A wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals

Abstract

This invention discloses a wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals. The steps include: acquiring voltage and current signals, with the number of sampling points M being the product of 5 and powers of 2; determining the fundamental frequency of the acquired voltage signal; windowing the signal based on its frequency offset; using a hybrid basis set algorithm to transform and calculate the acquired current and voltage signals respectively, obtaining the spectral data of the current and voltage; and finally, calculating the harmonic energy from the spectral data. This invention avoids the limitations of traditional FFT algorithms in processing non-power-of-two data points, improves computational efficiency, ensures accurate analysis of signals with large frequency offsets, and effectively processes signals over a wide frequency range, meeting the requirements for high-precision and high-efficiency harmonic analysis.

Description

Technical Field

[0001] This invention belongs to the field of power signal processing and analysis, and specifically relates to a wide frequency range harmonic analysis method. Background Technology

[0002] With the widespread application of nonlinear loads in power systems, harmonic pollution has become increasingly serious. Accurate analysis of harmonics and calculation of electrical energy have become crucial for power meters and data acquisition terminals to assess and control power quality.

[0003] Traditional harmonic analysis mainly relies on the Fast Fourier Transform (FFT) technique. Although it is computationally efficient, it still has the following limitations:

[0004] 1. Data Point Limitation: Traditional FFT algorithms require the number of sampling points of the input signal to be an integer power of 2, which limits the flexibility of signal processing. Generally, the IEC-specified power quality spectral resolution is 5Hz, with the first harmonic calculated at 10 cycles. Typically, the sampling rate of an ADC is a multiple of 2. Furthermore, considering that a larger number of samples usually provides more accurate spectral estimation, the number of sampling points is generally set to a large number such as 1280 or 2560, making traditional FFT unsuitable.

[0005] 2. Impact of Frequency Offset and Spectral Leakage: In power system or industrial equipment monitoring, the signal to be analyzed may have a frequency offset (e.g., frequency fluctuations caused by changes in power equipment load, environmental factors, etc.). Traditional FFT methods assume that the signal frequency is stable. However, when the signal has frequency offset or non-periodic characteristics, traditional FFT methods may experience spectral leakage, meaning that the energy distribution of the signal is no longer concentrated on the correct frequency, resulting in a large error in the calculation of harmonic energy.

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

[0007] To address the aforementioned issues, existing technologies have proposed related improvements, such as Short-Time Fourier Transform (STFT) and Wavelet Transform. While these technologies have overcome the frequency offset problem to some extent, they suffer from high computational complexity, poor real-time performance, and limitations in harmonic analysis over a wide frequency range. Summary of the Invention

[0008] This invention proposes a wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals. Its objectives are: 1. to solve the problem of data point limitations in traditional analysis methods; 2. to solve the problem of large calculation errors in harmonic energy caused by frequency offset and spectral leakage; and 3. to solve the problem that traditional methods cannot analyze signals with a wide frequency range.

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

[0010] A wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals includes the following steps: Step 1, acquiring voltage and current signals; the number of sampling points M is the product of 5 and 2 raised to the power of 2: M = 5 * 2 R ;

[0011] Step 2: Determine the fundamental frequency f0 of the acquired voltage signal;

[0012] Step 3: Window the signal based on the frequency deviation of the acquired voltage signal;

[0013] Step 4: Use the hybrid basis subgroup algorithm to transform and calculate the acquired current signal and the voltage signal processed in Step 3 respectively, and obtain the spectrum data of current and voltage.

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

[0015] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals, in step 2, the autocorrelation method is used to detect the fundamental period:

[0016] Step 2-1: Calculate the autocorrelation function:

[0017]

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

[0019] Step 2-2: Determine the fundamental period based on the autocorrelation function;

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

[0021]

[0022] Among them, f s The frequency at which the signal is collected;

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

[0024]

[0025] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals, step 3 is as follows:

[0026] Step 3-1: Calculate the frequency deviation Δf:

[0027]

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

[0029] Step 3-2: Determine the relationship between the frequency offset rate Δf and the preset threshold. If it is less than or equal to the preset threshold, the current acquired signal is directly used as the processed signal; otherwise, the acquired signal is windowed.

