A Time-Frequency Analysis Method for Power Faults Based on Synchronous Extraction Transformation

Abstract

This invention relates to the field of power system fault signal processing, specifically to a power fault time-frequency analysis method based on synchronization extraction transform. The invention employs a Rogowski coil sensing system to acquire transient fault signals, obtains an initial time-frequency representation through short-time Fourier transform, and derives a corrected time-frequency representation using the derivative of a window function. Based on the ratio of the two representations, the instantaneous frequency trajectory is calculated. A synchronization extraction operator is constructed using a binarization criterion with discrete frequency intervals as an adaptive threshold. Only time-frequency coefficients on the instantaneous frequency trajectory are retained, rather than all coefficients in the concentrated energy diffusion region, resulting in a highly concentrated energy time-frequency representation. This method significantly improves time-frequency resolution while exhibiting stronger noise robustness and multi-component signal separation capabilities, providing an effective technical means for rapid and accurate fault location in distribution networks.

Description

Technical Field

[0001] This invention relates to the field of power system fault signal processing, specifically to a power fault time-frequency analysis method based on synchronous extraction and transformation. Background Technology

[0002] The safe and reliable operation of distribution networks is crucial to modern power systems. Fault transient signal analysis is the foundation of fault location and diagnosis, and the ability to quickly and accurately extract fault characteristic parameters is of great significance for the reliable operation of protection devices.

[0003] Traditional fault transient signal analysis mainly employs methods such as Fourier transform, but these methods cannot effectively handle non-stationary signals. While the Short-Time Fourier Transform (STFT) introduces time localization, it is limited by the Heisenberg uncertainty principle, resulting in energy diffusion in its time-frequency representation and insufficient time-frequency resolution. The Synchronous Compression Transform (SST), although improving energy concentration, requires aggregating all correlation coefficients in the energy diffusion region, leading to poor noise robustness in noisy environments. Furthermore, for fault transient signals containing multiple frequency components, existing methods struggle to effectively separate the time-varying characteristics of each component, limiting the accuracy of fault diagnosis. Summary of the Invention

[0004] This invention provides a power fault time-frequency analysis method based on synchronous extraction transformation. By accurately extracting the time-frequency coefficients on the instantaneous frequency trajectory, it improves the time-frequency resolution of the fault transient signal, enhances noise robustness, and enables rapid and accurate location of distribution network faults.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A time-frequency analysis method for power faults based on synchronization extraction transformation includes:

[0007] S100: The transient signal of the power distribution network fault is acquired by the Rogowski coil sensing system operating in the self-integrating state. The secondary output voltage of the Rogowski coil sensing system is proportional to the rate of change of the measured current. The frequency response range is determined by the sampling resistor, distributed capacitance, coil resistance and coil inductance.

[0008] S200: Perform a short-time Fourier transform on the fault transient signal, and use a real even window function to extend the fault transient signal from the one-dimensional time domain to the two-dimensional time-frequency plane to obtain the initial time-frequency representation;

[0009] S300: Using the derivative of the window function with respect to time, perform a corrected short-time Fourier transform on the fault transient signal to obtain a corrected time-frequency representation;

[0010] S400: Calculate the two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the corrected time-frequency representation;

[0011] S500: Based on the ratio of the initial time-frequency representation and the modified time-frequency representation, a synchronization extraction operator is constructed using a binarization judgment criterion. The discrete frequency interval is used as the judgment threshold. The synchronization extraction operator takes a value of 1 when the threshold condition is met and a value of 0 when the threshold condition is not met.

[0012] S600: Multiply the initial time-frequency representation with the synchronization extraction operator, retain only the time-frequency coefficients corresponding to the synchronization extraction operator value of 1, and remove the time-frequency coefficients corresponding to the synchronization extraction operator value of 0, to obtain the time-frequency representation of energy concentrated on the instantaneous frequency trajectory, thus completing the time-frequency analysis of the fault transient signal.

[0013] As a preferred embodiment of the present invention, the Rogowski coil sensing system includes:

[0014] The system comprises a Rogowski coil, a sampling resistor, and an integrating circuit. The secondary coil of the Rogowski coil is connected in series with the sampling resistor to form a self-integrating loop. The measured current flows through the primary side of the Rogowski coil, and the induced current output by the secondary coil flows through the sampling resistor to generate an output voltage signal. The integrating circuit is used to condition and amplify the output voltage signal.

[0015] As a preferred embodiment of the present invention, the step of obtaining the initial time-frequency representation includes:

[0016] The real even window function is moved along the time axis, and the fault transient signal is windowed at each time point and then subjected to Fourier transform to obtain the time-frequency coefficients at different times and frequencies, which constitute the initial time-frequency representation.

[0017] As a preferred embodiment of the present invention, the step of obtaining the corrected time-frequency representation includes:

[0018] The time derivative of the real even window function is obtained by taking its derivative. The window function derivative is then shifted along the time axis. At each time step, the fault transient signal is windowed and then subjected to a Fourier transform to obtain the corrected time-frequency representation.

