Accurate estimation method for power grid frequency

Abstract

This invention discloses a method for accurate estimation of power grid frequency. The steps include: selecting consecutive sampling points from the sampled data based on the monotonically increasing principle to correspond to the first and second zero-crossing moments; obtaining the fitting index values ​​corresponding to the first and second zero-crossing moments based on the two sets of consecutive sampling points; and finally calculating the estimated power grid frequency based on the fitting index values ​​corresponding to the first and second zero-crossing moments. This invention reduces the influence of harmonics on the estimation results, not only improving the accuracy of the estimation but also requiring only one cycle of data to complete the frequency estimation, significantly shortening the estimation time. Furthermore, this invention utilizes the characteristic that the derivative value is largest at the zero point of a sinusoidal signal, and further optimizes the results of different fitting methods based on polynomial fitting, further improving the estimation accuracy of the zero-crossing point.

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] Grid frequency is a crucial parameter in modern electricity metering technology. It has wide applications in power quality estimation, dynamic adjustment of sampling rates, and calculation of energy integration intervals, and is of great significance for the accurate measurement of electricity. Therefore, engineering projects require the rapid and accurate estimation of grid frequency based on sampled signals.

[0003] In engineering implementation, zero-crossing estimation is a commonly used method for estimating power grid frequency. The principle of this 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 within a certain time period, the estimated value of the power grid frequency can be calculated.

[0004] However, current zero-crossing estimation methods suffer from susceptibility to harmonic interference and relatively poor accuracy. When harmonics are present in the voltage signal, the zero-crossing values ​​may fluctuate, resulting in multiple zero-crossings within a single cycle. These erroneous zero-crossings severely impact the accuracy of the frequency estimate. Furthermore, the time value of each zero-crossing is obtained by fitting the sampled points, but existing fitting methods are relatively simplistic, and the resulting fittings often fail to provide accurate zero-crossing time values.

[0005] On the other hand, since the estimation error of the zero-crossing point is one sampling point, multiple consecutive zero-crossing point estimations are required to obtain a more accurate frequency estimate. Generally, in order to achieve the required resolution, sampling of tens or even hundreds of cycles is usually required, with the sampling time alone exceeding one second. The estimation time is too long and cannot meet the real-time requirements. Summary of the Invention

[0006] This invention proposes a method for accurate estimation of power grid frequency, the purpose of which is to: 1. solve the problem of poor accuracy in power grid frequency estimation; 2. solve the problem of excessively long estimation time.

[0007] The technical solution of this invention is as follows:

[0008] A method for accurate estimation of power grid frequency, comprising the following steps:

[0009] Step 1: Use the continuous sampling method based on the monotonically increasing principle to select the associated sampling points before and after the first zero crossing time from the sampled data, and set the index value of any sampling point in the associated sampling points before and after the first zero crossing time to 0. Integer index values ​​are assigned to the associated sampling points before and after the first zero crossing time and subsequent sampling points according to the principle of increasing with the sampling order.

[0010] Step 2: Use the continuous sampling method based on the monotonically increasing principle to select the associated sampling points before and after the second zero-crossing time from the sampled data;

[0011] Step 3: Determine the validity of the associated sampling points before and after the second zero-crossing moment: If it is determined to be valid, proceed to step 4; otherwise, abandon the currently selected associated sampling points before and after the second zero-crossing moment, and return to step 2 to continue selecting associated sampling points before and after the second zero-crossing moment.

[0012] Step 4: Fit the data based on the associated sampling points before and after the first zero-crossing moment to obtain the fitting index value corresponding to the first zero-crossing moment; and fit the data based on the associated sampling points before and after the second zero-crossing moment to obtain the fitting index value corresponding to the second zero-crossing moment.

[0013] Step 5: Calculate the estimated value of the power grid frequency based on the fitted index values ​​corresponding to the first and second zero-crossing moments.

[0014] As a further improvement to the aforementioned method for accurate estimation of power grid frequency, the continuous point-taking method based on the monotonically increasing principle refers to:

[0015] Step A1: First, find the zero-preceding sampling point and the zero-postceding sampling point from the sampled data that simultaneously meet the following conditions: the sampled value of the zero-preceding sampling point is less than 0, the sampled value of the zero-postceding sampling point is greater than or equal to 0, and the zero-preceding sampling point and the zero-postceding sampling point are consecutive sampling points.

