and (7), respectively: (6)Ft=1−e−t−γηβ,(7)λt=βηt−γηβ−1.Among them,ß and η are called shape and scale parameters; ℇ is called position parameter, and ℇ ≥ 0 is satisfied.The three-parameter Weibull distribution function is used to fit the aging failure characteristics, and the shape, scale, and position parameters are calculated by the least square method to realize the fitting of the aging failure rate, and then the total failure rate is obtained according to the result of the accidental failure rate., paving the way for further research on the risk assessment system.


### 4.3. Research on Algorithm of Relay Protection Device

When processing the basic data, the LS-SVM algorithm is used to preprocess some data, and when the Weibull distribution parameters are fitted, the LS-SVM algorithm is used to estimate the parameters. In this paper, the empirical risk is generally used to replace the expected risk R(f), and the specific formula is as follows:(8)Rf=∑i=1lcxi,yi,fi.Equation (9) is used to estimate the function(9)y=fx=w⋅ϕx+b.Take a very low value for the optimization objective:(10)minQ=12w2+C∑i=1Nξi·+ξi,where C is the penalty factor, ξ is the relaxation factor and ε is the loss function; a loss function with good ε is introduced, which can be defined as follows: (11)Lεy=0fx−y<εfx−y−εfx−y≥ε.For nonlinear cases, a kernel function is often introduced to represent the regression function(12)fx=∑i=1nai−ai∗kxi,yi+b.The essence of the support vector machine regression problem is to findf(x) according to the training of the data. Its expected output and yi in the training data only account for at most, and the function f(x) is as flat as possible, that is to say, don’t care. Errors less than ε but no errors greater than ε are allowed. Therefore, support vector machine regression is widely used in error correction and output control. According to the LS-SVM theory, the regression least squares support vector machine can finally be reduced to the problem of constrained optimization, and the vector mechanism model supported by the regression least squares method is (13)y=∑i=1NaiKx,xi+b.


### 4.4. Establishment of a Failure Rate Calculation Model for Relay Protection Devices Based on LS-SVM Model

In the previous study, the least squares method was used to estimate the Weibull parameters, and the effect was good, but this was based on a large amount of basic data [17]. In the face of the difficulty in collecting basic data of the relay protection system and the lack of effective data, the Weibull in the estimation of the three parameters, the fitting sample data is too small, and there is a problem of low-fitting accuracy. To solve this problem, the LS-SVM algorithm is introduced into the project to improve fitting accuracy. The basic data of the relay protection system are collected at a certain time, and the data itself contain time information. However, LS-SVM itself has this function, but the time factor must be implied into the data samples. Therefore, before LS-SVM fitting, the data samples must be reconstructed so that the time information can be included in the training samples. LS-SVM needs to construct input and output samples during implementation.When solving the parameters of Weibull distribution in this study, the collected basic data are used as the data input book, the three parametersβ, η, and λ of the Weibull distribution are used as the output samples, the failure rate error is used as the objective function, and the cross-validation method is used to solve the problem. The regularity in the LS-SVM algorithm is the factor and radial basis parameters, and finally the actual values of the three parameters are obtained. Run the test with actual data, and its running data is shown in Figure 4.Figure 4
