Fast grid frequency estimation method

Abstract

The application discloses a power grid frequency rapid estimation method, and steps include: selecting first zero-crossing time and second zero-crossing time nearby continuous sampling points from sampling data by continuous incremental sampling point method, obtaining floating point number value corresponding to the first zero-crossing time and the second zero-crossing time based on two groups of nearby continuous sampling points, and finally calculating the estimation value of the power grid frequency according to the floating point number value corresponding to the first zero-crossing time and the second zero-crossing time. The application selects two groups of nearby continuous sampling points by the continuous incremental sampling point method, filters the sampling points near the zero-crossing time according to the principle of monotone increasing during selection, reduces the influence of harmonics on the estimation result, and can obtain a result closer to the theoretical zero-crossing time based on fitting of the selected sampling points, so that the frequency estimation can be completed only by one cycle of data, the estimation time is significantly shortened, and the estimation accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of electrical variable data measurement, specifically designing a method for estimating power grid frequency. Background Technology

[0002] The grid frequency is one of the important parameters for electricity meter measurement. When the electricity meter is working, it needs to quickly estimate the grid frequency based on the sampled data.

[0003] Current technologies primarily employ the zero-crossing method to estimate power grid frequency. The working principle of the zero-crossing method is as follows: when the voltage signal changes from a negative value to a non-negative value, this moment is recorded as a zero-crossing point. Since the voltage signal is a sinusoidal signal, theoretically there is only one zero-crossing point per cycle. Therefore, by counting the number of zero-crossing points over a certain period and then calculating the average value, the power meter can obtain an estimated value of the power grid frequency.

[0004] Due to the presence of harmonic interference, it is necessary to collect as many periodic data points as possible during calculation. By averaging, the impact of harmonic interference can be reduced, resulting in more accurate results. For example, at a sampling frequency of 6.4 kHz, to achieve a resolution of 0.001 Hz, the electricity meter needs to collect zero-crossing points for 100 cycles. For a 50 Hz power grid frequency, it would take approximately 2 seconds to obtain an estimate, which is too long and cannot meet the requirements for timeliness. Summary of the Invention

[0005] This invention proposes a fast method for estimating power grid frequency, the purpose of which is to solve the problem that it takes too long to calculate the estimated power grid frequency.

[0006] The technical solution of this invention is as follows:

[0007] A method for fast estimation of power grid frequency, comprising the following steps:

[0008] Step 1: Use the continuously increasing sampling method to select consecutive sampling points near the first zero-crossing moment from the sampled data;

[0009] Step 2: Set the number of any sampling point in the continuous sampling points near the first zero crossing time to 0, and assign integer number values ​​to the continuous sampling points near the first zero crossing time and subsequent sampling points according to the principle of increasing in the sampling order.

[0010] Step 3: Use the continuously increasing sampling method to select consecutive sampling points near the second zero-crossing time from the sampled data;

[0011] Step 4: Fit the data based on the continuous sampling points near the first zero-crossing moment to obtain the floating-point number value corresponding to the first zero-crossing moment; and fit the data based on the continuous sampling points near the second zero-crossing moment to obtain the floating-point number value corresponding to the second zero-crossing moment.

[0012] Step 5: Calculate the estimated value of the power grid frequency based on the floating-point number values ​​corresponding to the first and second zero-crossing moments.

[0013] As a further improvement to the aforementioned fast power grid frequency estimation method, the continuously increasing point selection method refers to:

[0014] Step A1: First, find the sampling points before and after the zero-crossing that simultaneously satisfy the following conditions from the sampled data:

[0015] Condition a1: The sampled value of the sampling point before zero crossing is less than 0;

[0016] Condition a2: The sampled value of the sampling point after zero crossing is greater than or equal to 0.

[0017] Condition a3: The sampling points before and after the zero-crossing are continuous sampling points;

[0018] Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions:

[0019] Condition b1: The four sampling points include the sampling points before and after the zero-crossing mentioned above;

[0020] Condition b2: The sampled values ​​of the four sampling points are monotonically increasing;

[0021] The four selected sampling points were used as nearby continuous sampling points.

