CN110348114A - A kind of non-precision fault recognition method of power grid completeness status information reconstruct - Google Patents
A kind of non-precision fault recognition method of power grid completeness status information reconstruct Download PDFInfo
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Abstract
The invention discloses a kind of non-precision fault recognition methods of power grid completeness status information reconstruct, phasor measurement is synchronized using the WAMS of RTU, PMU, and provide wide area fault message, meet the real-time and requirement of overall importance of trend fingerprint collecting as far as possible, and under fault sample and the incomplete situation of information, it introduces non-precision principle of probability to go to study, meets the requirement of fault-tolerance as far as possible；In addition, the fault message that the trend fingerprint of RTU, PMU obtain is bound to non-precision principle, to carry out fault identification in power grid uncertainty situation using wide area measurement as background.
Description
Technical Field
The invention belongs to the technical field of power system fault diagnosis, and particularly relates to a non-accurate fault identification method for power grid completeness state information reconstruction.
Background
With the implementation of the 'smart grid' strategy in China and the formation of the extra-high voltage and large grid interconnection pattern, the development of fault diagnosis and fault positioning technology is urgently needed to safely protect the driving of the large grid. The SCADA/EMS system is an online monitoring and data acquisition system commonly used by various domestic power grid companies at present, and the EMS is an energy management system with the most perfect functions currently applied to the field of power systems. The RTU is the basis and the core of the SCADA system, mainly completes functions such as data acquisition, data communication and execution of control center commands, and the communication network transmits the data acquired by the RTU to the control center in time, but the information space is local, the time is asynchronous, and the instantaneity is not high. The WAMS can simultaneously observe the overall view of the global electromechanical dynamic process of the power system in a time-space-amplitude three-dimensional coordinate system, so that the WAMS has spatial wide area and temporal synchronism, and provides high-precision real-time wide area measurement information with unified time scales. The PMU is based on a synchronous phase angle testing technology, the monitoring of the dynamic process of the power system can be realized through a wide area measuring system of the synchronous phase angle testing unit PMU which is gradually distributed with key measuring points of the whole network, the measured data can reflect the dynamic behavior characteristics of the system, and the real-time performance is ensured. Therefore, the application research of the WAMS in the field of power grid fault diagnosis has practical significance and practical value.
At present, many methods are provided for fault diagnosis of power systems at home and abroad, and mainly include power system fault diagnosis based on an expert system principle, application of an artificial neural network in fault diagnosis, power system fault diagnosis based on an optimization technology, power system fault diagnosis based on a rough set theory, power system fault diagnosis based on a fuzzy set theory, power system fault diagnosis based on a genetic algorithm, power system fault diagnosis based on a Petri network and the like. The methods have the characteristics that the problem of grid fault diagnosis is solved in different ways, but the methods also have respective defects.
With the current methods, fault diagnosis is mostly based on the fact that the dispatching center obtains complete information, and the information is completely reliable. However, in the actual operation process, since the result of fault diagnosis is often directly affected by error information or missing useful information such as malfunction or non-operation of electrical equipment such as a protection device and a circuit breaker, and it is very difficult to send all relay protection state information to the dispatching center, many methods cannot be satisfied in such a case. Therefore, intensive research on fault diagnosis methods under the condition of incomplete information is needed, a method which can better overcome the difficulty and produce reasonable diagnosis results under the condition of incomplete information is sought, and combined application of a plurality of diagnosis methods is considered, so that the diagnosis capability of the system is improved. And the inaccuracy principle can enhance the fault tolerance, and other traditional methods can make up the previous defects to a certain extent. Therefore, under the objective condition that fault samples and information cannot be complete, it is of great significance to introduce non-accurate probability to describe the fault.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a non-accurate fault identification method for power grid completeness state information reconstruction.