[0019] As a preferred embodiment of the present invention, the calculation of the two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the corrected time-frequency representation includes:

[0020] The complex ratio of the corrected time-frequency representation to the initial time-frequency representation at each time-frequency point is calculated. A phase extraction operation is performed on the complex ratio, and the instantaneous frequency value corresponding to each point on the two-dimensional time-frequency plane is obtained by combining the frequency variable, thus forming the two-dimensional instantaneous frequency trajectory.

[0021] As a preferred embodiment of the present invention, the binarization determination criterion includes:

[0022] Calculate the complex ratio of the corrected time-frequency representation to the initial time-frequency representation, extract the real part of the complex ratio and take its absolute value, compare the absolute value with half of the discrete frequency interval, determine that the threshold condition is met when the absolute value is less than half of the discrete frequency interval, and determine that the threshold condition is not met when the absolute value is greater than or equal to half of the discrete frequency interval.

[0023] As a preferred embodiment of the present invention, the discrete frequency interval is:

[0024] The frequency difference between two adjacent discrete frequency sampling points is set by discretizing the frequency axis during short-time Fourier transform.

[0025] As a preferred embodiment of the present invention, the time-frequency representation of energy concentrated on the instantaneous frequency trajectory includes:

[0026] On the two-dimensional time-frequency plane of the initial time-frequency representation, for each moment, the time-frequency coefficient at the frequency position corresponding to the instantaneous frequency trajectory is extracted as the effective time-frequency coefficient at that moment, and the time-frequency coefficients at other frequency positions at that moment are set to zero.

[0027] As a preferred embodiment of the present invention, when the fault transient signal is a multi-component signal, the method further includes the following step after S600:

[0028] Determine whether the instantaneous frequency derivative interval of different modes meets the separation condition. When the separation condition is met, separate or reconstruct each single-component mode from the multi-component signal according to the time-frequency coefficients corresponding to each mode in the time-frequency representation.

[0029] As a preferred embodiment of the present invention, the separation conditions are as follows:

[0030] The difference between the instantaneous frequency derivatives of adjacent modes is greater than twice the frequency support width of the window function, and the change in amplitude function and frequency deviation function of each mode is less than the preset threshold.

[0031] The beneficial effects of this invention are:

[0032] 1. This invention introduces a binarized synchronous extraction operator based on the modified STFT derivative relationship. This operator precisely extracts time-frequency coefficients directly related to the instantaneous frequency trajectory, rather than simply aggregating all coefficients in the energy diffusion region. This design, combined with adaptive threshold control of discrete frequency intervals, effectively eliminates the energy diffusion phenomenon caused by the Heisenberg uncertainty principle, resulting in a high concentration of energy in the time-frequency representation near the instantaneous frequency trajectory. This significantly improves time-frequency resolution compared to traditional STFT methods.

[0033] 2. This invention employs a strategy of retaining only the maximum energy coefficient on the instantaneous frequency trajectory, rather than the approach of synchronous compression transform which requires gathering all correlation coefficients in the energy diffusion region. This scheme gives the time-frequency coefficients optimal noise robustness, effectively suppressing the influence of random noise on the time-frequency analysis results, and enabling stable tracking of multi-component signal characteristics even in strong noise environments.

[0034] 3. This invention integrates the entire chain of technologies, including signal acquisition, time-frequency transformation, instantaneous frequency estimation, and synchronous extraction, supporting the effective separation or reconstruction of each single-component mode from multi-component fault transient signals while meeting the frequency interval requirements between adjacent modes. This complete solution combines theoretical rigor with engineering practicality, providing reliable time-frequency characteristic support for the identification and location of fault types in distribution networks. Attached Figure Description

[0035] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0036] Figure 1 This is a flowchart illustrating a power fault time-frequency analysis method based on synchronous extraction transformation according to the present invention. Detailed Implementation

[0037] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0038] Example 1: As Figure 1 As shown, the present invention provides a power fault time-frequency analysis method based on synchronization extraction transformation, comprising:

[0039] S100: The transient signal of the power distribution network fault is acquired by the Rogowski coil sensing system operating in the self-integrating state. The secondary output voltage of the Rogowski coil sensing system is proportional to the rate of change of the measured current. The frequency response range is determined by the sampling resistor, distributed capacitance, coil resistance and coil inductance.

[0040] Furthermore, the Rogowski coil sensing system includes:

[0041] The system comprises a Rogowski coil, a sampling resistor, and an integrating circuit. The secondary coil of the Rogowski coil is connected in series with the sampling resistor to form a self-integrating loop. The measured current flows through the primary side of the Rogowski coil, and the induced current output by the secondary coil flows through the sampling resistor to generate an output voltage signal. The integrating circuit is used to condition and amplify the output voltage signal.

[0042] Specifically, the Rogowski coil sensing system consists of the following three parts:

[0043] The Rogowski coil is designed using PCB technology and includes a primary side and a secondary side. The primary side is the feedthrough coil of the circuit under test, through which the measured current passes. The secondary side consists of multi-turn windings wound around a magnetic core in a specific helical structure. Through improved coil structure and anti-interference technology, this coil can achieve ideal amplitude-frequency and phase-frequency characteristics of a bandpass filter when operating in self-integrating mode.

[0044] Rogowski coil secondary coil and sampling resistor A self-integrating circuit is formed by connecting them in series. The resistance of the sampling resistor is a few tenths of an ohm to a few ohms. When a system fault occurs, the measured current... The rate of change is large, and when the induced current generated by the secondary coil flows through the sampling resistor, it will produce a significant output voltage signal.

