CN111913065A - Bayesian network transformer state evaluation method based on Pair-Copula - Google Patents

Bayesian network transformer state evaluation method based on Pair-Copula Download PDF

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CN111913065A
CN111913065A CN202010691097.0A CN202010691097A CN111913065A CN 111913065 A CN111913065 A CN 111913065A CN 202010691097 A CN202010691097 A CN 202010691097A CN 111913065 A CN111913065 A CN 111913065A
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copula
transformer
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于婷
杨俊杰
吕思潼
林锦晨
耿传平
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Shanghai Dianji University
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention relates to a Bayesian network transformer state evaluation method based on Pair-Copula, which comprises the following steps: 1) collecting sample set data of a transformer to be evaluated, wherein the sample set data comprises 6 characteristic variables of voltage, current, active power, reactive power, transformer temperature and environment temperature, and correspondingly constructing a characteristic variable set; 2) selecting an optimal Copula function according to the Pair-Copula structure to describe the correlation between the transformer temperature and other characteristic variables, and calculating to obtain a rank correlation coefficient corresponding to the optimal Copula function; 3) and constructing a Bayesian network model, namely a PCBN model, of the transformer temperature based on Pair-Copula, acquiring a joint density function of the PCBN model, and finishing the state evaluation of the transformer. Compared with the prior art, the method has the advantages of continuity, high flexibility, accurate quantitative description correlation and the like.

Description

Bayesian network transformer state evaluation method based on Pair-Copula
Technical Field
The invention relates to the technical field of transformer fault detection, in particular to a Bayesian network transformer state evaluation method based on Pair-Copula.
Background
The power supply reliability of a power system directly affects national electrical safety, especially, the safe operation of electrical equipment is guaranteed, and taking a transformer as an example, because the transformer has complex and various fault reasons and fault characteristics, accurate judgment on the operation state and fault type of the transformer is difficult to realize. Therefore, how to effectively evaluate the state of the power system has important practical significance for the power system.
Before the on-line monitoring mode appears, the state monitoring of important high-voltage electrical equipment at home and abroad mainly adopts a scheme of regular power failure maintenance, namely, the whole power failure maintenance is carried out on the electrical equipment at fixed intervals. The state evaluation of the transformer needs to comprehensively utilize all state information such as operation conditions, temperature, electromagnetism and the like, the principle is to process, classify and evaluate the collected equipment state information, and the later equipment maintenance is technically supported by the method. In the state evaluation, the fault prediction alarm of the transformer is most widely applied. The transformer fault on-line monitoring mainly predicts the state of a certain fault according to the symptom information of the fault, wherein the symptom information of the fault comprises temperature, current and voltage, gas content and the like. The fault early warning system mainly carries out early warning and alarming on equipment which is in fault germination or has failed according to collected fault symptom information, reports fault positions, judges the state grade of the equipment as fast as possible and carries out corresponding maintenance schemes. At present, the on-line monitoring of the transformer state has important research and application values. The method is applied to the state evaluation of the electrical equipment, so that the working cost can be saved, the service life of the equipment can be prolonged, and the operation reliability of the power system can be greatly improved.
In the existing state evaluation technology, a BP neural network classifier is constructed to identify electrical equipment, meanwhile, a relative temperature difference discrimination method is adopted to diagnose faults of the equipment, or a Bayesian evaluation model is introduced, so that the problem that the operation state of the electrical equipment is judged by adopting a maximum membership function, and the application of Bayesian network and BP neural network algorithms is successful, but the accuracy is not high enough is solved.
In the existing method, while electrical equipment is identified by constructing a BP neural network classifier, a relative temperature difference discrimination method is adopted to diagnose the fault of the equipment, but the method adopted for the equipment with smaller temperature difference can cause inaccurate evaluation result; the Bayes evaluation model is introduced, the maximum membership function is used for judging the running state of the electrical equipment, and the method is added with the correction model but the processing data is more complex; the other method is a thermal fault discrimination method based on the shell temperature gradient, which can diagnose the GIS contact overheating fault, but has the defect of inaccurate discrimination.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and reduce the inspection burden of workers, and provides a Bayesian network transformer state evaluation method based on Pair-Copula, which establishes a state evaluation model and performs more accurate correlation analysis on the measured temperature, so that the method can not only give an alarm in the early stage of the failure of the power equipment, but also perform failure diagnosis in time when a certain failure symptom occurs, and protect the safe operation of the equipment.