Weibull distribution parameter map.It can be seen from Figure4 that although there are certain differences in the three parameters of different devices, the aging node parameter and the aging time parameter are always in a state higher than the aging rate parameter. This plays a key role in subsequent analysis by determining the failure rate model.Its failure rate curve is shown in Figure5.Figure 5
Failure rate curve.Figure5 can clearly reflect the general trend of the failure rate, and the failure rate increases significantly with the increase of η, thus laying a foundation for the determination of the maintenance cycle.Since most of the substations currently operating are not new-generation smart substations and do not have the conditions to send the internal temperature of the relay protection device to the outside, it is impossible to obtain accurate temperatures in different periods. In this study, according to the operating characteristics of each module, 10 modules were selected that were put into operation for 1 to 3 years, 4 to 6 years, and 6 to 8 years, respectively, and their internal temperatures were measured with infrared thermometers (The room temperature of the protection chamber is 20∼25°C). The unknown parameters A andß in (7) are estimated by using the operating years t and the corresponding temperature T (in practical applications, the measured temperature of the new generation of smart substations is entered after processing) and the failure rate λ. Among them, the failure activation energy E of the power module, CPU module and optical module is taken as 0.65 eV, 1.2 eV, and 0.5 eV, respectively. The temperature change curve parameters of each module are shown in Figures 6 and 7 and Table 1.Figure 6
Temperature change curve of each module.Figure 7
Trend chart of time-varying aging failure rate of each module.Table 1
Model parameters of aging failure rate of each module.
Module nameParameterAβPower supply0.1032852.983486CPU0.0682424.225761Optical module0.1771483.867354The relationship between the relay protection device and the main internal functional modules constitutes a series system relationship. The failure of any functional module will lead to the failure of the entire device, and the failure rate of each module is composed of accidental failure rate and aging failure rate. It can be seen that the failure rate of devices with lower operating temperatures is relatively low, and after entering the aging period, the difference in failure rates of relay protection devices operating at different temperatures will become larger and larger, so the operating temperature also affects important factor in failure rate.For static indicators such as defects and running time, refer to the processing method of one-way change indicators. The specific threshold value is determined according to relevant specifications, operation, and maintenance experience. For example, the upper limit of the running time of switching power supply is 5 years. The condition and maintenance reference period of the relay protection device is 5 years, so the failure rate of the protection device in this area after 4 years of operation can be selected as a good range reference value, and the actual engineering experience shows that most of the relay protection devices can reach 10 to 12 years, so the failure rate of the protection device in this area after 10 years of operation can be taken as the threshold value [18].The advantage of the method based on LS-SVM model is that it is a simple model when used in complex systems, it considers the relaxation of time constraints and maintenance of time constraints, the distribution of parameters in the system is relatively simple, and the range of output duration is considered in the required variation range. Therefore, this method has high applicability for those systems that are difficult to model and cannot be modeled.


