CN110727908A - Modal analysis method for solving complex electrical fault - Google Patents
Modal analysis method for solving complex electrical fault Download PDFInfo
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Abstract
The invention provides a modal analysis method for solving complex electrical faults. The method is characterized by comprising the following steps: (1) performing high-dimensional degradation processing on the electrical data by adopting an algorithm taking intrinsic orthogonal decomposition as a core; (2) and then carrying out matching analysis, specifically comprising energy ratio analysis, visual display analysis of the change of the modal coefficient along with time steps, and matching frequency modal analysis and Lissajous graphical analysis of the modal coefficient. The beneficial effects of the invention also include: 1. fault parameter information as much as possible can be obtained, and a high-quality data analysis basis is provided for a high-level algorithm; 2. providing an information algorithm with a mature flow for electrical fault data analysis; 3. powerful decision information is provided for the electrical big data platform.
Description
Technical Field
The invention relates to a modal analysis method for solving complex electrical faults.
Background
The power system is composed of generators, transformers, lines and users which produce, transmit, distribute and consume electric energy, and is a unified system which converts primary energy into electric energy and transmits and distributes the electric energy to each user. Because the electric power system occupies an important position in national economy and people's life, the research of the electric power system fault analysis method is continuously paid more attention by people. In the existing fault judgment mode, frequency analysis is carried out through Fourier transform, if the energy contributed by a high-frequency component is larger than a certain threshold value, the system is considered to be in fault, corresponding protection measures are carried out through identifying other characteristics, such as overcurrent or zero-sequence overvoltage, and the like, so that the mode can play a good matching role for common short-circuit faults or common faults, but the problems that misjudgment can be carried out when some very common faults occur, and the fault reason cannot be determined occur.
The power system fault processing process is to determine the analyzed fault area from the system and reduce the range as much as possible. Then, some fault symptom information is obtained from some detection quantity of the analyzed area, the early information is analyzed and processed, the specific position of the fault is judged according to the signal of the protection action, the fault element is isolated from the non-fault network, the system topological structures before and after the fault are identified by adopting a real-time line connection method, and then the difference of the two system topological structures is found out, so that some simple faults of the fault area can be identified, and even the element which generates the fault can be directly identified. The mechanism and the fault reason of some uncomplicated faults can be known in detail by the existing system, but the mechanism analysis with evidence is difficult to be made for some complicated faults, such as long-time unstable fluctuation of electric signals and the like.
Disclosure of Invention
The invention aims to provide a modal analysis method for solving complex electrical faults, which can obtain fault parameter information as much as possible, and can perform more detailed fault analysis and provide more accurate protection starting decision by matching a frequency modal decomposition method in fault analysis and electrical intelligent decision making.
A modal analysis method for solving complex electrical faults is characterized by comprising the following steps:
(1) performing high-dimensional degradation processing on the electrical data by adopting an algorithm taking intrinsic orthogonal decomposition as a core;
(2) and then carrying out matching analysis, specifically comprising energy ratio analysis, visual display analysis of the change of the modal coefficient along with time steps, and matching frequency modal analysis and Lissajous graphical analysis of the modal coefficient.
The step (1) is to collect the required unstable electrical data segment, and to perform reduced order decomposition on the electrical data segment into an expansion sequence of a function only related to time and a function only related to space, namely
In the formula (I), the compound is shown in the specification,
fluctuation amount of variable representing mean value at removal time, ai(t) represents the modal coefficient in units of the variable analyzed; phi is aiAnd (x, y) is a dimensionless spatial characteristic function, and the sequence is subjected to intrinsic orthogonal decomposition of the matrix to obtain a coefficient matrix and a mode matrix.
The energy ratio analysis in the step (2) is specifically based on a mode decomposition principle, that is, firstly, how many orders of modes can contain most of information in an original electric field needs to be known, that is, each order of POD modes needs to be obtained, and according to a POD solving process, by solving a characteristic value lambda of a covariance matrix RiAnd arranging the POD modes in a descending order to obtain the proportion of POD modes of each order and establishing the order of the modes which is enough to contain most information of the original electrical data.