The purpose of the invention can be realized by the following technical scheme:
a Bayesian network transformer state evaluation method based on Pair-Copula comprises the following steps:
1) collecting sample set data of a transformer to be evaluated, wherein the sample set data comprises 6 characteristic variables of voltage, current, active power, reactive power, transformer temperature and environment temperature, and correspondingly constructing a characteristic variable set;
2) selecting an optimal Copula function according to the Pair-Copula structure to describe the correlation between the transformer temperature and other characteristic variables, and calculating to obtain a rank correlation coefficient corresponding to the optimal Copula function;
3) and constructing a Bayesian network model, namely a PCBN model, of the transformer temperature based on Pair-Copula, acquiring a joint density function of the PCBN model, and finishing the state evaluation of the transformer.
In the step 2), the Copula function comprises a normal Copula function, a t-Copula function, a Gumbel function, a Clayton function and a Frank function, and the normal Copula function and the t-Copula function with symmetrical tail correlation are selected to form a Pair-Copula structure.
In the step 2), an optimal Copula function in a Pair-Copula structure is selected according to the Euclidean distance squared minimum by introducing an empirical Copula function.
The empirical Copula function Cn(u, v) is defined as:
Figure BDA0002589401460000021
Figure BDA0002589401460000031
wherein F (X) and G (Y) are empirical distribution functions of random vectors X and Y, respectively, u, v ∈ [0,1 ∈ [ ]]Parameters of empirical Copula function, I[·]Is an indicative function of empirical Copula, xi、yiI-th observation point data representing random vectors X and Y, n being the total number of observation points.
The expression of the squared euclidean distance is as follows:
Figure BDA0002589401460000032
wherein the content of the first and second substances,
Figure BDA0002589401460000033
is the squared euclidean distance corresponding to the dyadic normal Copula function,
Figure BDA0002589401460000034
is the squared Euclidean distance, C, corresponding to a binary t-Copula functionGa(ui,vi)、Ct(ui,vi)、Cn(ui,vi) Respectively representing a binary normal Copula function, a binary t-Copula function and a channelExamine Copula function.
In the step 2), the rank correlation coefficient includes a Kendall rank correlation coefficient τ for reflecting whether the variation trends among the characteristic variables are correlated and consistentkAnd Spearman rank correlation coefficient rho reflecting the difference multiple of the probability of consistent and inconsistent changes between feature variabless。
The step 3) specifically comprises the following steps:
31) constructing a Bayesian network structure;
32) substituting the characteristic variables into the Bayesian network structure chart, and performing parameter estimation by combining a D-vine structure;
33) determining a Copula type and parameters of a condition relation corresponding to each edge in the Bayesian network structure;
34) and forming a complete PCBN model, and quantitatively describing the weight relation among the characteristic variables according to the joint density function, thereby providing a correction basis for subsequent transformer state evaluation.
The step 31) specifically comprises the following steps:
311) constructing a completely undirected graph D with 15 edges according to 6 characteristic variables of voltage, current, active power, reactive power, transformer temperature and ambient temperatureF；
312) Expressing the correlation measure among the characteristic variables according to Kendall rank correlation coefficient and Spearman rank correlation coefficient, and completely undirected graph DFTransition to preliminary undirected graph DU；
313) Determining a preliminary undirected graph D according to the magnitude relation of Kendall rank correlation coefficient sums in the correlation measureUIn (1) to form a chain diagram DLAnd finishing the construction of the Bayesian network structure.
Said step 312), the mismatch (τ) is determinedk+ρs) The edge corresponding to the correlation measure data corresponding to the/2 is more than or equal to 0.6 and is from a completely undirected graph DFRemoving to form a preliminary undirected graph DU。
In the step 313), the Kendall rank correlation coefficient and the larger characteristic variable are used as the pointed main variables.
Compared with the prior art, the invention has the following advantages:
aiming at a transformer equipment operation system with a large number of uncertain factors, the invention adopts a Bayesian network model based on a Pair-Copula function by combining the advantages of continuity of a Bayesian network and high flexibility of the Copula function, can effectively and accurately quantitatively describe the correlation between various parameters and variables in the system, and tests show that the PCBN model can intuitively reflect the correlation of transformer parameters, obtain parameter correlation analysis related to the temperature of a transformer, construct a complete correlation reasoning model, establish a joint density function conforming to equipment conditions, and provide a correction basis for subsequent state evaluation.
Drawings
FIG. 1 is a flow chart of PCBN model construction.
