A method and apparatus for adaptive threshold extraction of broadband oscillation components in power systems

Abstract

This invention discloses a method and apparatus for adaptive threshold extraction of broadband oscillation components in power systems. First, the spectrum and normalized power spectrum of the power signal in the power system are acquired. Based on the spectrum and normalized power spectrum, the mean and variance of the normalized power spectrum are obtained, and the largest spectral value representing the effective frequency component is removed. This process is iterated until the variance of the normalized power spectrum is less than 4. At this point, the standard deviation of the normalized power spectrum whose variance is closest to 4 is searched, and this standard deviation is set as the broadband component extraction threshold. Using this method and apparatus, when broadband oscillations occur in the power system, the threshold can be adaptively set, thereby ignoring the influence of different noise levels and extracting broadband component parameters in the frequency domain.

Description

Technical Field

[0001] This invention relates to the field of broadband measurement technology, and in particular to a method and apparatus for adaptive threshold extraction of broadband oscillation components in power systems. Background Technology

[0002] With the rapid development of new energy power generation, various power electronic devices have been widely used in power systems, giving them power electronic characteristics. The extensive deployment of power electronic equipment injects a large amount of harmonics and interharmonics into the system during rectification and inversion. Furthermore, the interactions between power electronic devices and between the devices and the power grid cause broadband oscillations such as subsynchronous / supersynchronous oscillations and mid-to-high frequency oscillations, threatening the safe and stable operation of the system. Therefore, there is an urgent need to develop broadband measurement devices for power systems to monitor the broadband oscillation components of the system, thereby providing effective data for oscillation suppression and alarm applications.

[0003] Typical wideband oscillation extraction algorithms include the Discrete Fourier Transform (DFT) and its improved versions. These algorithms are numerically stable and have fast implementations, thus they are widely used in power systems. However, wideband oscillation components and noise coexist in electrical signals. Determining whether a component is effective or noise during spectrum analysis is a challenge in wideband measurement. Most existing methods use a fixed threshold method, setting a fixed threshold based on the fundamental frequency component; components exceeding this threshold are considered effective wideband components. However, the noise content of electrical signals varies across different lines and power grid regions. Sampling with a fixed threshold often fails to adapt to complex on-site wideband signals, missing some wideband components and affecting the accurate analysis of the wideband oscillation process. Therefore, it is necessary to develop an adaptive threshold setting method for wideband oscillation signals, which can ignore the influence of varying noise content and adaptively extract wideband components. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for adaptive threshold extraction of broadband oscillation components in power systems. Using this method and apparatus, when broadband oscillations occur in a power system, a threshold can be adaptively set to ignore the influence of different noise levels and extract broadband component parameters in the frequency domain.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for adaptive threshold extraction of broadband oscillation components in a power system, the method comprising:

[0007] Step 1: Obtain the spectrum and normalized power spectrum of the power signal in the power system;

[0008] Step 2: Based on the spectrum and normalized power spectrum of the power signal, obtain the mean and variance of the normalized power spectrum, and remove the maximum spectral value representing the effective frequency component.

[0009] Step 3: Iterate through the operations of steps 1 and 2 until the variance of the normalized power spectrum is less than 4. At this point, search for the standard deviation of the normalized power spectrum whose variance is closest to 4, and set this standard deviation as the threshold for broadband component extraction.

[0010] As can be seen from the technical solution provided by the present invention, the above method and device can adaptively set a threshold to separate effective components and noise when broadband oscillations occur in the power system, thereby ignoring the influence of different noise contents and accurately extracting broadband component parameters in the frequency domain. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a schematic flowchart of a method for adaptive threshold extraction of broadband oscillation components in a power system provided in an embodiment of the present invention;

[0013] Figure 2 This is a schematic diagram of the simulation results of the adaptive threshold setting method provided in the embodiment of the present invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments, and do not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0015] like Figure 1 The diagram shows a flowchart of a method for adaptive threshold extraction of broadband oscillation components in a power system according to an embodiment of the present invention. The method includes:

[0016] Step 1: Obtain the spectrum and normalized power spectrum of the power signal in the power system;

