Frequency and amplitude phase estimation method of cosine jump signal based on DFT (Discrete Fourier Transform)

Abstract

The invention discloses a DFT (Discrete Fourier Transform)-based frequency and amplitude-phase estimation method of a cosine jump signal. The method aims at realizing accurate detection and efficient processing of amplitude-phase parameter step change of the cosine signal. According to the method, for signals with unknown jump points, the approximate range of the jump points can be estimated through a sliding window method, signal parameter values are obtained through a frequency estimation method at all possible step points in the range so as to reconstruct the signals, errors between the signals and input signals are calculated, and the point corresponding to the minimum absolute error is the needed jump point. And after the jump point is determined, performing parameter estimation on the signal by adopting the frequency estimation method again. According to the method, through innovative jump point determination and frequency estimation steps and in combination with DFT bins near the maximum peak value, the calculation amount is remarkably reduced while the signal parameter estimation precision is improved, and therefore the problems that in the prior art, precision is insufficient, calculation complexity is high, and applicability is limited are effectively solved.

Description

Technical Field

[0001] The present invention relates to a method for estimating the frequency and amplitude-phase of a cosine jump signal, and particularly to a method for estimating the frequency and amplitude-phase of a cosine jump signal based on DFT. Background Art

[0002] In a rapidly expanding power grid, phasor measurement is crucial for grid monitoring, control, and security. During the instability process of the power transmission and distribution system, a stable and accurate measurement technique is required for calculating the electrical signal parameters. The components of power system signals are all real-valued sine signals. In this regard, the interpolated discrete Fourier transform (IpDFT) method starts from a real-valued sine model and is suitable for the background of power system signal measurement applications. However, the parameter step change signal is one of the most critical and fundamental signal types in the power system. The step change can be interpreted as a sudden transition between two steady-state conditions. This discontinuity is difficult to represent with a slow-modulated sine signal model, which is traditionally used in many power system monitoring and management units (PMUs). One possible solution includes applying step detection techniques and adjusting the estimation algorithm accordingly, but these solutions require too much computational effort to be implemented in a real-time PMU system. As an outstanding representative of frequency-domain methods, the IpDFT-based methods have played an important role in phasor estimation in recent decades. Due to their high computational speed and simplified hardware implementation, they are widely used in PMU tests. However, when some parameters in the sampling sequence undergo step changes, the Fourier transform (DFT) coefficients will be distorted, resulting in an estimation error problem when using the IpDFT method. Therefore, it is very crucial to study the frequency of the step parameter real-valued sine model estimated by the IpDFT method, and the key challenge lies in not only fully eliminating the influence of step parameters but also fully eliminating the influence of the fence effect and spectral leakage on the results.

[0003] When the amplitude-phase parameters of a cosine signal undergo step changes, traditional signal processing methods often have difficulty accurately determining the jump point position and precisely estimating the frequency of the signal. In the prior art, for signals with known jump points, although the frequency can be estimated by some methods, in the case where the jump points are unknown, the parameter estimation accuracy of the signal is low, and the computational complexity is high, making it difficult to meet the high requirements for signal processing accuracy and efficiency in practical applications. In addition, when dealing with signals, existing methods often cannot balance accuracy and computational effort simultaneously, resulting in certain limitations in practical applications. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention proposes a method for estimating the frequency and amplitude-phase of a cosine jump signal based on DFT.

[0005] The technical solution of the present invention is as follows:

[0006] A method for estimating the frequency, amplitude and phase of a cosine jump signal based on DFT, comprising:

[0007] Step 1) Establish a cosine jump signal model, simplify the estimator based on the cosine jump signal model, convert the direct estimator composed of frequency and step points into an intermediate estimator, and establish a received signal vector;

[0008] Step 2) For a signal with a known step position, after performing DFT transformation on the received signal vector, select different DFT spectral lines to construct an equation, solve the equation to determine the intermediate estimator, use 5 DFT bins to establish a matrix solution model, and solve the frequency, amplitude and phase of the signal by matrix inversion;

[0009] Step 3) For a signal with an unknown step position, first calculate the frequency through a no-step algorithm. If there is a large jump in the frequency, it means a step occurs, and at the same time, determine the approximate position of the step. Based on Step 2), first construct an initial signal, then calculate the reconstruction error. Through iterative calculation, select the step position corresponding to the signal with the smallest error as the step position of the signal at this moment, and then perform fine estimation to determine the frequency and amplitude and phase of the signal.

