Power system nonlinear load power metering method based on improved s-transform

Abstract

The application discloses a power system nonlinear load power metering method based on improved S transformation, and comprises the following steps: step one, extracting voltage and current fundamental component and distortion component based on IST, and obtaining voltage and current fundamental part and distortion part signals respectively; step two, reconstructing voltage and current signal fundamental discrete signals and distortion discrete signals through IST inverse transformation; step three, carrying out dot product and operation on the reconstructed voltage and current signal fundamental discrete signals and distortion discrete signals, and thus power metering of the signals can be completed. The decomposition and reconstruction algorithm based on IST provided by the application can significantly improve metering precision when metering power under the condition of existing harmonics and nonlinear load, and the application provides theoretical support and application guidance for applying the IST method to new power system power metering with a high proportion of nonlinear load.

Description

TECHNICAL FIELD

[0001] The present application relates to a power metering algorithm, in particular to a power metering algorithm for nonlinear load of power system based on improved Stockwell transform (IST). BACKGROUND

[0002] With the development of science and technology, the proportion of nonlinear load in new power system is getting higher and higher. The frequent start and shutdown of nonlinear load cause a large number of harmonics, interharmonics and continuous transient signals in system voltage and current. The use of various power electronic devices and power switching devices makes the load of power grid show strong nonlinear characteristics and time-varying characteristics. The traditional power metering algorithm is no longer suitable for new power system. How to accurately and reasonably calculate the power consumed by the load has become a research hotspot.

[0003] The internationally recognized and adopted power metering standard is IEEE Std 1459 based on fast Fourier transform (FFT). Although FFT provides good frequency domain information of signals, it loses time domain information and cannot accurately analyze nonlinear signals. Therefore, IEEE Std 1459 is not suitable for new power system with high proportion of nonlinear load and non-stationary system voltage and current. At present, the research on power metering algorithm under nonlinear conditions mainly focuses on analyzing voltage and current signals by using time-frequency method and calculating corresponding power through time-frequency distribution coefficient.

[0004] Because wavelet transform (WT) and its related transform can provide a "time-frequency" window that changes with frequency, it has become an ideal tool for analyzing and processing nonlinear signals in the time-frequency domain. Yoon and Devaney first applied discrete wavelet transform to power measurement, divided the frequency spectrum into frequency bands, and calculated the root mean square and power value, providing application guidance for using WT to measure the power of fundamental or harmonic components. As a typical time-frequency analysis method, the Stockwell transform (ST) can separately estimate each frequency component, which can greatly reduce the measurement error compared to applying WT to measurement. ST can be regarded as a frequency-dependent short-time Fourier transform (STFT), which is also a phase correction of WT. ST inherits and develops the localization idea of STFT and WT, can overcome the defects caused by the fixed width of the STFT window, and can avoid the energy leakage effect caused by WT. Although ST shows good applicability in the process of analyzing nonlinear loads, the results of ST contain a large amount of time-frequency information, which means that the algorithm has a large amount of calculation and poor real-time performance. SUMMARY

[0005] In view of the problem that the proportion of nonlinear loads in the new power system is increasing, which leads to serious distortion of system voltage and current waveform, and the traditional power measurement algorithm is no longer applicable to the new power system, the application provides a power measurement method for nonlinear loads in a power system based on IST. The method introduces multiple parameters that can control the Gaussian window based on ST, thereby improving the flexibility of the Gaussian window. Further, the optimal window parameters are selected by using inequality constraint optimization based on the clustering degree measurement method, so that the IST has better time-frequency domain analysis capability. Simulation results show that the power measurement method based on IST has higher measurement accuracy compared with existing measurement methods.

