A method for monitoring broadband oscillations in power systems based on optimized variational mode decomposition

Abstract

A method for monitoring broadband oscillations in power systems based on optimized variational mode decomposition is proposed. Aiming at the new broadband oscillation problem of power systems caused by high proportion of renewable energy and related high proportion of power electronic equipment connected to the grid, a method for monitoring broadband oscillations in power systems based on optimized variational mode decomposition (VMD) is proposed. Aiming at the problem of broadband oscillation multi-mode, the VMD algorithm is optimized, and an adaptive mode decomposition method is designed. The optimal number of modes is determined by defining the energy loss. In addition, in order to solve the problem of broadband oscillation high noise, the noise component is suppressed and the effective information of the oscillation signal is retained by combining the autocorrelation coefficient with the threshold, so as to complete the broadband oscillation identification and monitoring. Therefore, the method can maintain the quality of broadband oscillation monitoring under high-intensity random noise, and has good application in broadband oscillation signal monitoring in actual power systems.

Description

Technical Field

[0001] The present invention relates to the field of broadband oscillation of power systems, and in particular to a method for monitoring broadband oscillation of power systems based on optimized variational mode decomposition. Background Art

[0002] With the proposal of carbon peak and carbon neutrality goals, my country's energy will accelerate its transformation to green and clean. In the future, the power system will have a high proportion of renewable energy and a high proportion of power electronic equipment ("double high") connected to the grid. The interaction of high-penetration "double high" equipment will significantly change the dynamic characteristics and operation mode of the power system, leading to frequent new types of oscillation instability in the power system. The oscillation frequency presents a wide-band characteristic, ranging from a few hertz to several thousand hertz, and the noise interference is serious, which will threaten the safety and stability of the power system.

[0003] In 2012, the interaction between the doubly-fed wind turbine group and the series compensation device in Guyuan, Hebei Province caused subsynchronous oscillation. After the series compensation capacitor was removed, the oscillation was quickly quelled. In 2015, the direct-drive wind turbine group in Hami, Xinjiang, interacted with the weak AC power grid, causing subsupersynchronous oscillation, which caused the torsional vibration of the thermal power unit shaft system and caused tripping. In addition, the Southern Power Grid has also experienced subsupersynchronous oscillation caused by the interaction between the static synchronous compensator (STATCOM) and the weak AC power grid; the high-frequency harmonic oscillation caused by the interaction between the flexible direct current transmission (VSC-HVDC) and the weak AC power grid also appeared in the Luxi flexible direct current transmission system. It can be seen that the broadband oscillation caused by the grid connection of renewable energy and power electronic equipment has been common in recent years, which has a serious impact on the stable operation of the power system.

[0004] Due to the large-scale access of renewable energy generation, energy storage and electric vehicles, and the frequent switching of power electronic switches, broadband signals are seriously polluted by high-intensity noise. Common signal monitoring methods for power systems include Prony algorithm, wavelet transform, empirical mode decomposition (EMD), and variational mode decomposition (VMD) using linear combinations of exponential functions to estimate the oscillation frequencies. The Prony algorithm can identify the components of the signal, but it is sensitive to noise and cannot process non-stationary signals. The wavelet transform method can suppress noise, but the accuracy of noise reduction is overly dependent on the selection of wavelet basis. EMD decomposes the signal into p intrinsic mode functions (IMF) and uses Hilbert transform (HT) to measure the oscillation information, but EMD has problems such as endpoint effect and modal aliasing, and cannot separate frequencies with similar frequencies (f 1 <f 2 <2f 1) components, which will lead to inaccurate measurement of broadband signals. The VMD algorithm makes up for the shortcomings of EMD, but broadband oscillations may have multiple oscillation frequencies, the decomposition number p value is difficult to select, and some noise will be mixed in the effective IMF and cannot be eliminated. How to quickly suppress high-intensity random noise and effectively identify oscillation information is a key issue in broadband monitoring research, and existing monitoring methods cannot provide data support for broadband generation mechanism and operation control research. At present, no description or report of a method similar to the present invention has been found, and similar information at home and abroad has not been collected. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the existing methods, the present invention provides a method for monitoring wide-band oscillation of a power system based on optimized variational mode decomposition.

