A method and apparatus for detecting high-frequency harmonics in a flexible DC transmission system

Abstract

This invention provides a method and apparatus for high-frequency harmonic detection in flexible DC transmission systems, relating to the field of power system power quality monitoring and signal processing technology. The method includes: probing the flexible DC transmission system to obtain probe data; performing frequency domain analysis on the probe data and dynamically determining frequency domain boundary parameters based on the analysis results; performing adaptive dual-channel parallel sampling and frequency domain fusion of the two channels' sampled data on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal; dividing the full-band into at least three sub-bands according to the physical characteristics of different frequency components; performing high-frequency harmonic analysis on the full-band digital signal using a spectrum aggregation strategy for each sub-band; the spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band. This invention solves the problems of spectral leakage and low frequency resolution and accuracy in the high-frequency harmonic detection process of flexible DC systems.

Description

Technical Field

[0001] This invention relates to the field of power system power quality monitoring and signal processing technology, specifically to a high-frequency harmonic detection method and device for flexible DC transmission systems. Background Technology

[0002] With the widespread application of flexible DC transmission systems, high-frequency harmonic disturbances caused by the switching operations of power electronic converters are becoming increasingly prominent. Their frequency range typically covers from 2 kHz to hundreds of kHz or even MHz, far exceeding the scope of traditional power quality analysis. These high-frequency harmonics are characterized by wide frequency spectrum, strong time-varying behavior, and asynchronous operation with the power frequency. They can easily lead to localized overheating of equipment, accelerated insulation aging, and may interfere with system control and communication, posing a potential threat to the safe and stable operation of the power grid.

[0003] Traditional high-frequency harmonic analysis techniques for power quality monitoring revolve around the Discrete Fourier Transform (DFT) and are primarily used for analyzing periodic steady-state signals. To meet this requirement and ensure the measurement accuracy of low-frequency harmonics, current standards (such as the International Electrotechnical Commission standard IEC 61000-4-30) mostly employ synchronous sampling with the fundamental frequency of the power grid and a fixed-length analysis window. When this high-frequency harmonic analysis method is directly applied to the detection of high-frequency harmonics in flexible DC systems, the use of synchronous sampling with a fixed window width leads to severe spectral leakage and insufficient frequency resolution because high-frequency harmonics do not have a direct integer multiple relationship with the fundamental frequency. Furthermore, it fails to accurately capture the rapid time-varying characteristics of the signal, resulting in low accuracy in high-frequency harmonic detection. Summary of the Invention

[0004] To overcome the problems of spectral leakage and low frequency resolution and accuracy in the high-frequency harmonic detection process of flexible DC systems, the present invention provides a high-frequency harmonic detection method and apparatus for flexible DC transmission systems.

[0005] On one hand, the present invention provides a high-frequency harmonic detection method for a flexible DC transmission system, comprising: The flexible DC transmission system is probed and sampled to obtain probe data; frequency domain analysis is performed on the probe data for power frequency harmonics and switching frequency harmonics, and frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results; adaptive dual-channel parallel sampling and frequency domain fusion of the sampled data from the two channels are performed on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal; Based on the physical characteristics of different frequency components, the entire frequency band is divided into at least three sub-bands; a spectrum aggregation strategy for each sub-band is used to perform high-frequency harmonic analysis on the digital signal of the entire frequency band. The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

[0006] Optionally, probing sampling is performed on the flexible DC transmission system to obtain probe data, including: Asynchronous sampling of electrical signals is performed on target monitoring points within the flexible DC transmission system to obtain detection data; The detection data is subjected to frequency domain analysis, and frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results, including: Perform a fast Fourier transform on the detection data to obtain the corresponding detection amplitude spectrum; The frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum are identified, and then the frequency domain boundary parameters are dynamically determined.