[0045] The integrator circuit is used to condition and amplify the output voltage signal generated across the sampling resistor, ensuring that the subsequent analog-to-digital conversion and signal processing units can accurately acquire transient signals.

[0046] When the Rogowski coil operates in self-integration mode, the secondary output voltage is proportional to the rate of change of the measured current, and the relationship is as follows:

[0047] ;

[0048] in: This is the secondary side detection voltage; The measured current; This is the secondary side output current; For sampling resistors; This refers to the number of turns in the secondary coil.

[0049] Under normal circumstances, the measured current The value is very small, and the induced voltage signal detected by the secondary side of the Rogowski coil is very small. Very small; when a system fault occurs, the measured current... rate of change The voltage is very large, enabling the detection of a significant voltage signal on the secondary side of the Rogowski coil. This characteristic allows the Rogowski coil to effectively detect rapidly changing transient signal pulses when operating in self-integration mode, while exhibiting low sensitivity to steady-state signals, thus achieving effective extraction of fault transient signals.

[0050] When the Rogowski coil operates in self-integration mode, the system transfer function is:

[0051] ;

[0052] in: This is the Laplace transform of the secondary-side output voltage; This is the Laplace transform of the secondary-side output current; The inductance of the coil is determined by the structural parameters of the coil. The distributed capacitance includes the distributed capacitance between the secondary coils and the distributed capacitance to ground; The coil resistance; For sampling resistors; Mutual inductance coefficient represents the degree of magnetic coupling between the primary and secondary coils, and is determined by the coil geometry and turns ratio. This is the Laplace transform operator.

[0053] The amplitude-frequency characteristics of the system can be derived from the transfer function:

[0054] ;

[0055] in, imaginary unit Commonly used in electrical engineering The imaginary unit is used to distinguish it from the symbol for electric current. ; ω is the angular frequency; K is the correction constant; Distributed capacitance; For sampling resistors; This is the coil resistance.

[0056] The phase frequency characteristic is:

[0057] ;

[0058] in, This represents the phase response of the system, and the parameters in the formula have the same meaning as above.

[0059] The frequency response range is determined by both the upper and lower frequency limits:

[0060] The upper limit frequency is determined by the sampling resistor. and distributed capacitance The resonant characteristics determine:

[0061] ;

[0062] The lower limit frequency is determined by the coil inductance. Coil resistance and sampling resistor Joint decision:

[0063] ;

[0064] By designing the sampling resistor Resistance value, optimized coil inductance and coil resistance and control of distributed capacitance This allows the sensing system's frequency response range to cover the main frequency components of the fault transient signal (typically in the kHz to MHz range), thereby ensuring the sensitivity and reliability of fault transient signal acquisition. Within this frequency range, the Rogowski coil possesses ideal amplitude-frequency and phase-frequency characteristics, ensuring the complete reconstruction of the original waveform of the transient signal.

[0065] The Rogowski coil sensing system designed above automatically acquires fault transient signals in the power distribution network by passing its primary side through the path of the current being measured. Because the Rogowski coil does not exhibit magnetic saturation, it maintains good linearity even under high current surges, enabling the acquired transient signals to accurately reflect the high-frequency oscillation and pulse characteristics during the fault process, providing high-quality input signals for subsequent time-frequency analysis.

[0066] S200: Perform a short-time Fourier transform on the fault transient signal, and use a real even window function to extend the fault transient signal from the one-dimensional time domain to the two-dimensional time-frequency plane to obtain the initial time-frequency representation;

[0067] Furthermore, the step of obtaining the initial time-frequency representation includes:

[0068] The real even window function is moved along the time axis, and the fault transient signal is windowed at each time point and then subjected to Fourier transform to obtain the time-frequency coefficients at different times and frequencies, which constitute the initial time-frequency representation.

[0069] Specifically, the Short Time Fourier Transform (STFT) expands a one-dimensional time series signal into a two-dimensional time-frequency plane by windowing the signal in the time domain using a moving window, and then performing a Fourier transform on the windowed signal segment. Compared to the traditional Fourier transform, STFT can simultaneously preserve the time and frequency characteristics of non-stationary signals (such as fault transient signals).

[0070] A real even window function is used in STFT processing. The real even window function satisfies... Symmetry conditions are required, and common choices include the Hamming window, Heining window, and Gaussian window. These window functions have good energy concentration characteristics in both the time and frequency domains, effectively balancing time resolution and frequency resolution and avoiding spectral leakage problems.

[0071] According to the definition of STFT, let the acquired fault transient signal be... Using real even window functions Initial time-frequency representation The acquisition process is as follows:

[0072] ;

[0073] in: For time integration variables; The imaginary unit; It is a complex exponential function used for frequency decomposition; This is a time parameter, representing the position of the window function on the time axis; This refers to the angular frequency parameter; To translate along the time axis to the position Window function; This is a fault transient signal; For at any time ,frequency The time-frequency coefficients at the given point are complex numbers. This expression extends a one-dimensional time-series signal to a two-dimensional time-frequency (TF) plane, allowing for the observation and extraction of the instantaneous amplitude (IA) and instantaneous frequency (IF) information of the signal.