[0006] The object of the application is achieved by the following technical solutions:

[0007] A power measurement method for nonlinear loads in a power system based on IST, comprising the following steps:

[0008] Step one, extract the voltage and current fundamental component and distortion component based on IST, respectively obtain the voltage and current fundamental component and distortion component signal, wherein: for the fundamental component of the voltage and current signal, the corresponding ST only has a value when the frequency is the fundamental wave, and the rest of the frequency is zero; for the distortion signal of the voltage and current signal, the corresponding ST is only zero when the frequency is the fundamental wave, thereby obtaining the decomposed voltage and current fundamental component and distortion component; the specific extraction method is as follows:

[0009] (1) Calculate the N-point FFT spectrum of the signal x(nT)

[0010] (2) Extract the characteristic frequency point k of the signal according to the envelope extremum method i The specific steps are as follows:

[0011] According to Find all the maximum points of , and all the maximum points form a maximum value sequence with a length of L, denoted as Where l = 0, 1, 2,..., L-1, i = 0, 1, 2,..., N-1;

[0012] Suppose there are M l frequency points between each adjacent maximum value point, then The maximum envelope of is represented as: q = 0, 1, 2,..., M l-1 , l = 1, 2,..., L-1;

[0013] Find the maximum value of , and at the same time, introduce a threshold ε to reduce the influence of noise on the spectrum, then the characteristic frequency point k i satisfies:

[0014]

[0015]

[0016] (3) According to the characteristics of the signal, adaptively select the parameters of the Gaussian window to obtain a Gaussian adaptive optimization window; Wherein:

[0017] Adaptively select the parameters of the Gaussian window according to the following conditions:

[0018]

[0019] The Gaussian adaptive optimization window is:

[0020]

[0021] (4) Calculate the FFT of the Gaussian window at the characteristic frequency point k i

[0022]

[0023] The parameter a determines the width of the Gaussian window; The parameter b is the window factor; The parameter c represents the trade-off between ST and STFT; The parameter d represents the change rate of the width of the Gaussian window;

[0024] (5) Substitute ​Spectrum panning obtains

[0025] (6) Calculate The product of W(r, k i ) and G(r, k i ):

[0026]

[0027] (7) Let time shift factor tau = mT, and perform IFFT on G(r, k i ) to obtain the corresponding IST of k i :

[0028]

[0029] (8) Repeat (4)-(7) to complete the IST corresponding to all characteristic frequency points, and obtain the complete IST matrix, wherein the rows of the IST matrix represent frequencies, the columns represent times, and the matrix elements represent the amplitude and phase information of the signal at the corresponding time and frequency, respectively;

[0030] Step two, reconstruct the fundamental discrete signal and the distortion discrete signal of the voltage and current signals through IST inverse transformation, and the specific reconstruction method is as follows:

[0031] (1) Perform row summation on the IST matrix to obtain a spectrum vector

[0032] (2) Perform IFFT on the obtained spectrum vector to obtain a characteristic signal x(nT), and complete the reconstruction of the signal;

[0033] Step three, perform dot product and operation on the reconstructed fundamental discrete signal and the distortion discrete signal of the voltage and current signals, and the power metering of the signal can be completed.

[0034] Compared with the prior art, the present application has the following advantages:

[0035] The application proposes a new IST method for controlling a Gaussian window by multiple parameters, and adopts a sequential quadratic programming method to optimize the process to determine the window parameters, and finally obtains the IST method of multiple window parameters. Through time-frequency analysis of three common power quality composite disturbance signals, the detection ability and reliability of IST are verified. On this basis, a nonlinear load power metering method based on decomposition and reconstruction algorithm is proposed. On the basis of analyzing the principles and implementation steps of ST and decomposition and reconstruction algorithm, the power metering ability for nonlinear loads is simulated and analyzed. Simulation analysis shows that, compared with existing metering methods, the decomposition and reconstruction algorithm based on IST proposed in the application can significantly improve the metering accuracy under the condition of metering harmonic and nonlinear load, and the application provides theoretical support and application guidance for applying the IST method to power metering of new power systems with high proportion of nonlinear loads. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 For envelope extremum algorithm simulation results, (a) signal time domain waveform diagram, (b) signal spectrum maximum envelope diagram;

[0037] Figure 2 For WT, ST and IST time-frequency conversion results of test signal C1, (a) test signal (C1), (b) WT, (c) WT, (d) ST, (e) ST, (f) ST, (g) IST, (h) IST, (i) IST;