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

[0031]

[0032] Where ω(n) is the weighting value corresponding to the nth acquired signal value;

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

[0034] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and acquisition terminals: the hybrid basis subgroup algorithm first performs a 5-point WFTA transformation, and then performs a radix-2 FFT transformation.

[0035] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals, the specific process of the hybrid basis subgroup algorithm is as follows:

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

[0037]

[0038] Where, x in (n) represents the nth sampling point in the input signal of the hybrid basis subgroup algorithm;

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

[0040] Let the values ​​of a row in matrix X be respectively If ω5 = 0, 1, 2, 3, 4, then this row can be transformed using a 5-point WFTA method to obtain 5 complex values.

[0041]

[0042] Step 4-3, construct a 2 R Given a matrix Y of size × 5, if we take the five complex values ​​obtained by performing a 5-point WFTA transformation on each row of matrix X as the elements of the corresponding rows in matrix Y, then matrix Y is:

[0043]

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

[0045] Step 4-4: Perform 2x2 operations on each column of matrix Y. R Point-based radix-2 FFT transform:

[0046] Let the values ​​of a certain column in matrix Y be respectively Then this column is processed according to the following formula 2 R Point radix-2 transformation yields 2 R A complex value

[0047]

[0048] Steps 4-5: Construct a 2 R Given a 5×5 matrix Z, the columns of matrix Y are transformed by 2... R The 2 obtained by point basis 2FFT transformation R If each complex value is used as an element of the corresponding column in matrix Z, then matrix Z is:

[0049]

[0050] in, For the c-th column of matrix Y, pass through 2 R The first point-radix 2 FFT transformation yields the... A complex value, Expanding matrix Z by rows yields the spectrum data for point M.

[0051] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals: In step 5, for the m-th harmonic, the formula for calculating harmonic energy is:

[0052] P m =U m ·I m ·cos(θ m );

[0053] Among them, U m Let I be the voltage amplitude of the m-th harmonic. m Let θ be the current amplitude of the m-th harmonic.m Let be the phase difference between the voltage and current of the m-th harmonic.

[0054] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and acquisition terminals: In step 5, for the m-th harmonic, the amplitude and phase of its voltage and current are determined as follows: based on the frequency resolution of the spectrum data and the frequency corresponding to the m-th harmonic, the corresponding complex values ​​are found from the corresponding current spectrum data or voltage spectrum data, and the complex values ​​are converted into amplitude and phase.

[0055] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and acquisition terminals, step 6 is also included: quantitatively evaluating and analyzing the calculation results of harmonic energy, including single harmonic energy uncertainty analysis, total harmonic energy uncertainty analysis, and determining the total uncertainty at a specific confidence level.

[0056] As a further improvement to the wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals, step 6 includes:

[0057] Step 6-1, Uncertainty Analysis of Single Harmonic Energy:

[0058] For the m-th harmonic, the uncertainty of the harmonic energy u(P) m The calculation method for ) is as follows:

[0059]

[0060] Among them, u(U m ) represents the uncertainty of the voltage amplitude of the m-th harmonic, obtained through instrument calibration; u(I) m ) represents the amplitude uncertainty of the m-th harmonic current, obtained from the calibration data of the measuring equipment; u(cos(θ) m The phase angle uncertainty of the m-th harmonic is determined experimentally; Step 6-2, analysis of the total electrical energy uncertainty from the 2nd to the H-th 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 advantages:

[0066] 1. This invention uses a hybrid basis subgroup algorithm to process signals. First, a 5-point WFTA transformation is performed, followed by a radix-2 FFT transformation. This enables the processing of sampling points that are integer powers of 5 and 2, and is compatible with the commonly used 1280 and 2560 point numbers. This effectively avoids the limitations of traditional FFT algorithms when processing non-power-2 data points and improves computational efficiency.

