Power grid voltage sag detection method based on improved discrete Fourier transform

Abstract

The invention discloses a power grid voltage sag detection method based on improved discrete Fourier transform, and belongs to the field of power quality detection, and the method comprises the steps: S1, converting a three-phase power grid voltage signal under a three-phase static coordinate system (a, b, c) into a two-phase static coordinate system (alpha, beta) through 3s / 2s coordinate transformation; s2, enabling the voltage signal under the coordinate system (alpha, beta) to sequentially pass through a comb filter Gf (z), a resonator # imgabs0 # and an adjustment factor Ga (z) so as to obtain a phasor signal of a positive sequence fundamental frequency component; and S3, calculating the mode length of the positive sequence fundamental frequency component phasor signal to obtain the amplitude of the positive sequence fundamental frequency voltage, and comparing the amplitude with a power grid voltage sag detection threshold to judge whether the power grid voltage sags or not. According to the algorithm provided by the invention, the accurate detection of the voltage sag event of the power grid can be realized under the non-ideal power grid condition of harmonic distortion and three-phase voltage imbalance.

Description

Technical Field

[0001] The present invention belongs to the field of power quality detection, and particularly relates to a method for detecting grid voltage sags based on an improved discrete Fourier transform. Background Technique

[0002] A class of grid voltage sag detection algorithms based on coordinate transformation is a commonly used class of detection algorithms in the industrial field. This class of detection algorithms has a simple structure and is easy to implement. The most commonly used detection algorithms include the grid voltage sag detection algorithm based on a synchronous rotating coordinate system with a phase-locked loop (Synchronous Reference Frame-Phase Locked Loop, SRF-PLL), the detection algorithm based on a decoupled double synchronous rotating coordinate system with a phase-locked loop (Decoupled Double Synchronous Reference Frame-Phase Locked Loop, DDSRF-PLL), and the detection algorithm based on a double second-order generalized integrator with a phase-locked loop (Double Second Order Generalized Integrator-Phase Locked Loop, DSOGI-PLL). However, upon careful analysis of this class of detection algorithms, they all contain filters or structures similar to filter characteristics. When considering both filtering performance and dynamic performance, the cut-off frequency of the algorithm will be of the same order of magnitude as the fundamental frequency of the grid voltage (50 Hz), and the detection delay will also be of the same order of magnitude as the power frequency period (20 ms). However, since the relevant standard stipulates that the switching time of the shunt DVR shall not be greater than 5 ms, this delay time is unacceptable.

[0003] Therefore, in order to reduce the delay generated by the detection algorithm, the filtering link is improved by introducing the discrete Fourier transform (Discrete Fourier Transform, DFT) as the filtering link to reduce the influence of harmonic and negative sequence components on the grid voltage sag detection algorithm.

[0004] DFT can transform the time-domain signal sequence into the frequency domain, and then analyze the spectral composition of the signal. Its input signal sequence can be either a scalar signal or a complex vector signal, which is very suitable for harmonic extraction and analysis of a three-phase system, and thus can be used for the detection of three-phase grid voltage sags. The DFT algorithm expression for extracting the k-th spectral unit under the input of a complex vector signal sequence is shown in formula (1-1).

[0005]

[0006] In the formula, is the k-th spectral unit of the input signal, represented by a complex number;

[0007] is the input complex vector signal sequence;

[0008] n is the time-domain index value of the signal sequence;

[0009] k is the frequency-domain index value of the signal sequence;

[0010] N is the sequence length of each frame of the DFT algorithm,

[0011] N = f s / f 0 where f s is the sampling frequency and f 0 is the fundamental frequency.

[0012] As can be seen from Equation (1-1), when performing DFT on a signal, N samplings are required, and multiple complex multiplications and complex additions need to be performed. The amount of computation is extremely large, and the resulting delay is also relatively high. Therefore, for occasions with high real-time requirements, Equation (1-1) can be further derived. By subtracting the k-th spectral unit calculated at the current (n-th moment) from the k-th spectral unit calculated at the previous (n-1-th moment), the basic expression of the Sliding Discrete Fourier Transform (SDFT) can be derived, as shown in Equation (1-2).