[0038] Figure 3 For time-frequency conversion results of signal C2, (a) test signal (C2), (b) WT, (c) WT, (d) ST, (e) ST, (f) ST, (g) IST, (h) IST, (i) IST;

[0039] Figure 4 For time-frequency conversion results of signal C3, (a) test signal (C3), (b) WT, (c) WT, (d) ST, (e) ST, (f) ST, (g) IST, (h) IST, (i) IST;

[0040] Figure 5 For reconstruction of test signals, (a) voltage fundamental signal, (b) voltage distortion signal, (c) current fundamental signal, (d) current distortion signal;

[0041] Figure 6 Flowchart of power metering algorithm based on improved S transform. DETAILED DESCRIPTION

[0042] The technical solutions of the present application are further described below with reference to the drawings, but are not limited thereto, and any modification or equivalent replacement within the spirit and scope of the technical solutions of the present application shall be covered in the protection scope of the present application.

[0043] The present application provides a power system nonlinear load power metering method based on IST, which combines envelope extremum method and threshold control to extract characteristic frequency points of voltage and current signals, and eliminates non-characteristic information, thereby reducing the amount of calculation for applying IST without loss of metering accuracy. In order to avoid the defect that the definition of inter-harmonic power is not given in IEEE Std1459-2010 standard, firstly, the characteristics of IST, i.e., good time resolution at low frequency and good frequency domain resolution at high frequency, are utilized to decompose and reconstruct the voltage and current fundamental characteristic signals and distortion characteristic signals in the power system; secondly, the obtained fundamental and harmonic power is calculated through dot product and operation, so as to realize power metering based on non-steady voltage and current.

[0044] The principle of IST algorithm, power metering algorithm based on IST, IST detection capability verification, and nonlinear load power metering example are described below.

[0045] I. Principle of IST algorithm

[0046] 1. ST and its inverse transform

[0047] As the development of STFT and WT algorithm, ST overcomes the shortcomings of fixed window size of STFT and only stretching and contraction of WT window at fixed time position. Compared with the result of WT, the result obtained after ST processing of the signal is more easy to understand. The result obtained by ST can directly obtain the frequency components existing at each time, and also can directly obtain the distribution of different frequencies on the time component.

[0048] The ST of a function can be obtained by STFT transformation. If the given known signal x(t) is known, the mathematical expression of its STFT is:

[0049]

[0050] In the formula, x(t) is a given known signal; S * (τ,f) represents the short-time Fourier transform of the signal x(t); w * (τ-t) is the window function of Fourier transform; τ is the time shift factor; f is the signal frequency.

[0051] The Gaussian window with variable window shape is selected as the window function:

[0052]

[0053] where σ is the scale factor of the Gaussian window function.

[0054] Substituting equation (2) into equation (1) can obtain the expression of ST:

[0055]

[0056] where S(τ,f) is the expression of S transform;

[0057] According to the convolution theorem, equation (1) can be expressed as the convolution of two functions:

[0058]

[0059] Definition:

[0060]

[0061] According to the convolution theorem, equation (3) can be written as

[0062]

[0063] The inverse fast Fourier transform (IFFT) of ψ(β,f) can obtain ST:

[0064]

[0065] Using FFT, the inverse transform of ST can be realized, and the signal reconstruction can be completed:

[0066]

[0067] According to the derivation of ST above, ST can be realized by FFT and IFFT, so the fast calculation of discrete S transform can be realized by FFT, and the reconstruction of the original signal can also be completed by IFFT.