In order to achieve the above object, the present invention provides a method for identifying a non-precise fault of power grid completeness state information reconstruction, which is characterized by comprising the following steps:
(1) acquiring operation parameters and topological parameters of the power grid and fault characteristic vectors of the power grid in a fault mode;
(2) inputting the obtained operation parameters, topology parameters and fault characteristic vectors into a Wide Area Measurement System (WAMS);
(3) solving the optimal configuration model to realize the RTU or PMU optimal configuration of the power grid node;
wherein X ═ X1,x2,…,xi,…,xn]Representing RTU or PMU configuration vectors of the power grid nodes, wherein n is the number of the power grid nodes;a is a node incidence matrix; y is1,Y2Is a subset of Y, Y1Representing vectors corresponding to nodes not associated with the zero-injected node, Y2Representing the associated nodes of the zero injection nodes to correspond to the vector set; assuming that m nodes are not associated with a zero injection node, I ═ 1,1]T m×1Is an m × 1 matrix, TinjA relational matrix representing zero injection nodes and their associated nodes, BinjIs the corresponding vector set;
(4) marking the power grid nodes which realize the RTU or PMU optimal configuration as power flow characteristic points;
(5) and constructing a preset fault data fingerprint database
(5.1) sequentially numbering each line in the power grid as 1-n, and taking the single fault or the combined fault of each line as a type of fault, thereby constructing a preset fault set;
(5.2) acting any type of faults in a preset fault set on the load flow characteristic points, and then calculating the average voltage amplitude U on each load flow characteristic point according to the following formulai；
Wherein T represents the time when the fault acts on the characteristic point of the power flow, ui(t) a voltage signal representing the ith power flow characteristic point;
then all U's are putiForm the eigenvector x ═ U1,U2,…,Ui,...]；
(5.3) forming an expected fault data fingerprint database in one-to-one correspondence with each group of average voltage amplitude and corresponding fault category;
(6) solving the nonlinear model
(6.1) in f (x-A)j) And in P (A)i) The above introduces a non-accuracy model, wherein f (x-A)j) Indicating that the characteristic quantity x is at fault AjLower Gaussian Joint Density function, P (A)j) Indicates a failure AjProbability of occurrence, AjIndicating a jth fault;
(6.2) orderVariance ofExpanding a non-precise interval of expectation and variance through the parameter beta; expanding a non-precise interval of expectation and variance;
wherein,representing the desired maximum likelihood estimate value(s),a maximum likelihood estimate representing a variance;
(6.3) establishing a non-precise interval constraint condition;
dirichlet model from non-precision, combined with P (A)j) The normalization and non-negativity conditions jointly form constraint conditions;
wherein, let M ═ Σ MjThe total number of times of faults of all lines under all fault classes in one year of a certain actual power grid; m isjThe number of times of faults of all lines under the j-th type of fault is obtained; s is a non-accuracy parameter of each line with a fault; e [. C]Which means that the desired minimum value is sought,indicating that the expected maximum value is obtained;
(6.4) substituting the imprecise constraint condition established in the step (6.3) into f (x-A) in the step (6.1) according to the constraint conditionj)And P (A)j) In this way, the objective function F (x, P (A) is obtainedj) And constitutes a nonlinear optimization equation set of the following formula:
wherein j ═ j ', j, j' is epsilon [1, K ], and K is the total number of fault categories;
(7) and (5) calculating the probability value of the inaccurate interval under each fault class through the step (6), and selecting the fault class corresponding to the highest probability value as a fault diagnosis result, namely completing fault identification.
The invention aims to realize the following steps:
the invention relates to a non-precise fault identification method for power grid completeness state information reconstruction, which utilizes WAMS of RTU and PMU to carry out synchronous phasor measurement and provide wide-area fault information, meets the requirements of real-time performance and global performance of tidal current fingerprint acquisition as much as possible, introduces a non-precise probability principle to research under the condition of incomplete fault samples and information, and meets the requirement of fault tolerance as much as possible; in addition, with wide area measurement as a background, fault information obtained by flow fingerprints of the RTU and the PMU is combined to a non-accuracy principle, so that fault identification is carried out under the condition of uncertainty of a power grid.
Meanwhile, the method for identifying the inaccurate fault of the power grid completeness state information reconstruction further has the following beneficial effects:
(1) compared with the conventional power grid fault diagnosis, the method has the characteristics of strong real-time performance, high fault tolerance, strong theoretical basis and strong practicability by taking the RTU and the PMU of the WAMS as the features for extracting the whole power flow and referring to a non-precise theory to describe the non-precise probability of fault occurrence.
(2) Compared with the conventional method of distributing the RTU and the PMU to the whole power grid, the method disclosed by the invention optimizes the configuration of the RTU and the PMU by using an integer programming method, so that the cost can be reduced and the monitoring efficiency can be improved.
(3) Compared with the existing expert system, the petri method and the like, the knowledge base in the expert system does not have the capability of simulating learning, the fault tolerance capability is low, the petri net has low capability of identifying errors, the defects are avoided by a non-accurate probability theory, and the diagnosis result is obtained by a more rigorous probability method.