[0013]

[0014] Although the SDFT shown in Equation (1-2) reduces the amount of computation, it does not reduce the delay. The resulting delay is still one fundamental period. Therefore, it is necessary to consider further improving the SDFT. Re-examining Equation (1-1), although this equation gives the basic implementation method of the DFT, it is difficult to see the mechanism of extracting the k-th harmonic. Therefore, the DFT algorithm will be re-analyzed from the perspective of the transfer function below. From the inverse Fourier transform, the time-domain expression of the k-th harmonic at time n can be obtained, as shown in Equation (1-3).

[0015]

[0016] By combining Equation (1-1) and Equation (1-3), the expression shown in Equation (1-4) is obtained.

[0017]

[0018] By performing the Z-transform on both sides of Equation (1-4), the expression shown in Equation (1-5) is obtained.

[0019]

[0020] By appropriately arranging Equation (1-5), the DFT transfer function expression for extracting the k-th harmonic is obtained, as shown in Equation (1-6).

[0021]

[0022] As shown in Equation (1-6), the DFT algorithm essentially consists of three parts, which are respectively named the comb filter G f (z), the resonator and the adjustment factor G a (z), as Figure 1 shown.

[0023] The first part, the comb filter G f (z), can achieve the filtering of specific frequency components in the input signal. When the number of samples N in the DFT algorithm takes the value of 25 and the fundamental frequency ω 0 takes the value of 100π, the Bode plot of its transfer function can be drawn from the expression of the comb filter G f (z) in Equation (1-6), as Figure 2 shown. It can be seen that the amplitude gain of G f (z) is 0 at the harmonic frequencies (±kω 0 , k = 0, 1, …, (N / 2)-1), and the phase is linearly distributed in segments between 90° and -90°.

[0024] Through certain mathematical derivations, the transfer function of the comb filter G f (z) is decomposed, as shown in Equation (1-7).

[0025]

[0026] The second part is the resonator acting on the k-th harmonic component which introduces a pole at kω 0 in the z-domain to cancel the zero at this point of the comb filter G f (z), so that the component signal with a frequency of kω 0 in the input signal can be extracted. Figure 3 The zero-pole diagram of the DFT algorithm is given, and the process of zero-pole cancellation can be clearly observed from the figure. It should be noted that since the pole introduced by the resonator is canceled by the comb filter G f (z), there are only zeros in the system, and the system is absolutely stable.

[0027] After the processing of the first two parts, the comb filter G f (z) and the resonator , only the target signal frequency (kω 0), but its amplitude and phase are different from the component signal with frequency kω in the original signal. Therefore, the third part of the adjustment factor G 0 (z) is needed for correction. It should be noted that the adjustment factor G a (z) is a constant and will not introduce additional zeros and poles to the system. Therefore, it will not affect the stability of the system. Its purpose is only to ensure that the DFT algorithm has the characteristics of unit gain and zero phase shift at the kth frequency. a (z) is a constant and will not introduce additional zeros and poles to the system. Therefore, it will not affect the stability of the system. Its purpose is only to ensure that the DFT algorithm has the characteristics of unit gain and zero phase shift at the kth frequency.

[0028] For the power grid voltage sag detection algorithm, its core goal is to quickly extract the positive-sequence fundamental frequency component in the power grid voltage signal, which perfectly matches the function of the DFT algorithm. Just set Figure 1 the k value in the DFT algorithm structure diagram shown to +1, and the extraction of the positive-sequence fundamental frequency component can be completed, and then the detection of the power grid voltage sag can be realized.

