Method and system for estimating aliasing harmonic values of a low sampling rate measurement and control device

Abstract

The application provides a low sampling rate measurement and control device aliasing harmonic value estimation method, and belongs to the electrical measurement field. The method comprises the following steps: searching for impedance deviation coefficient effective maximum values and minimum values, taking adjacent effective maximum values as analysis intervals, and analyzing the correlation of capacitor branch voltage and current fundamental wave components in each analysis interval; according to the sampling frequency of the measurement and control device and the correlation analysis result, the components of aliasing harmonic components in the analysis interval are determined, and the impedance deviation coefficient effective minimum value in the corresponding analysis interval is used to estimate the aliasing harmonic value; the application also provides a low sampling rate measurement and control device aliasing harmonic value estimation system; and the aliasing harmonic value of the low sampling rate measurement and control device can be estimated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electrical measurement technology, and particularly relates to an aliasing harmonic value estimation method and system for a low sampling rate measurement and control device. BACKGROUND

[0002] The measurement and control device is a key equipment of the substation integrated automation system, and undertakes data acquisition, protection measurement, automatic control, remote management and many other functions. It is the "sensing organ" of the power grid state and the "control center" of the behavior, and plays an irreplaceable role in improving the reliability, safety and intelligence of the power system. Therefore, the stability, reliability and accuracy of the measurement data collected and sent by the measurement and control device are of great significance.

[0003] With the rapid advancement of new power system construction, new energy power generation represented by photovoltaic and wind power, high-voltage transmission and flexible DC power transmission, flexible interconnection and DC distribution network, and various types of power converters as power conversion interfaces of power utilization equipment have developed rapidly, which has continuously improved the degree of power electronics in each link of power generation, transmission, distribution and utilization. This brings two consequences: (1) The stability problem of power electronic equipment leads to an increase in the probability of low-frequency oscillation and sub- / super-synchronous oscillation in the power system, which seriously endangers the reliability of the power system operation; (2) The power conversion process of power electronic equipment generates a large amount of harmonics, which leads to the deterioration of harmonics in the power system and shows a high-frequency trend. The measurement and control device mainly focuses on the measurement of the fundamental component. In order to reduce the data operation amount and the cost of the control device, the existing massive measurement and control devices in the power grid have the status of low sampling frequency, no anti-aliasing filter or poor filtering effect, and non-synchronous sampling in data acquisition. The high-frequency harmonics inevitably cause aliasing problems in the low sampling rate measurement and control device. When the sampling frequency matches the harmonic frequency, aliasing can even occur to the fundamental wave. Under the condition of the fundamental frequency of the power system being near the time-varying power frequency, non-synchronous sampling will cause different degrees of leakage interference, which will cause the fundamental wave measurement result of the measurement and control device to appear pseudo-oscillation, thereby causing the relevant professionals in the power grid protection, regulation and control to be unable to distinguish whether the fundamental wave voltage and current oscillation measured by the measurement and control device is a pseudo-oscillation illusion caused by measurement aliasing or a real oscillation caused by power electronic devices, which is easy to misjudge the operation state of the power grid and cause serious consequences.

[0004] In the prior art, the Chinese patent application with the publication number CN105629189A discloses a method for determining pseudo-oscillation in power frequency measurement, which comprises the following steps: calculating the oscillation frequency of the fundamental wave measurement result of a set power grid position, extracting the power grid fundamental wave frequency in the fundamental wave measurement result, and calculating the frequency offset of the power grid fundamental wave frequency relative to a power grid rated frequency; and determining whether the oscillation in the fundamental wave measurement result is pseudo-oscillation according to one or more of the oscillation frequency, the frequency offset and the known signal harmonic number of the set power grid position. The method for determining pseudo-oscillation is to determine the relationship between the ratio of the oscillation frequency and the deviation of the fundamental wave frequency relative to the power frequency (50 Hz) and the aliasing harmonic number, which mainly identifies the frequency characteristics, involves the measurement of the fundamental wave frequency, but the current frequency measurement is based on the voltage waveform signal, and in the case of voltage oscillation, the measurement of the fundamental wave frequency will have a significant error, which will affect the calculation of the deviation of the fundamental wave frequency and cause the failure of the identification method or the error of the result, and the method is only applicable to the case of current oscillation but no voltage oscillation, but the conditions for meeting this scenario in the actual power grid are relatively harsh, and the size of the harmonic value cannot be estimated. SUMMARY

[0005] The technical problem to be solved by the present application is how to estimate the aliasing harmonic value of a low sampling rate measurement and control device.

[0006] The present application solves the above technical problems by the following technical scheme: a method for estimating the aliasing harmonic value of a low sampling rate measurement and control device, which comprises the following steps:

[0007] searching for effective maximum and minimum values of the impedance deviation coefficient, taking adjacent effective maximum values as analysis intervals, and analyzing the correlation of the fundamental wave components of the capacitor branch voltage and current in each analysis interval;

[0008] determining the components of the aliasing harmonic components in the analysis interval according to the sampling frequency of the measurement and control device and the correlation analysis result, and estimating the aliasing harmonic value according to the effective minimum value of the impedance deviation coefficient in the corresponding analysis interval.

[0009] Beneficial effects: The present application analyzes the correlation of the fundamental wave components of the capacitor branch voltage and current in each analysis interval, determines the components of the aliasing harmonic components in the analysis interval according to the sampling frequency of the measurement and control device and the correlation analysis result, and estimates the aliasing harmonic value according to the effective minimum value of the impedance deviation coefficient in the corresponding analysis interval, which expands the high-frequency harmonic measurement capability of the low sampling rate measurement and control device, improves the adaptability of the measurement and control device to the new power system through the technical means of the present application, expands the observability of the device non-power frequency electrical quantity, and provides necessary technical support for the high-reliability and low-risk operation of the existing power system in the transition stage to the new power system.

[0010] Preferably, the calculation process of the impedance deviation coefficient is as follows:

[0011] The full-wave Fourier algorithm is used to calculate the discrete data of voltage and current waveforms of the capacitor branch with oscillations measured by the measurement and control device cycle by cycle, so as to obtain the fundamental components of voltage and current in each cycle.

[0012] The fundamental impedance value of the capacitor for each cycle is obtained by calculating the ratio of the fundamental components of voltage and current in each cycle.

[0013] The impedance deviation coefficient for each cycle is obtained by calculating the ratio of the fundamental impedance value of the capacitor to the actual impedance value of the capacitor.

[0014] Preferably, the effective maximum and minimum values ​​of the impedance deviation coefficient are searched for, including:

[0015] Search for points where the impedance deviation coefficient is greater than the left and right adjacent impedance deviation coefficients to obtain the maximum impedance deviation coefficient r(a). i );

[0016] At adjacent impedance deviation coefficient maxima r(a) i ) and r(a i+1 ), the maximum value of the adjacent impedance deviation coefficient r(a) i+1 ) and r(a i+2 Between these points, search for points where the impedance deviation coefficient is less than the left and right adjacent impedance deviation coefficients, and obtain the minimum value r(b) of the adjacent impedance deviation coefficients. i ) and r(b i+1 );

[0017] Based on the minimum value of the adjacent impedance deviation coefficient r(b) i ) and r(b i+1 The relationship between impedance deviation coefficient and effective maximum and minimum values ​​is determined by considering the relationship between impedance deviation coefficient and impedance deviation coefficient.