[0006] According to one aspect of the present invention, there is provided a method for monitoring wideband oscillation of a power system based on optimized variational mode decomposition, comprising:

[0007] Constructing a broadband oscillation variational model containing multiple modes, wherein the variational model assumes that the broadband oscillation signal can be decomposed into multiple intrinsic mode functions (IMFs), each of which is a finite bandwidth with a center frequency, and the variational model is constructed to find multiple mode functions, so that the sum of the estimated bandwidth of each mode is minimized when the sum of each mode is equal to the broadband oscillation signal;

[0008] For the broadband oscillation variational model containing multiple modes, the optimal solution of the variational model is solved, the Lagrange multiplication operator and the quadratic penalty function term are introduced, the constrained model is converted into an unconstrained model, and the alternating direction multiplier method is used to solve it;

[0009] Aiming at the problem that the broadband oscillation signal may have multiple modes whose numbers are difficult to determine, the energy loss is defined to measure the VMD decomposition effect, the VMD algorithm is further optimized, and the number of decomposition layers is adaptively determined;

[0010] In view of the fact that the power system signal is seriously affected by high-intensity random noise, the modulus IMF after the VMD adaptive decomposition is subjected to noise reduction processing. Since part of the random noise will be separated into the pure noise IMF, the other part will be mixed in the effective IMF. The noise component is suppressed and the effective information of the oscillation signal is retained by combining the autocorrelation coefficient with the threshold.

[0011] For the monitoring of effective IMF oscillation information after noise reduction, the center frequency of the effective IMF is analyzed and its corresponding amplitude is obtained through Hilbert Transform (HT), thus completing the monitoring of broadband oscillation information.

[0012] According to another aspect of the present invention, there is provided a method for constructing a broadband oscillation variational model containing multiple modes, comprising:

[0013] Assume that the broadband oscillation signal x(t) can be decomposed into p IMF components u p (t), through Hilbert transform analysis, we get its one-sided spectrum,

[0014]

[0015] Among them, δ(t) is the Dirichlet function, u p (t) is the modal function. Estimate the center frequency ω of each IMF analytical signal p , each mode u p The spectrum of (t) is transferred to the corresponding baseband to obtain:

[0016]

[0017] Among them, ω p is the estimated center frequency.

[0018] According to the Gaussian smoothness and gradient square L of the above demodulated signal 2 The norm criterion is used to estimate the bandwidth of each mode, and the constrained VMD variational model can be constructed as:

[0019]

[0020] Among them, {u p}={u 1 ,u 2 ,…,u p} is the set of modal functions, {ω p}={ω 1 ,ω 2 ,…,ω p} is the set of center frequencies.

[0021] According to a third aspect of the present invention, a method for solving an optimal solution of a variational model is provided, comprising:

[0022] The Lagrange multiplication operator λ(t) and the quadratic penalty function term α are introduced to transform the constrained model into an unconstrained model, in which the Lagrange multiplication operator can maintain the strictness of the constraints, and the quadratic penalty function term can distinguish the oscillation characteristics of the signal in the presence of high-intensity noise. The expression of the expanded variational model is:

[0023]

[0024] The variational model is extended using the alternating direction multiplier method, which alternately calculates the update and Iteratively solve the saddle point of the extended Lagrangian variational model.

[0025] The modal The expression to be solved is:

[0026]

[0027] In the formula, Abbreviated as ω p ,u p (t) n+1 Abbreviated as u p (t). Perform Fourier transform on it and transform it into the frequency domain:

[0028]

[0029] Use ω-ω p Substituting ω in the first term and converting the integration interval of the second norm to non-negative frequencies, we obtain:

[0030]

[0031] When ω<0, the value of 1+sgn(ω) is 0. Further simplifying formula (A4), converting the integral interval of the second norm to non-negative frequency, we can obtain:

[0032]

[0033] Solve this quadratic optimization problem, the solution is:

[0034]

[0035] In the formula, Equivalent to the original signal Subtract the remaining modal Wiener filters and perform an inverse Fourier transform on them, and the actual part is u p (t).

[0036] Similarly, the center frequency ω p The value problem is:

[0037]

[0038] The above formula is transformed into the frequency domain through Fourier transform and simplified to:

[0039]

[0040] Solving for the center frequency ω p The iterative method is:

[0041]

[0042] In the formula, Equivalent to the center of gravity of the power spectrum of the current mode function.