[0068] 2. Principle of multi-window parameter IST

[0069] Although ST has strong advantages in window adjustment compared with STFT and WT, it is still subject to some constraints. According to the Heisenberg-Gabor uncertainty principle, the signal cannot obtain high time resolution and frequency resolution at the same time in time-frequency analysis. One of the resolutions is improved, and the other resolution is reduced. In order to improve the time-frequency resolution of ST, the present application proposes to introduce four parameters to give the Gaussian window greater flexibility, and the new scale factor σ of the window function is

[0070]

[0071] At this time, the Gaussian window function becomes

[0072]

[0073] Improved S transform is

[0074]

[0075] In the formula, parameters a, b, c, d are the Gaussian window adjustment factors introduced by the improved S transform; parameter a determines the Gaussian window width; parameter b is the window factor; parameter c represents the trade-off between ST and STFT; parameter d represents the change rate of the Gaussian window width. When a = 1, b = 0, c = 0, d = 1, ST will be obtained; when a = 1, b = 0, c = 2, d = 1, STFT will be obtained.

[0076] In order to better select the parameters adaptively, the clustering measure method is applied to the IST to obtain the target function:

[0077]

[0078] In the formula, CM (a, b, c, d) is the result of applying the clustering measure method; In order to normalize the ST, it is expressed as

[0079]

[0080] The clustering measure method shows that the higher the signal energy clustering degree, that is, the larger the CM value, the more ideal the time-frequency resolution obtained by the signal in time-frequency analysis. At this time, the target optimization function can be expressed as

[0081]

[0082] When solving the target function, it needs to be reasonably constrained. In order to ensure the appropriate time-frequency resolution, the window width should neither be set too narrow nor be set too wide. Therefore, the window width is considered as a constraint condition of the optimization method in the application, at this time, the window function scale factor σ is limited to

[0083]

[0084] In the formula, σ min is the lower limit of the scale factor; σ max is the upper limit of the scale factor; T s is the sampling time.

[0085] In formula (15), m and n are positive integers; in order to ensure the minimum time resolution, the value of n must be greater than 1; after a large number of experiments, n is 3 and m is 1000 in the subsequent content.

[0086] Equation (15) can be decomposed into two inequality constraints, the first inequality constraint is

[0087]

[0088] where f∈(f min ,f max ), f min =1; f max is determined according to the analyzed signal.

[0089] Further expanding equation (16), we can obtain:

[0090]

[0091]

[0092] In equation (18), f min =1, so the first inequality constraint expression is

[0093]

[0094] Similarly, the second inequality constraint expression is

[0095]

[0096] In addition to the constraint on the window function scale factor σ, the value range of the four parameters should also be constrained. After weighing the window width and the STFT and ST results, the third constraint condition is

[0097] 0≤a,b,c,d≤1 (21)

[0098] At this point, all the optimization constraints have been set, and the overall optimization problem can be summarized as

[0099]

[0100] Thus, the parameter selection problem has been completely converted into a nonlinear optimization problem with constraints, and the sequential quadratic programming method is used to solve it. As an optimization algorithm, the sequential quadratic programming method constantly updates the current solution by iteratively solving quadratic programming sub-problems, so that the value of the objective function is constantly reduced, and finally the optimal solution is obtained after a finite number of iterations.

[0101] II. Power metering algorithm based on IST

[0102] 1. Envelope extremum algorithm

[0103] The result of ST often contains a large amount of time-frequency information, which means that a large amount of operation is needed, and the IST also has the problem of large operation amount. In view of this, the envelope extreme value method is combined with threshold control to extract the characteristic frequency points of the signal, and the IST is preprocessed, so that the accuracy of time-frequency analysis is ensured while the operation amount is reduced.

[0104] It is known that is the discrete Fourier transform of the discrete sampling sequence x(nT), and there is

[0105]

[0106] In formula (23), i=0, 1, 2,..., N-1.

[0107] According to formula (23), all maximum points of can be obtained, and all maximum points are used to form a maximum value sequence with a length of L, which is denoted as wherein l=0, 1, 2,..., L-1. It is assumed that there are M l frequency points between each adjacent maximum value point, and then the maximum envelope of can be represented as

[0108]

[0109] In formula (24), q=0, 1, 2,..., M l-1 , and l=1, 2,..., L-1.