[0022] As a further improvement to the aforementioned fast power grid frequency estimation method, the specific process of step A2 is as follows:

[0023] Step A2-1: Select the sampling points before and after the zero-crossing;

[0024] Step A2-2: Determine whether the sampled value of the next sampled point after the zero-crossing is greater than the sampled value of the next sampled point after the zero-crossing. If the condition is met, select the next sampled point.

[0025] Step A2-3: Determine whether the sampled value of the sampling point before the zero-crossing sampling point is less than the sampled value of the sampling point before the zero-crossing sampling point. If the condition is met, select the previous sampling point.

[0026] Step A2-4: Process the data according to the currently selected sampling points:

[0027] Case 1: If 4 sampling points have already been selected, then the selection is complete;

[0028] Case 2: If the number of currently selected sampling points is 2, then discard the current sampling points before and after the zero crossing, and return to step A1 to select the next set of sampling points before and after the zero crossing that meet the conditions.

[0029] Case 3: If the number of currently selected sampling points is 3 and includes the sampling point before the zero-crossing sampling point, then continue to determine whether the sampling value of the second sampling point before the zero-crossing sampling point is less than the sampling value of the sampling point before the zero-crossing sampling point: if it is satisfied, then select the second sampling point before the zero-crossing sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-crossing sampling point and zero-crossing sampling point, and return to step A1 to select the next set of zero-crossing sampling points and zero-crossing sampling points that meet the conditions.

[0030] Case 4: If the number of currently selected sampling points is 3 and includes the sampling point after the zero-crossing sampling point, then continue to determine whether the sampling value of the second sampling point after the zero-crossing sampling point is greater than the sampling value of the sampling point after the zero-crossing sampling point: if it is satisfied, then select the second sampling point after the zero-crossing sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then abandon the current sampling point before the zero-crossing and sampling point after the zero-crossing, and return to step A1 to select the next set of sampling points before the zero-crossing and sampling points after the zero-crossing that meet the conditions.

[0031] As a further improvement to the fast power grid frequency estimation method, after selecting the continuous sampling points near the second zero-crossing time in step 3, the validity of the continuous sampling points near the second zero-crossing time must be judged: if it is determined to be valid, then step 4 is executed; otherwise, the currently selected continuous sampling points near the second zero-crossing time are abandoned, and subsequent sampling data is read and a new continuous sampling point near the second zero-crossing time is selected.

[0032] As a further improvement to the fast power grid frequency estimation method, the method for determining the validity of the continuous sampling points near the second zero-crossing time in step 3 is as follows: Let n be the difference between the index value of the sampling point before the zero-crossing in the continuous sampling points near the second zero-crossing time and the index value of the sampling point before the zero-crossing in the continuous sampling points near the first zero-crossing time, and let f be the current theoretical value of the power grid frequency. m The sampling frequency is f s Then the theoretical number of sampling points per cycle is C. s =f s / f m If 0.9C s ≤n≤1.1C s Then the continuous sampling points near the second zero crossing time are considered valid.

[0033] As a further improvement to the aforementioned fast power grid frequency estimation method, the specific steps in step 4 for fitting and solving the corresponding floating-point number values ​​based on nearby continuous sampling points are as follows:

[0034] Step C1: Construct a polynomial, which is a first-order polynomial or a second-order polynomial;

[0035] Step C2: Take the number values ​​of each sampling point in the preceding and following associated sampling points as the independent variable of the polynomial, and take the sampling values ​​of each sampling point in the nearby continuous sampling points as the dependent variable, substitute them into the polynomial, and then use the least squares method to obtain the design matrix A of the polynomial.

[0036] Step C3: Obtain the polynomial after solving the design matrix A, and then find the value of the independent variable when the polynomial equals 0. The value of the independent variable is the floating-point number value corresponding to the continuous sampling points in the vicinity of the group.

[0037] As a further improvement to the aforementioned fast power grid frequency estimation method, the specific calculation method for the estimated power grid frequency in step 5 is as follows:

[0038] Let the floating-point number at the first zero-crossing moment be x. 0_1 The floating-point number corresponding to the second zero-crossing moment is x. 0_2 The estimated value of the power grid frequency f m_e =f s / (x 0_2 -x 0_1 ), where f s The sampling frequency.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. This invention uses a continuously increasing sampling method to select two sets of nearby continuous sampling points. When selecting, the sampling points near the zero-crossing time are screened according to the principle of monotonically increasing, which reduces the influence of harmonics on the estimation results. Based on the selected sampling points, fitting can obtain results that are closer to the theoretical zero-crossing time. Thus, only one cycle of data is needed to complete the frequency estimation, which significantly shortens the estimation time and improves the estimation accuracy.