### 4.5. Simulation Analysis of Circuit Calculation of Relay Protection Device Based on LS-SVM Model

In order to achieve a more accurate simulation effect, a suitable, accurate, and flexible power system model must be built. Choose MATLAB as the simulation tool. First, a 200 km long 220 kV transmission line model is established in LS-SVM according to the distribution parameters.In this paper, based on LS-SVM, a simulation model of the current differential protection of transmission lines is established. The current differential protection criterion of the line is written by the S function in LS-SVM, which is a computer language description of a dynamic system. A specific calling syntax allows the function to interact with the LS-SVM solver, which can implement the line differential protection action criterion [19]. The data processing module adopts Fast Fourier Transform (FFT), which is a fast algorithm of discrete Fourier transform. Fourier algorithm has been widely used in relay protection, including full-wave Fourier algorithm, half-wave Fourier algorithm, and discrete Fourier algorithm. The full-wave Fourier algorithm is sample data at N points in a cycle, and its data window is a whole cycle r, so the response speed is slow; the half-wave Fourier algorithm requires a relatively short data window, which is equivalent to the full-wave Fourier algorithm. Half, the response speed is fast, but it cannot effectively filter out DC components and even harmonics; when the number of sampling points is N, the FFT algorithm also reduces the amount of computation, and has great advantages over full-wave and half-wave [20]. Therefore, this paper chooses FFT algorithm for signal processing.In this simulation, the data output by CT is sent to the preimprovement criterion, and the data output by ECT is processed and judged by the preimprovement and postimprovement criteria, and a large number of simulations are used to verify the sensitivity and reliability of the improved criterion for protection and other performance improvements.Select the fault pointE, 70 km away from the M side in the area, the power angle σ is 0, the fault type is set to A phase grounding, and the fault time is 0.02 s to 0.04 s. The measured values are shown in Figures 8 and 9.Figure 8
M and N side secondary current measured by ECT.Figure 9
M and N side secondary current measured by CT.Differential current and braking current waveforms obtained by FFT and other mathematical operations based on the M-side and N-side currents measured by CT and ECT. It can be seen that due to CT saturation, its braking current increases and the differential current decreases, while the braking current based on ECT is very small, and the differential current is much larger than the braking current.Select the fault point ink point outside the area, the power angleσ is 30, the fault type is set to A phase grounding, and the fault start time is 0.02 s. The CT on the N side is severely saturated and the current is distorted, but the CT on the M side is not saturated [21]. However, ECT shows good transfer characteristics under the action of short-circuit fault current, and accurately follows the change of primary current.This paper mainly analyzes the influence of the relay protection device on the differential protection and improves the traditional differential protection criterion according to its characteristics, in order to improve the integrated protection performance of the substation. In order to compare with the traditional electromagnetic transformer, the influence of its saturation characteristics on the differential protection is mainly analyzed to reflect the superior performance of the relay protection device [22]. The factors that affect CT saturation are numerous and complex. This paper mainly selects CT when there is no remanence, which is deeply saturated by sudden fault current. The same is true in the following simulations of transformer differential protection.After a large number of simulations, it can be known that malfunction or delayed action may occur due to CT saturation when short-circuit faults occur outside or within the region, and the differential protection based on ECT, no matter what kind of fault occurs outside the area, it will not act reliably, and it can act quickly when the fault occurs in the area. Under the improved differential protection criterion, the sensitivity and reliability of the ECT-based differential protection are improved compared with those before the improved criterion.Set the fault module to make the line in O. Three-phase, short-circuit fault occurred in 04 s, and the differential protection based on CT and ECT were analyzed as shown in Figure10.Figure 10
Differential current diagram based on ECT and CT.According to the dynamic process of the power system after the disturbance, it can be divided into electromagnetic transient, electromechanical transient, and medium and long-term dynamic process according to the time constant of its change. The simulation scale of electric transient is relatively large, and there is no limit in theory, while electromagnetic transient is limited by computer storage capacity and algorithm, and the system to be simulated needs to be equivalently simplified. Due to the nonlinear characteristics of the CT core, under normal line current, the CT works in an unsaturated state; when a serious fault occurs in the power system, the fault current is much larger than the normal operating current, especially when it contains a large nonperiodic component. The magnetic flux quickly reaches saturation and cannot correctly reflect the current signal on the primary side of the power grid, which is likely to cause malfunction, refusal, or delayed action of the relay protection device.


## 4.1. Brief Introduction to the Principle of Failure Rate of Relay Protection

Failure refers to the loss of the original function of the equipment. The index of failure is usually expressed by the failure rate function, also known as the failure rate, which is denoted asφ(t) to describe the probability of the protection device not failing within the time t of failure per unit time. If X is used to represent the fault-free running time of the device, and Pr is used to represent the probability of occurrence of an event, then the failure rate function is (3)ϕt=limΔt⟶0PrX<t+Δt|X>tΔt.Failure rate is similar to failure frequency and is used to reflect equipment reliability. According to the relevant definition, the reliabilityR(t) is often used to represent the probability that the equipment does not have abnormal conditions at time t, which is related to the failure rate satisfying (4)Rt=e−∫0tϕtdt.Iff(t) and F(t) are used to describe the probability density and distribution function of equipment uptime Z, respectively, the failure rate is (5)ϕt=ftRt=ft1−Ft.