[0067] 2. When the frequency offset is large, this invention first applies a Hanning window to the signal before performing hybrid basis subgroup algorithm analysis. The Hanning window effectively reduces and suppresses spectral leakage, ensuring that signals with large frequency offsets can still be accurately analyzed.

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

[0069] 4. This invention can accurately calculate the electrical energy and uncertainty of each harmonic, and control the total electrical energy uncertainty within 0.10%, thus ensuring the reliability of the harmonic analysis results.

[0070] In summary, this invention, by optimizing the signal processing flow and combining an innovative hybrid basis subgroup algorithm and windowing technology, solves problems such as frequency offset, sampling point limitations, and spectral leakage, significantly improving the accuracy and applicability of harmonic analysis. This method is widely applicable to power quality monitoring, harmonic pollution detection, load monitoring, and other application scenarios, and has high engineering application value. Attached Figure Description

[0071] Figure 1 This is a flowchart of the present invention;

[0072] Figure 2 This is a flowchart of the hybrid basis subgroup algorithm. Detailed Implementation

[0073] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0074] like Figure 1 A wide-frequency-range harmonic analysis method for electricity meters and data acquisition terminals, comprising the following steps:

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

[0076] The signal to be analyzed is typically a 50Hz fundamental frequency signal from a power system, containing multiple harmonic components and noise interference. Assume the sampling frequency is f. s=12800Hz, the number of sampling points is the product of 5 and 2 raised to the power of an integer, denoted as M = 5 * 2 R In this embodiment, the number of sampling points is 2560. Therefore, the signal duration is:

[0077]

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

[0079]

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

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

[0082] To quickly determine the fundamental frequency f0, the autocorrelation method is used to detect the fundamental period. The autocorrelation method has the advantages of low computational complexity and high adaptability, making it 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] Where i is the number of delay points of the signal, R x (i) represents the autocorrelation function value corresponding to the delay point i, M represents the number of sampling points of the signal, and x(n) represents the nth signal value in the acquired signal.

[0086] Step 2-2: Determine the fundamental period based on the autocorrelation function.

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

[0088]

[0089] Among them, f s This represents the signal acquisition frequency.

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

[0091]

[0092] In this embodiment, the sampling frequency fs =12800Hz, assuming the location of the first peak of the detected autocorrelation function is z1 = 256, then the fundamental frequency is: Step 3: Window the signal according to the frequency deviation of the collected voltage signal.

[0093] The specific process is as follows:

[0094] Step 3-1: Calculate the frequency deviation Δf:

[0095]

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

[0097] Step 3-2: Determine the relationship between the frequency offset rate Δf and the preset threshold. If it is less than or equal to the preset threshold (4% in this embodiment), the current acquired signal is directly used as the processed signal; otherwise, the acquired signal is windowed.

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

[0099]

[0100] Where ω(n) is the weighted value corresponding to the nth acquired signal value.

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

[0102] Step 4: Use the hybrid basis subgroup algorithm to transform and calculate the acquired current signal and the voltage signal processed in Step 3, respectively, to obtain the spectrum data of current and voltage. The hybrid basis subgroup algorithm first performs a 5-point WFTA transform, then a radix-2 FFT transform. For example... Figure 2 The specific process is as follows:

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

[0104]

[0105] Where, x in (n) represents the nth sampling point in the input signal of the hybrid basis subgroup algorithm.

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

[0107] Let the values ​​of a row in matrix X be respectively If ω5 = 0, 1, 2, 3, 4, then this row can be transformed using a 5-point WFTA method to obtain 5 complex values.