[0010] Further, the specific method for establishing a cosine jump signal model, simplifying the estimator based on the cosine jump signal model, converting the direct estimator composed of frequency and step points into an intermediate estimator, and establishing a received signal vector includes:

[0011] Establish a cosine jump signal model. The real-valued sine signal under noise conditions can be expressed as:

[0012] y(n) = s(n) + q(n) (1)

[0013] In the formula, q(n) is additive white Gaussian noise with a variance of ;

[0014] When a parameter step change occurs, the signal s(n) can be expressed as:

[0015]

[0016] In the formula, V m and are the m-th amplitude and phase of the unknown modulation signal, m = 1, 2, and the parameter changes at P; ω0 = 2πf0 / f s is the angular frequency, where f0 is the signal frequency and f s is the sampling frequency;

[0017] When obtaining a sequence s(n) with length N, the normalized frequency is rewritten as ω0 = 2πl0 / N = 2π(k0 + δ0) / N, where l0 is the frequency of the signal, and its integer part and fractional part are k0 and δ0 respectively. The value range of k0 is [0, 1, …, N - 1], and the value range of δ0 is [-0.5, 0.5].

[0018] Furthermore, for a signal with a known step position, after performing DFT transformation on the received signal vector, different DFT spectral lines are selected to construct an equation, and the intermediate estimator is determined by solving the equation. The specific method for solving the frequency and amplitude-phase of the signal by establishing a matrix solution model using 5 DFT bins and performing matrix inversion includes:

[0019] Let S(k) be the DFT transformation of the sequence s(n). S(k) can be obtained as follows:

[0020]

[0021] where

[0022]

[0023] Furthermore, it can be obtained that:

[0024]

[0025] where

[0026] When obtaining five different DFT bins S(k i ) near the maximum peak, where i = 1, 2, …, 5, the following linear equation is obtained:

[0027] S = Wη(6)

[0028] where

[0029]

[0030] η = [a1, a2, a3, a4, b] (8)

[0031]

[0032] According to formula (6), η is estimated as:

[0033]

[0034] where and Y are the observed values of W and S under noise conditions, denotes the estimated value of ·;

[0035] Based on b = cos(ω0), the angular frequency ω0 is estimated as:

[0036]

[0037] When ω0 is estimated, Equation (3) is reformulated as:

[0038]

[0039] Where:

[0040]

[0041] Simplified to:

[0042] W Aest μ = 2S′ (14)

[0043] Where:

[0044] μ = [μ1, μ2, μ3, μ4] T (15)

[0045] S′ = [S(k1), S(k2), S(k3), S(k4)] T (16)

[0047]

[0048] In the presence of noise, Y represents the observed value of S'. Using any four different DFT bins Y(k i ), i = 1, 2, 3, 4, we get:

[0049]

[0050] Adopt a matrix solution method to solve for the variable μ, thereby determining the amplitude and phase values;

[0051] When μ1, μ2, μ3, and μ4 can be estimated, V1, V2, and are estimated as:

[0052]

[0053] Furthermore, for a signal with an unknown step position, first calculate the frequency through a step - free algorithm. If there is a large jump in the frequency, it indicates the occurrence of a step, and at the same time, roughly determine the position of the step. Based on step 2), first construct the initial signal, then calculate the reconstruction error. Through iterative calculation, select the step position corresponding to the signal with the smallest error as the step position of the signal at that moment, and then perform fine estimation to determine the specific method of the frequency and amplitude - phase of the signal, including:

[0054] When using the wrong ω0, formulas (11) and (19) are used to estimate the frequency, amplitude, and phase, thereby forming an estimated signal:

[0055]

[0056] where V1′, V2′, and ω0′ are the estimated signal parameters, and the k-th DFT bin of the estimated signal has a mutation, which is described as:

[0057]

[0058] The reconstruction error is expressed as:

[0059]

[0060] Obviously, when P' is equal to P, |s(n) - s′(n)| is the smallest. When estimating with the wrong P' under noise conditions, let ε s represent the sum of the reconstruction errors between the estimated signal and the original noise signal:

[0061]

[0062] ε s is the smallest when P' is equal to P. Find the minimum value of ε s corresponding to it That is, the jump point P. After determining the jump point P, the signal is accurately estimated by the method proposed in step 2) to determine the frequency and amplitude-phase of the signal.

