State Analysis of Protection Device Considering Primary Equipment

At present, the state monitoring models of relay protection use constant fault probability to predict the failure rate of protection devices, fail to consider the dynamic impact of equipment aging on failure rate, and only analyze the status of protection devices. In view of this, an improved Markov state prediction method based on Weibull distribution is proposed, combining the primary equipment’s state space to analyze the state of the protection device. First, the failure model of the relay protection device is established by the GM-SVR method. Then the 13-state Markov chain is established by combining primary equipment and the protection device. Finally, after introducing the failure model, the prediction of the line protection operation state is realized. The simulation results show that the optimized Markov chain is more in line with the actual operating conditions and can more effectively predict the operating state of the equipment during the operating life.


INTRODUCTION
With the grid-connected operation of new energy and the widespread popularity of many intelligent substations, the flexibility and complexity of power grid operation are gradually improved, and the requirements for protection reliability are also gradually improved.In recent years, operation statistics show that the failure and misoperation of intelligent IED modules are the main factors causing chain accidents [1,2].However, the traditional operation and maintenance methods are difficult to cope with many real-time updated intelligent devices, so the real-time monitoring and prediction of the status of protection devices become particularly important.
At present, some scholars have studied the relevant content.The static Markov risk transfer network is used to evaluate the risk of relay protection devices in intelligent substations, but the static Markov chain finally obtains the stationary probability distribution.It is difficult to describe the intermediate state transfer process [3].The reliability of protection devices is evaluated based on the condition-based maintenance transfer matrix.Still, the state division is relatively rough, and there needs to be in-depth research on the correlation between primary equipment and secondary protection [4].The transfer state of line protection is studied using a continuous Markov chain.Still, the constant failure rate is selected to describe rejection and misoperation, and the description of the whole operation process needs to be more accurate [5].
After comprehensively considering the advantages and disadvantages of existing scholars' research results [6][7][8][9], this paper establishes a state transfer model considering primary equipment and secondary protection.The continuous-time Markov chain is improved by a three-parameter Weibull time-varying failure rate, which can accurately describe the state probability of protection refusal and misoperation.
It can also predict the real-time state and behavior of the protection device.The simulation results show that the method provided in this paper can be effectively applied to the operation and maintenance site.

State space of joint primary equipment and secondary protection equipment
Taking the line relay protection device as an example [10], when the line fault occurs, the state of the protection device will be transferred from the inactive state to the operating state.Moreover, with the construction of an intelligent substation, the protection device has fully realized the self-test function.However, after the equipment has been put into operation for a certain number of years, due to the influence of aging, the equipment may refuse to operate and misoperate because of the failure of the self-test.The maintenance work is to transfer the protection device from the failure state to the normal state, simultaneously reducing the equipment's aging impact and reducing the probability of incorrect behavior of the protection device.The influence of the non-operation and misoperation behavior of the protection device on the line state and maintenance behavior is as follows: after the misoperation of the relay protection device, the line will be isolated no matter what state it is in.When misoperation occurs, if the self-test device fails and the line still cannot be automatically reset after maintenance, the operation will be isolated again, so it must be shut down and overhauled.The protection device and the line will be repaired before normal operation is restored.After the rejection occurs, if the line is normal, it will continue to operate, but the rejection cannot be detected by itself.The fault range will be further expanded if the line fault occurs.For the state of the self-testing protection device, after the fault occurs, the lock is performed, and the fault protection is repaired.In the non-self-checking state, the protection fails, resulting in misoperation or refusal to operate.In addition, it is determined that the non-self-testing state of the protection device can be restored to the self-testing state only after a power outage and maintenance.According to the above, a device state space with 13 states can be established, as shown in Figure 1  are the misoperation probability and rejection probability of the preservation device.S is the probability of self-inspection of the protection device, and Q is the reciprocal of periodic maintenance.
For the state of the self-testing protection device, after the fault occurs, the lock is performed, and the fault protection is repaired.In the non-self-checking state, the protection fails, resulting in misoperation or refusal to operate.

