A power grid voltage sag detection method based on improved discrete fourier transform

Abstract

The application discloses a power grid voltage sag detection method based on improved discrete Fourier transform and belongs to the field of power quality detection. f (z), a resonator and an adjustment factor G a (z), so as to obtain a phase signal of a positive sequence fundamental component; S3: the module length of the phase signal of the positive sequence fundamental component is calculated, so as to obtain the amplitude of the positive sequence fundamental voltage; after the amplitude is compared with a power grid voltage sag detection threshold, whether the power grid voltage is sagged can be judged. The algorithm can realize accurate detection of the power grid voltage sag event under the non-ideal power grid condition of harmonic distortion and three-phase voltage imbalance.

Description

Technical Field

[0001] This invention belongs to the field of power quality detection, specifically relating to a method for detecting grid voltage sags based on an improved discrete Fourier transform. Background Technology

[0002] A class of grid voltage sag detection algorithms based on coordinate transformation are commonly used in industry. These algorithms are simple in structure and easy to implement. The most commonly used algorithms include the Synchronous Reference Frame-Phase Locked Loop (SRF-PLL) based on a synchronous rotating coordinate system, the Decoupled Double Synchronous Reference Frame-Phase Locked Loop (DDSRF-PLL) based on a decoupled dual synchronous rotating coordinate system, and the Double Second Order Generalized Integrator-Phase Locked Loop (DSOGI-PLL) based on a dual second-order generalized integrator. However, a closer analysis of these algorithms reveals that they all contain filters or structures with filter-like characteristics. When considering both filtering performance and dynamic performance, the algorithm's cutoff frequency will be on the same order of magnitude as the grid voltage fundamental frequency (50Hz), and the detection delay will also be on the same order of magnitude as the power frequency period (20ms). However, since the relevant standards stipulate that the switching time of parallel DVRs must not exceed 5ms, this delay is unacceptable.

[0003] Therefore, in order to reduce the delay caused by the detection algorithm, the filtering stage was improved by introducing Discrete Fourier Transform (DFT) as a filtering stage to reduce the impact of harmonics and negative sequence components on the grid voltage sag detection algorithm.

[0004] The Directional Transform (DFT) can transform a time-domain signal sequence into the frequency domain, thereby analyzing the spectral composition of the signal. Its input signal sequence can be either a scalar signal or a complex vector signal, making it highly suitable for harmonic extraction and analysis in three-phase systems, and thus for detecting voltage sags in three-phase power grids. The DFT algorithm for extracting the k-th order spectral unit with a complex vector signal sequence input is expressed as equation (1-1).

[0005]

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

[0007] The input is a 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 in the DFT algorithm.

[0011] N = f s / f0,f s f0 is the sampling frequency, and f0 is the fundamental frequency.

[0012] As shown in Equation (1-1), performing a DFT on a signal requires N sampling operations and multiple complex multiplications and additions, resulting in a huge computational load and high latency. Therefore, for applications with high real-time requirements, Equation (1-1) can be further derived by subtracting the k-th spectral unit calculated at the current time (n-1) from the k-th spectral unit calculated at the previous time (n-1). This yields the basic expression of the Sliding Discrete Fourier Transform (SDFT), as shown in Equation (1-2).

[0013]

[0014] While the SDFT shown in Equation (1-2) reduces the computational load, it does not reduce the delay; the resulting delay is still one fundamental period. Therefore, further improvements to the SDFT are needed. Re-examining Equation (1-1), although it provides the basic implementation method of the DFT, it is difficult to discern the mechanism for extracting the k-th harmonic. Therefore, the DFT algorithm will be re-analyzed from the perspective of the transfer function. From the inverse Fourier transform, the time-domain expression for the k-th harmonic at time n can be obtained, as shown in Equation (1-3).

[0015]

[0016] Combining equations (1-1) and (1-3), we obtain the expression shown in equation (1-4).

[0017]

[0018] Applying the Z-transform to both sides of equation (1-4) yields the expression shown in equation (1-5).

[0019]

[0020] By rearranging equation (1-5), we obtain the DFT transfer function expression for extracting the k-th harmonic, as shown in equation (1-6).

