CN115099280A - Prony iterative analysis method, computing equipment, storage medium and power grid system - Google Patents
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Abstract
The invention provides a Prony iteration analysis method, a calculation device, a storage medium and a power grid system, which relate to the technical field of oscillation analysis and comprise the following steps: the method comprises the steps of carrying out data sampling on an oscillation signal to be identified according to a set sampling rate, carrying out preprocessing with abnormal data detection and correction on a one-dimensional sample set obtained through sampling, expanding a multi-dimensional sample set, adopting a Prony model of a P order to infer the multi-dimensional sample set according to the multi-dimensional sample set, detecting whether P reaches an expected value or not according to an oscillation parameter set, if not, adopting an iteration method to heighten the Prony model by one order, if so, determining and outputting an oscillation analysis result, overcoming the defect that the accuracy is difficult to promote due to the fact that a traditional Prony oscillation analysis method is limited by the signal-to-noise ratio and the fixed-order accuracy of the sample, avoiding the fixed-order in the Prony oscillation analysis process, simplifying the fixed-order mode, reducing noise interference, promoting the fixed-order accuracy and being beneficial to promoting the accuracy and efficiency of Prony oscillation analysis.
Description
Technical Field
The invention relates to the technical field of oscillation analysis, in particular to a Prony iteration analysis method, computing equipment, a storage medium and a power grid system.
Background
With more and more new energy devices being connected to the power grid system, the damping and inertia of the power grid system are reduced, different oscillation modes are easier to excite, oscillation phenomena are more frequent, the stability and the safety of the power grid system are seriously threatened, the power grid system can generate oscillation signals in the oscillation process, the oscillation signals in the power grid system are analyzed, and the method is particularly important for online early warning, power grid transformation and the like.
Compared with a Fourier algorithm and a least square algorithm, the Prony model fits signals by using a group of linear combinations of exponential functions with any amplitude, phase, frequency and damping coefficient, has the advantages of no need of frequency domain response, sample autocorrelation estimation and the like, and is more suitable for analyzing oscillation signals.
At present, in the Prony oscillation analysis process, an extended order matrix is constructed according to a plurality of data points acquired from an oscillation signal to be identified, after an effective rank P (namely, the order of a Prony model) is determined for the extended order matrix by adopting a singular value decomposition method, a P-dimensional linear equation set is solved based on the extended order matrix to obtain an equation coefficient sequence one and minimum error energy, a characteristic equation is solved based on the equation coefficient sequence one to obtain a root sequence, a van der waals equation set is solved by combining the root sequence and a plurality of data points acquired by sampling to obtain an equation coefficient sequence two, an amplitude measuring and calculating sequence and a phase sequence are calculated based on the equation coefficient sequence two, and the amplitude sequence, the phase sequence, the frequency sequence and the damping coefficient sequence are output as an oscillation analysis result based on the root sequence and the damping coefficient sequence.
Wherein, the equation coefficient sequence one can be expressed as [ a ] 1 ，…，a i ，…，a P ] T The root sequence may be represented as [ z ] 1 ，…，z i ，…，z P ] T The sequence of approximate points can be expressed as
The equation coefficient sequence two can be expressed as [ b ] 1 ，…，b i ，…，b P ] T And i is a positive integer from 1 to P.
Wherein the amplitude sequence can be represented as [ A ] 1 ，…，A i ，…，A P ] T The phase sequence can be expressed as [ theta ] 1 ，…，θ i ，…，θ P ] T The frequency sequence may be represented as f 1 ，…，f i ，…，f P ] T The damping coefficient sequence can be expressed as [ alpha ] 1 ，…，α i ，…，α P ] T 。
However, the accuracy of the existing Prony oscillation analysis method is difficult to improve due to the limitation that the signal-to-noise ratio of the sample is higher or/and the order-fixing precision is lower.
Disclosure of Invention
The present invention is directed to solve the technical problems of the related art at least to some extent, and to achieve the above objects, the present invention provides a Prony iterative analysis method, a computing device, a non-transitory computer-readable storage medium, and a power grid system.