Time-varying failure rate model of the protection device
After the relay protection device is put into its failure distribution is like the bathtub curve, so the three-parameter Weibull distribution is used to model and analyze the reliability of the protection device.The three-parameter Weibull distribution function is: ; .
In the formula,  is the position parameter,  is the scale parameter,  is the shape parameter, and x is the time.And the order is >0, >0, >0.This paper uses the GM-SVR method to solve the related parameters.
The time-varying failure rate model of the protection device is shown in Formula (4): .

STATE SPACE SOLUTION OF TIME-VARYING FAILURE RATE
The state space designed in this paper accords with continuous-time Markov, and its state transition rate matrix A is shown in Formula (5).
(5) The rejection rate and misoperation rate of the protection device account for approximately half of the total failure rate [6], so the state space matrix of the time-varying failure rate can be obtained by modifying the failure  and  with G (t). Combined with the Kolmogorov backward Equation (6) and Equation ( 7) satisfied by the continuous-time Markov chain.The initial condition of the matrix is the unit matrix, and the State Transition Probability Matrix (8) can be obtained.

 
A P (7) (8) If the stationary probability distribution of each state is required, it can be obtained from Formula (9). PA P (9)

Basic data
The failure operation data of the protection device are shown in Table 1.With the introduction of the failure data of protective devices in the literature, the three-parameter Weibull distribution's relevant parameters are obtained using the GM-SVR method, as shown in Table 1.The improved state transition rate matrix parameters combined with the fault failure rate and its threshold parameters are shown in Table 2.
Table 1 Parameter estimation result and test The total failure rate of protective devices obtained according to Table 1 is shown in Formula (10).
Figure 2 Comparison diagram of different failure rates Due to the failure data of the protection device collected on the site, the impact of maintenance needs to be taken into account, so this paper will not correct the failure rate.The comparison between timevarying and constant failure rates is shown in Figure 2.

. Comparison of methods
The system is usually in a normal state.After introducing the relevant parameters, the time-varying probability curves of the system state maintained in the initial state 1 under different failure rates can be obtained, as shown in Figure 3.It can be seen that because the time-varying failure rate is lower than the constant failure rate at the initial stage, the prediction system can be better maintained in the normal state in the early stage.When the transnational threshold parameters of the protection device enter the aging period, the equipment will accelerate aging, and the probability of the system remaining in state 1 will decline rapidly.The probability of the system using constant failure rate prediction to maintain in state 1 decreases faster, finally converging to the stationary distribution.It is obvious that if the state prediction under a constant failure rate is used to guide the maintenance work, it is easy to cause overmaintenance and waste-related resources.Under the guidance of the prediction state under the timevarying failure rate, we can set the threshold period.For example, in the range of [0.97~0.98],we can consider arranging the maintenance work to achieve a better balance between reliability and economy.If we want to consider the influence of maintenance behavior on the line after the incorrect action of the protection device, we take state 5 as an example; at this time, the protection device will isolate the line due to the misoperation of the non-self-test after the fault occurs, according to the different maintenance rate of the protection device, the earlier the emergency intervention of the maintenance personnel is, the faster the maintenance speed is, the shorter it takes for the system to transfer from the fault state to the normal state.The specific change trend is shown in Figure 4.As the line is a normal line isolated by misoperation at this time, we can consider whether to put in the emergency protection device if the line cannot return to normal loading within the maximum tolerable time.

CONCLUSION
This paper establishes the state transition model of relay protection devices considering primary equipment.The three-parameter Weibull time-varying failure efficiency is introduced to improve the time-varying model of the continuous-time Markov chain.Compared with the basic model under a constant failure rate, the future transformation trend of the system in a certain state can be predicted more accurately.The simulation results show that the time-varying trend curve accords with the objective development law of protection.The model can provide auxiliary support for operation and maintenance and some help for maintenance arrangements.

Figure 3
Figure 3 Probability of state P11 under different failure rates

Figure 4
Figure 4 Transition probability of state 5 under different repair rates .
Secondary equipment state space considering line stateAs shown in the figure,  is the repair rate of the protection device. is the line fault repair rate.E is the reciprocal of the emergency maintenance time to the site. is the line failure rate. and 

Table 2
Parameters required for state transition rate matrix