(4) According to the invention, the RTU and PMU configuration nodes of the WAMS are used as power grid flow fingerprint feature points, so that wide-area, synchronous and on-line collection of power grid flow fingerprints is realized; secondly, the probability calculation of the power grid line fault is realized by combining the collected fault data with a non-accuracy principle, and then the fault result is quickly and accurately identified.
Drawings
FIG. 1 is a flow chart of a method for non-precise fault identification for power grid integrity status information reconstruction in accordance with the present invention;
fig. 2 is an IEEE11 node system;
FIG. 3 is a simulated waveform diagram of the characteristic point simulated fault voltage amplitude;
FIG. 4 is a graph of fault probability intervals corresponding to different beta values;
fig. 5 is a diagram of various types of fault intervals corresponding to different values of s.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
For convenience of description, the related terms appearing in the detailed description are explained:
WAMS (Wide-Area Measurement System): a wide area measurement system;
RTU (remote Terminal Unit): remote terminal control system
Pmu (phase Measurement unit): measuring synchronous phasor of the power system;
odp (optimal Device plan): optimally configuring the device;
fig. 1 is a flowchart of a method for identifying a non-precise fault based on power grid integrity status information reconstruction according to the present invention.
In this embodiment, as shown in fig. 1, a method for identifying a non-precise fault based on power grid integrity status information reconstruction according to the present invention includes the following steps:
s1, acquiring operation parameters and topological parameters of the power grid and fault characteristic vectors of the power grid in a fault mode;
s2, inputting the acquired operation parameters, topology parameters and fault feature vectors into a Wide Area Measurement System (WAMS);
s3, solving the optimal configuration model to realize the RTU or PMU optimal configuration of the power grid node;
based on the RTU and PMU optimal configuration of the WAMS, the power grid has different power flow distributions before and after a fault, the power flow fingerprint can reflect the distribution characteristics of the power grid, and the power grid power flow fingerprint has a mapping relation with the topological structure, the operation mode, the fault condition and the like of the power grid, which is similar to the uniqueness of human fingerprints. Therefore, key nodes are selected as characteristic points, the characteristic points can reflect local power flow of the power grid, global observation can be carried out on the power grid by selecting a plurality of characteristic points, and the whole power flow characteristic is reflected. The attribute of each characteristic point is characterized by fingerprint characteristic quantity, including characteristic point voltage phasor and current phasor, active power flow and reactive power flow of associated branch circuits.
For a node system, the ODP problem considering grid observability can be described by the following mathematical model:
wherein X ═ X1,x2,…,xi，…,xn]RTU or PMU configuration vectors, ω, representing grid nodesiIs a configuration cost factor, x, considered unchanged at the same timeiIs a binary variable, and satisfies the following conditions:
(x) is a vector function, and f (x) AX, I is a column vector with elements 1; a is a node incidence matrix, the main diagonal elements of which are all 1, and if two nodes are associated with each other, the corresponding element is 1, otherwise, the corresponding element is 0.
In the traditional 0-1 integer programming method, if the branch flow and node injection data are not considered as constraint conditions, the ODP problem is a linear integer programming problem and is convenient to solve, but when the known branch flow data or power injection nodes in the network are used as the constraint conditions, the configuration number of RTUs and PMUs is greatly reduced on the premise of meeting the observability of a power grid; there is a disadvantage in that the optimal configuration problem is transformed into a non-linear integer programming problem, thereby affecting the speed and quality of the solution.
The information of the electrical quantity is completely based on RTU and PMU data sources, branch flow data are unknown, and only a zero-power injection node is considered. The objective function in the above model is also adopted, and for research convenience, it is assumed that the objective function RTU and the configuration cost coefficient ω in PMU are the samei(i 1,2, …, n) 1, the improved model is as follows:
wherein X ═ X1,x2,…,xi,…,xn]Representing RTU or PMU configuration vectors of the power grid nodes, wherein n is the number of the power grid nodes;a is a node incidence matrix; y is1,Y2Is a subset of Y, Y1Representing vectors corresponding to nodes not associated with the zero-injected node, Y2Representing the associated nodes of the zero injection nodes to correspond to the vector set; assuming that m nodes are not associated with a zero injection node, I ═ 1,1]T m×1Is an m × 1 matrix, TinjA relational matrix representing zero injection nodes and their associated nodes, BinjIs the corresponding vector set;
therefore, the RTU and PMU optimal configuration of the power grid node can be realized.