[0108]

[0109] Step 4-3, construct a 2 R Given a matrix Y of size × 5, if we take the five complex values ​​obtained by performing a 5-point WFTA transformation on each row of matrix X as the elements of the corresponding rows in matrix Y, then matrix Y is:

[0110]

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

[0112] Step 4-4: Perform 2x2 operations on each column of matrix Y. R Point-based radix-2 FFT transform:

[0113] Let the values ​​of a certain column in matrix Y be respectively In this embodiment, 2 R =512, then the column is processed according to the following formula 2. R Point radix-2 transformation yields 2 R A complex value

[0114]

[0115] Steps 4-5: Construct a 2 R Given a 5×5 matrix Z, the columns of matrix Y are transformed by 2... R The 2 obtained by point basis 2FFT transformation R If each complex value is used as an element of the corresponding column in matrix Z, then matrix Z is:

[0116]

[0117] in, For the c-th column of matrix Y, pass through 2 R The first point-radix 2 FFT transformation yields the... A complex value, Expanding matrix Z by rows yields the spectrum data for point M.

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

[0119] For the m-th harmonic, the formula for calculating harmonic energy is:

[0120] P m =Um ·I m ·cos(θ m );

[0121] Among them, U m Let I be the voltage amplitude of the m-th harmonic. m Let θ be the current amplitude of the m-th harmonic. m Let be the phase difference between the voltage and current of the m-th harmonic.

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

[0123] Step 6: Quantitatively evaluate and analyze the calculation results of harmonic energy, including uncertainty analysis of single harmonic energy, uncertainty analysis of total harmonic energy, and determination of total uncertainty at a specific confidence level.

[0124] Step 6-1, Uncertainty Analysis of Single Harmonic Energy:

[0125] For the m-th harmonic, the uncertainty of the harmonic energy u(P) m The calculation method for ) is as follows:

[0126]

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

[0128] Step 6-2, Analysis of the uncertainty of total electrical 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] Where e is the confidence factor at a confidence level of 95%, and in this embodiment e = 2.

[0134] The accuracy and reliability of this invention were verified through analysis of actual power signals. Comparative results show that, even with significant frequency deviation, the accuracy of harmonic amplitude and power calculations using this invention is significantly better than the traditional FFT method, with an uncertainty consistently less than 0.10%.

[0135] This invention successfully solves the problems of frequency offset and point count limitations by optimizing the signal processing flow and algorithm design, making it applicable to various power harmonic analysis scenarios and possessing significant engineering application value. It should be noted that, for those skilled in the art, it is obvious that this invention is not limited to the details of the above exemplary embodiments, and that it can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. The scope of this invention is defined by the claims rather than the foregoing description.

