Wide-frequency-range harmonic analysis method for electric energy meter and acquisition terminal

Abstract

The invention discloses a wide-frequency-range harmonic analysis method for an electric energy meter and an acquisition terminal, and the method comprises the steps: collecting a voltage signal and a current signal, and enabling the number M of sampling points to be the product of the integer power of 5 and 2; determining the fundamental frequency of the acquired voltage signal; windowing the signal according to the frequency offset condition of the collected voltage signal; and performing conversion calculation on the acquired current signal and the voltage signal by using a mixed base subgroup algorithm to obtain frequency spectrum data of current and voltage, and finally performing harmonic electric energy calculation on the frequency spectrum data. According to the method, the limitation of a traditional FFT algorithm in the process of processing non-second power data points is avoided, the calculation efficiency is improved, it is guaranteed that signals with large frequency deviation can still be accurately analyzed, signals within a wide frequency range can be effectively processed, and the high-precision and high-efficiency harmonic analysis requirement is met.

Description

Technical Field

[0001] The invention belongs to the field of power signal processing and analysis, and in particular relates to a wide frequency range harmonic analysis method. Background Art

[0002] With the widespread use of nonlinear loads in power systems, the problem of harmonic pollution is becoming increasingly serious. Accurately analyzing harmonics and calculating electric energy has become the key to power quality assessment and control by electric energy meters and data collection terminals.

[0003] Traditional harmonic analysis mainly relies on fast Fourier transform (FFT) technology. Although it has high computational efficiency, it still has the following limitations:

[0004] 1. Data point limit: Traditional FFT algorithms require that the sampling points of the input signal must be an integer power of 2, which limits the flexibility of signal processing. Generally, the spectrum resolution of power quality specified by IEC is 5Hz, and the first harmonic is calculated in 10 cycles. Usually, the sampling rate of ADC is an integer multiple of 2. Considering that a larger number of samples can usually provide more accurate spectrum estimation, the sampling points are generally set to a larger number such as 1280 or 2560, which is not applicable to traditional FFT.

[0005] 2. Influence of frequency deviation and spectrum leakage: In power system or industrial equipment monitoring, the signal to be analyzed may have frequency deviation (for example, frequency fluctuation caused by load changes of power equipment, environmental factors, etc.). The traditional FFT method assumes that the signal frequency is stable. However, when the signal has frequency deviation or non-periodic characteristics, the traditional FFT method may have spectrum leakage, that is, the energy distribution of the signal is no longer concentrated on the correct frequency, resulting in large errors in the calculation of harmonic power.

[0006] 3. Not suitable for analysis of signals in a wide frequency range: Traditional harmonic analysis methods are usually only applicable to narrow-band signals and have limited processing capabilities for signals in a wide frequency range.

[0007] For the above problems, the prior art has proposed related improved technologies, such as short-time Fourier transform (STFT) and wavelet transform. Although these technologies have overcome the frequency deviation problem to a certain extent, they have high computational complexity, poor real-time performance, and still have limitations in harmonic analysis over a wide frequency range. Summary of the invention

[0008] The present invention proposes a wide frequency range harmonic analysis method for electric energy meters and data acquisition terminals, the purposes of which are: 1. to solve the problem of data point limitations in traditional analysis methods; 2. to solve the problem of large errors in harmonic electric energy calculation caused by frequency deviation and spectrum leakage; 3. to solve the problem that traditional methods cannot analyze signals in a wide frequency range.

[0009] The technical solution of the present invention is as follows:

[0010] A wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, comprising the following steps: Step 1, collecting voltage signals and current signals; the number of sampling points M is the product of 5 and an integer power of 2: M = 5*2 R ;

[0011] Step 2, determining the fundamental frequency f0 of the collected voltage signal;

[0012] Step 3: Perform windowing on the signal according to the frequency deviation of the collected voltage signal;

[0013] Step 4: Use a hybrid basis subgroup algorithm to transform and calculate the collected current signal and the voltage signal processed in step 3 to obtain spectrum data of current and voltage;

[0014] Step 5: Calculate harmonic power based on the spectrum data obtained in step 4.