[0021]

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

[0023] Part 1: Comb Filter G f (z) can filter out specific frequency components in the input signal. When the number of samples N in the DFT algorithm is 25 and the fundamental frequency ω0 is 100π, the comb filter G in formula (1-6) can be used to achieve this. f The expression for (z) can be used to plot the Bode plot of its transfer function, as follows: Figure 2 As shown. It can be seen that G f (z) The amplitude gain is 0 at the harmonic frequency (±kω0, k=0,1,…,(N / 2)-1), and the phase is piecewise linearly distributed between 90° and -90°.

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

[0025]

[0026] The second part is the resonator acting on the k-th harmonic component. It introduces a pole at kω0 in the z-domain to cancel the comb filter G. f (z) is at the zero point, so the component signal with frequency kω0 in the input signal can be extracted. Figure 3 The pole-zero plot of the DFT algorithm is given, from which the pole-zero cancellation process can be clearly observed. It should be noted that, due to the resonator... The introduced poles are filtered by the comb filter G f (z) cancels out, so there is only a zero in the system and the system is absolutely stable.

[0027] After the first two comb filters G f (z) and resonator After processing, only the target signal frequency (kω0) remains in the spectrum of the input signal, but its amplitude and phase are different from the component signal with frequency kω0 in the original signal. Therefore, a third adjustment factor G is needed. a(z) is used for correction. It should be noted that the adjustment factor G... a (z) is a constant and will not introduce additional zeros or poles into the system. Therefore, it will not affect the stability of the system. Its purpose is only to ensure that the DFT algorithm has unity gain and zero phase shift at the kth frequency.

[0028] For grid voltage sag detection algorithms, the core objective is to quickly extract the positive-sequence fundamental frequency component from the grid voltage signal, which perfectly aligns with the function of the DFT algorithm. Simply by... Figure 1 In the DFT algorithm structure diagram shown, the value of k is set to +1, which can complete the extraction of the positive sequence fundamental frequency component and thus realize the detection of grid voltage sag.

[0029] From the analysis of the mechanism of the DFT algorithm for extracting the positive-sequence fundamental frequency component, it is not difficult to find that regardless of the type of harmonic components contained in the original input signal, the comb filter G... f (z) introduces N zeros, but obviously not all of these N zeros will be effective, leading to redundancy and waste of zeros and affecting the dynamic performance of the algorithm. Furthermore, the introduction of N zeros will affect the comb filter G. f (z) has N delay elements, which will ensure that the algorithm's delay is at least one fundamental frequency period. Removing redundant zeros will shorten the algorithm's delay time and improve its dynamic performance. Summary of the Invention

[0030] To address the above shortcomings, this invention provides a 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 existing detection methods.

[0031] The technical solution adopted in this invention is as follows: A method for detecting grid voltage sag based on improved discrete Fourier transform, comprising the following steps:

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

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

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

[0035] S21: Comb filter G f(z) Introduce a set of zeros at the harmonic frequencies and the negative-sequence fundamental frequency to completely filter out integer multiples of the fundamental frequency, including the positive-sequence fundamental frequency component; the expression for the zeros is shown in formula (2-1).

[0036]

[0037] Comb filter G f The expression for (z) is shown in formula (2-2).

[0038]

[0039] From formula (2-2), we can see that the comb filter contains a delay element z^(-N / 6). When N / 6 is not an integer, a 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 decimal part of N / 6, N ε =N / 6-N m ;

[0043] The fractional delay is approximated by a filter based on Lagrange interpolation, as shown in equation (2-4), where the coefficient A k From formula (2-5),

[0044]

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

[0046]

[0047] S22: Resonator A pole located at the positive-sequence fundamental frequency is introduced to cancel 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).

[0048]

[0049] When implementing this resonator in a digital system, the input signal can first be shifted by -ω0 in the frequency domain, then the signal can be passed through a DC component resonator, and finally the signal can be shifted by +ω0 in the frequency domain to indirectly achieve resonance of the input signal at +ω0.

[0050] Among them, the DC component resonator The expression 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 To address the phase shift and amplitude gain caused by the positive-sequence fundamental frequency component, and to achieve unity gain and zero phase shift in the overall DFT algorithm at the positive-sequence fundamental frequency, the adjustment factor G is used. a (z) As shown in formula (2-9),

[0053]

[0054] S3: Calculate the magnitude of the positive sequence fundamental frequency component phasor signal to obtain the amplitude of the positive sequence fundamental frequency voltage. Compare it with the grid voltage sag detection threshold to determine whether the grid voltage has sagged.