The step (2) of performing visual display analysis on the change of the modal coefficient along with the time step specifically includes establishing a curve of the change of the corresponding modal coefficient along with the time step, wherein the meaning of the modal coefficient to the instantaneous electrical field refers to the projection of the electrical data to the modal, that is, the magnitude of the energy captured by the modal by the instantaneous electrical data.
In the step (2), a joint frequency modal analysis method, namely fast fourier transform, is specifically adopted in cooperation with the frequency modal analysis, and information for analysis decision is provided by analyzing the same characteristic points and the characteristic points with larger difference between the two modes.
The Lissajous figure analysis of the mode coefficient in the step (2) is to firstly collect the objective data volume from a box type transformer box of a certain model and then analyze the data volume.
The method provided by the invention is a novel data analysis method suitable for the electrical field, and can obtain fault parameter information as much as possible, so that the obtained massive data can be analyzed in a mode-uncoupled mode. The beneficial effects of the invention also include: 1. fault parameter information as much as possible can be obtained, and a high-quality data analysis basis is provided for a high-level algorithm; 2. providing an information algorithm with a mature flow for electrical fault data analysis; 3. powerful decision information is provided for the electrical big data platform.
Drawings
FIG. 1 is an analysis chart of a Lissajous figure of the modal coefficient in step (4) of example 1 of the present invention;
fig. 2 is a diagram illustrating a variation trend of a ratio of a characteristic value of a 50-order POD mode in step (5) in embodiment 1 of the present invention to an energy share;
FIG. 3 is a graph of the change of the mode 1 and 2 coefficients with time step in step (6) of example 1 of the present invention;
FIG. 4 is a graph of the change of the mode 3 and 4 coefficients with time step in step (6) of example 1 of the present invention;
FIG. 5 is a graph of the change of the mode 5 and 6 coefficients with time step in step (6) of example 1 of the present invention;
FIG. 6 is a graph of the change of the mode 7 and 8 coefficients with time step in step (6) of example 1 of the present invention;
FIG. 7 is a first-order frequency mode diagram of step (7) of example 1 of the present invention;
FIG. 8 is a second order frequency mode diagram of step (7) of example 1 of the present invention;
FIG. 9 is a third order frequency mode diagram of step (7) of example 1 of the present invention;
FIG. 10 is a fourth-order frequency mode diagram of step (7) in example 1 of the present invention;
FIG. 11 is a fifth-order frequency mode diagram of step (7) in example 1 of the present invention;
FIG. 12 is a six-order frequency mode diagram of step (7) in example 1 of the present invention;
FIG. 13 is a seven-order frequency mode diagram of step (7) in example 1 of the present invention;
FIG. 14 is an eighth-order frequency mode diagram of step (7) in example 1 of the present invention;
FIG. 15 is a Lissajous diagram of the mode 1 and mode 2 coefficients of step (8) of example 1 of the present invention;
FIG. 16 is a Lissajous diagram of the mode 3 coefficient and the mode 4 coefficient in step (8) of example 1 of the present invention;
FIG. 17 is a Lissajous diagram of the modal coefficients 5 and 6 in step (8) of example 1 of the present invention;
FIG. 18 is a Lissajous diagram of the mode shape coefficients 7 and 8 in step (8) of example 1 of the present invention;
FIG. 19 is a Lissajous diagram of the mode 1 and mode 3 coefficients of step (8) of example 1 of the present invention;
FIG. 20 is a Lissajous diagram of the mode 1 and mode 5 coefficients of step (8) of example 1 of the present invention;
FIG. 21 is a Lissajous diagram of the mode 1 and mode 7 coefficients of step (8) of example 1 of the present invention.
