A method of harmonic and adjacent interharmonic parameter estimation

Abstract

The application discloses a harmonic and adjacent inter-harmonic parameter estimation method, comprising the following steps: S1, performing Fourier transform on sampling data of a preset time length to obtain frequency domain data; S2, based on the frequency domain data, calculating the amplitude, frequency and phase parameters of a fundamental wave by using a multi-layer interpolation method and removing the influence of the fundamental wave component, and calculating the mapping relationship of a leakage spectrum line and frequency offset of a harmonic component; S3, based on the spectral difference of a single adjacent inter-harmonic and a symmetric adjacent inter-harmonic pair, constructing an adjacent inter-harmonic type criterion, determining the threshold of the criterion according to the noise size in a power system to judge the adjacent inter-harmonic type information; and S4, constructing an adjacent inter-harmonic spectrum line equation set based on the adjacent inter-harmonic type information, and solving the adjacent inter-harmonic spectrum line equation set by using an eigenvalue decomposition method to obtain the amplitude, frequency and phase parameters of the harmonic and adjacent inter-harmonic. The application can judge the type of the inter-harmonic under the frequency offset scene of the power system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power systems, and particularly relates to a harmonic and adjacent interharmonic parameter estimation method. BACKGROUND

[0002] With the rapid development of new energy power generation technology and the large use of power electronic equipment in China, the content of harmonics and interharmonics in the power system increases dramatically. A large amount of harmonics and interharmonics can increase system loss, cause protection device misoperation, interfere with communication lines, and even induce system resonance, which seriously endangers the safe operation of the power system. Accurate estimation of harmonic / interharmonic parameters is the primary step of harmonic control, and is of great significance to improve power quality and ensure the safe and stable operation of the power system. Large-scale grid connection of new energy can induce the presence of adjacent interharmonic pairs or a single adjacent interharmonic in the power signal about the fundamental / harmonic symmetry. Existing harmonic / interharmonic parameter estimation methods often need to know the type of adjacent interharmonic to construct an accurate calculation model when estimating the parameters of each frequency component in the signal. When the grid frequency deviates from the rated value, spectral leakage interference will make this requirement difficult to achieve. SUMMARY

[0003] The technical problem to be solved by the application is to provide a harmonic and adjacent interharmonic parameter estimation method, which can accurately estimate the parameters of harmonics and adjacent interharmonics when the grid frequency deviates from the rated value.

[0004] To solve the above technical problem, the application provides a harmonic and adjacent interharmonic parameter estimation method, comprising:

[0005] Step S1, performing Fourier transform on the sampling data of a preset time length to obtain frequency domain data;

[0006] Step S2, based on the frequency domain data, calculating the amplitude, frequency and phase parameters of the fundamental wave using a multi-layer interpolation method and removing the influence of the fundamental wave component to calculate the mapping relationship between the leakage spectrum line and the frequency offset of the harmonic component;

[0007] Step S3, based on the spectral difference between a single adjacent interharmonic and a symmetric adjacent interharmonic pair, constructing an adjacent interharmonic type criterion, and determining the threshold of the criterion according to the noise size in the power system to determine the adjacent interharmonic type information;

[0008] Step S4, constructing an adjacent interharmonic spectrum line equation set based on the adjacent interharmonic type information, and solving the adjacent interharmonic spectrum line equation set using an eigenvalue decomposition method to obtain the amplitude, frequency and phase parameters of the harmonics and adjacent interharmonics.

[0009] Further, the step S1 specifically comprises:

[0010] Step S11, obtaining discrete sampling data; the discrete sampling data is shown in the following formula:

[0011]

[0012] Wherein, x[n] is a sampling signal, n is a sampling point sequence number, M is a total number of a fundamental wave, a harmonic wave and an inter-harmonic wave in the signal, Δt is a sampling interval, which is an inverse of a sampling frequency f s , a i , f i and are an amplitude, a frequency and a phase of x i [n] respectively, x i [n] is an i-th frequency component contained in the sampling signal x[n];

[0013] Step S12, obtaining frequency domain data according to the following formula:

[0014]

[0015] Wherein, j is an imaginary unit, N is a total sampling point number, k is a frequency domain index, which represents a k-th spectral line, Δf is a frequency resolution, M * is a number of harmonics and adjacent inter-harmonic waves near the current concerned frequency domain index.