[0029] From the process of analyzing the mechanism of the DFT algorithm for extracting the positive-sequence fundamental frequency component, it is not difficult to find that no matter what type of harmonic components are included in the original input signal, the comb filter G f (z) will introduce N zeros. However, obviously not all of these N zeros will play a role, which will cause redundancy and waste of zeros and affect the dynamic performance of the algorithm. In addition, the introduction of N zeros will make the comb filter G f (z) have N delay links, which will make the delay of the algorithm at least one fundamental wave period. If the redundant zeros can be removed, the delay time of the algorithm will be shortened, and the dynamic performance of the algorithm will be improved at the same time. Summary of the Invention

[0030] Based on the above deficiencies, the present invention provides a power grid voltage sag detection method based on an improved discrete Fourier transform, which can solve the problems of high delay and low dynamic performance of the existing detection methods.

[0031] The technical solution adopted by the present invention is as follows: A power grid voltage sag detection method based on an improved discrete Fourier transform, the steps are as follows:

[0032] S1: Use the 3s / 2s coordinate transformation to transform the three-phase power grid voltage signal in the three-phase stationary coordinate system (a, b, c) into the two-phase stationary coordinate system (α, β);

[0033] S2: Make the voltage signal in the coordinate system (α, β) pass through the comb filter G f (z), the resonator and the adjustment factor G a (z) in sequence to obtain the phasor signal of the positive-sequence fundamental frequency component;

[0034] Among them, the steps for extracting the positive-sequence fundamental frequency component are as follows:

[0035] S21: Comb Filter G f (z) Introduces a cluster of zeros at the harmonic frequencies and the negative-sequence fundamental frequency, and completely filters out the integer-multiple fundamental frequency components including the positive-sequence fundamental frequency component; among them, the expression of the zero is shown in Formula (2-1).

[0036]

[0037] Comb Filter G f (z) The expression is shown in Formula (2-2).

[0038]

[0039] It can be obtained from Formula (2-2) that the comb filter contains a delay link z^(-N / 6). When N / 6 is not an integer, fractional delay will occur, as shown in Formula (2-3).

[0040]

[0041] In the formula, N m —— The integer part of N / 6;

[0042] N ε —— The fractional part of N / 6, N ε = N / 6 - N m ;

[0043] The fractional delay is approximately realized by using a filter based on the Lagrange interpolation method, as shown in Formula (2-4), where the coefficient A k is obtained from Formula (2-5).

[0044]

[0045] When n takes the value of 3, The approximate expression is shown in Formula (2-6).

[0046]

[0047] S22: Resonator Introduces a pole at the positive-sequence fundamental frequency to cancel the zero introduced by Step S21 at the positive-sequence fundamental frequency, so as to achieve the purpose of extracting the positive-sequence fundamental frequency component while filtering out other harmonics. Its expression is shown in Formula (2-7).

[0048]

[0049] When implementing this resonator in a digital system, the input signal can be first shifted by -ω in the frequency domain 0 , then the signal is passed through a DC component resonator, and finally the signal is shifted by +ω in the frequency domain0 , in an indirect way to realize the input signal at +ω 0 The resonance at

[0050] Wherein, the DC component resonator The expression of is shown in formula (2-8),

[0051]

[0052] S23: Adjustment factor G a (z) is used to compensate the comb filter G f (z) and resonator The phase shift and amplitude gain caused by the positive sequence fundamental frequency component are adjusted to achieve the characteristics of unity gain and zero phase shift of the overall DFT algorithm at the positive sequence fundamental frequency. a (z) As shown in formula (2-9),

[0053]

[0054] S3: Obtain the modulus length of the positive-sequence fundamental frequency component phasor signal to obtain the amplitude of the positive-sequence fundamental frequency voltage, and compare it with the grid voltage sag detection threshold to determine whether the grid voltage has a sag.

[0055] Another object of the present invention is to provide a grid voltage sag detection system based on improved discrete Fourier transform, comprising: a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: when the computer program is executed by the processor, the grid voltage sag detection method based on improved discrete Fourier transform as described above is implemented.