[0018] Preferably, the time difference t between analysis intervals i The process of determining is as follows:

[0019] When the impedance deviation coefficient is at its minimum value r(b) i )≤1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When )≤1, the minimum value of the impedance deviation coefficient r(b) i The effective minimum value of the analysis interval is r(a), and the effective maximum value of the adjacent impedance deviation coefficient is r(a). i ) and r(a i+1 This allows us to obtain the start and end points of the analysis interval, and the time difference t of the i-th analysis interval. i for:

[0020]

[0021] When the impedance deviation coefficient is at its minimum value r(b)i ) > 1 and the impedance deviation coefficient minimum value r(b i+1 ) < 1, or the impedance deviation coefficient minimum value r(b i ) < 1 and the impedance deviation coefficient minimum value r(b i+1 ) > 1, the impedance deviation coefficient minimum value less than 1 is the effective minimum value of the analysis interval, and the adjacent impedance deviation coefficient effective maximum value is r(a i ) and r(a i+2 ), to obtain the start point and the end point of the analysis interval, the time difference t i of the i-th analysis interval is:

[0022]

[0023] wherein f0 is the power system frequency, a i , a i+1 , a i+2 are the cycle numbers corresponding to the i-th, i+1-th, i+2-th impedance deviation coefficient maximum values respectively, b i , b i+1 are the cycle numbers corresponding to the i-th, i+1-th impedance deviation coefficient minimum values respectively, and i = 1, 2, 3, ….

[0024] Preferably, the correlation of the capacitor branch voltage and current fundamental wave components in each analysis interval includes:

[0025] According to the cycle number c i corresponding to the effective maximum value at the start of each analysis interval and the cycle number c i+1 -1 corresponding to the previous effective maximum value at the end of each analysis interval, the capacitor branch voltage and current fundamental wave components are selected to form the voltage data set U i and the current data set I i :

[0026]

[0027] wherein H i is the number of voltage or current fundamental wave component data in the i-th analysis interval;

[0028] The Spearman correlation coefficient between the voltage data set U i and the current data set I i in each analysis interval is calculated.

[0029] Preferably, according to the sampling frequency of the measurement and control device and the correlation analysis result, the components of the aliasing harmonic components in the analysis interval include:

[0030] According to the sampling frequency f s of the measurement and control device,The ratio of the frequency to the power system frequency f0 is used to determine the harmonic frequencies h1 and h2 that can alias to the fundamental frequency and cause pseudo-oscillations.

[0031]

[0032] Based on the Spearman correlation coefficient β within the analysis interval i The magnitude distribution level is used to determine the aliased harmonic components that cause spurious oscillations:

[0033] When -1≤β i When the value is ≤-0.995, pseudo-oscillation is caused by the aliasing of the h1th harmonic;

[0034] When -0.995 < β i When ≤-0.5, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h1 harmonic is dominant;

[0035] When -0.5 < β i When <0.5, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, and the h1 and h2 harmonics are nearly the same;

[0036] When 0.5≤β i When <0.995, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h2 harmonic is dominant;

[0037] When 0.995≤β i When ≤1, pseudo-oscillation is caused by the superposition of the h2th harmonic.

[0038] Preferably, estimating the aliasing harmonic value using the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval includes:

[0039] When the Spearman correlation coefficient β i Satisfying -1≤β i When ≤-0.995, the h1th harmonic voltage content HRU i for:

[0040]

[0041] When the Spearman correlation coefficient β i Satisfies -0.995 < β i When ≤-0.5, the voltage content of the h1th harmonic is HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0042]

[0043] When the Spearman correlation coefficient β i Satisfying -0.5 < β iWhen <0.5, the h1th harmonic voltage content HRU h1,i h2 harmonic voltage content HRU h2,i for:

[0044]

[0045] When the Spearman correlation coefficient β i Satisfying 0.5≤β i When <0.995, the h1th harmonic voltage content HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0046]

[0047] When the Spearman correlation coefficient β i Satisfying 0.995≤β i When ≤1, the voltage content of the h2th harmonic is HRU h2,i for:

[0048]

[0049] Where r(d) i ) represents the effective minimum value of the impedance deviation coefficient within the i-th analysis interval.

[0050] Beneficial effects: This invention uses the clear phase angle relationship (180°, i.e., vector opposite) between the aliased harmonics and the fundamental component at the minimum value to estimate the harmonic value using a simple scalar superposition relationship (direct subtraction). It also describes the enhancement and attenuation relationship of different harmonics aliasing to the fundamental wave through correlation relationship, determines the harmonic components, and then uses the corresponding estimation formula to reduce estimation error.

[0051] Preferably, before analyzing the correlation of the fundamental components of the capacitor branch voltage and current within each analysis interval, the method further includes:

[0052] Based on the oscillation frequency of each analysis interval, the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient are calculated respectively, under the conditions of unknown and known fundamental frequency of the power grid.

[0053] Search for all effective maxima and minima of impedance deviation coefficients. If all effective maxima of impedance deviation coefficients are greater than the maximum threshold and all effective minima are less than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a pseudo oscillation. If all effective maxima of impedance deviation coefficients are less than the maximum threshold and all effective minima are greater than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a true oscillation.

[0054] Beneficial effects: This invention searches for the effective maximum and minimum values ​​of the impedance deviation coefficient, determines the analysis interval by using adjacent effective maximum values, calculates the corresponding oscillation frequency based on the time difference of the analysis interval, and calculates the threshold values ​​of the maximum and minimum values ​​of the impedance deviation coefficient corresponding to the oscillation frequency of each analysis interval. Based on the relationship between the effective maximum and minimum values ​​of the impedance deviation coefficient and the corresponding threshold values, it judges the authenticity of the oscillation measured by the measurement and control device, which can distinguish between real oscillations in the power grid and measurement pseudo-oscillations, and solves the risk of misjudgment caused by measurement pseudo-oscillations caused by high-frequency harmonic aliasing in the measurement and control device.

[0055] This invention identifies spurious oscillations by measuring the difference in capacitive reactance of capacitors. This difference is caused by the difference between the degree of voltage and current oscillations under true and false oscillations. It is applicable not only to current oscillations but also to voltage oscillations, thereby overcoming the defects of existing spurious oscillation identification methods that rely on frequency characteristics for identification, which may result in failure or incorrect results.

[0056] Preferably, the process of calculating the maximum and minimum threshold values ​​of the impedance deviation coefficient, respectively, based on the oscillation frequency of each analysis interval and under the conditions of unknown and known fundamental frequency of the power grid, includes:

[0057] When the fundamental frequency f of the power grid within the analysis interval is unknown, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0058]

[0059] When the fundamental frequency f of the power grid within the analysis interval is known and has a positive deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0060]

[0061] When the fundamental frequency f of the power grid within the analysis interval is known and has a negative deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0062]

[0063]

[0064] Where Δf is the fundamental frequency deviation of the power grid, f i α is the oscillation frequency, and α is the margin coefficient that comprehensively considers the errors of the full-wave Fourier algorithm leakage and the actual capacitance calculation.

[0065] Beneficial effects: Based on the oscillation frequency of each analysis interval, this invention can calculate the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient when the fundamental frequency of the power grid is unknown or known. First, it can accurately calculate different threshold values ​​corresponding to different oscillation frequencies, avoiding the problem of inconsistent identification accuracy at different frequencies caused by a constant threshold. Second, it satisfies the need for accurate threshold calculation in different scenarios (known and unknown fundamental frequencies), and does not always rely on the fundamental frequency, overcoming the problem of inaccurate frequency measurement caused by voltage fluctuations. Through the above formula, the applicability of the identification method is expanded, and the accuracy of identification is improved.