The first aspect of the present invention provides a Prony iterative analysis method, which includes:
s1, performing data sampling on the oscillation signal to be identified according to a set sampling rate to obtain a one-dimensional sample set with the length of N, wherein N is a positive integer greater than 2;
s2, preprocessing the one-dimensional sample set with abnormal data detection and correction;
s3, expanding a multi-dimensional sample set based on the preprocessed one-dimensional sample set;
s4, according to the multi-dimensional sample set, adopting a Prony model of order P to deduce an oscillation parameter set, wherein P is a positive integer larger than 1;
s5, detecting whether P reaches the expected value according to the oscillation parameter set, if not, executing S6, if yes, executing S7;
s6, returning to S4 after P +1 to raise the Prony model by one step;
and S7, determining and outputting an oscillation analysis result matched with the oscillation signal to be identified.
A second aspect of the invention provides a computing device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, when executing the computer program, implementing the Prony iterative analysis method according to the first aspect.
A third aspect of the invention provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the Prony iterative analysis method according to the first aspect.
A fourth aspect of the invention provides a power grid system, comprising the computing device according to the second aspect.
The Prony iterative analysis method, the computing equipment, the non-transitory computer readable storage medium and the power grid system have the advantages that: in consideration of the fact that data abnormality is easy to occur in the sampling process, the one-dimensional sample set obtained through sampling is corrected under the condition that the data abnormality occurs through preprocessing, the accuracy of a sample is improved, the sample data is expanded through the preprocessed one-dimensional sample set, the sample capacity is increased, the signal-to-noise ratio of the sample is improved, a circulation mechanism with mutual promotion of Prony oscillation analysis and order iteration is formed according to the multi-dimensional sample set obtained through expansion until the order is determined to a desired value, the defect that the accuracy of the traditional Prony oscillation analysis method is difficult to improve due to the fact that the traditional Prony oscillation analysis method is limited by the signal-to-noise ratio of the sample and the order accuracy is overcome, the order is not required to be determined in the Prony oscillation analysis process, the order determination mode is simplified, noise interference is reduced, the order determination accuracy is improved, and the accuracy and the efficiency of the Prony oscillation analysis are improved.
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FIG. 1 is a schematic flow chart of a Prony iterative analysis method according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of S2 in fig. 1;
FIG. 3 is a diagram of a subsequence of an embodiment of the present invention;
fig. 4 is a schematic flow chart of S3 in fig. 1;
FIG. 5 is a sequence diagram of an alternate (k + 1) th data point according to an embodiment of the present invention;
fig. 6 is a schematic flowchart of S4 in fig. 1;
FIG. 7a is a schematic waveform diagram illustrating the respective acquisition of oscillation signals from a plurality of buses according to an embodiment of the present invention;
FIG. 7b is a schematic diagram of waveforms for collecting the oscillation signal from the bus 5 according to the embodiment of the present invention;
FIG. 7c is a schematic diagram of waveforms for collecting the oscillation signal from the bus 13 according to the embodiment of the present invention;
FIG. 8a is a diagram of an oscillation mode corresponding to P being 3 according to an embodiment of the present invention;
FIG. 8b is a diagram illustrating the comparison between the to-be-identified oscillation signal and the fit oscillation signal corresponding to P being 3 according to the embodiment of the present invention;
FIG. 9a is a schematic diagram of two oscillation modes corresponding to P being 11 according to an embodiment of the present invention;
FIG. 9b is a diagram illustrating the comparison between the oscillation signal to be identified and the fitting oscillation signal corresponding to P11 according to the embodiment of the present invention;
FIG. 10a is a schematic diagram of three oscillation modes corresponding to P being 15 according to an embodiment of the present invention;
FIG. 10b is a diagram illustrating the comparison between the oscillation signal to be identified and the fitting oscillation signal corresponding to P15 according to the embodiment of the present invention;
FIG. 11a is a schematic diagram of three oscillation modes corresponding to P being 17 according to an embodiment of the present invention;
FIG. 11b is a diagram illustrating the comparison between the to-be-identified oscillation signal and the fitted oscillation signal corresponding to P17 according to the embodiment of the present invention.