[0016] Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions: the four sampling points include the zero-before sampling points and the zero-after sampling points mentioned above, and the sampled values ​​of the four sampling points are monotonically increasing.

[0017] The four selected sampling points were used as the associated sampling points.

[0018] As a further improvement to the aforementioned accurate power grid frequency estimation method, the specific process of step A2 is as follows: First, select the zero-preceding sampling point and the zero-after sampling point, then determine whether the sample value of the next sampling point of the zero-after sampling point is greater than the sample value of the zero-after sampling point. If the condition is met, select the next sampling point; then determine whether the sample value of the previous sampling point of the zero-preceding sampling point is less than the sample value of the zero-preceding sampling point. If the condition is met, select the previous sampling point.

[0019] If four sampling points have already been selected, the selection is complete.

[0020] If the number of currently selected sampling points is 2, discard the current zero-before sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-before sampling points and zero-after sampling points that meet the conditions;

[0021] If the current number of selected sampling points is 3 and includes the sampling point before the zero-preceding sampling point, then continue to determine whether the sampling value of the second sampling point before the zero-preceding sampling point is less than the sampling value of the sampling point before the zero-preceding sampling point: if it is satisfied, then select the second sampling point before the zero-preceding sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-preceding sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-preceding sampling points and zero-after sampling points that meet the conditions;

[0022] If the current number of selected sampling points is 3 and includes the sampling point after the zero-after sampling point, then continue to determine whether the sampling value of the second sampling point after the zero-after sampling point is greater than the sampling value of the sampling point after the zero-after sampling point: if it is satisfied, then select the second sampling point after the zero-after sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-before sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-before sampling points and zero-after sampling points that meet the conditions.

[0023] As a further improvement to the aforementioned accurate power grid frequency estimation method, the method for determining the validity of the associated sampling points before and after the second zero-crossing moment in step 3 is as follows: Let the difference between the index value of the zero-preceding sampling point in the associated sampling points before and after the second zero-crossing moment and the index value of the zero-preceding sampling point in the associated sampling points before and after the first zero-crossing moment be n, and the current theoretical power grid frequency value be f. m The sampling frequency is f s Then the theoretical number of sampling points per period is C. s =f s / f m If 0.9C s ≤n≤1.1C s Then the sampling points before and after the second zero-crossing moment are considered valid.

[0024] As a further improvement to the aforementioned accurate power grid frequency estimation method, the specific steps in step 4 for fitting and solving the corresponding fitting index value based on the associated sampling points are as follows:

[0025] Step B1: Construct the first-order polynomial and the second-order polynomial;

[0026] Step B2: For the first-order polynomial and the second-order polynomial, take the index value of each sampling point in the preceding and following associated sampling points as the independent variable of the polynomial and the sampling value of each sampling point in the preceding and following associated 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.

[0027] Step B3: Based on the solution results of 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 x1 corresponding to f1(x) = 0 and the value of the independent variable x2 corresponding to f2(x) = 0.

[0028] Step B4: Compare the derivative of the first-order polynomial at x1, f′1(x1), and the derivative of the second-order polynomial at x2, f′2(x2). If f′1(x1) > f′2(x2), then x1 is used as the fitting index value corresponding to the previous and subsequent associated sampling points of this group; otherwise, x2 is used as the fitting index value corresponding to the previous and subsequent associated sampling points of this group.

[0029] As a further improvement to the aforementioned accurate power grid frequency estimation method, the specific calculation method for the estimated power grid frequency in step 5 is as follows:

[0030] Let the fitting index value at the first zero-crossing time be x. 0_1 The fitted index value corresponding to the second zero-crossing time 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.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1. This invention uses a continuous sampling method based on the principle of monotonically increasing to select the associated sampling points before and after two adjacent zero-crossing times. During the selection process, the sampling points near the zero-crossing time are screened to reduce the influence of harmonics on the estimation results. The selected sampling points are closer to the theoretical zero-crossing time, which not only improves the accuracy of the estimation, but also requires only one cycle of data to complete the frequency estimation, significantly shortening the estimation time.

[0033] 2. This invention utilizes the characteristic that the derivative value of a sinusoidal signal is the largest at the zero point, and further optimizes the results of different fitting methods based on polynomial fitting, which significantly improves the estimation accuracy of the zero-crossing point.