[0056] Advantages and beneficial effects of the present invention: The algorithm of the present invention can accurately detect grid voltage sag events under non-ideal grid conditions of harmonic distortion and three-phase voltage imbalance. Its detection delay can reach T 0 / 6+T s (T 0 The fundamental period of the power grid is 20ms, T s The detection delay in conventional digital control systems can usually be controlled within 5ms, which significantly shortens the response time compared with traditional algorithms. If the detection algorithm provided by the present invention is applied to grid voltage sag control equipment, the rapid response capability of the grid voltage sag control equipment can be significantly improved, thereby enhancing the reliability of the power supply system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a structural diagram based on the DFT algorithm;

[0058] Figure 2For comb filter G f (z) Bode plot of the transfer function (N = 25, ω 0 = 100π);

[0059] Figure 3 Is the zero - pole plot of the DFT algorithm (N = 25);

[0060] Figure 4 Is the Bode plot of the transfer functions of different exact fractional delay and its approximate implementation (n = 3);

[0061] Figure 5 Is the comparison diagram of the resonator structure diagrams before and after improvement, (a) resonator structure diagram before improvement, (b) resonator structure diagram after improvement;

[0062] Figure 6 Is the structure diagram of the proposed improved DFT algorithm;

[0063] Figure 7 Is the simulation result diagram of various grid voltage sag detection algorithms under different non - ideal grid conditions. Detailed implementation manners

[0064] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0065] Embodiment 1

[0066] A grid voltage sag detection method based on an improved discrete Fourier transform, the steps are as follows:

[0067] S1: Using the 3s / 2s coordinate transformation, transform the three - phase grid voltage signal in the three - phase stationary coordinate system (a, b, c) into the two - phase stationary coordinate system (α, β);

[0068] S2: Make the voltage signal in the coordinate system (α, β) pass through the comb filter G f (z), resonator and the adjustment factor G a (z) in sequence to obtain the phasor signal of the positive - sequence fundamental - frequency component;

[0069] S3: Obtain the magnitude of the phasor signal of the positive - sequence fundamental - frequency component to get the amplitude of the positive - sequence fundamental - frequency voltage. After comparing it with the grid voltage sag detection threshold, it can be determined whether the grid voltage has a sag.

[0070] Among them, the steps of extracting the positive - sequence fundamental - frequency component are as follows:

[0071] S21: Comb filter G f(z) Introduces a cluster of zeros at integer multiples of the fundamental frequency, completely filtering out the integer multiple fundamental frequency components including the positive-sequence fundamental frequency component;

[0072] S22: Resonator Introduces a pole at the positive-sequence fundamental frequency to cancel out the zero introduced by S21 at the positive-sequence fundamental frequency, thereby achieving the purpose of extracting the positive-sequence fundamental frequency component while filtering out other harmonics;

[0073] S23: Adjustment factor G a (z) Is used to compensate for the phase shift and amplitude gain caused by the comb filter G f (z) And the resonator To achieve the characteristics that the overall DFT algorithm has unit gain and zero phase shift at the positive-sequence fundamental frequency.

[0074] Among them, the comb filter G described in this embodiment f (z) The improvement method is as follows:

[0075] In the DFT algorithm, only the comb filter G f (z) Will introduce zeros, so the key to algorithm improvement is the comb filter G f (z). First, consider eliminating the 6k + 1 harmonic components in the power grid. To eliminate this cluster of harmonic components, the zeros introduced by the comb filter need to fall at the 6k + 1 harmonic frequencies. Then, in the z-domain, the zero expression to be introduced is as shown in formula (3-1).

[0076]

[0077] The frequencies of the zero groups shown in formula (3-1) form an arithmetic sequence, and its common difference is 6, which means the spacing between the frequencies of each zero is 6. Therefore, first consider removing the zeros whose frequencies are not integer multiples of 6 based on formula (1-7), so that the zeros all fall at the 6k harmonic frequencies, as shown in formula (3-2).