Detailed Description
Embodiments of the invention will now be described in detail with reference to the drawings, wherein like reference numerals designate identical or similar elements throughout the different views unless otherwise indicated. It is to be noted that the embodiments described in the following exemplary embodiments do not represent all embodiments of the present invention. They are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as set forth in the claims, and the scope of the invention is not limited thereto. Features of the various embodiments of the invention may be combined with each other without departing from the scope of the invention.
Furthermore, the terms "sequence one", "sequence two" are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "a sequence one" or "a sequence two" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" or "multi-dimensional" means at least two dimensions, for example: two-dimensional or three-dimensional, etc., unless expressly specified otherwise.
Referring to fig. 1, the Prony iterative analysis method according to an embodiment of the present invention includes S1 to S7.
And S1, performing data sampling on the oscillation signal to be identified according to the set sampling rate to obtain a one-dimensional sample set with the length of N, wherein N is a positive integer greater than 2.
In the embodiment of the present invention, the one-dimensional sample set may be represented as X ═ X 1 ，…，x n ，…x N ]，x n The nth data point obtained by sampling is shown, N ranges from 1 to N, and it should be understood that the expression form of the one-dimensional sample set is not limited to be in a row vector form, and may also be in a column vector form, so that the N data points obtained by collecting can be stored in a sequence form, and a one-dimensional sample set can be formed.
S2, preprocessing with abnormal data detection and correction is carried out on the one-dimensional sample set.
And S3, expanding the multi-dimensional sample set based on the preprocessed one-dimensional sample set.
And S4, deducing the oscillation parameter set by adopting a Prony model of a P order according to the multi-dimensional sample set, wherein P is a positive integer larger than 1.
S5, detecting whether P reaches the expected value according to the oscillation parameter set, if not, executing S6, and if so, executing S7.
S6, let P be P +1, and return to S4 to raise the Prony model by one step.
And S7, determining and outputting an oscillation analysis result matched with the oscillation signal to be identified.
By using the Prony iterative analysis method, considering that data abnormity is easy to occur in the sampling process, the one-dimensional sample set obtained by sampling is corrected under the condition of data abnormity through preprocessing, the accuracy of the sample is improved, the preprocessed one-dimensional sample set expands the sample data, increases the sample capacity, is beneficial to improving the signal-to-noise ratio of the sample, a circulation mechanism for mutual promotion of Prony oscillation analysis and order iteration is formed on the basis of a multi-dimensional sample set obtained through capacity expansion until the order is fixed to a desired value, the defect that the accuracy is difficult to improve due to the fact that a traditional Prony oscillation analysis method is limited by a sample signal-to-noise ratio and order fixing precision is overcome, order fixing is not needed in the Prony oscillation analysis process, an order fixing mode is simplified, noise interference is reduced, order fixing precision is improved, and accuracy and efficiency of Prony oscillation analysis are improved.
Alternatively, referring to fig. 2, S2 includes S21 to S26.
S21, selecting the nth data point as the detected data point in the one-dimensional sample set, and making each of the plurality of data points listed on both sides of and consecutive to the detected data point as a sub-sequence of reference data points, wherein n starts from 2.
S22, according to the multiple reference data points, detecting whether the detected data point is abnormal, if yes, executing S23 and then executing S24, if no, executing S24 directly.
And S23, correcting the detected data points.
S24, detecting whether N reaches N-1, if not, executing S25, if yes, executing S26;
at S25, n is set to n +1, and the process returns to S21, so that the subsequence is shifted forward by one bit in synchronization with the detected data point.
S26, outputting the preprocessed one-dimensional sample set for use in S3.
