Power system low frequency oscillation identification method based on ubss algorithm

Abstract

The present application relates to the technical field of power system, specifically relates to a power system low-frequency oscillation identification method based on UBSS algorithm, steps are as follows: through space-time conversion, real-time observation information mining is realized, and the observation multi-channel is expanded, and the UBSS problem is converted into BSS problem;The source number estimation of observation information is carried out using the Bayesian information criterion, the number of dominant oscillation modes is determined, the modal order is realized, and the modal decomposition task is completed using the BSS algorithm, and the estimation of oscillation mode parameters is realized.This method can decompose the main component in the complex signal under the condition of underdetermination, compared with HHT and Prony, has better noise robustness;In the calculation error of parameter estimation accuracy, the performance of the method is better, and dynamic information of modal parameters can be provided;Based on the observation signal, the number of low-frequency oscillation modes can be accurately estimated in the absence of system topology, the dependence on system information is reduced, and the applicability of the method is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system, in particular to a power system low-frequency oscillation identification method based on UBSS algorithm. BACKGROUND

[0002] For a long time, people study low-frequency oscillation problem through small signal stability analysis and linearization processing, and have achieved certain effect. Common methods include two categories of analysis method based on mathematical model and signal analysis method based on measured signal.

[0003] The modal parameter identification method based on mathematical model has the characteristics of strong theory and clear physical meaning, but its existing difficulties are obvious. The system is increasingly complex and large, and the specific model is difficult to establish. The "dimension disaster" in the characteristic root algorithm, the non-linear equation needs to be calculated by order reduction, the calculation complexity problem caused by the large amount of calculation and time consumption of time domain simulation method and the non-linear problem of power system itself caused by the time-varying and coupling of system structure parameters.

[0004] The analysis method based on measured signal is different. The output data of the power system measuring element is the reflection of the real running state of the corresponding time, and clearly records the conversion of the power system between different running states, and can present the results that the model cannot simulate. The measured data commonly used for low-frequency oscillation analysis mainly includes the swing curve of generator power angle and the oscillation curve of output power. At present, the modal parameter identification methods based on measured data mainly include Fourier method, Prony algorithm, total least squares-rotation invariant algorithm, matrix pencil algorithm, random subspace method and Hilbert-Huang transform.

[0005] For low-order power system, the analysis method based on physical model can be used for low-frequency oscillation analysis. With the complication of power system, the system size expands rapidly, the system order grows continuously, the accurate model is difficult to establish, the mathematical analysis operation amount increases by geometric multiple, and the noise interference is also one of the challenges faced by model method. Therefore, more effective and more reliable low-frequency oscillation mode identification method is urgently needed to study, and hopes to be able to solve the problem of complex multi-modal low-frequency oscillation identification. SUMMARY

[0006] The application is based on underdetermined blind source analysis principle, and provides a power system low-frequency oscillation identification method based on UBSS algorithm.

[0007] The embodiment of the application is implemented by the following technical scheme: the power system low-frequency oscillation identification method based on UBSS algorithm comprises the following steps:

[0008] Step 1: information mining of real-time observation is realized through space-time conversion, observation multi-channels are expanded, and the UBSS problem is converted into the BSS problem;

[0009] Step 2: the number of sources of observation information is estimated by using the Bayesian information criterion, the number of dominant oscillation modes is determined, mode order is realized, the mode decomposition task is completed by using the BSS algorithm, and the estimation of oscillation mode parameters is realized.

[0010] According to a preferred embodiment, before the step 1, the method further comprises defining a low-frequency oscillation energy ratio function P NR The real-time observation signal x(t) is subjected to singularity detection, and the expression of x(t) is as follows:

[0011]

[0012] In the above formula, n represents the number of different low-frequency oscillation modes, Amp i represents the relative amplitude of the i th low-frequency oscillation mode in x(t), ζ i represents the damping coefficient of the i th low-frequency oscillation mode in x(t), f i represents the oscillation frequency of the i th low-frequency oscillation mode in x(t), and φ i represents the phase shift of the i th low-frequency oscillation mode in x(t).

[0013] According to a preferred embodiment, the low-frequency oscillation energy ratio function P NR is expressed as follows:

[0014]

[0015] In the above formula, P NR represents the energy ratio of the latter half to the former half in the time window, T0 represents the starting point of the time window, and T represents the total length of the time window.

[0016] The expression of the singularity detection is P NR ≥ ε, ε represents a threshold value.

[0017] According to a preferred embodiment, the threshold value ε is formulated based on the total width of the time window T and the sampling frequency of the power system.