[0017] In this step, the sampled values ​​y(n) of the power signal in the power system are first obtained, and their spectrum is obtained through spectral analysis:

[0018]

[0019] Where y(n) represents the sampled value of the power signal; M d To calculate the number of sampled values ​​within the data window; j is the imaginary unit; k and n are natural numbers representing sequence indices; Y(k) is the spectrum of the power signal, containing both real and imaginary parts, expressed as:

[0020] R Y (k)=real[Y(k)],I Y (k) = imag[Y(k)]

[0021] Among them, R Y (k) represents the real part of the power signal spectrum; I Y (k) represents the imaginary part of the power signal spectrum;

[0022] The normalized power spectrum of an electrical signal is expressed as:

[0023]

[0024] in, This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the real part of the power signal spectrum at the i-th iteration; Let represent the imaginary part of the power signal spectrum at the i-th iteration; The standard deviation of the power signal spectrum at the i-th iteration is expressed as:

[0025]

[0026] Where std(·) represents the standard deviation of the returned sequence; It is by and The vector formed is represented as:

[0027]

[0028] Step 2: Based on the spectrum and normalized power spectrum of the power signal, obtain the mean and variance of the normalized power spectrum, and remove the maximum spectral value representing the effective frequency component.

[0029] In this step, the mean and variance of the normalized power spectrum are expressed as:

[0030]

[0031] in, This represents the variance of the normalized power spectrum at the i-th iteration; This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the mean of the normalized power spectrum at the i-th iteration, which is 2 under all conditions;

[0032] After obtaining the mean and variance, the real and imaginary parts after removing the maximum spectral value representing the effective frequency components are:

[0033]

[0034]

[0035] Where m is the index corresponding to the maximum spectral value.

[0036] The following is a detailed derivation of why the mean of the normalized power spectrum is always 2 under all conditions:

[0037] Let the real and imaginary parts of the spectrum of any signal be R(k) and I(k) (0≤k≤M). d -1), and combine them into a vector:

[0038] RI = [R(0), R(1), ..., R(M)] d -1), I(0), I(1), ...I(M) d -1)]

[0039] The mean μ and variance σ of RI can then be expressed as:

[0040]

[0041]

[0042] The normalized power spectrum of any signal is:

[0043]

[0044] Therefore, the mean of the normalized power spectrum can be expressed as:

[0045]

[0046] Substituting equation (2) into equation (4) yields the mean μ. P =2, therefore the mean μ of the normalized power spectrum of any signal is 2. P It must be 2.

[0047] Step 3: Iterate through the operations of steps 1 and 2 until the variance of the normalized power spectrum is less than 4. At this point, search for the standard deviation of the normalized power spectrum whose variance is closest to 4, and set this standard deviation as the threshold for broadband component extraction.

[0048] In this step, the standard deviation of the normalized power spectrum whose variance is closest to 4 is expressed as:

[0049]

[0050] Wherein, the subscript Y represents the standard deviation of the power signal, and the subscript V represents the standard deviation of the normalized power spectrum whose variance is closest to 4; i v The index of the variance closest to 4 is represented as:

[0051]

[0052] Here, min(·) is defined as a function that returns the index of the minimum value in the sequence; The variance of the normalized power spectrum is represented by i; max This represents the length of the normalized power spectrum variance sequence;

[0053] The broadband component extraction threshold is:

[0054] S th =3.04σ V

[0055] Among them, S th This represents the threshold for broadband component extraction; the coefficient 3.04 is an empirical value obtained in this embodiment after multiple tests.

[0056] The following is a detailed explanation of why a variance of 4 is used for judgment:

[0057] Power signals consist of noise and broadband components. To set a threshold, it is necessary to first analyze the distribution characteristics of the noise in the frequency spectrum. Now, we assume that the random noise in the power signal follows a normal distribution:

[0058] v(k)~N(μ,σ) 2 0≤k≤M d -1

[0059] Where μ is the mean of the normal distribution. Generally, μ is set to 0, in which case the noise is Gaussian white noise.

[0060] The spectrum of a noise sequence is a complex sequence, and its value can be expressed as:

[0061] V v (k)=R v (k)+jI v (k)

[0062] Among them, V v (k) represents the noise spectrum; R v (k) and I v (k) represents the real and imaginary parts of the noise spectrum.