[0066] This invention also provides a system for estimating aliasing harmonic values ​​in low sampling rate measurement and control devices, the system further comprising:

[0067] The correlation analysis module is used to search for the effective maxima and minima of the impedance deviation coefficient. It uses adjacent effective maxima as the analysis interval to analyze the correlation between the fundamental components of the capacitor branch voltage and current within each analysis interval.

[0068] The aliasing harmonic value estimation module is used to determine the components of the aliasing harmonics within the analysis interval based on the sampling frequency and correlation analysis results of the measurement and control device, and to estimate the aliasing harmonic value by corresponding to the effective minimum value of the impedance deviation coefficient within the analysis interval. Attached Figure Description

[0069] Figure 1 This is a flowchart of the method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device provided in Embodiment 1 of the present invention;

[0070] Figure 2(a) is a schematic diagram of the process of determining the effective maximum and minimum values ​​of the impedance deviation coefficient in case 1 in the method for estimating the aliased harmonic values ​​of the low sampling rate measurement and control device provided in Embodiment 1 of the present invention.

[0071] Figure 2(b) is a schematic diagram of the process of determining the effective maximum and minimum values ​​of the impedance deviation coefficient in case 2 in the method for estimating the aliased harmonic value of the low sampling rate measurement and control device provided in Embodiment 1 of the present invention.

[0072] Figure 2(c) is a schematic diagram of the process of determining the effective maximum and minimum values ​​of the impedance deviation coefficient in case 3 in the method for estimating the aliased harmonic value of the low sampling rate measurement and control device provided in Embodiment 1 of the present invention.

[0073] Figure 3 This is a flowchart of the method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device provided in Embodiment 2 of the present invention;

[0074] Figure 4 This is a schematic diagram of the aliasing harmonic value estimation system of the low sampling rate measurement and control device provided in Embodiment 3 of the present invention;

[0075] Figure 5The waveform diagram of the voltage and current of the capacitor branch measured by the measurement and control device in Example 5;

[0076] Figure 6 This is a schematic diagram of the fundamental components of the oscillation voltage and current analyzed periodically using the full-wave Fourier algorithm in Example 5.

[0077] Figure 7 This is a graph showing the impedance deviation coefficient and its effective maximum and minimum values ​​in Example 5. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0079] Example 1

[0080] See Figure 1 This embodiment provides a method for estimating aliasing harmonic values ​​in a low-sampling-rate measurement and control device. This method is used to estimate the aliasing harmonic values ​​when a low-sampling-rate measurement and control device in a capacitor branch experiences measurement spurious oscillations. The method includes the following steps:

[0081] Step 1: Search for the effective maximum and minimum values ​​of the impedance deviation coefficient. Use adjacent effective maximum values ​​as the analysis interval to analyze the correlation between the fundamental components of the capacitor branch voltage and current within each analysis interval.

[0082] The specific calculation process for the impedance deviation coefficient includes:

[0083] Step 1.1.1: Determine the number of sampling points N within one cycle of voltage or current based on the sampling frequency of the measurement and control device; the formula for calculating the number of sampling points N is:

[0084]

[0085] Among them, f s f is the sampling frequency of the measurement and control device, measured in Hz. s It can be obtained through the product's instruction manual or specification label, etc. f0 is the power system frequency, f0 = 50Hz.

[0086] Step 1.1.2: Using the full-wave Fourier algorithm, calculate the discrete waveform data of the capacitor branch voltage and current exhibiting oscillations in the measurement and control device cycle by cycle to obtain the fundamental voltage and current components (amplitudes) for each cycle. The data acquisition time should not be too short; it is recommended to be no less than 10 minutes. The formulas for calculating the fundamental voltage amplitude U(k) and fundamental current amplitude I(k) in the k-th cycle are as follows:

[0087]

[0088] Where U(k) is the amplitude of the fundamental voltage in the k-th period, in V, and I(k) is the amplitude of the fundamental current in the k-th period, in A. k (n), i k (n) represents the nth sample value of the voltage waveform and the nth sample value of the current waveform in the kth period, respectively, k = 1, 2, 3, ..., N is the number of sampling points in the period.

[0089] Step 1.1.3: Calculate the fundamental impedance value of the capacitor for each cycle by taking the ratio of the fundamental voltage and current components; the fundamental impedance value Z of the capacitor is... m (k) is:

[0090]

[0091] Among them, Z m (k) is the measured value of the fundamental impedance of the capacitor in the kth period, in Ω, k = 1, 2, 3, ...

[0092] Step 1.1.4: Collect the rated capacity Q of the capacitors (banks) in the capacitor branch. co and capacitor (bank) rated voltage U c Calculate the actual impedance value Z of the capacitor (bank). co Actual impedance value Z of the capacitor co for:

[0093]

[0094] Among them, the actual impedance value Z of the capacitor co This is the actual value of the fundamental impedance of the capacitor (bank), in Ω and Q. co The rated capacity of the capacitor (bank), in Mvar, U c This is the rated voltage of the capacitor (bank), in kV.

[0095] Step 1.1.5: Using the fundamental impedance value Z of the capacitor m (k) and the actual impedance value Z of the capacitor coThe ratio calculation yields the impedance deviation coefficient r(k) for each cycle, which is:

[0096]

[0097] Where r(k) is the impedance deviation coefficient of the kth period.

[0098] The search for the effective maximum and minimum values ​​of the impedance deviation coefficient includes the following process:

[0099] Step 1.2.1: According to the conditions of formula (6), search for points where the impedance deviation coefficient is greater than the left and right adjacent impedance deviation coefficients, and obtain the maximum value of the impedance deviation coefficient r(a). i );

[0100]

[0101] Among them, a i Let i be the number of cycles corresponding to the maximum value of the i-th impedance deviation coefficient, i = 1, 2, 3, ...

[0102] Step 1.2.2: At adjacent impedance deviation coefficient maxima r(a) i ) and r(a i+1 ), the maximum value of the adjacent impedance deviation coefficient r(a) i+1 ) and r(a i+2 Between ), according to the conditions of formula (7), search for points where the impedance deviation coefficient is less than the left and right adjacent impedance deviation coefficients, and obtain the minimum value r(b) of the adjacent impedance deviation coefficient. i ) and r(b i+1 );

[0103]

[0104] Among them, b i Let i be the number of cycles corresponding to the minimum value of the i-th impedance deviation coefficient, i = 1, 2, 3, ...

[0105] Step 1.2.3: Based on the minimum value r(b) of the adjacent impedance deviation coefficient i ) and r(b i+1 The relationship between the impedance deviation coefficient and its effective maximum and minimum values ​​is determined. Each analysis interval is then determined using the effective maximum values ​​of adjacent impedance deviation coefficients. The time difference t between the analysis intervals is calculated based on the number of periods corresponding to each analysis interval. i .

