This application claims the priority benefit of China application serial no. 202010455962.1, filed on May 26, 2020. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification.
The disclosure relates to a transformer condition evaluation field, and in particular, relates to a transformer condition evaluation method combining a fuzzy analytic hierarchy process-decision making trial and evaluation laboratory method (FAHP-DEMATEL method) and a criteria importance through intercriteria correlation method (CRITIC method).
The safety of transformers is an important factor for the normal operation of a power grid. In order to prevent transformer failures, time for maintenance and repair of the transformers may be determined in a timely and reasonable manner, and the level of operation and maintenance of the power transformers may be improved, and these are important issues to be addressed. At present, among the several maintenance strategies which are currently available, the most advanced and cost-saving maintenance strategy is to rely on the condition evaluation close to the actual operation condition of the transformers, and that the maintenance time and plan may be accordingly selected.
Nevertheless, a transformer has a complex structure and exhibits a large number of condition quantities, and further, interference occurs among indicator quantities. As affected by the above-mentioned problems, it is difficult to achieve accurate evaluation of transformer conditions. When calculating the weights of evaluation indicators through a conventional method, interference among indicators is ignored. In order to reduce the evaluation deviation caused by the mutual influence among evaluation indicators, in the disclosure, the fuzzy analytic hierarchy process-decision making trial and evaluation laboratory method (FAHP-DEMATEL method) and the criteria importance through intercriteria correlation method (CRITIC method) are combined. The weights of the indicators are calculated from a subjective level and an objective level to reduce the interference. In this way, the evaluation result that is closest to the actual health conditions of the transformers may be accordingly obtained.
The disclosure aims to solve the technical problem of inaccurate final evaluation results caused by mutual interference among evaluation indicators and provides a transformer condition evaluation method combining a fuzzy analytic hierarchy process-decision making trial and evaluation laboratory method (FAHP-DEMATEL method) and a criteria importance through intercriteria correlation method (CRITIC method).
The technical solutions adopted by the disclosure includes the following.
The disclosure provides a transformer condition evaluation method combining a FAHP-DEMATEL method and a CRITIC method, and the method includes the following steps.
In step one, a plurality sets of condition quantities most relevant to a transformer health condition is selected, and a hierarchical indicator system is built.
In step two, a degree of influencing and a degree of being influenced among a plurality of indicators of the condition quantities are calculated through the DEMATEL method, and a weighted value of each of the indicators of the condition quantities are calculated through the FAHP method. A subjective weight of each of the indicators is calculated and obtained by combining the degree of influencing and the degree of being influenced among the indicators of the condition quantities. A plurality groups of transformers and corresponding indicators of condition quantities thereof are selected, and objective weights of the indicators are calculated and obtained through the CRITIC method.
In step three, an optimal weight is calculated according to the subjective weights of the indicators and the objective weights of the indicators, such that it is satisfied that a total difference value between a weight vector obtained through the optimal weight and a weight vector obtained through each of the methods is minimum.
In step four, a condition score is calculated layer by layer from an indicator layer to a factor layer for each of the transformers to be evaluated according to the hierarchical indicator system and the obtained optimal weight of the indicators, the condition score of each of the transformers is weighted and obtained, and an actual health condition of each of the transformers is determined through the condition score of each of the transformers.
In an embodiment of the disclosure, the step of building the hierarchical indicator system in step one specifically includes the following steps.
24 sets of the condition quantities most relevant to the transformer health condition are selected, and the hierarchical indicator system is built. The hierarchical indicator system is divided into three layers from top to bottom: a target layer, the factor layer, and the indicator layer. The target layer is a comprehensive condition of each of the transformers. 9 failure types influencing conditions of the transformers the most are selected for the factor layer, and a plurality of specific variables having most significant influencing factors in the failure types are selected for the indicator layer.
In an embodiment of the disclosure, in step one of building the target layer, the factor layer, and the indicator layer,
the target layer is the comprehensive condition of each of the transformers.