[0063] The Fourier transform of a normally distributed sequence still follows a normal distribution, and its real and imaginary parts of the spectrum have the same mean and standard deviation as the time-domain sequence. Therefore:

[0064]

[0065] Where, σ R and σ I σ represents the standard deviation of the real and imaginary parts of the noise spectrum. V The standard deviation of the noise spectrum.

[0066] The power spectrum and amplitude spectrum of Gaussian white noise can be expressed as:

[0067]

[0068] Among them, P v (k) and X v (k) represent the power spectrum and amplitude spectrum of random noise, respectively.

[0069] If multiple random variables all follow a standard normal distribution, then the new random variable formed by the sum of their squares follows a chi-square distribution, and the degrees of freedom of the chi-square distribution are equal to the number of random variables. Based on this property, if the real and imaginary parts of the noise spectrum are normalized to make them follow a standard normal distribution:

[0070]

[0071]

[0072] The normalized power spectrum then follows a chi-square distribution:

[0073]

[0074] Among them, P′ v (k), R′ v (k) and I′ v (k) represent the normalized noise power spectrum and its real and imaginary parts, respectively; Let the chi-square distribution with 2 degrees of freedom be defined as follows:

[0075]

[0076] Where Γ(·) represents the Gamma function; n represents the degrees of freedom, and in this embodiment n=2; since the degrees of freedom are 2, according to the properties of the chi-square distribution, its variance must be 4.

[0077] Therefore, as long as the variance of the normalized power spectrum is 4, it indicates that the remaining frequency components after removing the effective components are invalid noise. Based on this characteristic, the broadband component extraction threshold can be set.

[0078] Based on the above method, embodiments of the present invention also provide an apparatus for adaptive threshold extraction of broadband oscillation components in power systems, the apparatus comprising:

[0079] The spectrum and normalized power spectrum acquisition unit is used to acquire the spectrum and normalized power spectrum of the power signal in the power system.

[0080] The mean and variance acquisition unit is used to obtain the mean and variance of the normalized power spectrum based on the power signal spectrum and normalized power spectrum obtained by the spectrum and normalized power spectrum acquisition unit, and to remove the maximum spectral value representing the effective frequency component.

[0081] The broadband component extraction threshold setting unit is used to search for the standard deviation of the normalized power spectrum whose variance is closest to 4 based on the calculation results of the mean and variance acquisition unit, and set the standard deviation as the broadband component extraction threshold.

[0082] The specific implementation methods of each unit in the above-mentioned device are described in the above-mentioned method embodiments.

[0083] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0084] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0085] To demonstrate the effectiveness of the method proposed in the embodiments of the present invention, the following simulation tests were conducted:

[0086] The electrical signals during simulation are:

[0087]

[0088] During the test, 40dB of noise was superimposed on the signal, such as Figure 2 The figure shows the simulation results of the adaptive threshold setting method provided in the embodiment of the present invention. Figure 2 The figure shows the amplitude spectrum of the simulated signal under a 4s data window and the obtained noise reduction threshold. The dashed line in the figure represents the noise reduction threshold, which is 0.0423A. Most components are less than 0.0423A, so the broadband components can be effectively extracted.

