A real-time dynamic harmonic detection method and system for a traction power supply system

Abstract

The present invention provides a real-time dynamic harmonic detection method and system for a traction power supply system, which relates to the technical field of harmonic detection. The detection method includes the following steps: collecting voltage signals of the traction power supply system in real time, and dynamically tracking the fundamental frequency fluctuation through a phase-locked loop technology; dynamically adjusting the data window length of the FFT analysis; dynamically adjusting the spectrum calculation kernel of the FFT; and linearly compensating the detected harmonic phase; taking the preliminarily detected harmonic parameters as initial values, and iteratively updating the harmonic parameters until convergence by minimizing the signal reconstruction error; dynamically adjusting the sampling interval according to the fundamental frequency fluctuation, and performing anti-aliasing processing by using a filter with a variable cut-off frequency; constructing a matrix model containing fundamental frequency fluctuation parameters, and calculating the true harmonic parameters by using the least squares method. The method of the present invention can systematically solve the detection defects of the fixed-window FFT in the case of frequency fluctuation, and provides high-reliability real-time data support for the harmonic resonance suppression of electrified railways.

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 to electric trains. It is named so because corresponding electrification equipment needs to be installed along the line of such a railway to provide power support for the trains. Since electric locomotives have stronger transport capacity advantages than 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 have become increasingly complex, which has further led to the more prominent problem of induced harmonic resonance. 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 in the case of frequency fluctuations has become an urgent problem to be solved. Summary of the Invention

[0006] In order 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:

[0008] 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:

[0009] 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;

[0010] Step S2: Dynamically adjust the data window length of the FFT analysis according to the real-time fundamental frequency estimate value;

[0011] Step S3: Dynamically adjust the spectral calculation kernel of the FFT according to the fundamental frequency fluctuation amount to compensate for the offset of the harmonic frequency point when the fundamental frequency decreases; and linearly compensate the detected harmonic phase;

[0012] Step S4: Use the preliminarily detected harmonic parameters as the initial values, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error;

[0013] 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;

[0014] Step S6: Construct a matrix model containing fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least squares method.

[0015] Optionally, step S1 specifically includes:

[0016] Step S1-1: Real-time collect the voltage signal of the traction power supply system;

[0017] Step S1-2: Perform Hilbert transform on the collected voltage signal to extract the instantaneous phase information:

[0018]

[0019] Where, 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;

[0020] Step S1-3: Establish a second-order phase-locked loop model, and its dynamic equation is:

[0021]

[0022] Where, is the real-time estimated fundamental frequency angular frequency, is the initial fundamental frequency angular frequency, and are the proportional and integral coefficients of the phase-locked loop respectively, is the instantaneous phase deviation at time point and , is the current sampling moment, .

[0023] Optionally, step S2 specifically includes:

[0024] Step S2-1: Dynamically adjust the FFT window length according to the real-time fundamental frequency estimation value :

[0025]

[0026] Where, 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.

[0027] Optionally, step S2 further includes:

[0028] Step S2-2: Apply a Hanning window to the truncated signal to suppress spectral sidelobe leakage:

[0029]

[0030] In the formula, is the Hanning window function value, is the sampling point index value and .

[0031] Optionally, step S3 specifically includes:

[0032] Step S3-1: Construct a modified FFT kernel function:

[0033]

[0034] 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;

[0035] Step S3-2: Linearly compensate the phase of the th harmonic:

[0036]

[0037] 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.

[0038] Optionally, step S4 specifically includes:

[0039] Establish a harmonic parameter iteration equation:

[0040]

[0041] In the formula, is the corrected harmonic complex parameter, is the harmonic complex parameter before correction, is the convergence factor, is the th harmonic complex parameter and , is the th harmonic amplitude, is the th harmonic phase, is the th original signal at the sampling point, is the harmonic complex exponential term generated with the estimated fundamental frequency ;

[0042] When the residual energy , terminate the iteration.

[0043] Optionally, the step S5 specifically includes:

[0044] Step S5-1: Adjust the sampling interval according to the fundamental frequency fluctuation amount :

[0045]

[0046] In the formula, is the dynamically adjusted sampling interval, is the adaptive coefficient, is the fundamental frequency fluctuation amount and ;

[0047] Step S5-2: Perform anti-aliasing processing using a filter with a variable cut-off frequency to prevent high-frequency harmonic aliasing.

