CN110967556A - Real-time harmonic detection method based on feedback neural network - Google Patents
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Abstract
The invention discloses a real-time harmonic detection method based on a feedback neural network, which comprises the steps of constructing a sine basis function feedback neural network structure, designing an excitation function design and a network weight matrix suitable for harmonic detection, constructing a quadratic programming problem, obtaining the optimal weight of the sine basis function weight neural network by operating the feedback neural network, calculating the accurate amplitude and phase of fundamental waves and each subharmonic according to the estimated value of the weight matrix, and reconstructing the fundamental waves and each subharmonic. The real-time harmonic detection method overcomes the defects of complex network structure, multiple iteration times, low algorithm precision and the like of the traditional harmonic detection method, and can obtain a network containing harmonic amplitude and phase information only through a simple feedback network; the detection efficiency is high, the precision is high, and the network structure is simple.
Description
Technical Field
The invention relates to the field of power systems, in particular to a real-time harmonic detection method based on a feedback neural network.
Background
A large number of nonlinear devices exist in the power system to rectify and invert the voltage and current of a power grid to generate time-varying harmonic waves, so that the problem of power harmonic pollution is increasingly serious, the quality of electric energy is seriously influenced, and meanwhile, the safety, stability and high-efficiency operation of the power system are threatened; moreover, due to the randomness generated by the harmonic waves of the power system, the harmonic waves are seriously influenced by the nonlinear complexity of the power grid, and the difficulty in real-time detection of the harmonic waves of the power grid is high, so that the real-time accurate detection of the power harmonic waves at the present stage has important significance.
The traditional harmonic measurement method based on analog filter is eliminated because the ability to resist harmonic distortion rate is large and have voltage with additional phase shift is too weak; the Fourier transform method has the defects of frequency spectrum leakage, barrier effect, incapability of detecting non-stationary harmonic waves and the like; the wavelet detection method has good advantages in detecting transient signals or singularities of signals of a power grid, but signal decomposition performed by the method can cause interleaving between high-pass filter groups and low-pass filter groups, a mixing aliasing phenomenon occurs, and the problem that window energy is not concentrated exists. Other harmonic detection methods based on an intelligent optimization algorithm exist, but the optimization algorithm evolution is carried out after time-frequency transformation is carried out, so that the complexity is high.
The basic idea of the neural network algorithm is to adopt a physically realizable system to simulate the structure and the functional system of human brain nerve cells, the algorithm has good nonlinear expression capability, parallel processing capability, strong robustness and self-organizing self-learning capability, and is widely applied to the fields of signal processing and pattern recognition, the harmonic detection problem is equivalent to a signal detection problem, the feedback neural network has a simple structure and is convenient to realize, and the invention tries to solve the harmonic detection problem by using the feedback neural network method.
Disclosure of Invention
The invention aims to provide a real-time harmonic detection method based on a feedback neural network, which enhances the real-time performance of harmonic detection and achieves the aim of detecting each harmonic.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a real-time harmonic detection method based on a feedback neural network comprises the following steps:
1) the periodic signal containing each harmonic in the power electronic system is expressed as:
wherein, w0At fundamental angular frequency, w 02 pi f, f is the fundamental frequency, k is the harmonic order, akAnd
amplitude and phase of the kth harmonic, respectively; m is the highest harmonic number; discretizing the above expression and expanding the discretized expression into a matrix form, then tiEach sample value is represented as
Wherein,
Tsthe sampling period is generally not more than 100 milliseconds;
(ii) a T represents a matrix transposition operation; w is the grid angular frequency;
2) designing an excitation function g (-) of an input and output layer of the feedback neural network: g (x) ═ (x + asin (pi x)); wherein a is more than 0, x is more than infinity and pi is a circumferential rate; sampling value signal x (t)i) As an input signal of the excitation function, an output signal g (x (t) is obtainedi))；
3) Establishing a sine basis weight function matrix as follows:
wherein R represents a real number domain;
4) the following quadratic programming optimization problem is constructed:
wherein:
represents a 2-norm; d ═ diag [ d (0), d (1), …, d (n)]Diag is a diagonal matrix with main diagonal elements of d (0), d (1), … and d (n), and any other elements are 0,
α is a normal number, α ∈ (0,1)]P is the total number of times of feedback of the neural network; w is a weight matrix, and W is a weight matrix,
5) solving the quadratic programming optimization problem to obtain an estimated value of a weight matrix W
And calculating the accurate amplitude and phase of the fundamental wave and each harmonic according to the estimated value of the weight matrix W, and reconstructing the fundamental wave and each harmonic.