[0063] An electronic device, the electronic device includes a memory and a processor, the memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to execute the method described in any one of the above.

[0064] A computer-readable storage medium, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the steps of the method described in any one of the above.

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

[0066] The present invention proposes a method for estimating the frequency and amplitude-phase of a cosine jump signal based on DFT, which aims to achieve accurate detection and efficient processing of the step changes in the amplitude-phase parameters of the cosine signal. For a signal with unknown jump points, this method can estimate the approximate range of the jump points using a sliding window method. For each jump point within this range, a frequency estimation method is used to obtain the signal parameter values to reconstruct the signal, and the error from the input signal is calculated. The point corresponding to the minimum absolute error is the required jump point. After determining the jump point, the frequency estimation method is used again to estimate the signal parameters. Through innovative jump point determination and frequency estimation steps, combined with DFT bins near the maximum peak, this method significantly reduces the computational complexity while improving the accuracy of signal parameter estimation, effectively solving the problems of insufficient accuracy, high computational complexity, and limited applicability in the prior art, and providing a more efficient, accurate, and practical technical solution for the fields of signal processing and frequency analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flowchart of the method for estimating the frequency and amplitude-phase of a cosine jump signal based on DFT in the embodiment;

[0068] Figure 2(a) is a schematic diagram of the reconstruction error ε corresponding to l0 = 2.55 and N = 128 in the embodiment s Schematic diagram;

[0069] Figure 2(b) is a schematic diagram of the reconstruction error ε corresponding to l0 = 2.55 and N = 256 in the embodiment s Schematic diagram;

[0070] Figure 2(c) is a schematic diagram of the reconstruction error ε corresponding to l0 = 2.55 and N = 512 in the embodiment s Schematic diagram;

[0071] Figure 2(d) is a schematic diagram of the reconstruction error ε corresponding to l0 = 2.55 and N = 1024 in the embodiment s Schematic diagram;

[0072] Figure 3 It is a schematic diagram of TVE, FE, and RFE during the amplitude step test in the embodiment;

[0073] Figure 4 It is a schematic diagram of TVE, FE, and RFE during the phase step test in the embodiment;

[0074] Figure 5 It is a schematic diagram of the frequency estimation result when SNR = 70dB in the embodiment;

[0075] Figure 6(a) is a schematic diagram of the instantaneous signal of the current corresponding to Example 1 in the embodiment;

[0076] Figure 6(b) is a schematic diagram of the instantaneous signal of the current corresponding to Example 2 in the embodiments. Detailed implementation manners

[0077] The present invention will be further illustrated below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0078] Embodiment 1:

[0079] A method for estimating the frequency, amplitude and phase of a cosine jump signal based on DFT according to the present invention, as Figures 1 to 6(b) shown, includes:

[0080] Step 1) Establish a cosine jump signal model, simplify the estimator based on the cosine jump signal model, convert the direct estimator composed of frequency and step points into an intermediate estimator, and establish a received signal vector;

[0081] Step 2) For a signal with a known step position, after performing DFT transformation on the received signal vector, select different DFT spectral lines to construct an equation, solve the equation to determine the intermediate estimator, use 5 DFT bins to establish a matrix solution model, and solve the frequency, amplitude and phase of the signal by matrix inversion;

[0082] Step 3) For a signal with an unknown step position, first calculate the frequency through a no-step algorithm. If a large jump in frequency occurs, it means a step occurs, and at the same time, roughly determine the position of the step. Based on Step 2, first construct an initial signal, then calculate the reconstruction error. Through iterative calculation, select the step position corresponding to the signal with the smallest error as the step position of the signal at this moment, and then perform fine estimation to determine the frequency, amplitude and phase of the signal.