[0034] 3. The present invention also judges the validity of the associated sampling points before and after the second zero crossing time, ensuring that the two sets of associated sampling points selected are located at the beginning and end of a cycle, which further improves the accuracy of frequency estimation. Detailed Implementation

[0035] The technical solution of the present invention is described in detail below:

[0036] A method for accurate estimation of power grid frequency, comprising the following steps:

[0037] Step 1: Select the associated sampling points before and after the first zero-crossing moment from the sampled data using the continuous sampling method based on the monotonically increasing principle. Set the index value of any sampling point among the associated sampling points before and after the first zero-crossing moment to 0, and assign integer index values ​​to the associated sampling points before and after the first zero-crossing moment and subsequent sampling points according to the principle of increasing with the sampling order.

[0038] Specifically, the continuous point selection method based on the monotonically increasing principle refers to:

[0039] Step A1: First, find the zero-preceding sampling point and the zero-postceding sampling point that simultaneously meet the following conditions from the sampled data: the sampled value of the zero-preceding sampling point is less than 0, the sampled value of the zero-postceding sampling point is greater than or equal to 0, and the zero-preceding sampling point and the zero-postceding sampling point are continuous sampling points.

[0040] Generally, if the index value of the zero-preceding sampling point at the first zero-crossing moment is set to 0, then the index value of the zero-following sampling point is 1, the index value of the sampling point before the zero-preceding sampling point is -1, and so on.

[0041] Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions: the four sampling points include the zero-before sampling point and the zero-after sampling point mentioned above, and the sampled values ​​of the four sampling points are monotonically increasing.

[0042] Specifically, first select the zero-preceding sampling point and the zero-after sampling point (both of which must be included). Then, determine whether the sample value of the next sampling point (index value 2) after the zero-after sampling point is greater than the sample value of the zero-after sampling point (index value 1). If so, select the next sampling point (index value 2). Next, determine whether the sample value of the previous sampling point (index value -1) before the zero-preceding sampling point is less than the sample value of the zero-preceding sampling point (index value 0). If so, select the previous sampling point (index value -1).

[0043] At this point, if four sampling points have already been selected, namely the four sampling points with index values ​​of -1, 0, 1, and 2, then the selection is complete.

[0044] If the number of currently selected sampling points is 2, that is, there are only 2 sampling points with index values ​​of 0 and 1, it means that the principle of monotonically increasing is not satisfied on both sides. Therefore, the current zero-preceding sampling point and zero-following sampling point are abandoned, and the process returns to step A1 to select the next set of zero-preceding sampling points and zero-following sampling points that meet the conditions.

[0045] If the currently selected sampling points are 3 and include the sampling point before the zero-preceding sampling point (index value -1), then continue to check whether the sampling value of the second sampling point before the zero-preceding sampling point (index value -2) is less than the sampling value of the sampling point before the zero-preceding sampling point: if it is satisfied, then select the second sampling point before the zero-preceding sampling point, and complete the selection of 4 sampling points. At this time, the 4 sampling points with index values ​​of -2, -1, 0, and 1 are selected; if it is not satisfied, it means that it is impossible to find 4 sampling points that are continuously monotonically increasing. Therefore, discard the current zero-preceding sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-preceding sampling points and zero-after sampling points that meet the conditions.

[0046] If the current selected sampling points are 3 and include the sampling point after the zero-after sampling point (index value 2), then continue to determine whether the sampling value of the second sampling point after the zero-after sampling point (index value 3) is greater than the sampling value of the sampling point after the zero-after sampling point: if it is satisfied, then select the second sampling point after the zero-after sampling point, and complete the selection of 4 sampling points. At this time, the 4 sampling points with index values ​​of 0, 1, 2, and 3 are selected; if it is not satisfied, then discard the current zero-before sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-before sampling points and zero-after sampling points that meet the conditions.

[0047] The four selected sampling points were used as the associated sampling points.

[0048] 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 "preceding and following correlated sampling points" at the beginning and end of each cycle.

[0049] The found related sampling points are placed in the cache. The index values ​​of the four sampling points are arranged in one of the following three ways: -2, -1, 0, 1, or -1, 0, 1, 2, or 0, 1, 2, 3.

