Research on Condition Assessment Method of Transformer Based on Cloud Model

The traditional evaluation method of transformer has the problems of strong subjectivity of threshold value and fuzzy correlation of state quantity, which is difficult to accurately evaluate the operation quality of transformer. In order to solve these problems, this paper proposes a comprehensive evaluation method of transformer performance evaluation and operation quality based on cloud model. The evaluation index system of power transformer operation quality considering performance is constructed, including target layer, performance layer and index layer. The triangular fuzzy number is used to optimize the set of expert opinions, and the indexes are combined and weighted by fuzzy analytic hierarchy process and entropy weight method. After the data is degraded, the membership matrix of transformer operation index is constructed by using the cloud model, and the performance state weighting and membership degree are comprehensively considered to realize the performance evaluation of transformer and the comprehensive evaluation of operation quality based on performance. By using this method to predict 10 transformers in operation for a period of one month, it is possible to accurately identify abnormal situations on site, with a prediction accuracy of 96.28%. Compared with the traditional method of “predicting first and then diagnosing”, it has improved by 14.32%, overcoming the shortcomings of subjectivity, ambiguity, and ignoring the correlation of state variables in traditional evaluation methods. This method provides new ideas and methods for accurate evaluation of transformers.


Introduction
As an important hub equipment in the power system, the stable operation of power transformers is a necessary foundation for ensuring normal power supply.Therefore, in order to ensure the safe and stable operation of transformers, the cumulative deduction system evaluation method based on state evaluation guidelines is widely used in the operation and maintenance process.Although this method has the advantage of being simple and easy to implement, it does not effectively solve the problem of information uncertainty in the evaluation process, making it difficult to draw targeted evaluation conclusions.With the development of state detection technology, the state information of power transformers gradually presents typical big data characteristics such as large volume and diverse types.Quality assessment is the use of data analysis methods to comprehensively evaluate the basic data collected from transformers, such as operation and testing, to determine their actual operating quality [1,2].However, it is difficult to reflect the true operating status of power transformers solely based on the environment or a certain indicator [3].
2 Due to the complex relationship between the various indicators of transformers and their performance, the evaluation process and results have a certain degree of ambiguity and uncertainty.In response to this issue, Zeinoddini Meymand used the transformer health prediction formula from EA Power Company in the UK to calculate the health index (HI), and constructed an artificial neural network (ANN) nonlinear model and a multiple linear regression (MLR) model to accurately indicate the health status of the transformer [4].Qi Bo used the inverse cumulative distribution function to calculate the attention and warning values of dissolved gas volume fraction and gas recovery in oil under different attributes, achieving differential evaluation of transformers [5].Wang Qingjie uses similarity analysis of electrical parameters to quantitatively analyze the electrical status of transformers [6].The above studies mostly use subjective fuzzy qualitative evaluation method or comprehensive weighting method, with a single level of indicator system.However, in the state evaluation of power transformers, the ambiguity and uncertainty of state information can greatly affect the evaluation results.
To address the aforementioned issues, this article proposes a cloud model-based method for evaluating transformer performance and operational quality.This method combines relevant standards and guidelines to construct a three-layer indicator system for evaluating the operational quality of power transformers considering performance, including the target layer, performance layer, and indicator layer.Firstly, triangular fuzzy numbers are used to optimize the expert opinion set, and then based on the fuzzy analytic hierarchy process, the monitoring data is transformed into weighted scores of transformer performance status.Finally, a cloud model is used to objectively solve the problem of state classification.The membership degree of the corresponding performance state of the transformer operation indicators is analyzed through the degraded indicator data, and the operation status of the power transformer is comprehensively evaluated based on performance state weighting combined with membership degree.Compared to traditional prediction algorithms, the method proposed in this article has higher prediction accuracy.