In one example, the 2 nd data point is a subject data point, and the 1 st data point and the 3 rd data point can each be reference data points; the 3 rd data point is a detected data point, and the 2 nd data point and the 4 th data point can be reference data points respectively; by analogy, the (N-1) th data point is the detected data point, and the (N-2) th data point and the (N) th data point can be the reference data point respectively.
In another example, the 2 nd data point is a subject data point, and the 1 st, 3 rd, 4 th and 5 th data points can each be reference data points; the 3 rd data point is a detected data point, and the 1 st data point, the 2 nd data point, the 4 th data point and the 5 th data point can be respectively reference data points and are sequentially extrapolated to the N-2 th data point; the (N-1) th data point is a detected data point, and the (N-4) th data point, the (N-3) th data point, the (N-2) th data point, and the (N) th data point may each be a reference data point.
It should be understood that the number of reference data points located before the detected data point and the number of reference data points located after the detected data point may be the same and remain the same, or may be adaptively changed depending on the location of the detected data point; the sub-sequence may be viewed as a data window to define a data range, and the length of the sub-sequence may depend on the actual situation of the one-dimensional sample set, for example, if N equals 100, the length of the sub-sequence may be 5, and if N equals 150, the length of the sub-sequence may be 8.
And for the one-dimensional sample set, in the process of traversing the (N-1) th data point from the 2 nd data point, carrying out anomaly detection on each data point, only correcting each data point in an abnormal condition, and keeping each data point in a normal condition unchanged so as to prevent error and leakage and take simplicity and accuracy into account.
Optionally, the plurality of reference data points and the detected data point with the abnormality satisfy the following abnormal data detection model:
wherein, x' n The representation is adapted to replace the examined data point x n New data point of from x n-i To x n-1 Each representing a reference data point preceding the examined data point, from x n+1 To x L+n-i-1 Each representing a reference data point, C, located after the examined data point 0 Denotes a predetermined threshold value greater than zero, L denotes the length of the subsequence, L is [3, N-1%]I is [1, L-2 ]]Is a positive integer of (1).
Illustratively, referring to fig. 3, the nth data point with abnormality is the detected data point, the respective normal nth-2 data point, nth-1 data point, nth +1 data point and nth +1 data point are all reference data points, the four reference data points are monotonically increasing, for example, the five data points may be 1.2, 3.6, 10, 6.8 and 9 in sequence, C 0 Can take a value of 3, new data point x' n At 5.2, the present examples are intended to aid in understanding the sample set processing process and should not be construed as limiting the practical circumstances of the sample set.
In the abnormal data detection model, the plurality of reference data points are limited to be monotonically increased or monotonically decreased, the abnormal detected data points are also limited to lose monotonicity, the plurality of reference data points and the normal detected data points do not meet the abnormal data detection model, and simplicity and accuracy are both considered.
Optionally, S23 includes: at two reference data points x n-1 And x n+1 To the detected data point x n After deletion, new data point x 'is interpolated' n To prevent disorders, with simplicity and reliability.
Alternatively, referring to fig. 4, S3 includes S31 to S35.
And S31, constructing and initializing a two-dimensional array, wherein the preprocessed one-dimensional sample set is set as a 1 st-dimensional vector in the two-dimensional array.
And S32, copying the 1 st-dimensional vector into a (k + 1) th-dimensional vector for the kth time, and replacing the (k + 1) th data point with a new data point obtained by performing linear interpolation measurement on the kth data point and the (k + 2) th data point in the (k + 1) th-dimensional vector, wherein k starts from 1.
Illustratively, referring to fig. 5, two solid circles respectively represent the kth data point and the (k + 2) th data point, an arithmetic mean of the two data points is calculated as a new data point, and after the (k + 1) th data point represented by a cross is deleted, the new data point represented by a dotted circle is interpolated.
S33, checking whether k reaches N-2, if not, executing S34, if yes, executing S35.
S34, let k be k +1, then return to S32 to reconstruct the next one-dimensional vector in the two-dimensional array according to the 1 st vector.
S35, outputting the two-dimensional array with the N-1-dimensional vector as a multi-dimensional sample set for use in S4.
