Research on the Prediction Method of Equipment Status in Power Transformation and Distribution Based on Grey Model

With the continuous increase in the demand for electricity in our country, the reliability requirements of the power distribution network are gradually increasing, and the difficulty of predicting the state of key equipment in the power distribution network is also increasing. In response to this issue, this paper proposes a typical reliability prediction model for key equipment in the power distribution network based on an unbiased grey correlation model. Firstly, a grey model is established to model the reliability of typical key equipment in the power distribution network, and to conduct reliability analysis and life prediction. Secondly, an unbiased grey model is introduced to avoid the problem of the grey model leading to less than ideal life prediction accuracy when the growth rate of the original data sequence is high. Finally, taking the No. 1 main transformer of the 220 kV Lanshan substation under the jurisdiction of Ningxia Shizuishan Power Supply Company as an example, the oil chromatography data is cleaned using the KNN interpolation method and input into the prediction model to analyze and predict the failure rate during actual operation. The results show that this model has certain advantages in terms of life prediction accuracy and calculation time, and can play an auxiliary role in the process of predicting the state of key equipment in the power distribution network.


Introduction
Due to the construction and development of the energy internet, the construction and development of the energy Internet, the working data of power equipment will gradually be integrated and shared on a unified information platform, thus promoting the development of technologies for condition assessment, diagnosis and prediction of power equipment to a comprehensive analysis based on panoramic state.However, many considerations affect the operation status of power equipment [1][2][3].The current methods make it difficult to comprehensively address these data.In this context, data-driven resolves technology provides a new solution and skill.
For power distribution equipment such as GIS and other switch equipment, it is mainly based on partial discharge, density and mechanical characteristics of circuit breakers.CIGRE suggests that the risk assessment of GIS insulation defects should be based on the partial discharge measurement of internal defects, which is also the focus of current research [4].For the assessment of the risk degree of GIS internal defects, some foreign scholars have carried out different degrees of research work [5].
2 Domestic experts and scholars have not systematically studied the risk of insulation defects in GIS.Only some universities have carried out research on the characteristics of different defects in different stages of development.
The current research mainly focuses on the fault diagnosis of some information in a single system, because most of them are based on simple threshold determination to detect anomalies in the actual operation and maintenance of the equipment, which leads to the low accuracy of state evaluation and the low utilization of equipment information [6][7].Therefore, the data-driven analysis technology has certain research value.The evolution law of equipment failure is found from the existing state data, and these laws are used to predict the future state or unobservable state.

The Establishment of Grey GM (1,1) Model
Using the grey model to model the reliability of typical power distribution key equipment can accurately predict its reliability and life, which can provide an idea and a method for formulating the maintenance and repair strategy and condition-based maintenance of typical power distribution key equipment.
The model established for the grey process is known as the grey model, the acronym is GM.The grey model is a model that show the evolving changes process of things within the system.The model establishment process is as follows.
(2)Accumulated generation, according to Formula (1), the original data sequence is accumulated to generate a new data sequence.
The new sequence generated after accumulation is : =[ (1), (2),... ( ),... ( )] jn (3) The accumulation matrix B and the constant vector Y are constructed, and the adjacent mean sequence of λ (1) is generated according to the formula. (1) (1) where The adjacent generated sequence is : [ ( 2), (3),... ( )..., ( )] z z z k z n = Z (5) Then there exists a constant vector Y and an accumulation matrix B : The differential equations of the model were established and the differential equations of the GM (1,1) model were built for the cumulative data series λ (1) : Among them, a is the development factor and b is the grey action parameters.
(5) Model parameter identification, set the parameter vector, using the least squares method to estimate the value of a, the approximate solution is : By restoring the formula (10), the prediction function can be obtained as follows : The average relative error is : The sum of residual squares is : 2), (4), , ( )] ()