Fig. 2 is a completely undirected graph.
Fig. 3 is a flow chart of bayesian network structure determination.
Fig. 4 is a diagram of a transformer temperature Pair-Copula bayes network.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
The invention provides a Bayesian network transformer state evaluation method based on Pair-Copula, a Copula function has higher flexibility and can construct correlation among variables, the Bayesian network is widely applied to uncertainty system modeling and reasoning and is a graph network model for describing uncertainty causal relations among the variables, partial state parameters of the transformer are subjected to correlation analysis through the Pair-Copula model, a PCBN structure model which is more in line with the actual operation state of equipment is established to obtain accurate quantitative description of the correlation among the variables, and the subsequent analysis evaluation of the operation state of the transformer is realized.
Introduction of related art:
1.1 Pair-Copula model
In 1959, Sklar proposed Copula theory, which combines the edge distribution of d variables with a Copula function describing the correlation of the variablesAnd forming an integral multi-variable joint distribution function. If X is ═ X1,X2,···,Xd) Is a d-dimensional random variable, F1(x1),F2(x2),···,Fd(xd) Is [0,1 ]]The edge distribution function over the interval, the joint distribution function of X being F (X)1,x2,···,xd) With the Copula function parameter k, there is a d-dimensional Copula function C satisfying the following formula:
F(x1,x2,···,xd)＝Cκ(F1(x1),F2(x2),···,Fd(xd))
the Copula function contains many distribution families, and the distribution function of a typical Copula function is shown in table 1.
TABLE 1 typical Copula function
Figure BDA0002589401460000051
The elliptic family Copula is more convenient for simulation experiments than the archimedes family, and has symmetrical tail correlation, so that the operation is performed by adopting a binary normal Copula function and a binary t-Copula function in the elliptic family Copula function in the example.
The distribution function of the binary normal Copula function is:
Figure BDA0002589401460000052
the normal Copula density function is:
Figure BDA0002589401460000053
wherein, kappa E [ -1,1]In order to be a parameter of the correlation,
Figure BDA0002589401460000054
is a one-dimensional standard normal distribution function,
Figure BDA0002589401460000055
is an inverse function.
The distribution function of the binary t-Copula function is:
Figure BDA0002589401460000056
the t-Copula density function is:
Figure BDA0002589401460000061
wherein κ and μ denote a correlation parameter and a degree of freedom parameter, respectively, Tμ(. cndot.) is a unitary t-distribution function,
Figure BDA0002589401460000062
is an inverse function.
In order to better describe a related structure with complex fault factors of electrical equipment and establish a model easy to understand, the Pair-Copula structure is selected. And the Pair-Copula structure (PCC) is not unique, so the flexibility of the model is higher than that of the Copula function. In a multivariable correlation structure, the PCC can more flexibly represent the dependency relationship of the variables while maintaining the dependency relationship between the variables, and the defects of the traditional Copula function in this respect are overcome.
1.2 empirical Copula function
The generation of the Pair-Copula structure is used for selecting an optimal Copula function, aiming at each group of Pair-Copula functions, an empirical Copula function is introduced, and Euclidean distance calculation is carried out on binary normal Copula and binary t-Copula, so that the advantages and the disadvantages of the two methods are judged, and the criterion is that the smaller the Euclidean distance square value is, the higher the model fitting degree of the group of Pair-Copula functions is. The empirical Copula function is defined as follows:
Figure BDA0002589401460000063
whereinF (X) and G (Y) represent empirical distribution functions of random vectors X and Y, respectively, u, v ∈ [0,1 ∈]；I[·]An illustrative function of empirical Copula is shown. And satisfies the following conditions:
Figure BDA0002589401460000064
let binary normal Copula be CGaThe binary t-Copula is CtExperience with Copula as CnThen the euclidean distance squared formula is:
Figure BDA0002589401460000065
1.3 rank correlation coefficient
The Copula function is connected with two or more correlation edge distribution functions, correlation coefficients are required to be introduced for measuring the correlation degree between variables, and Kendall rank correlation coefficients and Spearman correlation coefficients are adopted for evaluating the correlation structure between the variables.