[0078]

[0079] Furthermore, if it is desired that the zero group falls at the 6k + 1 harmonic frequency, formula (3-2) also needs to be modified to rotate the zero group, as shown in formula (3-3).

[0080]

[0081] Secondly, in order to filter out the negative-sequence fundamental frequency component (i.e., the -1st harmonic) simultaneously, it is necessary to cascade a -1st harmonic filter on the basis of the 6k + 1st harmonic filter to achieve the purpose of filtering out all harmonics in the original grid voltage signal. Then the final expression of the improved comb filter is shown in Equation (3-4).

[0082]

[0083] As can be seen from Equation (3-4), the improved comb filter contains a delay link \(z^{(-N / 6)}\). When \(N / 6\) is not an integer, fractional delay will occur, as shown in Equation (3-5).

[0084]

[0085] where \(N\) m —— the integer part of \(N / 6\);

[0086] \(N\) ε —— the fractional part of \(N / 6\), \(N\) ε \(= N / 6 - N\) m

[0087] The implementation of fractional delay can take various forms. In this embodiment, the fractional delay is approximately realized by a filter based on the Lagrange interpolation method, as shown in Equation (3-6), where the coefficient \(A\) k can be obtained from Equation (3-7).

[0088]

[0089] Specifically, when \(n\) takes the value of 3, the approximate expression is shown in Equation (3-8).

[0090]

[0091] To measure the accuracy of the approximate realization of fractional delay by the filter based on the Lagrange interpolation method when \(n = 3\), based on Equation (3-8), as Figure 4 shown, the Bode plots of the exact fractional delay and its approximate realization transfer function are given when \(N\) ε is 0.1 and 0.5 respectively. In the figure, \(F\) d (z) represents the Bode plot of the exact fractional delay, while \(F\) ad (z) represents the Bode plot of the transfer function of the third-order filter based on the Lagrange interpolation method. It can be seen from the figure that the frequency response curves of \(F\) d (z) and \(F\) ad (z) have high similarity in a relatively wide frequency range. Therefore, a third-order filter based on the Lagrange interpolation method can be selected to approximately realize fractional delay.

[0092] It is not difficult to find from formula (3-4) that the delay introduced by the improved comb filter is only T 0 / 6 + T s (T 0 represents the fundamental frequency period, and T s represents the sampling period), which is much smaller than the delay of one T s introduced by the comb filter in the traditional DFT algorithm. This is undoubtedly very beneficial for the requirement of fast detection of grid voltage sags. After the comb filter filters out all the harmonic components contained in the power grid, the positive-sequence fundamental frequency component in the input signal sequence can be restored by the resonator and the adjustment factor G a (z) to complete the detection of grid voltage sags. The improvement method of the resonator described in this embodiment is as follows:

[0093] For the resonator , its function is to introduce poles at the positive-sequence fundamental frequency, so as to achieve zero-pole cancellation to extract the positive-sequence fundamental frequency component. Since the function of the resonator remains unchanged before and after the improvement of the DFT algorithm, no change is made to the transfer function of the resonator, and the expression is the same as that in formula (1-6) .

[0094] However, as Figure 3 can be seen, the poles introduced by the resonator are located on the unit circle. In theory, these poles can cancel the zeros introduced by the comb filter at this point, and the system can operate stably. However, in actual engineering, the word length of the digital system is limited. Therefore, there will inevitably be a certain quantization error in the process of implementing the rotation factor exp(j2π / N) of the resonator. This error may cause the introduced poles not to be on the unit circle. If the poles happen to deviate outside the unit circle, the system will become unstable, which is very terrible for the entire system. Therefore, how to avoid the system instability phenomenon that may be caused by quantization errors in the process of digital implementation of the resonator has become the idea for improving the resonator.