[0055] Another objective of this invention is to provide a power grid voltage sag detection system based on an 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, it implements a power grid voltage sag detection method based on an improved discrete Fourier transform as described above.

[0056] Advantages and benefits of this invention: The algorithm of this invention can accurately detect voltage sag events in a non-ideal power grid under conditions of harmonic distortion and three-phase voltage imbalance. Its detection delay can reach T0 / 6+T. s (T0 is the fundamental frequency period of the power grid, 20ms, T s (Considering the system sampling delay), the detection delay in conventional digital control systems can typically be controlled within 5ms, significantly shortening the response time compared to traditional algorithms. Applying the detection algorithm provided by this invention to power grid voltage sag mitigation equipment can significantly improve the equipment's rapid response capability, thereby enhancing the reliability of the power supply system. Attached Figure Description

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

[0058] Figure 2 For comb filter G f (z) Bode plot of transfer function (N=25, ω0=100π);

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

[0060] Figure 4 Bode plots for transfer functions with different exact fractional delays and their approximate implementations (n=3);

[0061] Figure 5 The diagrams show a comparison of the resonator structure before and after the improvement: (a) the resonator structure before improvement, and (b) the resonator structure after improvement.

[0062] Figure 6 The structure diagram of the proposed improved DFT algorithm is shown below;

[0063] Figure 7 The figures show the simulation results of various grid voltage sag detection algorithms under different non-ideal grid conditions. Detailed Implementation

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

[0065] Example 1

[0066] A method for detecting grid voltage sags based on an improved discrete Fourier transform, comprising the following steps:

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

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

[0069] S3: Calculate the magnitude of the positive sequence fundamental frequency component phasor signal to obtain the amplitude of the positive sequence fundamental frequency voltage. Compare it with the grid voltage sag detection threshold to determine whether the grid voltage has sagged.

[0070] The steps for extracting the positive-sequence fundamental frequency component are as follows:

[0071] S21: Comb filter G f (z) Introduce a set of zeros at integer multiples of the fundamental frequency to completely filter out integer multiples of the fundamental frequency, including the positive-sequence fundamental frequency component.

[0072] S22: Resonator A pole located at the positive-sequence fundamental frequency is introduced to cancel 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 the comb filter G. f (z) and resonator The phase shift and amplitude gain caused by the positive-sequence fundamental frequency component are reduced to achieve unity gain and zero phase shift in the overall DFT algorithm at the positive-sequence fundamental frequency.

[0074] In this embodiment, the comb filter G f The improved method for (z) is as follows:

[0075] In the DFT algorithm, only the comb filter G... f (z) introduces zeros, therefore the focus of algorithm improvement is on the comb filter G. f (z), first consider eliminating the 6k+1th harmonic component in the power grid. To eliminate this cluster of harmonic components, the zeros introduced by the comb filter need to fall at the 6k+1th harmonic frequency. In the z domain, the expression for the zeros to be introduced is shown in formula (3-1).

[0076]

[0077] The zero group shown in formula (3-1) has an arithmetic sequence of frequencies with a common difference of 6, which means that the interval between the frequencies of each zero is 6. Therefore, we first consider removing the zeros whose frequencies are not multiples of 6 based on formula (1-7), so that all the zeros fall at the 6k harmonic frequency, as shown in formula (3-2).

[0078]

[0079] Furthermore, if it is desired that the zero group falls at the 6k+1th harmonic frequency, it is necessary to modify formula (3-2) by rotating the zero group, as shown in formula (3-3).

[0080]

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

[0082]

[0083] As shown in formula (3-4), the improved comb filter contains a delay element z^(-N / 6). When N / 6 is not an integer, a fractional delay will occur, as shown in formula (3-5).

[0084]

[0085] In the formula N m —The integer part of N / 6;

[0086] N ε —The decimal part of N / 6, N ε =N / 6-N m

[0087] Fractional delay can be implemented in various ways. In this embodiment, a filter based on Lagrange interpolation is used to approximate the fractional delay, as shown in formula (3-6), where the coefficient A... k It can be obtained from formula (3-7).

