Real-time dynamic harmonic detection method and system for traction power supply system

Abstract

The invention provides a real-time dynamic harmonic detection method and system for a traction power supply system, and relates to the technical field of harmonic detection, and the detection method comprises the following steps: collecting a voltage signal of the traction power supply system in real time, and dynamically tracking fundamental frequency fluctuation through a phase-locked loop technology; dynamically adjusting the data window length of FFT analysis; dynamically adjusting a frequency spectrum calculation kernel of the FFT; carrying out linear compensation on the detected harmonic phase; taking the preliminarily detected harmonic parameter as an initial value, and iteratively updating the harmonic parameter until convergence by minimizing a signal reconstruction error; dynamically adjusting a sampling interval according to the fundamental frequency fluctuation, and carrying out anti-aliasing processing by adopting a filter with a variable cut-off frequency; and constructing a matrix model containing a fundamental frequency fluctuation parameter, and calculating a real harmonic parameter through a least square method. According to the method, the detection defect of the fixed window FFT during frequency fluctuation can be systematically solved, and high-reliability real-time data support is provided for harmonic resonance suppression of the electrified railway.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic detection, and particularly to a real-time dynamic harmonic detection method and system for a traction power supply system. Background Art

[0002] An electrified railway refers to a railway that can supply power for electric trains. It gets its name because corresponding electrification equipment needs to be installed along the line of such railways to provide power for trains. Since electric locomotives have stronger transport capacity advantages compared to diesel locomotives, the transport capacity of electrified railways is far greater than that of non-electrified railways under the same scale, making it the mainstream type of modern railways.

[0003] Currently, with the increasing number of electric locomotives connected year by year, the harmonic characteristics of the traction power supply system of electrified railways are becoming increasingly complex, which in turn leads to more prominent harmonic resonance problems. In severe cases, it may cause many problems such as traction locking, train delays, and passenger detention.

[0004] However, in actual engineering, it is difficult to maintain the operating frequency of the traction power supply system at a constant fundamental frequency. The deviation of its operating frequency will cause spectral leakage in the FFT analysis with a traditional fixed time window, making the detected harmonic components inaccurate.

[0005] Therefore, how to solve the detection accuracy of the fixed-window FFT when the frequency fluctuates has become an urgent problem to be solved. Summary of the Invention

[0006] To solve the technical problems in the related art, the present invention provides a real-time dynamic harmonic detection method and system for a traction power supply system.

[0007] To achieve the above object, the technical solutions adopted by the present invention include: According to the first aspect of the present invention, a real-time dynamic harmonic detection method for a traction power supply system is provided, including the following steps: Step S1: Real-time collect the voltage signal of the traction power supply system, and dynamically track the fundamental frequency fluctuation through the phase-locked loop technology; Step S2: Dynamically adjust the data window length of the FFT analysis according to the real-time fundamental frequency estimate; Step S3: Dynamically adjust the spectral calculation kernel of the FFT according to the fundamental frequency fluctuation amount, so as to compensate for the offset of the harmonic frequency point when the fundamental frequency decreases; and linearly compensate the detected harmonic phase; Step S4: Take the preliminarily detected harmonic parameters as the initial value, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error; Step S5: Dynamically adjust the sampling interval according to the fundamental frequency fluctuation, and perform anti-aliasing processing using a filter with a variable cut-off frequency; Step S6: Construct a matrix model containing the fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least squares method.

[0008] Optionally, the step S1 specifically includes: Step S1-1: Collect the voltage signal of the traction power supply system in real time; Step S1-2: Perform Hilbert transform on the collected voltage signal to extract the instantaneous phase information: In the formula, is the analytic signal, is the original signal, is the original signal after Hilbert transform, is the imaginary unit, used to construct the complex analytic signal, is the time variable; Step S1-3: Establish a second-order phase-locked loop model, and its dynamic equation is: In the formula, is the fundamental frequency angular frequency estimated in real time, is the initial fundamental frequency angular frequency, and are the proportional and integral coefficients of the phase-locked loop respectively, is at the time point the instantaneous phase deviation and , is the current sampling moment, .

[0009] Optionally, the step S2 specifically includes: Step S2-1: Dynamically adjust the FFT window length according to the real-time fundamental frequency estimate value : In the formula, is the dynamically adjusted FFT window length, is the rounding function, is the sampling rate, is the window length adjustment coefficient, used to balance the spectral resolution and real-time performance, is a preset constant to prevent the denominator from being zero.

[0010] Optionally, the step S2 further includes: Step S2-2: Apply a Hanning window to the truncated signal to suppress the spectral sidelobe leakage: In the formula, is the value of the Hanning window function, is the sampling point index value and .

[0011] Optionally, step S3 specifically includes: Step S3-1: Construct a modified FFT kernel function: In the formula, is the FFT result of the th frequency point after modification, is the signal value of the th sampling point, is the frequency deviation compensation factor and , is the harmonic order; Step S3-2: Linearly compensate the phase of the th harmonic: In the formula, is the phase of the th harmonic after compensation, represents the FFT result at the th frequency point after modification, is the actual frequency point position and , is the rounding operation.

[0012] Optionally, step S4 specifically includes: Establish a harmonic parameter iteration equation: In the formula, is the modified harmonic complex parameter, is the harmonic complex parameter before modification, is the convergence factor, is the complex parameter of the th harmonic and , is the th harmonic amplitude, is the th harmonic phase, is the original signal of the th sampling point, is the harmonic complex exponential term generated with the estimated fundamental frequency ; When the residual energy terminate the iteration.

[0013] Optionally, step S5 specifically includes: Step S5-1: According to the fundamental frequency fluctuation amount Adjust the sampling interval: Wherein, is the sampling interval after dynamic adjustment, is the adaptive coefficient, is the fundamental frequency fluctuation amount and ; Step S5-2: Perform anti-aliasing processing using a filter with a variable cut-off frequency to prevent high-frequency harmonic aliasing.

[0014] Optionally, the cut-off frequency of the filter is set to: Wherein, is the real-time cut-off frequency of the filter.