The Kendall rank correlation coefficient calculation formula is as follows:
τ＝P{(X1-X2)(Y1-Y2)＞0}-P{(X1-X2)(Y1-Y2)＜0}
let f (X) and g (Y) be edge distribution functions of the continuous random variables X and Y, respectively, C (u, v) is a Copula function, and let u ═ f (X), v ═ g (Y), and τ can be expressed as:
Figure BDA0002589401460000071
spearman rank correlation coefficient rho can be obtained according to Copula functionsExpressed as:
Figure BDA0002589401460000072
1.4 Bayesian networks
The Bayesian network theory (BN) is an extension of the Bayes method, and Judea Pearl proposes the theory in 1988, and is one of the most effective theoretical models for the uncertain knowledge expression and reasoning field. For the research on complex systems such as medical diagnosis, power equipment fault diagnosis and the like, the theory can effectively analyze faults caused by a plurality of uncertain factors. The Bayesian network is composed of nodes, directed links and conditional probability tables represented by the nodes, and a Directed Acyclic Graph (DAG) construction model is used for reflecting the dependence and independence relation among different variables. The nodes represent random variables in the model, directed connecting lines represent causal dependence among the nodes, and the node probability table is used for representing the degree of interaction among the variables.
The Bayesian network can carry out forward reasoning under the condition that the prior probability is known so as to obtain the corresponding posterior probability, and conversely, the Bayesian network carries out reverse reasoning under the condition that the posterior probability is known so as to obtain the prior probability corresponding to the prior probability. This is the forward and backward reasoning of the bayesian network. Usually, when a multivariate analysis model is constructed, in order to improve the efficiency of the algorithm, multivariate normality assumptions are often adopted, but the method has the defect that all variables cannot meet normal distribution conditions, so that the Bayesian network cannot realize the description of the causal relationship of the nonlinear structure, and the method realizes the description of the causal relationship of the nonlinear structure by combining a Pair-Copula model and the Bayesian network.
1.5 Bayesian network model based on Pair-Copula (PCBN)
The Bayesian network has the advantage of continuity, the Copula function has high flexibility, the PCBN combines the advantages of the two models and fuses, and a more accurate and convenient model is provided for selection of parameters and variables in state analysis of a system with a large number of uncertain factors.
For a Directed Acyclic Graph (DAG), let D ═ V, E, V denote nodes, E denote directed edges, and the moral graph of D is Dm. For a certain node V ∈ V, the association relationship between the nodes is shown in table 2.
TABLE 2 directed acyclic graph node association relation table
Figure BDA0002589401460000081
Let P be RdThe probability measure above, d ═ V |, X ═ X1,···,XdIs a d-dimensional random variable with a probability distribution P. For any V ∈ V, the probability distribution P satisfies the following formula:
Xv⊥Xnd(v)\pa(v)|Xpa(v)
p has a D-local Markov property. If for any pairwise disjoint sets
Figure BDA0002589401460000086
And satisfies the following conditions:
Figure BDA0002589401460000082
p has a global D-markov attribute.
BN adopts a joint distribution probability decomposition mode to remove the conditional independence of variables. Let f (-) be a probability density function of P, knowing Xpa(v)＝xpa(v)，XvIs used as the conditional probability density function ofv|pa(v)(·|xpa(v)) And (4) showing. When P satisfies the D-Markov property, the D-recursion factor is:
Figure BDA0002589401460000083
PCBN model introduces Pair-Copula function Cv,w|pa(v)V ∈ V, w ∈ pa (V), and x ═ x (x)v)v∈V∈RdThe probability density function f (-) of P is further decomposed to obtain a Pair-Copula Bayesian network model (PCBN):
Figure BDA0002589401460000084
wherein pa (v; w) satisfies:
Figure BDA0002589401460000085
examples
In the actual operation process of the transformer, the temperature of the transformer is used as one of indexes for checking the health of the transformer, whether the operation of the transformer is in a normal state or not can be visually reflected, and in the state evaluation process, the temperature of the transformer is influenced by components of equipment or ambient factors, so that the measured temperature has deviation. In order to more accurately analyze the relation between the temperature and the state detection of the transformer, the invention collects 6 characteristic quantities of the voltage, the current, the active power, the reactive power, the node temperature of the transformer and the ambient temperature of the SF 1025000/110 transformer from an SCADA system, and a data set in a data sample expresses real-time data generated every 10min within one month.
1. Selecting an optimal Copula function
In the example, in order to select the optimal Copula function among all characteristic values, the binary normal Copula function and the binary t-Copula function are compared and analyzed by an empirical Copula method, wherein Kendall reflects whether the variation trends among random variables are related and consistent, Spearman reflects the multiple of the probability difference between the variation consistency and the variation inconsistency among the random variables, parameter estimation is respectively carried out by a maximum likelihood estimation method, and the result pair is shown in a table 3.