Detailed Description
The invention can provide researchers or intelligent decision units with as much information as possible through a plurality of aspects to analyze the failure mechanism and make decisions on protective measures under the condition that electrical failures with complex structures occur, and particularly provides detailed analysis processes and reference suggestions by adopting an efficient dimension reduction method (intrinsic orthogonal decomposition). The method mainly performs dimensionality reduction approximate description on most random processes and extracts essential features in complex random processes, so that results of high-dimensional experimental and simulation data are displayed by using a relatively ideal low-order model. The basic idea is to decompose the stochastic process to be studied into a time-dependent function and a space-dependent two-point function expansion sequence. Therefore, the simplified analysis of the data with reduced dimension is realized.
Example 1:
a novel modal analysis method based on electrical data comprises the following steps:
1. and performing high-dimensional degradation processing on the electrical data by adopting an algorithm taking intrinsic orthogonal decomposition as a core.
2. The matching analysis process adopting the method comprises energy ratio analysis, visual display analysis of the change of the modal coefficient along with time steps, matching frequency modal analysis and Lissajous graphic analysis of the modal coefficient.
The method comprises the following specific steps:
1. introduction of the decomposition method:
the basic idea is to decompose the stochastic process to be studied into an expanded sequence of functions that are only time-dependent and functions that are only space-dependent, i.e.
In the formula (I), the compound is shown in the specification,
representing the fluctuation amount (removed time mean) of the variable, then ai(t) represents the modal coefficient in units of the variable analyzed; phi is ai(x, y) is a dimensionless spatial feature function. To obtain the basis functions of the spatial modes, the method of "snapshots" proposed by Sirovich et al, i.e. from the results of numerical simulation or experiment, is usually adoptedAnd selecting n samples at the moment to perform solution analysis.
Suppose that for a certain physical quantity U (x, y) in two-dimensional space, U (x, y, t) is assumedi) (i ═ 1,2, …, N) denotes time period [0, T ═ Tn]The spatial distribution of the N selected moments in time (called snapshot sets). The mean and pulsatility values of the set of samples are defined as:
according to the basic idea of the POD method, the pulsating quantity V (x, y, t) can be adjustedi) Decomposition into spatial modes phii(x, y) and mode shape coefficient aiFunction of (t):
in practice, the spatial mode phi is solvedi(x, y) is equivalent to solving the following maximum problem:
and satisfies the condition that (phi ) | | phi | | air count2＝1
Wherein (·,. cndot.) and |. cn| | | | represent L on region Ω, respectively2Inner product and L2-a norm.
Using the variational method, the above maximum problem can be transformed into the following eigenvalue problem:
wherein:
is a ViIs also called the core [ i ] of POD](ii) a The characteristic mode can be expressed by utilizing the linear combination of the pulsating quantity of the spatial snapshot of the original function, namely
Wherein the coefficients
Is pending.
Substituting the above formula (2-8) into the formula (2-7) yields the following eigenvalue problem:
in the formula:
since the matrix R is a symmetric matrix, there is a corresponding eigenvalue λ1≥λ2≥…λNA complete set of orthogonal eigenvector bases A of > 01,A2,…,AN. From this, the POD basis function space can be expressed as:
Φ＝span(φ1,φ2,…,φN)
the eigenvalues λ of each order solved by the above methodiThe proportion of the sum of all characteristic values has definite physical significance and represents the contribution capacity to the total energy of the system, and the total energy of the dynamic system can be expressed as the sum of all order characteristic values
The percentage of energy occupied by each stage is Ei＝λi/E。
For model simplification, POD modes corresponding to small characteristic values can be ignored by defining related energy information, and one dimension is selected to be M (M: (M))<<N) a low-dimensional basis vector space. Definition ofM is chosen such that E (M) is ≧ σ, which is generally chosen to be slightly less than 1 to capture most of the energy of the snapshot set. Based on M POD moulds that above soughtThe state, the dimensionality reduction mode of the original velocity field can be expressed as:
thus, a dimension reduction space expanded by the M POD basis functions is obtained, and the dimension reduction space is solved. Projecting a mode equation into a dimension reduction space expanded by POD basis functions by using Galerkin approximation to obtain a solving modal coefficient aiThe mode coefficient a can be obtained by the ordinary differential equation set of (t)iAnd (t), finally completing the construction of the dimension reduction mode of the POD.