[0015] Optionally, the specific steps of step S6 include: Step S6-1: Construct a Vandermonde matrix according to the harmonic distribution characteristics : Wherein, is the actual harmonic frequency and , is the harmonic order, represents the time coordinate of the first sampling point, represents the th sampling point's time coordinate; Step S6-2: Calculate the compensated spectrum: Wherein, is the compensated harmonic parameter vector, is the conjugate transpose of the matrix , is the original FFT spectrum vector.

[0016] According to the second aspect of the present invention, there is also provided a real-time dynamic harmonic detection system for a traction power supply system, which is applied to the real-time dynamic harmonic detection method for a traction power supply system described in any one of the technical solutions in the first aspect of the present invention. The real-time dynamic harmonic detection system for a traction power supply system includes: A data acquisition module for real-time collecting voltage signals of the traction power supply system; A dynamic fundamental frequency tracking module for dynamically tracking fundamental frequency fluctuations through phase-locked loop technology; A dynamic window length adjustment module for dynamically adjusting the data window length of FFT analysis according to the real-time fundamental frequency estimation value; Adaptive FFT Harmonic Analysis Module, which is used to dynamically adjust the spectrum calculation kernel of FFT according to the fundamental frequency fluctuation amount, so as to automatically compensate the offset of harmonic frequency points when the fundamental frequency decreases; and linearly compensate the detected harmonic phase; Harmonic Parameter Recursive Correction Module, which is used to take the preliminarily detected harmonic parameters as the initial values and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error; Synchronous Sampling Module, which is used to dynamically adjust the sampling interval according to the fundamental frequency fluctuation and perform anti-aliasing processing using a filter with a variable cut-off frequency; Dynamic Error Matrix Compensation Module, which is used to construct a matrix model containing fundamental frequency fluctuation parameters and calculate the true harmonic parameters by the least squares method.

[0017] Beneficial Effects: 1. In this embodiment, first, the present invention can effectively solve the problem of the failure of the traditional fixed fundamental frequency assumption by using a phase-locked loop to track the fundamental frequency fluctuation in real time, thereby avoiding spectrum leakage caused by frequency offset, and thus can significantly improve the accuracy of harmonic component detection.

[0018] Second, the present invention can make the signal truncation close to an integer period and suppress side lobe leakage by dynamically adjusting the FFT window length and calculation kernel function; the frequency offset compensation mechanism can correct the harmonic frequency point offset, and thus can ensure the accurate measurement of amplitude and phase.

[0019] Third, the present invention combines dynamic sampling interval adjustment and variable cut-off filters, which can effectively avoid high-frequency harmonic aliasing when the fundamental frequency fluctuates, thereby ensuring the integrity of signal sampling and the reliability of the analysis frequency band.

[0020] Fourth, the present invention can effectively overcome the limitations of traditional single FFT analysis by gradually approaching the true harmonic parameters through the iterative process of minimizing the reconstruction error, and thus improve the detection accuracy in complex harmonic scenarios.

[0021] Fifth, the dynamic compensation based on the matrix model and the least squares method in the present invention can effectively eliminate the systematic error introduced by the fundamental frequency fluctuation, so that the final calculation results of harmonic parameters (amplitude, phase, frequency) are closer to the true values.

[0022] Generally speaking, the method of the present invention forms a closed-loop harmonic detection process through the coordination of multiple links (dynamic tracking - window length adjustment - kernel function correction - iterative optimization - anti-aliasing - model compensation), which has high precision, strong real-time performance (the dynamic adjustment of the window length and the rapid convergence of the iterative algorithm can ensure real-time performance and is applicable to the traction power supply monitoring scenario with millisecond-level response) and engineering practicability (the anti-aliasing design and matrix correction enhance the robustness of the method to complex working conditions such as on-site noise and frequency mutation and can be directly embedded in the existing traction substation monitoring devices). In this way, the dynamic adjustment mechanism and mathematical model correction of the present invention can systematically solve the detection defects of the fixed-window FFT when the frequency fluctuates, providing high-reliability real-time data support for the suppression of harmonic resonance in electrified railways.

[0023] 2. Other beneficial effects or advantages of the present invention will be described in detail in the specific implementation manners. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0025] Wherein: Figure 1 is a schematic flow chart of the steps of the real-time dynamic harmonic detection method for the traction power supply system provided by an exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0027] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0028] The following will elaborate on the technical solutions of the present invention with reference to the drawings.

[0029] As Figure 1 shown, this embodiment provides a real-time dynamic harmonic detection method for a traction power supply system, including the following steps: Step S1: Collect the voltage signal of the traction power supply system in real time, and dynamically track the fundamental frequency fluctuation through the phase-locked loop technology; Step S2: Dynamically adjust the data window length of the FFT analysis according to the real-time fundamental frequency estimation value; Step S3: Dynamically adjust the spectral calculation kernel of the FFT according to the fundamental frequency fluctuation amount: when the fundamental frequency decreases, automatically compensate for the offset of the harmonic frequency points; and linearly compensate for the detected harmonic phases; Step S4: Take the preliminarily detected harmonic parameters as the initial values, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error; Step S5: Dynamically adjust the sampling interval according to the fundamental frequency fluctuation, and perform anti-aliasing processing using a filter with a variable cut-off frequency; Step S6: Construct a matrix model containing the fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least squares method.

[0030] In this embodiment, first, the present invention can effectively solve the problem of the failure of the traditional fixed fundamental frequency assumption by tracking the fundamental frequency fluctuation in real time through the phase-locked loop, thereby avoiding spectral leakage caused by frequency offset, and thus can significantly improve the accuracy of harmonic component detection.

[0031] Second, the present invention suppresses sidelobe leakage by dynamically adjusting the FFT window length and the calculation kernel function to make the signal truncation close to an integer period; the frequency offset compensation mechanism can correct the harmonic frequency point offset, and thus can ensure the accurate measurement of the amplitude and phase.