[0095] In particular, when the rotation factor contained in the resonator is 1, that is, when poles are introduced at the DC component, there will be no decimals in the resonator, and the pole of z = 1 can be accurately introduced into the system. At this time, the expression of the DC component resonator is as shown in formula (3-9).

[0096]

[0097] Based on this, the structure diagram of the resonator in the traditional DFT algorithm is equivalently transformed in this embodiment, as Figure 5 shown. Among them, Figure 5(a) is the structural diagram of the resonator in the traditional DFT algorithm. The rotation factor exp(j2π / N) is located in the feedback channel. If there is quantization error in its implementation process, it may lead to system instability. Different from Figure 5 the way of directly introducing the pole z = exp(j2π / N) in (a), Figure 5 (b) shows that the improved resonator structural diagram first moves the input signal by -ω in the frequency domain 0 , then passes through the DC component resonator, and finally moves the signal by +ω in the frequency domain 0 , achieving the resonance of the input signal at ω 0 in an indirect way, and cleverly moving the complex rotation factor from the feedback channel to the forward channel. In this way, poles can be accurately introduced into the system, effectively avoiding the system instability problem caused by quantization error.

[0098] Next, the equivalence of the resonator before and after improvement will be discussed. For the improved resonator, formula (3-10) holds.

[0099]

[0100] From formula (3-10), formula (3-11) holds.

[0101]

[0102] Combining formula (3-10) and formula (3-11), formula (3-12) holds.

[0103]

[0104] From formula (3-12), the transfer function of the improved resonator can be obtained, as shown in formula (3-13).

[0105]

[0106] Comparing the expression of the resonator before improvement in formula (1-7) with the expression of the improved resonator shown in formula (3-13) , it is not difficult to find that the resonators before and after improvement are equivalent. However, since the complex rotation factor of the improved resonator is moved out of the feedback channel, the system stability is guaranteed.

[0107] The improvement method of the adjustment factor G a (z) described in this embodiment is as follows:

[0108] It can be known from formula (1-7) that in the traditional DFT algorithm, the adjustment factor G a (z) = 1 / N. However, since the comb filter G in this embodiment has beenf The transfer function of (z) has been modified, so the adjustment factors also need to be changed accordingly to ensure that the entire algorithm exhibits unity gain and zero phase shift characteristics at the positive sequence fundamental frequency.

[0109] When the DFT algorithm has the characteristics of unit gain and zero phase shift at the positive sequence fundamental frequency, formula (3-14) holds.

[0110]

[0111] However, it is not difficult to see that when z→exp(j2π / N), the numerator and denominator of formula (3-14) tend to 0, and the adjustment factor G cannot be directly solved. a (z), so consider using L’Hôpital’s rule to solve it, as shown in formula (3-15).

[0112]

[0113] Where G f ′(z)——G f (z) Differentiate the variable z.

[0114] Combining formula (3-14) and formula (3-15), we can get the adjustment factor G a The value of (z) is shown in formula (3-16).

[0115]

[0116] Finally, we get Figure 6 As shown, the improved structural diagram of the present invention for extracting the positive sequence fundamental frequency component.

[0117] Example 2

[0118] In order to verify the performance of the network voltage sag detection method based on improved DFT proposed in Example 1, a corresponding simulation model was built and compared with other traditional detection algorithms in the simulation. The detailed simulation parameters are shown in Table 1.

[0119] Table 1 Parameters involved in simulating the grid voltage sag detection algorithm

[0120]

[0121] It is worth noting that in order to fully test the robustness, accuracy and speed of the proposed detection algorithm under non-ideal grid conditions, it is necessary to consider the case where the detection algorithm has the largest delay, that is, the case where the voltage sag depth is the smallest. Therefore, the voltage sag depth is set to 0.1 in the simulation. The following non-ideal grid conditions are simulated in the simulation, including unbalanced sag, phase jump and harmonic interference: (all conditions consider the 5th negative sequence and 7th positive sequence background harmonics)

[0122] 1) Condition 1: A symmetrical voltage sag event with a sag depth of U dep occurs in the three-phase power grid;

[0123] 2) Condition 2: An asymmetrical voltage sag event with a sag depth of U dep occurs in the three-phase power grid (only voltage sags occur in phases b and c), accompanied by phase jumps;

[0124] 3) Condition 3: An asymmetrical voltage sag event with a sag depth of U dep occurs in the three-phase power grid (only voltage sags occur in phases b and c), accompanied by sudden changes in the amplitudes of the 3rd zero-sequence and 5th negative-sequence harmonics.