[0018] According to a preferred embodiment, the real-time observation information mining through space-time conversion includes:

[0019] The detected signal mutation information X 1×N = (x1, x2, …, x N ) is used to construct a multi-channel mixing matrix X M×N using dimension space theory.

[0020] According to a preferred embodiment, a random time delay method is used to construct a virtual observation multi-channel.

[0021] According to a preferred embodiment, the step 2 specifically includes:

[0022] The number of source signals n * is estimated using the Bayesian information criterion, and the source signal components in X M×N are decomposed through source signal stripping to form a source signal estimation matrix Y M×N ;

[0023] Y M×N is processed through Hilbert transform to obtain low-frequency oscillation mode parameters, including Amp i , fav i , ζ i , and fav i represents the mean value of the oscillation frequency.

[0024] Each component representing the characteristics of the low-frequency oscillation is extracted from n * and fav i one by one to obtain the number of low-frequency oscillation modes n.

[0025] According to a preferred embodiment, the FastICA algorithm is used to strip and decompose the source signal components in X M×N .

[0026] According to a preferred embodiment, the extraction of each component representing the characteristics of the low-frequency oscillation from n * and fav i specifically includes:

[0027] Based on the fixed frequency range (f min , f max ) of the low-frequency oscillation, n * and favi Screening components meeting the low-frequency oscillation characteristics, determining the number n of low-frequency oscillation modes;

[0028] When f min ≤ fav ≤ f max , n = n * , otherwise n = n * -1.

[0029] According to a preferred embodiment, the processing of Y M×N by Hilbert transform to obtain low-frequency oscillation mode parameters specifically includes:

[0030] Processing Y M×N by Hilbert transform to obtain instantaneous parameters Amp i (t) and f i (t) of the low-frequency oscillation mode, and deriving Amp i 9t) to obtain Amp i (t)'.

[0031] Averaging Amp i (t), f i (t) and Amp i (t)' respectively to obtain the low-frequency oscillation mode parameters Amp i , fav i and ζ i .

[0032] The technical scheme of the power system low-frequency oscillation identification method based on the UBSS algorithm of the embodiment of the present application has at least the following advantages and beneficial effects: (1) the method can decompose the main components in a complex signal under underdetermined conditions, has better noise robustness compared with HHT and Prony, and can be used for low-frequency oscillation mode identification; (2) in terms of calculation error of parameter estimation accuracy, the performance of the method is better than that of HHT and Prony methods, and dynamic information of modal parameters can be provided; (3) based on the observation signal, the method can accurately estimate the number of low-frequency oscillation modes in the absence of system topology structure, reduce the dependence on system information, and improve the applicability of the method; therefore, the method provided by the present application is an innovative and effective means, which can solve the underdetermined blind source separation problem and realize low-frequency oscillation dominant mode parameter identification, and provide necessary reference information for locating the oscillation source and adjusting the system parameters. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 A flowchart of the power system low-frequency oscillation identification method provided for the embodiment 1 of the present application is shown;

[0034] Figure 2A UBSS (underdetermined blind source separation) schematic diagram provided for the embodiment 1 of the present application;

[0035] Figure 3 An influence diagram of time window width on detection result provided for the embodiment 1 of the present application;

[0036] Figure 4 A decomposition effect diagram of the UBSS algorithm on equation (17) under no noise interference provided for the embodiment 1 of the present application;

[0037] Figure 5 A decomposition effect diagram of the UBSS algorithm on equation (17) under noise interference provided for the embodiment 1 of the present application;

[0038] Figure 6 A source number estimation test result of equation (17) provided for the embodiment 1 of the present application;

[0039] Figure 7 A distribution comparison diagram of mode parameter identification result of equation (17) by different methods provided for the embodiment 1 of the present application, wherein blue-UBSS, magenta-HHT, SNR=100dB;

[0040] Figure 8 A standard deviation distribution comparison diagram of low frequency oscillation mode parameter of equation (17) by two methods under large interference condition provided for the embodiment 1 of the present application;

[0041] Figure 9 A separation result of 12 by the UBSS algorithm under small disturbance condition provided for the embodiment 1 of the present application;

[0042] Figure 10 A separation result of 24 by the UBSS algorithm under large disturbance condition provided for the embodiment 1 of the present application;

[0043] Figure 11 Active waveforms of P1 and P2 recorded in situ provided for the embodiment 1 of the present application;

[0044] Figure 12 A main mode instantaneous mode parameter based on the UBSS algorithm provided for the embodiment 1 of the present application. DETAILED DESCRIPTION

[0045] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0046] Embodiment 1

[0047] Referring to Figure 1 as shown, Figure 1 The flowchart of the power system low-frequency oscillation identification method provided by the embodiment 1 of the present application.