[0032] Third, the present invention combines dynamic sampling interval adjustment and a variable cut-off filter to effectively avoid high-frequency harmonic aliasing when the fundamental frequency fluctuates, thereby ensuring the integrity of signal sampling and the reliability of the analysis frequency band.

[0033] Fourth, the present invention can effectively overcome the limitations of the traditional single FFT analysis by gradually approaching the true harmonic parameters through the iterative process of minimizing the reconstruction error, and further improve the detection accuracy in complex harmonic scenarios.

[0034] Fifth, the dynamic compensation based on the matrix model and the least squares method of the present invention can effectively eliminate the systematic error introduced by the fundamental frequency fluctuation, so that the final calculation results of the harmonic parameters (amplitude, phase, frequency) are closer to the true values.

[0035] Generally speaking, the method of the present invention forms a closed-loop harmonic detection process through multi-link collaboration (dynamic tracking - window length adjustment - kernel function correction - iterative optimization - anti-aliasing - model compensation), which has high precision, strong real-time performance (the dynamic adjustment of the window length and the rapid convergence of the iterative algorithm can ensure real-time performance and can be applied to the traction power supply monitoring scenario with millisecond-level response) and engineering practicability (the anti-aliasing design and matrix correction enhance the robustness of the method to complex working conditions such as on-site noise and frequency mutation and can be directly embedded in existing traction substation monitoring devices). In this way, the dynamic adjustment mechanism and mathematical model correction of the present invention can systematically solve the detection defects of the fixed-window FFT in the case of frequency fluctuation and provide high-reliability real-time data support for the suppression of harmonic resonance in electrified railways.

[0036] In one embodiment of the present invention, step S1 may specifically include: Step S1-1: Real-time collect the voltage signal of the traction power supply system; Step S1-2: Perform Hilbert transform on the collected voltage signal to extract the instantaneous phase information: In the formula, is the analytic signal, is the original signal, is the original signal after Hilbert transform (representing the orthogonal component of the original signal), is the imaginary unit, used to construct the complex analytic signal, is the time variable; Step S1-3: Establish a second-order phase-locked loop model, and its dynamic equation is: In the formula, is the base frequency angular frequency estimated in real time, is the initial base frequency angular frequency, and are the proportional and integral coefficients of the phase-locked loop respectively (used to adjust the dynamic response speed and stability), is the instantaneous phase deviation at time point (the instantaneous phase deviation is used to represent the difference between the actual signal phase and the reference phase) and , is the current sampling moment, .

[0037] In this embodiment, first, the present invention converts the real signal into an analytic signal through Hilbert transform, so that the instantaneous phase information can be directly obtained, and the phase misjudgment under noise interference of the traditional zero-crossing detection method can be avoided, and the real-time performance and accuracy of phase tracking can be significantly improved.

[0038] Second, the second-order phase-locked loop model (proportional-integral control) of the present invention can eliminate the steady-state frequency error, so that it can still quickly converge to the true frequency when the fundamental frequency suddenly changes or fluctuates continuously, and can effectively solve the tracking lag problem of the traditional first-order phase-locked loop in dynamic scenarios.

[0039] Third, due to the natural anti-high-frequency noise characteristic of the analytical signal construction of the Hilbert transform, combined with the smoothing effect of the integral link of the phase-locked loop on low-frequency noise, the fundamental frequency estimation can remain stable in a complex electromagnetic interference environment and has good anti-noise robustness.

[0040] Fourth, through the coordinated adjustment of the proportional coefficient ( ) and the integral coefficient ( ) in the dynamic equation of the present invention, the frequency capture bandwidth of the phase-locked loop can cover the fundamental frequency fluctuation range of ±5 Hz (such as 45 Hz to 55 Hz), so that the frequency tracking range can be extended to meet the actual working conditions of the electrified railway traction network.

[0041] In this embodiment, it should be noted that, first, for the construction of the analytical signal, the Hilbert transform converts the real signal ( ) into the analytical signal ( ). In this way, the instantaneous phase ( ) of the analytical signal can be directly obtained through the argument calculation ( ), and the delay of waiting for the signal to cross the zero point required by the traditional zero-crossing detection method can be avoided, realizing the real-time extraction of phase information. (The traditional zero-crossing detection method calculates the frequency depending on the signal crossing the zero point, which is prone to false triggering in the case of harmonic distortion or noise interference and cannot track continuous phase changes in real time) Second, since the Hilbert transform is equivalent to suppressing the negative frequency components in the frequency domain, the analytical signal only retains the positive frequency components, which can effectively suppress the interference of high-frequency noise on phase extraction. At the same time, through the discrete Hilbert transform (for example, implemented by an FIR filter), the phase information can be updated in real time at the sampling point level to meet the dynamic tracking requirements of milliseconds.

[0042] Third, for the phase-locked loop model, its proportional term ( ) is used to quickly respond to the phase deviation and shorten the frequency locking time, and its integral term ( ) is used to eliminate the steady-state error and ensure that the frequency estimation value ( ) finally converges to the true fundamental frequency. (The traditional first-order phase-locked loop only contains a proportional coefficient, has a steady-state frequency error, and has a limited capture bandwidth) Generally speaking, this technical solution extracts the instantaneous phase through Hilbert transform and dynamically tracks with a second-order phase-locked loop, which can effectively solve the problem of tracking failure of traditional methods under noise interference and frequency fluctuations, and can provide a high-precision fundamental frequency estimation value for subsequent dynamic FFT analysis.

[0043] In addition, it can be understood that for the proportional coefficient ( ), it determines the initial response speed of the phase-locked loop. If it is too large, it will cause oscillation; if it is too small, it will prolong the locking time. For the integral coefficient ( ), it determines the steady-state accuracy. If it is too large, it will introduce low-frequency noise sensitivity; if it is too small, it will cause residual error. Therefore, in actual engineering, the and can be determined by the Ziegler-Nichols tuning method or the frequency-domain sweep method to ensure stable operation within the typical frequency fluctuation range of the traction network.