[0043] According to a fourth aspect of the present invention, a VMD optimization method for adaptively determining the number of decomposition levels is provided, comprising:

[0044] Determine the optimal modal number p from the energy perspective. In the frequency domain, periodic signals with different frequencies are orthogonal to each other, and the energy of the original signal in the frequency domain is equal to the energy sum of each frequency component. For a signal z(t), its frequency domain transform is Z(f), and Parseval's theorem shows:

[0045]

[0046] When the p value is large, a certain frequency may be decomposed into more than one modal component. Assume that the amplitude of the broadband oscillation signal x(t) at frequency f is Z. If it is decomposed into two modes, the amplitudes are Z 1 and Z 2 , Z 1 and Z 2 If it is not 0, then there must be:

[0047]

[0048] Therefore, the signal energy will be reduced when over-decomposition is performed. p The energy calculation formula of (t) is:

[0049]

[0050]

[0051] In the formula, i is the time series value, N is the signal length, E tol is the original signal energy, E p is the energy of each modal component.

[0052] The energy loss is defined to measure the VMD decomposition effect. The energy loss expression is:

[0053]

[0054] When k is increased successively, if η>0, it means that k+1 modes are over-decomposed. At this time, the k value is the adaptive optimal mode number.

[0055] According to a fifth aspect of the present invention, a method for denoising the IMF after the VMD adaptive decomposition is provided, comprising:

[0056] Construct a high-intensity random noise model:

[0057] N(t)=N G (t)+NP (t)

[0058] Among them, N G (t) is the background noise, N P (t) is random pulse noise.

[0059] After VMD decomposition, part of the random noise will be separated into the pure noise IMF, and the other part will be mixed in the effective IMF. By calculating the autocorrelation coefficient of each component, the pure noise IMF and the noisy IMF can be distinguished. The calculation formula of the autocorrelation coefficient is:

[0060]

[0061] Among them, cov[u p (t 1 ),u p (t 2 )] is the covariance of the two periods before and after the mode p, and this paper takes t 1 is the first half sampling time, t 2 is the sampling time of the second half, and σ is the standard deviation. Since random noise takes random values ​​at any time, the correlation between different time periods is very low, while the effective IMF oscillates periodically according to the central frequency, and the degree of autocorrelation is high. According to the range of the Pearson correlation coefficient, the correlation coefficient value of 0.8-1 indicates extremely strong correlation, 0.6-0.8 indicates strong correlation, 0.4-0.6 indicates moderate correlation, 0.2-0.4 indicates weak correlation, and 0-0.2 indicates extremely weak correlation or no correlation. After calculating the autocorrelation coefficient, each IMF can be divided into pure noise IMF and noisy IMF. In order to fully ensure the retention of effective IMF, the threshold of the autocorrelation coefficient is set to 0.2, and the IMF less than the threshold is determined as pure noise IMF for removal.

[0062] After removing the pure noise IMF, each noisy IMF doped with noise is further de-noised. The frequency spectrum is detected according to the adaptive threshold. If the frequency amplitude exceeds the threshold, it is retained. If it is lower than the threshold, it is forced to zero, that is:

[0063]

[0064] Where the subscript i represents the i-th noisy IMF, f traverses the entire spectrum, and T i is the threshold value, here we take σ i is the standard deviation of the ith noisy IMF, and N is the signal length.

[0065] According to a sixth aspect of the present invention, a method for monitoring effective IMF oscillation information after noise reduction is provided, comprising:

[0066] Analysis of effective IMFu p(t) The center frequency ω p If a frequency IMF other than the base frequency is detected, HT transformation is performed on this IMF to obtain:

[0067]

[0068] u p (t) and Y(t) form a conjugate complex pair and obtain the analytical signal:

[0069] Z(t)=u p (t)+jY(t)=a(t)e jθ(t)

[0070] Where a(t) and θ(t) are the instantaneous amplitude and phase, respectively.