## 4.2. Failure Rate Curve and Estimation Process of Relay Protection Device

The failure rate function is widely used in reliability calculation and risk assessment, which lays a foundation for the hidden danger risk assessment work. From the failure rate formula, it can be seen that the failure rate is related to the timet, so the failure rate of the relay protection device is a graph that follows the time-varying law. Most of the reliability models are determined by the time-varying failure probability. In reality, there are many uncertain factors, resulting in a basin-shaped function graph, as shown in Figure 2.Figure 2
Time-varying curve of failure rate.Generally speaking, failures are divided into accidental failures and aging failures. Among them, the failure caused by accident is called accidental failure, and the failure caused by component aging is called aging failure. Therefore, the failure rate must be calculated from these two aspects. Supposeδ0 is the accidental failure rate, λ1(t) is the aging failure rate, and λ(t) is the total failure rate. The estimation process is shown in Figure 3.Figure 3
Flowchart of total failure rate estimation.The traditional two-parameter Weibull distribution aging phenomenon runs through the entire operation of the equipment, which is inconsistent with reality. The three-parameter Weibull distribution does not appear aging before the critical point, and then begins to appear aging, which perfectly fits the failure rate curve in reality. Therefore, the three-parameter Weibull distribution is used to fit the failure rate.When the three-parameter Weibull distribution is satisfied, the failure distribution and failure rate functions are (6) and (7), respectively: (6)Ft=1−e−t−γηβ,(7)λt=βηt−γηβ−1.Among them,ß and η are called shape and scale parameters; ℇ is called position parameter, and ℇ ≥ 0 is satisfied.The three-parameter Weibull distribution function is used to fit the aging failure characteristics, and the shape, scale, and position parameters are calculated by the least square method to realize the fitting of the aging failure rate, and then the total failure rate is obtained according to the result of the accidental failure rate., paving the way for further research on the risk assessment system.


## 4.3. Research on Algorithm of Relay Protection Device

When processing the basic data, the LS-SVM algorithm is used to preprocess some data, and when the Weibull distribution parameters are fitted, the LS-SVM algorithm is used to estimate the parameters. In this paper, the empirical risk is generally used to replace the expected risk R(f), and the specific formula is as follows:(8)Rf=∑i=1lcxi,yi,fi.Equation (9) is used to estimate the function(9)y=fx=w⋅ϕx+b.Take a very low value for the optimization objective:(10)minQ=12w2+C∑i=1Nξi·+ξi,where C is the penalty factor, ξ is the relaxation factor and ε is the loss function; a loss function with good ε is introduced, which can be defined as follows: (11)Lεy=0fx−y<εfx−y−εfx−y≥ε.For nonlinear cases, a kernel function is often introduced to represent the regression function(12)fx=∑i=1nai−ai∗kxi,yi+b.The essence of the support vector machine regression problem is to findf(x) according to the training of the data. Its expected output and yi in the training data only account for at most, and the function f(x) is as flat as possible, that is to say, don’t care. Errors less than ε but no errors greater than ε are allowed. Therefore, support vector machine regression is widely used in error correction and output control. According to the LS-SVM theory, the regression least squares support vector machine can finally be reduced to the problem of constrained optimization, and the vector mechanism model supported by the regression least squares method is (13)y=∑i=1NaiKx,xi+b.