[0044] In an embodiment of the present invention, step S2 may specifically include: Step S2-1: Dynamically adjust the FFT window length according to the real-time fundamental frequency estimation value : In the formula, is the dynamically adjusted FFT window length (its unit can be the number of sampling points), is the rounding function, is the sampling rate, is the window length adjustment coefficient, which is used to balance the spectral resolution and real-time performance (its specific value can be calibrated through actual measurement. For example, its value range can be set from 0.1 to 1.0), is a preset constant, which is used to prevent the denominator from being zero (for example, can be set to 0.01 Hz).

[0045] In this embodiment, first, the adaptive suppression of spectral leakage in this embodiment, specifically, by dynamically adjusting the FFT window length, the intercepted signal segment is made close to an integer multiple of the fundamental wave period, so that the spectral energy leakage caused by asynchronous sampling can be significantly reduced, and then the detection accuracy of the harmonic amplitude and phase can be improved.

[0046] Second, the set window length adjustment coefficient can flexibly control the sensitivity of the window length change, and can maintain a long window length to maintain high frequency resolution when the fundamental frequency fluctuates within a small range. At the same time, when the fluctuation range is large, the window length is shortened to meet the real-time performance requirements.

[0047] Thirdly, this embodiment can also achieve anti-fundamental frequency mutation interference. Specifically, when the fundamental frequency changes rapidly (for example, the frequency drops suddenly due to a traction network short-circuit fault), the window length dynamic adjustment mechanism can respond quickly, thereby avoiding the misjudgment of harmonic parameters caused by signal truncation mismatch in the traditional fixed window length FFT.

[0048] Fourthly, the preset constant introduced in the formula of this embodiment can prevent the denominator from being zero to ensure the stability of the window length when the fundamental frequency is exactly 50 Hz (nominal value), thereby avoiding the drastic jump of the window length caused by too small a denominator.

[0049] In this embodiment, it should also be noted that for the fundamental frequency deviation sensitive term ( ), the greater the deviation of the fundamental frequency from the nominal value (50 Hz), the greater the value of the denominator term, resulting in a decrease in the window length . In particular, when , the denominator degenerates into the preset constant , and at this time the window length is stable at , which can avoid numerical instability caused by the denominator being zero. For the window length , it is inversely proportional to the fundamental frequency deviation. When the fundamental frequency fluctuates, the window length is dynamically adjusted, so that the intercepted signal segment can be as close as possible to an integer multiple of the fundamental wave period to meet the synchronous sampling condition of FFT analysis.

[0050] In an embodiment of the present invention, step S2 may further include: Step S2-2: Apply a Hanning window to the truncated signal to suppress spectral sidelobe leakage: In the formula, is the Hanning window function value, is the sampling point index value and .

[0051] In this embodiment, firstly, by applying a Hanning window to the truncated signal, spectral sidelobe leakage can be suppressed (the Hanning window smooths the edges of the truncated signal, gradually changing the signal ends to zero, reducing the energy diffusion of the spectral sidelobes caused by time-domain truncation, making the harmonic main lobe sharper and avoiding mutual interference between adjacent frequency points), improving the accuracy of harmonic detection.

[0052] Secondly, the design of the Hanning window function in this embodiment is closely combined with the dynamic window length . The coefficients of the Hanning window function are automatically adjusted with the change of the dynamic window length, so as to ensure that the sidelobe suppression effect under different window lengths can tend to be consistent.

[0053] Third, compared with the rectangular window (no window function), the Hanning window sacrifices part of the main lobe width to further reduce the sidelobe peak attenuation, and can be adapted to the accurate detection of high-order harmonics. At the same time, the Hanning window has a better noise suppression effect on both ends of the signal than the rectangular window, and can reduce the spread of noise energy in the spectrum in the high-noise environment of the traction network.

[0054] The principle of the Hanning window to suppress sidelobe leakage is described below.

[0055] First, the source of spectral leakage is that when the signal truncation length is not an integer multiple of the fundamental wave period, the time-domain truncation is equivalent to multiplying the signal by a rectangular window, and its spectrum is the convolution of the original signal spectrum and the rectangular window spectrum. The sidelobes of the rectangular window are relatively high, resulting in energy leakage to adjacent frequency points. Second, the main lobe width of the Hanning window is twice that of the rectangular window, but the sidelobe attenuation is significantly improved. In this way, by suppressing the sidelobes, the harmonic energy is more concentrated at the main lobe frequency points, reducing the interference of adjacent harmonics or noise.

[0056] Generally speaking, the dynamic Hanning window windowing method of this embodiment combines window function design, dynamic window length adaptation, and amplitude-phase compensation algorithms, which can significantly improve the accuracy and anti-interference ability of harmonic detection, and provide a reliable data basis for harmonic governance of the traction power supply system.

[0057] In an embodiment of the present invention, step S3 specifically includes: Step S3-1: Construct a modified FFT kernel function: In the formula, is the FFT result of the th frequency point after modification, is the signal value of the th sampling point, is the frequency deviation compensation factor and , is the harmonic order, Step S3-2: Perform linear compensation on the th harmonic phase: In the formula, is the th harmonic phase after compensation, represents the FFT result at the th frequency point after modification, is the actual frequency point position and , is the rounding operation.

[0058] In this implementation, first, this implementation can achieve dynamic compensation of harmonic frequency deviation and improve the amplitude detection accuracy. Specifically, when the fundamental frequency fluctuates, the fixed frequency point of the traditional FFT cannot accurately match the actual harmonic frequency (for example, when the fundamental frequency 50Hz changes to 49Hz, the 5th harmonic shifts from 250Hz to 245Hz). This implementation introduces a frequency deviation compensation factor , dynamically adjust the frequency point position of the FFT kernel function so that the frequency point calculated by FFT is aligned with the actual frequency of the harmonic, thereby reducing spectrum leakage and significantly improving the detection accuracy of the harmonic amplitude.