Illustratively, the multi-dimensional sample set may be represented as follows:
wherein x is (k，n) Representing the nth data point in the k-dimensional vector, k being from 1 to N-1.
And (3) expanding N-2-dimensional vectors except the 1 st-dimensional vector by utilizing the preprocessed one-dimensional sample set and by means of a two-dimensional array, and taking simplicity and accuracy into consideration.
Optionally, referring to fig. 6, S4 includes S41 to S47.
S41, solving a P-dimensional linear equation set based on the k-dimensional vector in the multi-dimensional sample set to obtain a k-dimensional equation coefficient sequence I, wherein k is iterated again from 1, and 2P is less than or equal to N.
Substituting each data point in the kth-dimensional vector into the P-dimensional linear system of equations can be expressed as follows:
wherein, the coefficient sequence one of the kth equation can be expressed as [ a ] (k，1) ，…，a (k，j) ，…，a (k，P) ] T And j is a positive integer from 1 to P.
And S42, solving the characteristic equation based on the kth equation coefficient sequence I to obtain the kth root sequence.
The k-th equation coefficient sequence is integrated into the characteristic equation and can be expressed as follows:
wherein z is (k，j) Represents the root adapted to the jth coefficient in the kth equation coefficient sequence one, and the kth root sequence can be expressed as [ z (k，1) ，…，z (k，j) ，…，z (k，P) ] T 。
And S43, solving the Van der Monte equation system based on the kth root sequence and the kth-dimension vector to obtain a kth equation coefficient sequence II.
Substituting the kth root sequence and the first P data points in the kth dimension vector into the Van der Monte equation set can be expressed as follows:
wherein, the kth equation coefficient sequence two can be expressed as [ b (k，1) ，…，b (k，j) ，…，b (k，P) ] T 。
S44, respectively measuring a kth amplitude sequence and a kth phase sequence based on the kth equation coefficient sequence II; and respectively measuring and calculating the kth frequency sequence and the kth damping coefficient sequence based on the kth root sequence.
Calculating the coefficient sequence two of the kth equation by the formula (1) to obtain the kth amplitude sequence which can be shown in the tableShown as [ A ] (k，1) ，…，A (k，2) ，…，A (k，P) ] T 。
Formula (1): a. the (k，j) ＝|b (k，j) |。
Calculating the coefficient sequence two of the kth equation by the formula (2) to obtain the kth phase sequence, wherein the kth phase sequence can be expressed as [ theta ] (k，1) ，…，θ (k，j) ，…，θ (k，P) ] T 。
Formula (2): theta (k，j) ＝arctan[Im(b (k，j) )/Re(b (k，j) )]Wherein arctan represents an arctangent function, Im represents taking a complex imaginary part function, and Re represents taking a complex real part function.
The kth root sequence is measured and calculated through the formula (3), so that the kth frequency sequence is obtained, and the kth frequency sequence can be expressed as [ f [ ] (k，1) ，…，f (k，j) ，…，f (k，P) ] T 。
Formula (3): f. of (k，j) ＝arctan[Im(z (k，j) )/Re(z (k，j) )]。
Calculating the kth root sequence by the formula (4) to obtain the kth damping coefficient sequence, wherein the kth damping coefficient sequence can be expressed as [ alpha ] (k，1) ，…，α (k，j) ，…，α (k，P) ] T 。
Formula (4): alpha is alpha (k，j) ＝In|z (k，j) I/Δ t, where In represents a natural log function and Δ t represents a sampling interval.
S45, checking whether k reaches N-1, if not, executing S46, if yes, executing S47.
In S46, k is changed to k +1, and the process returns to S41.
And S47, combining the N-1 amplitude sequences, the N-1 phase sequences, the N-1 frequency sequences and the N-1 damping coefficient sequences to obtain the oscillation parameter set.
For example, N-1 amplitude sequences may be combined into a two-dimensional array, and similarly, the combination manner of the N-1 phase sequences, the N-1 frequency sequences, and the N-1 damping coefficient sequences may be the same as that of the N-1 amplitude sequences, and thus, the details are not repeated here.