[0048] The power system low-frequency oscillation identification method based on the UBSS algorithm provided by the embodiment of the present application comprises the following steps:

[0049] (1) Signal singularity detection: when low-frequency oscillation occurs, the signal of the oscillation source will change significantly, which causes the energy of the observed signal to change. Considering the actual detection effect, algorithm complexity and other factors, the energy ratio function is used to realize the start detection process of low-frequency oscillation in the embodiment.

[0050] It should be noted that the energy ratio method is to determine the mutation of the signal by the ratio of the effective values of the energy of the two parts of the signal in a fixed time window. The time window is a fixed time interval, and the sampling point number can be converted according to the sampling frequency when calculating.

[0051] Specifically, the embodiment defines a low-frequency oscillation energy ratio function P NR The singularity of the real-time observed signal x(t) is detected by using the low-frequency oscillation energy ratio function P NR The expression of the low-frequency oscillation energy ratio function P

[0052]

[0053] In the above formula, P NR represents the energy ratio of the latter half to the former half in the time window, T0 represents the starting point of the time window, and T represents the total length of the time window.

[0054] It should be noted that, as shown in Figure 3 The selection of the width of the time window is very critical when using the energy ratio method to extract the signal mutation information. Therefore, when using the energy ratio method to detect singularity, the width of the time window should be selected comprehensively to determine the occurrence of low-frequency oscillation.

[0055] Further, the embodiment formulates a threshold value ε based on the width of the time window T and the sampling frequency f0 of the power system. The energy ratio P NR The criterion for detecting the singularity of the signal is P NR ≥ ε. It should be noted that only when the parameters are matched, the sensitivity can be accurately captured to resist the interference of noise signals, and the signal mutation characteristics will not be submerged in the interference noise.

[0056] Further, the expression of the real-time observed signal x(t) is as follows:

[0057]

[0058] In the above formula, n represents the number of different low-frequency oscillation modes, and Amp i ζ represents the relative amplitude of the i-th low-frequency oscillation mode in x(t). i f represents the damping coefficient of the i-th low-frequency oscillation mode in x(t). i Let φ represent the oscillation frequency of the i-th low-frequency oscillation mode in x(t). i This represents the phase shift of the i-th low-frequency oscillation mode in x(t).

[0059] (2) Constructing a virtual multi-channel matrix: For the problem of identifying low-frequency oscillations in power systems, the observation information provided by channels based on the system topology is often insufficient, or even only a single observation channel is available, which is a typical UBSS problem. For most UBSS problems in physical space, the observed signal contains a data sequence containing multi-dimensional information such as space and time.

[0060] Furthermore, this embodiment defines the function F:R n →R m It is a function that maps from n-dimensional Euclidean space to m-dimensional Euclidean space. When UBSS is applied to a wider range of multidimensional spaces, the observed signal X is represented as:

[0061] X = F(v1, v2, ..., v n )+C (3)

[0062] In the above formula, v1, v2, ..., v n Let X be a multidimensional reference coordinate system. Then the Jacobian matrix of the observed signal X is:

[0063]

[0064] Assume that *i* is any one of the *m* observed signals, *k* is the time dimension in *n*-dimensional space, and *j* is any dimension other than *k* in *n*-dimensional space. Considering the most severe case of missing source signal information in the UBSS problem, where the observed signal has only one unique coordinate representation in all dimensions represented by the power system topology, then:

[0065]

[0066] In the above formula, c represents a constant, c∈R, j≠k. Differential operators representing the time dimension, i.e.

[0067] In addition to the time dimension, no other dimension can further dig more information about the source signal. Therefore, the embodiment seeks more information from the time dimension to reconstruct enough virtual observation signals to realize the positive definitization of the underdetermined blind source separation. At this time, the observation signal only contains useful information in the time dimension, and the n-dimensional space can be reduced in dimension, so that the unique representation of all observation channel signals in the n-dimensional space is z, and the n-dimensional space is converted into a one-dimensional space about time.

[0068] Further, by expanding the dimension in the one-dimensional space, a virtual observation channel is constructed. Considering that the use of interpolation method will introduce new interference signals, resulting in the destruction of the structure of the source signal, and the use of ordinary time delay theory may cause modal aliasing of the signal due to the periodicity of the observation signal, resulting in the inability to separate the source signal. Based on this, the embodiment uses a random time delay method to construct a virtual observation channel.