[0074] The real even window function is shifted along the time axis, and the fault transient signal is windowed at each time step before performing a Fourier transform. (Selecting the real even window function) Move it along the timeline to various moments. At that moment At the location, for fault transient signals After adding a window, the result is... Perform a Fourier transform on the windowed signal to calculate different frequencies. The complex value is used to obtain the time-frequency coefficient corresponding to that moment. Repeat the above process throughout the entire time range of the fault transient signal to obtain the complete result. .

[0075] Through the above processing, the fault transient signal is extended from the one-dimensional time domain to the two-dimensional time-frequency plane, forming an initial time-frequency representation. This indicates that the time-varying characteristics of the fault transient signal are fully preserved.

[0076] S300: Using the derivative of the window function with respect to time, perform a corrected short-time Fourier transform on the fault transient signal to obtain a corrected time-frequency representation;

[0077] Furthermore, the step of obtaining the corrected time-frequency representation includes:

[0078] The time derivative of the real even window function is obtained by taking its derivative. The window function derivative is then shifted along the time axis. At each time step, the fault transient signal is windowed and then subjected to a Fourier transform to obtain the corrected time-frequency representation.

[0079] Specifically, to improve the accuracy of subsequent time-frequency analysis, the STFT results are corrected. Based on Parseval's theorem, an additional phase shift factor is introduced into the STFT expression. The corrected STFT expression is:

[0080] ;

[0081] in, For window functions Fourier transform at frequency The value at; For signal Fourier transform at frequency The value at; For frequency integral variables; This is the phase shift factor.

[0082] To obtain the corrected time-frequency representation, the time derivative of the window function is needed. Taking the time derivative of the corrected STFT, the following relationship can be established:

[0083] ;

[0084] in, This is a time parameter, representing the observation time in the time-frequency analysis; Let be the time integral variable, representing the signal at various moments on the time axis; Indicates time The partial derivative operator; To translate along the time axis to the position Window function; This is a fault transient signal; For at any time ,frequency The initial time-frequency representation at point is a complex number; At any moment ,frequency The local frequency analysis kernel at that location is composed of Moved to the time Let's calculate. Applying the rule of differentiation, the above equation expands to:

[0085] ;

[0086] in, For window functions The first derivative with respect to its variable; the first integral term represents the contribution from the window function derivative; the second integral term is the original STFT multiplied by This indicates that the time-frequency representation has been corrected. With the derivative of the window function There is an inherent connection between them.

[0087] Real even window function By taking the time derivative, we obtain the derivative of the window function. The derivative of the window function Moving along the timeline, at each moment At that place, At that moment At the location, for fault transient signals After adding a window, the result is... Perform a Fourier transform on the windowed signal to calculate different frequencies. The complex value is then used. The above process is repeated throughout the entire time range of the fault transient signal, combined with the initial time-frequency representation. Based on the aforementioned derivative information, a modified time-frequency representation is constructed according to the definition of the modified STFT. .

[0088] Through the above processing, the corrected time-frequency representation is obtained. Its relationship with the initial time-frequency representation Together, they provide a foundation for subsequent instantaneous frequency estimation.

[0089] S400: Calculate the two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the corrected time-frequency representation;

[0090] Further, the calculation of the two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the corrected time-frequency representation includes:

[0091] The complex ratio of the corrected time-frequency representation to the initial time-frequency representation at each time-frequency point is calculated. A phase extraction operation is performed on the complex ratio, and the instantaneous frequency value corresponding to each point on the two-dimensional time-frequency plane is obtained by combining the frequency variable, thus forming the two-dimensional instantaneous frequency trajectory.

[0092] Specifically, the initial time-frequency representations are obtained from S200 and S300 respectively. and corrected time-frequency representation Instantaneous frequency (IF) is a key parameter describing the time-varying frequency characteristics of non-stationary signals. Based on the time derivative relationship established in the S300 implementation details:

[0093] ;

[0094] By transforming this equation, we can obtain:

[0095] ;

[0096] in, This indicates that the corrected time-frequency representation is related to time. The partial derivatives; To utilize the derivative of the window function The calculated time-frequency representation is defined as follows:

[0097] ;

[0098] in, This is a time parameter, representing the observation time in the time-frequency analysis; Let be the time integral variable, representing the signal at various moments on the time axis; For window functions The first derivative with respect to the variable; This is a fault transient signal; At any moment ,frequency The local frequency analysis kernel at that location is composed of Moved to the time To calculate.

[0099] For each time-frequency point on the two-dimensional time-frequency plane Calculate the complex ratio of the correlation term in the corrected time-frequency representation to that in the initial time-frequency representation. Compare the result with the frequency variable Adding them together gives the instantaneous frequency value at that time-frequency point. By traversing all time-frequency points on the time-frequency plane and repeating the above process, a complete two-dimensional instantaneous frequency distribution can be obtained. .

[0100] The combination of instantaneous frequency values ​​corresponding to all time and frequency points forms a two-dimensional instantaneous frequency trajectory. This trajectory describes the variation of the signal's instantaneous frequency with time and frequency position on the time-frequency plane, providing a basis for subsequent synchronization extraction.

