An evaluation strategy for relay protection status based on the cloud model

After the relay protection secondary equipment is put into operation for a period of time, it will be affected by aging, faults, and other factors, resulting in the gradual decline of the health state of the equipment. Therefore, considering the uncertainty of the influencing factors of equipment aging fault, a relay protection state evaluation method based on the cloud model is proposed. The factors affecting the real-time health state of equipment were analysed, the evaluation indexes were selected, and the weights of each index were calculated. Considering the randomness and fuzziness of the influence factors, a comprehensive evaluation model was established based on boundary fuzzy processing and cloud parameter calculation. Finally, an example was given to verify the rationality and effectiveness of the proposed algorithm.


Introduction
The secondary equipment of relay protection is in good health when it is first put into operation, but after a period of service, the equipment will be affected by aging, faults, and other factors, leading to a gradual decline in the health status of the equipment [1][2][3].Therefore, in order to scientifically and objectively evaluate the health status of equipment in operation, it is necessary to comprehensively evaluate various indicators that affect the real-time health status of the equipment [4][5][6].
Domestic and foreign researchers have carried out a lot of research on the relaying characteristics of power systems.In [7], the adaptability of relay protection setting calculation and the rationality of reclosing device switching are studied, and the principle of protection setting switching of relay protection and reclosing device in ring network is given.Based on the existing defects in the operation of 110-kV ring network, a new calculation principle for ring network operation protection setting is proposed in [8][9].The verification results confirm that the proposed setting principle plays an important role in reducing the probability of protection rejection under fault conditions and improving the reliability of power supply.In [10], the initial location of directed loop retrieval is found by ranking the degree of protection dependence, and the depth of protection dependency set is searched preferentially to find all directed simple loops.The verification results fully demonstrate the simplicity and effectiveness of this method in the calculation of distance protection and zero-sequence protection setting.Based on the minimum cut set theory, a reliability evaluation method suitable for distribution systems with ring networks is proposed in [11][12].It adopts the strategy of searching node group components to simulate the active faults of components, taking into account the capacity limitation of components, maintenance plan and the correlation of standby power supply.The reliability indexes and weak links of the system and load nodes are analysed with the power flow calculation method based on the compensation method.
The studies above have included research on the characteristics of relay protection actions from multiple perspectives, providing corresponding relay protection control strategies, but rarely exploring the uncertainty of the influencing factors of relay protection equipment.Therefore, in this article, research on the evaluation of relay protection status based on cloud models is conducted.First, the basic concepts of cloud models are analysed, and a comprehensive evaluation model of relay protection based on the cloud is established.The selection of evaluation indicators and the weights of subjective and objective impact factors are calculated, and boundary fuzzy processing and cloud parameter calculation methods should be used to analyse and process the data.The effectiveness of the proposed method is verified through examples.

Basic concepts of cloud models
In this article, an uncertainty evaluation method is adopted that can comprehensively handle randomness and fuzziness factors for evaluation [13][14], and a relay protection status evaluation based on cloud models is proposed.The mathematical characteristics of cloud models are usually characterized by three values: expectation Ex, entropy En, and overentropy He [15].Due to the relatively small number of relay protection faults in intelligent substations, a normal cloud generator can be used to describe them.The expression for normal cloud droplets is: In the formula, x is a cloud droplet on the model that satisfies condition x = NORM(Ex, En); En' is a normally distributed random number that satisfies condition En'= NORM(En, Ee).
The quantitative value of cloud droplets is calculated based on the digital characteristics of the cloud model and the number of cloud droplets, as shown in Figure 1.To facilitate the determination of the risk level of each evaluation indicator and eliminate the impact of indicator category differences, the evaluation values and risk level standard set of each indicator are uniformly normalized to the [0,1] interval.0 represents a negligible risk of relay protection equipment, and 1 represents an unacceptable risk.That is, the larger the standardized value, the more unacceptable the risk of the protection equipment.Selected status information is classified and processed: A normal distribution function is applied to fuzzily quantify degree type indicators, and the specific calculation formula is as follows [16].
A larger normal distribution function is used to represent incremental indicators: A slightly smaller normal distribution function is used to represent decreasing indicators: In the formula, σ = (xm -x0)/3; x0 represents the optimal operating value of the state indicator, which can also be determined based on the factory value of the device; xm represents the boundary value of the unacceptable level of risk for protective equipment, which is determined based on relevant regulations and operating experience.
Due to the fact that the reliability of electrical components such as relay protection equipment during operation follows the "bathtub curve" law [15], the exponential distribution of operating years and device correct action rate is approximated: For the state parameters such as the average correct action rate and the proportion of precise evaluation of countermeasures expressed as percentages, as continuous changes in data can reflect the aging and maintenance risks of the device, it is proposed to adopt linear changes in the distribution of ascending and descending trapezoidal functions, as shown in Formulae ( 5) and (6).
For benefit indicators: For cost-based indicators: In the formula, xi is the measured value of the state indicator; x0 is the optimal operating state value of the indicator, which can also be determined based on the factory value of the equipment; xm is the quantity value of the indicator in a deteriorating state, which can be determined through corresponding standards, specifications, and engineering experience; Vc(xi) is the standardized evaluation value of indicator i.

Term weighting
The relative significance of unascertained rational number evaluation indicators is introduced to assign weights to the indicators, which can to some extent eliminate the subjective randomness in the expert evaluation process.As shown in Figure 2, it is the process for calculating the weight of unascertained rational numbers [17].Assuming that m experts evaluate the significance of n indicators in the historical statistical data of relay protection, the estimated values of these n indicators can be obtained.Under the same evaluation value of indicator j, the reliability value is multiplied by the normalized expert weight value, and then they are merged separately to obtain the unascertained rational number of the significance of indicator j.
where E(A) is the expectation of an unascertained rational number and E(A) is the first-order unascertained rational number.Only when x has credibility at a point, that point is clearly the weight value of the indicator.