[0069] It should be noted that the random time delay method refers to constructing a virtual reference coordinate system by a random time delay method to expand a new dimension space. Further, the embodiment is implemented by using regular values, and any expanded observation channel signal z I The expression is as follows:

[0070]

[0071] In the above formula, A represents a scaling factor, τ I represents the corresponding time delay factor of the I virtual channel signal. It should be noted that the number of low-frequency oscillation modes generally does not occur at the same time, and therefore the embodiment sets the value range of I as i=[1, 10] to meet the engineering needs. Wherein, τ i satisfies

[0072] τ ij = β·(j-1) + γ (7)

[0073] In the above formula, β represents an interval coefficient of different virtual channel signals, and γ represents a time delay constant.

[0074] It should be noted that for different virtual new channels, the scaling factor a determines the sampling interval of the signal. Modern measurement equipment often has high sampling accuracy, and the frequency of low-frequency oscillation is relatively low, so it brings inconvenience to measurement. When the system sampling frequency f0 is very high, the actual sampling frequency of the measured signal can be reasonably controlled by the scaling factor a to obtain a virtual channel signal with a suitable frequency. The interval coefficient β determines the mutual interval of different virtual channels, and reasonable control of the interval coefficient β can fully reflect the difference between different virtual channels on the premise of containing the source signal, and construct a usable virtual multi-channel signal to convert the UBSS problem into a BSS problem.

[0075] Based on the above principle, in one embodiment of the present embodiment, the recording measurement signal is X 1×N = (x1, x2, …, x N ), a multi-channel mixing matrix X M×N is constructed using dimension space theory, and the UBSS problem is converted into a BSS problem.

[0076] (3) Signal source number estimation. Before low-frequency oscillation parameter identification, a key problem is the estimation of the number of oscillation sources. In the present embodiment, the number of source signals n * is adaptively judged by using the Bayesian information criterion based on the observed signal information.

[0077] The Bayesian information criterion is described in detail as follows:

[0078] Suppose that the number of signal sources is n, and the probability density of the observed signal X is represented by the variable θ. In the absence of prior information, it is assumed that n satisfies a uniform distribution, and the optimal model under the Bayesian optimal decision rule is:

[0079]

[0080] In the above formula, n * represents the Bayesian optimal decision estimate value of n, and P(n|X) represents the probability that the number of source signals is n.

[0081] According to the Bayesian relationship, the probability that the condition of the observed signal X has n source signals can be expressed as:

[0082]

[0083] In the above formula, P(X|n) represents the maximum likelihood probability, and P(n) represents the prior probability. Since there is a lack of prior knowledge, a uniform distribution is used to replace it in the present embodiment, that is:

[0084]

[0085] In the above formula, M represents the maximum value of the observed signal number m. Thus, the model probability density P(X|n) can be expressed as:

[0086] P(X|n) = ∫P(X|θ, n)P(θ|n)dθ (11)

[0087] Among them, the model parameter is expressed by θ, and the corresponding model probability density is P(X|θ, n).

[0088] P(X|n) = ∫P(X|θ, n)P(θ, n)dθ (12)

[0089] Since integral calculations are too complex, this embodiment uses an approximation based on the Bayesian information criterion. Assuming the signal follows a Gaussian distribution, we approximate the integral by maximizing the integral, obtaining the explicit expression for P(X|n), which is:

[0090]

[0091] In the above formula, θ * This represents the maximum a posteriori parameter of the model, and N represents the number of samples.

[0092] It is worth mentioning that the estimated number of signal sources n * This does not imply the determination of the order of a low-frequency oscillation system.

[0093] (4) Source signal stripping, see Figure 2 As shown, using BSS technology is one of the optimal methods for source signal stripping. In this embodiment, the FastICA algorithm is selected to strip and decompose the X signal. M×N The source signal components in the matrix form the source signal estimation matrix Y. M×N .

[0094] (5) Low-frequency oscillation mode parameter estimation: The task of UBSS is to separate the source signal from the observed signal. Therefore, accurate identification of the parameters of the source signal, i.e., the oscillation component, is another key issue. Specifically, in this embodiment, the parameter identification of the oscillation component is achieved through Hilbert transform to determine the number of dominant oscillation modes.