[0101] S500: Based on the ratio of the initial time-frequency representation and the modified time-frequency representation, a synchronization extraction operator is constructed using a binarization judgment criterion. The discrete frequency interval is used as the judgment threshold. The synchronization extraction operator takes a value of 1 when the threshold condition is met and a value of 0 when the threshold condition is not met.

[0102] Furthermore, the binarization determination criteria include:

[0103] Calculate the complex ratio of the corrected time-frequency representation to the initial time-frequency representation, extract the real part of the complex ratio and take its absolute value, compare the absolute value with half of the discrete frequency interval, determine that the threshold condition is met when the absolute value is less than half of the discrete frequency interval, and determine that the threshold condition is not met when the absolute value is greater than or equal to half of the discrete frequency interval.

[0104] Furthermore, the discrete frequency interval is:

[0105] The frequency difference between two adjacent discrete frequency sampling points is set by discretizing the frequency axis during short-time Fourier transform.

[0106] Specifically, the Synchronous Extraction Operator (SEO) is the core of the synchronous extraction transform method. Its function is to accurately extract the time-frequency coefficients directly related to the instantaneous frequency trajectory and filter out coefficients in the energy diffusion region. Based on the two-dimensional instantaneous frequency obtained above... The synchronous extraction operator can be defined as: .

[0107] According to the Dirac function The definition of a synchronous extraction operator should satisfy:

[0108] ;

[0109] Substituting the instantaneous frequency calculation formula into the equation, we get:

[0110] ;

[0111] in, To correct the time-frequency representation; To utilize the derivative of the window function The calculated time-frequency representation.

[0112] In practical applications, due to computational errors and discretization, the strict equality condition is difficult to achieve. Therefore, a binarized criterion is adopted, and a threshold is introduced to construct a robust synchronous extraction operator. Considering that practical applications require the real part of the complex ratio for judgment, the synchronous extraction operator is rewritten as follows:

[0113] ;

[0114] in, To take the real part of a complex number, This indicates taking the absolute value. The discrete frequency interval is used as the judgment threshold. Defined as:

[0115] ;

[0116] in, Represents the frequency axis angular frequency values ​​at discrete frequency sampling points Indicates the first The angular frequency values ​​are obtained from discrete frequency sampling points. When performing a short-time Fourier transform, the frequency axis needs to be discretized. The frequency sampling range is set to... The total number of frequency sampling points is Then the discrete frequency interval can be expressed as:

[0117] ;

[0118] in, This represents the upper limit of the frequency sampling range; This is the lower limit of the frequency sampling range; This represents the total number of frequency sampling points.

[0119] For each discrete time-frequency point on the time-frequency plane Calculate the complex ratio of the correlation term in the corrected time-frequency representation to that in the initial time-frequency representation, and multiply the complex ratio by the imaginary unit. ,get Extract the real part of the complex number expression above and take its absolute value. Calculate the discrete frequency interval corresponding to this time-frequency point. The absolute value is compared with the judgment threshold. Compare. If If so, it is determined that the threshold condition is met, let ;like If the threshold condition is not met, then let By traversing all discrete time-frequency points on the time-frequency plane and repeating the above process, a complete distribution of the synchronization extraction operator can be obtained. .

[0120] Through discrete frequency intervals Adaptive threshold control is achieved, retaining only the time-frequency coefficients on the instantaneous frequency trajectory, effectively eliminating the energy diffusion effect and significantly improving time-frequency resolution.

[0121] S600: Multiply the initial time-frequency representation with the synchronization extraction operator, retain only the time-frequency coefficients corresponding to the synchronization extraction operator value of 1, and remove the time-frequency coefficients corresponding to the synchronization extraction operator value of 0, to obtain the time-frequency representation of energy concentrated on the instantaneous frequency trajectory, thus completing the time-frequency analysis of the fault transient signal.

[0122] Furthermore, the obtained time-frequency representation of energy concentrated on the instantaneous frequency trajectory includes:

[0123] On the two-dimensional time-frequency plane of the initial time-frequency representation, for each moment, the time-frequency coefficient at the frequency position corresponding to the instantaneous frequency trajectory is extracted as the effective time-frequency coefficient at that moment, and the time-frequency coefficients at other frequency positions at that moment are set to zero.

[0124] Specifically, the core idea of ​​Synchronous Extraction Transform (SET) is to selectively extract from the initial time-frequency representation using a synchronous extraction operator to generate a new time-frequency representation with highly concentrated energy. The mathematical expression for SET is defined as:

[0125] ;

[0126] in, To synchronously extract the transformed time-frequency representation; This is the initial time-frequency representation; For the synchronous extraction operator in the form of a Dirac function, only when The value at one position is 1, and the value at all other positions is 0; It is a two-dimensional instantaneous frequency trajectory.

[0127] This expression shows that the synchronization extraction transform is achieved by multiplying the initial time-frequency representation by the synchronization extraction operator point by point. Since the synchronization extraction operator is a binary representation, taking only 0 or 1 values, the essence of this multiplication operation is the selective retention or removal of the time-frequency coefficients.