S4, marking the power grid nodes which realize the RTU and PMU optimal configuration as power flow characteristic points;
the configuration points as the flow fingerprint feature points should satisfy the following two points:
firstly, when the power grid fails, the complete observability of the power grid is ensured, so that the dynamic behavior of the power grid failure is effectively tracked and recorded;
secondly, in view of economic and technical conditions, and considering that the increase of the number will cause the increase of the fault information amount, the minimum number of RTUs and PMUs are configured on the premise of ensuring the diagnosis precision, so that the rapid processing capability of the diagnosis method is improved.
S5, constructing a preset fault data fingerprint database
When a power grid fails, the RTU and the PMU which are optimally configured firstly acquire fault characteristic quantities, all the RTUs or PMUs (namely, tidal current fingerprints) arranged at the nodes (buses) keep observability on the whole power grid, and the acquired data have real-time dynamic property and can well reflect the state of the power grid. In practical application, x is chosen to be [ U A ]U I AI P Q]A six-dimensional vector as a feature quantity, where U: node voltage amplitude AU: node voltage phase angle I and branch current amplitude AIBranch current phase angle P: active power is injected into a node, and Q: reactive power is injected into the nodes, the coverage information of the characteristic quantity is complete, the fault tolerance is higher, and the accuracy is higher.
Taking the amplitude of the collected voltage phasor as an example, the voltage amplitudes collected by all RTU or PMU nodes form a feature vector. For final fingerprint identification, a mapping relation is established, empirical data is obtained through a large number of experiments (fault setting is carried out on each position of a line), the empirical data is combined into a set, and the set is combined into an expected fault data fingerprint database after the mapping relation is established with a preset fault set.
The expected fault data fingerprint database is characterized by experience and mapping, the experience is that the database is required to have a large amount of characteristic fingerprint information, and the characteristic vector x has errors due to measurement errors of an RTU and a PMU and the objective trend influence of an actual power grid. We consider that the feature vector has a mapping with the fault class within a certain error range. The mapping ensures that the power flow after the fault is in one-to-one correspondence with the characteristic vectors, the distribution change after the power flow is caused by different types of fault categories (single or cascading faults), the time of the state before the relay protection action removes the fault of the power grid and the fault is supposed to be recorded as delta t, and the characteristic fingerprint vectors recorded in the time are in one-to-one correspondence with the fault combinations.
We describe the construction embodiments below, as follows:
s5.1, numbering each line in the power grid as 1-n in sequence, wherein each line can generate various faults, and the fault mainly comprises 5 basic fault types (broken line [ F ]1]Single phase earth short circuit [ F ]2]Two-phase short circuit [ F3]Two-phase ground short circuit [ F ]4]Three-phase short circuit [ F ]5]Taking the single fault or the combined fault of each line as a type of fault, thereby constructing a preset fault set;
s5.2, acting any kind of faults in the preset fault set on the tidal current characteristic point, collecting the voltage phasor of the tidal current characteristic point when the faults occur, and assuming that the tidal current characteristic point is set as Y1，Y2，...，YMMeasured voltage is U1，U2，...，UMForm a feature vector x ═ U1,U2,...,UM]Short circuits are provided at different positions of the line for each fault class. Starting when the fault is set from 2s, continuously removing the fault for 0.2s, obtaining a waveform curve of the bus voltage amplitude of the characteristic point by system simulation, testing every N% from 0 to 100% in a tested range, and recording 100/N test points as N1～N100/nThus, 100/n sets of test data were obtained. The time before reaching the steady state is recorded as T, namely the fault duration, and an average voltage amplitude algorithm is adopted, so that the equation is shown as U11～U1,100/n，U21～U2,100/n，…，UM1～UM,100/nCalculating the average voltage amplitude U at each power flow characteristic point by using the following formulai；
Wherein T represents the time when the fault acts on the characteristic point of the power flow, ui(t) a voltage signal representing the ith power flow characteristic point;
then all U's are putiForm the eigenvector x ═ U1,U2,…,Ui,...]；