For the order-reduced model, the important concern is the truncation of the order, that is, how many orders of the model are needed to reconstruct the original information under the condition of meeting the precision requirement; one concern is also the number and characteristics of modes that dominate electrical faults, which is a very important aid in the analysis of fault structures. The POD method can extract a certain amount of eigenmodes from an electric field in a period of time, adopts the mode of eigenmode series expansion to express electric information, and expresses the eigenmodes of each order according to corresponding characteristic value lambdaiThe sizes of the contained electrical energy are sequenced from high to low, so that the main fault structure characteristics of the original electrical field can be well described by judging the required number of orders of modes through characteristic values.
2. A matched analysis process:
(1) energy ratio analysis:
according to the mode decomposition principle, firstly, we need to know how many orders of modes can contain most information in the original electric field, which needs to obtain each order of POD mode. According to the POD solving process described earlier, by solving the eigenvalues λ of the covariance matrix RiAnd arranging the POD modes in a descending order to obtain the proportion of each POD mode, so as to establish the most information of the original electrical data.
(2) Analysis of modal transformation over time:
the corresponding mode shape coefficient is changed along with the time step. The meaning of the modal coefficients to the instantaneous electrical field refers to the projection of the electrical data to the modal, i.e. to the amount of energy captured by the modal by the instantaneous electrical data.
(3) And (3) matching with frequency modal analysis:
the frequency modal analysis method, namely fast Fourier transform, can achieve the complementary effect of the defects of the modal analysis method, and information for analysis and decision is provided by analyzing the same characteristic points and the characteristic points with larger difference between the two modes.
(4) Analysis of mode shape coefficients lissajous figures:
Lissajous-Figure (Lissajous-Figure) is a regular, stable periodic Figure synthesized by simple harmonic vibrations with two frequencies in mutually perpendicular directions being simple integer ratios.
As shown in FIG. 1, the method is used for solving and analyzing an unknown fault of an unstable electrical data with a burr signal in high-low voltage complete equipment, and filtering a signal component generated by the fault. The method comprises the steps that firstly, objective data volume is collected from a box type transformer box of a certain model, and the higher the density of the collected data volume is, the more accurate the analysis result is. The graph illustrates an analysis of a piece of electrical instability data collected by a box-type converter during an unknown fault.
(5) Energy ratio analysis: the table can be obtained by calculating the proportional magnitude of the energy share and the total energy share of the characteristic value of the first 10-order POD mode of the electrical instability data generated by the fault (proportional magnitude of the energy share and the total energy share of the characteristic value of the first 10-order POD mode). It can be seen from the table that the sum of the energies of the modes 15 reaches 99%, which indicates that the fluctuation of the fault electrical data (electrical data) is particularly strong.
Fig. 2 shows the variation trend of the ratio of the characteristic value of the 50 th-order POD mode to the energy share, in which the abscissa is the order i of the characteristic value and the ordinate is the ratio of each order to the total energy expressed in logarithmic form.
As can be seen from fig. 2 and the above table, the obtained feature values are all present in pairs, and the energy occupied by the pair of feature values is substantially the same. Wherein the proportion of the fluctuation energy occupied by the first pair of POD modes is 42.4% and 42.37%, respectively. The total energy occupied by the remaining POD modes is not more than 5%, and the total energy occupied by the first 2-order POD mode is 84.77% according to the definition of E (k). Therefore, it can be considered that most of the electrical signal characteristics (a large portion of the electrical signal characteristics) generated due to the unknown fault are included in the first 2-order mode; the proportion of the first 8-order mode to the total energy is as high as 96.65%. It can be seen that the first 6-stage POD mode can fully grasp the main characteristics of the fault electric field, (but) compared with the stable electric data of the box-type transformer box (other) in normal operation, it can be seen that the energy occupancy rate of the electric field in the high-order mode is very high, which indicates that the fluctuation of the fault electric data is particularly strong.