[0083] Further, the specific method for establishing a cosine jump signal model, simplifying the estimator based on the cosine jump signal model, converting the direct estimator composed of frequency and step points into an intermediate estimator, and establishing a received signal vector includes:

[0084] Establish a cosine jump signal model. A real-valued sinusoidal signal under noise conditions can be expressed as:

[0085] y(n) = s(n) + q(n) (1)

[0086] In the formula, q(n) is additive white Gaussian noise (AWGN) with a variance of ;

[0087] When a parametric step change occurs, the signal s(n) can be expressed as:

[0088]

[0089] Wherein, V m and are the m-th amplitude and phase of the unknown modulation signal, where m = 1, 2, and the parameter changes at P; ω0 = 2πf0 / f s is the angular frequency, where f0 is the signal frequency and f s is the sampling frequency;

[0090] When obtaining the sequence s(n) with length N, the normalized frequency is rewritten as ω0 = 2πl0 / N = 2π(k0 + δ0) / N, where l0 is the number of cycles of the signal, and its integer part and fractional part are k0 and δ0 respectively. The value range of k0 is [0, 1,..., N - 1], and the value range of δ0 is [-0.5, 0.5].

[0091] Furthermore, for the signal with known step position, after performing DFT transformation on the received signal vector, different DFT spectral lines are selected to construct an equation, and the intermediate estimator is determined by solving the equation. The specific method for solving the frequency and amplitude-phase of the signal by using 5 DFT bins to establish a matrix solution model and through matrix inversion includes:

[0092] Let S(k) be the DFT transform of the sequence s(n), S(k) can be obtained:

[0093]

[0094] Wherein,

[0095]

[0096] Furthermore, it is obtained that:

[0097]

[0098] Wherein,

[0099] When obtaining five different DFT bins S(k i ) near the maximum peak, where i = 1, 2,..., 5, the following linear equation is obtained:

[0100] S = Wη(6)

[0101] Wherein,

[0102]

[0103] η = [a1, a2, a3, a4, b] (8)

[0104]

[0105] According to Equation (6), η is estimated as:

[0106]

[0107] where, and Y are the observed values of W and S under noise conditions, represents the estimated value of ·;

[0108] According to b = cos(ω0), the angular frequency ω0 is estimated as:

[0109]

[0110] When ω0 is estimated, Equation (3) is reformulated as:

[0111]

[0112] where:

[0113]

[0114] Simplified to:

[0115] W Aest μ = 2S′ (14)

[0116] where:

[0117] μ = [μ1, μ2, μ3, μ4] T (15)

[0118] S′ = [S(k1), S(k2), S(k3), S(k4)] T (16)

[0120]

[0121] Therefore, only four different DFT bins are needed to solve for the parameters. In the presence of noise, Y represents the observed value of S'. Using any four different DFT bins Y(k i ), i = 1, 2, 3, 4, we get:

[0122]

[0123] Adopt a matrix solution method similar to that used for frequency estimation to solve for the variable μ, thereby determining the amplitude and phase values;

[0124] When μ1, μ2, μ3, and μ4 can be estimated, V1, V2, and is estimated to be:

[0125]

[0126] Furthermore, for a signal with an unknown step position, first calculate the frequency through a step - free algorithm. If there is a large jump in the frequency, it indicates the occurrence of a step, and at the same time, roughly determine the position of the step. Based on step 2), first construct the initial signal, then calculate the reconstruction error. Through iterative calculation, select the step position corresponding to the signal with the smallest error, which is the step position of the signal at this moment, and then perform fine estimation. The specific method for determining the frequency and amplitude - phase of the signal includes:

[0127] To estimate the correct value of ω0, the proposed method must assume that each P is known. During the calculation process, if any value of P is incorrect, it will cause a frequency - estimation error. However, it is impossible to know the transition time in advance in any measurement. Therefore, how to accurately estimate the actual value of P is the key to this method.