S5.3, forming an expected fault data fingerprint database in one-to-one correspondence with each group of average voltage amplitude and corresponding fault category;
s6 solving nonlinear model
S6.1, in f (x-A)j) And in P (A)i) The above introduces a non-accuracy model, wherein f (x-A)j) Indicating that the characteristic quantity x is at fault AjLower Gaussian Joint Density function, P (A)j) Indicates a failure AjProbability of occurrence, AjIndicating a jth fault;
s6.2, orderVariance ofExpanding a non-precise interval of expectation and variance through the parameter beta; expanding a non-precise interval of expectation and variance;
wherein,representing the desired maximum likelihood estimate value(s),a maximum likelihood estimate representing a variance;
s6.3, establishing a non-precise interval constraint condition;
dirichlet model from non-precision, combined with P (A)j) The normalization and non-negativity conditions jointly form constraint conditions;
wherein, let M ═ Σ MjThe total number of times of faults of all lines under all fault classes in one year of a certain actual power grid; m isjThe number of times of faults of all lines under the j-th type of fault is obtained; s is a non-accuracy parameter of each line with a fault, which determines the influence degree of the prior information on the statistical result, and the larger s is, the more samples are needed to eliminate the influence of the prior information on the statistical result, and usually [1,2 ] is taken]。；E[·]Which means that the desired minimum value is sought,indicating that the expected maximum value is obtained;
beta describes the inaccuracy of the distribution of the fault characteristic quantity of each line, and s describes the inaccuracy of the fault of each line, and the two parameters have definite physical meanings.
S6.4, substituting the imprecise constraint condition established in the step S6.3 into f (x-A) in the step S6.1 according to the constraint conditionj) And P (A)j) In this way, the objective function F (x, P (A) is obtainedj) And constitutes a nonlinear optimization equation set of the following formula:
wherein j ═ j ', j, j' is epsilon [1, K ], and K is the total number of fault categories;
and S7, calculating the probability value of the inaccurate interval under each fault class through the step S6, and selecting the fault class corresponding to the highest probability value as a fault diagnosis result, namely completing fault identification.
Examples of the invention
Taking the IEEE11 system as an example, the simulation is performed using the PSASP.
Each line in the system is separately added with two-phase short-circuit ground faults, and 10 positions of the line, namely 0%, 10%, 20%, …, 90% and 100%, are tested, and the 10 positions are classified into 10 fault categories. Is marked as Ai(i ═ 1,2, …, 10). The 10 lines are numbered sequentially as A1～A10. As shown in fig. 2, when a fault occurs, the PMU after the optimal configuration acquires voltage phasor of a device point, assuming that the RTU or PMU device point after the optimization is set as a bus 3, 5, or 6, the measured voltage is U1、U2、U3Forming a feature vector x ═ U1U2U3]。
As shown in FIG. 3, an AB two-phase short circuit earth fault is added at the midpoint position of No. 5-7 lines, the fault time is set to be 2-2.2 s, the voltage amplitude waveform of the characteristic points (3, 5, 6) is simulated by the system,
suppose UiI-1, 2, …, n obeys a gaussian distribution and each gaussian random variable is independent of the others, then its linear combination must be gaussian, UiI-1, 2, …, n obeys a joint gaussian distribution, i.e.:
solving the maximum likelihood estimation of the mean fault voltage expectation and the variance of 10 groups of data under each type of fault, as shown in table 1;
table 1 is the maximum likelihood estimate of mean fault voltage expectation and variance under each fault class;
TABLE 1
In this example, because each fault is independent of the other, so
And when M is 21, MiE is e {1,2,3}, and 1 is taken when i is 1,2, 3; when i is 4,5, 6, then 2; when i is 7,8, 9, 10, 3 is taken, and the influence of the parameters β and s on the distribution is discussed below.
1) Influence of parameter beta (s ═ 1)
Beta mainly affects the inaccuracy of the distribution of the characteristic quantity of each line fault, s is set to be 1, and A is used5For example, when x is (0.2436,0.2776,0.2128) feature quantity, the maximum and minimum values of the probability under the corresponding fault class are obtained by calculation. As shown in fig. 4, β is the fault probability intervals of 0.05, 0.10, 0.15, and 0.20.
It is seen from fig. 4 that as the value of β increases, the length of the probability interval of the faulty line gradually widens, the maximum value increases, the minimum value decreases, and the length of the probability interval of the non-faulty line decreases as β increases, the maximum value decreases, and the minimum value increases.