(6) Analysis of modal transformation over time:
fig. 3, 4, 5, and 6 show curves of changes in mode coefficients corresponding to 8 modes (i.e., the first 8 modes) having high energy in POD analysis of a fault electrical signal with time steps. The meaning of the modal coefficients to the instantaneous electrical data refers to the projection of the electrical data to the modal, i.e. to the amount of energy captured by the modal by the instantaneous electrical data. It can be seen from the figure that the change development of the modal coefficients along the time step shows strong regularity and periodicity. The adjacent mode pairing phenomenon is also obviously reflected in the curve, the amplitude of the 3-order and 4-order mode coefficients is directly reduced by a quantity level compared with the 1-order and 2-order modes, the occupied energy share is obviously reduced, and the fluctuation frequency is obviously improved. The mode coefficients of the first 4 orders also show good periodicity characteristics, and the periodicity characteristics from the 5 th order mode are not obvious.
(7) And (3) matching with frequency modal analysis:
after FFT decomposition of the mode coefficients, the first 8 modes are analyzed in summary, and from fig. 7, 8, 9, 10, 11, 12, 13, and 14, the phenomenon can be seen that, in the modes 1 and 2, the main frequency peak is 1064hz (1.07BPF) and the secondary frequency peak is 3304 hz; in modes 3 and 4, the main frequency peak is 2133hz, the auxiliary frequency peak is 4023hz, and the small frequency peak is near 1000 hz. And the frequency glitches in 3, 4 order modes are increased remarkably; in 5 and 6-order modes, the peak value of the main frequency is 1104hz, the peak value of the auxiliary frequency is 3295hz, and 2139 hz; in the 7 and 8-order modes, the main frequency peak is near 1054hz, and the auxiliary frequency peak is 3266 hz. In summary, it can be seen that there are representations of the main frequencies RI in the relative coordinate systems 1,2, 5, 6, 7, and 8. The multi-peak characteristic appears in the 3, 4, 5, 6 and order mode pairs, and the gradual increase of the mode also means representing the higher order pseudo-sequence structure frequency in the electric field, and the fluctuation instability phenomenon is most obvious in the aspect of fluctuation instability, namely in the two groups of mode pairs.
(8) Mode coefficient lissajous figure analysis:
fig. 15, 16, 17, 18, 19, 20, and 21 are lissajous diagrams of modal coefficients of respective orders, and it can be seen that the ratio of the two modal coefficients in each of the adjacent modes (first order, second order), (third order, fourth order), (fifth order, sixth order), (seventh order, eighth order) is 1: 1, (first order, third order, fifth order) frequency ratio is 1: 2: 3. it can be seen that the frequency of the 3 and 4 order mode coefficients is twice the frequency of the 1 and 2 orders, which reflects the higher frequency quasi-sequence structure in the fluctuation (fault) unstable electric field, but it also can be seen that the 3 and 4 order amplitudes are very small, i.e. the quasi-sequence structure has small contribution to the whole fluctuation (fault) unstable electric field structure. It can be seen from the figure that the mode coefficients after POD decomposition are coupled with each other, and the higher the order, the higher the frequency of the mode coefficient corresponding to the higher frequency, that is, the higher frequency of the pseudo-sequence structure in the fault electric field.
When only the traditional Fourier transform is used, the modal distribution condition of the data in a frequency domain can be obtained, and the frequency modal analysis result shows that only the signal component energy which is not fundamental frequency is obtained, so that the fundamental frequency energy proportion is reduced, and the problem of inaccurate precision of the conversion of the fundamental frequency voltage is caused. But the true source of the failure cannot be analyzed.