[0128] When using the wrong ω0, formulas (11) and (19) are used to estimate the frequency, amplitude, and phase, thus forming an estimated signal:

[0129]

[0130] where V1′, V2′, and ω0′ are the estimated signal parameters, and the k - th DFT bin of the estimated signal has a mutation, which is described as:

[0131]

[0132] The reconstruction error is expressed as:

[0133]

[0134] Obviously, when P' is equal to P, |s(n)-s′(n)| is the smallest. When estimating with the wrong P' under noise conditions, let ε s represent the sum of the reconstruction errors between the estimated signal and the original noise signal:

[0135]

[0136] ε s is the smallest when P' is equal to P. Find the minimum value of ε s corresponding to it which is also the jump point P. After determining the jump point P, through the method proposed in step 2), perform fine estimation on the signal to determine the frequency and amplitude - phase of the signal.

[0137] This example uses two simulation tests to evaluate the technical effect of the method of the present invention. The first simulation test evaluates the sensitivity of the method of the present invention to the change of reconstruction error, fixing l0=2.55 and considering different signal lengths (i.e., N=128, 256, 512, and 1024). It is worth noting that the jump point P is located at the center of the signal, mathematically expressed as P=N / 2. In addition, the other parameters of the signal are set as follows: V1=0.5, V2=1, and Figure 2 shows the performance of the proposed method under different signal lengths and signal-to-noise ratios (SNRs). The ordinate represents the error of the estimated signal, which is defined in equation (23). Regardless of the signal length, the error curve is funnel-shaped, and the minimum error occurs at P' = P. Since the proposed method sums the errors of all samples, longer signals will result in an increase in the relative error. Therefore, as the signal length increases, the error value at the lowest point will also increase. ε s As the difference between P' and P increases, when P' equals P, ε s As shown in Figure 2, the graph is funnel-shaped. When P' is equal to P, ε s It has a minimum value, and when the signal is noise-free, its value is at least less than 10 -11 Even in the presence of noise, when P' equals P, ε s It still has a minimum value. It is worth noting that when SNR ≥ 40dB, this effect becomes more obvious, which helps to accurately identify the lowest point. Based on the initial estimate provided by the proposed method, the exact value of P can be determined by the following subsequent steps:

[0138] Step 1: Obtain possible values ​​of P by sliding window DFT method: P = [P1′, P2′, P3′, …].

[0139] Step 2: Estimate the signal sequence and then calculate ε for different P' s .

[0140] Step 3: Find the corresponding ε s Minimum Then get the correct

[0141] The method of the present invention was used to estimate the value of P when P ranged from 1 to N-1. 10,000 estimates were performed and the estimate was considered accurate when the accuracy reached 94%. Table I gives the conditions that allow accurate estimation under various noise levels. In an ideal noise-free environment, accurate determinations can be made at different signal-to-noise ratios and P values. However, under noisy conditions, the estimation performance degrades and the number of incorrectly estimated P points increases proportionally with increasing signal length.

[0142] Table I

[0143] The N - interval of P can be accurately estimated at different N and SNR.

[0144]

[0145] When considering N = 128 and l0 = 2.55, Table II shows the estimated P' and the corresponding MSE at different signal - to - noise ratios and P, especially when P ≤ 5 (close to the signal end). The MSE is defined as the error between the estimated frequency and the actual frequency, as shown in Equation (23). This paper presents the mean square error of the frequency estimation given by the proposed estimator for both the estimated P' and the actual P'. When P is close to the middle position of the signal, the proposed estimator can achieve accurate estimation and has good anti - noise performance.

[0146] Table II

[0147] Comparison of MSE between the estimated P' and the actual P at different signal - to - noise ratios

[0148]

[0149]

[0150] When P is too large, it means that the number of samples belonging to the second segment of the signal is very small, resulting in an inability to accurately estimate the amplitude V2 and the phase. At such a small sampling length, the anti - noise ability of the proposed method is theoretically limited. Similarly, if P is too small, that is, the number of points in the first segment is too small, there will not be enough samples to accurately estimate the amplitude V1 and the phase. As shown in Table II, when the SNR is low, or when P is close to the signal end, the method of the present invention may produce an estimation error of P, resulting in P'≠P. It can be clearly seen from Table II that at a higher SNR, the difference between the estimated P' and the actual P is small, and the MSE of the result is also very close. However, when the SNR is below 50 dB, the difference between P' and P becomes more obvious because P is close to the signal boundary, resulting in insufficient information in the shorter part of the signal. By adopting the criterion based on the selection of the minimum error, the characteristics of the signal, especially its amplitude and phase, can be more accurately represented. Focusing on the signal segment where the method performs best ensures that the frequency estimation remains reliable even if there are challenges in other parts of the signal. Therefore, there is no significant difference between the MSE of the frequency estimation with the actual P and the MSE with the estimated P'. The selection of P' based on error minimization serves as a quality - control mechanism to ensure that the output of the estimation process meets the predefined accuracy level.