[0048] Optionally, the cut-off frequency of the filter is set to:

[0049]

[0050] In the formula, is the real-time cut-off frequency of the filter.

[0051] Optionally, the step S6 specifically includes:

[0052] Step S6-1: Construct a Vandermonde matrix according to the harmonic distribution characteristics:

[0053]

[0054] In the formula, is the actual harmonic frequency and , is the harmonic order, represents the time coordinate of the first sampling point, represents the time coordinate of the

[0055] Step S6-2: Calculate the compensated spectrum:

[0056]

[0057] In the formula, is the compensated harmonic parameter vector, is the conjugate transpose of the matrix , is the original FFT spectrum vector.

[0058] 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:

[0059] A data acquisition module for real-time collecting voltage signals of the traction power supply system;

[0060] A dynamic fundamental frequency tracking module for dynamically tracking fundamental frequency fluctuations through a phase-locked loop technology;

[0061] 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;

[0062] An adaptive FFT harmonic analysis module for dynamically adjusting the spectrum calculation kernel of FFT according to the fundamental frequency fluctuation amount, so as to automatically compensate the offset amount of harmonic frequency points when the fundamental frequency decreases; and linearly compensating the detected harmonic phase;

[0063] A harmonic parameter recursive correction module for using the preliminarily detected harmonic parameters as initial values and iteratively updating the harmonic parameters until convergence by minimizing the signal reconstruction error;

[0064] A synchronous sampling module for dynamically adjusting the sampling interval according to the fundamental frequency fluctuation and performing anti-aliasing processing by using a filter with a variable cut-off frequency;

[0065] A dynamic error matrix compensation module for constructing a matrix model containing fundamental frequency fluctuation parameters and calculating the true harmonic parameters by the least squares method.

[0066] Beneficial effects:

[0067] 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 spectral leakage caused by frequency offset, and significantly improving the accuracy of harmonic component detection.

[0068] Second, the present invention suppresses side lobe leakage by dynamically adjusting the FFT window length and calculating the kernel function to make the signal truncation close to an integer period; the frequency offset compensation mechanism can correct the harmonic frequency point offset, thus ensuring accurate measurement of amplitude and phase.

[0069] Third, the present invention combines dynamic sampling interval adjustment and variable cut-off filters to effectively avoid high-frequency harmonic aliasing during fundamental frequency fluctuation, thereby ensuring the integrity of signal sampling and the reliability of the analysis frequency band.

[0070] Fourth, the present invention gradually approximates the true harmonic parameters through an iterative process of minimizing the reconstruction error, effectively overcoming the limitations of traditional single-shot FFT analysis, and further improving the detection accuracy in complex harmonic scenarios.

[0071] 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 harmonic parameters (amplitude, phase, frequency) are closer to the true values.

[0072] 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 fast 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 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 during frequency fluctuation, providing high-reliability real-time data support for harmonic resonance suppression in electrified railways.

[0073] 2. Other beneficial effects or advantages of the present invention will be described in detail in the specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] 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 following drawings are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative efforts.

[0075] Wherein:

[0076] Figure 1 It is a schematic diagram of the step flow of a real-time dynamic harmonic detection method for a traction power supply system provided by an exemplary embodiment of the present invention. Specific Embodiment

[0077] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0078] 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. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0079] The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

[0080] As Figure 1 shown, this embodiment provides a real-time dynamic harmonic detection method for a traction power supply system, including the following steps:

[0081] 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;

[0082] Step S2: Dynamically adjust the data window length of the FFT analysis according to the real-time fundamental frequency estimation value;

[0083] Step S3: Dynamically adjust the spectrum 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 the detected harmonic phases;

[0084] Step S4: Use the preliminarily detected harmonic parameters as the initial values, and iteratively update the harmonic parameters until convergence by minimizing the signal reconstruction error;

[0085] 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;

[0086] Step S6: Construct a matrix model containing the fundamental frequency fluctuation parameters, and calculate the true harmonic parameters by the least squares method.

[0087] 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 spectral leakage caused by frequency offset, and thus significantly improving the accuracy of harmonic component detection.