[0015] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, in step 2, an autocorrelation method is used to detect the fundamental wave period:

[0016] Step 2-1, calculate the autocorrelation function:

[0017]

[0018] Among them, i is the number of delay points of the signal, R x (i) is the autocorrelation function value corresponding to the delay point number i, M is the number of sampling points of the signal, and x(n) is the nth signal value in the collected signal;

[0019] Step 2-2, determining the fundamental wave period according to the autocorrelation function;

[0020] By analyzing the periodic peak of the autocorrelation function, the first non-zero periodic peak position z1 is found, and the fundamental period corresponding to this position is set to:

[0021]

[0022] Among them, f s is the acquisition frequency of the signal;

[0023] Step 2-3: Determine the fundamental frequency based on the fundamental period:

[0024]

[0025] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, the specific process of step 3 is as follows:

[0026] Step 3-1, calculate the frequency deviation rate Δf:

[0027]

[0028] Where f0 is the fundamental frequency of the signal;

[0029] Step 3-2: determine the magnitude relationship between the frequency deviation rate Δf and a preset threshold value. If it is less than or equal to the preset threshold value, directly use the current collected signal as the processed signal; otherwise, perform windowing processing on the collected signal.

[0030] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, the windowing process in step 3-2 refers to Hanning windowing process, and the window function is defined as:

[0031]

[0032] Among them, ω(n) is the weighted value corresponding to the nth collected signal value;

[0033] The nth signal value in the windowed voltage signal is: x h (n) = x(n)·ω(n).

[0034] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals: in the mixed basis subgroup algorithm, a 5-point WFTA transformation is first performed, and then a basis 2 FFT transformation is performed.

[0035] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, the specific process of the mixed basis subgroup algorithm is as follows:

[0036] Step 4-1: For the input signal of the mixed basis subgroup algorithm, take every 5 sampling points as a row in the matrix in order to obtain a 2 R ×5 matrix X:

[0037]

[0038] Among them, x in (n) is the nth sampling point in the input signal of the mixed basis subgroup algorithm;

[0039] Step 4-2: Perform a 5-point WFTA transformation on each row of the matrix X:

[0040] Suppose the values ​​of a row in matrix X are ω5=0,1,2,3,4, then the row is transformed into 5 complex values ​​by 5-point WFTA according to the following formula

[0041]

[0042] Step 4-3: Build a 2 R ×5 matrix Y, the five complex values ​​obtained by the five-point WFTA transformation of each row of matrix X are used as the elements of the corresponding row in matrix Y, then the matrix Y is:

[0043]

[0044] in, is the ω5th complex value of the lth row in the matrix X obtained by the 5-point WFTA transformation, ω5 = 0, 1, 2, 3, 4;

[0045] Step 4-4: Perform 2 on each column of matrix Y. R Point-based 2FFT transform:

[0046] Suppose the values ​​of a column in matrix Y are Then the column is processed as follows2 R The point basis 2 transformation gives 2 R Complex value

[0047]

[0048] Step 4-5: Build a 2 R ×5 matrix Z, pass each column of matrix Y through 2 R The 2 obtained by the point-based 2FFT transformation R complex values ​​as the elements of the corresponding columns in the matrix Z, then the matrix Z is:

[0049]

[0050] in, For the cth column in matrix Y, pass 2 R The first complex value, The matrix Z is expanded row by row to obtain M-point spectrum data.

[0051] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals: in step 5, for the mth harmonic, the harmonic electric energy calculation formula is:

[0052] P m =U m I m ·cos(θ m );

[0053] Among them, U m is the voltage amplitude of the mth harmonic, I m is the current amplitude of the mth harmonic, θm is the phase difference between the mth harmonic voltage and current.

[0054] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals: in step 5, for the mth harmonic, the amplitude and phase of its voltage and current are determined as follows: according to the frequency resolution of the spectrum data and the frequency corresponding to the mth harmonic, the corresponding complex value is found from the corresponding current spectrum data or voltage spectrum data, and the complex value is converted into amplitude and phase.