[0106] Figure 2 is a schematic diagram illustrating the process of determining the effective maximum and minimum values ​​of the impedance deviation coefficient. See Figure 2(a), which represents case 1: when the impedance deviation coefficient reaches its minimum value r(b) i )≤1 and the impedance deviation coefficient is at its minimum value r(b)i+1 When )≤1, the minimum value of the impedance deviation coefficient r(b) i The effective minimum value of the analysis interval is r(a), and the effective maximum value of the adjacent impedance deviation coefficient is r(a). i ) and r(a i+1 This allows us to obtain the start and end points of the analysis interval, and the time difference t of the i-th analysis interval. i for:

[0107]

[0108] See Figures 2(b) and 2(c), where Figure 2(b) represents case 2 and Figure 2(c) represents case 3: when the impedance deviation coefficient is at its minimum value r(b) i )>1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When )≤1 (Case 2), or the impedance deviation coefficient is at its minimum value r(b) i )≤1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When ) > 1 (Case 3), the minimum value of the impedance deviation coefficient less than 1 is the effective minimum value of the analysis interval, and the effective maximum value of the adjacent impedance deviation coefficient is r(a). i ) and r(a i+2 The start and end points of the analysis interval are obtained. According to formula (9), the time difference t of the i-th analysis interval is calculated based on the number of cycles corresponding to the start and end points of the analysis interval. i for:

[0109]

[0110] Where f0 is the power system frequency, a i a i+1 a i+2 These represent the number of cycles corresponding to the maximum values ​​of the impedance deviation coefficients at the i-th, i+1-th, and i+2-th points, respectively, and b. i b i+1 These are the cycle numbers corresponding to the minimum values ​​of the impedance deviation coefficients at the i-th and i+1-th intervals, respectively, where i = 1, 2, 3, ...

[0111] Step 1.2.4: Based on the time difference t of the analysis interval i The reciprocal of the oscillation frequency f is calculated to obtain the corresponding oscillation frequency f. i oscillation frequency f i The calculation formula is:

[0112]

[0113] Among them, f i Let be the oscillation frequency corresponding to the i-th analysis interval, where i = 1, 2, 3, ...

[0114] The subsequent harmonic estimation process only involves the effective maxima and minima within the analysis interval. The number of periods corresponding to the effective maxima (the starting point of the analysis interval) and minima within the i-th analysis interval are denoted as c. i and d i .

[0115] The correlation analysis of the fundamental components of capacitor branch voltage and current within each analysis interval includes:

[0116] Step 1.3: Determine that the oscillation is an artifact caused by aliasing in the measurement and control device, and determine the number of periods c corresponding to the effective maximum value at the beginning of each analysis interval. i The number of cycles c preceding the effective maximum at the end. i+1 -1, select the fundamental components of the capacitor branch voltage and current to construct the voltage dataset U. i Current Dataset I i :

[0117]

[0118] Among them, H i The number of fundamental voltage or current components within the i-th analysis interval;

[0119] Step 1.4: Calculate the voltage dataset U for each analysis interval. i and current dataset I i The Spearman correlation coefficient between the two intervals is used to perform correlation analysis within that interval, specifically including the following procedures:

[0120] Step 1.4.1: Arrange the fundamental components of the voltage and current datasets corresponding to the analysis intervals from smallest to largest, and obtain the number of permutations R[U(j)] and R[I(j)] within the analysis interval, j = 1, 2, 3, ..., H. i If there are duplicate data, the number of times the data is arranged is replaced by the average number of times the data is arranged.

[0121] Step 1.4.2: Calculate and analyze the difference D between the number of times the voltage and current data are arranged within the interval. j The calculation formula is:

[0122] D j =R[U(j)]-R[I(j)] (12)

[0123] The Spearman correlation coefficient β within the analysis interval is calculated according to formula (13). i for:

[0124]

[0125] Among them, D jTo analyze the difference in the number of times the voltage and current data are arranged within the analysis interval, R[U(j)] and R[I(j)] are the number of times the fundamental components of the voltage and current datasets corresponding to the analysis interval are arranged from smallest to largest within the analysis interval, j = 1, 2, 3, ..., H. i .

[0126] Step 2: Based on the sampling frequency and correlation analysis results of the measurement and control device, determine the components of the aliased harmonics within the analysis interval, and then estimate the aliased harmonic value using the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval.

[0127] Based on the sampling frequency and correlation analysis results of the measurement and control device, the determination of the components of the aliased harmonics within the analysis interval specifically includes the following process:

[0128] Step 2.1: Based on the sampling frequency f of the measurement and control device s The ratio of the power system frequency f0 to the fundamental frequency (i.e., the number of sampling points per cycle) is used to determine the harmonic frequencies h1 and h2 that can be aliased to the fundamental frequency and cause pseudo-oscillations, according to formula (14):

[0129]

[0130] Step 2.2: Based on the Spearman correlation coefficient β within the analysis interval... i The magnitude distribution level is used to determine the aliased harmonic components that cause spurious oscillations, in order to analyze the effective minimum value of the impedance deviation coefficient within the interval. Based on the aliased harmonic components determined by different distribution levels of the correlation coefficient, the corresponding harmonic voltage content is estimated.

[0131] In step 2.2, the Spearman correlation coefficient β within the analysis interval is used... i The process of determining the aliased harmonic components that cause spurious oscillations, based on the magnitude distribution levels, includes:

[0132] Level 1: When -1 ≤ β i When the value is ≤-0.995, pseudo-oscillation is caused by the aliasing of the h1th harmonic;

[0133] Level 2: When -0.995 < β i When ≤-0.5, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h1 harmonic is dominant;

[0134] Level 3: When -0.5 < β i When <0.5, pseudo-oscillation is caused by the superposition of the j1 and h2 harmonics, and the h1 and h2 harmonics are nearly the same;

[0135] Level 4: When 0.5 ≤ β i When <0.995, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h2 harmonic is dominant;

[0136] Level 5: When 0.995 ≤ β i When ≤1, pseudo-oscillation is caused by the superposition of the h2th harmonic.

[0137] Step 2.2, which involves estimating the corresponding harmonic voltage content, includes:

[0138] When analyzing the Spearman correlation coefficient β within the interval i When the level 1 condition is met, the h1th harmonic voltage content HRU i for:

[0139]

[0140] When analyzing the Spearman correlation coefficient β within the interval i When the level 2 condition is met, the h1th harmonic voltage content HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0141]

[0142] When analyzing the Spearman correlation coefficient β within the interval i When the level 3 condition is met, the h1th harmonic voltage content HRU h1,i h2 harmonic voltage content HRU h2,i for:

[0143]

[0144] When analyzing the Spearman correlation coefficient β within the interval i When the level 4 condition is met, the h1th harmonic voltage content HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0145]

[0146] When analyzing the Spearman correlation coefficient β within the interval i When the level 5 condition is met, the h2th harmonic voltage content HRU h2,i for:

[0147]

[0148] Where r(d) i ) represents the effective minimum value of the impedance deviation coefficient within the i-th analysis interval.

[0149] When the oscillation measured by the measurement and control device is a pseudo-oscillation, this invention analyzes the correlation of the fundamental components of the capacitor branch voltage and current within each analysis interval. Based on the sampling frequency of the measurement and control device and the correlation analysis results, it determines the components of the aliased harmonics within the analysis interval. Then, it estimates the aliased harmonic value using the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval. This expands the high-frequency harmonic measurement capability of low-sampling-rate measurement and control devices. Through the technical means of this invention, the adaptability of existing measurement and control devices to new power systems with power electronics is improved, and the observability of non-power frequency electrical quantities of the device is expanded. This provides necessary technical support for high-reliability, low-risk operation during the transition from existing power systems to new power systems. The aliased harmonic value estimation method of this invention can also be integrated into the measurement and control device to achieve real-time estimation and observe the changes in harmonic magnitude.