Boundary fuzzy processing and cloud parameter calculation
The adjacent evaluation levels have a dynamic transition characteristic, and the artificial hard grading has fuzziness and subjectivity.Obviously, the uncertainty of the two points in xi and xi+1 belonging to different states is consistent, then: e Hs = (13) In the formula, xi and xi+1 are two adjacent level boundaries, respectively; S is a constant with a value of 0.005.The cloud feature parameters are calculated using the formula above.

Establishment of a comprehensive evaluation model
Based on the statistical data of the evaluated equipment, the judgment degree of each level belonging to each indicator is calculated, and it is combined with the weight of the corresponding factor to obtain the comprehensive judgment degree.Combining cloud models with variable fuzzy comprehensive evaluation methods for comprehensive evaluation, the variable fuzzy comprehensive evaluation model is shown in Formula ( 14).
In the formula, ωi represents the weight; according to the changes in model parameters, α and ρ can be combined into four configurations; α = 1, 2 are the least squares criterion and the least squares criterion, respectively; ρ = 1, 2 are the Hamming distance and the Euclidean distance, respectively.
There are usually four combinations.

Example analysis
A 220-kV new intelligent substation is selected and a differential protection device is used for a certain line as the research object to verify the effectiveness and feasibility of the method proposed in this chapter.The historical status information of the protection device is obtained from the equipment ledger information and historical operation and maintenance records.The risk assessment statistical data is shown in Table 2.The significance of historical state information evaluation indicators is evaluated and weights are assigned to the evaluation values of five highly authoritative experts based on the theory of unascertained rational numbers.The authority of five experts is quantified to obtain the importance of each expert's evaluation.The quantification table of expert authority is shown in Table 3, and the allocation of expert weights is calculated according to Formula (15).
Taking the calculation of average action time weight as an example, the significance evaluation and signal ratio distribution of 0-10 for the average action time of relay protection devices are given through expert investigation, as shown in Table 3.The distribution of the confidence ratio density function for the unascertained rational number of the importance of the average action time calculated is shown in Formula (16).0.1594, 4.5 0.1406, 5 0.1520, 5.5 () 0.1692, 6 0.3188, 6.5 0, The mathematical expected value for solving the unascertained rational number of average action time is as follows: The calculated average action time weight assignment result is 5.6848.Similarly, the weight assignment results for correct action rate, number of device defects, operation time, maintenance status, and precise evaluation of countermeasures can be obtained, which are  4, where the x-axis represents the fuzzy quantified evaluation value, and the y-axis represents the degree of membership of the evaluation value corresponding to the risk level.Taking the average action time as an example, the calculation result of risk level membership is [0, 0.0009, 0.  13), the comprehensive membership degree of the evaluation indicators can be calculated to obtain the membership degree of the evaluation level under four different model parameters.The calculation results are shown in Table 5, and the risk level assessment is completed based on the principle of eigenvalue judgment.From Table 5, it can be seen that the distribution of the comprehensive membership degree vector is relatively uniform at each level and is in the V3 level.The average characteristic value of the level is obtained to be 2.86.It is comprehensively determined that the risk of the protection device is not expected, and it is pointed out that the risk of the device is further increasing.After analysis, the indicator of V3 level risk is related to the reliability of the device.Obviously, the reliability of the device has decreased due to its long operating years.However, its maintenance status and real-time operation status cannot be ignored.Based on the actual operation status of the protection device, it is evaluated as an abnormal state.After timely maintenance, its normal operation can be met.Based on the risk assessment criteria in this article, it is comprehensively determined that the operating status of the protection device is at an unexpected risk level, which is V3 level.

Conclusions
In this article, research on the evaluation of relay protection status is conducted based on cloud models: (1) The basic concepts of cloud models are analysed, and based on historical statistical data of relay protection, and considering the fuzziness and uncertainty of the boundary division of relay protection evaluation levels, a relay protection risk method based on normal cloud models is proposed.
(2) Considering the uncertainty of the influencing factors of relay protection equipment, the selection of evaluation indicators for the comprehensive evaluation model and the calculation of the weights of subjective and objective influencing factors are carried out.Boundary fuzzy processing and cloud parameter calculation methods are applied to analyse and process the data, which to some extent eliminates the influence of uncertain factors in the weight calculation process.
(3) The case analysis verifies the rationality and effectiveness of the evaluation method proposed in this article in risk assessment.
In the formula,[x1, xk]  is the interval of unknown rational number values; φA(x) is the density function of the signal-to-ratio distribution; ̅ ai represents the importance value of each indicator, which is the sum of xi evaluator's confidence ratios.The formula for calculating the expected rational number without certainty,

Table 1 .
Scoring criteria of selected indicators.

Table 2
Risk assessment data of relay protection device.

Table 4 .
6.7421, 4.0905, 1.8161, 3.8449, The boundary of the relay protection level is treated as a double constraint condition [xi, xi+1], the cloud model interval eigenvalue formula is applied to calculate the boundary level eigenvalues Ex, En, and He of each indicator, and finally the normal cloud model of relay protection evaluation indicators is output to achieve "softening" of the boundary.The statistical data of evaluation indicators is standardized, and the calculation results are shown in Table 4. Treatment results of evaluation index standard.If the evaluation value of a certain indicator is known, it is easy to determine the risk level of the indicator from the level boundary cloud model.The risk level models for each indicator are shown in Figure

Table 5 .
Calculation results of comprehensive membership degree vector and level eigenvalue under four model parameters.