[0110] The maximum value of is obtained, and at the same time, a threshold value ε is introduced to reduce the influence of noise on the frequency spectrum, so that the frequency point k i needs to meet:

[0111]

[0112]

[0113] The value of the threshold coefficient ε in formula (26) is determined according to factors such as the amplitude of the characteristic frequency interference point caused by the noise spectrum and the minimum amplitude of the harmonic. A large number of experiments show that when ε=0.01p.u., the accuracy of the result of the algorithm is relatively high.

[0114] The frequency point k i that meets the requirements of formula (25) and (26) is the characteristic frequency point to be obtained.

[0115] Figure 1 is the envelope extreme value algorithm simulation result of the voltage harmonic and flicker signal with a signal-to-noise ratio of 30dB added; Figure 1(a) is the time-domain waveform of the signal after FFT; Figure 1 (b) shows the envelope extreme value curve and the characteristic frequency points (the first 500 Hz) of the signal after envelope extreme value algorithm. The simulation results show that the envelope extreme value algorithm not only eliminates the information of non-characteristic frequency points and realizes accurate extraction of the characteristic frequency points of the signal, but also greatly reduces the operation amount of the IST algorithm.

[0116] 2. Power metering method using IST

[0117] The IST result is a two-dimensional complex matrix, the rows of the matrix represent the frequency and the columns represent the time, and the matrix elements represent the amplitude and phase information of the signal at the corresponding time and frequency. The specific implementation steps are as follows:

[0118] (1) Calculate the N-point FFT spectrum of the signal x(nT)

[0119] (2) Extract the characteristic frequency point k of the signal according to the envelope extreme value method i ;

[0120] (3) According to the characteristics of the signal, adaptively select the parameters of the Gaussian window to obtain the Gaussian adaptive optimization window;

[0121] (4) Calculate the FFT of the Gaussian window at the characteristic frequency point k i :

[0122]

[0123] (5) Shift the spectrum to obtain

[0124] (6) Calculate the product of and W(r, k i ):

[0125]

[0126] (7) Let the time shift factor τ = mT, and perform IFFT on G(r, k i ) to obtain the IST corresponding to k i :

[0127]

[0128] (8) Repeat steps (4)-(7) to complete the IST corresponding to all characteristic frequency points and obtain the complete IST matrix.

[0129] After completing the decomposition of the signal, the measured signal can be reconstructed by means of IFFT, and the specific process is as follows:

[0130] ​(1) Sum the IST matrix by row to obtain the spectrum vector

[0131] (2) Perform IFFT on the obtained spectrum vector to obtain the characteristic signal x(nT), and complete the reconstruction of the signal.

[0132] According to the intersection theory of sinusoidal signals, only voltage distortion components and current distortion components of the same frequency can generate active power, and the result of discrete time integration of voltage components and current components of different frequencies is zero. Therefore, as shown in Figure 6 , when IST is applied to power measurement, first, the extraction of voltage and current fundamental component and distortion component is performed: for the fundamental component of voltage and current signal, the corresponding ST only has a value at the fundamental frequency, and the rest of the frequencies are zero. For the distortion signal of voltage and current signal, the corresponding ST is only zero at the fundamental frequency, thereby obtaining the decomposed voltage and current fundamental component and distortion component. Then, after IST inverse transformation, the fundamental discrete signal and the distortion discrete signal of the signal are reconstructed. Finally, the point product and operation of the reconstructed voltage and current time domain discrete signals are performed, and the power measurement of the signal is completed.

[0133] III. Verification of IST detection capability

[0134] In order to verify the detection capability of IST for nonlinear load, in this section, according to IEEE Std.1159-1995, three common power quality composite disturbances are simulated using MATLAB. Including: test signal C1 double disturbance power quality composite disturbance: voltage flicker + harmonic; test signal C2 three-component mixed disturbance: voltage sag + harmonic + transient oscillation; test signal C3 four-component disturbance: voltage sag + harmonic + transient oscillation + transient pulse. The sampling time is set to 0.001s, i.e. the sampling frequency is 1000Hz. The basic frequency of the mixed disturbance model studied is 50Hz, and the parameters are randomly generated within the set range.