[0088]

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

[0090]

[0091] To measure the accuracy of the fractional delay approximation achieved by the filter based on Lagrange interpolation when n=3, based on formula (3-8), such as Figure 4 As shown, when N ε Bode plots of the exact fractional delay and its approximate realization transfer function at 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 a third-order filter based on Lagrange interpolation. As can be seen from the figure, F d (z) and F ad The frequency response curve of (z) has high similarity over a wide frequency range, so a third-order filter based on Lagrange interpolation can be used to approximate the fractional delay.

[0092] It is easy to see from formula (3-4) that the delay introduced by the improved comb filter is only T0 / 6+T s (T0 represents the fundamental frequency period, T) s (representing the sampling period), compared to a T introduced by the comb filter in the traditional DFT algorithm. sThe delay is significantly reduced, which is undoubtedly a major advantage for meeting the requirement of rapid voltage sag detection. After the comb filter removes all harmonic components in the power grid, the resonator can then... and adjustment factor G a (z) Restore the positive-sequence fundamental frequency component in the input signal sequence to complete the detection of the grid voltage sag. This embodiment describes the resonator... The improvement method is as follows:

[0093] For resonators In essence, its function is to introduce a pole at the positive-sequence fundamental frequency, thereby achieving zero-pole cancellation to extract the positive-sequence fundamental frequency component. Since the resonator's function remains unchanged before and after the DFT algorithm improvement, no changes are made to the resonator transfer function; the expression is the same as in formula (1-6). The expression.

[0094] But by Figure 3 It can be seen that the resonator The introduced pole lies on the unit circle, and theoretically, this pole can cancel out the zero introduced by the comb filter at this point, allowing the system to operate stably. However, in practical engineering, the word length of digital systems is finite. Therefore, a certain amount of quantization error is inevitable in the process of implementing the resonator twiddle factor exp(j2π / N). This error may cause the introduced pole to be off-circle. If the pole happens to deviate from the unit circle, the system will become unstable, which is extremely detrimental to the entire system. Therefore, how to avoid system instability caused by quantization errors during the digital implementation of the resonator has become the key to improving the resonator.

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

[0096]

[0097] Based on this, this embodiment performs an equivalent transformation on the structure diagram of the resonator in the traditional DFT algorithm, such as... Figure 5 As shown. Among them, Figure 5 (a) shows the structure of the resonator in the traditional DFT algorithm. The rotation factor exp(j2π / N) is located in the feedback channel. If there is a quantization error in its implementation, it may lead to system instability. Unlike... Figure 5 (a) directly introduces the pole z = exp(j2π / N). Figure 5(b) shows the improved resonator structure. First, the input signal is shifted by -ω0 in the frequency domain, then it passes through the DC component resonator, and finally the signal is shifted by +ω0 in the frequency domain. This indirectly achieves the resonance of the input signal at ω0. The complex rotation factor is cleverly moved 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] The equivalence of the resonators before and after the improvement will be discussed below. For the improved resonator, formula (3-10) holds true.

[0099]

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

[0101]

[0102] By combining equations (3-10) and (3-11), equation (3-12) holds true.

[0103]

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

[0105]

[0106] Compare the resonator before improvement in formula (1-7) The expression and formula (3-13) show the improved resonator. From the expression, it is not difficult to see that the resonators before and after the improvement are equivalent. However, since the improved resonator moves the complex rotation factor out of the feedback channel, the system stability is guaranteed.

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

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

[0109] When the DFT algorithm has unity gain and zero phase shift at the positive-sequence fundamental frequency, equation (3-14) holds true.

[0110]

[0111] However, it is not difficult to see that when z→exp(j2π / N), both the numerator and denominator of formula (3-14) tend to 0, making it impossible to directly solve for the adjustment factor G. a The value of (z) is determined by L'Hôpital's rule, as shown in formula (3-15).

[0112]

[0113] In the formula G f ′(z)——G f (z) is the differential of the variable z.

[0114] By combining equations (3-14) and (3-15), the adjustment factor G can be obtained. a The value of (z) is shown in formula (3-16).

[0115]

[0116] The final result is as follows Figure 6 The diagram shows the improved structure for extracting the positive-sequence fundamental frequency component according to the present invention.