[0095] The expression for the Hilbert transform is as follows:

[0096]

[0097]

[0098]

[0099] In the above formula, y i (t) represents Y M×N The source signal components in Y. This embodiment utilizes the Hilbert transform to analyze the source signal components in Y. M×N Through processing, the instantaneous frequency and instantaneous amplitude of the signal can be directly expressed, and the frequencies f of each decomposed component can be obtained. i (t), Amplitude Amp i (t) can be calculated from the mean, and the damping coefficient ζ is obtained through Amp. i (t) Curve fitting and differentiation Amp i (t)′ is used to obtain the low-frequency oscillation mode parameter Amp. i ,fav i and ζ iIt should be noted that, considering the influence of the boundary effect, the data in the middle section is taken and the data near the beginning and end is discarded.

[0100] (6) Modal order of low-frequency oscillation, result of source number estimation n * It is shown that the mixed signal contains the number of signal sources, which is different from the number of low-frequency oscillation modes and the order of the oscillation system, and needs to be further clarified.

[0101] In one implementation of the embodiment, each component representing the characteristics of low-frequency oscillation is extracted from n * and fav i to obtain the number of low-frequency oscillation modes n. Specifically, the embodiment is based on the fixed frequency range (f min , f max ) of low-frequency oscillation, and components meeting the characteristics of low-frequency oscillation are screened from n * and fav i to determine the number of low-frequency oscillation modes n; when f min ≤ fav≤ f max , n = n * , otherwise n = n * -1, so as to realize modal order determination of the oscillation system.

[0102] To verify the effectiveness of the method, the existing low-frequency oscillation model is used for simulation verification, and the following provides a simulation verification process of the power system low-frequency oscillation identification method based on the UBSS algorithm of the application:

[0103] The expression of the existing low-frequency oscillation model is as follows:

[0104]

[0105] Taking the mixed signals x, s1, s2 and s3, in the case of no noise interference, the decomposed components are as shown in Figure 4 For ideal low-frequency oscillation signals, the UBSS algorithm can realize effective separation.

[0106] In blind source separation, noise can be regarded as a source, which is a random and nonlinear signal, and the interference signal only increases a decomposition component. For the UBSS method, the dimension transformation also acts on the interference signal. A random white noise signal is added to test the effectiveness of UBSS under interference conditions.

[0107] Figure 5 The UBSS decomposition effect under noise interference conditions is shown, which verifies the effectiveness of the UBSS method under noise interference conditions, and shows that the UBSS has the possibility of being applied to power system low-frequency oscillation mode identification.

[0108] Before the identification of low frequency oscillation mode, the source number estimation (i.e. modal order estimation) is an indispensable step. In the condition of no noise interference, the result of source number estimation will appear the probability of 1 for the actual value P(X|n=n * ) and 0 for others.

[0109] Considering the inevitable influence of electromagnetic interference in engineering, a suitable interval parameter is set, 100 dB of random white noise is added to the observation signal mixed by s1, s2 and s3, and the number of oscillation components is estimated, and the test results are shown in Figure 6 .

[0110] Figure 6 It is shown that the probability distribution of source number estimation is different from the ideal state under the influence of noise interference signal, but the P value still reaches the maximum when n=3, indicating that the possibility of n * =3 is the largest. The existence of interference signal causes the observation signal to be damaged to a certain extent, resulting in a decrease in probability value, but it still remains the maximum. This fully verifies the effectiveness of the proposed source number estimation method.

[0111] For the detection of low frequency oscillation, frequency and attenuation coefficient are the most important indicators to characterize low frequency oscillation. In this paper, Prony algorithm and nonlinear HHT method are selected as the control group, and the aforementioned signal is subjected to LFO mode parameter identification test under the condition of noise interference: the sampling frequency is 500 Hz, the signal length is 10 s, the interference signal is 100 dB of random white noise, and the test is repeated 100 times.

[0112] Figure 7 The test result distribution of the three methods under small interference conditions is shown, and Table 1 records the results of repeated tests. Among them, f av is the average value of the oscillation frequency of a certain oscillation mode, ξ av is the average value of the attenuation coefficient of the corresponding oscillation mode, δ f and δ ξ are the deviation values of frequency and attenuation coefficient, respectively, and Std f and Std ξ are the standard deviations of frequency and attenuation coefficient, respectively. Through the test, the following conclusions are drawn: compared with UBSS, the stability and accuracy of HHT method frequency measurement are inferior to the former due to the influence of modal aliasing effect, and the test result distribution is also more dispersed; the experimental results of PORNY algorithm under the condition of no interference are relatively ideal.