[0071]

[0072] The above formula can be used to solve the amplitude corresponding to the IMF component, thereby realizing the monitoring of effective IMF oscillation information.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] The present invention provides a method for monitoring wide-band oscillations of a power system based on optimized variational modal decomposition. Aiming at the new wide-band oscillation problem of a power system caused by high proportion of renewable energy and related high proportion of power electronic equipment connected to the grid, a method for monitoring wide-band oscillations of a power system based on optimized variational modal decomposition is proposed. Aiming at the problem of multi-mode of wide-band oscillation, the VMD algorithm is optimized, and an adaptive modal decomposition method is designed. The optimal number of modes is determined by defining the energy loss. In addition, in view of the problem of high noise of wide-band oscillation, the noise component is suppressed and the effective information of the oscillation signal is retained by combining the autocorrelation coefficient with the threshold, so as to complete the identification and monitoring of wide-band oscillations. Therefore, the method can maintain the quality of wide-band oscillation monitoring under the condition of high-intensity random noise, and has good application in the monitoring of wide-band oscillation signals of actual power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0076] Figure 1 It is a flow chart of a method for monitoring wide-band oscillation of a power system based on optimized variational mode decomposition in one embodiment of the present invention;

[0077] Figure 2 It is a schematic diagram of the monitoring result of a multi-modal broadband oscillation signal in a preferred embodiment of the present invention;

[0078] Figure 3A schematic diagram of simulation of a broadband original signal and a noise-added signal in a preferred embodiment of the present invention;

[0079] Figure 4 A schematic diagram of IMF waveforms decomposed by VMD in a preferred embodiment of the present invention;

[0080] Figure 5 A schematic diagram showing the comparison between a broadband noise reduction signal and an original signal in a preferred embodiment of the present invention;

[0081] Figure 6 This is a schematic diagram of the DC end-to-end structure of a wind farm in North China in a preferred embodiment of the present invention;

[0082] Figure 7 This is a schematic diagram of bus A voltage recording in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following is a detailed description of the embodiments of the present invention: This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given. It should be pointed out that for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

[0084] Figure 1 The flowchart of the method for monitoring wideband oscillation of power system based on optimized variational mode decomposition in one embodiment of the present invention is shown.

[0085] like Figure 1 As shown, the method for monitoring wide-band oscillation of a power system based on optimized variational mode decomposition provided in this embodiment may include the following steps:

[0086] S100, a method for constructing a broadband oscillatory variational model with multiple modes, comprising:

[0087] Assume that the broadband oscillation signal x(t) can be decomposed into p IMF components u p (t), through Hilbert transform analysis, we get its one-sided spectrum,

[0088]

[0089] Among them, δ(t) is the Dirichlet function, u p (t) is the modal function. Estimate the center frequency ω of each IMF analytical signal p , each mode u p The spectrum of (t) is transferred to the corresponding baseband to obtain:

[0090]

[0091] Among them, ω pis the estimated center frequency.

[0092] According to the Gaussian smoothness and gradient square L of the above demodulated signal 2 The norm criterion is used to estimate the bandwidth of each mode, and the constrained VMD variational model can be constructed as:

[0093]

[0094] Among them, {u p}={u 1 ,u 2 ,…,u p} is the set of modal functions, {ω p}={ω 1 ,ω 2 ,…,ω p} is the set of center frequencies.

[0095] S200 provides a method for finding the optimal solution of a variational model, including:

[0096] The Lagrange multiplication operator λ(t) and the quadratic penalty function term α are introduced to transform the constrained model into an unconstrained model, in which the Lagrange multiplication operator can maintain the strictness of the constraints, and the quadratic penalty function term can distinguish the oscillation characteristics of the signal in the presence of high-intensity noise. The expression of the expanded variational model is:

[0097]

[0098] The variational model is extended using the alternating direction multiplier method, which alternately calculates the update and Iteratively solve the saddle point of the extended Lagrangian variational model.

[0099] The modal The expression to be solved is:

[0100]

[0101] In the formula, Abbreviated as ω p ,u p (t) n+1 Abbreviated as u p (t). Perform Fourier transform on it and transform it into the frequency domain:

[0102]

[0103] Use ω-ω p Substituting ω in the first term and converting the integration interval of the second norm to non-negative frequencies, we obtain:

[0104]

[0105] When ω<0, the value of 1+sgn(ω) is 0. Further simplifying formula (A4), converting the integral interval of the second norm to non-negative frequency, we can obtain:

[0106]

[0107] Solve this quadratic optimization problem, the solution is:

[0108]

[0109] In the formula, Equivalent to the original signal Subtract the remaining modal Wiener filters and perform an inverse Fourier transform on them, and the actual part is u p (t).

