Harmonic detection method based on sliding DFT

Abstract

The invention discloses a harmonic detection method based on sliding DFT, and relates to the technical field of power control and protection, and the method comprises the steps: sampling a voltage signal and a current signal of a to-be-measured power distribution network, and obtaining a discrete voltage signal and a discrete current signal; obtaining amplitude data and phase data based on the discrete voltage signal and the discrete current signal, respectively obtaining an amplitude square differential signal and a phase differential signal based on the amplitude data and the phase data, and respectively obtaining an amplitude variance and a phase variance based on the amplitude square differential signal and the phase differential signal; and obtaining a discrimination result based on the amplitude variance and the phase variance, thereby solving the problem that the optimization rate of a power system and the accuracy rate of a fault diagnosis result are low due to errors of a sampling data operation result caused by the lack of discrimination of whether secondary / inter-harmonics exist or not in a power distribution network protection and measurement device.

Description

Technical Field

[0001] The present invention relates to the technical field of power control and protection, and in particular to a harmonic detection method based on sliding DFT. Background Art

[0002] In the distribution network, real-time monitoring of power parameters is crucial to ensure the safe and stable operation of the distribution network. Usually, protection and measurement devices are required to sample signals. Through sampling, the measured values ​​of grid frequency, fundamental voltage and fundamental current amplitude, phase, active power, reactive power, harmonics and other parameters are obtained in time, so as to realize real-time monitoring and protection of the power system. The sampled digital signal is also used for further data processing and analysis, such as applying algorithms such as discrete Fourier transform (DFT) to the sampled data to analyze the amplitude and phase of the fundamental voltage and current of the signal, and at the same time calculate the amplitude and phase of each harmonic voltage and current as needed, so as to realize the optimized operation and fault diagnosis of the power system.

[0003] The sampling principle of the current device is: take the fundamental period corresponding to the power frequency as the benchmark (for example, when the power frequency is 50Hz, the fundamental period is 20ms, which is taken as the benchmark), sample N points at equal intervals in each fundamental period, perform operations on these N points, and continuously take points and perform operations in this way. When the voltage and current signals do not contain sub- / inter-harmonics, the signal can be approximately considered as a band-limited periodic signal. At this time, the above sampling process is synchronous sampling at equal intervals, and the amplitude and phase results calculated by DFT are accurate; but when the voltage and current signals contain sub- / inter-harmonics, the signal is no longer a band-limited periodic signal, and the DFT results will have errors, resulting in low optimization rate of the power system and low accuracy of fault diagnosis results.

[0004] Moreover, most existing algorithms assume the existence of sub-harmonics and inter-harmonics and achieve targeted and accurate measurements, which results in a large amount of computation. Summary of the invention

[0005] In order to solve the problem that the protection and measurement devices of the distribution network lack the ability to distinguish whether sub-harmonics or inter-harmonics exist, which leads to errors in the calculation results of the sampling data, and further leads to low optimization rate and accuracy of fault diagnosis results of the power system, the present invention provides a harmonic detection method based on sliding DFT, the method comprising: sampling the voltage signal and the current signal of the distribution network to be measured to obtain a discrete voltage signal and a discrete current signal; obtaining voltage amplitude data and voltage phase data based on the discrete voltage signal, and obtaining current amplitude data and current phase data based on the discrete current signal; obtaining voltage amplitude square difference signal and current phase data based on the voltage amplitude data and the current amplitude data, respectively. A current amplitude square difference signal is obtained based on the voltage phase data and the current phase data to obtain a voltage phase difference signal and a current phase difference signal respectively; a voltage amplitude variance and a current amplitude variance are obtained based on the voltage amplitude square difference signal and the current amplitude square difference signal respectively; a voltage phase variance and a current phase variance are obtained based on the voltage phase difference signal and the current phase difference signal respectively; a voltage discrimination result is obtained based on the voltage amplitude variance and the voltage phase variance, a current discrimination result is obtained based on the current phase variance and the current amplitude variance, and a discrimination result is obtained based on the voltage discrimination result and the current discrimination result.