[0007] Optionally, identifying the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum, and then dynamically determining the frequency domain boundary parameters, includes: Construct a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring points; For each candidate frequency in the candidate frequency set, construct the spectrum template corresponding to that candidate frequency; Based on the amplitude spectrum data, the detected amplitude spectrum is aggregated at each octave point to obtain the aggregated amplitude at each octave point; For each candidate frequency, the matching score of the candidate frequency is obtained by weighted summing of the spectral template corresponding to the candidate frequency and the corresponding aggregate amplitude. The matching score is penalized and corrected based on the number of octaves of the candidate frequency; the frequency domain boundary parameter is selected from the candidate frequency set based on the corrected matching score. The spectral template takes a non-zero value at integer multiples of the candidate frequency, and a zero value at all other frequency points.

[0008] Optionally, the matching score of the candidate frequencies is as follows:

[0009]

[0010] in, Candidate frequency Match score, For the first Weighting coefficients for subharmonics Candidate frequency The maximum harmonic order, For aggregated amplitude, For harmonic order index, The attenuation compensation index, For a set of frequency indexes within a preset aggregation range, Let be the amplitude of the j-th spectral line of the detected amplitude spectrum.

[0011] Optionally, the dynamic determination of frequency domain boundary parameters further includes: The frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters of the previous period to obtain the updated reference parameters. When constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated with the updated reference parameters as the center.

[0012] Optionally, the step of performing adaptive dual-channel parallel sampling and frequency domain fusion of the two channels' sampled data on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal includes: A synchronous analog-to-digital converter is used to synchronously sample the electrical signals of the flexible DC transmission system. The synchronously sampled data is then input into a low-pass filter to obtain the sampled low-frequency components. A asynchronous analog-to-digital converter is used to asynchronously sample the electrical signals of the flexible DC transmission system. The asynchronous sampled data is then input into a high-pass filter to obtain the sampled high-frequency components. The full-band digital signal is reconstructed by time-domain superposition of the sampled low-frequency component and the sampled high-frequency component. The synchronous analog-to-digital converter (ADC) and the asynchronous ADC operate in parallel. The sampling frequency of the synchronous ADC tracks the fundamental frequency of the power grid. The sampling frequency of the asynchronous ADC is determined based on the frequency domain boundary parameter. The cutoff frequencies of the low-pass filter and the high-pass filter are both configured to use the frequency domain boundary parameter.

[0013] Optionally, dividing the full frequency band into at least three sub-bands includes: The entire frequency band is divided into the first sub-band, the second sub-band, and the third sub-band; The first sub-band is a frequency band from 2kHz to 9kHz, the second sub-band is a frequency band from 9kHz to 150kHz, and the third sub-band is a frequency band above 150kHz.

[0014] Optionally, the high-frequency harmonic analysis using a spectrum aggregation strategy for each sub-band includes: A first spectrum aggregation strategy is used to perform harmonic analysis on the first sub-band. The first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. A second spectrum aggregation strategy is adopted to perform harmonic analysis on the second and third sub-bands. The second spectrum aggregation strategy is used to balance transient feature capture and data compression efficiency.

[0015] Optionally, a first spectrum aggregation strategy is used to perform harmonic analysis on the first sub-frequency band, including: The full-band digital signal is subjected to Fourier transform using a rectangular window of the first cycle to obtain the first amplitude spectrum; The first sub-band is divided into multiple consecutive first bandwidths according to the first bandwidth interval. The energy of the spectral lines in each first bandwidth in the first amplitude spectrum is aggregated to obtain the aggregated amplitude corresponding to each first bandwidth. The amplitude of each harmonic in the first sub-band is determined based on the center frequency and aggregate amplitude corresponding to each first bandwidth.

[0016] Optionally, a second spectrum aggregation strategy is used to perform harmonic analysis on the second and third sub-bands, including: Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands.

[0017] Optionally, based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands, including: The full-band digital signal is high-pass filtered to extract the high-frequency components of the signal; Perform Hilbert transform on the high-frequency components of the signal to extract the envelope sequence; The envelope sequence is divided into time periods, and the volatility index for each time period is calculated; the time-varying index of the full-band digital signal is determined based on the volatility index for each time period. Harmonic analysis is performed by dynamically selecting either the first aggregation scheme or the second aggregation scheme based on the time-varying index.