[0113] Table 1. Test results of equation (17) under different algorithms (SNR=100 dB)

[0114]

[0115] To further explore the adaptability of UBSS algorithm to interference signals, ten noise interference levels are set, and comparative tests are carried out under different multiple interference signal conditions. Since the Prony algorithm will fail as the noise interference intensity increases, the frequency is taken as the main test object, and the anti-interference performance of UBSS and HHT algorithms is compared, and the test results are shown in Figure 8 , where f1, f2, and f3 are three frequency oscillation modes, and the test results are the standard deviation of the frequency distribution measured by the two methods under the condition of 1-10 times intensity interference based on 100 dB. The results show that both methods can identify under interference conditions, and the former is generally better than the latter in terms of frequency distribution standard deviation measured under different interference conditions.

[0116] Through noise interference tests, Prony algorithm has effectiveness, accuracy, and stability under small interference, but it is sensitive to noise interference; HHT is a relatively mature nonlinear method that can identify the main vibration frequency, but due to modal aliasing effect, HHT method is powerless when dealing with similar frequency signals, and its anti-interference ability is not as good as UBSS algorithm. In comparison, UBSS algorithm can separate each oscillation component and identify the main parameters of each oscillation mode, and it can still identify the main oscillation mode parameters under large interference conditions.

[0117] Modeling and simulation verification:

[0118] To verify the UBSS algorithm, a four-machine two-area classical model is selected, and simulation experiments are carried out in MATLAB software under small disturbance conditions (PSS is not put into operation) and large disturbance conditions (PSS is put into operation) by setting different parameters. The system power frequency is 60 Hz, and the sampling frequency is 1 kHz.

[0119] Test under small disturbance conditions:

[0120] Under the condition that the system region one G1 (G represents the generator) has a 5% disturbance at 1-1.2 s, the difference between the angular velocities of G1 and G2 within 5 s after the disturbance occurs is selected as the test object, PSS is not in action, and under the condition of 100 dB noise interference intensity, Prony, HHT, and UBSS are used for low-frequency oscillation parameter identification test. After the system is disturbed, it enters the transient process, and the waveform of the difference between the angular velocities of G1 and G2 has obvious low-frequency oscillation, indicating that the system has low-frequency oscillation after being disturbed, as shown in Figure 9 .

[0121] Unlike EMD decomposition, which is difficult to obtain the physical meaning of the component, Figure 9The y1 and y2 are the oscillation mode components decomposed by the UBSS method, which have obvious low-frequency oscillation characteristics. After the disturbance, the system generates obvious decaying low-frequency oscillation modes to resist the changes caused by the disturbance; at the same time, the system gradually loses stability and excites unstable divergent oscillation modes due to the inaction of the PSS. The three methods are used to identify the oscillation mode parameters in the above process, and the test results are shown in Table 2.

[0122] Table 2. Low-frequency oscillation mode parameter identification results of four-machine two-area system under small disturbance by different algorithms (SNR = 100 dB)

[0123]

[0124] The test results show that the system in the region 1 has low-frequency oscillation of mode 1 (f1 = 0.60 Hz, z1 = 0.04) and mode 2 (f2 = 1.10 Hz, z2 = -0.60) after G1 is disturbed by a small disturbance, and the three methods can identify the main oscillation modes and realize the parameter identification of the oscillation modes. Under the condition of 100 dB noise interference, the accuracy of the parameter identification of the UBSS method is slightly better than that of the other two methods.

[0125] Test under large disturbance condition:

[0126] To verify the effectiveness of the algorithm under the condition of large disturbance of the system, it is assumed that a transient ground fault occurs at the midpoint of a tie line of the cross-region power system at 1s, the fault is restored after 0.2s, and 100db noise interference signal is added to the system. The difference 24 between the angular velocities of G2 and G4 within 5s after the disturbance is selected as the test object, and the Prony, HHT and UBSS methods are used for low-frequency oscillation parameter identification test under the condition of PSS.

[0127] Due to the regulation of the PSS, the waveform of the difference 24 between the angular velocities of G2 and G4 is seriously smoothed, and it is difficult to directly judge whether low-frequency oscillation occurs through the waveform. The UBSS algorithm can directly face the time domain signal, excavate the component information through the construction of virtual multiple channels, and then accurately judge the occurrence of low-frequency oscillation and identify the related parameters of each oscillation component, as shown in Table 3. Figure 10 Obviously, even under the condition of large disturbance and PSS, the algorithm can separate different oscillation components with similar frequencies, and the test results are shown in Table 3.