[0006] The principle of the present invention is as follows: the voltage and current signals are sampled based on the fundamental wave period to obtain discrete signals of the voltage and current, the discrete signals are subjected to sliding discrete Fourier transform point by point, the amplitude and phase of the fundamental wave component are obtained, the square difference and variance of the amplitude are calculated in turn, the difference and variance of the phase are calculated, and then compared with the threshold value to determine whether sub-harmonics or inter-harmonics exist; the fluctuation degree of the amplitude and phase results after the sliding discrete Fourier transform of the voltage and current signals is quantitatively analyzed to determine whether sub-harmonics or inter-harmonics exist in the signal, thereby selectively enabling the correction algorithm or the sub-harmonics or inter-harmonics precise measurement algorithm, thereby improving the operation efficiency and the measurement accuracy of the protection and measurement devices, and improving the optimization rate of the power system and the accuracy of the fault diagnosis results.

[0007] Sliding Discrete Fourier Transform (SDFT), a method for calculating the local spectrum of a signal, can apply discrete Fourier transform on a sliding window of the signal to obtain information about the signal at different times and frequencies.

[0008] A discrete signal is a signal obtained by sampling a continuous signal.

[0009] The fundamental component refers to the component with ordinal number 1 in the Fourier series of a periodic quantity.

[0010] Furthermore, the sampling method is: performing synchronous sampling at equal intervals based on the fundamental wave period.

[0011] Furthermore, the method obtains amplitude data and phase data based on a first preset method, wherein the first preset method is: obtaining a number of sampling points of each fundamental wave period of the input signal, exchanging each of the sampling points, obtaining a number of fundamental wave results, obtaining the fundamental wave amplitude and fundamental wave phase of each of the fundamental wave results based on the fundamental wave component, and obtaining amplitude data and phase data. Since the voltage and current signals are mainly fundamental waves, the presence or absence of sub-harmonics and inter-harmonics will have an effect on the fundamental wave amplitude and phase of the voltage and current that is significantly different from other interferences. Taking the amplitude and phase of the fundamental wave component will make the discrimination feature quantity obvious and the discrimination accuracy high.

[0012] Furthermore, the method obtains a square difference signal based on a second preset method, and the second preset method is: obtaining the kth first numerical value and the k+1th second numerical value in the input signal, obtaining the square value of the first numerical value and the second numerical value, obtaining the first square value and the second square value respectively, obtaining the square difference between the second square value and the first square value, and obtaining the kth square difference signal.

[0013] Furthermore, the method obtains a differential signal based on a third preset method, and the third preset method is: obtaining the kth third value and the k+1th fourth value in the input signal, obtaining the difference between the third value and the fourth value, and obtaining the kth differential signal.

[0014] Furthermore, the method obtains the variance based on a fourth preset method, and the fourth preset method is: obtaining the variance of the input signal based on a preset average value. Setting the average value simplifies the calculation, reduces the amount of calculation, and makes the determination process simple and fast.

[0015] Furthermore, the specific steps for obtaining the judgment result include: judging whether the voltage amplitude variance exceeds the first threshold value, and whether the voltage phase variance exceeds the second threshold value, if both conditions are met, the voltage has inter-harmonics; judging whether the current amplitude variance exceeds the third threshold value, and whether the current phase variance exceeds the fourth threshold value, if both conditions are met, the current has inter-harmonics.

[0016] Furthermore, a first calculation formula for obtaining the voltage amplitude square difference signal and the current amplitude square difference signal is:

[0017] A(k)=U1 2 (k);

[0018] dA(k)=A(k+1)-A(k);

[0019] Where A(k) represents the square of the kth fundamental wave amplitude, U1(k) represents the kth fundamental wave amplitude, k represents the sequence number, and dA(k) represents the value of the square difference of the kth fundamental wave amplitude;

[0020] The second calculation formula for obtaining the voltage phase differential signal and the current phase differential signal is:

[0021] dψ(k)=ψ(k+1)-ψ(k);

[0022] Among them, ψ(k) represents the kth fundamental wave phase, k represents the sequence number, and dψ(k) represents the value of the kth fundamental wave phase difference.