[0125] In addition, in order to demonstrate the superiority of the proposed grid voltage sag detection algorithm, traditional grid voltage sag detection algorithms such as SRF-PLL, DSOGI-PLL, and DDSRF-PLL are also implemented in the simulation. Figure 7 The simulation results of various grid voltage sag detection algorithms under different non-ideal grid conditions are given. Among them, the rapidity of the grid voltage sag detection algorithm can be characterized by the detection delay t d , which is the time interval from the occurrence of the grid voltage sag event to the output of the detection algorithm when the fundamental positive-sequence amplitude drops to the sag threshold.

Claims

1. A method for detecting grid voltage sag based on improved discrete Fourier transform, characterized in that: Here are the steps: S1: Use 3s / 2s coordinate transformation to transform the three-phase grid voltage signal in the three-phase stationary coordinate system (a, b, c) into the two-phase stationary coordinate system (α, β); S2: Make the voltage signal under the coordinate system (α, β) pass through the comb filter G in sequence f (z), resonator G r +1 (z) and adjustment factor G a (z), to obtain the phasor signal of the positive sequence fundamental frequency component; The steps of extracting the positive sequence fundamental frequency component are as follows: S21: Comb filter G f (z) A cluster of zero points is introduced at the harmonic frequency and the negative sequence fundamental frequency to completely filter out the integer multiple fundamental frequency components including the positive sequence fundamental frequency components; the expression of the zero point is shown in formula (2-1), Comb filter G f The expression of (z) is shown in formula (2-2), From formula (2-2), it can be concluded that the comb filter contains a delay link z^(-N / 6). When N / 6 is not an integer, a fractional delay will occur, as shown in formula (2-3). Where N m ——the integer part of N / 6; N ε ——The fractional part of N / 6, N ε =N / 6-N m ; The fractional delay is realized by using a filter approximation based on Lagrange interpolation method, as shown in formula (2-4), where the coefficient A k From formula (2-5), we can get: When n is 3, The approximate expression of is shown in formula (2-6), S22: Resonator A pole located at the positive sequence fundamental frequency is introduced to offset the zero introduced at the positive sequence fundamental frequency in step S21, thereby achieving the purpose of extracting the positive sequence fundamental frequency component while filtering out other harmonics. Its expression is shown in formula (2-7), First, the input signal is shifted by -ω0 in the frequency domain, then the signal is passed through a DC component resonator, and finally the signal is shifted by +ω0 in the frequency domain to indirectly realize the resonance of the input signal at +ω0; wherein the DC component resonator H r 0 The expression of is shown in formula (2-8), S23: Adjustment factor G a (z) is used to compensate the comb filter G f (z) and resonator The phase shift and amplitude gain caused by the positive sequence fundamental frequency component are adjusted to achieve the characteristics of unity gain and zero phase shift of the overall DFT algorithm at the positive sequence fundamental frequency. a (z) As shown in formula (2-9), S3: Obtain the modulus length of the positive-sequence fundamental frequency component phasor signal to obtain the amplitude of the positive-sequence fundamental frequency voltage, and compare it with the grid voltage sag detection threshold to determine whether the grid voltage has a sag.

2. A grid voltage sag detection system based on improved discrete Fourier transform, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that when the computer program is executed by the processor, a method for detecting a grid voltage sag based on an improved discrete Fourier transform as claimed in claim 1 is implemented.

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