As shown above, the N-1 amplitude sequences are combined in a two-dimensional array.
Optionally, S5 includes:
respectively carrying out averaging measurement and calculation processing on the N-1 amplitude sequences, the N-1 phase sequence, the N-1 frequency sequence and the N-1 damping coefficient sequence to obtain an amplitude mean value sequence, a phase mean value sequence, a frequency mean value sequence and a damping mean value sequence;
constructing a fitting oscillation signal based on the amplitude mean sequence, the phase mean sequence, the frequency mean sequence and the damping mean sequence;
and detecting whether the fitting degree of the fitting oscillation signal is greater than preset convergence precision, if so, determining that P does not reach an expected value, and if not, determining that P has reached the expected value.
Illustratively, to
Represents a sequence of amplitude means to
Represents a sequence of phase means to
Representing a sequence of frequency means to
Representing a sequence of damping means.
Exemplaryly,
wherein,
which represents the fitting of the oscillating signal to the oscillator,
representing the jth average amplitude in the amplitude mean sequence,
represents the jth average damping coefficient in the sequence of damping means,
representing the jth average frequency in the sequence of frequency means,
representing the jth average phase in the sequence of phase means,
t represents time.
Illustratively, the degree of fitting as mentioned above is estimated by equation (5), and equation (5) is as follows:
wherein s is 2 The degree of fit is expressed in terms of,
representing the m-th data point, x, in the fitted oscillator signal m Representing data points corresponding to the m-th point in the oscillation signal to be recognized
The data points of (a).
Illustratively, the predetermined convergence accuracy may be 0.0001, if the fitting degree is greater than 0.0001, it is reflected that P has not reached the desired value, and if the fitting degree is less than or equal to 0.0001, it is reflected that P has reached the desired value, and under the condition that P has reached the desired value, the amplitude mean sequence, the phase mean sequence, the frequency mean sequence, and the damping mean sequence may be combined as the oscillation analysis result.
The signals are fitted through the four oscillation parameter sequences after the averaging processing, so that the accuracy of fitting the oscillation signals is improved, and the accuracy of identifying the order is improved.
A computing device according to another embodiment of the invention comprises a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the Prony iterative analysis method as mentioned above when executing the computer program. It will be appreciated that the aforementioned computing device may be a server or a terminal device such as a desktop or laptop computer, wherein the processor may be connected to the memory via a universal serial control bus.
A power grid system of another embodiment of the present invention includes the computing device as mentioned above.
In the embodiment of the invention, after a power grid system fails, multiple buses oscillate in a period of time, and oscillation modes are mainly divided into 0.08Hz, 0.15Hz and 0.31Hz, wherein two buses are respectively a bus 5 and a bus 13, fig. 7a shows a schematic waveform diagram of oscillation signals respectively collected from the multiple buses, fig. 7b shows a waveform diagram of oscillation signals collected from the bus 5, and fig. 7c shows a waveform diagram of oscillation signals collected from the bus 13.
In the embodiment of the present invention, referring to fig. 8a and 8b, when the order P of the Prony model is 3, an oscillation mode of 0.31Hz is analyzed, two oscillation modes of 0.15Hz and 0.08Hz are not analyzed, and the fitting oscillation signal and the signal to be identified have a large difference.
In the embodiment of the present invention, referring to fig. 9a and 9b, when the order P of the Prony model is 11, two oscillation modes, i.e. 0.31Hz and 0.15Hz, are analyzed, and no oscillation mode of 0.08Hz is analyzed, and compared with the case where P is 3, the fitted oscillation signal is closer to the signal to be identified, but for the fitted oscillation signal, the oscillation mode of 0.15Hz belongs to the attenuation process, and does not conform to the actual situation of the oscillation signal to be identified, and the order needs to be continuously adjusted higher.