[0023] Furthermore, a third calculation method for obtaining the voltage amplitude variance and the current amplitude variance is:

[0024]

[0025] Among them, S A (k) represents the variance of the k-th amplitude square difference signal, k and i both represent serial numbers, N1 represents the number of sampling points when calculating the variance each time, dA(i) represents the k-th amplitude square difference signal, and 0 represents the average value.

[0026] Furthermore, a fourth calculation method for obtaining the voltage phase variance and the current phase variance is:

[0027]

[0028] Among them, S ψ (k) represents the variance of the kth phase difference signal, k and i both represent the serial numbers of the amplitude square difference signal, N1 represents the number of sampling points when calculating the variance each time, dψ(i) represents the kth phase difference signal, 2π / N represents the average value, and N represents the number of sampling points of the fundamental wave period.

[0029] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0030] 1. Sample the voltage and current signals based on the fundamental wave period to obtain discrete signals of voltage and current, perform sliding discrete Fourier transform on the discrete signals point by point, take the amplitude of the fundamental wave component, calculate the square difference and variance in turn, take the phase of the fundamental wave component, calculate the difference and variance in turn, and then compare with the threshold value to determine whether sub-harmonics / inter-harmonics exist; quantitatively analyze the fluctuation degree of the amplitude and phase results after sliding discrete Fourier transform of the voltage and current signals, accurately determine whether sub-harmonics / inter-harmonics exist in the signal, and selectively enable the correction algorithm or the sub-harmonic / inter-harmonic precise measurement algorithm, simplify the correction logic, improve the operation efficiency and the measurement accuracy of the protection and measurement devices, and improve the optimization rate of the power system and the accuracy of the fault diagnosis results.

[0031] 2. Based on the results of sliding DFT of discrete signals, the existence of sub-harmonics and inter-harmonics can be determined by solving the variance of simple differential sequences. The computational complexity is small, the determination process is simple and easy to implement, and it is easy to implement in embedded devices.

[0032] 3. Take the amplitude of the fundamental wave component, calculate the square difference and variance thereof in turn, take the phase of the fundamental wave component, calculate the difference and variance thereof in turn, the discrimination feature quantity is obvious and the discrimination accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation on the embodiments of the present invention;

[0034] Figure 1 It is a flow chart of a harmonic detection method based on sliding DFT in the present invention;

[0035] Figure 2 is the graph of the variance of the squared difference signal of the amplitude as a function of k when sub-harmonics / inter-harmonics exist;

[0036] Figure 3 is the graph of the variance of the phase difference signal as a function of k when subharmonics / interharmonics exist;

[0037] Figure 4 This is the graph of the variance of the amplitude square difference signal as a function of k when there are no sub-harmonics or inter-harmonics;

[0038] Figure 5 is the variation of the variance of the phase difference signal with k when there is no sub-harmonic or inter-harmonic;

[0039] Wherein, k represents the sequence number of the signal. DETAILED DESCRIPTION

[0040] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0041] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those within the scope of this description. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0042] Embodiment 1

[0043] refer to Figure 1 , this embodiment provides a harmonic detection method based on sliding DFT, the method comprising:

[0044] The voltage signal and the current signal of the distribution network to be measured are sampled to obtain discrete voltage signals and discrete current signals; wherein the sampling method is: synchronous sampling at equal intervals based on the fundamental wave period.

[0045] Voltage amplitude data and voltage phase data are obtained based on the discrete voltage signal, and current amplitude data and current phase data are obtained based on the discrete current signal; wherein, the method obtains the amplitude data and phase data of the voltage and current based on a first preset method, and the first preset method is: obtaining a number of sampling points of each fundamental wave period of the input signal, exchanging each of the sampling points, obtaining a number of fundamental wave results, obtaining the fundamental wave amplitude and fundamental wave phase of each of the fundamental wave results based on the fundamental wave component, and obtaining the amplitude data and phase data.