[0041] 2. The present invention further determines whether two sets of nearby continuous sampling points are located near the beginning and end of a cycle, eliminating erroneous continuous sampling points introduced by harmonic interference, and ensuring that a more accurate estimation result can be obtained based on the sampling data of a single cycle.

[0042] 3. This invention is based on the least squares method for fitting, which has the advantages of high computational efficiency and high fitting accuracy. Detailed Implementation

[0043] The technical solution of the present invention is described in detail below:

[0044] Example 1

[0045] A method for fast estimation of power grid frequency, comprising the following steps:

[0046] Step 1: Use the continuously increasing sampling method to select the continuous sampling points near the first zero crossing moment from the sampled data.

[0047] Step 2: Set the number of any sampling point in the continuous sampling points near the first zero crossing time to 0, and assign integer number values ​​to the continuous sampling points near the first zero crossing time and subsequent sampling points according to the principle of increasing in the sampling order.

[0048] Specifically, the continuously increasing point selection method refers to:

[0049] Step A1: First, find the sampling points before and after the zero-crossing that simultaneously satisfy the following conditions from the sampled data:

[0050] Condition a1: The sampled value of the sampling point before zero crossing is less than 0;

[0051] Condition a2: The sampled value of the sampling point after zero crossing is greater than or equal to 0.

[0052] Condition a3: The sampling points before and after the zero crossing are continuous sampling points.

[0053] Generally, if the number of the sampling point before the first zero crossing is set to 0, then the number of the sampling point after the zero crossing is 1, the number of the sampling point before the zero crossing is -1, and so on.

[0054] Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions:

[0055] Condition b1: The four sampling points include the sampling points before and after the zero-crossing mentioned above;

[0056] Condition b2: The sampled values ​​of the four sampling points are monotonically increasing.

[0057] Specifically, first select the sampling point before and after the zero-crossing (both sampling points must be included). Then, determine whether the sample value of the next sampling point after the zero-crossing (numbered 2) is greater than the sample value of the sampling point after the zero-crossing (numbered 1). If so, select the next sampling point (numbered 2). Then, determine whether the sample value of the previous sampling point before the zero-crossing (numbered -1) is less than the sample value of the sampling point before the zero-crossing (numbered 0). If so, select the previous sampling point (numbered -1).

[0058] At this point, the following cases are handled based on the currently selected sampling points:

[0059] Case 1: If four sampling points have already been selected, namely the four sampling points with the numbers -1, 0, 1, and 2, then the selection is complete.

[0060] Case 2: If the number of currently selected sampling points is 2, that is, there are only 2 sampling points with the numbers 0 and 1, it means that the principle of monotonically increasing is not satisfied on both sides. Therefore, the current sampling points before and after the zero crossing are abandoned, and the process returns to step A1 to select the next set of sampling points before and after the zero crossing that meet the conditions.

[0061] Case 3: If the currently selected number of sampling points is 3 and includes the sampling point before the zero-crossing sampling point (numbered -1), then continue to determine whether the sampling value of the second sampling point before the zero-crossing sampling point (numbered -2) is less than the sampling value of the sampling point before the zero-crossing sampling point: If it is satisfied, then select the second sampling point before the zero-crossing sampling point, completing the selection of 4 sampling points. At this time, the selected 4 sampling points are numbered -2, -1, 0, and 1; if it is not satisfied, it means that it is impossible to find 4 continuously monotonically increasing sampling points. Therefore, abandon the current zero-crossing sampling point and zero-crossing sampling point, and return to step A1 to select the next set of zero-crossing sampling points and zero-crossing sampling points that meet the conditions.