Construction of Power Transformer State Evaluation Index System
According to the current State Grid Corporation of China power transformer condition evaluation guidelines Q/GDW169-2008 'oil-immersed transformer (reactor) condition evaluation guidelines' and China Southern Power Grid condition evaluation guidelines Q/CSG11001-2010 '35kV ~ 500kV oilimmersed power transformer (high resistance) condition evaluation guidelines', a three-tier index system of power transformer operating status is established, as shown in Figure 1.In this paper, the comprehensive weighting method of entropy weight-fuzzy analytic hierarchy fusion is introduced to determine the comprehensive weight of power transformer operation state, and then the state index is standardized according to the degree of deterioration, and the membership degree of each index is calculated by cloud model.The comprehensive weight and membership degree are combined to determine the performance and overall operation quality of power transformer by the principle of maximum membership degree.This method can effectively consider the randomness and fuzziness in the evaluation process, and its process is shown in Figure 2.

Fuzzy Analytic Hierarchy Process for Calculating Index Weights
Compared to the traditional Analytic Hierarchy Process (AHP), the AHP method based on triangular fuzzy numbers can solve the uncertainty of expert subjective consciousness and fuzzy environment.Unlike traditional AHP, the judgment matrix is composed of triangular fuzzy numbers rather than a single real number, which leads to different methods for solving weight vectors [7].Collect pairwise importance evaluations of indicators by experts based on the 0.1-0.9scale.(1) Build a fuzzy judgment matrix.The pairwise importance evaluation of indicators i and j by expert k is represented by element    = (   ,    ,    ),    is the lower limit value of triangular fuzzy judgment,    is the median, and    is the upper limit value.Taking the average of fuzzy judgments from k experts to obtain the fuzzy judgment matrix A: (2) Calculate the fuzzy consistency matrix.Perform the following transformation operation on   in the fuzzy judgment matrix A to convert it into a fuzzy consistency matrix  1 . (2) Determining the consistency of the fuzzy consistency matrix  1 by formula  = (3) Calculate indicator weights.Calculate the comprehensive importance of the i-th evaluation criterion relative to all other criteria according to formula 3. Select its minimum value as the initial indicator weight.
The weight set can be obtained after normalization.

Entropy Weight Method for Determining Indicator Weights
The entropy weight method comprehensively evaluates the importance and information content of each indicator, which can more objectively determine the weight of indicators than the fuzzy analytic hierarchy process.Using the concept and solution method of entropy to determine the objective weight values of various indicators in the state evaluation of power transformers.According to formula 5, the entropy value   of each index is calculated, which indicates the probability of different values of   evaluation index i.
(5) The greater the information entropy, the lower the utility of the index value to distinguish different evaluation objects, and the lower the weight.The utility value of information is calculated according to the formula   = 1 −   .
Normalize the information utility value   of each indicator to obtain the weight   =   ∑   and weight set  2 of each indicator in the entropy weight method.

Determine the final weight using the combination weighting method
When determining the final indicator weight, the statistical rules of historical indicator data and expert experience should be considered, and a combination weighting method combining fuzzy AHP and entropy weighting should be adopted.Determine the final comprehensive weight according to formula 6.
In the formula,  1 is the weight calculated by fuzzy AHP for indicator i,  2 is the weight calculated by entropy weight method for indicator i, and   is the final weight determined by comprehensive weighting method for indicator i.

Calculation Method for Indicator Membership Degree
This article uses a cognitive model cloud model to describe the uncertainty of concepts.If U is a domain and a normal cloud,  ̃ is a concept in the domain U.If  ∈  is a random instantiation of concept  ̃ and satisfies ~(,  ′2 ),  ′ ~(,  2 ), then the certainty that x belongs to concept  ̃ is y [8].
(7)  is the mathematical expectation for cloud droplets, and entropy  is determined by the randomness and fuzziness of the concept.Super entropy  is the uncertainty of entropy .
( Use Python to draw these five state evaluation criteria cloud maps as shown in Figure 3. (2) Calculate the degree to which the measured values of the indicators deviate from the normal values (the degree of deterioration).The calculation formulas for positive and negative degradation state variables are shown in equations ( 8) and (9).
Standardize positive indicators for larger and better parameters,   represents the optimal value,   represents the limit value, and   represents the measured value.
Standardize negative indicators for smaller and better parameters,   represents the optimal value,   represents the limit value, and   represents the measured value.
(  =   ×  1 +  ℎ ×  2   is the electrical performance, ( e ) is the weight of the electrical performance index, (  ) is the membership matrix of the electrical performance index,  ℎ is the thermal performance, ( h ) is the weight of the thermal performance index, ( h ) is the membership matrix of the thermal performance index,  is the operating quality of the power transformer,  1 and  2 are the weights of the electrical performance and thermal performance.