TABLE 3 estimation of random variables parameters
Figure BDA0002589401460000091
By calculating the squared euclidean distance between both binary normal Copula and binary t-Copula and the empirical Copula function.
2. PCBN model establishment
As shown in fig. 1, the specific steps of establishing the PCBN model are as follows:
step 1: constructing a characteristic variable X ═ X (X) of the temperature of the plant1,···,Xn) And determining an edge distribution function by using a kernel density estimation method and establishing a Pair-Copula function.
Step 2: and determining the optimal solution in all Pair-Copula functions by using the empirical Copula function, and marking the finally selected Copula type and parameters. Calculating Kendall rank correlation coefficient tau of each Pair of Pair-Copula functionsi,jAnd Spearman rank correlation coefficient ρi,j. Comparing the two correlation measures to find a set of characteristic variables with higher correlation, so that the directed acyclic graph D can form a preliminary undirected graph DU。
And step 3: utilizing a summation formula to sum Kendall rank correlation coefficients to obtain each group of Pair-Copula functions
Figure BDA0002589401460000101
Selecting the main variable in each group of characteristic variables as a father node to form a link pointing to a child node from the father node, and forming an undirected graph DUConversion into chain diagram DL。
And 4, step 4: chain diagram D adopting D-vine structureLPerforming parameter estimation on each edge in the graph to determine the optimal Copula function type, and forming a final directed acyclic graph D and a joint density function of the Pair-Copula Bayesian network.
FIG. 2 is a completely undirected graph D that can be formed by 6 characteristic variablesF. Wherein, the numbers 1-6 represent respectively: transformer temperature, voltage, current, active power, ambient temperature, reactive power. Under the premise of not considering the correlation, the structural relationship formed by the six characteristic variables is a completely undirected graph with 15 edges.
The correlation in each group of Pair-Copula was judged by using Kendall and Spearman rank correlation coefficients, and the specific comparison results are shown in Table 4. Because of space limitations, A to F are used to represent: transformer temperature, voltage, current, active power, reactive power, ambient temperature. According to the correlation measure, the variable with the highest temperature correlation with the transformer is the current, and the completely undirected graph D is obtained by taking the analysis table of the measure as the standardFTransition to preliminary undirected graph DU。
TABLE 4 correlation measure analysis
Figure BDA0002589401460000102
By following (τ)k+ρs) The principle that/2 is more than or equal to 0.6 is adopted, the relevant variables which do not meet the conditions are removed (the black data in the table 4 are reserved), and several groups of Pair-Copula with higher relevance are selected to form a new completely undirected graph DUAs can be seen from table 4, the Kendall coefficient and Spearman coefficient of the reactive power are small, so this variable is eliminated from consideration. In addition, according to Kendall rank correlation coefficient sum corresponding to correlation measure of each group of Pair-Copula in Table 4
Figure BDA0002589401460000103
Determining the directional relation, i.e. pointing, between characteristic variables
Figure BDA0002589401460000104
Larger variables, will be completely undirected graph DUSelecting the main variable of 7 groups of Pair-Copula to obtain a chain diagram DLThe specific bayesian network structure determination flow is shown in fig. 4.
After a Bayesian network structure is constructed, specific variables are substituted into the structure diagram, parameter estimation is carried out by combining a D-vine structure, for determining the condition relationship corresponding to each edge, the Pair-Copula type represented by each dependent structure is selected, a group with a larger numerical value is selected as the correlation relationship by referring to Kendall rank correlation coefficient values, so that the Copula type and the parameter of each group of condition relationship are determined, and finally, a complete transformer temperature Pair-Copula Bayesian network structure diagram is formed as shown in FIG. 4.
The joint density function corresponding to the constructed PCBN model is as follows:
Figure BDA0002589401460000111
the PCBN model can reasonably convert data into understandable knowledge, more intuitively understand the relation of various factors influencing the temperature of the transformer, and provide quantitative basis for temperature correction in the later-stage transformer state evaluation.

Claims (10)

1. A Bayesian network transformer state evaluation method based on Pair-Copula is characterized by comprising the following steps:
1) collecting sample set data of a transformer to be evaluated, wherein the sample set data comprises 6 characteristic variables of voltage, current, active power, reactive power, transformer temperature and environment temperature, and correspondingly constructing a characteristic variable set;
2) selecting an optimal Copula function according to the Pair-Copula structure to describe the correlation between the transformer temperature and other characteristic variables, and calculating to obtain a rank correlation coefficient corresponding to the optimal Copula function;
3) and constructing a Bayesian network model, namely a PCBN model, of the transformer temperature based on Pair-Copula, acquiring a joint density function of the PCBN model, and finishing the state evaluation of the transformer.