[0128] According to the definition of the synchronous extraction operator, the synchronous extraction transformation can be rewritten as:

[0129] ;

[0130] This expression clearly illustrates the principle of selective extraction of time-frequency coefficients. When the time frequency point... frequency Equal to the instantaneous frequency at that point When the point is located on the instantaneous frequency trajectory, the initial time-frequency coefficients of that point are preserved. ; frequency at that time frequency Not equal to the instantaneous frequency at that point When the point is located in the energy diffusion region, the time-frequency coefficient of that point is set to zero.

[0131] In theory, the operator only extracts the instantaneous frequency trajectory. Place The time-frequency coefficients were selected, and the remaining time-frequency coefficients were removed. The results show that most time-frequency coefficients were removed, with only a few remaining. .

[0132] On the two-dimensional time-frequency plane of the initial time-frequency representation, for each time... Based on the two-dimensional instantaneous frequency trajectory and synchronous extraction operator Determine the frequency position corresponding to the instantaneous frequency trajectory at that moment. Find the position that satisfies... frequency points Extracting the initial time-frequency representation In the moment And the time-frequency coefficients located on the instantaneous frequency trajectory, i.e., extracting the coefficients that satisfy the conditions... The time frequency point corresponding to The value is taken as the effective time-frequency coefficient at that moment. The time-frequency coefficients at other frequency positions at that moment are set to zero, i.e., for those satisfying... The time and frequency points make Perform multiplication. This operation automatically achieves selective preservation of time-frequency coefficients. By iterating through all time points and repeating the above process, a complete synchronous extraction transform time-frequency representation is obtained. .

[0133] Using the above synchronization extraction method, a new time-frequency representation is obtained. Compared to the original corrected STFT results It can concentrate energy more effectively, and the time-frequency resolution is greatly improved. On the time-frequency plane, the signal energy is only distributed in a narrow region near the instantaneous frequency trajectory, and the energy diffusion phenomenon is effectively eliminated.

[0134] Compared to the Synchronous Compression Transform (SST) method, which focuses all correlation coefficients in the energy diffusion region, the synchronous extraction transform method of this invention uses only the maximum value of the time-frequency coefficients to generate a new time-frequency representation. Original time-frequency representation It can reach its maximum value in the instantaneous frequency trajectory, the time-frequency coefficient. It exhibits optimal noise robustness. Therefore, this invention uses only the time-frequency coefficients in the instantaneous frequency trajectory. A new time-frequency representation is generated, effectively suppressing noise interference. Through the above synchronous extraction and transformation process, a high-resolution time-frequency representation with energy concentrated on the instantaneous frequency trajectory is obtained. The time-frequency analysis of fault transient signals was completed, laying the foundation for further extraction of fault characteristic parameters and realizing rapid and accurate fault location in the distribution network.

[0135] Furthermore, when the fault transient signal is a multi-component signal, the following is included after S600:

[0136] Determine whether the instantaneous frequency derivative interval of different modes meets the separation condition. When the separation condition is met, separate or reconstruct each single-component mode from the multi-component signal according to the time-frequency coefficients corresponding to each mode in the time-frequency representation.

[0137] Furthermore, the separation condition is:

[0138] The difference between the instantaneous frequency derivatives of adjacent modes is greater than twice the frequency support width of the window function, and the change in amplitude function and frequency deviation function of each mode is less than the preset threshold.

[0139] Specifically, in practice, the measured fault transient signal is usually a superposition of several modes generated by different excitation sources. For a multi-component fault transient signal, it can be expressed as:

[0140] ;

[0141] in, The number of signal components. For the first A single-component mode, For the first The instantaneous amplitude function of each mode, For the first The instantaneous phase function of each mode, For the first The instantaneous frequency of each mode. In complex exponential form, it represents the first... The phase of each mode changes over time.

[0142] The time-frequency representation of the synchronous extraction transform is used. In this model, the energy of different modes is concentrated on their respective instantaneous frequency trajectories. If the instantaneous frequency trajectories of different modes have sufficient intervals on the time-frequency plane, the separation or reconstruction of each single-component mode can be achieved.

[0143] For fault transient signals, if the different modes are spaced sufficiently apart, i.e., the difference in the instantaneous frequency derivatives of adjacent modes satisfies:

[0144] ;

[0145] in, , The first The first mode and the first The modality at time... The instantaneous frequency; Let be the frequency support width of the window function, representing the effective range of the window function in the frequency domain. Simultaneously, the amplitude function changes and frequency deviation function changes of each mode should satisfy the constraints. Assume that for... There are very small ones , so that:

[0146] ;

[0147] ;

[0148] in, For the first The derivative of the amplitude function of each mode with respect to time represents the rate of change of amplitude; For the first The frequency deviation function of each mode represents the degree of deviation of the instantaneous frequency from the average frequency; The preset threshold is set according to the separation accuracy requirements in actual applications, and is usually selected as a value between 0.01 and 0.1.

[0149] To determine whether the instantaneous frequency derivative intervals of different modes satisfy the separation condition: first, extract the time-frequency representation of the transform from the synchronization. The energy ridges corresponding to each mode are identified, and the energy ridges are determined at each time step. Searching for time-frequency representation Local peak values ​​can be used to identify the instantaneous frequency trajectories of different modes. The instantaneous frequency functions of each mode are then extracted. ,in Indicates the mode number. Calculates the instantaneous frequency difference between adjacent modes at each time step. Determine the frequency support width of the window function. Determine if it is at all times. All meet Check whether the changes in the amplitude function and frequency deviation function of each mode are less than a preset threshold. Comprehensive judgment: The separation condition is deemed satisfied and modal separation can be performed only when both the instantaneous frequency interval condition and the constraint condition are satisfied; otherwise, the separation condition is deemed not satisfied.