[0062] Case 4: If the currently selected number of sampling points is 3 and includes the sampling point after the zero-crossing sampling point (number 2), then continue to determine whether the sampling value of the second sampling point after the zero-crossing sampling point (number 3) is greater than the sampling value of the sampling point after the zero-crossing sampling point: if it is satisfied, then select the second sampling point after the zero-crossing sampling point, completing the selection of 4 sampling points. At this time, the 4 sampling points with numbers 0, 1, 2, and 3 are selected; if it is not satisfied, then discard the current sampling points before and after the zero-crossing sampling points, and return to step A1 to select the next set of sampling points before and after the zero-crossing sampling points that meet the conditions.

[0063] The four selected sampling points were used as nearby continuous sampling points.

[0064] Voltage signals in the power grid have certain unique characteristics, specifically that the amplitude of the power frequency voltage signal is much larger than that of harmonics. Generally, the harmonic amplitude is less than 10% of the power frequency signal amplitude, and in China, it is typically less than 5%. Therefore, even if harmonics affect the zero-crossing point, the monotonically increasing voltage characteristics on both sides of the zero-crossing point will not be affected simultaneously. Thus, even considering the requirements of monotonically increasing voltage and continuous sampling, it is possible to find suitable "nearby continuous sampling points" at the beginning and end of each cycle.

[0065] The found nearby consecutive sampling points are placed in the buffer. The number values ​​of the 4 sampling points are arranged in one of the following three cases: -2, -1, 0, 1, or -1, 0, 1, 2, or 0, 1, 2, 3.

[0066] Step 3: Use the continuously increasing sampling method to select consecutive sampling points near the second zero-crossing time from the sampled data. The selection process can be referred to in Step 1 and will not be repeated here.

[0067] Similarly, if the number of the sampling points before the zero crossing in the continuous sampling points near the second zero crossing time is n, then the number values ​​of the four sampling points in the continuous sampling points near the second zero crossing time can be arranged in one of the following three cases: n-2, n-1, n, n+1, or n-1, n, n+1, n+2, or n, n+1, n+2, n+3.

[0068] Furthermore, the validity of the continuous sampling points near the second zero-crossing moment needs to be determined: if it is determined to be valid, then step 4 is executed. Otherwise, the currently selected continuous sampling points near the second zero-crossing moment are discarded, and subsequent sampling data is read and a new continuous sampling point near the second zero-crossing moment is selected.

[0069] Specifically, the difference between the index value of the sampling point before the zero crossing in the continuous sampling points near the second zero crossing and the index value of the sampling point before the zero crossing in the continuous sampling points near the first zero crossing is n, and the theoretical value of the current power grid frequency is f. m The sampling frequency is f s Then the theoretical number of sampling points per cycle is C. s =f s / f m If 0.9C s ≤n≤1.1C s Then the continuous sampling points near the second zero crossing time are considered valid.

[0070] Step 4: Fit the data based on the continuous sampling points near the first zero-crossing moment to obtain the floating-point number value corresponding to the first zero-crossing moment; and fit the data based on the continuous sampling points near the second zero-crossing moment to obtain the floating-point number value corresponding to the second zero-crossing moment.

[0071] For either the first or second zero-crossing moment, the specific steps for fitting and solving the corresponding floating-point number value based on nearby continuous sampling points are the same:

[0072] Step B1: Construct a first-order polynomial and a second-order polynomial.

[0073] Step B2: For the first-order polynomial and the second-order polynomial, take the number value of each sampling point in the nearby continuous sampling points as the independent variable of the polynomial and the sampling value of each sampling point in the nearby continuous sampling points as the dependent variable, substitute them into the corresponding polynomial, and then use the least squares method to obtain the design matrices A1 and A2 of the first-order polynomial and the second-order polynomial respectively.

[0074] Suppose that the first-order polynomial constructed when solving for the floating-point number corresponding to the first zero-crossing time is f1(x) = a 1_1 +a 1_2 Let x be the numbering values ​​of the four selected sampling points, which are -2, -1, 0, and 1, respectively, and the corresponding sampling values ​​are S. -2 S -1 Given S0 and S1, we have:

[0075]

[0076] This can be represented by a matrix as follows:

[0077] XA1 = S;

[0078]

[0079] The solution is A1 = (X T X) -1 (X T S).

[0080] Similarly, if it is a quadratic polynomial f2(x) = a 2_1 +a 2_2 x+a 2_3 x 2 ,but Solution results

[0081] Because solutions to first-order and second-order polynomials are relatively easy to obtain, and in actual power grid frequency calculations, solutions to first-order and second-order polynomials are already accurate enough, polynomials of degree higher are rarely used.