[0016] Further, the step S2 specifically comprises:

[0017] Step S21, calculating an amplitude, a frequency and a phase of the fundamental wave according to the following formula:

[0018]

[0019] Wherein, k1 is an index of x[k], abs(·) is an amplitude operation, angle(·) is a phase operation, and the interpolation operator R is calculated in the following manner:

[0020]

[0021] Wherein, a phase compensation manner and a rotation factor r are as follows:

[0022] x (r) [k]=rx[k]

[0023]

[0024] Step S22, suppressing a fundamental wave spectrum leakage according to the following formula:

[0025]

[0026] Wherein, y (r) [k] is a spectrum after suppressing the fundamental wave spectrum leakage;

[0027] Step S23, assuming no inter-harmonic effect, obtain the mapping relationship between the leakage spectrum line of the harmonic component and the frequency offset:

[0028]

[0029]

[0030] The spectrum leakage of the harmonic is suppressed by the following formula:

[0031]

[0032]

[0033] Wherein, z[k i +1] and z[k i -1] represent the spectrum after the harmonic spectrum leakage is suppressed, k i represents the frequency domain index of the harmonic main spectrum line.

[0034] Further, step S3 specifically includes:

[0035] Step S31, determine whether the adjacent inter-harmonic spectrum line is a real inter-harmonic;

[0036] Step S32, when there is an adjacent inter-harmonic, further determine the category of the adjacent inter-harmonic.

[0037] Further, the step S31 specifically includes:

[0038]

[0039]

[0040] Wherein, and is an adjacent inter-harmonic existence index, used to determine whether there is an adjacent inter-harmonic at k i -1 and k i +1; set a threshold λ1, if there is or , it is determined that there is an adjacent inter-harmonic near the harmonic, otherwise it is determined that there is no adjacent inter-harmonic.

[0041] Further, the step S32 specifically includes: assuming abs(z[k i -1])>abs(z[k i +1]), record:

[0042] c2=abs(z[k i -1] / z[k i +1])

[0043] A threshold λ2 is set, if c2> λ2, then the adjacent inter-harmonics are determined as single adjacent inter-harmonics, otherwise as symmetric adjacent inter-harmonic pairs.

[0044] Further, the step S4 specifically comprises: obtaining the frequency spectrum line y (r) The relationship satisfied by [k] is as follows:

[0045]

[0046] Wherein, A i and B i are functions of the amplitude, frequency and phase of the i-th frequency component:

[0047]

[0048] Further, the adjacent inter-harmonic spectrum line equation is constructed according to the following formula:

[0049]

[0050] Wherein, U = 2M * -1, C l is a function of B i , affected by the number of adjacent inter-harmonics M * ; when M * = 3, C l(3) = (-1) 3 , when M * = 2, C l(2) = (-1) 2 , Solving obtains the C l parameter.

[0051] Further, the frequency spectrum line satisfies the following formula:

[0052]

[0053] Solving obtains the B i parameter.

[0054] Further, the amplitude, frequency and phase parameters of the harmonics and adjacent inter-harmonics are calculated according to the following formula:

[0055]

[0056] The present application has the following advantages: the present application can determine the type of inter-harmonic when the power system has frequency deviation, and can accurately estimate the amplitude, frequency and phase parameters of the harmonic and adjacent inter-harmonic, thereby providing accurate basis for the selection of various method calculation models, which is of great significance for the treatment of harmonic problems, the improvement of power quality and the safe and stable operation of the power system; the present application can effectively reduce the calculation amount and speed up the calculation speed based on the fast Fourier analysis data; the present application takes into account the main lobe interference of the harmonic and adjacent inter-harmonic, and the algorithm calculation result is relatively accurate and fast, the error is small, and the present application has good practicability. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort.