The factor layer includes: a winding failure, a core failure, arc discharge, partial discharge, oil discharge, insulation damping, insulation aging, insulation oil deterioration, and current loop overheating.
The indicator layer includes: dielectric loss of insulation oil, a water content in oil, an oil breakdown voltage, an insulation resistance absorption ratio, a polarization indicator, a volume resistivity H2, a core ground current, a core insulation resistance, C2H6, C2H4, a mutual difference of winding direct current resistance, CO, a relative gas production rate, CO2, a relative gas production rate, an initial value difference of winding short-circuit impedance, winding insulation dielectric loss, an initial value difference of winding capacitance, C2H2, a partial discharge amount, a gas content in oil, CH4, a neutral point oil flow static current, a furfural content, and a cardboard polymerization degree.
In an embodiment of the disclosure, the step of calculating and obtaining the subjective weights of the indicators in step two specifically includes the following steps.
The degree of influencing and the degree of being influenced among indicators are calculated for each of the indicators under the factor layer by using the DEMATEL method. A direct influence matrix A among the indicators is determined for each of the indicators under the factor layer by using an expert scoring method, and a variable a is an element in the direct influence matrix A.
Normalization is performed through
to obtain a matrix G, where n is a number of the indicators of the condition quantities under the factor layer. A comprehensive influence matrix is calculated through T=G(I−G)−1, where a variable t is an element in a comprehensive influence matrix T.
A degree of influencing fi and a degree of being influenced ei are determined through a formula
fi is a sum of row elements in the comprehensive influence matrix T, indicating a direct degree of influencing or an indirect degree of influencing of an indicator i of the condition quantities on an indicator j of the condition quantities, and ei is a sum of column elements in the comprehensive influence matrix T, indicating a value of the indicator of the condition quantities corresponding to each row influenced by other indicators of the condition quantities.
A condition quantity weighted value W1 is calculated through the FAHP method, a relationship matrix between the degree of influencing and the degree of being influenced is obtained through the DEMATEL method according to a formula d=fT*e, a diagonal line element is taken to form a vector of the degree of influencing d=fT*e of the indicators, the degree of influencing of the indicator i is calculated, and a corresponding weighted value W2 is obtained through a formula
The DEMATEL method and the FAHP method are combined, a weight W is obtained through a formula W=W12, and a comprehensive weight
In an embodiment of the disclosure, the step of calculating and obtaining the objective weights of the indicators in step two specifically includes the following steps.
The plurality of groups of the transformers and the condition quantities thereof are selected, standardization processing is performed on condition quantity data of each of the transformers, and a formula thereof is: standardized quantity=(this value−lowest value)/(highest value−lowest value).
Contrast intensity σj, conflict Rj, and an information amount Cj are calculated through formulas provided as follows:
The contrast intensity is a difference between a same indicator of different individuals, and a standard deviation is used to represent the contrast intensity σj.
An objective weighted value Wj is calculated and obtained through a formula provided as follows:
where i and j represent the condition quantities, n represents a total number of the condition quantities, and rij represents a correlation coefficient provided between the condition quantities i and j.
In an embodiment of the disclosure, the step of calculating the optimal weight in step three specifically includes the following steps.
The optimal weight is calculated according to the calculated and obtained subjective weights of the indicators and objective weights of the indicators based on a minimum-variance principle through a method of Lagrange multipliers for finding an extremum. The total difference value between the weight vector obtained through the optimal weight and the weight vector obtained through each of the methods is minimum. A method of calculating the optimal weight is provided as follow.
A weight vector of a jth indicator of a certain weight calculation method is Wj=(Wj1, Wj2, Wj3, . . . , Wjn), a most reasonable attribute weight vector under weighting of two weight calculation methods is W=(W1, W2, W3, . . . Wm), m and n are both numbers of indicators of a certain factor layer, and a single-target planning model is accordingly built:
A corresponding Lagrangian function is constructed, and the extremum is found:
The following may be derived:
when k=1 and 2, a system of equations formed by 3 unknowns and 3 equations is constructed, the two methods respectively account for a=(a1, a2) of the weighting after solving the system of equations, and that an optimal weight vector is accordingly obtained.