2) Influence of parameter s (β ═ 0.05)
The fixed beta is 0.05, and s is 1, 5, 10, 20,
it can be observed from fig. 5 that as s increases, the length of the probability interval of the faulty line gradually widens, the maximum value increases, and the minimum value decreases, and as s increases, the length of the probability interval of the non-faulty line decreases, the maximum value decreases, and the minimum value increases.
From fig. 4 and 5, it can be seen that β and s have approximately the same influence characteristics on the distribution. As can be seen from fig. 2 and 3, when the feature value x is (0.2436,0.2776,0.2128), the probability of the occurrence on the 5-7 line is 0.6582 to 0.7364, and the probability of the occurrence on the other lines is as small as less than 0.2, which is obtained by performing a search in the expected failure data fingerprint database and calculating the data, so that it is highly reliable that the failure occurs on the 5-7 line. And the nodes similar to the table are obtained through the setting of different fault lines and the division of different fault classes (based on different fingerprint libraries), thereby proving the correct effectiveness of the method.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (1)
1. A non-precise fault identification method for power grid completeness state information reconstruction is characterized by comprising the following steps:
(1) acquiring operation parameters and topological parameters of the power grid and fault characteristic vectors of the power grid in a fault mode;
(2) inputting the obtained operation parameters, topology parameters and fault characteristic vectors into a Wide Area Measurement System (WAMS);
(3) solving the optimal configuration model to realize the RTU or PMU optimal configuration of the power grid node;
wherein X ═ X1,x2,…,xi,…,xn]An RTU or PMU configuration vector representing a grid node;a is a node incidence matrix; y is1,Y2Is a subset of Y, Y1Representing vectors corresponding to nodes not associated with the zero-injected node, Y2Representing the associated nodes of the zero injection nodes to correspond to the vector set; assuming that m nodes are not associated with a zero injection node, I ═ 1,1]T m×1Is an m × 1 matrix, TinjMatrix of moments of relationship representing zero-injected nodes and their associated nodes, BinjIs the corresponding vector set;
(4) marking the power grid nodes which realize the RTU or PMU optimal configuration as power flow characteristic points;
(5) and constructing a preset fault data fingerprint database
(5.1) sequentially numbering each line in the power grid as 1-n, and taking the single fault or the combined fault of each line as a type of fault, thereby constructing a preset fault set;
(5.2) acting any type of faults in a preset fault set on the load flow characteristic points, and then calculating the average voltage amplitude U on each load flow characteristic point according to the following formulai；
Wherein T represents the time when the fault acts on the characteristic point of the power flow, ui(t) a voltage signal representing the ith power flow characteristic point;
then all U's are putiForm the eigenvector x ═ U1,U2,…,Ui,...]；
(5.3) forming an expected fault data fingerprint database in one-to-one correspondence with each group of average voltage amplitude and corresponding fault category;
(6) solving the nonlinear model
(6.1) in f (x-A)j) And in P (A)i) The above introduces a non-accuracy model, wherein f (x-A)j) Indicating that the characteristic quantity x is in fault AjLower Gaussian Joint Density function, P (A)j) Indicates a failure AjProbability of occurrence, AjIndicating a jth fault;
(6.2) orderVariance ofExpanding a non-precise interval of expectation and variance through the parameter beta; expanding a non-precise interval of expectation and variance;
wherein,representing the desired maximum likelihood estimate value(s),a maximum likelihood estimate representing a variance;
(6.3) establishing a non-precise interval constraint condition;
dirichlet model from non-precision, combined with P (A)j) The normalization and non-negativity conditions jointly form constraint conditions;
wherein, let M ═ Σ MjThe total number of times of faults of all lines under all fault classes in one year of a certain actual power grid; m isjThe number of times of faults of all lines under the j-th type of fault is obtained; s is a non-accuracy parameter of each line with a fault; e [. C]Which means that the desired minimum value is sought,indicating that the expected maximum value is obtained;
(6.4) substituting the imprecise constraint condition established in the step (6.3) into f (x-A) in the step (6.1) according to the constraint conditionj) And P (A)j) In this way, the objective function F (x, P (A) is obtainedj) And constitutes a nonlinear optimization equation set of the following formula:
wherein j ═ j ', j, j' is epsilon [1, K ], and K is the total number of fault categories;
(7) and (5) calculating the probability value of the inaccurate interval under each fault class through the step (6), and selecting the fault class corresponding to the highest probability value as a fault diagnosis result, namely completing fault identification.
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