[0046] Based on the voltage amplitude data and the current amplitude data, a voltage amplitude square differential signal and a current amplitude square differential signal are obtained respectively; based on the voltage phase data and the current phase data, a voltage phase differential signal and a current phase differential signal are obtained respectively; wherein, the method obtains the amplitude square differential signal based on a second preset method, and the second preset method is: obtaining the kth first value and the k+1th second value in the input signal, obtaining the square values ​​of the first value and the second value, obtaining the first square value and the second square value respectively, obtaining the square difference between the second square value and the first square value, and obtaining the kth square differential signal; the method obtains the differential signal based on a third preset method, and the third preset method is: obtaining the kth third value and the k+1th fourth value in the input signal, obtaining the difference between the third value and the fourth value, and obtaining the kth differential signal.

[0047] Based on the voltage amplitude square difference signal and the current amplitude square difference signal, the voltage amplitude variance and the current amplitude variance are obtained respectively; based on the voltage phase differential signal and the current phase differential signal, the voltage phase variance and the current phase variance are obtained respectively; wherein, the method obtains the variance based on a fourth preset method, and the fourth preset method is: based on a preset average value, obtaining the variance of the input signal.

[0048] Based on the voltage amplitude variance and the voltage phase variance, a voltage discrimination result is obtained; based on the current phase variance and the current amplitude variance, a current discrimination result is obtained; and based on the voltage discrimination result and the current discrimination result, a discrimination result is obtained. The specific steps for obtaining the discrimination result include: judging whether the voltage amplitude variance exceeds the first threshold value, and whether the voltage phase variance exceeds the second threshold value, if both conditions are met, the voltage has inter-order harmonics; judging whether the current amplitude variance exceeds the third threshold value, and whether the current phase variance exceeds the fourth threshold value, if both conditions are met, the current has inter-order harmonics.

[0049] Embodiment 2

[0050] On the basis of the first embodiment, in this embodiment, the first calculation formula for obtaining the voltage amplitude square difference signal and the current amplitude square difference signal is:

[0051] A(k)=U1 2 (k);

[0052] dA(k)=A(k+1)-A(k);

[0053] Among them, A(k) represents the square of the kth fundamental wave amplitude, U1(k) represents the kth fundamental wave amplitude, k represents the sequence number, and dA(k) represents the value of the square difference of the kth fundamental wave amplitude.

[0054] The second calculation formula for obtaining the voltage phase differential signal and the current phase differential signal is:

[0055] dψ(k)=ψ(k+1)-ψ(k);

[0056] Among them, ψ(k) represents the kth fundamental wave phase, k represents the sequence number, and dψ(k) represents the value of the kth fundamental wave phase difference.

[0057] A third calculation method for obtaining the voltage amplitude variance and the current amplitude variance is:

[0058]

[0059] Among them, S A (k) represents the variance of the k-th amplitude square difference signal, k and i both represent serial numbers, N1 represents the number of sampling points when calculating the variance each time, dA(i) represents the k-th amplitude square difference signal, and 0 represents the average value.

[0060] A fourth calculation method for obtaining the voltage phase variance and the current phase variance is:

[0061]

[0062] Among them, Sψ (k) represents the variance of the kth phase difference signal, k and i both represent the serial numbers of the amplitude square difference signal, N1 represents the number of sampling points when calculating the variance each time, dψ(i) represents the kth phase difference signal, 2π / N represents the average value, and N represents the number of sampling points of the fundamental wave period.

[0063] Embodiment 3

[0064] refer to Figure 2-Figure 5 Based on the above embodiment, in this embodiment, an example is given to illustrate the existence of sub-harmonics and inter-harmonics:

[0065] Taking the voltage signal as an example, assuming that the voltage signal contains a subharmonic or interharmonic, the signal can be expressed as:

[0066]

[0067] Among them, f is the fundamental frequency of the signal, h is the harmonic number of the signal, H is the highest harmonic number of the signal, and U is h , are the amplitude and phase of the hth harmonic component of the signal, U p , are the amplitude and phase of the sub-harmonic component and inter-harmonic component respectively, p is the frequency coefficient of the sub-harmonic component and is a non-integer. When p<1, the component is a sub-harmonic, and when p>1, the component is an inter-harmonic. T represents time and j represents an imaginary unit. That is, the voltage signal containing sub-harmonic components can be expressed as the superposition of sub-harmonic signals and band-limited periodic signals, where the frequency of sub-harmonics can be expressed as pf.