[0110] Similarly, the center frequency ω p The value problem is:

[0111]

[0112] The above formula is transformed into the frequency domain through Fourier transform and simplified to:

[0113]

[0114] Solving for the center frequency ω p The iterative method is:

[0115]

[0116] In the formula, Equivalent to the center of gravity of the power spectrum of the current mode function.

[0117] S300 provides a VMD optimization method for adaptively determining the number of decomposition levels, including:

[0118] Determine the optimal modal number p from the energy perspective. In the frequency domain, periodic signals with different frequencies are orthogonal to each other, and the energy of the original signal in the frequency domain is equal to the energy sum of each frequency component. For a signal z(t), its frequency domain transform is Z(f), and Parseval's theorem shows:

[0119]

[0120] When the p value is large, a certain frequency may be decomposed into more than one modal component. Assume that the amplitude of the broadband oscillation signal x(t) at frequency f is Z. If it is decomposed into two modes, the amplitudes are Z 1 and Z 2 , Z 1 and Z 2 If it is not 0, then there must be:

[0121]

[0122] Therefore, the signal energy will be reduced when over-decomposition is performed. p The energy calculation formula of (t) is:

[0123]

[0124]

[0125] In the formula, i is the time series value, N is the signal length, E tol is the original signal energy, E p is the energy of each modal component.

[0126] The energy loss is defined to measure the VMD decomposition effect. The energy loss expression is:

[0127]

[0128] When k is increased successively, if η>0, it means that k+1 modes are over-decomposed. At this time, the k value is the adaptive optimal mode number.

[0129] S400, providing a denoising method for the IMF after the VMD adaptive decomposition, including:

[0130] Construct a high-intensity random noise model:

[0131] N(t)=N G (t)+N P (t)

[0132] Among them, N G (t) is the background noise, N P (t) is random pulse noise.

[0133] After VMD decomposition, part of the random noise will be separated into the pure noise IMF, and the other part will be mixed in the effective IMF. By calculating the autocorrelation coefficient of each component, the pure noise IMF and the noisy IMF can be distinguished. The calculation formula of the autocorrelation coefficient is:

[0134]

[0135] Among them, cov[u p (t 1 ),u p (t 2 )] is the covariance of the two periods before and after the mode p, and this paper takes t 1 is the first half sampling time, t 2is the sampling time of the second half, and σ is the standard deviation. Since random noise takes random values ​​at any time, the correlation between different time periods is very low, while the effective IMF oscillates periodically according to the central frequency, and the degree of autocorrelation is high. According to the range of the Pearson correlation coefficient, the correlation coefficient value of 0.8-1 indicates extremely strong correlation, 0.6-0.8 indicates strong correlation, 0.4-0.6 indicates moderate correlation, 0.2-0.4 indicates weak correlation, and 0-0.2 indicates extremely weak correlation or no correlation. After calculating the autocorrelation coefficient, each IMF can be divided into pure noise IMF and noisy IMF. In order to fully ensure the retention of effective IMF, the threshold of the autocorrelation coefficient is set to 0.2, and the IMF less than the threshold is determined as pure noise IMF for removal.

[0136] After removing the pure noise IMF, each noisy IMF doped with noise is further de-noised. The frequency spectrum is detected according to the adaptive threshold. If the frequency amplitude exceeds the threshold, it is retained. If it is lower than the threshold, it is forced to zero, that is:

[0137]

[0138] Where the subscript i represents the i-th noisy IMF, f traverses the entire spectrum, and T i is the threshold value, here we take σ i is the standard deviation of the ith noisy IMF, and N is the signal length.

[0139] S500 provides a method for monitoring effective IMF oscillation information after noise reduction, including:

[0140] Analysis of effective IMFu p (t) The center frequency ω p If a frequency IMF other than the base frequency is detected, HT transformation is performed on this IMF to obtain:

[0141]

[0142] u p (t) and Y(t) form a conjugate complex pair and obtain the analytical signal:

[0143] Z(t)=u p (t)+jY(t)=a(t)e jθ(t)

[0144] Where α(t) and θ(t) are the instantaneous amplitude and phase, respectively.

[0145]

[0146] The above formula can be used to solve the amplitude corresponding to the IMF component, thereby realizing the monitoring of effective IMF oscillation information.