[0082] Step B3: Based on the results of solving design matrices A1 and A2, obtain the solved first-order polynomial f1(x) and second-order polynomial f2(x), and then calculate the value of the independent variable x corresponding to f1(x) = 0: x1 = -a 1_1 / a 1_2 The value of the independent variable x corresponding to f2(x) = 0

[0083] Step B4: Compare the derivative f′1(x1) of the linear polynomial at x1 and the derivative f′2(x2) of the quadratic polynomial at x2. If f′1(x1) > f′2(x2), then x1 is used as the floating-point number corresponding to the nearest consecutive sampling point in this group; otherwise, x2 is used as the floating-point number corresponding to the nearest consecutive sampling point in this group. Obviously, the floating-point number here is not necessarily an integer.

[0084] In this step, taking advantage of the fact that the derivative value of the sinusoidal signal is the largest at the zero point, the optimal selection of the results of different fitting methods is further made based on the two polynomial fitting methods, which significantly improves the estimation accuracy of the zero crossing point.

[0085] Step 5: Calculate the estimated value of the power grid frequency based on the floating-point numbers corresponding to the first and second zero-crossing moments. The specific calculation method is as follows:

[0086] Let the floating-point number at the first zero-crossing moment be x. 0_1 The floating-point number corresponding to the second zero-crossing moment is x. 0_2 The estimated value of the power grid frequency f m_e =f s / (x 0_2 -x 0_1 ), where f s The sampling frequency.

[0087] Considering that the actual power grid frequency may fluctuate slightly, and that a power grid fault can cause significant fluctuations between two adjacent cycles, numerical stability can be enhanced by appropriately increasing the sliding window averaging or adding a hysteresis interval. These two techniques are common and will not be elaborated upon here.

[0088] Actual testing showed that when the sampling frequency is 6.4 kHz and the theoretical power grid frequency is 50 Hz, this method, using a 3-cycle sliding window, can achieve a power grid frequency estimation accuracy of 0.005 Hz.

[0089] Example 2

[0090] The difference between this embodiment and Embodiment 1 is that the specific method for fitting and solving the corresponding floating-point number value based on nearby continuous sampling points in step 4 is different:

[0091] Step C1: Construct a polynomial, which is a first-order polynomial or a second-order polynomial.

[0092] Step C2: Take the index values ​​of each sampling point in the preceding and following associated sampling points as the independent variable of the polynomial, and the sampling values ​​of each sampling point in the nearby continuous sampling points as the dependent variable, substitute them into the polynomial, and then use the least squares method to obtain the design matrix A of the polynomial. The solution process can be found in Example 1.

[0093] Step C3: Obtain the polynomial after solving the design matrix A, and then find the value of the independent variable when the polynomial equals 0. The value of the independent variable is the floating-point number value corresponding to the continuous sampling points in the vicinity of the group.

[0094] The calculation steps in this embodiment are simpler and faster, but the accuracy is slightly inferior to that of Embodiment 1.