In an embodiment of the disclosure, the step of calculating the condition scores in step four specifically includes the following steps.
The condition scores are calculated on the indicator layer according to data values of the transformers to be evaluated, and a calculation expression for calculating the condition scores on the indicator layer is provided as follows:
where xi is the condition score of an indicator, when xi<0, let xi=0, when xi>1, take xi=1, z is an attention value, zn is an experimental value of this time, and zf is an initial value of the indicator of the condition quantity.
a condition score Xi of the factor layer is weighted and calculated by using known weights and the condition scores of the indicator layer. A fuzzy determination matrix of the factor layer is built by using the condition scores of the failure types of the factor layer, weighted values of the failure types of the factor layer are obtained according to the fuzzy determination matrix, the condition scores of the transformers are finally obtained through weighting and calculating.
The fuzzy determination matrix of the failure types is:
A calculation formula of an internal element rij is:
The disclosure is further described in detail in combination with accompanying FIGURES and embodiments, and the following FIGURES are provided.
To better illustrate the goal, technical solutions, and advantages of the disclosure, the following embodiments accompanied with drawings are provided so that the disclosure are further described in detail. It should be understood that the specific embodiments described herein serve to explain the disclosure merely and are not used to limit the disclosure.
As shown in
In step one, a plurality sets of condition quantities most relevant to a transformer health condition is selected, and a hierarchical indicator system is built.
In step two, a degree of influencing and a degree of being influenced among a plurality of indicators of the condition quantities are calculated through the DEMATEL method, and a weighted value of each of the indicators of the condition quantities are calculated through the FAHP method. A subjective weight of each of the indicators is calculated and obtained by combining the degree of influencing and the degree of being influenced among the indicators of the condition quantities. A plurality groups of transformers and corresponding indicators of condition quantities thereof are selected, and objective weights of the indicators are calculated and obtained through the CRITIC method.
In step three, an optimal weight is calculated according to the subjective weights of the indicators and the objective weights of the indicators, such that it is satisfied that a total difference value between a weight vector obtained through the optimal weight and a weight vector obtained through each of the methods is minimum.
In step four, a condition score is calculated layer by layer from an indicator layer to a factor layer for each of the transformers to be evaluated according to the hierarchical indicator system and the obtained optimal weight of the indicators, the condition score of each of the transformers is weighted and obtained, and an actual health condition of each of the transformers is determined through the condition score of each of the transformers.
In the disclosure, a condition evaluation model of the transformers is built first, and level standards are classified. Next, the DEMATEL method is combined with the FAHP method on a subjective level, the CRITIC method is adopted for calculating a weight on an objective level, and the optimal weight is calculated by adopting an optimal weigh calculation method. Finally, the condition scores are calculated layer by layer, final condition scores of the transformers are obtained, and conditions of the transformers may thus be accordingly evaluated.
With reference to Table 1, a transformer condition evaluation indicator system is built. With reference to Table 2, corresponding relationships between the health conditions and the condition scores of the transformers are provided. The indicator system is divided into three layers from top to bottom: a target layer, the factor layer, and the indicator layer. The target layer is a comprehensive condition of each of the transformers. 9 failure types influencing conditions of the transformers considerably are selected for the factor layer, and these failure types are: a winding failure, a core failure, arc discharge, partial discharge, oil discharge, insulation damping, insulation aging, insulation oil deterioration, current loop overheating. A plurality of specific variables having significant influencing factors in the failure types are selected for the indicator layer, and these specific variables are: dielectric loss of insulation oil, a water content in oil, an oil breakdown voltage, an insulation resistance absorption ratio, a polarization indicator, a volume resistivity H2, a core ground current, a core insulation resistance, C2H6, C2H4, a mutual difference of winding direct current resistance, CO, a relative gas production rate, CO2, a relative gas production rate, an initial value difference of winding short-circuit impedance, winding insulation dielectric loss, an initial value difference of winding capacitance, C2H2, a partial discharge amount, a gas content in oil, CH4, a neutral point oil flow static current, a furfural content, and a cardboard polymerization degree.