[0147] In order to verify the monitoring accuracy of the power system broadband oscillation monitoring method based on optimized variational modal decomposition designed by the present invention for multi-modal broadband oscillation phenomenon, the frequency relative error (FRE) and the amplitude relative error (ARE) are used as judgment indicators, namely:

[0148]

[0149]

[0150] Among them, f and a are the theoretical values ​​of frequency and amplitude respectively, and are the monitoring values ​​of frequency and amplitude respectively.

[0151] For the effectiveness of the present invention under high-intensity random noise interference, the relative root mean square error (RRMSE) and signal to noise ratio (SNR) are used as evaluation indicators, namely:

[0152]

[0153]

[0154] Among them, S is the original signal without random noise interference, It is the effective signal after suppressing noise interference. The smaller the RRMSE, the closer the signal after suppressing noise interference is to the original signal; the larger the SNR, the lower the noise content and the better the noise reduction effect.

[0155] The test signal shown in the following formula is established. Considering that the broadband oscillation frequency has a wide distribution range and may have multiple components, three broadband oscillation frequencies of 589 Hz, 5000 Hz and 7894 Hz are generated in addition to the base frequency of 50 Hz. The oscillation amplitude is randomly generated, N G (t) and N P (t) is set to 0, the sampling frequency is set to 25.6kHz, and the simulation time is set to 1s. The test signal model used is:

[0156] x(t)=sin(2π×50t)+0.87sin(2π×589t)+0.21sin(2π×5000)+0.48sin(2π×7894t)+N G (t)+N P (t)

[0157] Figure 2The schematic diagram of the monitoring result of the multi-modal broadband oscillation signal is shown in FIG. 1 . The signal to be measured is processed by the power system broadband oscillation monitoring method based on optimized variational modal decomposition of the present invention, and the adaptive modal decomposition number is 4. Figure 2 The left half is the time domain decomposition result of the IMF part. The oscillation information of each IMF is calculated by HT. The amplitude-frequency result is as follows: Figure 2 In the right half, the test results show that the proposed method can effectively separate the IMFs and effectively identify the oscillation information of each IMF.

[0158] Figure 3 Figure 1 is a schematic diagram of the simulation of the original signal and the simulated signal after adding noise. To simulate high-intensity random noise, based on the above model, N G (t) Add Gaussian white noise with a signal-to-noise ratio of 10dB, N P (t) A random pulse noise with an amplitude 4 times that of the background noise is added, and its coverage in the time domain is 5%.

[0159] Figure 4 Figure 1 is a schematic diagram of the IMF waveforms decomposed by VMD. Through calculation, the relative root mean square error of the signal after adding noise is 0.4233, which shows that the noise seriously interferes with the original signal. Adaptive modal decomposition is performed on the noisy signal, and the optimal number of modes is determined to be 5. The center frequency of each mode is distributed from low frequency to high frequency. The decomposition results are shown in Figure 1. Figure 4 The autocorrelation coefficients of the IMFs are calculated to be 0.9922, 0.9785, 0.6571, 0.9066, and 0.0056, respectively. It can be determined that the first four components are noisy IMFs, and the last component is a pure noise IMF.

[0160] The pure noise IMF is discarded and this process is named as primary denoising. The remaining four noisy IMFs are retained. At this time, the relative root mean square error is 0.2009, and the noise content is reduced by 52.54%. Although the denoising effect is obvious, the noise content is still high. Continue to perform threshold denoising on each noisy IMF to further remove the noise component in the noisy IMF. This process is named secondary denoising. RRMSE and SNR are used to quantitatively evaluate the effects of the two denoising. The before and after comparison results are shown in Table 1.

[0161] Table 1 Comparison of noise reduction effects

[0162]

[0163] It can be seen from Table 1 that after two noise reduction processes, the RRMSE is less than 1%, the SNR is greatly improved, and the added noise is basically completely removed.

[0164] Figure 5FIG. 1 is a schematic diagram showing the comparison between the broadband noise reduction signal and the original signal in a preferred embodiment of the present invention. In order to more intuitively observe the relationship between the noise reduction signal and the original signal without noise, the time domain waveforms of the two are plotted as follows: Figure 5 As shown, the overall waveform shows that the denoised signal is highly consistent with the original signal. Randomly selecting a local image for magnification shows that the local waveforms are highly overlapped. The denoised signal can retain the effective oscillation information of the original signal while eliminating the noise.