In the embodiment of the present invention, referring to fig. 10a and 10b, when the order P of the Prony model is 15, three oscillation modes of 0.31Hz, 0.15Hz, and 0.08Hz are analyzed, and the degree of fitting the oscillation signal to approach the oscillation signal to be identified is the highest, where 15 is an expected value and represents an optimal order.
In the embodiment of the present invention, referring to fig. 11a and 11b, when the order P of the Prony model is 17, compared with the order P of 15, although the fitting effect is increased by two orders, the fitting effect is not improved, and instead, the interference is generated due to the analysis of the oscillation mode that does not exist in the signal to be identified.
It should be noted that any one of fig. 8b, 9b, 10b and 11b is presented in upper and lower sub-graphs, where a solid line in the upper sub-graph represents the oscillation signal to be identified corresponding to the bus 5, a solid line in the lower sub-graph represents the oscillation signal to be identified corresponding to the bus 13, and a dotted line represents the corresponding fitted oscillation signal.
A non-transitory computer-readable storage medium of another embodiment of the invention stores a computer program which, when executed by a processor, implements the Prony iterative analysis method as mentioned above.
The above-mentioned computing device, non-transitory computer-readable storage medium, and power grid system may be referred to the above-mentioned specific description of the Prony iterative analysis method and its beneficial effects, and are not described herein again.
Generally, the computer instructions to implement the methods of the present invention may be carried on any combination of one or more computer-readable storage media. Non-transitory computer readable storage media may include any computer readable medium except for the signal itself, which is propagating on a temporary basis.
A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAk), a read-only memory (ROk), an erasable programmable read-only memory (EPROk or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROk), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
Computer program code for carrying out operations for aspects of the present invention may be written in one or more programming languages, including an object oriented programming language such as Java, Skalltalk, C + +, or a combination thereof, as well as conventional procedural programming languages, such as the "C" language or similar programming languages, and in particular Python languages suitable for neural network computing and platform frameworks based on tensrflow, PyTorch, etc., may be used. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
Although embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are illustrative and not to be construed as limiting the present invention, and that changes, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (10)
1. A Prony iterative analysis method, comprising:
s1, performing data sampling on the oscillation signal to be identified according to a set sampling rate to obtain a one-dimensional sample set with the length of N, wherein N is a positive integer greater than 2;
s2, preprocessing the one-dimensional sample set with abnormal data detection and correction;
s3, expanding a multi-dimensional sample set based on the preprocessed one-dimensional sample set;
s4, according to the multi-dimensional sample set, adopting a Prony model of order P to deduce an oscillation parameter set, wherein P is a positive integer larger than 1;
s5, detecting whether P reaches the expected value according to the oscillation parameter set, if not, executing S6, if yes, executing S7;
s6, returning to S4 after P +1 to raise the Prony model by one step;
and S7, determining and outputting an oscillation analysis result matched with the oscillation signal to be identified.
2. The Prony iterative analysis method of claim 1, wherein said S2 comprises:
s21, selecting the nth data point as the detected data point in the one-dimensional sample set, and making each of the plurality of data points listed on both sides of the detected data point and consecutive thereto in a subsequence as a reference data point, wherein n starts from 2;
s22, detecting whether the detected data point is abnormal or not according to the reference data points, if so, executing S23 and then executing S24, and if not, directly executing S24;
s23, correcting the detected data point;
s24, detecting whether N reaches N-1, if not, executing S25, if yes, executing S26;
s25, after n is equal to n +1, returning to S21 to make the subsequence advance by one bit synchronously with the detected data point;
s26, outputting the preprocessed one-dimensional sample set for use by the S3.
3. The Prony iterative analysis method of claim 2, wherein a plurality of said reference data points and said subject data points where an anomaly occurs satisfy the following anomaly data detection model:
wherein, x' n Representing data points x suitable for replacing said examined data point n New data point of from x n-i To x n-1 Each representing the reference data point preceding the examined data point, from x n+1 To x L+n-i-1 Each representing the reference data point, C, after the examined data point 0 Represents a preset threshold, L represents the length of the subsequence, and L is [3, N-1 ]]Wherein i is [1, L-2 ]]Is a positive integer of (1).