[0018] Optionally, if the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis, and the first aggregation scheme includes: The full-band digital signal is subjected to a short-time window Fourier transform using a Hanning window to obtain a second amplitude spectrum, and the amplitude results of integer multiples of the first frequency in the second amplitude spectrum are extracted. The statistical characteristic values ​​of the amplitude results extracted within the first time period are calculated as the harmonic detection results for the second and third sub-bands.

[0019] Optionally, if the time-varying index is less than a preset threshold, the second aggregation scheme is selected for harmonic analysis, and the second aggregation scheme includes: The full-band digital signal is subjected to a long-time window Fourier transform using a second-cycle rectangular window to obtain the third amplitude spectrum; The second sub-band is divided into multiple consecutive second bandwidths according to the second bandwidth interval. The spectral lines in each second bandwidth in the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each second bandwidth. The amplitude of each harmonic in the second sub-band is determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The third sub-band is divided into multiple consecutive third bandwidths according to the third bandwidth interval. The spectral lines in each third bandwidth of the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each third bandwidth. The amplitude of each harmonic in the third sub-band is determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth.

[0020] Optionally, the process of determining the time-varying index further includes: The quantile of the volatility index within the preset sliding window is used as the reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying volatility index.

[0021] Optionally, it also includes: Based on the spectrum aggregation results of the first sub-band, the high-frequency harmonic voltage content rate and the total high-frequency harmonic distortion rate of the voltage are calculated. Based on the spectrum aggregation results of the second sub-band, the over-frequency harmonic voltage content and the voltage over-frequency harmonic total distortion rate are calculated. Based on the spectrum aggregation results of the third sub-band, the voltage content of ultra-high frequency harmonics and the total voltage ultra-high frequency harmonic distortion rate are calculated. The high-frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the first sub-frequency band; the super harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the second sub-frequency band; and the ultra-high frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the third sub-frequency band. The total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the first sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the second sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of ultra-high frequency is used to characterize the ratio of the root mean square value of each harmonic voltage in the third sub-frequency band to the effective value of the fundamental voltage.

[0022] On the other hand, the present invention also provides a high-frequency harmonic detection device for a flexible DC transmission system, comprising: The detection module is used to perform probing sampling on the flexible DC transmission system to obtain detection data; to perform frequency domain analysis on the detection data for power frequency harmonics and switching frequency harmonics, and to dynamically determine the frequency domain boundary parameters based on the frequency domain analysis results; An adaptive sampling module is used to perform adaptive dual-channel parallel sampling and frequency domain fusion of the two channel sampling data on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal. The high-frequency harmonic analysis module is used to divide the entire frequency band into at least three sub-bands based on the physical characteristics of different frequency components; and to perform high-frequency harmonic analysis on the digital signal of the entire frequency band using a spectrum aggregation strategy for each sub-band. The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

[0023] On the other hand, the present invention also provides an electronic device, comprising: at least one processor and a memory; the memory and the processor are connected via a bus; The memory is used to store one or more programs; When the one or more programs are executed by the at least one processor, the method described in any of the foregoing is implemented.