[0088] Second, the present invention suppresses sidelobe leakage by dynamically adjusting the FFT window length and calculating the 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 amplitude and phase.

[0089] Third, the present invention combines dynamic sampling interval adjustment and variable cut-off filters 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.

[0090] Fourth, the present invention gradually approaches the true harmonic parameters through an iterative process of minimizing the reconstruction error, can effectively overcome the limitations of traditional single FFT analysis, and further improve the detection accuracy in complex harmonic scenarios.

[0091] 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.

[0092] Generally speaking, the method of the present invention forms a closed-loop harmonic detection process through multi-link cooperation (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 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.

[0093] In an embodiment of the present invention, step S1 may specifically include:

[0094] Step S1-1: Collect the voltage signal of the traction power supply system in real time;

[0095] Step S1-2: Perform Hilbert transform on the collected voltage signal to extract the instantaneous phase information:

[0096]

[0097] where, is the analytical signal, is the original signal, is the original signal is the signal after Hilbert transform (representing the quadrature component of the original signal), is the imaginary unit, used to construct the complex analytical signal, is the time variable;

[0098] Step S1-3: Establish a second-order phase-locked loop model, and its dynamic equation is:

[0099]

[0100] In the formula, is the fundamental angular frequency estimated in real time, is the initial fundamental angular frequency, and are the proportional and integral coefficients of the phase-locked loop (used to adjust the dynamic response speed and stability) respectively, 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, .

[0101] In this embodiment, first, the present invention converts the real signal into an analytical signal through Hilbert transform, so that the instantaneous phase information can be directly obtained, and the phase misjudgment under noise interference in the traditional zero-crossing detection method can be avoided, and the real-time performance and accuracy of phase tracking can be significantly improved.

[0102] 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 problem of tracking lag of the traditional first-order phase-locked loop in dynamic scenarios.

[0103] Third, due to the natural anti-high-frequency noise characteristic of the analytical signal construction of 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.

[0104] 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 ±5Hz (such as 45Hz to 55Hz), so that the frequency tracking range can be extended to meet the actual working conditions of the electrified railway traction network.

[0105] In this embodiment, it should be noted that, first, for the construction of the analytical signal, the Hilbert transform converts a real signal ( ) into an analytical signal ( ). In this way, the instantaneous phase ( ) of the analytical signal can be directly obtained through the calculation of the argument ( ), thus avoiding the delay of waiting for the signal to cross zero in the traditional zero-crossing detection method and realizing the real-time extraction of phase information. (The traditional zero-crossing detection method calculates the frequency depending on the signal zero-crossing 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)

[0106] 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 (e.g., implemented by a FIR filter), the phase information can be updated in real time at the sampling point level to meet the dynamic tracking requirements at the millisecond level.

[0107] 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 estimate 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)

[0108] Generally speaking, this technical solution can effectively solve the problem of tracking failure of traditional methods under noise interference and frequency fluctuations by extracting the instantaneous phase through the Hilbert transform and the dynamic tracking of the second-order phase-locked loop, and can provide a high-precision fundamental frequency estimate value for subsequent dynamic FFT analysis.

[0109] 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, and 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 sensitivity to low-frequency noise, and if it is too small, it will cause residual error. Therefore, in actual engineering, the and can be determined through 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.

[0110] In an embodiment of the present invention, step S2 may specifically include:

[0111] Step S2-1: According to the real-time fundamental frequency estimation value , dynamically adjust the FFT window length:

[0112]

[0113] Wherein, 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 0.01Hz).

[0114] In this embodiment, first, the adaptive suppression of spectral leakage in this embodiment is specifically achieved by dynamically adjusting the FFT window length, so that the intercepted signal segment is close to an integer multiple of the fundamental wave period, thereby significantly reducing the spectral energy leakage caused by asynchronous sampling, and further improving the detection accuracy of harmonic amplitude and phase.

[0115] 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.

[0116] Third, 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.

[0117] Fourth, 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 50Hz (nominal value), thereby avoiding the drastic jump of the window length caused by too small denominator.