[0150] Under the condition of separation described above, the expression for synchronous extraction transformation should be written as:

[0151] ;

[0152] in, Indicates the multi-component signal at time and frequency points The instantaneous frequency at a given point. Since the instantaneous frequency trajectories of each mode are separated from each other on the time-frequency plane, the energy of each mode is concentrated only near its corresponding instantaneous frequency trajectory.

[0153] Therefore, the synchronous extraction operator based on instantaneous frequency trajectory can accurately distinguish each mode on the time-frequency plane, so that the time-frequency coefficients corresponding to each single-component mode can be effectively separated, thereby realizing mode separation or reconstruction of multi-component fault transient signals.

[0154] In summary, this method effectively eliminates energy diffusion caused by the Heisenberg uncertainty principle by accurately extracting time-frequency coefficients directly related to the instantaneous frequency trajectory, significantly improving time-frequency resolution. Compared to synchronous compression transform, this method only uses the maximum energy coefficient to generate a new time-frequency representation, minimizing the impact of noise on the time-frequency results and enhancing noise robustness. When the fault transient signal is a multi-component signal and satisfies the separation condition that the instantaneous frequency interval between adjacent modes is greater than twice the frequency support width of the window function, each single-component mode can be effectively separated or reconstructed from the time-frequency representation, providing a theoretical basis and technical means for rapid and accurate fault location and fault diagnosis in distribution networks.

[0155] Example 2: During six months of operation monitoring, a 110kV distribution network experienced several fault events, including single-phase grounding faults, phase-to-phase short-circuit faults, and switch operation overvoltages. Traditional fault transient signal analysis methods (based on Fast Fourier Transform and Standard Short-Time Fourier Transform) struggle to accurately separate the time-varying characteristics of each frequency component in complex multimodal transient signals, leading to insufficient fault location accuracy and difficulty in fault type identification. Therefore, during this six-month monitoring period, a power fault time-frequency analysis method based on synchronous extraction transform, proposed in this invention, was used for verification.

[0156] The Rogowski coil sensing system described in Embodiment 1 of this invention is used to collect fault transient currents in the distribution network online. The Rogowski coil operates in a self-integrating state, with a frequency response range of [missing information]. to It can accurately capture the high-frequency oscillation components (typically ranging from 1 kHz to 500 kHz) and low-frequency attenuation components (50 Hz and its harmonics) generated by faults. The sampling rate is set to 1 MHz to ensure sufficient coverage of all frequency components of the transient process.

[0157] Eight fault events were recorded during the six-month monitoring period. The transient signals of these eight faults were processed using both the conventional STFT method and the method of this invention, and the results are compared below:

[0158] Traditional STFT method: For most fault signals, in the time-frequency representation generated by traditional STFT, the energy corresponding to each frequency component is dispersed in... Within the frequency range, The frequency support width of the window function is used. This energy diffusion phenomenon leads to insufficient time-frequency resolution. High-frequency transient characteristics are easily masked by low-frequency background noise and power frequency interference. The time accuracy of fault location is often in the millisecond range, making it impossible to accurately determine the instant of fault occurrence.

[0159] The method of this invention: employs synchronous extraction transformation, and corrects the time-frequency representation by calculating the derivative of the window function to obtain the two-dimensional instantaneous frequency trajectory. Based on discrete frequency intervals Adaptive thresholds are used to construct a binarized synchronous extraction operator. The time-frequency representation obtained by multiplying the initial time-frequency representation with the synchronization extraction operator is... In this method, the energy of each frequency component is precisely concentrated on its instantaneous frequency trajectory. In these 8 fault events, the fault characteristics appear as clear energy ridges on the time-frequency map generated by this method. The time-frequency resolution is improved by 5-10 times compared with the traditional STFT, and the time accuracy of fault location is improved to the microsecond level.

[0160] Of the eight fault events, five were multimodal transient signals (containing two or three main frequency components). Multi-component separation analysis was performed on these events: the instantaneous frequency derivatives of each mode were calculated, and the compatibility of adjacent modes was checked. The interval condition is defined as follows: In 4 out of 5 multimodal events, this condition is met, and the amplitude variation and frequency deviation variation of each mode are both less than the preset threshold. The satisfaction rate reached 80%. For these four events that met the separation conditions, in the time-frequency representation of the synchronous extraction transform, the energy ridges corresponding to different modes were separated from each other on the time-frequency plane, and the characteristic parameters of each mode could be accurately extracted and analyzed.

[0161] In summary, based on application data from eight fault events over six months, the method of this invention achieved highly concentrated energy, with a time-frequency resolution 6-8 times higher than the traditional STFT, and fault location time accuracy improved from milliseconds to microseconds. In two high-noise interference events (signal-to-noise ratio below 5dB), this method achieved a 100% feature extraction success rate by retaining only the maximum energy coefficient on the instantaneous frequency trajectory, while the traditional STFT method could not effectively extract it. In five multimodal events, four met the separation conditions, and the amplitude and frequency characteristics of each mode could be analyzed independently. The six months of application verification fully demonstrates the effectiveness, robustness, and practical value of the method of this invention in the analysis of transient signals during distribution network faults.