The Example Analysis
To verify the accuracy and reliability of the quality status evaluation method designed by this method, historical monitoring data of several 10kV oil immersed transformers in a certain city were collected as the method training set, and current testing data of transformers were collected and analyzed as the testing set for method validation.

Determine Indicator Weights Using the Comprehensive Weighting Method
(1) AHP to calculate weight   : using triangular fuzzy numbers to record expert opinions and stratify the weights of quantitative indicators, the results are shown in table 2. (2) Calculating weight by entropy method, the entropy weight method weight of each index is calculated by the formula 5 and 6, normalize the calculation results of the entropy weight method to obtain objective weights, as shown in table 3. (3) The combination weighting method determines the final weight.Use formula 7 for each evaluation level to obtain the final weight, and the distribution of each weight is shown in Figure 4.

Calculating The Membership Degree of Indicators Based on Cloud Models
To verify the effectiveness of the method, multiple data were collected on the no-load loss, load loss, mean temperature rise of high-voltage winding, mean temperature rise of low-voltage winding, maximum phase reactance difference, and mean temperature rise of high voltage winding of one transformer over a period of time.Degradation was performed according to formulas 8 and 9, and the average degradation degree of each indicator is shown in table 4 Based on the comprehensive weight  and membership degree  obtained from the solution, the evaluation results   and  h .The evaluation results determined based on the maximum membership degree are shown in table 6.It can be seen that the overall operating quality of the transformer is normal, but due to the membership degree of 0.268 in "Attention" being greater than 0.1194 in "Excellent", the overall transformer is in a normal lower state.It can also be seen that the electrical performance of this transformer is normal, and the thermal performance is between "Normal" and "Attention".The followup monitoring focus for this transformer should be on thermal performance.The results are consistent with the actual detection results, verifying the accuracy of this method.

Summary and Conclusion
This article proposes a cloud model-based method for evaluating the operational status of power transformers.Compared with other methods, it can comprehensively consider the overall situation of transformers and evaluate the electrical and thermal performance status.It has fine evaluation, intuitiveness, and high accuracy.The conclusion is as follows: (1) This article evaluates the electrical and thermal performance of power transformers accurately and finely, as well as the specific degradation results, by considering the fuzzy analytic hierarchy process evaluation index system for performance construction.This method was used to predict 10 transformers that have been running for one month, with a prediction accuracy of 96.28%, which is 14.32% higher than the traditional 'prediction before diagnosis' method, achieving accurate comprehensive evaluation of the operation quality of power transformers.
(2) A standard cloud model for power transformer status was constructed based on actual situations.Using cloud theory algorithms to determine membership degrees after data degradation processing can effectively consider the randomness and uncertainty in the evaluation process, and make the evaluation results more intuitive and visible.
(3) The results have been verified in practice, which can provide accurate and intuitive opinions for power personnel to determine the operation quality and trend of power transformers, and provide a new method for the operation quality evaluation of power transformers.The subsequent research will improve the evaluation index system of transformer cloud models, add more transformer performance indicators, and further improve the accuracy of evaluation results.

Figure 1 .
Figure 1. the operation quality evaluation index system of power transformer.

Figure 2 .
Figure 2. the operation quality evaluation flow chart of power transformer.

Table 1 .
State cloud model parameters.
1) Generate a normally distributed random number   ′ with expected value of  and variance of  2 .Divide the domain [0,1] into 5 levels, with the center point 0.5 of the domain [0,1] as the ) According to formula 7, apply the cloud model method to calculate 5 possible states for n evaluation indicators, forming a membership matrix Y.  = ( e ) × (  )  ℎ = ( h ) × ( h ) (4) Calculate the performance evaluation results and transformer operation quality evaluation results based on the final weight and membership matrix.

Table 4 .
the deterioration degree of index.Substitute the degradation degree of each indicator in table 4 into Formula 8. Obtain the membership matrix of electrical and thermal performance for each indicator, as shown in table 5.