[0118] 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 (50Hz), the greater the value of the denominator term, resulting in the reduction of the window length . Especially, when , the denominator degenerates into the preset constant , and at this time the window length is stabilized at , it is possible to avoid numerical instability caused by a zero denominator. For the window length it is inversely proportional to the deviation from the fundamental frequency. 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 conditions for FFT analysis.

[0119] In an embodiment of the present invention, step S2 may further include:

[0120] Step S2-2: Applying a Hanning window to the truncated signal to suppress spectral sidelobe leakage:

[0121]

[0122] In the formula, is the value of the Hanning window function, is the sampling point index value and .

[0123] In this embodiment, first, 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 changes the signal at both ends to zero, reduces the energy diffusion of the spectral sidelobes caused by time-domain truncation, makes the harmonic main lobe sharper, and avoids mutual interference between adjacent frequency points), improving the accuracy of harmonic detection.

[0124] Second, 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 according to the change of the dynamic window length, so as to ensure that the sidelobe suppression effect is consistent under different window lengths.

[0125] Third, compared with the rectangular window (without a 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 diffusion of noise energy in the spectrum in the high-noise environment of the traction network.

[0126] The principle of the Hanning window suppressing sidelobe leakage is described below.

[0127] First, the source of spectral leakage is: when the signal truncation length is not an integer multiple of the fundamental wave period, 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.

[0128] In general, the dynamic Hanning windowing processing method of this implementation combines window function design, dynamic window length adaptation and amplitude and phase compensation algorithm, which can significantly improve the accuracy and anti-interference ability of harmonic detection, and provide a reliable data basis for harmonic control of traction power supply systems.

[0129] In one embodiment of the present invention, step S3 specifically includes:

[0130] Step S3-1: Construct a modified FFT kernel function:

[0131]

[0132] Where, After the correction The FFT result of each frequency point, For the The signal value of the sampling point, is the frequency deviation compensation factor and , is the harmonic order,

[0133] Step S3-2: Subharmonic phase linear compensation:

[0134]

[0135] Where, After compensation Subharmonic phase, Indicates the corrected The FFT results at the frequency points are: is the actual frequency point position and , This is a rounding operation.

[0136] In this embodiment, first, this embodiment can realize 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 embodiment 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.

[0137] Second, this implementation can correct the phase nonlinearity error and ensure phase accuracy. Specifically, the fundamental frequency fluctuation will cause the harmonic phase to accumulate linear deviation 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).

[0138] Third, this implementation can adaptively track the fundamental frequency fluctuation and enhance the system robustness. Specifically, the fundamental frequency estimated in real time by the phase-locked loop is , this implementation can dynamically adjust and phase compensation to adapt to the continuous fluctuation of the fundamental frequency, avoid detection failure caused by frequency mutations in traditional methods, and improve the stability of the detection method under complex working conditions.

[0139] 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 FFT frequency point so that the corrected frequency point corresponds to the actual harmonic frequency , thus avoiding spectrum leakage. From a mathematical point of view, this is equivalent to digital frequency modulation of the signal, aligning the main lobe of the harmonics with the FFT frequency point, thereby improving the amplitude detection accuracy.

[0140] In addition, in this embodiment, the frequency deviation compensation factor , is to The offset from the fundamental frequency ( ) and dynamically adjust the harmonic frequency position.

[0141] 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 discrete FFT, this change is manifested as the linear accumulation of phase with sampling point n, and the compensation term By estimating The contribution of the harmonics is used to offset the linear phase error introduced by the frequency offset and window length adjustment. In this way, the phase measurement results can reflect the true initial phase of the harmonics rather than the observed value contaminated by frequency fluctuations.

[0142] An exemplary embodiment is described below.

[0143] 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, , adjust the FFT kernel function frequency points to such that the 245th frequency point (245 Hz) falls within the main lobe range. In this way, the linear phase deviation caused by a frequency shift of 4.9 frequency points can be eliminated, and the true phase can be restored.

[0144] In an embodiment of the present invention, step S4 may specifically include:

[0145] Establish a harmonic parameter iteration equation:

[0146]

[0147] 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, and generally it needs to satisfy 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 based on the estimated fundamental frequency (i.e., 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);

[0148] When the residual energy terminates the iteration.

