Old transformer equipment management method based on improved TOPSIS-grey correlation analysis
By using the improved TOPSIS-grey relational analysis method, a multi-dimensional evaluation index system was constructed. Combined with dynamic resolution coefficient and weighted Mahalanobis distance, the problems of resource waste and safety hazards in the management of old transformers were solved, and the accurate classification and decision-making of transformer status were realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-17
- Publication Date
- 2026-04-07
AI Technical Summary
The lack of unified standards for the management of old transformers in current technology leads to resource waste or safety hazards. Furthermore, existing assessment methods fail to comprehensively consider the degree of aging, operating status, and economic efficiency, making it difficult to scientifically classify them and formulate strategies for reuse or scrapping.
An improved TOPSIS-grey relational analysis method was adopted to construct a multi-dimensional evaluation index system. Combining dynamic resolution coefficient, weighted Mahalanobis distance and comprehensive grey relational degree, transformer condition assessment was carried out. Through mixed weight determination and data normalization processing, accurate condition classification and decision-making were achieved.
It significantly improves the accuracy and scientific nature of transformer condition assessment, enables refined management of old transformers, and provides reliable decisions on whether to reuse or scrap them.
Smart Images
Figure CN121808720A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power equipment management technology, and in particular to a management method for old transformer equipment based on improved TOPSIS-grey relational analysis, which is used to scientifically determine the age level of transformers and clarify their reuse or scrapping decisions. Background Technology
[0002] As a critical piece of equipment in the power system, the operating status of transformers directly affects the safety and stability of the power grid. With increasing service life, transformers gradually age, leading to problems such as insulation deterioration and increased failure rates. Currently, the management of aging transformers lacks unified standards, often relying on experience-based decisions, resulting in resource waste or safety hazards. While existing technologies include condition-based assessment methods, they do not comprehensively consider the degree of aging, operating status, and economic efficiency, making it difficult to scientifically classify and formulate strategies for reuse or scrapping. Therefore, a quantitative assessment and management method is urgently needed to achieve refined management of aging transformers. Existing assessment and management methods mostly employ simple weighted summation models, failing to fully consider the inherent correlation between indicators and the relative closeness of the assessment sample to the ideal state. The TOPSIS method combined with grey relational analysis can simultaneously assess equipment status from two dimensions: distance and shape similarity. However, traditional methods suffer from fixed resolution coefficients and inaccurate distance measurements. This invention introduces dynamic resolution coefficients, weighted Mahalanobis distance, and comprehensive grey relational analysis, significantly improving the accuracy of condition assessment and management. Summary of the Invention
[0003] The purpose of this invention is to provide a management method for old transformer equipment based on improved TOPSIS-grey relational analysis, which significantly improves the accuracy of transformer condition assessment and management.
[0004] To achieve the above objectives, the technical solution adopted by the present invention is a management method for aging transformer equipment based on improved TOPSIS-grey relational analysis, characterized by the following steps: 1) Construct an evaluation index system: covering three dimensions: operating status, technical indicators, and historical records, including seven core indicators such as service life, overhaul status, failure rate, insulation status, load rate, degree of technological obsolescence, and family-related defects; 2) Determining the mixed weights: The G1 method (subjective) and the entropy weight method (objective) are combined, and the comprehensive weights are calculated through the moment estimation theory, taking into account both expert experience and data characteristics; 3) Data normalization: The original indicator data is normalized and dimensionless to eliminate the influence of dimensions; 4) Improve grey relational analysis: Introduce segmented dynamic resolution coefficients to replace fixed values and improve the model's sensitivity to data differences; combine traditional grey relational degree (curve shape similarity) and grey absolute relational degree (data change rate similarity) to form a comprehensive grey relational degree. 