[0024] On the other hand, the present invention also provides a readable storage medium having an executable program stored thereon, wherein when the executable program is executed, it implements the method described in any one of the above.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a high-frequency harmonic detection method and apparatus for a flexible DC transmission system. First, the flexible DC transmission system is probed and sampled, and the probed data is analyzed in the frequency domain for power frequency harmonics and switching frequency harmonics. Based on the frequency domain analysis results, the frequency domain boundary parameter is dynamically determined. Based on the frequency domain boundary parameter, adaptive dual-channel parallel sampling and frequency domain fusion are performed to obtain a full-band digital signal. Overcoming the problem of missing spectral prior information caused by the fixed synchronous sampling window width in traditional methods, this method addresses the complex characteristics of high-frequency harmonics in flexible DC transmission systems, such as wide spectral width, strong time-varying nature, and asynchronous operation with power frequency. Dynamic detection can perceive the actual frequency domain energy distribution boundary of the signal in real time, and adaptive dual-channel parallel sampling is performed based on the perception results. This avoids spectral aliasing and resolution mismatch caused by fixed parameters from the source, and simultaneously meets the contradictory requirements of time resolution and frequency resolution in both low-frequency and high-frequency bands in a wide bandwidth (kHz to MHz level). It also balances the deficiencies of steady-state low-frequency harmonic accuracy and non-stationary high-frequency harmonic capture capability, significantly improving the fidelity of the full-band signal and laying the foundation for high-precision analysis of high-frequency harmonics.

[0026] This invention divides the entire frequency band into at least three sub-bands and employs a sub-band spectrum aggregation strategy based on the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics to perform high-frequency harmonic analysis on the entire frequency band digital signal. By using targeted aggregation strategies for harmonic analysis based on the spectral characteristics of different sub-bands, differentiated matching analysis of the physical characteristics of high-frequency harmonic signals is achieved, significantly improving the accuracy and robustness of detection. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a high-frequency harmonic detection method for a flexible DC transmission system according to the present invention. Figure 2 This is a schematic diagram illustrating the signal acquisition principle of a flexible DC transmission system, as an example of the present invention. Figure 3 This is an example of the present invention, showing a primary voltage waveform obtained by adaptive sampling of a flexible DC transmission system; Figure 4 An example of the present invention is a current time-domain waveform obtained by performing adaptive sampling on a flexible DC transmission system; Figure 5 The curve showing the variation of total harmonic distortion of voltage as a function of operating power at a monitored converter station in the range of 2kHz to 9kHz is an example of the present invention. Figure 6 The total harmonic distortion rate of the voltage as a function of power at a monitored converter station in the range of 9kHz to 150kHz is an example of the present invention. Figure 7 The curve showing the variation of total harmonic distortion of voltage with power at a monitored converter station in the frequency band above 150kHz, as an example of the present invention. Figure 8 This is a structural block diagram of an electronic device according to the present invention. Detailed Implementation

[0028] Current standards generally require synchronous sampling with the grid fundamental frequency and fixed-length analysis windows. While this approach is mature and effective in assessing low-frequency harmonics in traditional nonlinear loads, it struggles to achieve effective quantitative characterization and accurate monitoring when directly applying traditional harmonic analysis methods to high-frequency harmonic detection in flexible DC systems. For example, the International Electrotechnical Commission (IEC) standard IEC 61000-4-30, in its Annex C, defines a recommended measurement method for conducted emissions in the 2-150 kHz frequency band. This method involves performing Discrete Fourier Transform (DFT) analysis on 32 discrete data windows of 0.5 ms each, non-continuously within a fixed 200 ms measurement and analysis interval to obtain the spectral information for that frequency band, with a frequency resolution of 2 kHz. This design aims to achieve periodic monitoring of high-frequency signals with low sampling and computational load. Although this approach is computationally efficient, this intermittent sampling mode may lead to the omission of some rapidly changing transient high-frequency emission characteristics when dealing with high-frequency harmonics. This discontinuous sampling method can only measure the amplitude of harmonics at a specific frequency and cannot fully reflect the time-varying characteristics of high-frequency harmonics.