The following available information is obtained from the calculated data obtained by the above calculation and analysis:
1. the data are decomposed in mutually orthogonal dimensions, and the main energy distribution of the data is mainly distributed in the first two-order modes, which means that the effect of dimension reduction and simple processing can be achieved by carrying out detailed analysis on the first two-order modes, and the mode components with low energy contribution rate are ignored as far as possible under the condition of ensuring the effectiveness of the data.
2. The data obtained by visualizing the mode coefficient along with the time change shows that the data has the coupling phenomenon of paired modes, namely every two-order mode has the trend of mutually conjugate modes, and the periodicity of the mode coefficient gradually becomes worse.
3. The data subjected to the frequency domain modal decomposition is subjected to the modal analysis method, the decomposition modal in the frequency domain is subjected to modal decomposition, and the fact that the dimension of the modal between each frequency does not have influence on each other is found, but the mutual coupling capacity is found to be larger and larger along with the gradual increase of the modal coefficient is also found, which can be clearly seen from the lissajous figure.
4. From the above, it can be concluded that the multi-mode coupling phenomenon due to electromagnetic interference occurs due to the superposition of signals with excessively different frequencies.
This phenomenon makes it more difficult to accurately find the cause of a fault by making it impossible to identify the cause of the fault by means of fourier changes alone. Through the POD decomposition method and the Fourier transform, accurate fault information can be obtained, fault parameters are filtered, and powerful information is provided for the accuracy of electrical data acquisition and the decision of an electrical big data platform.
Claims (6)
1. A modal analysis method for solving complex electrical faults is characterized by comprising the following steps:
(1) performing high-dimensional degradation processing on the electrical data by adopting an algorithm taking intrinsic orthogonal decomposition as a core;
(2) and then carrying out matching analysis, specifically comprising energy ratio analysis, visual display analysis of the change of the modal coefficient along with time steps, and matching frequency modal analysis and Lissajous graphical analysis of the modal coefficient.
2. The modal resolution method for resolving complex electrical faults as recited in claim 1, wherein: the step (1) is to collect the required unstable electrical data segment, and to perform reduced order decomposition on the electrical data segment into an expansion sequence of a function only related to time and a function only related to space, namely
In the formula (I), the compound is shown in the specification,
fluctuation amount of variable representing mean value at removal time, ai(t) represents the modal coefficient in units of the variable analyzed; phi is aiAnd (x, y) is a dimensionless spatial characteristic function, and the sequence is subjected to intrinsic orthogonal decomposition of the matrix to obtain a coefficient matrix and a mode matrix.
3. The modal resolution method for resolving complex electrical faults as recited in claim 1, wherein: the energy ratio analysis in the step (2) is specifically based on a mode decomposition principle, that is, firstly, how many orders of modes can contain most of information in an original electric field needs to be known, that is, each order of POD modes needs to be obtained, and according to a POD solving process, by solving a characteristic value lambda of a covariance matrix RiAnd arranging the POD modes in a descending order to obtain the proportion of POD modes of each order and establishing the order of the modes which is enough to contain most information of the original electrical data.
4. The modal resolution method for resolving complex electrical faults as recited in claim 1, wherein: the step (2) of performing visual display analysis on the change of the modal coefficient along with the time step specifically includes establishing a curve of the change of the corresponding modal coefficient along with the time step, wherein the meaning of the modal coefficient to the instantaneous electrical field refers to the projection of the electrical data to the modal, that is, the magnitude of the energy captured by the modal by the instantaneous electrical data.
5. The modal resolution method for resolving complex electrical faults as recited in claim 1, wherein: in the step (2), a joint frequency modal analysis method, namely fast fourier transform, is specifically adopted in cooperation with the frequency modal analysis, and information for analysis decision is provided by analyzing the same characteristic points and the characteristic points with larger difference between the two modes.
6. The modal resolution method for resolving complex electrical faults as recited in claim 1, wherein: the Lissajous figure analysis of the mode coefficient in the step (2) is to firstly collect the objective data volume from a box type transformer box of a certain model and then analyze the data volume.
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