2. The method for estimating transformer state of Bayesian network based on Pair-Copula as recited in claim 1, wherein in the step 2), the Copula function comprises normal Copula function, t-Copula function, Gumbel function, Clayton function and Frank function, and the normal Copula function and t-Copula function with symmetric tail correlation are selected to form Pair-Copula structure.
3. The method for evaluating the state of the transformer of the bayesian network based on Pair-Copula according to claim 2, wherein in the step 2), an optimal Copula function in the Pair-Copula structure is selected according to the euclidean distance squared minimum by introducing an empirical Copula function.
4. The method for estimating transformer state of Bayesian network based on Pair-Copula as claimed in claim 3, wherein said empirical Copula function Cn(u, v) is defined as:
Figure FDA0002589401450000011
Figure FDA0002589401450000012
wherein F (X) and G (Y) are empirical distribution functions of random vectors X and Y, respectively, u, v ∈ [0,1 ∈ [ ]]Parameters of empirical Copula function, I[·]Is an indicative function of empirical Copula, xi、yiI-th observation point data representing random vectors X and Y, n being the total number of observation points.
5. The method for estimating the state of the transformer of the Bayesian network based on Pair-Copula as claimed in claim 4, wherein the expression of the squared Euclidean distance is as follows:
Figure FDA0002589401450000021
wherein the content of the first and second substances,
Figure FDA0002589401450000022
is the squared euclidean distance corresponding to the dyadic normal Copula function,
Figure FDA0002589401450000023
is the squared Euclidean distance, C, corresponding to a binary t-Copula functionGa(ui,vi)、Ct(ui,vi)、Cn(ui,vi) Respectively representing a binary normal Copula function, a binary t-Copula function and an empirical Copula function.
6. The method for estimating the state of the transformer of the Bayesian network based on Pair-Copula as claimed in claim 3, wherein the method is based on the state estimation of the transformer of the Bayesian network based on Pair-CopulaCharacterized in that, in the step 2), the rank correlation coefficient comprises a Kendall rank correlation coefficient tau for reflecting whether the variation trends among the characteristic variables are consistent or notkAnd Spearman rank correlation coefficient rho reflecting the difference multiple of the probability of consistent and inconsistent changes between feature variabless。
7. The method for evaluating the state of the transformer of the bayesian network based on Pair-Copula according to claim 6, wherein the step 3) specifically comprises the following steps:
31) constructing a Bayesian network structure;
32) substituting the characteristic variables into the Bayesian network structure chart, and performing parameter estimation by combining a D-vine structure;
33) determining a Copula type and parameters of a condition relation corresponding to each edge in the Bayesian network structure;
34) and forming a complete PCBN model, and quantitatively describing the weight relation among the characteristic variables according to the joint density function, thereby providing a correction basis for subsequent transformer state evaluation.
8. The method for evaluating the state of the transformer of the bayesian network based on Pair-Copula according to claim 7, wherein the step 31) specifically comprises the following steps:
311) constructing a completely undirected graph D with 15 edges according to 6 characteristic variables of voltage, current, active power, reactive power, transformer temperature and ambient temperatureF；
312) Expressing the correlation measure among the characteristic variables according to Kendall rank correlation coefficient and Spearman rank correlation coefficient, and completely undirected graph DFTransition to preliminary undirected graph DU；
313) Determining a preliminary undirected graph D according to the magnitude relation of Kendall rank correlation coefficient sums in the correlation measureUIn (1) to form a chain diagram DLAnd finishing the construction of the Bayesian network structure.
9. A method as claimed in claim 8The method for evaluating the transformer state of the Bayesian network based on Pair-Copula is characterized in that in the step 312), the state does not conform to (tau)k+ρs) The edge corresponding to the correlation measure data corresponding to the/2 is more than or equal to 0.6 and is from a completely undirected graph DFRemoving to form a preliminary undirected graph DU。
10. The method for estimating transformer state of bayesian network based on Pair-Copula according to claim 8, wherein in step 313), Kendall rank correlation coefficient and larger characteristic variable are used as pointed main variables.
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Application publication date: 20201110