4. The Prony iterative analysis method of claim 3, wherein the S23 comprises: at two of said reference data points x n-1 And x n+1 For the examined data point x n After deletion, the new data point x 'is interpolated' n 。
5. The Prony iterative analysis method of claim 1, wherein said S3 comprises:
s31, constructing and initializing a two-dimensional array, wherein the preprocessed one-dimensional sample set is set as a 1 st-dimensional vector in the two-dimensional array;
s32, copying the 1 st-dimensional vector into a (k + 1) th-dimensional vector for the kth time, and replacing the (k + 1) th data point with a new data point obtained by performing linear interpolation measurement on the kth data point and the (k + 2) th data point in the (k + 1) th-dimensional vector, wherein k starts from 1;
s33, detecting whether k reaches N-2, if not, executing S34, if yes, executing S35;
s34, returning to S32 after k is k +1, so as to reconstruct a next one-dimensional vector in the two-dimensional array according to the 1 st-dimensional vector;
s35, outputting the two-dimensional array with N-1 dimensional vectors for use by the S4 as the multi-dimensional sample set.
6. The Prony iterative analysis method of claim 5, wherein the S4 comprises:
s41, solving a P-dimensional linear equation set based on the kth-dimensional vector in the multi-dimensional sample set to obtain a kth equation coefficient sequence I, wherein k is iterated again from 1;
s42, solving a characteristic equation based on the kth equation coefficient sequence I to obtain a kth root sequence;
s43, solving a Van der Monte equation set based on the kth root sequence and the kth-dimension vector to obtain a kth equation coefficient sequence II;
s44, respectively measuring a kth amplitude sequence and a kth phase sequence based on the kth equation coefficient sequence II, and respectively measuring a kth frequency sequence and a kth damping coefficient sequence based on the kth root sequence;
s45, detecting whether k reaches N-1, if not, executing S46, and if yes, executing S47;
s46, when k is k +1, returns to S41;
and S47, combining the N-1 amplitude sequences, the N-1 phase sequences, the N-1 frequency sequences and the N-1 damping coefficient sequences to obtain the oscillation parameter set.
7. The Prony iterative analysis method of any of claims 1-6, wherein said set of oscillation parameters comprises N-1 sequences of amplitude, N-1 sequences of phase, N-1 sequences of frequency, and N-1 sequences of damping coefficients;
the S5 includes:
respectively carrying out averaging measurement and calculation processing on the N-1 amplitude sequences, the N-1 phase sequence, the N-1 frequency sequences and the N-1 damping coefficient sequences to obtain an amplitude mean value sequence, a phase mean value sequence, a frequency mean value sequence and a damping mean value sequence;
constructing a fitting oscillation signal based on the amplitude mean sequence, the phase mean sequence, the frequency mean sequence and the damping mean sequence;
and detecting whether the fitting degree of the fitting oscillation signal is greater than preset convergence precision, if so, determining that P does not reach the expected value, and if not, determining that P has reached the expected value.
8. A computing device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the computer program, implements the Prony iterative analysis method of any of claims 1-7.
9. A non-transitory computer-readable storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, implements the Prony iterative analysis method of any of claims 1-7.
10. A power grid system comprising the computing device of claim 8.
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| CN118013304A (en) * | 2024-02-19 | 2024-05-10 | 国网湖北省电力有限公司襄阳供电公司 | Transformer fault positioning method and system based on clustering algorithm |
| CN118250106A (en) * | 2024-05-30 | 2024-06-25 | 南京华飞数据技术有限公司 | Prony algorithm-based network transmission data management system and method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN118013304A (en) * | 2024-02-19 | 2024-05-10 | 国网湖北省电力有限公司襄阳供电公司 | Transformer fault positioning method and system based on clustering algorithm |
| CN118250106A (en) * | 2024-05-30 | 2024-06-25 | 南京华飞数据技术有限公司 | Prony algorithm-based network transmission data management system and method |
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