[0029] For example, the conducted emissions measurement method based on the International Special Committee on Radio Interference (CISPR) standard 16:2010 employs a digital quasi-peak detection process. This method typically involves two stages: first, the signal is processed and root mean square (RMS) spectra for each frequency band are generated according to standards such as IEC 61000-4-7; second, these RMS spectrum data are input into a CISPR 16-compliant digital quasi-peak detector for weighted and peak-hold processing, ultimately outputting quasi-peak values ​​for electromagnetic compatibility (EMC) assessment. A typical implementation uses a 20-millisecond Lanczos window for DFT calculations and obtains continuous time series through a 90% window overlap, achieving a frequency resolution of approximately 50 Hz. However, when dealing with high-frequency harmonic analysis, the 90% window overlap requires a large amount of data and computational frequency, making it computationally intensive and difficult to apply directly to power system sites requiring long-term, real-time online monitoring; furthermore, the limited time-domain resolution fails to reflect the time-varying characteristics of high-frequency harmonics within their periods.

[0030] Currently, traditional harmonic detection methods are mainly based on Fourier transform, employing fixed window widths and synchronous sampling, suitable for steady-state harmonic analysis in the low-frequency band. However, in the high-frequency band of flexible DC systems, disturbances mainly originate from the switching actions of power electronic converters, and their frequency components have no direct multiple relationship with the power frequency. If traditional synchronous sampling methods are used, the non-stationary characteristics of the signal and its asynchrony with the power frequency will lead to problems such as spectral leakage, insufficient frequency resolution, and inability to accurately capture time-varying characteristics.

[0031] To address the aforementioned problems, this invention provides a high-frequency harmonic detection method suitable for flexible DC transmission systems. The method aims to achieve high-precision measurement, adaptive feature extraction, and hierarchical quantization evaluation of wide-band harmonics above 2 kHz, thereby overcoming the shortcomings of existing methods in terms of frequency coverage, measurement adaptability, computational efficiency, and engineering practicality.

[0032] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0033] Example 1 This invention provides a high-frequency harmonic detection method for a flexible DC transmission system, the schematic diagram of which is shown below. Figure 1 As shown, the method includes: Step S110: Perform probing sampling on the flexible DC transmission system to obtain probe data; perform frequency domain analysis on the probe data for power frequency harmonics and switching frequency harmonics, and dynamically determine the frequency domain boundary parameters based on the frequency domain analysis results; Step S120: Based on the frequency domain boundary parameters, the flexible DC transmission system is subjected to adaptive dual-channel parallel sampling and frequency domain fusion of the sampling data from the two channels to obtain a full-band digital signal; Step S130: Based on the physical characteristics of different frequency components, the entire frequency band is divided into at least three sub-bands; a spectrum aggregation strategy for each sub-band is used to perform high-frequency harmonic analysis on the digital signal of the entire frequency band. The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