[0150] This invention utilizes the clear phase angle relationship (180°, i.e., vector opposite) between the aliased harmonics and the fundamental component at the minimum value. It can estimate the harmonic value using a simple scalar superposition relationship (direct subtraction). Furthermore, it describes the enhancement and attenuation relationship of different harmonics aliasing to the fundamental frequency through correlation relationships, determines the harmonic components, and then uses the corresponding estimation formula to reduce estimation errors.

[0151] Example 2

[0152] See Figure 3 The difference between this embodiment and Embodiment 1 is that Embodiment 1 includes the following step before analyzing the correlation of the fundamental components of the capacitor branch voltage and current within each analysis interval:

[0153] The oscillation frequency is calculated based on the time difference of the analysis interval. The maximum and minimum threshold values ​​of the impedance deviation coefficient corresponding to the oscillation frequency for each analysis interval are then calculated. By analyzing the relationship between the effective maximum and minimum values ​​of the impedance deviation coefficient and the corresponding threshold values, the authenticity of the oscillation measured by the measurement and control device is identified. The specific identification process is as follows:

[0154] Based on the oscillation frequency of each analysis interval, the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient are calculated respectively, under the conditions of unknown and known fundamental frequency of the power grid.

[0155] Search for all effective maxima and minima of impedance deviation coefficients. If all effective maxima of impedance deviation coefficients are greater than the maximum threshold and all effective minima are less than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a pseudo oscillation. If all effective maxima of impedance deviation coefficients are less than the maximum threshold and all effective minima are greater than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a true oscillation.

[0156] When the fundamental frequency f of the power grid within the analysis interval is unknown, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0157]

[0158] When the fundamental frequency f of the power grid within the analysis interval is known and has a positive deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0159]

[0160] When the fundamental frequency f of the power grid within the analysis interval is known and has a negative deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0161]

[0162] Wherein, Δf is the fundamental frequency deviation of the power grid, and its upper limit can be determined according to the limit specified in the standard "GB / T 15945-2008 Power Quality Power System Frequency Deviation", with a value range of 0Hz≤Δf≤0.2Hz; α is a margin coefficient that comprehensively considers the leakage of the full-wave Fourier algorithm and the error of actual capacitance calculation, with a value range of 1.05≤α≤1.2.

[0163] This invention, based on the oscillation frequency of each analysis interval, can calculate the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient when the fundamental frequency of the power grid is unknown and known, respectively. First, it can accurately calculate different threshold values ​​corresponding to different oscillation frequencies, avoiding the inconsistency in identification accuracy at different frequencies caused by a constant threshold. Second, it satisfies the need for accurate threshold calculation in different scenarios (known and unknown fundamental frequencies), not always relying on the fundamental frequency, overcoming the problem of inaccurate frequency measurement due to voltage fluctuations. Through the above formula, it aims to expand the applicability of the identification method and improve its accuracy.

[0164] The effective maxima and minima of all impedance deviation coefficients are compared one by one with the threshold. The authenticity of the measurement oscillation of the measurement and control device is determined based on the comparison results. When all effective maxima of impedance deviation coefficients are greater than the maximum threshold and all effective minima are less than the minimum threshold, the measurement oscillation of the measurement and control device is determined to be a pseudo oscillation, that is, the measurement oscillation of the measurement and control device is an illusion caused by measurement aliasing, which is expressed by formula (26):

[0165]

[0166] When all effective maxima of impedance deviation coefficients are less than the maximum threshold and all effective minima are greater than the minimum threshold, it is determined that the oscillation measured by the measurement and control device is a true oscillation, and there is an oscillation phenomenon in the power grid, which is expressed by formula (27):

[0167]

[0168] Among them, c i The effective maximum value of the impedance deviation coefficient r(c) within the i-th analysis interval. i The corresponding period number, d i The effective minimum value of the impedance deviation coefficient r(d) within the i-th analysis interval. i The corresponding number of cycles.

[0169] If the effective maximum or minimum value of the impedance deviation coefficient being searched is both greater than or less than the corresponding threshold, then the authenticity of the oscillation measured by the measurement and control device cannot be determined.

[0170] This invention analyzes the fundamental components of voltage and current in capacitor branches exhibiting oscillations in a measurement and control device on a cycle-by-cycle basis, calculates the impedance deviation coefficient for each cycle, searches for the effective maximum and minimum values ​​of the impedance deviation coefficient, determines the analysis interval using adjacent effective maximum values, and calculates the corresponding oscillation frequency based on the time difference of the analysis interval. The true or false oscillations measured by the measurement and control device are determined by the relationship between the effective maximum and minimum values ​​of the impedance deviation coefficient and the corresponding threshold. This invention primarily utilizes the known relationship between capacitor capacitive reactance and harmonic frequency, identifying the difference in impedance between the capacitor under true and false oscillations. This difference is caused by the difference in the degree of voltage and current oscillation under true and false oscillations, thus distinguishing between real oscillations and measurement pseudo-oscillations in the power grid, and resolving the risk of misjudgment caused by measurement pseudo-oscillations due to high-frequency harmonic aliasing in the measurement and control device.

[0171] This invention identifies spurious oscillations by measuring the difference in capacitive reactance of capacitors. This difference is caused by the difference between the degree of voltage and current oscillations under true and false oscillations. It is applicable not only to current oscillations but also to voltage oscillations, thereby overcoming the defects of existing spurious oscillation identification methods that rely on frequency characteristics for identification, which may result in failure or incorrect results.

[0172] Example 3

[0173] See Figure 4 This embodiment provides a system for estimating aliasing harmonic values ​​in a low sampling rate measurement and control device. The system includes:

[0174] The correlation analysis module is used to search for the effective maxima and minima of the impedance deviation coefficient. It uses adjacent effective maxima as the analysis interval to analyze the correlation between the fundamental components of the capacitor branch voltage and current within each analysis interval.

[0175] The calculation process for the impedance deviation coefficient is as follows:

[0176] Step 1.1.1: Use the full-wave Fourier algorithm to calculate the discrete data of the voltage and current waveforms of the capacitor branch with oscillations measured by the measurement and control device cycle by cycle, and obtain the fundamental components of voltage and current for each cycle;

[0177] Step 1.1.2: Calculate the fundamental impedance value of the capacitor for each cycle by the ratio of the fundamental voltage and current components in each cycle;

[0178] Step 1.1.3: Calculate the impedance deviation coefficient for each cycle by using the ratio of the fundamental impedance value of the capacitor to the actual impedance value of the capacitor.

[0179] The search for effective maxima and minima of the impedance deviation coefficient includes:

[0180] Step 1.2.1: Search for points where the impedance deviation coefficient is greater than the left and right adjacent impedance deviation coefficients, and obtain the maximum value of the impedance deviation coefficient r(a). o );

[0181] Step 1.2.2: At adjacent impedance deviation coefficient maxima r(a) i ) and r(a i+1 ), the maximum value of the adjacent impedance deviation coefficient r(a) i+1 ) and r(a i+2 Between these points, search for points where the impedance deviation coefficient is less than the left and right adjacent impedance deviation coefficients, and obtain the minimum value r(b) of the adjacent impedance deviation coefficients. i ) and r(b i+1 );

[0182] Step 1.2.3: Based on the minimum value r(b) of the adjacent impedance deviation coefficient i ) and r(b i+1 The relationship between impedance deviation coefficient and effective maximum and minimum values ​​is determined by considering the relationship between impedance deviation coefficient and impedance deviation coefficient.