[0089] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for adaptive threshold extraction of broadband oscillation components in a power system, characterized in that, The method includes: Step 1: Obtain the spectrum and normalized power spectrum of the power signal in the power system; The process of step 1 is as follows: First, obtain the sampled value y(n) of the power signal in the power system, and then perform spectral analysis to obtain the spectrum: ； Where y(n) represents the sampled value of the power signal; M d To calculate the number of sampled values ​​within the data window; j is the imaginary unit; k and n are natural numbers representing sequence indices; Y(k) is the spectrum of the power signal, containing both real and imaginary parts, expressed as: ； in, Represents the real part of the power signal spectrum; Represents the imaginary part of the power signal spectrum; The normalized power spectrum of an electrical signal is expressed as: ； in, This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the real part of the power signal spectrum at the i-th iteration; Let represent the imaginary part of the power signal spectrum at the i-th iteration; The standard deviation of the power signal spectrum at the i-th iteration is expressed as: ； Where std(·) represents the standard deviation of the returned sequence; It is by and The vector formed is represented as: ； Step 2: Based on the spectrum and normalized power spectrum of the power signal, obtain the mean and variance of the normalized power spectrum, and remove the maximum spectral value representing the effective frequency component. In step 2, the mean and variance of the normalized power spectrum are expressed as follows: ； in, This represents the variance of the normalized power spectrum at the i-th iteration; This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the mean of the normalized power spectrum at the i-th iteration, which is 2 under all conditions; After obtaining the mean and variance, the real and imaginary parts after removing the maximum spectral value representing the effective frequency components are: ； ； Where m is the index corresponding to the maximum spectral value; Step 3: Iterate through the operations of steps 1 and 2 until the variance of the normalized power spectrum is less than 4. At this point, search for the standard deviation of the normalized power spectrum whose variance is closest to 4, and set this standard deviation as the broadband component extraction threshold. In step 3, the standard deviation of the normalized power spectrum whose variance is closest to 4 is expressed as: ； Wherein, the subscript Y represents the standard deviation of the power signal, and the subscript V represents the standard deviation of the normalized power spectrum whose variance is closest to 4; The index of the variance closest to 4 is represented as: ； Here, min(·) is defined as a function that returns the index of the minimum value in the sequence; The variance of the normalized power spectrum is represented by i; max The length of the normalized power spectrum variance sequence; The broadband component extraction threshold is: ； in, This represents the threshold for broadband component extraction; the coefficient 3.04 is an empirical value obtained after multiple tests.

2. A device for adaptive threshold extraction of broadband oscillation components in a power system, characterized in that, The device includes: The spectrum and normalized power spectrum acquisition unit is used to acquire the spectrum and normalized power spectrum of the power signal in the power system. First, obtain the sampled value y(n) of the power signal in the power system, and then perform spectral analysis to obtain the spectrum: ； Where y(n) represents the sampled value of the power signal; M d To calculate the number of sampled values ​​within the data window; j is the imaginary unit; k and n are natural numbers representing sequence indices; Y(k) is the spectrum of the power signal, containing both real and imaginary parts, expressed as: ； in, Represents the real part of the power signal spectrum; Represents the imaginary part of the power signal spectrum; The normalized power spectrum of an electrical signal is expressed as: ； in, This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the real part of the power signal spectrum at the i-th iteration; Let represent the imaginary part of the power signal spectrum at the i-th iteration; The standard deviation of the power signal spectrum at the i-th iteration is expressed as: ； Where std(·) represents the standard deviation of the returned sequence; It is by and The vector formed is represented as: ； The mean and variance acquisition unit is used to obtain the mean and variance of the normalized power spectrum based on the power signal spectrum and normalized power spectrum obtained by the spectrum and normalized power spectrum acquisition unit, and to remove the maximum spectral value representing the effective frequency component; wherein, the mean and variance of the normalized power spectrum are expressed as: ； in, This represents the variance of the normalized power spectrum at the i-th iteration; This represents the normalized power spectrum of the power signal at the i-th iteration; Let represent the mean of the normalized power spectrum at the i-th iteration, which is 2 under all conditions; After obtaining the mean and variance, the real and imaginary parts after removing the maximum spectral value representing the effective frequency components are: ； ； Where m is the index corresponding to the maximum spectral value; The broadband component extraction threshold setting unit is used to search for the standard deviation of the normalized power spectrum whose variance is closest to 4 based on the calculation results of the mean and variance acquisition unit, and set the standard deviation as the broadband component extraction threshold. The standard deviation of the normalized power spectrum whose variance is closest to 4 is expressed as: ； Wherein, the subscript Y represents the standard deviation of the power signal, and the subscript V represents the standard deviation of the normalized power spectrum whose variance is closest to 4; The index of the variance closest to 4 is represented as: ； Here, min(·) is defined as a function that returns the index of the minimum value in the sequence; The variance of the normalized power spectrum is represented by i; max The length of the normalized power spectrum variance sequence; The broadband component extraction threshold is: ； in, This represents the threshold for broadband component extraction; the coefficient 3.04 is an empirical value obtained after multiple tests.

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