5) Improved TOPSIS analysis: Weighted Mahalanobis distance is used instead of Euclidean distance to consider the correlation between indicators and more accurately measure the distance from the ideal state; the weighted Mahalanobis distance and comprehensive grey relational degree between each transformer and the positive and negative ideal states are calculated. 6) Calculation of overall state proximity: Combine distance proximity and correlation proximity to obtain the final overall state proximity. 7) Aging Classification and Decision-Making: Based on the comprehensive condition closeness, transformers are classified into three levels: Level 1 (reuse), Level 2 (reuse after repair), and Level 3 (scrapping); Level 1 is for reuse, Level 2 is for reuse after repair, and Level 3 is for scrapping; the comprehensive scoring formula is as follows: Data normalization: (1) In the formula, This represents the normalized value of the transformer, ranging from [0, 1]. This represents the original value of the i-th transformer on the j-th index; This represents the maximum value of the j-th index among all transformers; The evaluation objects are: transformers T1, T2, T3; j represents the evaluation indicators: X1, X2, ..., X7; X1, X2, ..., X7 correspond to 7 core indicators: service life, overhaul status, failure rate, insulation condition, load rate, degree of technological backwardness, and family-related defects. This represents the minimum value of the j-th index in the transformer; Dynamic resolution coefficient: (2) In the formula, This represents the dynamic resolution coefficient, whose value is between (0,1). The greater the data dispersion, the smaller the value, and the stronger the discrimination ability. This represents the standard deviation of the j-th indicator data sequence, measuring the degree of dispersion of the data; This represents the average difference, which is the average of the differences between each transformer's index value and the ideal solution. This represents the absolute difference between the data sequence of the j-th index and the ideal solution sequence; This represents an adjustment parameter, usually a small positive number (such as 0.001) to prevent the denominator from being zero; n represents the number of objects being evaluated, i.e., the total number of transformers. This represents the overall state closeness of the i-th transformer, i.e., the final evaluation score, which reflects the overall state level of the transformer. Overall grey relational degree: (3) In the formula, The overall grey relational degree of the i-th transformer is represented by {+ indicates positive (good), - indicates negative (poor)}; This represents the weighting coefficient, used to balance the importance of traditional correlation and absolute correlation. Its value ranges from [0,1], and a value of 0.5 is recommended. The traditional grey relational degree of the i-th transformer (+ indicates positive, - indicates negative) reflects the proximity of the curve shapes; The gray absolute correlation degree of the i-th transformer (+ indicates positive, - indicates negative) reflects the similarity of the data change rate.
[0005] Weighted Mahalanobis distance: (4) In the formula, This represents the weighted Mahalanobis distance between the i-th transformer and the ideal solution (positive or negative); Represents the normalized index vector of the i-th transformer; T represents the ideal solution vector (positive or negative ideal solution); T represents the matrix transpose operation; W represents the diagonal matrix composed of the combined weights of each index. This represents the inverse matrix of the covariance matrix of the evaluation indicators, used to consider the correlation structure between indicators; Overall similarity: (5) In the formula, This represents the overall state closeness of the i-th transformer, i.e., the final score. The closer it is to 1, the better the state. This represents the weighting coefficient, used to balance the importance of traditional correlation and absolute correlation. Its value ranges from [0,1], and a value of 0.5 is recommended. This represents the proximity of the i-th transformer to the "worst-case" state. We want it to be as large as possible, calculated based on weighted Mahalanobis distance. Let represent the proximity of the i-th transformer to the "optimal state". We want it to be as small as possible, calculated based on weighted Mahalanobis distance. The correlation proximity of the i-th transformer is the similarity of the curve to the "best state". We hope that it is as large as possible. It is calculated based on the comprehensive grey relational degree. The correlation proximity of the i-th transformer is the similarity of the curve to the "worst state". We hope that it is as small as possible, and it is calculated based on the comprehensive grey relational degree. Grading standards: Level 1 (Reuse): A i ≥0.6 indicates the equipment is in good condition and can continue to be used directly; This represents the overall state closeness of the i-th transformer, i.e., the final evaluation score, which reflects the overall state level of the transformer. Level 2 (Reuse after repair): 0.40≤A i <0.6, the equipment is in fair condition and needs maintenance before use; Level 3 (Scrapped): A i <0.40, the equipment is in poor condition and it is recommended to scrap and replace it.