[0068] The signal is sampled at equal intervals based on the cycle period to obtain a discrete voltage signal. Suppose the sampling interval is T S , then:

[0069]

[0070] Where N is the number of sampling points per fundamental wave.

[0071] Take a sampling point obtained from a fundamental wave period, that is, let n∈[k,N+k-1], k is a non-negative integer, then equation (2) becomes:

[0072]

[0073] Perform DFT operation on equation (3) and take the fundamental component, then we have:

[0074]

[0075]

[0076] Among them, U1, They represent the amplitude and phase of the fundamental voltage, that is, when h=1 in equation (1), U h , The value of

[0077] When there are no subharmonics or interharmonics, ρ p (1) = 0, then equation (4) becomes:

[0078]

[0079] Let k be a continuous natural number whose maximum value is K, then sliding DFT can be implemented. Each k corresponds to the k-th result. The amplitude and phase of each DFT fundamental wave result are calculated and stored. The fundamental wave amplitude and phase obtained for the k-th time are recorded as U(k) and ψ(k), respectively.

[0080] Find the square of the amplitude of the kth fundamental wave, expressed as A(k), that is:

[0081] A(k)=U 2 (k); (6)

[0082] The square difference signal of the amplitude and the phase difference signal are obtained by making a difference, which are expressed as dA(k) and dψ(k), that is:

[0083] dA(k)=A(k+1)-A(k); (8)

[0084] dψ(k)=ψ(k+1)-ψ(k); (9)

[0085] From equations (4) and (5), it can be seen that when there are no subharmonics or interharmonics, the differential signal of the DFT amplitude result is always 0, and the differential signal of the DFT phase result is always When subharmonics / interharmonics are present, the differential signal of the amplitude is no longer constant to 0, and the differential signal of the phase is no longer constant to

[0086] Therefore, to simplify the calculation, assume that the average values ​​of the amplitude square difference signal and the phase difference signal are 0 and The process of finding the variance is:

[0087]

[0088]

[0089] Assume that the amplitude threshold is ε1 and the phase threshold is ε2. A (k)>ε1 and s ψ When (k)>ε2, it is determined that there are sub-harmonics / inter-harmonics in the original signal, otherwise there are no sub-harmonics / inter-harmonics.

[0090] Since the actual voltage and current signals cannot contain only fundamental components, but also harmonic components, in order to better verify the accuracy of the solution in dealing with actual signals, the second harmonic is added in this embodiment.

[0091] Assuming that there are subharmonics and interharmonics, set f = 50 Hz, p = 1.44, U1 = 10, U2 = 1, U p =1, Among them, U2, They represent the amplitude and phase of the second harmonic respectively, that is, when h=2 in equation (1), U h , The value of is, N = 64, K = 1216, N1 = 64, the amplitude threshold ε1 = 0.05, the phase threshold ε2 = 0.005, then the variance of the amplitude square difference signal and the variance of the phase difference signal change with k as shown below: Figure 2 and Figure 3 As shown, they are all greater than the threshold value.

[0092] Assuming that there are no sub-harmonics or inter-harmonics, set f = 50 Hz, U1 = 10, U2 = 1, U p =1, N = 64, K = 1216, N1 = 64, amplitude threshold ε1 = 0.05, phase threshold ε2 = 0.005, then the variance of the amplitude square difference signal and the variance of the phase difference signal change with k as follows: Figure 4 and Figure 5 As shown, they are all smaller than the threshold value.