Claims

1. A wide frequency range harmonic analysis method for electric energy meters and collection terminals, characterized by the steps of Comprise: Step 1, collect voltage signal and current signal; sampling point number is a product of 5 and an integer power of 2: ; Step 2, determining the fundamental frequency of the collected voltage signal using autocorrelation method ; Step 3, according to the frequency deviation of the collected voltage signal, the signal is windowed; Specifically comprising: Step 3-1, based on fundamental frequency Computing frequency offset ; Step 3-2, judge the frequency offset rate If the size is less than or equal to the preset threshold, the current acquisition signal is directly used as the processed signal, otherwise the acquisition signal is subjected to window processing. Step 4, using hybrid basis subgroup algorithm to transform and calculate the collected current signal and the voltage signal after step 3 processing respectively, get the frequency spectrum data of current and voltage; In the hybrid basis subgroup algorithm, first 5-point WFTA transformation is carried out, and then base 2 FFT transformation is carried out; The specific process of hybrid basis subgroup algorithm is: Step 4-1, for the input signal of the hybrid basis sub-group algorithm, take every 5 sampling points as a row in the matrix in order, to get a matrix of ​ ； wherein, is the mth sample point in the input signal for the hybrid basis sub-algorithm; is the mth sample point in the input signal for the hybrid basis sub-algorithm; Step 4-2, 5-point WFTA transform on each row of the matrix respectively. Let matrix The values of a certain row in the matrix are , The row is then transformed by a 5-point WFTA to obtain 5 complex values : ； Step 4-3, construct a matrix of the matrix , transform each row of the matrix by the 5-point WFTA to obtain 5 complex values, and then use these 5 complex values as the elements of the corresponding row in the matrix , then the matrix is: ； wherein is a matrix in the row through the 5-point WFTA transform to obtain the complex value, ; Step 4 - 4, apply a point-wise 2 FFT transform to each column of the matrix point-wise 2 FFT transform:​ Let matrix The values of a certain column in the matrix are , The column is then processed according to Point base 2 transform gives complex values : ； Step 4-5, construct a matrix of size , where each column of the matrix is obtained by point-wise complex FFT transforming the complex values obtained from the corresponding column of the matrix , and the matrix is given by: ； wherein is a matrix in the column through point base 2 FFT transform to obtain the complex value, ; matrix in rows point spectral data; Step 5, based on the frequency spectrum data obtained in step 4, the harmonic electric energy is calculated; For the The formula for calculating harmonic energy is as follows: ； wherein is the voltage amplitude of the th harmonic, is the current amplitude of the th harmonic, is the phase difference of the th harmonic voltage and current; Step 6, the calculation results of harmonic electric energy are quantitatively evaluated and analyzed, including single harmonic electric energy uncertainty analysis, total harmonic electric energy uncertainty analysis and total uncertainty under a certain confidence level, specifically comprising: Step 6-1, single harmonic electric energy uncertainty analysis: For the first harmonic, the uncertainty of the harmonic power is calculated as: ； in, For the first The uncertainty of the amplitude of the second harmonic voltage is obtained by calibrating the instrument. For the first The uncertainty of the amplitude of the second harmonic current is obtained from the calibration data of the measuring equipment; For the first The phase angle uncertainty of the subharmonic was determined experimentally. Step 6 - 2nd harmonic to 1st Total electrical energy uncertainty analysis: ； Step 6-3, total uncertainty under a certain confidence level is determined: ； wherein is a confidence factor.

2. The wide frequency range harmonic analysis method for electric energy meters and collection terminals according to claim 1, characterized in that, In step 2, the steps of using autocorrelation method to realize the detection of fundamental wave period are as follows: Step 2-1, calculate autocorrelation function: ； wherein, is a delay point number of the signal, is a delay point number is a corresponding autocorrelation function value, is a sampling point number of the signal, is a signal value in the collected signal; and is a signal value in the collected signal. Step 2-2, determine the fundamental wave period according to the autocorrelation function; By analyzing the periodic peaks of the autocorrelation function, find the position of the first non-zero periodic peak , let the fundamental period corresponding to the position be: ； wherein, is the sampling frequency of the signal; Step 2-3, determine the fundamental wave frequency according to the fundamental wave period: 。 3. The wide frequency range harmonic analysis method for electric energy meters and collection terminals according to claim 1, characterized in that, The frequency offset rate calculated in step 3-1 The formula is: ； wherein is the fundamental frequency of the signal.

4. The wide frequency range harmonic analysis method for electric energy meters and collection terminals according to claim 3, characterized in that, The windowing processing in step 3-2 refers to Hanning windowing processing, and the window function is defined as: ； wherein, is the weighting value corresponding to the i-th acquired signal value; and is the weighting value corresponding to the i-th acquired signal value; and The first signal value in the windowed voltage signal is: .​ 5. The wide frequency range harmonic analysis method for electric energy meters and collection terminals according to claim 1, characterized in that: In step 5, for the 2nd harmonic, the amplitudes and phases of the voltage and current are determined by finding the corresponding complex value from the corresponding current frequency spectrum data or voltage frequency spectrum data according to the frequency resolution of the frequency spectrum data and the frequency corresponding to the 2nd harmonic, and converting the complex value to amplitude and phase. In step 5, for the 2nd harmonic, the amplitudes and phases of the voltage and current are determined by finding the corresponding complex value from the corresponding current frequency spectrum data or voltage frequency spectrum data according to the frequency resolution of the frequency spectrum data and the frequency corresponding to the 2nd harmonic, and converting the complex value to amplitude and phase.​

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