[0128] Table 3. Low-frequency oscillation mode parameter identification results of four-machine two-area system under large disturbance by different algorithms (SNR = 100 dB)

[0129]

[0130] Table 3 shows the results of two test cases, one with no noise interference and one with noise interference of 100 dB, under large disturbance, where f Ⅰ , ξ Ⅰ represents the test results under no noise interference, f Ⅱ , ξ Ⅱ represents the test results under noise interference of 100 dB. The test results show that when the tie line has a transient fault, the system after disturbance has mode 1 (f1=0.54 Hz, z1=-0.50) and mode 2 (f2=0.60 Hz, z2=-0.50) low-frequency oscillations. In the case of no noise interference, the three methods can identify the main oscillation mode and realize parameter identification of the oscillation mode. Under the condition of noise interference of 100 dB, since the time domain signal can be directly decomposed and the decomposition components have clear physical meaning, the stability (anti-interference ability) of the parameter identification result of the UBSS algorithm is better than that of the other two methods, which also verifies the identification ability of the UBSS algorithm for low-frequency oscillation modes with similar frequencies.

[0131] Field data verification:

[0132] Taking low-frequency oscillation occurred in a large hydropower station in the southwest region as an example, the performance of the proposed method is verified. The operating personnel of the power station manually increased and decreased the load when calibrating the flood discharge curve, and the unit active power curve is shown in Figure 11 . Among them, P1 and P2 are the unit active power curves when the load is increased and decreased, respectively. Obviously, low-frequency oscillation occurs in the process of increasing and decreasing the load.

[0133] The active power data recorded by the PMU device are selected for research, and the 10s data (denoted as P1 and P2) after the start of low-frequency oscillation in the P1 and P2 curves are taken as research objects for experimental verification. The system sampling frequency is 100 Hz.

[0134] The virtual multi-channel signal is constructed, and the number of source signals contained in the P1 and P2 curves is estimated using the BIC principle, and the test results are shown in Table 4. The estimated values of the oscillation components under the two conditions are n*P1=3 and n*P2=2, respectively. In the table, the frequency detection results f p1 in the process of increasing the load have only one oscillation frequency in the range of 0.2-2.5 Hz, and it is determined that there is only one low-frequency oscillation mode in the process of increasing the load, i.e. n p1 =1, and the corresponding oscillation frequency is f p11 =0.5918 Hz; the frequency detection results f p2 in the process of decreasing the load have two oscillation frequencies in the range of 0.2-2.5 Hz, and it is determined that there are two low-frequency oscillation modes in the process of decreasing the load, i.e. n p2 =2, and the corresponding oscillation frequencies are f p21= 0.5522 Hz and f p22 = 0.6487 Hz.

[0135] Table 4. The results of the UBSS algorithm for the oscillation mode parameter identification of the field recording

[0136]

[0137] After determining the number of low-frequency oscillation modes, the UBSS method is used to process the virtual multi-channel signal, separate the components corresponding to the effective low-frequency oscillation modes, and identify the target parameters. Figure 12 The component y p21 (t) and the frequency f p21 (t) are shown after processing the p2 component. p21 (t) curve.

[0138] The target data is processed using PRONY, HHT, and UBSS methods, and the experimental results are shown in Table 5.

[0139] Table 5. Comparison of low-frequency oscillation mode parameter identification results under different algorithms

[0140]

[0141] Past experiments have verified that the inherent frequency of the turbine's draft tube vortex band is about 0.6 Hz. Due to the influence of hydraulic and mechanical factors, when the vibration zone is crossed for a long time, the unit will experience low-frequency oscillation. The data in Table 5 shows that the three methods can identify the components near the main vibration frequency, but due to the influence of noise signals, the Prony algorithm cannot directly determine the order of the oscillation mode in the identification process. The experimental results of the HHT algorithm are relatively reliable under single-mode oscillation, but there is a modal aliasing effect for oscillation modes with similar frequencies, and the frequency identified by the HHT algorithm is quite different from the actual frequency. The UBSS method can accurately estimate the number of oscillation modes and complete the identification of the main parameters.

[0142] The purpose of low-frequency oscillation mode identification is to determine the fault category, locate the fault source, and then adjust from the source to avoid the recurrence of low-frequency oscillation. Generally, we need to process multiple system physical quantities to determine the fault category and further locate the fault source. Taking the field recording data in this paper as an example, the UBSS algorithm is used to process the collected reactive power Q ex , excitation voltage E ex , and excitation current I ex , and the experimental results are shown in Table 6.