[0058] Figure 1 is a flowchart of a harmonic and adjacent inter-harmonic parameter estimation method according to an embodiment of the present application.

[0059] Figure 2 is a schematic diagram of the threshold value calculation according to an embodiment of the present application.

[0060] Figure 3 is an effect diagram of the adjacent inter-harmonic type criterion according to an embodiment of the present application.

[0061] Figure 4 is a standard diagram of the threshold value λ1 and the threshold value λ2 selection under different noise according to an embodiment of the present application.

[0062] Figure 5 is an error comparison diagram of the present application and other commonly used methods according to an embodiment of the present application. DETAILED DESCRIPTION

[0063] The following description of the embodiments is with reference to the drawings, which are used to illustrate specific embodiments in which the present application can be implemented.

[0064] Please refer to Figure 1 , the present application provides a harmonic and adjacent inter-harmonic parameter estimation method, which comprises:

[0065] Step S1, performing Fourier transform on the sampling data of a preset time length to obtain frequency domain data;

[0066] Step S2, based on the frequency domain data, calculating the amplitude, frequency and phase parameters of the fundamental wave and removing the influence of the fundamental wave component by using a multi-layer interpolation method, and calculating the mapping relationship of the leakage spectrum line of the harmonic component and the frequency deviation.

[0067] Step S3, constructing a criterion of adjacent inter-harmonic type based on the spectral difference between a single adjacent inter-harmonic and a pair of symmetric adjacent inter-harmonics, and determining a threshold of the criterion according to the noise level in the power system to determine the adjacent inter-harmonic type information;

[0068] Step S4, constructing an adjacent inter-harmonic spectral line equation set based on the adjacent inter-harmonic type information, and solving the adjacent inter-harmonic spectral line equation set by using an eigenvalue decomposition method to obtain the amplitude, frequency and phase parameters of the harmonics and adjacent inter-harmonics.

[0069] Specifically, in step S1, the preset time length is set to 200 ms, and the sampling data includes the recorded wave data of voltage and current. The step S1 specifically includes:

[0070] Step S11, obtaining discrete sampling data;

[0071] In this embodiment, the discrete sampling data is shown in the following formula (1):

[0072]

[0073] Wherein, x[n] is a sampling signal, n is a sampling point sequence number, M is the total number of fundamental wave, harmonics and inter-harmonics in the signal, Δt is a sampling interval, which is the reciprocal of the sampling frequency f s , a i , f i and are the amplitude, frequency and phase of x i [n] respectively, and x i [n] is the i-th frequency component contained in the sampling signal x[n].

[0074] Step S12, obtaining frequency domain data according to the following formula (2):

[0075]

[0076] Wherein, j is an imaginary unit, N is the total number of sampling points, k is the frequency domain index, indicating the k-th spectral line, Δf is the frequency resolution, which is usually 5 Hz; since the influence of negative frequency component on positive frequency component is usually small, the negative frequency part is ignored; the leakage component of each harmonic will quickly decay, so it can be approximately considered that x[k] near a certain harmonic is composed of M * frequency component (harmonic and adjacent inter-harmonic) vectors. M * is the number of harmonics and adjacent inter-harmonics near the current frequency domain index, when there is no adjacent inter-harmonic M * =1, when there is a single adjacent inter-harmonic M * =2, and when there is a pair of symmetric adjacent inter-harmonics M * =3.

[0077] Step S2 is used to suppress the influence of fundamental and harmonic spectrum leakage, and specifically includes:

[0078] Step S21, the amplitude, frequency and phase of the fundamental are calculated according to the following formula (3):

[0079]

[0080] Where k1 is the index of x[k], abs(·) is the amplitude operation, angle(·) is the phase operation, and the interpolation operator R is calculated as follows:

[0081]

[0082] Where the phase compensation method is as follows:

[0083] x (r) [k]=rx[k] (5)

[0084]

[0085] Step S22, the fundamental spectrum leakage is suppressed;

[0086] As shown in the following formula (7), y (r) [k] is the spectrum after suppressing the fundamental spectrum leakage:

[0087]

[0088] Step S23, assuming that there is no influence of the inter-harmonic, the mapping relationship of the leakage spectrum line and the frequency offset of the harmonic component is obtained:

[0089]

[0090] Since the harmonic amplitude is generally greater than the inter-harmonic amplitude, it is considered that the harmonic main spectrum line is much greater than the leakage spectrum line of the inter-harmonic, and the harmonic spectrum leakage is suppressed by formula (9):

[0091]

[0092] Where z[k i +1] and z[k i -1] represent the spectrum after suppressing the harmonic spectrum leakage, k i represents the frequency domain index of the harmonic main spectrum line.

[0093] Step S3 specifically includes:

[0094] Step S31, it is judged whether the adjacent inter-harmonic spectrum line is a real inter-harmonic;

[0095] The spectrum line adjacent to the inter-harmonic is affected by the spectrum leakage of the fundamental wave and the harmonic wave and the system noise. After the de-harmonic adjacent spectrum line is obtained, it is first judged whether the adjacent inter-harmonic spectrum line is a real inter-harmonic, that is,

[0096]

[0097] wherein, and is an adjacent inter-harmonic existence index, which is used for judging whether the adjacent inter-harmonic exists at the frequency domain index k i -1 and k i +1; a threshold λ1 is set, if there is or it is considered that the adjacent inter-harmonic exists around the harmonic, otherwise the adjacent inter-harmonic does not exist. The value of the threshold λ1 is related to the size of the system noise. Since the signal-to-noise ratio of the main network of the power system is generally not less than 40 dB, λ1 is taken as 0.0025.

[0098] In step S32, when the adjacent inter-harmonic exists, the category of the adjacent inter-harmonic is further judged.

[0099] When the adjacent inter-harmonic is a single adjacent inter-harmonic or a symmetric adjacent inter-harmonic pair, the de-harmonic adjacent spectrum line has a certain amplitude difference. It is assumed that abs(z[k i -1])>abs(z[k i +1]), that is,

[0100] c2=abs(z[k i -1] / z[k i +1]) (11)

[0101] A threshold λ2 is set, if c2>λ2, it is considered that the adjacent inter-harmonic is a single adjacent inter-harmonic, otherwise it is a symmetric adjacent inter-harmonic pair. The value of the threshold λ2 is related to the distance between the harmonic and the inter-harmonic, the amplitude of the inter-harmonic and the size of the system noise. λ2 is taken as 1.44.

[0102] Step S4 specifically comprises:

[0103] In step S41, the spectrum spectrum line y (r) [k] after the influence of the fundamental wave is removed satisfies the relationship:

[0104]

[0105] wherein, A i and B i are functions about the amplitude, frequency and phase of the i-th frequency component; B i =f i / Δf; when the adjacent inter-harmonic does not exist, M *= 1; M * = 2; M * = 3.

[0106] Step S42, constructing the adjacent inter-harmonic spectrum line equation according to the following formula (13):

[0107]

[0108] Wherein, U = 2M * -1, C l is a function about B i , affected by the number of adjacent inter-harmonics M * ; when M * = 3, C l(3) = (-1) 3 , when M * = 2, C l(2) = (-1) 2 , Solving to obtain C l parameters. Because the frequency of the harmonic is an integer multiple of the fundamental frequency, the harmonic frequency is known after the fundamental frequency is estimated, and the C l expression can be used to solve each B i parameter.

[0109] At the same time, the spectrum spectrum line satisfies:

[0110]

[0111] Solving equation (14) to obtain B i parameters.

[0112] Step S43, the amplitude, frequency and phase parameters of the harmonic and adjacent inter-harmonic are solved in the following way:

[0113]

[0114] It should be noted that when the embodiment is implemented, the selection range of the threshold λ1 and the threshold λ2 needs to be determined. The determination method is to set the simulation signal as shown in Table 1, and set the signal-to-noise ratio to 40dB.