[0149] In this embodiment, first, this embodiment can dynamically correct the initial estimation error and improve the accuracy of harmonic parameters. Specifically, traditional FFT may have errors in the initial harmonic parameters (amplitude, phase) due to spectral leakage when the fundamental frequency fluctuates. This embodiment dynamically corrects the initial estimated value through iterative optimization, using the reconstruction error as feedback, gradually approaching the true harmonic parameters, and significantly improving the detection accuracy, especially when the fundamental frequency fluctuates rapidly.

[0150] Second, this embodiment can track the time-varying characteristics of harmonics in real time and enhance the system adaptability. Specifically, the harmonic amplitude and phase of the traction power supply system may fluctuate dynamically due to changes in locomotive load. The iterative equation updates in real time , combined with the fundamental frequency provided by the phase-locked loop , so that the harmonic model is always synchronized with the current system state, adapts to the time-varying characteristics of harmonics, and avoids the detection failure caused by parameter lag in traditional methods.

[0151] Third, this embodiment can suppress noise interference and improve the anti-interference ability. Specifically, in the present invention, by minimizing the signal reconstruction error, the iterative process essentially has a low-pass filtering effect on noise and interference. Random noise is averaged out during multiple iterations, while the true harmonic components are retained due to their correlation, thereby improving the robustness of the detection results in a noisy environment.

[0152] Fourth, this embodiment can be compatible with high-order harmonic analysis and avoid missing key components. Specifically, in this embodiment, the upper limit of the summation in the equation is the 15th harmonic ( ), covering the typical high-order harmonic range of electrified railways (for example, 3rd, 5th, 7th, etc.). By optimizing multiple harmonic parameters simultaneously, it avoids the model incompleteness caused by only focusing on a single harmonic, ensuring the comprehensiveness and reliability of the detection results.

[0153] In this embodiment, it should be noted that, first, for the harmonic parameter iterative equation, its reconstruction error part is: , its harmonic rotation factor is: , and its mathematical derivation process is:

[0154] This equation is derived from the least mean square error criterion, and the goal is to minimize the square of the instantaneous reconstruction error:

[0155]

[0156] Among them, is a complex parameter;

[0157] Therefore, its expanded error expression is:

[0158]

[0159] In this formula, denotes the complex conjugate;

[0160] Then, for the complex parameter take the derivative:

[0161] In the complex domain, gradient descent needs to be calculated for the conjugate derivative (Wirtinger derivative):

[0162]

[0163] This is because the effective gradient direction for complex optimization is with respect to the derivative;

[0164] In this way, the parameter update direction should be the negative gradient direction:

[0165]

[0166] In the formula, denotes being proportional to, indicating that the update amount is proportional to the gradient direction.

[0167] The conjugate of the negative exponential function satisfies:

[0168]

[0169] Therefore, the conjugate operation of the complex exponential term is actually implied in the parameter update formula. 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.

[0170] 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.

[0171] That is to say, due to the complex conjugate operation, the actual update equation is i.e., the actual harmonic parameter iteration equation is: .

[0172] 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 reconstruction signal is insufficient (the error is positive), then increase Magnitude; if the phase deviation causes error accumulation, then adjust Argument (phase).

[0173] In this embodiment, in the equation from the PLL real-time estimation of the foregoing technical solution to ensure that the fundamental frequency of the harmonic model is strictly consistent with the actual system frequency, avoiding the misalignment of harmonic frequency points caused by the fundamental frequency deviation. At the same time, each harmonic component The frequency of is , and it is adjusted in real time with the fluctuation of the fundamental frequency, so that the harmonic model always matches the current system state.

[0174] In this embodiment, it should also be noted that for the selection of the convergence factor , first, a smaller Its corresponding update step is small, the convergence is slow but the stability is high, which is suitable for high-noise environments. Second, a larger Its corresponding update step is large, the convergence is fast but it may oscillate, which 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.

[0175] In an embodiment of the present invention, step S5 may specifically include:

[0176] Step S5-1: Adjust the sampling interval according to the fundamental frequency fluctuation :

[0177]

[0178] In the formula, is the dynamically adjusted sampling interval, is the adaptive coefficient, is the fundamental frequency fluctuation and ;

[0179] Step S5-2: Perform anti-aliasing processing using a filter with a variable cut-off frequency to prevent high-frequency harmonic aliasing.