The specific calculation process of the estimated value of the weight matrix W comprises the following steps: order to
a) Derivative W and make its value equal to the zero vector:
b) let the r-th iteration fjWhere j is 0, …, n is fixed, let the first derivative be equal to 0, and a unique solution for W is obtained, then:
wherein the superscript-1 represents the matrix inversion operation,
is a main diagonal element of | x (j) & ltY2A diagonal matrix of (a); j ═ t1,t2,…,tn；
c) Setting an iterative formula of the r +1 th feedback network weight: w (r +1) ═ 1- μ g (W (r)) + μ W (0); wherein, mu belongs to (0,1), and W (0) is the initial value of the weight;
d) and repeating the steps a) to c) until the value of the cost function J (W) is not reduced any more, and obtaining a weight matrix, thereby obtaining an estimated value of the weight matrix W.
Reconstructed fundamental amplitude of
Phase is
Reconstructed kth1The amplitude and phase of the subharmonic are
Compared with the prior art, the invention has the beneficial effects that: the invention can enhance the real-time performance of harmonic detection, avoids the complex harmonic detection network structure in the traditional harmonic detection method, obtains the network weight containing harmonic amplitude and phase information through network self-operation, and further extracts the amplitude and phase of fundamental wave and each subharmonic from the weight matrix, thereby achieving the purpose of detecting each subharmonic; the invention has the advantages of high detection precision, good measurement accuracy, strong real-time property and good anti-interference performance.
Drawings
FIG. 1 shows the present invention in analyzing signals as
The fundamental frequency is 50Hz, harmonic waves and phases are randomly generated, and a oscillogram is obtained by analysis under the condition of white Gaussian noise of 10 decibels;
FIG. 2 shows the present invention in analyzing signals as
The fundamental frequency is 50Hz, harmonic waves and phases are randomly generated, and an input and output integral comparison graph is obtained by analysis under the condition of 10 dB Gaussian white noise;
FIG. 3 shows the present invention in analyzing signals as
The fundamental frequency is 50Hz, harmonic waves and phases are randomly generated, and an input and output amplitude error graph is obtained by analyzing under the condition of 10 dB Gaussian white noise.
FIG. 4 shows the present invention in analyzing signals as
The fundamental frequency is 50Hz, harmonic waves and phases are randomly generated, and an input and output phase error graph is obtained by analyzing under the condition of 10 dB Gaussian white noise.
Detailed Description
The invention provides a real-time harmonic detection method based on a feedback neural network, which comprises the following steps:
(1) according to the existing method, a periodic signal model containing each harmonic in a power electronic system is expanded by adopting a trigonometric function and a difference product formula, so that the periodic signal containing each harmonic in the power electronic system can be expressed as
Wherein, wiAngular frequency of the ith harmonic, w 02 pi f, f being the fundamental frequency, AiAnd
amplitude and phase of the ith harmonic, respectively(ii) a N is the highest harmonic order and m is the highest harmonic order. Further expressing equation (1) as a trigonometric function transformation equation
Wherein: w is a0Is the fundamental angular frequency, j is the harmonic order, TsIs the sampling period. Discretizing and expanding the formula (2) into a matrix form, tthiA sampling value x (t)i) This can be expressed as follows:
wherein,
the superscript T denotes the matrix transpose operation. .
(2) Setting an excitation function g (·), g (x) ═ x + asin (pi x)) of the input and output layers of the neural network; wherein a is more than 0, and x is less than + ∞; pi is the circumference ratio; sampling value signal x (t)i) I-1, 2, …, n as input signal for the excitation function.
(3) Designing a sine basis function neural network weight and constructing a basis function weight matrix;
slave matrix
The amplitude and phase information of the harmonic waves are contained in the matrix
And the matrix is independent of any signal input sample value; continuing to look at the matrix may find that its elements are composed of
Composition if applicableTo accurately obtain the values of the elements of the matrix, the amplitude and the corresponding phase of the ith harmonic can be accurately obtained according to the correlation property of the trigonometric function.