[0059] Second, this implementation can correct the phase nonlinearity error and ensure phase accuracy. Specifically, fundamental frequency fluctuations can cause the harmonic phase to accumulate linear deviations over time. This implementation uses the phase compensation term ( ) eliminates the linear phase deviation introduced by frequency adjustment and window function truncation, ensures the accuracy of harmonic phase parameters, and provides reliable phase information for subsequent harmonic control equipment (for example, active filters).

[0060] Third, this implementation can adaptively track the fundamental frequency fluctuation and enhance the system robustness. , this implementation can dynamically adjust and phase compensation to adapt to the continuous fluctuation of the fundamental frequency, avoid detection failure caused by frequency mutation in traditional methods, and improve the stability of the detection method under complex working conditions.

[0061] In this embodiment, it should be noted that, first, for the modified FFT kernel function, when the fundamental frequency fluctuates, the actual frequency of the harmonic is , while the frequency interval of traditional FFT is fixed at By changing the frequency index in the FFT kernel function from Corrected to , which is equivalent to offsetting the frequency point of FFT so that the corrected frequency point corresponds to the actual harmonic frequency , thus avoiding spectrum leakage. From a mathematical point of view, it is equivalent to digital frequency modulation of the signal, so that the harmonic main lobe is aligned with the FFT frequency point, thereby improving the detection accuracy of the amplitude.

[0062] In addition, in this embodiment, the frequency deviation compensation factor , is to The offset from the base frequency ( ) and dynamically adjust the harmonic frequency position.

[0063] Second, in the harmonic phase linear compensation formula, the compensation principle is: frequency offset When , the phase change of the time domain signal is , in the discrete FFT, this change is manifested as the linear accumulation of the phase with the sampling point n, and the compensation term by estimating 's contribution to cancel the linear phase error introduced by the frequency offset and window length adjustment. In this way, the phase measurement result can reflect the true initial phase of the harmonic, rather than the observed value contaminated by frequency fluctuations.

[0064] The following is described by an exemplary embodiment.

[0065] Assume that the fundamental frequency drops from 50 Hz to 49 Hz, and the 5th harmonic (actual frequency 245 Hz) is detected. In the traditional FFT, the FFT frequency point interval is 1 Hz, and 245 Hz is between the 245th frequency point. However, the traditional FFT uses 50 Hz as the fundamental frequency, and the 5th harmonic corresponds to 250 Hz (the 250th frequency point), resulting in spectral leakage. In this embodiment, , the FFT kernel function frequency points are adjusted to so that the 245th frequency point (245 Hz) enters the main lobe range. In this way, the linear phase deviation caused by the frequency shift of 4.9 frequency points can be eliminated, and the true phase can be restored.

[0066] In an embodiment of the present invention, step S4 may specifically include: Establish a harmonic parameter iterative equation: In the formula, is the corrected harmonic complex parameter, is the harmonic complex parameter before correction, is the convergence factor (controlling the parameter update speed, generally it needs to meet the stability condition , is the maximum eigenvalue of the input signal autocorrelation matrix), is the complex parameter of the th harmonic and (the complex form represents the amplitude and phase of the th harmonic), is the amplitude of the th harmonic, is the phase of the th harmonic, is the original signal at the th sampling point, is the harmonic complex exponential term generated with the estimated fundamental frequency (that is, the harmonic rotation factor generated based on the real-time fundamental frequency estimation to ensure that the model frequency is synchronized with the current fundamental frequency); When the residual energy the iteration is terminated.

[0067] In this implementation, first, this implementation can dynamically correct the initial estimation error and improve the accuracy of harmonic parameters. Specifically, when the fundamental frequency fluctuates, the traditional FFT may cause errors in the initial harmonic parameters (amplitude, phase) due to spectrum leakage. This implementation uses iterative optimization and reconstruction error as feedback to dynamically correct the initial estimation value, gradually approach the true harmonic parameters, and significantly improve the detection accuracy, especially when the fundamental frequency fluctuates rapidly.

[0068] Second, this implementation can track the time-varying characteristics of harmonics in real time and enhance the adaptability of the system. Specifically, the harmonic amplitude and phase of the traction power supply system may fluctuate dynamically due to changes in locomotive load. The iterative equation is updated in real time. , combined with the baseband frequency provided by the phase-locked loop , so that the harmonic model is always synchronized with the current system state, adapting to the time-varying characteristics of harmonics, and avoiding detection failure caused by parameter lag in traditional methods.

[0069] Third, this implementation can suppress noise interference and improve anti-interference ability. Specifically, the invention minimizes the signal reconstruction error, and the iterative process essentially has a low-pass filtering effect on noise and interference. Random noise is averaged in multiple iterations, while the real harmonic components are retained due to correlation, thereby improving the robustness of the detection result in a noisy environment.

[0070] Fourth, this implementation is compatible with high-order harmonic analysis to avoid missing key components. Specifically, in this implementation, the upper limit of the summation in the equation is 15th harmonic ( ), covering the typical high-order harmonic range of electrified railways (for example, 3rd, 5th, 7th, etc.). By optimizing multiple harmonic parameters simultaneously, we avoid the incomplete model caused by focusing only on a single harmonic, ensuring that the detection results are comprehensive and reliable.

[0071] In this implementation, it should be noted that, first, for the harmonic parameter iteration equation, the reconstruction error part is: , and its harmonic rotation factor is: , its mathematical derivation process is: This equation is derived from the minimum mean square error criterion, which aims to minimize the square of the instantaneous reconstruction error: in, is a complex parameter; Therefore, the expanded error expression is: In this formula represents complex conjugate; Then, for complex parameters Derivation: In the complex domain, gradient descent needs to be calculated for the conjugate derivative (Wirtinger derivative): This is because the effective gradient direction for complex optimization is with respect to the derivative; Thus, the parameter update direction should be the negative gradient direction: wherein, denotes proportional to, indicating that the update amount is proportional to the gradient direction.

[0072] The conjugate of the negative exponential function satisfies: Therefore, the parameter update formula actually implies a conjugate operation on the complex exponential term. To match the phase rotation direction of the complex parameter , the conjugated complex exponential term needs to be converted to the original rotation direction to maintain the consistency of phase adjustment.