[0050] Step 2: Use the continuous sampling method based on the monotonically increasing principle to select the associated sampling points before and after 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.

[0051] Similarly, if the index value of the zero-preceding sampling point in the associated sampling points before and after the second zero crossing time is n, then the index values ​​of the four sampling points in the associated sampling points before and after 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.

[0052] Step 3: Determine the validity of the associated sampling points before and after the second zero-crossing moment: If it is determined to be valid, proceed to Step 4. Otherwise, discard the currently selected associated sampling points before and after the second zero-crossing moment, and return to Step 2 to continue selecting associated sampling points before and after the second zero-crossing moment.

[0053] Specifically, the difference between the index value of the zero-preceding sampling point in the associated sampling points before and after the second zero-crossing moment and the index value of the zero-preceding sampling point in the associated sampling points before and after the first zero-crossing moment 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 period is C. s =f s / f m If 0.9C s ≤n≤1.1C s Then the sampling points before and after the second zero-crossing moment are considered valid.

[0054] Step 4: Fit the data based on the associated sampling points before and after the first zero-crossing moment to obtain the fitting index value corresponding to the first zero-crossing moment; and fit the data based on the associated sampling points before and after the second zero-crossing moment to obtain the fitting index value corresponding to the second zero-crossing moment.

[0055] For either the first or second zero-crossing moment, the specific steps for fitting the data based on the associated sampling points before and after the zero-crossing moment and solving for the corresponding fitting index value are the same:

[0056] Step B1: Construct the first-order polynomial and the second-order polynomial.

[0057] Step B2: For the first-order polynomial and the second-order polynomial, take the index values ​​of each sampling point in the preceding and following associated sampling points as the independent variables of the polynomial, and the sample values ​​of each sampling point in the preceding and following associated sampling points as the dependent variables, and substitute them into the corresponding polynomials. 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.

[0058] Suppose that the first-order polynomial constructed when solving for the fitted index value at the first zero-crossing time is f1(x) = a 1_1 +a 1_2 Let x be the index 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, then:

[0059]

[0060] This can be represented by a matrix as follows:

[0061] XA1 = S;

[0062]

[0063] The solution is A1 = (X T X) -1 (X T S).

[0064] Similarly, if it is a quadratic polynomial f2(x) = a 2_1 +a 2_2 x+a 2_3 x 2 ,but Solution results

[0065] 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.

[0066] 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

[0067] Step B4: Compare the derivative of the first-order polynomial at x1, f′1(x1), and the derivative of the second-order polynomial at x2, f′2(x2). If f′1(x1) > f′2(x2), then x1 is used as the fitting index value corresponding to the preceding and following associated sampling points; otherwise, x2 is used as the fitting index value corresponding to the preceding and following associated sampling points. Clearly, the fitting index value here is not necessarily an integer, but a natural number.

[0068] Step 5: Calculate the estimated value of the power grid frequency based on the fitted index values ​​corresponding to the first and second zero-crossing moments. The specific calculation method is as follows:

[0069] Let the fitting index value at the first zero-crossing time be x. 0_1 The fitted index value corresponding to the second zero-crossing time 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.

[0070] 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.

[0071] Actual testing showed that when the sampling frequency was 6.4 kHz and the theoretical power grid frequency was 50 Hz, the power grid frequency estimation accuracy using this method, through a 3-cycle sliding window calculation, could reach 0.005 Hz.