The degree of influencing and the degree of being influenced among indicators are calculated by using the DEMATEL method. Each factor is determined by using a Delphi method, and a direct influence matrix A (a variable a is an element in A) among the factors is determined. Normalization is performed through
to obtain a matrix G, and a comprehensive influence matrix is calculated through T=G(I−G)−1 (a variable t is an element in T). Finally, a degree of influencing fi and a degree of being influenced ei are determined through a formula
A weighted value W1 of each of the condition quantities is calculated through the FAHP method, as shown in Table 5.
A relationship matrix between the degree of influencing and the degree of being influenced is obtained through the DEMATEL method according to a formula d=fT*e. A diagonal line element is taken to form a vector of the degree of influencing d=fT*e of the indicators, and the degree of influencing of an indicator i is calculated. A corresponding weighted value W2 is obtained through a formula
Finally, the DEMATEL method and the FAHP method are combined. A weight W is obtained through a formula W=W12, and a comprehensive weight
With reference to Table 3, weights are assigned to 24 pieces of condition quantity data of four different groups of transformers through the CRITIC method.
The condition quantity data of each of the transformers is shown in Table 3. Data of Table 3 is standardized through “standardized quantity=(this value−lowest value)/(highest value−lowest value)”, and corresponding contrast intensity, conflict, an information amount, and an objective weight are calculated and obtained according to formulas (1), (2), and (3).
Table 4 shows the contrast intensity, conflict, information amounts, and objective weights calculated and obtained through the CRITIC method of 4 indicators under the winding failure.
A correlation coefficient rij is provided between the condition quantities i and j, and a calculation method is provided as follows:
After the weighted values of the indicators are calculated by using two methods, the optimal weight is calculated based on a minimum-variance principle through a method of Lagrange multipliers for finding an extremum. The total difference value between the weight vector obtained through the optimal weight and a weight vector obtained by each of the methods is minimum.
The condition scores are calculated on the indicator layer according to actual data values of the transformers, and a calculation expression of the condition scores is:
where xi is the condition score of an indicator, when xi<0 0, let xi=0, when xi>1, take xi=1, z is an attention value, zn is an experimental value of this time, and zf is an initial value of the indicator of the condition quantity.
Next, the condition scores of the factor layer are calculated by using known weights and the condition scores of the indicator layer, as shown in Table 6.
A fuzzy determination matrix of the factor layer is built by using the condition scores of the failure types of the factor layer, and weighted values of the failure types of the factor layer are shown in Table 7. The condition scores of the transformers are finally obtained through weighting and calculating. The actual health conditions of the transformers are determined through the condition scores of the transformers.
In view of the foregoing, through the transformer condition evaluation method combining the FAHP-DEMATEL method and the CRITIC method provided by the disclosure, interference between a target to be tested and the indicator values may be reduced, and therefore, stable evaluation results are provided, and incorrect diagnosis is prevented from occurring.
Effects produced by the disclosure includes the following.
(1) The evaluation method adopts the FAHP-DEMATEL method to calculate the weights of the indicators from a subjective level, adopts the CRITIC method to calculate the weights of the indicators from an objective level, and combines the two to obtain the optimal weight. In this way, the final weight calculation result is ensured to be close to the actual condition, and calculation deviation caused by human subjective factors is also lowered.
(2) Compared to a conventional evaluation method, through the evaluation method provided by the disclosure, when the weights of the indicators are calculated, errors of the final evaluation result caused by mutual interference among selected condition quantities are reduced. Therefore, an accurate and stable evaluation result is provided.
To make the aforementioned more comprehensible, several embodiments accompanied with drawings are described in detail as follows.
It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed embodiments without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the disclosure covers modifications and variations provided that they fall within the scope of the following claims and their equivalents.
Number | Date | Country | Kind |
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202010455962.1 | May 2020 | CN | national |