[0162] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A power fault time-frequency analysis method based on a synchrosqueezing transform, characterized in that, The method comprises the following steps: S100: collecting a fault transient signal of a power distribution network by a Rogowski coil sensing system working in a self-integration state, a secondary side output voltage of the Rogowski coil sensing system being proportional to a change rate of a measured current, and a frequency response range being determined by a sampling resistor, a distributed capacitor, a coil resistor and a coil inductance; S200: performing a short-time Fourier transform on the fault transient signal, and extending the fault transient signal from a one-dimensional time domain to a two-dimensional time-frequency plane by using a real even window function to obtain an initial time-frequency representation; S300: performing a modified short-time Fourier transform calculation on the fault transient signal by using a derivative of the window function with respect to time to obtain a modified time-frequency representation; S400: calculating a two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the modified time-frequency representation; S500: constructing a synchronous extraction operator by using a binary decision criterion based on a ratio relationship between the initial time-frequency representation and the modified time-frequency representation, and taking a discrete frequency interval as a decision threshold, the synchronous extraction operator taking a value of 1 when a threshold condition is met and taking a value of 0 when the threshold condition is not met; S600: multiplying the initial time-frequency representation and the synchronous extraction operator, retaining only time-frequency coefficients corresponding to the synchronous extraction operator taking the value of 1, removing time-frequency coefficients corresponding to the synchronous extraction operator taking the value of 0, and obtaining a time-frequency representation with energy concentrated on the instantaneous frequency trajectory to complete time-frequency analysis of the fault transient signal; The step of obtaining the modified time-frequency representation comprises: deriving the real even window function to obtain a window function derivative, moving the window function derivative along a time axis, performing windowing processing on the fault transient signal at each time instant, and performing a Fourier transform to obtain the modified time-frequency representation; The binary decision criterion comprises: calculating a complex number ratio of the modified time-frequency representation and the initial time-frequency representation, extracting a real part of the complex number ratio and taking an absolute value, comparing the absolute value with one-half of the discrete frequency interval, determining that a threshold condition is met when the absolute value is less than one-half of the discrete frequency interval, and determining that the threshold condition is not met when the absolute value is greater than or equal to one-half of the discrete frequency interval.

2. A synchronous extraction transform-based power fault time-frequency analysis method according to claim 1, characterized in that, The Rogowski coil sensing system comprises: a Rogowski coil, a sampling resistor and an integration circuit, a secondary coil of the Rogowski coil being connected in series with the sampling resistor to form a self-integration loop, a measured current flowing through a primary side of the Rogowski coil, an induced current output by the secondary coil generating an output voltage signal by flowing through the sampling resistor, and the integration circuit being used for conditioning and amplifying the output voltage signal.

3. The synchronous extraction-based time-frequency analysis method for power fault according to claim 1, characterized in that, The step of obtaining the initial time-frequency representation comprises: moving the real even window function along the time axis, performing windowing processing on the fault transient signal at each time instant, performing a Fourier transform to obtain time-frequency coefficients at different time instants and frequencies, and constituting the initial time-frequency representation.

4. The synchronous extraction-based time-frequency analysis method for power fault according to claim 1, characterized in that, The step of calculating the two-dimensional instantaneous frequency trajectory based on the initial time-frequency representation and the modified time-frequency representation comprises: A complex ratio of the modified time-frequency representation and the initial time-frequency representation at each time-frequency point is calculated, a phase extraction operation is performed on the complex ratio, and an instantaneous frequency value corresponding to each point on a two-dimensional time-frequency plane is obtained by combining a frequency variable to form the two-dimensional instantaneous frequency trajectory.

5. The synchronous extraction-based time-frequency analysis method for power fault according to claim 1, characterized in that, The discrete frequency interval is: A frequency difference between two adjacent discrete frequency sampling points set when performing a discrete processing on a frequency axis in a short-time Fourier transform.

6. The synchronous extraction-based time-frequency analysis method for power fault according to claim 1, characterized in that, The time-frequency representation with energy concentrated on the instantaneous frequency trajectory includes: On a two-dimensional time-frequency plane of the initial time-frequency representation, for each time, a time-frequency coefficient at a frequency position corresponding to the instantaneous frequency trajectory is extracted as an effective time-frequency coefficient of the time, and time-frequency coefficients of other frequency positions of the time are set to zero.

7. The synchronous extraction-based time-frequency analysis method for power fault according to claim 1, characterized in that, When the fault transient signal is a multi-component signal, after S600, the method further includes: It is judged whether intervals of instantaneous frequency derivatives of different modes satisfy a separation condition, when the separation condition is satisfied, each single-component mode is separated or reconstructed from the multi-component signal according to time-frequency coefficients corresponding to the modes in the time-frequency representation.

8. A synchronous extraction transform-based power fault time-frequency analysis method according to claim 7, characterized in that, The separation condition is: A difference between instantaneous frequency derivatives of adjacent modes is greater than twice a frequency support width of a window function, and a change amount of an amplitude function and a change amount of a frequency deviation function of each mode are less than a preset threshold.

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