[0180] 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 points during the fundamental frequency fluctuation, 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 harmonic frequency alignment accuracy, and reducing spectral leakage.

[0181] Second, this embodiment can adaptively allocate system resources and balance real-time performance and accuracy. Specifically, by parameter adjust the sensitivity of the sampling interval to the fundamental frequency fluctuation. For example, when the fundamental frequency fluctuates violently (e.g., when the locomotive accelerates or brakes), increase to quickly adjust the sampling rate and prioritize ensuring real-time performance. When the fundamental frequency is stable, can be reduced to maintain a high sampling rate and improve the spectral resolution.

[0182] In this embodiment, it should be noted that for the dynamic sampling interval adjustment (i.e., adjusting the sampling interval according to the fundamental frequency fluctuation ), when the fundamental frequency decreases, the fixed sampling rate in the existing related technologies may be too high, resulting in resource waste, and when the fundamental frequency increases, it may be insufficient. However, in this embodiment, by adjusting , the effective sampling rate changes with . For example, when , , at this time, will increase and the sampling rate will be reduced to match the low-frequency demand; when , , at this time will decrease and the sampling rate will be increased to avoid high-frequency harmonic aliasing.

[0183] In an embodiment of the present invention, the cut-off frequency of the filter is set to:

[0184]

[0185] wherein, is the real-time cut-off frequency of the filter.

[0186] In this embodiment, first, it can suppress high-frequency aliasing and 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 from aliasing into the effective frequency band and ensure the authenticity of the FFT analysis result.

[0187] Second, it can be compatible with wide-frequency harmonic analysis and avoid over-constraint of the fixed filter. Specifically, the 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.

[0188] Generally speaking, in the above embodiments, by dynamically adjusting the sampling rate and the anti-aliasing filter, the problems of oversampling or undersampling in the traditional fixed-parameter system when the fundamental frequency fluctuates 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.

[0189] In an embodiment of the present invention, step S6 may specifically include:

[0190] Step S6-1: Construct a Vandermonde matrix according to the harmonic distribution characteristics :

[0191]

[0192] In the formula, is the actual harmonic frequency and , is the harmonic order (generated according to the to be estimated by the phase-locked loop in real time to ensure that the model is synchronized with the current system frequency), represents the time coordinate of the first sampling point, represents the th sampling point's time coordinate;

[0193] Step S6-2: Calculate the compensated spectrum:

[0194]

[0195] In the formula, is the compensated harmonic parameter vector, is the conjugate transpose of the matrix , is the original FFT spectrum vector.

[0196] In this embodiment, first, by dynamically constructing a Vandermonde matrix containing the actual harmonic frequencies, the present invention can accurately represent 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 ( ), each row corresponds to different sampling time points , and its elements are , that is, the harmonic basis function in the form of a 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.

[0197] Second, the present invention compensates the FFT spectrum using the least squares method, effectively suppressing the spectrum leakage phenomenon caused by frequency offset, and making the detection results of harmonic amplitudes and phases closer to the true values. Specifically, assuming the observed signal spectrum can be expressed as , where is noise and error, and the corresponding minimized reconstruction error is: By solving the normal equation

[0198] the optimal harmonic parameters are obtained. The least squares solution projects the observed data onto the harmonic subspace, eliminating the misalignment of spectral components caused by frequency deviation, thereby correcting the amplitude and phase.

[0199] 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 fluctuations of the operating frequency of the traction power supply system and ensure the robustness of the detection method under complex working conditions.

[0200] 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.

[0201] In addition, it can be understood that this embodiment can be combined with the dynamic cut-off frequency filter in the above embodiment to pre-filter high-frequency interference and ensure that only effective harmonic components are included in the matrix model.

[0202] For example, in an exemplary embodiment, in a traction power supply system, the load change of electric locomotives often causes fluctuations in the fundamental frequency (for example, shifting 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 impossible to accurately detect the harmonics after the offset (for example, the 5th harmonic of the original 50 Hz, 250 Hz, may become 247.5 Hz). This embodiment accurately aligns the actual harmonic frequencies 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 spectrum leakage), false harmonic judgment (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).