Accordingly, we design the weight matrix of the neural network as
In the form of weight matrices
And (4) finishing.
Thus, once the weight matrix is obtained, the fundamental amplitude can be calculated as
Phase is
Similarly, the amplitude and phase of the obtained kth harmonic are respectively
Thereby reconstructing fundamental wave and each harmonic wave.
Because of CiIs a matrix whose element values are related only to the samples. CiThe function of the method is similar to that of performing function mapping on input sampling points to obtain function outputs, and then the matrix elements can be used as sine triangular basis functions.
Then, according to the input variation of the sampling point, the following sine basis function matrix can be constructed
Wherein: r represents a real number domain, 2m is the number of hidden layer neurons, n is the number of samples,
g(x(ti) Is the output signal after the input signal sample has been subjected to the excitation function, i ═ 1,2, …, n;
the design of the neural network is completed as above.
(4) Designing a quadratic programming optimization problem to obtain an estimated value of a weight matrix w;
specifically, the following quadratic programming optimization problem is constructed
Wherein:
is a sampling vector of the harmonic input signal, n is a sampling number, the superscript T represents a transposition operation,
representing a 2-norm. d ═ diag [ d (0), d (1), …, d (n)]Diag is the main diagonal elements d (0), d (1), …, d (n), and any other elements are diagonal arrays of 0, where
And P is the total number of times of the neural network feedback. The purpose of the introduced sigma is to recursively minimize wTAnd w, which does not participate in the algorithm iteration, but gradually reduces the order of the norm by "2" at each feedback.
(5) Derivative W and make its value equal to zero vector
Let, i.e. the kth iteration fjJ is 0, …, n is fixed, let the first derivative equal to 0, and obtain its unique solution, then there is
In the formula: the superscript-1 represents the matrix inversion operation,
is formed by rendering a main diagonal element as | x (j)2J is 0, …, n.
(6) Iterative formula for setting weight of (k +1) th feedback network
W(k+1)＝(1-μ)g(W(k))+μW(0) (7)
Where μ e (0,1), w (0) is the initial value of the weight, and is generally set to 0.05+ j0.05 for the center tap, and all the other tap values are 0.
The feedback neural network is operated until the value of the cost function J (W) is not reduced any more, namely the feedback network is considered to be converged, and therefore the network weight matrix is obtained.
Further, calculating the accurate amplitude and phase of the fundamental wave and each harmonic according to the estimated value of the weight matrix W, and reconstructing the fundamental wave and each harmonic; in particular, the fundamental amplitude is
Phase is
Similarly, the amplitude and phase of the obtained kth harmonic are respectively
The fundamental wave and each harmonic can be reconstructed accordingly.
The examples show that: suppose the analysis signal is
The fundamental frequency is 50Hz, the harmonic and the phase are randomly generated, and the noise is white Gaussian noise with 10 dB
FIG. 1 is a graph of waveforms obtained during analysis according to the present invention. Fig. 2 is a comparison of the input and output obtained by the method of the invention. Fig. 3 and 4 are graphs of amplitude and phase errors of input and output subharmonics, respectively, obtained by the method of the present invention. The result shows that the invention can obtain very good harmonic detection effect, has small detection error and high accuracy and has very good application value.
Claims (5)
1. A real-time harmonic detection method based on a feedback neural network is characterized by comprising the following steps:
1) the periodic signal containing each harmonic in the power electronic system is expressed as:
wherein, w0At fundamental angular frequency, w02 pi f, f is the fundamental frequency, k is the harmonic order, akAnd
amplitude and phase of the kth harmonic, respectively; m is the highest harmonic number; discretizing the above expression and expanding the discretized expression into a matrix form, then tiEach sample value is represented as
Wherein, i is 1,2, …, n,
Tsis a sampling period;
(ii) a T represents a matrix transposition operation; w is the grid angular frequency;
2) designing an excitation function g (-) of an input and output layer of the feedback neural network: g (x) ═ (x + asin (pi x)); wherein a is more than 0, x is more than infinity and pi is a circumferential rate; sampling value signal x (t)i) As an input signal of the excitation function, an output signal g is obtained(x(ti))；
3) Establishing a sine basis weight function matrix as follows:
wherein R represents a real number domain;
4) the following quadratic programming optimization problem is constructed:
wherein:
represents a 2-norm; d ═ diag [ d (0), d (1), …, d (n)]Diag is a diagonal matrix with main diagonal elements of d (0), d (1), … and d (n), and any other elements are 0,
l is 1,2, …,2m, α is a normal number, α ∈ (0,1)]P is the total number of times of feedback of the neural network; w is a weight matrix, and W is a weight matrix,
5) solving the quadratic programming optimization problem to obtain an estimated value of a weight matrix W
And calculating the accurate amplitude and phase of the fundamental wave and each harmonic according to the estimated value of the weight matrix W, and reconstructing the fundamental wave and each harmonic.