[0006] This invention upgrades transformer condition assessment from a simple weighted summation to a multi-dimensional, dynamically adaptive, and precise assessment by introducing an improved TOPSIS-grey relational analysis model. This method not only inherits the comprehensiveness of the original patent's indicator system but also significantly enhances the scientific rigor of condition classification and the reliability of decision-making through advanced mathematical tools, providing strong technical support for the refined management of aging transformers.
[0007] The beneficial effects of this invention are: by introducing dynamic resolution coefficient, weighted Mahalanobis distance and comprehensive grey relational degree, this invention significantly improves the accuracy of state assessment and management, and realizes accurate classification and decision-making of transformer state. Attached Figure Description
[0008] Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0009] like Figure 1 As shown, Evaluation indicators and mixed weights Indicator system: The original 7 indicators are retained, and their positive / negative attributes are clarified.
[0010] Mixed weights: Subjective weighting: The G1 method was used, with experts ranking the importance of the indicators.
[0011] Objective weights: The entropy weight method is used, and the weights are calculated based on the actual operating data of the transformer.
[0012] Comprehensive weight: Combining subjective and objective weights through the moment estimation theory. Example value: W=[0.22,0.18,0.14,0.18,0.09,0.09,0.10]; W represents the diagonal matrix composed of the comprehensive weights of the 7 evaluation indicators.
[0013] Improve the TOPSIS grey relational analysis process 1. Data normalization: process the original data matrix according to formula (1). 2. Determine the positive and negative ideal solutions: , This represents the positive ideal solution vector, the optimal value across all evaluation metrics; represents the negative ideal solution vector, the worst value across all evaluation metrics; , , This represents the specific value of the positive and negative ideal solution vectors on the j-th index; j represents the index of the evaluation index, used to traverse each evaluation index; m represents the total number of evaluation indexes. Calculate the dynamic resolution coefficient (Equation 2) Calculate the comprehensive grey relational degree (Equation 3): combine the traditional relational degree and the absolute relational degree (α can be taken as 0.5).
[0014] Calculate the weighted Mahalanobis distance (Equation 4): Consider the covariance structure and weights of the indicators.
[0015] Calculate the overall state proximity (Equation 5): Overall distance and associated information (a can be taken as 0.5).
[0016] Hierarchical Management and Decision-Making Level 1 (Reuse): Ai≥0.6, the equipment is in good condition and can be used directly.
[0017] Level 2 (Reuse after repair): 0.40≤Ai<0.6, the equipment is in fair condition and needs to be repaired before use.
[0018] Level 3 (Scrapped): Ai < 0.40, the equipment is in poor condition, and scrapping and replacement are recommended.
[0019] To verify the effectiveness and practicality of this method (a management method for old transformer equipment based on improved TOPSIS-grey relational analysis), three old transformers in operation of a power grid company were selected as evaluation objects for case analysis.
[0020] Step 1: Data Collection and Indicator Determination Raw data for three transformers (denoted as T1, T2, and T3) across seven evaluation indicators were collected, as shown in Table 1. Among them, service life, failure rate, load rate, and number of technologically outdated items are negative indicators (the smaller the value, the better); overhaul status, insulation condition, and family defect score are positive indicators (the larger the value, the better).
[0021] Table 1 Raw Data of Transformer Evaluation Indicators Step 2: Data Normalization Processing The original data in Table 1 is normalized according to formula (2) and transformed to the interval [0,1] to obtain a normalized matrix. For example, for the reverse indicator "service life (X1)", the maximum value is 35 years and the minimum value is 20 years. Then the normalized value of T1 is (35-35) / (35-20)=0; and T2 is (35-20) / (35-20)=1. For the positive indicator "major repair status (X2)", the normalized value of T1 is (30-30) / (80-30)=0; and T2 is (80-30) / (80-30)=1.