[0151] To verify the effectiveness of the proposed method, in this example, the method of the present invention was tested and evaluated according to the provisions of the P-class PMU standard. These PMU tests are specified in IEEE Std C37.118-2011 and were revised in the 2014 update. The tests mainly include static tests and dynamic tests. In the simulation, the sampling frequency f s was set to 5 kHz, the nominal frequency f n was 50 Hz, and l0 was set to 3. The duration of the entire signal was 1 second, and the signal amplitude V i was set to 1, and the signal phase was set to π / 18. In addition, AWGN noise with a signal-to-noise ratio of 70 dB was added to the test signal. TVE (Total Error), FE (Frequency Error), and RFE (Rate Error) were used as performance metrics to evaluate the proposed method.

[0152] Table III shows the maximum errors encountered in static and dynamic tests and the maximum allowable limits according to IEEE regulations. In addition, the FiIpDFT algorithm was selected for comparison because it is one of the best DFT-based PMU estimators. Obviously, the proposed method meets the requirements of the P-class standard while maintaining higher accuracy. The method of the present invention shows improved accuracy in frequency estimation, superior to the FiIpDFT algorithm. In terms of amplitude and phase estimation, compared with the FiIpDFT algorithm, the performance slightly decreases. However, the difference is still within an acceptable range and does not exceed one order of magnitude.

[0153] Table III

[0154] Maximum Errors in Static and Dynamic Tests

[0155]

[0156] In the step test, the responsiveness of the present invention under sudden transients was evaluated. Transient step simulations of sudden transients in the power system were performed, including amplitude (10%) and phase (π / 18) step tests. The P-class PMU requires that the response times of the phasor, frequency, and ROCOF estimators should not exceed 40, 90, and 120 ms, respectively. In addition, the delay time requirement should be kept below 0.05 ms. The maximum overshoot of the P-class PMU should be limited to 5% of the step amplitude. Figure 3 and 4Describes the variations of TVE, FE, and RFE, as well as the estimated magnitude (p.u.) and phase (rad). Within the allowable error range, there is no overshoot phenomenon, as shown in Table IV. The proposed method is capable of effectively tracking the frequency of the step signal under noisy conditions, so there is almost no delay time, and the test results meet the test standards. It is particularly noteworthy that the response time of the proposed method is zero in all tests, which is much shorter than that of FiIpDFT, which is at least 11.8 milliseconds.

[0157] Table IV

[0158] Consistency of step tests: maximum response times of different methods.

[0159]

[0160]

[0161] The second simulation experiment evaluates the performance of estimating the jump point of an unknown signal. For a signal with known P, the method of the present invention can achieve zero delay and real-time frequency estimation. However, for a signal with unknown P, the iterative method is required to estimate P, and since it is impossible to know the step time in advance in any measurement, the estimation of P has a delay. During the calculation process, for a signal with unknown P, the approximate range of P needs to be determined first. Assume that the signal length is 3000, where the parameter step change occurs at an unknown point (set the step position to 1500), and a rectangular window with a size of 128 and a step of 1 is used. The signal-to-noise ratio is set to 70 dB, and the reference frequency is 60 Hz. The estimation results are as Figure 5 shown.