[0055] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, it also includes step 6: quantitative evaluation and analysis of the calculation results of harmonic electric energy, including uncertainty analysis of single harmonic electric energy, uncertainty analysis of total harmonic electric energy and determination of total uncertainty at a specific confidence level.

[0056] As a further improvement of the wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, step 6 includes:

[0057] Step 6-1, single harmonic power uncertainty analysis:

[0058] For the mth harmonic, the uncertainty of harmonic energy u(P m ) is calculated as:

[0059]

[0060] Among them, u(U m ) is the uncertainty of the mth harmonic voltage amplitude, obtained by calibrating the instrument; u(I m ) is the uncertainty of the mth harmonic current amplitude, obtained through the calibration data of the measuring equipment; u(cos(θ m )) is the phase angle uncertainty of the mth harmonic, which is calibrated by experiment; Step 6-2, uncertainty analysis of total electric energy from the 2nd harmonic to the Hth harmonic:

[0061]

[0062] Step 6-3: Determine the total uncertainty at a specific confidence level:

[0063] U total =e·u(P total );

[0064] Where e is the confidence factor.

[0065] Compared with the prior art, the present invention has the following positive effects:

[0066] 1. The present invention adopts a mixed basis subgroup algorithm to process the signal, first performs a 5-point WFTA transform, and then performs a basis 2FFT transform, so that it can process sampling points whose sampling points are integer powers of 5 and 2, and is compatible with the currently commonly used 1280 and 2560 points, effectively avoiding the limitations of the traditional FFT algorithm in processing non-power of 2 data points and improving the calculation efficiency.

[0067] 2. When the frequency deviation is large, the present invention first performs Hanning window processing on the signal, and then performs mixed basis subgroup algorithm analysis. The Hanning window effectively reduces spectrum leakage, suppresses spectrum leakage phenomenon, and ensures that signals with large frequency deviation can still be accurately analyzed.

[0068] 3. The present invention can effectively process signals in a wide frequency range and meet the requirements of high-precision and high-efficiency harmonic analysis by setting a high sampling frequency (12800 Hz) and a long signal length (2560 points) in combination with a mixed-basis subgroup algorithm.

[0069] 4. The present invention can accurately calculate the electric energy and uncertainty of each harmonic, control the uncertainty of the total electric energy within 0.10%, and ensure the reliability of the harmonic analysis results.

[0070] In summary, the present invention solves the problems of frequency offset, sampling point limit and spectrum leakage by optimizing the signal processing flow, combining the innovative hybrid basis subgroup algorithm and windowing technology, and significantly improves the accuracy and applicability of harmonic analysis. This method is widely applicable to application scenarios such as power quality monitoring, harmonic pollution detection, load monitoring, etc., and has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flow chart of the present invention;

[0072] Figure 2 This is the flow chart of the mixed-basis subgroup algorithm. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0074] like Figure 1 , a wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, the steps comprising:

[0075] Step 1: Collect voltage and current signals.

[0076] The signal to be analyzed is usually a signal with a fundamental frequency of 50 Hz in the power system, which contains multiple harmonic components and noise interference. Assume that the sampling frequency is f s=12800Hz, the number of sampling points is the product of 5 and the integer power of 2, recorded as M=5*2 R In this embodiment, the number of sampling points is 2560. Then the time length of the signal is:

[0077]

[0078] The value of the nth signal value x(n) in the collected signal at time t can be expressed as:

[0079]

[0080] Among them: A h is the amplitude of the hth harmonic; H is the number of harmonics; f0 is the fundamental frequency, the nominal value is 50Hz; φ h is the phase angle of the hth harmonic; ∈(t) is the background noise and measurement error. The acquisition frequency and the number of sampling points of the voltage signal and the current signal are the same.

[0081] Step 2: Determine the fundamental frequency f0 of the collected voltage signal.