[0115] Table 1

[0116]

[0117] Using the present application to calculate abs(z[k i +1]) / a1 and abs(z[k i -1]) / a1, repeat the operation for 50 times, such as Figure 2The maximum value is selected as the threshold λ1. Then, the adjacent inter-harmonic groups symmetrical to each harmonic are set in turn, the amplitude of the inter-harmonic is 1 / 2 of the amplitude of the harmonic, and the frequency difference between the inter-harmonic group and the harmonic is changed between 1.5 Hz and 7 Hz. The application is used to calculate abs(z[k1-1] / z[k1+1]), and the maximum value is selected as the threshold λ2. When the adjacent inter-harmonics are single adjacent inter-harmonics and symmetrical adjacent inter-harmonic pairs respectively, the criterion abs(z[k1-1] / z[k1+1]) is as shown in the following table 1. Figure 3 The criterion proposed in the embodiment can accurately determine the type of the adjacent inter-harmonic. Then, the signal-to-noise ratio in the signal is gradually adjusted to obtain the threshold λ1 and the threshold λ2 under different noise conditions, as shown in the following table 2. Figure 4 The appropriate threshold λ1 and the threshold λ2 can be selected according to the noise size in the actual power grid. 11 and the threshold λ2.

[0118] In order to further illustrate the effect of the embodiment, a signal containing harmonics and adjacent inter-harmonics is set to verify the effect, and the signal parameters are as shown in the following table 2.

[0119] Table 2

[0120] Signal parameters

[0121]

[0122] The frequency component 1 is the fundamental wave, there is a frequency offset of 0.1 Hz, the frequency components 2-4 are harmonics, and the frequency components 5-9 are inter-harmonics of adjacent inter-harmonics. The frequency components 5 and 6 are adjacent inter-harmonic pairs symmetrical to the frequency component 2, the frequency components 8 and 9 are adjacent inter-harmonic pairs symmetrical to the frequency component 4, and the frequency component 7 is a single adjacent inter-harmonic. The amplitude, frequency and phase parameters of the harmonics and the inter-harmonics are calculated by using the application. The three-point interpolation method (method 2), the multi-layer interpolation method (method 3), the adjacent inter-harmonic parameter estimation method (method 4) and the Matrix Pencil method (method 5) are used as comparison, and the parameter estimation results are as shown in the following table 3, and the error is as shown in the following table 4. Figure 5 The precision of the application is much higher than that of other methods.

[0123] Table 3

[0124] Amplitude estimation value of the harmonics and the adjacent inter-harmonics

[0125]

[0126] Frequency estimation value of the harmonics and the adjacent inter-harmonics

[0127]

[0128] Phase estimation values of harmonics and adjacent interharmonics

[0129]

[0130] From the above description, compared with the prior art, the beneficial effects of the present application are that the present application can still judge the type of interharmonic under the scene of frequency offset of the power system, and can accurately estimate the amplitude, frequency and phase parameters of the harmonics and adjacent interharmonics, providing accurate basis for the selection of various method calculation models, which has important significance for governing harmonic problem, improving power quality and ensuring safe and stable operation of the power system; the present application can effectively reduce the calculation amount and speed up the calculation speed based on the fast Fourier analysis data; the present application simultaneously considers the main lobe interference of the harmonics and adjacent interharmonics, the algorithm calculation result is relatively accurate and fast, the error is small, and the present application has good practicability.

[0131] The above only discloses preferred embodiments of the present application, of course cannot limit the scope of the right of the present application, therefore the equivalent changes made according to the claims of the present application still belong to the scope covered by the present application.