## 4.4. Establishment of a Failure Rate Calculation Model for Relay Protection Devices Based on LS-SVM Model

In the previous study, the least squares method was used to estimate the Weibull parameters, and the effect was good, but this was based on a large amount of basic data [17]. In the face of the difficulty in collecting basic data of the relay protection system and the lack of effective data, the Weibull in the estimation of the three parameters, the fitting sample data is too small, and there is a problem of low-fitting accuracy. To solve this problem, the LS-SVM algorithm is introduced into the project to improve fitting accuracy. The basic data of the relay protection system are collected at a certain time, and the data itself contain time information. However, LS-SVM itself has this function, but the time factor must be implied into the data samples. Therefore, before LS-SVM fitting, the data samples must be reconstructed so that the time information can be included in the training samples. LS-SVM needs to construct input and output samples during implementation.When solving the parameters of Weibull distribution in this study, the collected basic data are used as the data input book, the three parametersβ, η, and λ of the Weibull distribution are used as the output samples, the failure rate error is used as the objective function, and the cross-validation method is used to solve the problem. The regularity in the LS-SVM algorithm is the factor and radial basis parameters, and finally the actual values of the three parameters are obtained. Run the test with actual data, and its running data is shown in Figure 4.Figure 4
Weibull distribution parameter map.It can be seen from Figure4 that although there are certain differences in the three parameters of different devices, the aging node parameter and the aging time parameter are always in a state higher than the aging rate parameter. This plays a key role in subsequent analysis by determining the failure rate model.Its failure rate curve is shown in Figure5.Figure 5
Failure rate curve.Figure5 can clearly reflect the general trend of the failure rate, and the failure rate increases significantly with the increase of η, thus laying a foundation for the determination of the maintenance cycle.Since most of the substations currently operating are not new-generation smart substations and do not have the conditions to send the internal temperature of the relay protection device to the outside, it is impossible to obtain accurate temperatures in different periods. In this study, according to the operating characteristics of each module, 10 modules were selected that were put into operation for 1 to 3 years, 4 to 6 years, and 6 to 8 years, respectively, and their internal temperatures were measured with infrared thermometers (The room temperature of the protection chamber is 20∼25°C). The unknown parameters A andß in (7) are estimated by using the operating years t and the corresponding temperature T (in practical applications, the measured temperature of the new generation of smart substations is entered after processing) and the failure rate λ. Among them, the failure activation energy E of the power module, CPU module and optical module is taken as 0.65 eV, 1.2 eV, and 0.5 eV, respectively. The temperature change curve parameters of each module are shown in Figures 6 and 7 and Table 1.Figure 6
Temperature change curve of each module.Figure 7
Trend chart of time-varying aging failure rate of each module.Table 1
Model parameters of aging failure rate of each module.
Module nameParameterAβPower supply0.1032852.983486CPU0.0682424.225761Optical module0.1771483.867354The relationship between the relay protection device and the main internal functional modules constitutes a series system relationship. The failure of any functional module will lead to the failure of the entire device, and the failure rate of each module is composed of accidental failure rate and aging failure rate. It can be seen that the failure rate of devices with lower operating temperatures is relatively low, and after entering the aging period, the difference in failure rates of relay protection devices operating at different temperatures will become larger and larger, so the operating temperature also affects important factor in failure rate.For static indicators such as defects and running time, refer to the processing method of one-way change indicators. The specific threshold value is determined according to relevant specifications, operation, and maintenance experience. For example, the upper limit of the running time of switching power supply is 5 years. The condition and maintenance reference period of the relay protection device is 5 years, so the failure rate of the protection device in this area after 4 years of operation can be selected as a good range reference value, and the actual engineering experience shows that most of the relay protection devices can reach 10 to 12 years, so the failure rate of the protection device in this area after 10 years of operation can be taken as the threshold value [18].The advantage of the method based on LS-SVM model is that it is a simple model when used in complex systems, it considers the relaxation of time constraints and maintenance of time constraints, the distribution of parameters in the system is relatively simple, and the range of output duration is considered in the required variation range. Therefore, this method has high applicability for those systems that are difficult to model and cannot be modeled.