[0082] In order to quickly determine the fundamental frequency f0, the autocorrelation method is used to detect the fundamental wave period. The autocorrelation method has the characteristics of small computational complexity and strong adaptability, and is very suitable for real-time analysis of the fundamental frequency of power signals. The process is as follows:

[0083] Step 2-1, calculate the autocorrelation function:

[0084]

[0085] Among them, i is the number of delay points of the signal, R x (i) is the autocorrelation function value corresponding to the delay point number i, M is the number of sampling points of the signal, and x(n) is the nth signal value in the collected signal.

[0086] Step 2-2: Determine the fundamental wave period according to the autocorrelation function.

[0087] By analyzing the periodic peak of the autocorrelation function, the first non-zero periodic peak position z1 is found, and the fundamental period corresponding to this position is set to:

[0088]

[0089] Among them, f s is the sampling frequency of the signal.

[0090] Step 2-3: Determine the fundamental frequency based on the fundamental period:

[0091]

[0092] In this embodiment, the sampling frequency fs =12800Hz, assuming that the position of the first peak point of the autocorrelation function is detected as z1=256, then the fundamental frequency is: Step 3: Perform windowing processing on the signal according to the frequency deviation of the collected voltage signal.

[0093] The specific process is:

[0094] Step 3-1, calculate the frequency deviation rate Δf:

[0095]

[0096] Where f0 is the fundamental frequency of the signal.

[0097] Step 3-2: determine the magnitude relationship between the frequency deviation rate Δf and a preset threshold. If it is less than or equal to the preset threshold (4% in this embodiment), directly use the current collected signal as the processed signal; otherwise, perform windowing on the collected signal.

[0098] Specifically, the windowing process refers to Hanning windowing process, and the window function is defined as:

[0099]

[0100] Wherein, ω(n) is the weighted value corresponding to the nth collected signal value.

[0101] The nth signal value in the windowed voltage signal is: x h (n) = x(n)·ω(n).

[0102] Step 4: Use the mixed basis subgroup algorithm to transform and calculate the collected current signal and the voltage signal processed in step 3 to obtain the spectrum data of current and voltage. In the mixed basis subgroup algorithm, a 5-point WFTA transformation is first performed, and then a basis 2 FFT transformation is performed. Figure 2 , the specific process is:

[0103] Step 4-1: For the input signal of the mixed basis subgroup algorithm, take every 5 sampling points as a row in the matrix in order to obtain a 2 R ×5 matrix X:

[0104]

[0105] Among them, x in (n) is the nth sampling point in the input signal of the mixed basis subgroup algorithm.

[0106] Step 4-2: Perform a 5-point WFTA transformation on each row of the matrix X:

[0107] Suppose the values ​​of a row in matrix X are ω5=0,1,2,3,4, then the row is transformed into 5 complex values ​​by 5-point WFTA according to the following formula

[0108]

[0109] Step 4-3: Build a 2 R ×5 matrix Y, the five complex values ​​obtained by the five-point WFTA transformation of each row of matrix X are used as the elements of the corresponding row in matrix Y, then the matrix Y is:

[0110]

[0111] in, is the ω5th complex value obtained by the 5-point WFTA transformation of the l-th row in the matrix X, ω5 = 0, 1, 2, 3, 4.

[0112] Step 4-4: Perform 2 on each column of matrix Y. R Point-based 2FFT transform:

[0113] Suppose the values ​​of a column in matrix Y are In this embodiment, R =512, then the column is processed as follows2 R The point basis 2 transformation gives 2 R Complex value

[0114]

[0115] Step 4-5: Build a 2 R ×5 matrix Z, pass each column of matrix Y through 2 R The 2 obtained by the point-based 2FFT transformation R complex values ​​as the elements of the corresponding columns in the matrix Z, then the matrix Z is:

[0116]

[0117] in, For the cth column in matrix Y, pass 2 R The first complex value, The matrix Z is expanded row by row to obtain M-point spectrum data.

[0118] Step 5: Calculate harmonic power based on the spectrum data obtained in step 4.