Claims

1. A method for fast estimation of power grid frequency, characterized by the following steps: include: Step 1: Use the continuously increasing sampling method to select consecutive sampling points near the first zero-crossing moment from the sampled data; The continuously increasing point selection method refers to: Step A1: First, find the sampling points before and after the zero-crossing that simultaneously satisfy the following conditions from the sampled data: Condition a1: The sampled value of the sampling point before zero crossing is less than 0; Condition a2: The sampled value of the sampling point after zero crossing is greater than or equal to 0. Condition a3: The sampling points before and after the zero-crossing are continuous sampling points; Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions: Condition b1: The four sampling points include the sampling points before and after the zero-crossing mentioned above; Condition b2: The sampled values ​​of the four sampling points are monotonically increasing; The four selected sampling points were used as nearby consecutive sampling points; Step 2: Set the number of any sampling point in the continuous sampling points near the first zero crossing time to 0, and assign integer number values ​​to the continuous sampling points near the first zero crossing time and subsequent sampling points according to the principle of increasing in the sampling order. Step 3: Use the continuously increasing sampling method to select consecutive sampling points near the second zero-crossing time from the sampled data; After selecting the continuous sampling points near the second zero-crossing time in step 3, the validity of the continuous sampling points near the second zero-crossing time must be judged: if it is determined to be valid, then proceed to step 4; otherwise, discard the currently selected continuous sampling points near the second zero-crossing time, continue to read subsequent sampling data, and reselect the continuous sampling points near the second zero-crossing time. The method for determining the validity of consecutive sampling points near the second zero-crossing time is as follows: Let the difference between the index value of the sampling point before the zero-crossing in the consecutive sampling points near the second zero-crossing time and the index value of the sampling point before the zero-crossing in the consecutive sampling points near the first zero-crossing time be... The current theoretical value of the power grid frequency is The sampling frequency is The theoretical number of sampling points per period is: ;if Then the consecutive sampling points near the second zero-crossing time are considered valid; Step 4: Fit the data based on the continuous sampling points near the first zero-crossing moment to obtain the floating-point number value corresponding to the first zero-crossing moment; and fit the data based on the continuous sampling points near the second zero-crossing moment to obtain the floating-point number value corresponding to the second zero-crossing moment. The specific steps for fitting and solving the corresponding floating-point number value based on nearby continuous sampling points are as follows: Construct linear and quadratic polynomials; For a first-order polynomial and a second-order polynomial, the number values ​​of each sampling point in the nearby continuous sampling points are taken as the independent variable of the polynomial, and the sampling values ​​of each sampling point in the nearby continuous sampling points are taken as the dependent variable. These are substituted into the corresponding polynomial, and then the design matrix of the first-order polynomial and the second-order polynomial are obtained by using the least squares method. Based on the solution of the design matrix, the first-order and second-order polynomials are obtained. Then, the values ​​of the independent variables corresponding to the first-order polynomial being equal to 0 are calculated. The value of the independent variable when the quadratic polynomial equals 0 ; Compare a linear polynomial in The derivative and the quadratic polynomial at point The magnitude of the derivative at a given point is used to select the value of the independent variable corresponding to the larger derivative as the floating-point number value corresponding to the continuous sampling points in the vicinity of that group. Step 5: Calculate the estimated value of the power grid frequency based on the floating-point numbers corresponding to the first and second zero-crossing moments. The specific calculation method is as follows: Let the floating-point number at the first zero-crossing moment be denoted as . The floating-point number corresponding to the second zero-crossing moment is _____. Estimated value of power grid frequency ,in The sampling frequency.

2. The method for fast estimation of power grid frequency as described in claim 1, characterized in that, The specific process of step A2 is as follows: Step A2-1: Select the sampling points before and after the zero-crossing; Step A2-2: Determine whether the sampled value of the next sampled point after the zero-crossing is greater than the sampled value of the next sampled point after the zero-crossing. If the condition is met, select the next sampled point. Step A2-3: Determine whether the sampled value of the sampling point before the zero-crossing sampling point is less than the sampled value of the sampling point before the zero-crossing sampling point. If the condition is met, select the previous sampling point. Step A2-4: Process the data according to the currently selected sampling points: Case 1: If 4 sampling points have already been selected, then the selection is complete; Case 2: If the number of currently selected sampling points is 2, then discard the current sampling points before and after the zero crossing, and return to step A1 to select the next set of sampling points before and after the zero crossing that meet the conditions. Case 3: If the number of currently selected sampling points is 3 and includes the sampling point before the zero-crossing sampling point, then continue to determine whether the sampling value of the second sampling point before the zero-crossing sampling point is less than the sampling value of the sampling point before the zero-crossing sampling point: if it is satisfied, then select the second sampling point before the zero-crossing sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-crossing sampling point and zero-crossing sampling point, and return to step A1 to select the next set of zero-crossing sampling points and zero-crossing sampling points that meet the conditions. Case 4: If the number of currently selected sampling points is 3 and includes the sampling point after the zero-crossing sampling point, then continue to determine whether the sampling value of the second sampling point after the zero-crossing sampling point is greater than the sampling value of the sampling point after the zero-crossing sampling point: if it is satisfied, then select the second sampling point after the zero-crossing sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then abandon the current sampling point before the zero-crossing and sampling point after the zero-crossing, and return to step A1 to select the next set of sampling points before the zero-crossing and sampling points after the zero-crossing that meet the conditions.

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