[0165] After the noise reduction is completed, the effective IMF is analyzed, and the frequency and amplitude of each IMF are obtained through HT transformation to verify its monitoring accuracy for oscillation information. The results of oscillation information analysis are shown in Table 2. Both FRE and ARE are very small. After suppressing noise interference, the oscillation information can be accurately identified.

[0166] Table 2 Broadband oscillation monitoring results

[0167]

[0168] Figure 6 In order to verify the effect of the power system broadband oscillation monitoring method based on optimized variational mode decomposition designed by the present invention in actual broadband oscillation monitoring, the measured data of a wind farm in North China was tested. Figure 6 shown.

[0169] Figure 7 This is a schematic diagram of bus A voltage recording in a preferred embodiment of the present invention. During the start-up and shutdown commissioning of the wind farm, bus A and bus B operate end-to-end with the negative poles in single-pole operation, and the positive pole is in maintenance status. Bus A is in island operation mode, and the DC power is zero. Part of the recorded data on the bus A side before and after the red switch is connected is shown in the figure below. Figure 7 As shown, it can be clearly seen that the bus A voltage exhibits broadband oscillation.

[0170] The broadband oscillation monitoring method of the power system based on optimized variational modal decomposition designed by the present invention is used to monitor the commissioning line of the wind farm online, collect the operating status data of each line in real time, reduce noise and identify the information of effective IMF. Since the occurrence of broadband oscillation may cause three-phase imbalance in the power grid and different dynamic behaviors, the three-phase signals must be monitored simultaneously. The monitoring results of the three-phase voltage of bus A when the accident occurred are shown in Table 3. It can be seen that broadband oscillation does occur after the red switch is turned on in the wind farm test. In addition to the base frequency of 50Hz, two frequency components appear, and the broadband oscillation frequency is concentrated at 1507.5Hz and 1607.5Hz. After the broadband oscillation is detected, the converter valve is locked and the oscillation line is cut off. It takes 0.441s, which can meet the real-time requirements. According to preliminary analysis, it is believed that after the wind farm is put into the 220kV AC line, the converter valve and the AC line constitute LC oscillation, thereby generating broadband oscillation components.

[0171] Table 3 Bus A voltage broadband monitoring results

[0172]