[0034] In this example implementation, probing data is first obtained by probing the flexible DC transmission system. Frequency domain analysis is then performed on this data to identify power frequency harmonics and switching frequency harmonics, dynamically determining frequency domain boundary parameters. Power frequency harmonics refer to harmonic components that are integer multiples of the grid fundamental frequency. Switching frequency harmonics originate from the high-frequency switching operations of the power electronic converters in the flexible DC transmission system, and their characteristic frequencies are related to the switching frequency, its sidebands, and harmonics. Based on this analysis, this method proactively acquires the actual frequency domain distribution of power frequency harmonics and switching frequency harmonics under the current operating conditions through probing sampling. For example, it identifies the energy concentration frequency of the power frequency harmonics and the main lobe center frequency of the switching frequency harmonics, thereby dynamically determining one or more frequency domain boundary parameters. This process allows subsequent sampling to adjust parameters based on the real-time detected frequency domain distribution characteristics, avoiding mismatch problems caused by preset fixed parameters. Next, adaptive dual-channel parallel sampling is performed on the flexible DC transmission system based on these frequency domain boundary parameters, and the sampled data from the two channels are fused in the frequency domain to obtain a full-band digital signal covering a wide frequency range. The essence of dual-channel parallel sampling is to set different sampling rates and window lengths for low-frequency bands (such as power frequency and low-order harmonics) and high-frequency bands (such as high-frequency harmonics near switching frequency and its harmonics). For example, the low-frequency channel uses synchronous sampling to ensure accurate tracking of the fundamental frequency, while the high-frequency channel uses a higher sampling rate determined based on frequency domain boundary parameters to capture rapidly changing transient components. The data from the two channels are spliced ​​and fused in the frequency domain, for example, through complementary filtering or wavelet packet reconstruction, to eliminate redundancy in overlapping frequency bands and fill in blank frequency bands, ultimately obtaining a continuous, high-fidelity full-band digital signal sequence ranging from a few hertz to hundreds of kilohertz or even megahertz. Then, based on the physical characteristics of different frequency components, the full-band is divided into at least three sub-bands. The signal generation mechanism, propagation characteristics, and impact on equipment are significantly different in each sub-band. For each sub-band, a spectrum aggregation strategy determined based on the signal characteristics of that sub-band is used to perform high-frequency harmonic analysis on the aforementioned full-band digital signal. The signal characteristics include continuous spectral cluster energy concentration features (e.g., the presence of dense harmonic spectral lines with highly concentrated energy within a narrow band) and / or time-varying non-stationary features (e.g., rapid fluctuations in harmonic amplitude due to converter operating mode switching). For sub-bands with continuous spectral cluster energy concentration features, the spectrum aggregation strategy can employ energy equivalent aggregation to combine multiple spectral lines within the bandwidth into a single representative amplitude, reducing the amount of data while preserving the overall energy information of the band. For sub-bands with time-varying non-stationary features, time-frequency analysis methods such as short-time Fourier transform or wavelet transform can be used to capture the transient changes and transient processes of harmonics.By employing this differentiated analysis strategy, this method can optimize the processing of harmonics in different frequency bands based on their physical nature. This avoids the shortcomings of traditional single Fourier transforms, which treat all frequency bands equally, resulting in severe low-frequency leakage, insufficient resolution in high-frequency bands, and an inability to track time-varying characteristics. Ultimately, the high-frequency harmonic analysis results output by this method not only include the amplitude and frequency information of each sub-band but also reflect the time-domain evolution of harmonic energy, providing accurate and comprehensive data support for harmonic mitigation, equipment protection, and control optimization in flexible DC transmission systems.

[0035] In some implementations, probing sampling is performed on the flexible DC transmission system to obtain probe data, including: Asynchronous sampling of electrical signals is performed on target monitoring points within the flexible DC transmission system to obtain detection data; The detection data is subjected to frequency domain analysis, and frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results, including: The detection data is subjected to a fast Fourier transform to obtain the corresponding detection amplitude spectrum; the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detection amplitude spectrum are identified, and then the frequency domain boundary parameters are dynamically determined.

[0036] In this example implementation, asynchronous sampling of electrical signals is performed on target monitoring points within the flexible DC transmission system to obtain detection data. Asynchronous sampling means that the sampling frequency does not require strict synchronization with the fundamental frequency of the power grid, nor does it require the sampling window length to be an integer multiple of the fundamental period. Its purpose is to quickly acquire a time-domain waveform with lower implementation complexity for preliminary analysis of frequency domain characteristics. Since asynchronous sampling does not introduce complex phase-locked loops or synchronization circuits, it can significantly reduce the overhead and response time of the detection phase. Then, a fast Fourier transform is performed on the detection data to obtain the corresponding detection amplitude spectrum. This example focuses on the approximate distribution of power frequency harmonics and switching frequency harmonics in the frequency domain, such as the frequency points where energy peaks occur and the interval patterns between these peaks. Next, the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detection amplitude spectrum are identified. Power frequency harmonics appear as a series of spectral line clusters located at integer multiples of the fundamental frequency in the amplitude spectrum. Since the switching frequency may vary within a certain range according to control commands during actual operation, the positions of its harmonic clusters will also drift accordingly. By analyzing the frequency points with significant energy spikes in the amplitude spectrum and their spacing, the current fundamental frequency and switching frequency can be estimated, and the frequency domain boundary parameters can be dynamically determined. For example, half the switching frequency or a transition frequency between the switching frequency and the highest analysis frequency can be used as the boundary parameter to distinguish the cutoff frequencies of the low-frequency and high-frequency channels in subsequent adaptive dual-channel sampling. This implementation requires only one Fast Fourier Transform to extract key frequency domain features from asynchronous sampling data. It has low computational complexity, high speed, and does not require prior knowledge of system parameters, relying entirely on real-time measurement data for adaptive adjustment. This ensures that subsequent sampling strategies closely follow the actual operating state of the system, avoiding full-band signal reconstruction distortion caused by incorrect parameter settings.