[0135] Take the form of test signal C1 (voltage flicker + harmonic) as follows:

[0136]

[0137] In formula (30), α f = 0.3-0.5, β = 0.1-0.4, α3 = 0-0.15, α5 = 0-0.15, α7 = 0-0.15,

[0138] Figure 2 The time-frequency domain analysis results of test signal C1 analyzed by WT, ST and IST are shown. The test signal waveform is shown in Figure 2 (a). Figure 2(b), (d), (g) show the 2-D time-frequency analysis results of WT, ST and IST respectively. Figure 2 (c), (f), (i) show the 3-D time-frequency analysis results of WT, ST and IST respectively. Figure 2 (e), (h) are the energy concentration diagrams of ST and IST respectively. By comparison, it can be seen that WT has good frequency resolution but poor time resolution and low energy concentration; ST has good time resolution at low frequency but low frequency resolution at high frequency; IST has similar time resolution at low frequency to ST but has obviously better frequency resolution at high frequency and higher energy concentration.

[0139] The test signal C2 (voltage sag + harmonics + transient oscillation) is in the form of:

[0140]

[0141] In formula (31), a = 0.1-0.9, a2 = 0.1-0.8, a3 = 0-0.15, a5 = 0-0.15, a7 = 0-0.15, τ = 0.008-0.04, t2-t1 = 4T-9T, t4-t3 = 0.05T-3T, f n = 300-900 Hz.

[0142] Figure 3 The time-frequency analysis results of the three methods under the condition of test signal C2 are shown. Figure 3 (a) shows the time-domain waveform of signal C2. Figure 3 (b), (d), (g) show the 2-D time-frequency analysis results of WT, ST and IST respectively. Figure 3 (c), (f), (i) show the 3-D time-frequency analysis results of WT, ST and IST respectively. Figure 3 (e), (h) are the energy concentration diagrams of ST and IST respectively. By comparison, it can be seen that WT has good frequency resolution but poor time resolution and low energy concentration; ST has good time resolution at low frequency but low frequency resolution at high frequency; IST has similar time resolution at low frequency to ST but has obviously better frequency resolution at high frequency and higher energy concentration. Figure 3 (b), (c) can see that WT has been unable to accurately analyze the time-frequency of the signal due to the limitation of the selection of the mother wavelet, at low frequency, the time resolution is very poor, and at high frequency, especially before 0.1s, the characteristics of the signal cannot be extracted. By comparing the time-frequency analysis results of ST and IST, it can be judged that compared with ST, IST has good time-frequency resolution and reasonable energy concentration at both low and high frequencies.

[0143] The test signal C3 (voltage sag + harmonics + transient oscillation + transient pulse) is in the form of:

[0144]

[0145] In formula (32), a = 0.1-0.9, a2= 0.1-0.8, a3= 0-0.15, a5= 0-0.15, a7= 0-0.15, a 22 = 1-10, t = 0.008-0.04, t2-t1= 4T-9T, t4-t3= 0.05T-3T, f n = 300-900Hz, t2= 0.008-0.04, t6-t5= 0.05T-3T.

[0146] Figure 4 The time-frequency analysis results of three methods under the condition of test signal C3 are shown. The test signal waveform is shown in Figure 4 (a). Figure 4 (b), (d), (g) respectively represent the two-dimensional time-frequency analysis results of WT, ST and IST. Figure 4 (c), (f), (i) respectively represent the three-dimensional time-frequency analysis results of WT, ST and IST. Figure 4 (e), (h) are energy concentration degree diagrams established for better comparison between ST and IST. By Figure 4 (b), (c) can be seen that WT has failed to accurately analyze the time-frequency of such a complex signal. By comparing Figure 4 (e), (h) can be seen: at low frequencies, IST has better frequency resolution and energy concentration than ST by sacrificing reasonable time resolution. The frequency resolution of IST is obviously better than that of ST at high frequencies. The time-frequency analysis capability of IST for complex signals is better than that of ST, and the analysis of complex signals is more efficient and accurate. Among the three compared transformations in the simulation, the detection ability of IST is the strongest.