## 4.5. Simulation Analysis of Circuit Calculation of Relay Protection Device Based on LS-SVM Model

In order to achieve a more accurate simulation effect, a suitable, accurate, and flexible power system model must be built. Choose MATLAB as the simulation tool. First, a 200 km long 220 kV transmission line model is established in LS-SVM according to the distribution parameters.In this paper, based on LS-SVM, a simulation model of the current differential protection of transmission lines is established. The current differential protection criterion of the line is written by the S function in LS-SVM, which is a computer language description of a dynamic system. A specific calling syntax allows the function to interact with the LS-SVM solver, which can implement the line differential protection action criterion [19]. The data processing module adopts Fast Fourier Transform (FFT), which is a fast algorithm of discrete Fourier transform. Fourier algorithm has been widely used in relay protection, including full-wave Fourier algorithm, half-wave Fourier algorithm, and discrete Fourier algorithm. The full-wave Fourier algorithm is sample data at N points in a cycle, and its data window is a whole cycle r, so the response speed is slow; the half-wave Fourier algorithm requires a relatively short data window, which is equivalent to the full-wave Fourier algorithm. Half, the response speed is fast, but it cannot effectively filter out DC components and even harmonics; when the number of sampling points is N, the FFT algorithm also reduces the amount of computation, and has great advantages over full-wave and half-wave [20]. Therefore, this paper chooses FFT algorithm for signal processing.In this simulation, the data output by CT is sent to the preimprovement criterion, and the data output by ECT is processed and judged by the preimprovement and postimprovement criteria, and a large number of simulations are used to verify the sensitivity and reliability of the improved criterion for protection and other performance improvements.Select the fault pointE, 70 km away from the M side in the area, the power angle σ is 0, the fault type is set to A phase grounding, and the fault time is 0.02 s to 0.04 s. The measured values are shown in Figures 8 and 9.Figure 8
M and N side secondary current measured by ECT.Figure 9
M and N side secondary current measured by CT.Differential current and braking current waveforms obtained by FFT and other mathematical operations based on the M-side and N-side currents measured by CT and ECT. It can be seen that due to CT saturation, its braking current increases and the differential current decreases, while the braking current based on ECT is very small, and the differential current is much larger than the braking current.Select the fault point ink point outside the area, the power angleσ is 30, the fault type is set to A phase grounding, and the fault start time is 0.02 s. The CT on the N side is severely saturated and the current is distorted, but the CT on the M side is not saturated [21]. However, ECT shows good transfer characteristics under the action of short-circuit fault current, and accurately follows the change of primary current.This paper mainly analyzes the influence of the relay protection device on the differential protection and improves the traditional differential protection criterion according to its characteristics, in order to improve the integrated protection performance of the substation. In order to compare with the traditional electromagnetic transformer, the influence of its saturation characteristics on the differential protection is mainly analyzed to reflect the superior performance of the relay protection device [22]. The factors that affect CT saturation are numerous and complex. This paper mainly selects CT when there is no remanence, which is deeply saturated by sudden fault current. The same is true in the following simulations of transformer differential protection.After a large number of simulations, it can be known that malfunction or delayed action may occur due to CT saturation when short-circuit faults occur outside or within the region, and the differential protection based on ECT, no matter what kind of fault occurs outside the area, it will not act reliably, and it can act quickly when the fault occurs in the area. Under the improved differential protection criterion, the sensitivity and reliability of the ECT-based differential protection are improved compared with those before the improved criterion.Set the fault module to make the line in O. Three-phase, short-circuit fault occurred in 04 s, and the differential protection based on CT and ECT were analyzed as shown in Figure10.Figure 10
Differential current diagram based on ECT and CT.According to the dynamic process of the power system after the disturbance, it can be divided into electromagnetic transient, electromechanical transient, and medium and long-term dynamic process according to the time constant of its change. The simulation scale of electric transient is relatively large, and there is no limit in theory, while electromagnetic transient is limited by computer storage capacity and algorithm, and the system to be simulated needs to be equivalently simplified. Due to the nonlinear characteristics of the CT core, under normal line current, the CT works in an unsaturated state; when a serious fault occurs in the power system, the fault current is much larger than the normal operating current, especially when it contains a large nonperiodic component. The magnetic flux quickly reaches saturation and cannot correctly reflect the current signal on the primary side of the power grid, which is likely to cause malfunction, refusal, or delayed action of the relay protection device.


## 5. Conclusion

This paper focuses on the study of hidden risks and considers the overall situation. It is aimed at the whole process of relay protection. From the actual situation of protection operation, the system evaluation of the whole process is carried out, and the standard and specification of the whole process operation are improved. Based on the actual failure statistics of relay protection devices, a support vector machine model method is proposed. On the whole, the aging failure rate accounts for a large proportion of the time-varying failure rate, and it gradually increases with the growth of time. This conclusion is in line with the bathtub rule. This paper focuses on the research of theoretical algorithms, and the results are implicit risk assessment verification software and operation management specifications. The risk assessment verification software is written according to the risk assessment modeling algorithm. The modeling process depends on a large amount of basic data. There are still some deficiencies in the software testing and application process, and a large amount of basic data need to be manually entered. If the data are missing or the data are not updated in time, the accuracy of risk assessment will decrease.Since some details of this study have no relevant research to refer to or lack of statistical data, this paper makes reasonable approximations and assumptions as much as possible in the research process. With the completion of the secondary system monitoring data in the new generation of smart substations and the development of related research, follow-up research will improve the existing deficiencies, and establish a state evaluation model based on the time-varying failure rate and other monitoring quantities to provide the relay. The practical application of condition-based maintenance of protection devices provides an important reference [23–26].



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*Source: 8221281-2022-07-07.xml*