[0073] The complex exponential term represents the rotation direction of the harmonic model. If is directly used, it is equivalent to reverse rotation, which will cause the phase update direction to be opposite to the actual change direction of the signal. Therefore, by taking the complex conjugate (i.e., sign flipping), the parameter update direction can be ensured to be consistent with the actual rotation direction of the signal, thereby correctly correcting the amplitude and phase.

[0074] That is to say, due to the complex conjugate operation, the actual update equation is , that is, the actual harmonic parameter iteration equation is: .

[0075] Its physical meaning is: at each iteration, the difference between the current sampling point and the harmonic reconstruction signal is used to calculate the parameter correction amount. At the same time, the amplitude and phase are adjusted. For example, if the amplitude of the reconstructed signal is insufficient (the error is positive), then the modulus (amplitude) is increased; if the phase deviation causes error accumulation, then the argument (phase) is adjusted.

[0076] In this embodiment, in the equation comes from the real-time estimation of the phase-locked loop in the foregoing technical solution to ensure that the fundamental frequency of the harmonic model is strictly consistent with the actual frequency of the system, and to avoid the harmonic frequency points being misaligned due to the fundamental frequency deviation. At the same time, the frequency of each harmonic component is , adjust in real time with the fluctuation of the fundamental frequency, so that the harmonic model always matches the current system state.

[0077] In this embodiment, it should also be noted that for the selection of the convergence factor , first, a smaller has a smaller corresponding update step size, slower convergence but higher stability, and is suitable for high-noise environments. Second, a larger has a larger corresponding update step size, faster convergence but may oscillate, and is suitable for quickly tracking dynamic changes. Therefore, in the actual application process, a variable step size strategy (for example, normalization) can be selected to adaptively adjust to balance the convergence speed and stability.

[0078] In an embodiment of the present invention, step S5 may specifically include: Step S5-1: Adjust the sampling interval according to the fundamental frequency fluctuation : In the formula, is the sampling interval after dynamic adjustment, is the adaptive coefficient, is the fundamental frequency fluctuation and ; Step S5-2: Perform anti-aliasing processing using a filter with a variable cut-off frequency to prevent high-frequency harmonic aliasing.

[0079] In this embodiment, first, this embodiment can dynamically match the fundamental frequency fluctuation and optimize the sampling resolution. Specifically, the traditional fixed sampling rate may cause the harmonic frequency to deviate from the integer multiple frequency point when the fundamental frequency fluctuates, resulting in spectral leakage. This embodiment dynamically adjusts the sampling interval so that the sampling rate changes synchronously with the fundamental frequency , ensuring that the number of sampling points within each fundamental frequency period is constant, improving the alignment accuracy of the harmonic frequency, and reducing spectral leakage.

[0080] Second, this embodiment can adaptively allocate system resources and balance real-time performance and accuracy. Specifically, the sensitivity of the sampling interval to the fundamental frequency fluctuation is adjusted through the parameter . For example, when the fundamental frequency fluctuates violently (for example, when the locomotive accelerates or brakes), increase so that the sampling rate is quickly adjusted to give priority to ensuring real-time performance. When the fundamental frequency is stable, can be reduced to maintain a high sampling rate and improve the spectral resolution.

[0081] In this embodiment, it should be noted that for the dynamic sampling interval adjustment (that is, according to the fundamental frequency fluctuation In terms of adjusting the sampling interval), when the fundamental frequency decreases, the fixed sampling rate in the existing related technologies may be too high, resulting in waste of resources. When the fundamental frequency increases, it may be insufficient. In this embodiment, by adjusting , the effective sampling rate changes with . For example, when , . At this time, will increase, reducing the sampling rate to match the low-frequency requirements; when , . At this time will decrease, increasing the sampling rate to avoid high-frequency harmonic aliasing.

[0082] In an embodiment of the present invention, the cut-off frequency of the filter is set to: In the formula, is the real-time cut-off frequency of the filter.

[0083] In this embodiment, first, high-frequency aliasing can be suppressed to ensure the authenticity of the spectrum. Specifically, when the fundamental frequency decreases, the highest harmonic frequency to be detected (such as the 15th harmonic) also decreases accordingly. This embodiment dynamically adjusts the cut-off frequency of the anti-aliasing filter to avoid high-frequency noise or unconcerned harmonics aliasing into the effective frequency band, ensuring the authenticity of the FFT analysis result.

[0084] Second, it can be compatible with wide-frequency harmonic analysis and avoid over-constraint of the fixed filter. Specifically, a traditional fixed cut-off frequency filter may over-filter high-order harmonics when the fundamental frequency decreases (for example, the 15th harmonic at a fundamental frequency of 49 Hz can be filtered out). However, the cut-off frequency of the filter in this embodiment will decrease with the fundamental frequency, which is beneficial to retaining the effective harmonic components while filtering out useless high-frequency noise.

[0085] Generally speaking, in the above embodiment, by dynamically adjusting the sampling rate and the anti-aliasing filter, the over-sampling or under-sampling problems of the traditional fixed-parameter system during the fundamental frequency fluctuation can be solved, providing a front-end signal guarantee for high-precision harmonic detection, which is the key design for the method of the present invention to achieve the balance between real-time performance and accuracy.

[0086] In an embodiment of the present invention, step S6 may specifically include: Step S6-1: Construct a Vandermonde matrix according to the harmonic distribution characteristics : In the formula, is the actual harmonic frequency and , is the harmonic order (which needs to be estimated in real time by the phase-locked loop to generate and ensure that the model is synchronized with the current system frequency), represents the time coordinate of the first sampling point, represents the time coordinate of the th sampling point; In the formula, is the harmonic parameter vector after compensation, is the conjugate transpose of the matrix , is the original FFT spectrum vector.