[0037] In some implementations, identifying the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum, and then dynamically determining the frequency domain boundary parameters, includes: Construct a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring points; For each candidate frequency in the candidate frequency set, construct the spectrum template corresponding to that candidate frequency; Based on the amplitude spectrum data, the detected amplitude spectrum is aggregated at each octave point to obtain the aggregated amplitude at each octave point; For each candidate frequency, the matching score of the candidate frequency is obtained by weighted summing of the spectral template corresponding to the candidate frequency and the corresponding aggregate amplitude. The matching score is penalized and corrected based on the number of octaves of the candidate frequency; the frequency domain boundary parameter is selected from the candidate frequency set based on the corrected matching score. The spectral template takes a non-zero value at integer multiples of the candidate frequency, and a zero value at all other frequency points.

[0038] In this example implementation, a refined algorithm based on candidate frequency matching and penalty correction is employed to dynamically determine the frequency domain boundary parameters in the process of identifying the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum. The specific steps are as follows: First, a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring point is constructed. The fundamental frequency refers to the power frequency fundamental wave frequency or switching frequency. The power frequency fundamental wave is typically between 49.5Hz and 50.5Hz (for a 50Hz system), while the switching frequency may range from hundreds of hertz to tens of thousands of hertz. The candidate frequency set covers all possible frequency values ​​within this range with a certain step size (e.g., 1Hz or 10Hz), forming a list containing numerous candidate frequencies. Then, for each candidate frequency in the candidate frequency set, a spectral template corresponding to that candidate frequency is constructed. This spectral template takes non-zero values ​​at integer multiples of the candidate frequency and zero values ​​at all other frequency points. In other words, the spectral template is an idealized comb function that indicates that if the true fundamental frequency equals the candidate frequency, then energy peaks should appear in the probe amplitude spectrum at 1st, 2nd, 3rd, etc., octaves of the candidate frequency. Based on the probe amplitude spectrum data, spectral aggregation is performed at each octave to obtain the aggregated amplitude for each octave. Due to asynchronous sampling and non-integer octave relationships, the actual energy may be dispersed across several spectral lines near the octave. Therefore, it is necessary to aggregate the amplitudes of all spectral lines within a preset frequency range around each octave (e.g., an interval centered on the octave and several hertz wide) (e.g., taking the square root of the sum of squares) to obtain the aggregated amplitude for that octave, thereby suppressing the impact of spectral leakage. For each candidate frequency, the spectral template corresponding to that candidate frequency is weighted and summed with the corresponding aggregated amplitude to obtain the matching score for that candidate frequency. For example, suppose the AC voltage signal of the converter station is... via asynchronous ADC at sampling rate After sampling, a discrete sequence is obtained. Performing a Fast Fourier Transform on the sequence yields an amplitude spectrum with a spectral resolution of 10 Hz. Analysis frequency upper limit is taken Construct a candidate frequency set. , For the Mth candidate frequency, Covering the possible high-frequency harmonic fundamental frequency range of the converter station (practical range can be taken) Step length For each candidate frequency Constructing the spectrum template function The template function takes a non-zero value only at integer multiples of the candidate frequency:

[0039] in, For the maximum harmonic order, As the independent variable, For the Dirac function, For the first The weighting coefficients for second harmonics. To compensate for the decrease in harmonic amplitude as the order increases, the weighting coefficients are set according to the following rules:

[0040] In the formula, The attenuation compensation index, This term normalizes the total energy of the template function at different candidate frequencies. Considering that the energy in a real signal may be dispersed across multiple frequency points near the true frequency due to frequency fluctuations, asynchronous sampling, etc., a spectral convergence mechanism is introduced at each octave. For the ... Subharmonics, with their theoretical frequency Centered on bandwidth (Right now Calculate the root sum of energy within the range of )

[0041] This aggregation method can capture harmonic energy that is dispersed due to frequency shift.