[0183] Analysis of the time difference t i The process of determining is as follows:

[0184] When the impedance deviation coefficient is at its minimum value r(b) i )≤1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When )≤1, the minimum value of the impedance deviation coefficient r(b) i The effective minimum value of the analysis interval is r(a), and the effective maximum value of the adjacent impedance deviation coefficient is r(a). i ) and r(a i+1 This allows us to obtain the start and end points of the analysis interval, and the time difference t of the i-th analysis interval. i for:

[0185]

[0186] When the impedance deviation coefficient is at its minimum value r(b) i )>1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When )≤1, or the impedance deviation coefficient is at its minimum value r(b) i )≤1 and the impedance deviation coefficient is at its minimum value r(b) i+1 When ) > 1, the minimum value of the impedance deviation coefficient less than 1 is the effective minimum value of the analysis interval, and the effective maximum value of the adjacent impedance deviation coefficient is r(a). i ) and r(a i+2 This allows us to obtain the start and end points of the analysis interval, and the time difference t of the i-th analysis interval. i for:

[0187]

[0188] Where f0 is the power system frequency, a i a i+1 a i+2 These represent the number of cycles corresponding to the maximum values ​​of the impedance deviation coefficients at the i-th, i+1-th, and i+2-th points, respectively, and b. i b i+1 These are the cycle numbers corresponding to the minimum values ​​of the impedance deviation coefficients at the i-th and i+1-th intervals, respectively, where i = 1, 2, 3, ...

[0189] The correlation analysis of the fundamental components of capacitor branch voltage and current within each analysis interval includes:

[0190] Step 1.3: Calculate the number of periods c corresponding to the effective maximum at the beginning of each analysis interval. i The number of cycles c preceding the effective maximum at the end. i+1 -1, select the fundamental components of the capacitor branch voltage and current to construct the voltage dataset U. i Current Dataset I i :

[0191]

[0192] Among them, H i The number of fundamental voltage or current components within the i-th analysis interval;

[0193] Step 1.4: Calculate the voltage dataset U for each analysis interval. i and current dataset I i The Spearman correlation coefficient between the two intervals is used to perform correlation analysis within that interval. The Spearman correlation coefficient β within the i-th analysis interval is... i for:

[0194]

[0195] Among them, D j To analyze the difference in the number of permutations of voltage and current data within an interval, D j = R[U(j)] - R[I(j)], where R[U(j)] and R[I(j)] are the ranking numbers of the fundamental components in the voltage and current datasets corresponding to the analysis interval, obtained by arranging them from smallest to largest, j = 1, 2, 3, ..., H. i .

[0196] The aliasing harmonic value estimation module is used to determine the components of the aliasing harmonics within the analysis interval based on the sampling frequency and correlation analysis results of the measurement and control device, and then estimate the aliasing harmonic value using the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval.

[0197] The process of determining the components of aliased harmonics within the analysis interval based on the sampling frequency and correlation analysis results of the measurement and control device includes the following steps:

[0198] Step 2.1: Based on the sampling frequency f of the measurement and control device s The ratio of the frequency to the power system frequency f0 is used to determine the harmonic frequencies h1 and h2 that can alias to the fundamental frequency and cause pseudo-oscillations.

[0199]

[0200] Step 2.2: Based on the Spearman correlation coefficient β within the analysis interval i The magnitude distribution level is used to determine the aliased harmonic components causing spurious oscillations, and to analyze the effective minimum value of the impedance deviation coefficient within the analysis interval. Based on the aliased harmonic components, the corresponding harmonic voltage content is estimated. In step 2.2, the Spearman correlation coefficient β within the analysis interval is used... i The process of determining the aliased harmonic components that cause spurious oscillations, based on the magnitude distribution levels, includes:

[0201] Level 1: When -1 ≤ β i When the value is ≤-0.995, pseudo-oscillation is caused by the aliasing of the h1th harmonic;

[0202] Level 2: When -0.995 < β i When ≤-0.5, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h1 harmonic is dominant;

[0203] Level 3: When -0.5 < β i When <0.5, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, and the h1 and h2 harmonics are nearly the same;

[0204] Level 4: When 0.5 ≤ β iWhen <0.995, pseudo-oscillation is caused by the superposition of the h1 and h2 harmonics, but the h2 harmonic is dominant;

[0205] Level 5: When 0.995 ≤ β i When ≤1, pseudo-oscillation is caused by the superposition of the h2th harmonic.

[0206] Step 2.3, which involves estimating the corresponding harmonic voltage content, includes:

[0207] When analyzing the Spearman correlation coefficient β within the interval i When the level 1 condition is met, the h1th harmonic voltage content HRU i for:

[0208]

[0209] When analyzing the Spearman correlation coefficient β within the interval i When the level 2 condition is met, the h1th harmonic voltage content HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0210]

[0211] When analyzing the Spearman correlation coefficient β within the interval i When the level 3 condition is met, the h1th harmonic voltage content HRU h1,i h2 harmonic voltage content HRU h2,i for:

[0212]

[0213] When analyzing the Spearman correlation coefficient β within the interval i When the level 4 condition is met, the h1th harmonic voltage content HRU h1,i With h2th harmonic voltage content HRU h2,i The sum is:

[0214]

[0215] When analyzing the Spearman correlation coefficient β within the interval i When the level 5 condition is met, the h2th harmonic voltage content HRU h2,i for:

[0216]

[0217] Where r(d) i ) represents the effective minimum value of the impedance deviation coefficient within the i-th analysis interval.

[0218] Example 4

[0219] The difference between this embodiment and embodiment 3 is that, based on the aliasing harmonic value estimation system of the low sampling rate measurement and control device in embodiment 3, this embodiment also includes:

[0220] The oscillation authenticity identification module is used to calculate the corresponding oscillation frequency based on the time difference of the analysis interval, calculate the maximum and minimum threshold values ​​of the impedance deviation coefficient corresponding to the oscillation frequency of each analysis interval, and identify the authenticity of the oscillation measured by the measurement and control device by the relationship between the effective maximum and minimum values ​​of the impedance deviation coefficient and the corresponding threshold values. The specific identification process includes:

[0221] Based on the oscillation frequency of each analysis interval, the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient are calculated respectively, under the conditions of unknown and known fundamental frequency of the power grid.

[0222] Search for all effective maxima and minima of impedance deviation coefficients. If all effective maxima of impedance deviation coefficients are greater than the maximum threshold and all effective minima are less than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a pseudo oscillation. If all effective maxima of impedance deviation coefficients are less than the maximum threshold and all effective minima are greater than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a true oscillation.

[0223] Based on the oscillation frequency of each analysis interval, the process of calculating the maximum and minimum threshold values ​​of the impedance deviation coefficient, under the conditions of unknown and known fundamental frequency of the power grid, includes:

[0224] When the fundamental frequency f of the power grid within the analysis interval is unknown, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0225]

[0226] When the fundamental frequency f of the power grid within the analysis interval is known and has a positive deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0227]

[0228] When the fundamental frequency f of the power grid within the analysis interval is known and has a negative deviation relative to the power system frequency f0, the threshold value p of the maximum impedance deviation coefficient is... i Minimum threshold q i They are respectively:

[0229]

[0230] Where Δf is the fundamental frequency deviation of the power grid, f iα is the oscillation frequency, and α is the margin coefficient that comprehensively considers the errors of the full-wave Fourier algorithm leakage and the actual capacitance calculation.