[0087] In this embodiment, first, by dynamically constructing a Vandermonde matrix containing the actual harmonic frequencies, the present invention can accurately characterize the frequency distribution of each harmonic under the fundamental frequency fluctuation, thereby avoiding the modeling error caused by the fixed frequency assumption of the traditional FFT. Specifically, each column of the matrix corresponds to an actual harmonic frequency component ( ), and each row corresponds to different sampling time points , and its element is , that is, the harmonic basis function in the form of complex exponential. This matrix decomposes the signal into a linear combination of each harmonic under the dynamic fundamental frequency, accurately matching the actual harmonic frequency, and providing an accurate mathematical model for subsequent optimization.

[0088] Second, the present invention uses the least squares method to compensate the FFT spectrum, effectively suppressing the spectrum leakage phenomenon caused by frequency offset, and making the detection results of harmonic amplitude and phase closer to the true values. Specifically, assuming that the observed signal spectrum can be expressed as , is noise and error, and the corresponding minimized reconstruction error is: , and the optimal harmonic parameters are obtained by solving the normal equation . The least squares solution projects the observed data onto the harmonic subspace, eliminating the misalignment of the spectrum components caused by frequency deviation, thereby correcting the amplitude and phase.

[0089] Third, the frequency parameters in the matrix model of the present invention are dynamically adjusted based on the real-time estimated fundamental frequency, which can adapt to the continuous fluctuation of the operating frequency of the traction power supply system and ensure the robustness of the detection method under complex working conditions.

[0090] Fourth, the optimization process of the least squares method of the present invention can suppress the influence of noise and interference, and improve the accuracy of harmonic parameter estimation by minimizing the reconstruction error, especially showing better performance in the scenario of multi-harmonic superposition.

[0091] In addition, it can be understood that this embodiment can be combined with the dynamic cut-off frequency filter in the above embodiments to pre-filter high-frequency interference and ensure that only effective harmonic components are included in the matrix model.

[0092] For example, in an exemplary embodiment, in a traction power supply system, the load change of an electric locomotive often causes the fundamental frequency to fluctuate (e.g., shift from 50 Hz to 49.5 Hz - 50.5 Hz). Due to the fixed window length and frequency resolution of the traditional FFT, it is unable to accurately detect the harmonics after the shift (e.g., the 5th harmonic of the original 50 Hz, which is 250 Hz, may become 247.5 Hz). This embodiment aligns the actual harmonic frequencies precisely to the analysis frequency points through dynamic matrix modeling and least squares optimization, thereby solving the following problems: underestimation / overestimation of harmonic amplitudes (compensating for the energy dispersion caused by spectral leakage), misjudgment of harmonics (avoiding false harmonic components caused by interference from adjacent frequency points), and phase distortion (jointly correcting the phase error through linear phase compensation and matrix optimization).

[0093] Generally speaking, this embodiment can achieve a significant leap in the accuracy of harmonic detection in the traction power supply system through the combination of dynamic frequency modeling and least squares optimization. Its core lies in embedding the real-time fundamental frequency tracking technology into the mathematical framework of spectral analysis, solving the inherent problems of traditional methods at the model level, and providing a highly reliable data basis for harmonic resonance suppression and power quality control.

[0094] According to the second aspect of the present invention, there is also provided a real-time dynamic harmonic detection system for a traction power supply system, which is applied to the real-time dynamic harmonic detection method of the traction power supply system in any one of the technical solutions in the first aspect of the present invention. The real-time dynamic harmonic detection system for a traction power supply system may include a data acquisition module, a dynamic fundamental frequency tracking module, a dynamic window length adjustment module, an adaptive FFT harmonic analysis module, a harmonic parameter recursive correction module, a synchronous sampling module, and a dynamic error matrix compensation module.

[0095] Among them, the data acquisition module is used to collect the voltage signals of the traction power supply system in real time. The dynamic fundamental frequency tracking module is used to dynamically track the fundamental frequency fluctuation through the phase-locked loop technology. The dynamic window length adjustment module is used to dynamically adjust the data window length of the FFT analysis according to the real-time fundamental frequency estimation value. The adaptive FFT harmonic analysis module is used to dynamically adjust the spectrum calculation kernel of the FFT according to the fundamental frequency fluctuation amount, so as to automatically compensate the offset of the harmonic frequency point when the fundamental frequency decreases; and linearly compensate the detected harmonic phase. The harmonic parameter recursive correction module is used to use the preliminarily detected harmonic parameters as the initial values, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error. The synchronous sampling module is used to dynamically adjust the sampling interval according to the fundamental frequency fluctuation, and perform anti-aliasing processing using a filter with a variable cut-off frequency. The dynamic error matrix compensation module is used to construct a matrix model containing the fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least squares method.

[0096] Through the real-time dynamic harmonic detection system of the traction power supply system of the present invention, first, it can effectively solve the problem of the failure of the traditional fixed fundamental frequency assumption, avoid spectrum leakage caused by frequency offset, and can significantly improve the accuracy of harmonic component detection. Second, by dynamically adjusting the FFT window length and the calculation kernel function, the signal truncation is close to an integer period, suppressing sidelobe leakage; the frequency offset compensation mechanism can correct the harmonic frequency point offset, and thus can ensure the accurate measurement of amplitude and phase. Third, combined with the dynamic sampling interval adjustment and the variable cut-off filter, it can effectively avoid high-frequency harmonic aliasing when the fundamental frequency fluctuates, thereby ensuring the integrity of signal sampling and the reliability of the analysis frequency band. Fourth, through the iterative process of minimizing the reconstruction error, the present invention gradually approaches the true harmonic parameters, can effectively overcome the limitations of the traditional single FFT analysis, and further improve the detection accuracy in complex harmonic scenarios. Fifth, the dynamic compensation based on the matrix model and the least squares method can effectively eliminate the systematic error introduced by the fundamental frequency fluctuation, so that the final calculation results of the harmonic parameters (amplitude, phase, frequency) are closer to the true values.

[0097] Generally speaking, the system of the present invention constructs a closed-loop detection chain of frequency tracking - window length adjustment - kernel function correction - parameter iteration - matrix compensation, enables the system to maintain the detection accuracy under time-varying working conditions, and can effectively reduce the harmonic impedance calculation error compared with the traditional FFT scheme, providing a reliable basis for the active filter control of the traction power supply system.