The Establishment of Unbiased Grey GM (1,1) Model
As an improved model of grey GM (1,1), the unbiased grey GM (1,1) model eliminates the phenomenon that the grey GM (1,1) model is prone to failure when the growth rate of the original data serials is large.Therefore, it is more accurate and reliable, and application range is wider than that of the grey GM (1,1) model.Additionally, the unbiased grey GM (1,1) model does not need to be decreased, which streamlining the modeling steps and improves the computational speed of the model.It has been well applied in various fields.The basic steps of its modeling are similar to those of the grey GM (1,1) model.After calculating the development coefficient and the grey action b of the grey GM (1,1) model, the parameters A and C of the unbiased grey model of GM (1,1) are calculated.The values are : Unbiased grey model of GM (1,1) is established : ˆ(1)

ˆ( ) e
Finally, the model accuracy test is carried out, and the process is the same as the accuracy test process of the grey GM (1,1) model, which is no longer repeated here.The establishment process of the unbiased grey GM(1,1) model is shown in Figure 1.

End
Figure1.GM(1,1) Modeling Process Flowchart in Unbiased Gray Scale.Due to various reasons, there are few perfect statistical data of power transformer failure, and the existing statistical data are mostly based on the capacity of power transformer, which does not meet the needs of reliability analysis, and it is difficult to obtain comprehensive failure data through a large number of investigations and statistics.Therefore, this paper will only model and predict the failure rate of power transformer.

Model Instance Application
According to Eq.( 2), the cumulative sequence of transformer failure rate is generated as follows : (1) 0.010009,0.032247,0.073270,0.136291,0.217621,0.319437,0.443581, 0.588461,0.762493,0.961 The adjacent mean generation of λ (1)  is performed once, and the adjacent generation sequence is : (1) 0.021128,0.052759,0.104781,0.176956,0.268529,0.381509,0.516021,0.675477,0.862 It can be obtained : The differential equation of GM (1,1) model is : The solution of the above differential equation can be obtained as follows : (1) 0.201745 ( ) 0.1810511e 0.171042 The prediction function of GM (1,1) model is : The prediction function of unbiased grey GM (1,1) model can be deduced from Eq.( 11) : (0) 0.222677( ˆ( ) 0.020682e 2, , The fitted failure rate is shown in Table 2 and the reliability model parameters are shown in Table 3 At the same time, the goodness test of the fitting results of the two models is carried out respectively.The results are shown in The analysis of the data in the table shows that when the development coefficient a≤0.3, the unbiased GM (1,1) model can be used for medium and long-term forecasting.Therefore, the established grey GM (1,1) model can be used to predict the failure rate of power transformers in the medium and long term.It can be seen from Table 2and Table 5that the failure rate of power transformer increases with the increase of its running time, and it should be maintained and repaired after a period of operation.

Conclusion
Based on the key parameters of operation state and the principle of unbiased grey model, this paper proposes a prediction method of operation state of power distribution key equipment based on long-term and short-term memory network, which realizes the preliminary early warning of potential faults of equipment.The feasibility and accuracy of the method are verified by an example analysis.By analyzing the correlation strength between each sequence through association rules, the time series combination with strong correlation is excavated, and then the parameter combination with strong correlation is extracted, which solves the problem that the parameter correlation of the existing prediction method is not strong.The research results of this paper will produce better economic and social benefits when applied to the actual production of power supply companies.In this paper, only one example of transformer is used to verify the method, and the key equipment of power transformation and distribution such as switchgear can be verified later.

( 6 )
Model accuracy test, mark the known data at k time as the calculated value of the model, then there are residuals and relative errors are :

Table 1 .
Chromatographic data table of transformer oil.
Taking the No.1 main transformer of 220 kV Lanshan Substation under the jurisdiction of Ningxia Shizuishan Power Supply Company as an example, the oil chromatographic data from January 26 to September 29,2022 were collected to verify the accuracy of the proposed method.The chromatographic data of Shizuishan transformer oil from January 26 to March 26,2022 are shown in table 1.

Table 4 Table 2 .
Failure rate after fitting.

Table 4 .
Simulation error.It can be seen from Table2thatthe precision of the unbiased GM ( 1,1 ) model is higher than that of the traditional GM (1,1) model.

Table 5 .
The failure rate after fitting.