[0022] Normalized evaluation matrix Step 3: Determine the positive and negative ideal solutions According to formula (3), the positive ideal solution is determined from the normalized matrix. (Optimal values for all indicators) and negative ideal solutions (Worst value for all indicators).
[0023] Positive Ideal Solution :[1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000] Negative ideal solution :[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000] Step 4: Calculate the overall grey relational degree Calculate the comprehensive grey relational coefficient: Calculate the correlation coefficient between each indicator of each transformer and the positive and negative ideal solutions. In this example, for the sake of simplification, the resolution coefficient ρ = 0.5 is taken. The correlation coefficient reflects the degree of closeness between the transformer under evaluation and the ideal state for a single indicator. The larger the coefficient, the closer the performance is to the ideal state for that indicator. According to formula (3), calculate the comprehensive grey relational degree between each transformer and the positive and negative ideal solutions. and For simplicity, we assume α=1 here, meaning we only use traditional grey relational analysis.
[0024] Comprehensive grey relational calculation results | Transformer | (Compared with the ideal solution) | (Compared to negative ideal solution) || T1 | 0.333 | 1.000 || T2 | 1.000 | 0.333 || T3 | 0.634 | 0.554 | Step 5: Calculate the weighted Mahalanobis distance First, determine the indicator weights: using the hybrid weighting method described in this invention, assume the final weights are as follows: W=[0.22,0.18,0.14,0.18,0.09,0.09,0.10].
[0025] Calculate the weighted Mahalanobis distance: According to formula (4), calculate the weighted Mahalanobis distance between each transformer and the positive and negative ideal solutions. and .
[0026] Weighted Mahalanobis distance calculation results | Transformer | (Compared with the ideal solution) | (With negative ideal solution) || T1 | 2.215 | 0.000 || T2 | 0.000 | 2.215 || T3 | 1.104 | 1.021 | Calculate the overall state closeness According to formula (5), calculate the overall state closeness A of each transformer. i Here, a weight of 0.5 is used to give equal importance to proximity and relevance.
[0027] Overall state relevance and final decision Summary of Implementation Examples and Strategy Implementation Transformer T1: The overall proximity score is only 0.125, far below the scrapping threshold of 0.40. All its indicators are close to the worst-case scenario (especially its long service life, high failure rate, and prominent risk of family-related defects), and the assessment result is Level III. Implementation strategy: This transformer should be immediately included in this year's technical renovation and overhaul project for scrapping, and the new equipment procurement process should be initiated to prevent major operational risks.
[0028] Transformer T2: The overall closeness score is as high as 0.875, indicating that its overall condition is very close to ideal. The assessment result is Level 1. Implementation strategy: It can continue to operate safely, be included in the routine inspection and preventive testing plan, require no additional maintenance, and achieve full utilization of the asset.
[0029] Transformer T3: The overall proximity score is 0.507, placing it in the second-level range of "reusing existing equipment after repair". Analysis of its data shows that the insulation condition and overhaul status are acceptable, but the load rate is relatively high and there are slight technological shortcomings. The assessment result is level two. Implementation strategy: A targeted repair plan should be developed within one month (e.g., replacing or upgrading outdated components, strengthening local insulation), and repairs should be completed within three months. A reassessment is required after repair; if the score improves to above 0.60, it can be upgraded to level one management.