[0119] For the mth harmonic, the harmonic energy calculation formula is:

[0120] P m =Um I m ·cos(θ m );

[0121] Among them, U m is the voltage amplitude of the mth harmonic, I m is the current amplitude of the mth harmonic, θ m is the phase difference between the mth harmonic voltage and current.

[0122] For the mth harmonic, the amplitude and phase of its voltage and current are determined as follows: according to the frequency resolution of the spectrum data and the frequency corresponding to the mth harmonic, the corresponding complex value is found from the corresponding current spectrum data or voltage spectrum data, and the complex value is converted into the amplitude and phase. In this embodiment, each point corresponds to a spectrum resolution of 5 Hz, the first harmonic is the data corresponding to the 10th point at 50 Hz, and the second harmonic is the data corresponding to the 20th point at 100 Hz.

[0123] Step 6: Conduct quantitative evaluation and analysis on the calculation results of harmonic electric energy, including uncertainty analysis of single harmonic electric energy, uncertainty analysis of total harmonic electric energy and determination of total uncertainty at a specific confidence level.

[0124] Step 6-1, single harmonic power uncertainty analysis:

[0125] For the mth harmonic, the uncertainty of harmonic energy u(P m ) is calculated as:

[0126]

[0127] Among them, u(U m ) is the uncertainty of the mth harmonic voltage amplitude, which is determined by the harmonic amplitude measurement error and obtained by calibrating the instrument; u(I m ) is the uncertainty of the mth harmonic current amplitude, which is determined by the harmonic amplitude measurement error and obtained through the calibration data of the measuring equipment; u(cos(θ m )) is the phase angle uncertainty of the m-th harmonic, which is related to the phase response characteristics of the measuring instrument and is usually calibrated through experiments.

[0128] Step 6-2, Uncertainty analysis of total electric energy from the 2nd harmonic to the Hth harmonic:

[0129]

[0130] In this embodiment, H=41.

[0131] Step 6-3: Determine the total uncertainty at a specific confidence level:

[0132] U total=e·u(P total );

[0133] Wherein, e is the confidence factor when the confidence level is 95%, and in this embodiment, e=2.

[0134] The accuracy and reliability of the present invention are verified by analyzing actual power signals. The comparison results show that the accuracy of harmonic amplitude and electric energy calculation of the present invention is significantly better than that of the traditional FFT method when the frequency deviation is large, and the uncertainty is always less than 0.10%.

[0135] The present invention successfully solves the frequency deviation and point number limitation problems by optimizing the signal processing flow and algorithm design, and is applicable to various power harmonic analysis scenarios, and has important engineering application value. It should be noted that for those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. The scope of the present invention is defined by the claims rather than the above description.

Claims

1. A wide frequency range harmonic analysis method for electric energy meters and acquisition terminals, characterized in that the steps include: Step 1, collecting voltage signals and current signals; The number of sampling points M is the product of 5 and an integer power of 2: M = 5*2 R ; Step 2, determining the fundamental frequency f0 of the collected voltage signal; Step 3: Perform windowing on the signal according to the frequency deviation of the collected voltage signal; Step 4: Use a hybrid basis subgroup algorithm to transform and calculate the collected current signal and the voltage signal processed in step 3 to obtain spectrum data of current and voltage; Step 5: Calculate harmonic power based on the spectrum data obtained in step 4.

2. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 1, characterized in that: In step 2, the autocorrelation method is used to detect the fundamental period: Step 2-1, calculate the autocorrelation function: Among them, i is the number of delay points of the signal, R x (i) is the autocorrelation function value corresponding to the delay point number i, M is the number of sampling points of the signal, and x(n) is the nth signal value in the collected signal; Step 2-2, determining the fundamental wave period according to the autocorrelation function; By analyzing the periodic peak of the autocorrelation function, the first non-zero periodic peak position z1 is found, and the fundamental period corresponding to this position is set to: Among them, f s is the acquisition frequency of the signal; Step 2-3: Determine the fundamental frequency based on the fundamental period:

3. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 1, characterized in that: The specific process of step 3 is: Step 3-1, calculate the frequency deviation rate Δf: Where f0 is the fundamental frequency of the signal; Step 3-2: determine the magnitude relationship between the frequency deviation rate Δf and a preset threshold value. If it is less than or equal to the preset threshold value, directly use the current collected signal as the processed signal; otherwise, perform windowing processing on the collected signal.

4. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 3, characterized in that: The windowing process in step 3-2 refers to the Hanning windowing process, and the window function is defined as: Among them, ω(n) is the weighted value corresponding to the nth collected signal value; The nth signal value in the windowed voltage signal is: x h (n) = x(n)·ω(n).

5. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to any one of claims 1 to 4, characterized in that: In the mixed-base subgroup algorithm, a 5-point WFTA transform is performed first, followed by a base-2 FFT transform.

6. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 5, characterized in that: The specific process of the mixed basis subgroup algorithm is: Step 4-1: For the input signal of the mixed basis subgroup algorithm, take every 5 sampling points as a row in the matrix in order to obtain a 2 R ×5 matrix X: Among them, x in (n) is the nth sampling point in the input signal of the mixed basis subgroup algorithm; Step 4-2: Perform a 5-point WFTA transformation on each row of the matrix X: Suppose the values ​​of a row in matrix X are ω5=0,1,2,3,4, then the row is transformed into 5 complex values ​​by 5-point WFTA according to the following formula Step 4-3: Build a 2 R ×5 matrix Y, the five complex values ​​obtained by the five-point WFTA transformation of each row of matrix X are used as the elements of the corresponding row in matrix Y, then the matrix Y is: in, is the ω5th complex value of the lth row in the matrix X obtained by the 5-point WFTA transformation, ω5 = 0, 1, 2, 3, 4; Step 4-4: Perform 2 on each column of matrix Y. R Point-based 2FFT transform: Suppose the values ​​of a column in matrix Y are Then the column is processed as follows2 R The point basis 2 transformation gives 2 R Complex value Step 4-5: Build a 2 R ×5 matrix Z, pass each column of matrix Y through 2 R The 2 obtained by the point-based 2FFT transformation R complex values ​​as the elements of the corresponding columns in the matrix Z, then the matrix Z is: in, For the cth column in matrix Y, pass 2 R The first complex value, The matrix Z is expanded row by row to obtain M-point spectrum data.

7. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 6, characterized in that: In step 5, for the mth harmonic, the harmonic energy calculation formula is: P m =U m ·AND m ·cos(θ m ); Among them, U m is the voltage amplitude of the mth harmonic, I m is the current amplitude of the mth harmonic, θ m is the phase difference between the mth harmonic voltage and current.

8. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 7, characterized in that: In step 5, for the mth harmonic, the amplitude and phase of its voltage and current are determined by finding the corresponding complex value from the corresponding current spectrum data or voltage spectrum data according to the frequency resolution of the spectrum data and the frequency corresponding to the mth harmonic, and converting the complex value into amplitude and phase.

9. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 7, characterized in that: It also includes step 6: quantitative evaluation and analysis of the calculation results of harmonic electric energy, including uncertainty analysis of single harmonic electric energy, uncertainty analysis of total harmonic electric energy and determination of total uncertainty at a specific confidence level.

10. The wide frequency range harmonic analysis method for electric energy meters and acquisition terminals according to claim 9, characterized in that: Step 6 includes: Step 6-1, single harmonic power uncertainty analysis: For the mth harmonic, the uncertainty of harmonic energy u(P m ) is calculated as: Among them, u(U m ) is the uncertainty of the mth harmonic voltage amplitude, obtained by calibrating the instrument; u(I m ) is the uncertainty of the mth harmonic current amplitude, obtained through the calibration data of the measuring equipment; u(cos(θ m )) is the phase angle uncertainty of the mth harmonic, which is calibrated by experiment; Step 6-2, Uncertainty analysis of total electric energy from the 2nd harmonic to the Hth harmonic: Step 6-3: Determine the total uncertainty at a specific confidence level: IN total =e·u(P total ); Where e is the confidence factor.

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