[0143] Table 6. Low-frequency oscillation mode parameter identification results based on Q, E ex , and I ex

[0144]

[0145] The results show that, after processing the reactive power Q, the excitation voltage E ex and the excitation current I ex , the UBSS algorithm finds the target frequency range near 0.6Hz, i.e. 0.5-0.7Hz, which further proves the effectiveness of the algorithm, which can identify the low-frequency oscillation mode parameters, and further provide more information for locating the fault source.

[0146] Further, the application range of the UBSS algorithm is not limited to low-frequency oscillation mode parameter identification. In fact, for high-frequency electromagnetic transient signals or lower frequency electromechanical transient signals, the UBSS method also has room to play.

[0147] The advantages of the method are summarized as follows: (1) the method can decompose the main components in the complex signal under the underdetermined condition, and compared with HHT and Prony, it has better noise robustness and can be used for low-frequency oscillation mode identification; (2) in terms of the calculation error of parameter estimation accuracy, the performance of the method is better than that of HHT and Prony methods, and it can provide dynamic information of modal parameters; (3) based on the observation signal, the method can accurately estimate the number of low-frequency oscillation modes without the system topology structure, reduce the dependence on system information, and improve the applicability of the method; therefore, the method provided by the application is an innovative and effective means, which can solve the underdetermined blind source separation problem and realize the identification of low-frequency oscillation dominant mode parameters, and provide necessary reference information for locating the oscillation source and adjusting the system parameters.

[0148] The above is only the preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for identifying low-frequency oscillations in power systems based on the UBSS algorithm, characterized in that, Includes the following steps: Step 1: Define the low-frequency oscillation energy ratio function For real-time observed signals Singularity detection is performed on the low-frequency oscillation energy ratio function. The expression is as follows: In the above formula, This indicates the energy ratio between the second half and the first half of the time window. Indicates the starting point of the time window. Indicates the total length of the time window; The expression for singularity detection is: , Indicates the threshold; Step 2: Real-time observation information mining is achieved through spatiotemporal transformation, expanding the observation channels and transforming the UBSS problem into a BSS problem; Step 3: Use the Bayesian information criterion to estimate the number of sources in the observation information, determine the number of dominant oscillation modes, achieve mode order determination, and use the BSS algorithm to complete the mode decomposition task to estimate the oscillation mode parameters.

2. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 1, characterized in that, The real-time observation signal The expression is as follows: In the above formula, This indicates the number of different low-frequency oscillation modes. express The Middle The relative amplitude of each low-frequency oscillation mode express The Middle Damping coefficient of a low-frequency oscillation mode, express The Middle The oscillation frequency of a low-frequency oscillation mode. express The Middle Phase shift of a low-frequency oscillation mode.

3. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 2, characterized in that, The threshold Based on the total width of the time window And the determination of the sampling frequency of the power system.

4. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 2, characterized in that, The method of realizing real-time observation information mining through spatiotemporal transformation includes: The detected signal mutation information Constructing a multi-channel mixing matrix using dimensional space theory .

5. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 4, characterized in that, A random time delay method is used to construct a virtual observation multi-channel.

6. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 4, characterized in that, Step 3 specifically includes: Estimating the number of source signals using the Bayesian information criterion And decomposed by source signal stripping in The source signal components in the matrix constitute the source signal estimation matrix. ; Through Hilbert transform Processing is performed to obtain parameters for each low-frequency oscillation mode, the low-frequency oscillation mode parameters including , , , This represents the average oscillation frequency; The components characterizing low-frequency oscillations are sequentially derived from... as well as Extracting from this, we obtain the number of low-frequency oscillation modes. .

7. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 6, characterized in that, The FastICA algorithm is used to strip and decompose the above. The source signal component in.

8. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 6, characterized in that, The components characterizing low-frequency oscillations are sequentially derived from... as well as The extraction specifically includes: Fixed frequency range based on low-frequency oscillation ,from as well as Components that conform to the characteristics of low-frequency oscillations are selected from the data to determine the number of low-frequency oscillation modes. ; When satisfied hour, ,otherwise .

9. The method for identifying low-frequency oscillations in power systems based on the UBSS algorithm as described in claim 6, characterized in that, The Hilbert transform pair The processing to obtain low-frequency oscillation mode parameters specifically includes: Using Hilbert transform The instantaneous parameters of the low-frequency oscillation mode were obtained through processing. as well as and to Perform differentiation ; To each , as well as The average value is used to obtain the parameters of the low-frequency oscillation mode. , as well as .

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