Claims

1. A method for accurately estimating power grid frequency, characterized by the following steps: include: Step 1: Use the continuous sampling method based on the monotonically increasing principle to select the associated sampling points before and after the first zero crossing time from the sampled data, and set the index value of any sampling point in the associated sampling points before and after the first zero crossing time to 0. Integer index values ​​are assigned to the associated sampling points before and after the first zero crossing time and subsequent sampling points according to the principle of increasing with the sampling order. The continuous point selection method based on the monotonically increasing principle refers to: Step A1: First, find the zero-preceding sampling point and the zero-postceding sampling point from the sampled data that simultaneously meet the following conditions: the sampled value of the zero-preceding sampling point is less than 0, the sampled value of the zero-postceding sampling point is greater than or equal to 0, and the zero-preceding sampling point and the zero-postceding sampling point are consecutive sampling points. Step A2: Select four consecutive sampling points from the sampled data that meet the following conditions: the four sampling points include the zero-before sampling points and the zero-after sampling points mentioned above, and the sampled values ​​of the four sampling points are monotonically increasing. The four selected sampling points were used as consecutive sampling points. Step 2: Use the continuous sampling method based on the monotonically increasing principle to select the associated sampling points before and after the second zero-crossing time from the sampled data; Step 3: Determine the validity of the associated sampling points before and after the second zero-crossing moment: If it is determined to be valid, proceed to step 4; otherwise, abandon the currently selected associated sampling points before and after the second zero-crossing moment, and return to step 2 to continue selecting associated sampling points before and after the second zero-crossing moment. Step 4: Fit the data based on the associated sampling points before and after the first zero-crossing moment to obtain the fitting index value corresponding to the first zero-crossing moment; and fit the data based on the associated sampling points before and after the second zero-crossing moment to obtain the fitting index value corresponding to the second zero-crossing moment. The specific steps in step 4 for fitting and solving the corresponding fitting index value based on the associated sampling points are as follows: Step B1: Construct the first-order polynomial and the second-order polynomial; Step B2: For both first-order and second-order polynomials, take the index values ​​of each sampling point in the preceding and following associated sampling points as the independent variables of the polynomials, and the sample values ​​of each sampling point in the preceding and following associated sampling points as the dependent variables. Substitute these values ​​into the corresponding polynomials, and then use the least squares method to obtain the design matrices for the first-order and second-order polynomials. and ; Step B3: Based on the design matrix and The solution result is a first-order polynomial. and quadratic polynomial Then calculate Corresponding independent variable value and Corresponding independent variable value ; Step B4: Compare the linear polynomials in... derivative at point and quadratic polynomials in derivative at point The size, if Then Used as the fitting index value corresponding to the preceding and following related sampling points in this group; otherwise, As the fitting index value corresponding to the preceding and following related sampling points in this group; Step 5: Calculate the estimated value of the power grid frequency based on the fitted index values ​​corresponding to the first and second zero-crossing moments.

2. The method for accurately estimating power grid frequency as described in claim 1, characterized in that, The specific process of step A2 is as follows: First, select the zero-before sampling point and the zero-after sampling point, and then determine whether the sampling value of the next sampling point after the zero-after sampling point is greater than the sampling value of the zero-after sampling point. If the condition is met, select the next sampling point. Then determine whether the sample value of the previous sample point is less than the sample value of the previous sample point. If the condition is met, then select the previous sample point. If four sampling points have already been selected, the selection is complete. If the number of currently selected sampling points is 2, discard the current zero-before sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-before sampling points and zero-after sampling points that meet the conditions; If the current number of selected sampling points is 3 and includes the sampling point before the zero-preceding sampling point, then continue to determine whether the sampling value of the second sampling point before the zero-preceding sampling point is less than the sampling value of the sampling point before the zero-preceding sampling point: if it is satisfied, then select the second sampling point before the zero-preceding sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-preceding sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-preceding sampling points and zero-after sampling points that meet the conditions; If the current number of selected sampling points is 3 and includes the sampling point after the zero-after sampling point, then continue to determine whether the sampling value of the second sampling point after the zero-after sampling point is greater than the sampling value of the sampling point after the zero-after sampling point: if it is satisfied, then select the second sampling point after the zero-after sampling point, and complete the selection of 4 sampling points; if it is not satisfied, then discard the current zero-before sampling point and zero-after sampling point, and return to step A1 to select the next set of zero-before sampling points and zero-after sampling points that meet the conditions.

3. The method for accurate estimation of power grid frequency as described in claim 1, characterized in that, The method for determining the validity of the associated sampling points before and after the second zero-crossing time in step 3 is as follows: Let the difference between the index value of the zero-preceding sampling point in the associated sampling points before and after the second zero-crossing time and the index value of the zero-preceding sampling point in the associated sampling points before and after 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 sampling points before and after the second zero-crossing moment are considered valid.

4. The method for accurately estimating power grid frequency as described in claim 1, characterized in that, The specific calculation method for the estimated power grid frequency in step 5 is as follows: Let the fitting index value at the first zero-crossing time be... The fitting index value corresponding to the second zero-crossing time is Estimated value of power grid frequency ,in The sampling frequency.

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