[0147] Four, nonlinear load power metering example

[0148] This section simulates and verifies the accuracy of the nonlinear load power metering algorithm based on IST. The fundamental frequency f1= 50Hz, the sampling frequency f s = 6.4kHz, and the sampling time is 1s. For the non-steady voltage and current test signal, a typical output signal model of power electronic frequency conversion device is selected, which has the following characteristics: in different time intervals, the voltage and current signals will suddenly increase a new frequency component. This non-steady test signal can be represented as:

[0149]

[0150]

[0151] In formula (33), (34), t1=0.2s, t2=0.4s, t3=0.7s, t4=1s.

[0152] Through the simulation analysis of the IST-based decomposition and reconstruction algorithm, the reconstructed voltage and current fundamental signals and the distortion signals can be obtained, and the analysis and processing results are shown in Figure 5

[0153] The voltage and current fundamental signals and the distortion signals can be obtained after IST transformation, and then the calculation can be performed. Through the measurement, the theoretical values of the DC, fundamental, harmonic and inter-harmonic power components formed by the above-mentioned non-steady-state voltage and current test signals, and the corresponding power metering comparison results of the FFT, ST and the proposed IST algorithm are shown in Table 1, and the error comparison results are shown in Table 2.

[0154] Table 1 Power metering results of three algorithms under non-steady state

[0155]

[0156] Table 2 Power metering error of three algorithms under non-steady state

[0157]

[0158] As can be seen from Table 1 and Table 2, since the DC and fundamental components exist all the time in the entire sampling period, which belong to steady-state components, therefore, there is no error in the DC and fundamental power component measurement of the FFT, ST and IST. As for the distortion signal, the metering error of the FFT algorithm is larger, resulting in a larger total power metering error; at this time, the IST has better metering accuracy in the distortion power metering, the total power metering error is smaller, and can meet the requirements of non-linear load power metering.​

Claims

1. A method for power metering of nonlinear loads in power systems based on modified S-transform, characterized by The method comprises the following steps: Step one, based on the improved S transform IST, the voltage and current fundamental component and distortion component are extracted, and the voltage and current fundamental component and distortion component signals are obtained, and the specific extraction method is as follows: (1) calculating the N-point FFT spectrum of the signal ;​ (2) According to the envelope extremum method, the characteristic frequency points of the signal are extracted The specific steps are as follows: According to find all the maximum points of , and all the maximum points form a maximum sequence with length L, denoted as , where , ; Let there be frequency points between each pair of adjacent maximum points, then the maximum envelope of is represented as: , , ; To maximize, while introducing a threshold reduce the effect of noise on the spectrum, then the characteristic frequency point satisfies: (3) According to the signal characteristics, the parameters of the Gaussian window are adaptively selected, and the Gaussian adaptive optimization window is obtained, wherein: The parameters of the Gaussian window are adaptively selected according to the following conditions: ； The Gaussian adaptive optimization window is: ； (4) Calculate characteristic frequency points FFT with Gaussian window: Parameter determines the Gaussian window width; parameter is a window factor; parameter represents the trade-off between ST and STFT; parameter denotes the rate of change of the Gaussian window width (5) to spectral translation ; (6) the product of the calculation with the product: (7) Let the time shift factor , and perform IFFT to get The corresponding IST: (8) Repeat (4)-(7) to complete the IST of all characteristic frequency points, and obtain the complete IST matrix; Step two, the voltage and current signal fundamental discrete signal and distortion discrete signal are reconstructed by IST inverse transformation, and the specific reconstruction method is as follows: (1) Sum the IST matrix by row to obtain a spectrum vector ; (2) performing IFFT on the obtained frequency spectrum vector to obtain a characteristic signal , and completing reconstruction of the signal; Step three, the point product and operation of the reconstructed voltage and current signal fundamental discrete signal and distortion discrete signal are performed, and the power metering of the signal is completed.

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