[0162] The first case is that the half window (with a length of N / 2) slides from left to right within the observation window (with a length of N). This small window with a length of N / 2 can be used to roughly estimate the signal parameters and the value of P. The result of frequency estimation using the method of the present invention (set P to 0, that is, without considering the step change) is similar to Figure 3As shown. It can be observed that when the window slides, the step point moves from the right edge to the left edge of the observation window. Accordingly, the frequency estimation error increases from small to large and then decreases because the number of relatively stable signals within the window changes from abundant to scarce and then to abundant. This results in obvious fluctuations, enabling the determination that the peak occurs to the left of the step change point. Therefore, the approximate position of the step change can be determined. At this time, the step change interval can be placed closer to the window center. This can improve the accuracy of P value estimation, as shown in Table II. Subsequently, for each point within the possible range of the step change, the absolute error between the reconstructed signal and the original signal is calculated, as shown in Equation (23). The corresponding P with the minimum error is identified as the step point. This iterative process is time-consuming and causes computational delay. After obtaining an accurate estimate of P, there is no need to use the P value estimation method for calculation. The frequency estimation method can be directly used.

[0163] Another case is that the observation window of length N slides over time. In this case, the length of the observation window remains constant over time, but the samples are updated. By directly applying the P value estimation method to the samples, the approximate position of the step change can be determined. At this moment, since the estimated P is close to the window edge, some errors may occur. However, the estimated frequency is still close to the actual frequency, as shown in Table II. During the entire sliding process, the position of P moves towards the center of the observation window, thereby improving the accuracy of P value estimation. Table I shows that when the SNR is 40 dB, the positions of approximately 80% of the Ps within the window can be accurately estimated.

[0164] To verify the practical implementation effect of the proposed method in hardware, an example is provided. The software used is Power System Computer Aided Design (PSCAD), which is an electrical power simulation software dedicated to electromagnetic transient including DC (EMTDC) simulation programs for power system modeling, simulation, and analysis. PSCAD provides a graphical user interface for EMTDC, enabling users to more conveniently perform design and simulation tasks related to power systems. In PSCAD, a cosine signal simulation with a mutation was conducted using a single-point synchronization model, and the instantaneous current signal in the single-point synchronization system was obtained.

[0165] The PSCAD model adopted is used to simulate the occurrence of medium and low voltage faults in the distribution network during the high-load summer electricity consumption period, especially in areas with a large integration of distributed photovoltaic systems. The model is constructed based on the actual operating parameters of a certain city in China to accurately reflect the scenarios of medium and low voltage fault occurrences in the distribution network. The first sampling point is marked as the zero moment, the entire signal lasts for 1 second, and the sampling frequency is 4000 Hz. The set window length is N = 128, which is consistent with the window length selected in the PMU test discussed earlier. Figure 6 shows the instantaneous current signals of a three-phase alternating current (AC) system, from which it can be observed that one of the three measured signals has experienced a sudden change. Table V provides the estimated P and MSE obtained by the proposed method under two different conditions, namely when extracting the signal of length N. Obviously, even when measuring signals under real-world conditions that may contain noise and other distortions, the method of the present invention can accurately estimate the frequency of the signal. When the step change occurs in the middle part of the sliding window, the ability of the method to estimate the frequency remains robust, which is consistent with the analysis proposed earlier.

[0166] This analysis emphasizes the robustness of the proposed method to signal mutations, which is a key feature for applications where signal integrity may be compromised, such as in power system monitoring and fault detection scenarios. It can provide real-time estimates even when the signal is abnormal, which highlights the potential reliability and practicality of the method in practical applications. Therefore, when actually estimating the P value, efforts should be made to locate the step change within the middle region of the sliding window. This strategy improves the accuracy of the estimate because it allows for a more precise capture of the signal characteristics during the step change, leveraging the best performance of the sliding window method.

[0167] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for estimating the frequency and amplitude-phase of a cosine hopping signal based on DFT, characterized in that, Including: Step 1) Establish a cosine jump signal model, simplify the estimator based on the cosine jump signal model, transform the direct estimator composed of frequency and step points into an intermediate estimator, and establish a received signal vector; Step 2) For a signal with a known step position, after performing DFT transformation on the received signal vector, select different DFT spectral lines to construct an equation, solve the equation to determine the intermediate estimator, establish a matrix solution model using 5 DFT bins, and solve for the frequency and amplitude-phase of the signal through matrix inversion; Step 3) For a signal with an unknown step position, first calculate the frequency through a no-step algorithm. If there is a large jump in the frequency, it means a step occurs, and at the same time, determine the approximate position of the step. Based on Step 2), first construct an initial signal, then calculate the reconstruction error, and through iterative calculation, select the step position corresponding to the signal with the minimum error as the step position of the signal at this moment, and then perform fine estimation to determine the frequency and amplitude-phase of the signal.