[0117] Example 2

[0118] To verify the performance of the network voltage sag detection method based on the improved DFT proposed in Example 1, a corresponding simulation model was built, and it was 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 mains voltage sag detection algorithm.

[0120]

[0121] It is worth noting that, to fully verify the robustness, accuracy, and speed of the proposed detection algorithm under non-ideal power grid conditions, it is necessary to consider the case with the maximum detection algorithm delay, i.e., the minimum voltage sag depth. Therefore, the voltage sag depth is set to 0.1 in the simulation. The simulation includes the following non-ideal power grid conditions: unbalanced sags, phase jumps, and harmonic interference: (All conditions consider background harmonics of the 5th negative sequence and the 7th positive sequence).

[0122] 1) Condition 1: A sag of depth U occurred in the three-phase power grid. dep Symmetric voltage dip events;

[0123] 2) Operating Condition 2: A sag of depth U occurred in the three-phase power grid. dep The asymmetrical voltage sag event (voltage sag occurs only in phases b and c) is accompanied by a phase jump;

[0124] 3) Operating Condition 3: A sag depth of U occurred in the three-phase power grid. dep The asymmetrical voltage sag event (voltage sag occurs only in phases b and c) is accompanied by abrupt changes in the amplitude of the 3rd zero-sequence and 5th negative-sequence harmonics.

[0125] In addition, to demonstrate the superiority of the proposed voltage sag detection algorithm, traditional SRF-PLL, DSOGI-PLL, and DDSRF-PLL voltage sag detection algorithms were also implemented in the simulation. Figure 7 Simulation results of various grid voltage sag detection algorithms under different non-ideal grid conditions are presented. The speedliness of the grid voltage sag detection algorithm can be demonstrated by the detection delay t. d The characterization is the time interval from the occurrence of a voltage sag event to the reduction of the fundamental positive sequence amplitude output by the detection algorithm to the sag threshold.

Claims

1. A method for detecting voltage sags in power grids based on an improved discrete Fourier transform, characterized in that, The steps are as follows: S1: Using 3s / 2s coordinate transformation, the three-phase grid voltage signal in the three-phase stationary coordinate system (a,b,c) is transformed into the two-phase stationary coordinate system (α,β); S2: Pass the voltage signal in coordinate system (α,β) through the comb filter G sequentially. f (z), Resonator G r +1 (z) and adjustment factor G a (z) is used to obtain the phasor signal of the positive sequence fundamental frequency component; The steps for extracting the positive-sequence fundamental frequency component are as follows: S21: Comb filter G f (z) Introduce a set of zeros at the harmonic frequencies and the negative-sequence fundamental frequency to completely filter out integer multiples of the fundamental frequency, including the positive-sequence fundamental frequency component; the expression for the zeros is shown in formula (2-1). Comb filter G f The expression for (z) is shown in formula (2-2). From formula (2-2), we can see that the comb filter contains a delay element z^(-N / 6). When N / 6 is not an integer, a fractional delay will occur, as shown in formula (2-3). In the formula N m —The integer part of N / 6; N ε —The decimal part of N / 6, N ε =N / 6-N m ; The fractional delay is approximated by a filter based on Lagrange interpolation, as shown in equation (2-4), where the coefficient A k From formula (2-5), When n takes the value 3 The approximate expression is shown in formula (2-6). S22: Resonator A pole located at the positive-sequence fundamental frequency is introduced to cancel 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. Finally, the signal is shifted by +ω0 in the frequency domain to indirectly achieve resonance of the input signal at +ω0. The DC component resonator H... r 0 The expression is shown in formula (2-8). S23: Adjustment factor G a (z) is used to compensate the comb filter G. f (z) and resonator To address the phase shift and amplitude gain caused by the positive-sequence fundamental frequency component, and to achieve unity gain and zero phase shift in the overall DFT algorithm at the positive-sequence fundamental frequency, the adjustment factor G is used. a (z) As shown in formula (2-9), S3: Calculate the magnitude of the positive sequence fundamental frequency component phasor signal to obtain the amplitude of the positive sequence fundamental frequency voltage. Compare it with the grid voltage sag detection threshold to determine whether the grid voltage has sagged.

2. A power 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, it implements a grid voltage sag detection method based on an improved discrete Fourier transform as described in claim 1.

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