[0173] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for monitoring broadband oscillations in a power system based on optimized variational mode decomposition, characterized in that: include: Construct a broadband oscillation variational model with multiple modes, including multiple intrinsic mode functions (IMFs), each of which is a finite bandwidth with a center frequency; By introducing Lagrange multiplication operators and quadratic penalty function terms, the constraints of the broadband oscillation variational model containing multiple modes are converted into an unconstrained model, and then the optimal solution of the variational model is solved by using the alternating direction multiplier method; Define the energy loss to measure the decomposition effect of variational mode VMD, further optimize VMD, and adaptively determine the number of decomposition levels; Performing denoising on the IMF after the VMD adaptive decomposition, suppressing the noise component and retaining the effective information of the oscillation signal by combining the autocorrelation coefficient with the threshold; Monitoring of effective IMF oscillation information after noise reduction, analyzing the center frequency of effective IMF and obtaining its corresponding amplitude through Hilbert transform HT, completing the monitoring of broadband oscillation information; Define the energy loss to measure the VMD decomposition effect, further optimize the VMD algorithm, and adaptively determine the number of decomposition levels, including: The energy E of the broadband oscillating signal x(t) tot and each modal component u p Energy E of (t) p , the calculation formula is as follows: In the formula, i is the time series value, and N is the signal length; The energy loss is defined to measure the VMD decomposition effect. The energy loss expression is: When k is increased successively, if η>0 appears, it means that k+1 modes are over-decomposed, and the k value at this time is the adaptive optimal mode number; The IMF after the VMD adaptive decomposition is subjected to denoising, and the noise component is suppressed and the effective information of the oscillation signal is retained by combining the autocorrelation coefficient with the threshold, specifically including: Construct a high-intensity random noise model: N(t)=N G (t)+N P (t) Among them, N G (t) is the background noise, N P (t) is random pulse noise; After VMD decomposition, part of the random noise will be separated into the pure noise IMF, and the other part will be mixed in the effective IMF. By calculating the autocorrelation coefficient of each component, the pure noise IMF and the noisy IMF can be distinguished. The calculation formula of the autocorrelation coefficient is: Among them, cov[u p (t1),u p (t2)] is the covariance of the two periods before and after the mode p, t1 is taken as the sampling time of the first half, t2 is taken as the sampling time of the second half, and σ is the standard deviation; according to the range of the Pearson correlation coefficient, the correlation coefficient value of 0.8-1 indicates a very strong correlation, 0.6-0.8 indicates a strong correlation, 0.4-0.6 indicates a moderate correlation, 0.2-0.4 indicates a weak correlation, and 0-0.2 indicates a very weak correlation or no correlation; After calculating the autocorrelation coefficient, each IMF is divided into pure noise IMF and noisy IMF. The threshold of the autocorrelation coefficient is set to 0.2, and the IMF less than the threshold is determined as pure noise IMF and removed; After removing the pure noise IMF, each noisy IMF doped with noise is further de-noised and detected according to the adaptive threshold in the spectrum. If the frequency amplitude exceeds the threshold, it is retained. If it is lower than the threshold, it is forced to zero, that is: Where the subscript i represents the i-th noisy IMF, f traverses the entire spectrum, and T i is the threshold value, here we take σ i is the standard deviation of the ith noisy IMF, and N is the signal length; The monitoring of effective IMF oscillation information after noise reduction is carried out by analyzing the center frequency of the effective IMF and obtaining its corresponding amplitude through Hilbert transform to complete the monitoring of broadband oscillation information, which specifically includes: Analysis of effective IMFu p (t) The center frequency ω p If a frequency IMF other than the base frequency is detected, HT transformation is performed on this IMF to obtain: u p (t) and Y(t) form a conjugate complex pair and obtain the analytical signal: Z(t)=u p (t)+jY(t)=a(t)e jθ(t) Where a(t) and θ(t) are the instantaneous amplitude and phase respectively; The above formula can be used to solve the amplitude corresponding to the IMF component, thereby realizing the monitoring of effective IMF oscillation information.

2. The method for monitoring wideband oscillation of a power system based on optimized variational mode decomposition according to claim 1, characterized in that: The construction of a broadband oscillation variational model containing multiple modes includes: Assume that the broadband oscillation signal x(t) is decomposed into p IMF components u p (t), through Hilbert transform analysis, we get its one-sided spectrum: Among them, δ(t) is the Dirichlet function, u p (t) is the modal function, and the center frequency ω of each IMF analytical signal is estimated p , each mode u p The spectrum of (t) is transferred to the corresponding baseband to obtain: Among them, ω p is the estimated center frequency; Calculate the square of the gradient of each demodulated signal L 2 norm, estimate the bandwidth of each mode, and construct the constrained VMD variational model as follows: Among them, {u p }={u1,u2,…,u p } is the set of modal functions, {ω p }={ω1,ω2,…,ω p } is the set of center frequencies.

3. The method for monitoring wideband oscillation of a power system based on optimized variational mode decomposition according to claim 2, characterized in that: The broadband oscillation variational model containing multiple modes, solving the optimal solution of the variational model, comprises: The Lagrange multiplication operator λ(t) and the quadratic penalty function term α are introduced to transform the constrained model into an unconstrained model. The expression of the expanded variational model is: The variational model is extended using the alternating direction multiplier method, which alternately calculates the update and Iteratively solve the saddle point of the extended Lagrangian variational model, The modal The expression to be solved is: In the formula, Abbreviated as ω p ,u p (t) n+1 Abbreviated as u p (t); perform Fourier transform on it and transform it into the frequency domain: Use ω-ω p Substituting ω in the first term and converting the integration interval of the second norm to non-negative frequencies, we obtain: When ω<0, the value of 1+sgn(ω) is 0. To further simplify the formula, convert the integral interval of the second norm to non-negative frequency: Solve this quadratic optimization problem, the solution is: In the formula, Equivalent to the original signal Subtract the remaining modal Wiener filters and perform an inverse Fourier transform on them, and the actual part is u p (t); Similarly, the center frequency ω p The value problem is: The above formula is transformed into the frequency domain through Fourier transform and simplified to: Solving for the center frequency ω p The iterative method is: In the formula, Equivalent to the center of gravity of the power spectrum of the current mode function.

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