2. The method for estimating the frequency and amplitude-phase of a cosine hopping signal based on DFT according to claim 1, characterized in that The specific method for establishing the cosine jump signal model, simplifying the estimator based on the cosine jump signal model, transforming the direct estimator composed of frequency and step points into an intermediate estimator, and establishing a received signal vector includes: Establish a cosine jump signal model. The real-valued sine signal under noise conditions can be expressed as: y(n) = s(n) + q(n) (1) where q(n) is additive white Gaussian noise with variance ; When a parameter step change occurs, the signal s(n) can be expressed as: Wherein, V m and are the m-th amplitude and phase of the unknown modulation signal, where m = 1, 2, and the parameter changes at P; ω0 = 2πf0 / f s is the angular frequency, where f0 is the signal frequency and f s is the sampling frequency; When obtaining a sequence s(n) with length N, rewrite the normalized frequency as ω0 = 2πl0 / N = 2π(k0 + δ0) / N, where l0 is the number of cycles of the signal, and its integer part and decimal part are k0 and δ0 respectively; the value range of k0 is [0, 1,..., N - 1], and the value range of δ0 is [-0.5, 0.5].

3. The frequency and amplitude-phase estimation method of the cosine hopping signal based on DFT according to claim 2, characterized in that The specific method for the signal with a known step position, after performing DFT transformation on the received signal vector, selecting different DFT spectral lines to construct an equation, solving the equation to determine the intermediate estimator, establishing a matrix solution model using 5 DFT bins, and solving for the frequency and amplitude-phase of the signal through matrix inversion includes: Let \(S(k)\) be the DFT of the sequence \(s(n)\). \(S(k)\) can be obtained as follows: Where, Furthermore, we get: Among them, When obtaining five different DFT bins S(k i ) near the maximum peak, for i = 1, 2, …, 5, the following linear equations are obtained: S = Wη (6) Where, η = [a1, a2, a3, a4, b] (8) According to formula (6), η is estimated as: Among them, and Y are the observed values of W and S under noise conditions, represents the estimated value of ·; According to b = cos(ω0), the angular frequency ω0 is estimated as: When ω0 is estimated, re-formulate equation (3): Where: Simplify to: W Aest μ = 2S′ (14) Where: μ = [μ1, μ2, μ3, μ4] T (15) S′ = [S(k1), S(k2), S(k3), S(k4)] T (16) In the presence of noise, let Y denote the observed value of S'. Using any four different DFT bins Y(k i ), where i = 1, 2, 3, 4, we obtain: Adopt a matrix solution method to solve the variable μ, thereby determining the amplitude and phase values; When μ1, μ2, μ3, and μ4 can be estimated, V1, V2, and are estimated as:

4. The method for estimating the frequency and amplitude-phase of a cosine hopping signal based on DFT according to claim 3, characterized in that The specific method for the signal with an unknown step position, first calculating the frequency through a no-step algorithm. If there is a large jump in the frequency, it means a step occurs, and at the same time, determining the approximate position of the step. Based on Step 2), first construct an initial signal, then calculate the reconstruction error, and through iterative calculation, select the step position corresponding to the signal with the minimum error as the step position of the signal at this moment, and then perform fine estimation to determine the frequency and amplitude-phase of the signal includes: When using the wrong ω0, formulas (11) and (19) are used to estimate the frequency, amplitude, and phase, thereby forming an estimated signal: where V1′, V2′, and ω0′ are the estimated signal parameters, and the k-th DFT bin of the estimated signal has a mutation, which is described as: The reconstruction error is expressed as: Obviously, when P' is equal to P, |s(n) - s′(n)| is minimized. When estimating with the wrong P' under noisy conditions, let ε s represent the sum of the reconstruction errors between the estimated signal and the original noise signal: ε s It is minimized when P' equals P, and ε is found s The corresponding minimum value That is, the jump point P; after determining the jump point P, the signal is accurately estimated by the method proposed in step 2) to determine the frequency and amplitude-phase of the signal.

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