2. The method according to claim 1, wherein the specific calculation of the estimated value of the weight matrix W comprises: order to
a) Derivative W and make its value equal to the zero vector:
b) let the r-th iteration fjWhere j is 0, …, n is fixed, let the first derivative be equal to 0, and a unique solution for W is obtained, then:
wherein the superscript-1 represents the matrix inversion operation,
is a main diagonal element of | x (j) & ltY2A diagonal matrix of (a); j ═ t1,t2,…,tn；
c) Setting an iterative formula of the r +1 th feedback network weight: w (r +1) ═ 1- μ g (W (r)) + μ W (0); wherein, mu belongs to (0,1), and W (0) is the initial value of the weight;
d) and repeating the steps a) to c) until the value of the cost function J (W) is not reduced any more, and obtaining a weight matrix, thereby obtaining an estimated value of the weight matrix W.
3. The feedback neural network-based real-time harmonic detection method according to claim 1 or 2, wherein the reconstructed fundamental wave amplitude is
Phase is
4. The feedback neural network-based real-time harmonic detection method according to claim 1 or 2, wherein the k-th reconstructed signal is1The amplitude and phase of the subharmonic are
k1＝2,3,…,m。
5. The feedback neural network-based real-time harmonic detection method of claim 1, wherein T iss≤100ms。
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112787491A (en) * | 2020-12-28 | 2021-05-11 | 中南大学 | Input current harmonic suppression method of three-stage AC/DC power supply |
| CN114252700A (en) * | 2021-10-26 | 2022-03-29 | 深圳市锐风电子科技有限公司 | Power harmonic detection method based on sine and cosine algorithm |
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| CN102353839A (en) * | 2011-07-18 | 2012-02-15 | 华北电力大学（保定） | Electric power system harmonics analysis method based on multilayered feedforward neural network |
| CN103383413A (en) * | 2013-07-09 | 2013-11-06 | 温州大学 | Real-time harmonic detection method based on direct weight determination method |
| CN104833852A (en) * | 2015-05-11 | 2015-08-12 | 重庆大学 | Power system harmonic signal estimation and measurement method based on artificial neural network |
| CN105305446A (en) * | 2015-10-22 | 2016-02-03 | 南京亚派科技股份有限公司 | Harmonic current tracking method based on intelligent control |
| CN109581054A (en) * | 2018-11-23 | 2019-04-05 | 温州晶彩光电有限公司 | A kind of real-time harmonic rapid detection method of bank base conversion power supply system peculiar to vessel |
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| CN102353839A (en) * | 2011-07-18 | 2012-02-15 | 华北电力大学（保定） | Electric power system harmonics analysis method based on multilayered feedforward neural network |
| CN103383413A (en) * | 2013-07-09 | 2013-11-06 | 温州大学 | Real-time harmonic detection method based on direct weight determination method |
| CN104833852A (en) * | 2015-05-11 | 2015-08-12 | 重庆大学 | Power system harmonic signal estimation and measurement method based on artificial neural network |
| CN105305446A (en) * | 2015-10-22 | 2016-02-03 | 南京亚派科技股份有限公司 | Harmonic current tracking method based on intelligent control |
| CN109581054A (en) * | 2018-11-23 | 2019-04-05 | 温州晶彩光电有限公司 | A kind of real-time harmonic rapid detection method of bank base conversion power supply system peculiar to vessel |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112787491A (en) * | 2020-12-28 | 2021-05-11 | 中南大学 | Input current harmonic suppression method of three-stage AC/DC power supply |
| CN114252700A (en) * | 2021-10-26 | 2022-03-29 | 深圳市锐风电子科技有限公司 | Power harmonic detection method based on sine and cosine algorithm |
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