[0203] According to a 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 of the first aspect of the present invention. The real-time dynamic harmonic detection system of the 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.

[0204] Among them, the data acquisition module is used to collect the voltage signal 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 square method.

[0205] 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 side lobe 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 in the present invention, the true harmonic parameters are gradually approximated, which can effectively overcome the limitations of the traditional single FFT analysis, and further improve the detection accuracy in complex harmonic scenarios. Fifth, based on the dynamic compensation of the matrix model and the least square method, it 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.

[0206] 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, enabling the system to maintain detection accuracy under time-varying working conditions. Compared with the traditional FFT scheme, it can effectively reduce the calculation error of harmonic impedance and provide a reliable basis for the active filtering control of the traction power supply system.

[0207] The above are only specific embodiments 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 It includes 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 spectrum calculation kernel of the FFT according to the fundamental frequency fluctuation amount, so as to compensate the offset amount 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 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; Among them, the said Step S2 includes: 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, 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; Step S2-2: Apply a Hanning window to the truncated signal to suppress the leakage of the spectrum side lobe: In the formula, is the value of the Hanning window function, is the sampling point index value and .

2. The real-time dynamic harmonic detection method for a traction power supply system according to claim 1, characterized in that The said 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 the 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: wherein, is the fundamental angular frequency estimated in real time, is the initial fundamental angular frequency, and are the proportional and integral coefficients of the phase-locked loop respectively, is the instantaneous phase deviation at time point and , is the current sampling moment, .

3. The real-time dynamic harmonic detection method for the traction power supply system according to claim 1, wherein, The said Step S3 specifically includes: Step S3-1: Construct a modified FFT kernel function: Wherein, is the FFT result of the th corrected frequency point, 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 phase of the th harmonic: In the formula, is the th harmonic phase after compensation, represents the FFT result at the th frequency point after correction, is the actual frequency point position and , is the rounding operation.

4. The real-time dynamic harmonic detection method for the traction power supply system according to claim 3, wherein The said Step S4 specifically includes: Establish a harmonic parameter iteration equation: In the formula, is the corrected harmonic complex parameter, is the harmonic complex parameter before correction, is the convergence factor, is the complex parameter of the -th harmonic and , 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 ; Terminate the iteration when the residual energy is reached.

5. The real-time dynamic harmonic detection method for a traction power supply system according to claim 4, wherein The said Step S5 specifically includes: Step S5-1: Adjust the sampling interval according to the fundamental frequency fluctuation amount : 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.

6. The real-time dynamic harmonic detection method for the traction power supply system according to claim 5, characterized in that The cut-off frequency of the said filter is set as: In the formula, is the real-time cut-off frequency of the filter.

7. The real-time dynamic harmonic detection method for the traction power supply system according to claim 5, characterized in that The said Step S6 specifically includes: 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 time coordinate of the sampling point; 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.

8. A real-time dynamic harmonic detection system for a traction power supply system, characterized in that, A real-time dynamic harmonic detection method applied to the traction power supply system described in any one of claims 1-7, the real-time dynamic harmonic detection system of the traction power supply system includes: A data acquisition module for collecting the voltage signal of the traction power supply system in real time; A dynamic fundamental frequency tracking module for dynamically tracking the fundamental frequency fluctuation through the phase-locked loop technology; A dynamic window length adjustment module for dynamically adjusting the data window length of the FFT analysis according to the real-time fundamental frequency estimation value; An adaptive FFT harmonic analysis module for dynamically adjusting the spectrum calculation kernel of the FFT according to the fundamental frequency fluctuation amount, so as to automatically compensate the offset amount of the harmonic frequency point when the fundamental frequency decreases; and linearly compensate the detected harmonic phase; A harmonic parameter recursive correction module for taking the preliminarily detected harmonic parameters as the initial values, and iteratively updating the harmonic parameters until convergence by minimizing the signal reconstruction error; A synchronous sampling module for dynamically adjusting the sampling interval according to the fundamental frequency fluctuation, and performing anti-aliasing processing using a filter with a variable cut-off frequency; A dynamic error matrix compensation module for constructing a matrix model containing the fundamental frequency fluctuation parameters, and calculating the true harmonic parameters by the least squares method.

Images