Claims

1. A method for estimating harmonic parameters and those of neighboring harmonics, characterized in that, include: Step S1: Perform Fourier transform on the sampled data for a preset time length to obtain frequency domain data; Step S2: Based on the frequency domain data, the amplitude, frequency and phase parameters of the fundamental wave are calculated using multi-layer interpolation and the influence of the fundamental wave component is removed. The mapping relationship between the leakage spectrum of the harmonic component and the frequency shift is calculated. Step S3: Based on the spectral difference between a single neighboring harmonic and a symmetrical neighboring harmonic pair, construct a neighboring harmonic type criterion, and determine the threshold of the criterion according to the noise level in the power system to determine the neighboring harmonic type information. Step S4: Construct a set of equations for adjacent interharmonic spectral lines based on the information on the type of adjacent interharmonics, and solve the set of equations for adjacent interharmonic spectral lines using the eigenvalue decomposition method to obtain the amplitude, frequency and phase parameters of the harmonics and adjacent interharmonics. Step S2 specifically includes: Step S21: Calculate the amplitude, frequency, and phase of the fundamental wave according to the following formula: Where k1 is the index of x[k], abs(·) is the magnitude operation, angle(·) is the phase operation, and the interpolation operator R is calculated as follows: The phase compensation method and rotation factor r are as follows: x (r) [k]=rx[k] Step S22, suppress fundamental frequency spectrum leakage using the following formula: Among them, y (r) [k] is the spectrum after suppressing fundamental frequency spectrum leakage; Step S23, assuming no interharmonic interference, obtain the mapping relationship between the leakage spectral lines of the harmonic components and the frequency shift: The following formula can be used to suppress harmonic spectral leakage: Among them, z[k i +1] and z[k i [-1] represents the spectrum after suppressing harmonic spectral leakage, k i Frequency domain index representing the main harmonic spectral line.

2. The method according to claim 1, characterized in that, Step S1 specifically includes: Step S11, obtain discrete sampling data; the discrete sampling data is shown in the following formula: Where x[n] is the sampled signal, n is the number of sampling points, M is the total number of fundamental, harmonic, and interharmonic waves in the signal, Δt is the sampling interval, and f is the sampling frequency. s The reciprocal of a i f i and x i The amplitude, frequency, and phase of [n], x i [n] represents the i-th frequency component contained in the sampled signal x[n]; Step S12, obtain the frequency domain data according to the following formula: Where j is the imaginary unit, N is the total number of sampling points, k is the frequency domain index, representing the k-th spectral line, Δf is the frequency resolution, and M... * This is to determine the number of harmonics near and between the nearest harmonics in the frequency domain of current interest.

3. The method according to claim 1, characterized in that, Step S3 specifically includes: Step S31: Determine whether the adjacent interharmonic spectral lines are true interharmonics; Step S32: If there are adjacent interharmonics, further determine the type of adjacent interharmonics.

4. The method according to claim 3, characterized in that, Step S31 specifically includes: remember: in, and The index for the presence of adjacent harmonics is used to determine the frequency domain index k. i -1 and k i Does a neighboring harmonic exist at point +1? Let the threshold be λ1. If so... or If a harmonic is found to be near a neighboring harmonic, it is determined that a neighboring interharmonic exists; otherwise, it is determined that no neighboring interharmonic exists.

5. The method according to claim 4, characterized in that, Step S32 specifically includes: Assume abs(z[k i -1])>abs(z[k i +1]), note: c2=abs(z[k i -1] / z[k i +1]) Let the threshold be λ2. If c2>λ2, then the neighboring harmonic is determined to be a single neighboring harmonic; otherwise, it is determined to be a symmetrical neighboring harmonic pair.

6. The method according to claim 1, characterized in that, Step S4 specifically includes: obtaining the spectral line y after removing the influence of the fundamental wave. (r) The relation satisfied by [k] is as follows: Among them, A i With B i Let the amplitude, frequency, and phase of the i-th frequency component be a function:

7. The method according to claim 6, characterized in that, The equations for neighboring interharmonic spectral lines are constructed based on the following formula: Where, U = 2M * -1, C l Regarding B i The function is affected by the number of neighboring harmonics M. * The effect; when M - When = 3, C l(3) =(-1) 3 , When M * When = 2, C l(2) =(-1) 2 , Solving for C l parameter.

8. The method according to claim 7, characterized in that, Spectral lines satisfy the following equation: Solve to obtain B i parameter.

9. The method according to claim 8, characterized in that, The amplitude, frequency, and phase parameters of the harmonic and its neighboring harmonics are calculated using the following formula:

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