[0231] Example 5

[0232] To better understand this invention, the above process is described in detail below with specific examples. The values ​​used in this example are merely illustrative, and users can make corresponding changes according to actual needs. A 35kV capacitor branch monitoring and control device exhibits oscillation phenomena when measuring voltage and current. The sampling frequency of this monitoring and control device is 1200Hz, and the sampled oscillation waveform is as follows... Figure 5 As shown, we will now identify the authenticity of the oscillation and estimate the aliased harmonic values.

[0233] Based on the sampling frequency of the measurement and control device, the number of sampling points for each cycle of the measured voltage and current is calculated to be N = 1200 / 50 = 24. Using the full-wave Fourier algorithm, the measurement and control device collects discrete data of the voltage and current waveforms of the capacitor branch with oscillation phenomena according to formula (2) to obtain the fundamental components (amplitude) of the voltage and current for each cycle. The results are as follows: Figure 6 As shown, the measured value of the fundamental impedance of the capacitor corresponding to each cycle is calculated according to formula (3). The capacitor branch measured in this example contains a capacitor bank with a rated voltage of 35kV and a rated capacity of 20Mvar. The actual value Z of the fundamental impedance of the capacitor (bank) is calculated according to formula (4). co =61.25Ω. Calculate the ratio of the measured to the actual fundamental impedance of the capacitor according to formula (5), and obtain the impedance deviation coefficient for each cycle, such as... Figure 7 As shown.

[0234] search Figure 7 The effective maxima and minima of the impedance deviation coefficient are used to obtain the corresponding period numbers. Adjacent effective maxima are used to form the start and end points of the analysis interval. The time difference between each analysis interval is then calculated using the corresponding period numbers, and finally, the corresponding oscillation frequency is obtained. The results are as follows: Figure 7 As shown in Table 1.

[0235] Table 1 Effective maxima, minima, corresponding period numbers, and analysis interval oscillation frequency

[0236]

[0237] This example calculates the threshold according to the maximum error principle. Since the fundamental frequency of the power grid is unknown, the fundamental frequency deviation is taken as the maximum value, Δf = 0.2Hz; the margin coefficient is also taken as the maximum value, α = 1.2. Based on the oscillation frequency of each analysis interval in Table 1, the threshold value p of the maximum impedance deviation coefficient is calculated according to formulas (20) and (21). i =1.013 and the minimum threshold qi =0.987. Comparing with all effective maxima and minima of the impedance deviation coefficient, it satisfies the condition that all effective maxima of the impedance deviation coefficient are greater than the corresponding threshold and all effective minima are less than the corresponding threshold. Therefore, it can be determined that the oscillation measured by the measurement and control device is a pseudo oscillation, which is an illusion caused by its measurement aliasing, and the authenticity of the oscillation can be accurately identified.

[0238] The Spearman correlation coefficient between voltage and current data in each analysis interval was calculated according to formulas (13) and (14), and the results are shown in Table 2. Since the sampling frequency of the measurement and control device is 1200Hz, according to formula (15), the 23rd and 25th harmonics can cause spurious oscillations, and the correlation coefficient between voltage and current in each analysis interval satisfies -1≤β. i ≤-0.995 (Level 1) indicates that the spurious oscillation is caused by the 23rd harmonic. At this time, according to formula (16), the voltage content of the 23rd harmonic causing the measurement oscillation of the measurement and control device is estimated to be about 1% by analyzing the effective minimum value within the interval (Table 1). The specific estimation results are shown in Table 2. This method overcomes the constraint of the Nyquist sampling theorem, realizes the estimation of high-frequency harmonics in low sampling rate measurement and control devices, and expands the observability of the power grid state of the measurement and control device.

[0239] Table 2. Estimation results of Spearman correlation coefficient and harmonic values.

[0240] Analysis interval number Spearman's correlation coefficient β i ]] Estimated harmonic voltage content (%) 1 -1.000 1.007 2 -0.999 1.004 3 -0.999 0.999 4 -0.999 0.995 5 -0.999 0.992 6 -0.998 0.991 7 -0.999 0.993 8 -0.999 0.997 9 -0.999 1.001

[0241] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device, characterized in that: The methods include: The full-wave Fourier algorithm is used to calculate the discrete data of voltage and current waveforms of the capacitor branch with oscillations measured by the measurement and control device cycle by cycle, so as to obtain the fundamental components of voltage and current in each cycle. The fundamental impedance value of the capacitor for each cycle is obtained by calculating the ratio of the fundamental components of voltage and current in each cycle. The impedance deviation coefficient for each cycle is obtained by calculating the ratio of the fundamental impedance value of the capacitor to the actual impedance value of the capacitor. Search for the effective maximum and minimum values ​​of the impedance deviation coefficient, and use adjacent effective maximum values ​​as the analysis interval to analyze the correlation between the fundamental components of the capacitor branch voltage and current within each analysis interval; Based on the sampling frequency of the measurement and control device and the correlation analysis results, the components of the aliased harmonics within the analysis interval are determined. With power system power frequency The ratio of these values ​​determines the harmonic frequencies that can alias to the fundamental frequency and cause pseudo-oscillations. , : Based on the Spearman correlation coefficient between the voltage and current datasets within the analysis interval The magnitude distribution level is used to determine the aliased harmonic components that cause spurious oscillations: When -1≤ When ≤-0.995, by h First harmonic aliasing causes pseudo-oscillation; When -0.995 < When ≤-0.5, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations, but h The first harmonic is dominant; When -0.5 < When <0.5, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations. h First harmonic and h The second harmonics are nearly identical; When 0.5≤ When <0.995, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations, but h The second harmonic is dominant; When 0.995≤ When ≤1, by h Second harmonic aliasing causes pseudo-oscillations; The aliasing harmonic value is estimated by the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval.

2. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 1, characterized in that: The search for effective maxima and minima of the impedance deviation coefficient includes: Search for points where the impedance deviation coefficient is greater than the left and right adjacent impedance deviation coefficients to obtain the maximum value of the impedance deviation coefficient. ; At adjacent impedance deviation coefficient maxima and Maximum value of adjacent impedance deviation coefficient and Between these points, search for points where the impedance deviation coefficient is less than the left and right adjacent impedance deviation coefficients to obtain the minimum value of the adjacent impedance deviation coefficients. and ; Based on the minimum value of the adjacent impedance deviation coefficient and The relationship is used to determine the effective maximum and minimum values ​​of the impedance deviation coefficient.

3. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 1, characterized in that: Analysis interval time difference The process of determining is as follows: When the impedance deviation coefficient is at its minimum value ≤1 and the impedance deviation coefficient is at its minimum value When ≤1, the impedance deviation coefficient is at its minimum value. This represents the effective minimum value of the analysis interval, and the effective maximum value of the adjacent impedance deviation coefficient is... and This yields the start and end points of the analysis interval, the th... i Time difference between analysis intervals for: When the impedance deviation coefficient is at its minimum value >1 and the impedance deviation coefficient is at its minimum value When ≤1, or the impedance deviation coefficient is at its minimum value. ≤1 and the impedance deviation coefficient is at its minimum value When the value is greater than 1, the minimum value of the impedance deviation coefficient less than 1 is the effective minimum value of the analysis interval, and the effective maximum value of the adjacent impedance deviation coefficient is... and This yields the start and end points of the analysis interval, the th... i Time difference between analysis intervals for: in, The power system frequency. , , The first , , The number of cycles corresponding to the maximum value of the impedance deviation coefficient , The first , The number of cycles corresponding to the minimum value of the impedance deviation coefficient. i =1, 2, 3, ...

4. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 1, characterized in that: The correlation analysis of the fundamental components of capacitor branch voltage and current within each analysis interval includes: According to the number of periods corresponding to the effective maximum at the beginning of each analysis interval. The number of cycles preceding the effective maximum at the end The fundamental components of the capacitor branch voltage and current are selected to form a voltage dataset U. i Current Dataset I i : in, For the first The number of fundamental voltage or current component data within each analysis interval; Calculate the voltage dataset U within each analysis interval i and current dataset I i The Spearman correlation coefficient between them.

5. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 1, characterized in that: The estimation of aliasing harmonic values ​​based on the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval includes: When Spearman correlation coefficient Satisfy -1≤ When ≤-0.995, Subharmonic voltage content for: When Spearman correlation coefficient Satisfies -0.995 < When ≤-0.5, Subharmonic voltage content and Subharmonic voltage content The sum is: When Spearman correlation coefficient Satisfy -0.5 < When <0.5, Subharmonic voltage content , Subharmonic voltage content for: When Spearman correlation coefficient Satisfying 0.5≤ When <0.995, Subharmonic voltage content and Subharmonic voltage content The sum is: When Spearman correlation coefficient Satisfying 0.995≤ When ≤1, Subharmonic voltage content for: in, For the first i The effective minimum value of the impedance deviation coefficient within each analysis interval.

6. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 1, characterized in that: Before analyzing the correlation of the fundamental components of capacitor branch voltage and current within each analysis interval, the following steps are also included: Based on the oscillation frequency of each analysis interval, the threshold values ​​for the maximum and minimum values ​​of the impedance deviation coefficient are calculated respectively, under the conditions of unknown and known fundamental frequency of the power grid. Search for all effective maxima and minima of impedance deviation coefficients. If all effective maxima of impedance deviation coefficients are greater than the maximum threshold and all effective minima are less than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a pseudo oscillation. If all effective maxima of impedance deviation coefficients are less than the maximum threshold and all effective minima are greater than the minimum threshold, the oscillation measured by the measurement and control device is determined to be a true oscillation.

7. The method for estimating aliased harmonic values ​​in a low sampling rate measurement and control device according to claim 6, characterized in that: Based on the oscillation frequency of each analysis interval, the process of calculating the maximum and minimum threshold values ​​of the impedance deviation coefficient, under the conditions of unknown and known fundamental frequency of the power grid, includes: When analyzing the fundamental frequency of the power grid within the interval When the value is unknown, the threshold value of the maximum value of the impedance deviation coefficient. Minimum threshold They are respectively: When analyzing the fundamental frequency of the power grid within the interval Known and relative to the power system frequency When the deviation is positive, the threshold value of the maximum value of the impedance deviation coefficient Minimum threshold They are respectively: When analyzing the fundamental frequency of the power grid within the interval Known and relative to the power system frequency When the deviation is negative, the threshold value of the maximum value of the impedance deviation coefficient is... Minimum threshold They are respectively: in, For the fundamental frequency deviation of the power grid, The oscillation frequency is... α To comprehensively consider the leakage of the full-wave Fourier algorithm and the margin factor calculated from the actual capacitance.

8. A system for estimating aliased harmonic values ​​in a low sampling rate measurement and control device, characterized in that: The system includes: The correlation analysis module is used to search for the effective maxima and minima of the impedance deviation coefficient. It uses adjacent effective maxima as the analysis interval to analyze the correlation between the fundamental components of the capacitor branch voltage and current within each analysis interval. The calculation process for the impedance deviation coefficient is as follows: The full-wave Fourier algorithm is used to calculate the discrete data of voltage and current waveforms of the capacitor branch with oscillations measured by the measurement and control device cycle by cycle, so as to obtain the fundamental components of voltage and current in each cycle. The fundamental impedance value of the capacitor for each cycle is obtained by calculating the ratio of the fundamental components of voltage and current in each cycle. The impedance deviation coefficient for each cycle is obtained by calculating the ratio of the fundamental impedance value of the capacitor to the actual impedance value of the capacitor. The aliasing harmonic estimation module is used to determine the components of aliasing harmonics within the analysis interval based on the sampling frequency of the measurement and control device and the correlation analysis results, and to estimate the aliasing harmonic value using the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval; wherein, based on the sampling frequency of the measurement and control device... With power system power frequency The ratio of these values ​​determines the harmonic frequencies that can alias to the fundamental frequency and cause pseudo-oscillations. , : Based on the Spearman correlation coefficient between the voltage and current datasets within the analysis interval The magnitude distribution level is used to determine the aliased harmonic components that cause spurious oscillations: When -1≤ When ≤-0.995, by h First harmonic aliasing causes pseudo-oscillation; When -0.995 < When ≤-0.5, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations, but h The first harmonic is dominant; When -0.5 < When <0.5, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations. h First harmonic and h The second harmonics are nearly identical; When 0.5≤ When <0.995, by h 1 and h The superposition of the two harmonics causes pseudo-oscillations, but h The second harmonic is dominant; When 0.995≤ When ≤1, by h The superposition of second harmonics causes pseudo-oscillations.

9. The aliasing harmonic value estimation system for a low sampling rate measurement and control device according to claim 8, characterized in that: The search for effective maxima and minima of the impedance deviation coefficient includes: Search for points where the impedance deviation coefficient is greater than the left and right adjacent impedance deviation coefficients to obtain the maximum value of the impedance deviation coefficient. ; At adjacent impedance deviation coefficient maxima and Maximum value of adjacent impedance deviation coefficient and Between these points, search for points where the impedance deviation coefficient is less than the left and right adjacent impedance deviation coefficients to obtain the minimum value of the adjacent impedance deviation coefficients. and ; Based on the minimum value of the adjacent impedance deviation coefficient and The relationship is used to determine the effective maximum and minimum values ​​of the impedance deviation coefficient.

10. The aliasing harmonic value estimation system for a low sampling rate measurement and control device according to claim 8, characterized in that: The estimation of aliasing harmonic values ​​based on the effective minimum value of the impedance deviation coefficient within the corresponding analysis interval includes: When Spearman correlation coefficient Satisfy -1≤ When ≤-0.995, Subharmonic voltage content for: When Spearman correlation coefficient Satisfies -0.995 < When ≤-0.5, Subharmonic voltage content and Subharmonic voltage content The sum is: When Spearman correlation coefficient Satisfy -0.5 < When <0.5, Subharmonic voltage content , Subharmonic voltage content for: When Spearman correlation coefficient Satisfying 0.5≤ When <0.995, Subharmonic voltage content and Subharmonic voltage content The sum is: When Spearman correlation coefficient Satisfying 0.995≤ When ≤1, Subharmonic voltage content for: in, For the first i The effective minimum value of the impedance deviation coefficient within each analysis interval.

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