Claims
1. A management method for aging transformer equipment based on improved TOPSIS-grey relational analysis, characterized in that... Includes the following steps: 1) Construct an evaluation index system: covering three dimensions: operating status, technical indicators, and historical records, including seven core indicators such as service life, overhaul status, failure rate, insulation status, load rate, degree of technological obsolescence, and family-related defects; 2) Determining the mixed weights: The G1 method and the entropy weight method are combined, and the comprehensive weights are calculated through the moment estimation theory, taking into account both expert experience and data characteristics; 3) Data normalization: The original indicator data is normalized and dimensionless to eliminate the influence of dimensions; 4) Improve grey relational analysis: Introduce segmented dynamic resolution coefficients to replace fixed values and improve the model's sensitivity to data differences; combine traditional grey relational degree and grey absolute relational degree to form a comprehensive grey relational degree. 5) Improved TOPSIS analysis: Use weighted Mahalanobis distance instead of Euclidean distance, consider the correlation between indicators, and more accurately measure the distance from the ideal state; Calculate the weighted Mahalanobis distance and the overall grey relational degree between each transformer and the positive and negative ideal states; 6) Calculation of overall state proximity: Combine distance proximity and correlation proximity to obtain the final overall state proximity. 7) Aging Classification and Decision-Making: Based on the comprehensive condition proximity, transformers are classified into three levels: Level 1 (reuse), Level 2 (reuse after repair), and Level 3 (scrapping). The comprehensive scoring formula is as follows: Data normalization: （1） In the formula, This represents the normalized value of the transformer, ranging from [0, 1]. This represents the original value of the i-th transformer on the j-th index; This represents the maximum value of the j-th index among all transformers; The evaluation objects are: transformers T1, T2, T3; j represents the evaluation indicators: X1, X2, ..., X7; X1, X2, ..., X7 correspond to 7 core indicators: service life, overhaul status, failure rate, insulation condition, load rate, degree of technological backwardness, and family-related defects. This represents the minimum value of the j-th index in the transformer; Dynamic resolution coefficient: （2） In the formula, This represents the dynamic resolution coefficient, whose value is between (0,1). The greater the data dispersion, the smaller the value, and the stronger the discrimination ability. This represents the standard deviation of the j-th indicator data sequence, measuring the degree of dispersion of the data; This represents the average difference, which is the average of the differences between each transformer's index value and the ideal solution. This represents the absolute difference between the data sequence of the j-th index and the ideal solution sequence; This represents an adjustment parameter, usually a small positive number to prevent the denominator from being zero; n represents the number of objects being evaluated, i.e., the total number of transformers. This represents the overall state closeness of the i-th transformer, i.e., the final evaluation score, which reflects the overall state level of the transformer. Overall grey relational degree: （3） In the formula, This represents the overall grey relational degree of the i-th transformer; This represents the weighting coefficient, used to balance the importance of traditional correlation and absolute correlation. Its value ranges from [0,1], and a value of 0.5 is recommended. The traditional grey relational degree of the i-th transformer reflects the proximity of the curve shapes; The gray absolute correlation degree of the i-th transformer reflects the similarity of the data change rate. Weighted Mahalanobis distance: （4） In the formula, This represents the weighted Mahalanobis distance between the i-th transformer and the ideal solution; Represents the normalized index vector of the i-th transformer; T represents the ideal solution vector; T represents the matrix transpose operation; W represents the diagonal matrix composed of the combined weights of each index. This represents the inverse matrix of the covariance matrix of the evaluation indicators, used to consider the correlation structure between indicators; Overall similarity: （5） In the formula, This represents the overall state closeness of the i-th transformer, i.e., the final score. The closer it is to 1, the better the state. This represents the weighting coefficient, used to balance the importance of traditional correlation and absolute correlation. Its value ranges from [0,1], and a value of 0.5 is recommended. This represents the proximity of the i-th transformer to the "worst-case" state. The larger it is, the better. It is calculated based on the weighted Mahalanobis distance. Let represent the proximity of the i-th transformer to the "optimal state". We want it to be as small as possible, calculated based on weighted Mahalanobis distance. This represents the proximity of the i-th transformer; the larger it is, the better. It is calculated based on the comprehensive grey relational analysis. The correlation proximity of the i-th transformer is the similarity to the curve of the "worst state". The smaller it is, the better. It is calculated based on the comprehensive grey relational degree. Grading standards: Level 1: A i ≥0.6 indicates the equipment is in good condition and can continue to be used directly; This represents the overall state closeness of the i-th transformer, i.e., the final evaluation score, which reflects the overall state level of the transformer. Level 2: 0.40≤A i <0.6, the equipment is in fair condition and needs maintenance before use; Level 3: A i <0.40, the equipment is in poor condition and it is recommended to scrap and replace it.