[0093] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0094] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A harmonic detection method based on sliding DFT, characterized in that: The method comprises: Sampling the voltage signal and the current signal of the distribution network to be measured to obtain a discrete voltage signal and a discrete current signal; Obtaining voltage amplitude data and voltage phase data based on the discrete voltage signal, and obtaining current amplitude data and current phase data based on the discrete current signal; obtaining a voltage amplitude square difference signal and a current amplitude square difference signal based on the voltage amplitude data and the current amplitude data, respectively, and obtaining a voltage phase difference signal and a current phase difference signal based on the voltage phase data and the current phase data, respectively; Based on the voltage amplitude square difference signal and the current amplitude square difference signal, a voltage amplitude variance and a current amplitude variance are obtained respectively; based on the voltage phase difference signal and the current phase difference signal, a voltage phase variance and a current phase variance are obtained respectively; A voltage discrimination result is obtained based on the voltage amplitude variance and the voltage phase variance, a current discrimination result is obtained based on the current phase variance and the current amplitude variance, and a discrimination result is obtained based on the voltage discrimination result and the current discrimination result.

2. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The sampling method is: synchronous sampling at equal intervals based on the fundamental wave period.

3. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The method obtains amplitude data and phase data based on a first preset method, wherein the first preset method is: Acquire several sampling points of each fundamental wave period of the input signal, perform DFT operation on each of the sampling points to obtain several fundamental wave results, obtain the fundamental wave amplitude and fundamental wave phase of each of the fundamental wave results based on the fundamental wave component, and obtain amplitude data and phase data.

4. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The method obtains a square difference signal based on a second preset method, where the second preset method is: Obtain the kth first value and the k+1th second value in the input signal, obtain the square values ​​of the first value and the second value, obtain the first square value and the second square value respectively, obtain the square difference between the second square value and the first square value, and obtain the kth square difference signal.

5. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The method obtains a differential signal based on a third preset method, and the third preset method is: The kth third value and the k+1th fourth value in the input signal are obtained, and the difference between the third value and the fourth value is obtained to obtain the kth differential signal.

6. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The method obtains the variance based on a fourth preset method, and the fourth preset method is: Based on the preset mean value, the variance of the input signal is obtained.

7. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The specific steps to obtain the discrimination results include: Determine whether the voltage amplitude variance exceeds the first threshold value, and whether the voltage phase variance exceeds the second threshold value. If both conditions are met, inter-harmonics exist in the voltage. Determine whether the current amplitude variance exceeds the third threshold value, and whether the current phase variance exceeds the fourth threshold value. If both conditions are met, inter-harmonics exist in the current.

8. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: The first calculation formula for obtaining the voltage amplitude square difference signal and the current amplitude square difference signal is: A(k)=U1 2 (to); dA(k)=A(k+1)-A(k); Where A(k) represents the square of the kth fundamental wave amplitude, U1(k) represents the kth fundamental wave amplitude, k represents the sequence number, and dA(k) represents the value of the square difference of the kth fundamental wave amplitude; The second calculation formula for obtaining the voltage phase differential signal and the current phase differential signal is: dψ(k)=ψ(k+1)-ψ(k); Among them, ψ(k) represents the kth fundamental wave phase, k represents the sequence number, and dψ(k) represents the value of the kth fundamental wave phase difference.

9. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: A third calculation method for obtaining the voltage amplitude variance and the current amplitude variance is: Among them, S A (k) represents the variance of the k-th amplitude square difference signal, k and i both represent serial numbers, N1 represents the number of sampling points when calculating the variance each time, dA(i) represents the k-th amplitude square difference signal, and 0 represents the average value.

10. The harmonic detection method based on sliding DFT according to claim 1, characterized in that: A fourth calculation method for obtaining the voltage phase variance and the current phase variance is: Among them, S ψ (k) represents the variance of the kth phase difference signal, k and i both represent the serial numbers of the amplitude square difference signal, N1 represents the number of sampling points when calculating the variance each time, dψ(i) represents the kth phase difference signal, 2π / N represents the average value, and N represents the number of sampling points of the fundamental wave period.

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