[0098] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A real-time dynamic harmonic detection method for a traction power supply system, characterized in that: The steps include: Step S1: collecting voltage signals of the traction power supply system in real time, and dynamically tracking fundamental frequency fluctuations through phase-locked loop technology; Step S2: dynamically adjusting the data window length of the FFT analysis according to the real-time fundamental frequency estimation value; Step S3: dynamically adjust the spectrum calculation kernel of FFT according to the fundamental frequency fluctuation to compensate for the offset of the harmonic frequency point when the fundamental frequency decreases; and perform linear compensation on the detected harmonic phase; Step S4: taking the initially detected harmonic parameters as initial values, iteratively updating the harmonic parameters until convergence by minimizing the signal reconstruction error; Step S5: dynamically adjusting the sampling interval according to the fundamental frequency fluctuation, and using a filter with a variable cutoff frequency to perform anti-aliasing processing; Step S6: construct a matrix model including fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least square method.

2. The real-time dynamic harmonic detection method of the traction power supply system according to claim 1 is characterized in that: The step S1 specifically includes: Step S1-1: collecting voltage signals of the traction power supply system in real time; Step S1-2: Perform Hilbert transform on the collected voltage signal to extract instantaneous phase information: In the formula, To analyze the signal, is the original signal, The original signal After Hilbert transformation, the signal is an imaginary unit used to construct complex analytical signals, is the time variable; Step S1-3: Establish a second-order phase-locked loop model, whose dynamic equation is: In the formula, is the real-time estimated fundamental angular frequency, is the initial fundamental angular frequency, and are the proportional and integral coefficients of the phase-locked loop, For at time point The instantaneous phase deviation of , is the current sampling time, .

3. The real-time dynamic harmonic detection method of the traction power supply system according to claim 2 is characterized in that: The step S2 specifically includes: Step S2-1: Based on the real-time base frequency estimation value , dynamically adjust the FFT window length: In the formula, is the dynamically adjusted FFT window length, is the rounding function, is the sampling rate, is the window length adjustment coefficient, which is used to balance spectrum resolution and real-time performance. is a preset constant to prevent the denominator from being zero.

4. The real-time dynamic harmonic detection method of the traction power supply system according to claim 3 is characterized in that: The step S2 further comprises: Step S2-2: Add a Hanning window to the truncated signal to suppress spectrum sidelobe leakage: In the formula, is the Hanning window function value, is the sampling point index value and .

5. The real-time dynamic harmonic detection method of the traction power supply system according to claim 4 is characterized in that: The step S3 specifically includes: Step S3-1: Construct a modified FFT kernel function: In the formula, After the correction The FFT result of each frequency point is: For the The signal value of the sampling point, is the frequency deviation compensation factor and , is the harmonic order; Step S3-2: Subharmonic phase linear compensation: In the formula, After compensation Subharmonic phase, Indicates the corrected The FFT result at each frequency point is: is the actual frequency point position and , This is a rounding operation.

6. The real-time dynamic harmonic detection method of the traction power supply system according to claim 5, characterized in that: The step S4 specifically includes: Establish the harmonic parameter iteration equation: In the formula, is the corrected harmonic complex parameter, is the harmonic complex parameter before correction, is the convergence factor, For the The complex parameters of the subharmonics and , For the The amplitude of the subharmonics, For the The phase of the subharmonics, For the The original signal of sampling points, To estimate the fundamental frequency The generated harmonic complex exponential terms; When the residual energy The iteration is terminated when .

7. The real-time dynamic harmonic detection method of the traction power supply system according to claim 6, characterized in that: The step S5 specifically includes: Step S5-1: Based on the fundamental frequency fluctuation Adjust the sampling interval: In the formula, is the dynamically adjusted sampling interval, is the adaptive coefficient, is the fundamental frequency fluctuation and ; Step S5-2: Use a filter with a variable cutoff frequency to perform anti-aliasing processing to prevent high-frequency harmonic aliasing.

8. The real-time dynamic harmonic detection method of the traction power supply system according to claim 7, characterized in that: The cutoff frequency of the filter is set to: In the formula, is the real-time cutoff frequency of the filter.

9. The real-time dynamic harmonic detection method of the traction power supply system according to claim 7, characterized in that: The step S6 specifically includes: Step S6-1: Construct a Vandermonde matrix based on the harmonic distribution characteristics : In the formula, is the actual harmonic frequency and , is the harmonic order, Indicates the time coordinate of the first sampling point, Indicates The time coordinates of the sampling points; Step S6-2: Calculate the compensated spectrum: In the formula, is the harmonic parameter vector after compensation, For the matrix The conjugate transpose of is the original FFT spectrum vector.

10. A real-time dynamic harmonic detection system for a traction power supply system, characterized in that: A real-time dynamic harmonic detection method for a traction power supply system applied to any one of claims 1 to 9, wherein the real-time dynamic harmonic detection system for the traction power supply system comprises: Data acquisition module, used to collect voltage signals of the power supply system in real time; Dynamic baseband tracking module, used to dynamically track baseband fluctuations through phase-locked loop technology; A dynamic window length adjustment module is used to dynamically adjust the data window length of FFT analysis according to the real-time fundamental frequency estimation value; Adaptive FFT harmonic analysis module, used to dynamically adjust the spectrum calculation kernel of FFT according to the fundamental frequency fluctuation, so as to automatically compensate for the offset of harmonic frequency points when the fundamental frequency decreases; and to perform linear compensation on the detected harmonic phase; A harmonic parameter recursive correction module is used to use the initially detected harmonic parameters as initial values, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error; Synchronous sampling module, used to dynamically adjust the sampling interval according to the fundamental frequency fluctuation, and use a filter with a variable cutoff frequency for anti-aliasing processing; The dynamic error matrix compensation module is used to construct a matrix model containing fundamental frequency fluctuation parameters and calculate the true harmonic parameters by the least square method.

Images