[0042] Candidate frequency The matching score is defined as the dot product of the template and the measured spectrum:

[0043] in, Candidate frequency Match score, For the first Weighting coefficients for subharmonics Candidate frequency The maximum harmonic order, For aggregated amplitude, For harmonic order index, The attenuation compensation index, For a set of frequency indexes within a preset aggregation range, , For frequency intervals, Let be the amplitude of the j-th spectral line of the detected amplitude spectrum.

[0044] Then, a penalty correction is applied to the matching score based on the number of octaves of the candidate frequency. Penalty correction means that if a candidate frequency has a high matching score but few effective octaves (e.g., only the fundamental and second harmonics have significant convergence amplitudes, while higher harmonics have almost no energy), then the candidate frequency may be a misjudgment due to random noise or a single harmonic. Through penalty correction, the score of candidate frequencies with insufficient octaves is reduced, thereby increasing the competitiveness of candidate frequencies that truly have a complete harmonic sequence (i.e., the power frequency fundamental or its integer multiples of the switching frequency have multiple harmonics). For example, since lower candidate frequencies contain more octaves within the analysis band (…),… (The harmonics are relatively large), and the lower harmonics fall in the low-frequency region with strong energy, so a penalty mechanism needs to be introduced to correct them.

[0045] in, The corrected matching score. The penalty index is the number of spectral lines. The sum of harmonic orders, after penalty, is the matching score. It can reflect the degree of agreement between the candidate frequency and the high-frequency harmonic structure in the signal, eliminating the influence of frequency on the score.

[0046] Finally, based on the corrected matching score, frequency domain boundary parameters are selected from the candidate frequency set. For example, the candidate frequency with the highest corrected matching score is selected as the detected power frequency fundamental wave or switching frequency, and the boundary parameters are calculated based on these frequency values. For instance, after calculating the penalized matching score for all candidate frequencies, the highest-scoring frequency is selected. The candidate frequencies constitute the candidate set. These frequencies correspond to several of the most prominent sets of equally spaced harmonic structures in the signal, among which the smallest candidate frequency is... This represents the natural boundary between the dominant power frequency harmonic band and the dominant high-frequency switching harmonic band, which is the frequency domain boundary parameter and the adaptive sampling switching threshold. Therefore, it is determined that:

[0047] This threshold can be used to distinguish the signal energy characteristics of different frequency bands. In frequency bands below this threshold, the signal energy mainly consists of integer multiples of the power frequency harmonics, and synchronous sampling is used to avoid spectral leakage. In frequency bands above this threshold, the signal energy mainly consists of high-frequency harmonics that are not synchronized with the power frequency (such as the switching frequency and its harmonics), and asynchronous sampling should be used to preserve the original time-domain characteristics of the signal. Through multiple mechanisms including template construction, spectral aggregation, weighted summation, and penalty correction, this algorithm can robustly identify the true fundamental frequency and switching frequency under conditions of strong noise, spectral leakage, and frequency shift, providing a reliable basis for subsequent adaptive sampling.

[0048] In some implementations, the dynamic determination of frequency domain boundary parameters further includes: The frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters of the previous period to obtain the updated reference parameters. When constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated with the updated reference parameters as the center.

[0049] In this example implementation, the example describes a time-domain smoothing and adaptive update mechanism for dynamically determining frequency domain boundary parameters. Specifically, the frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters from the previous period to obtain the updated reference parameters. The weighted smoothing can be achieved using a first-order low-pass filter; for example, the boundary parameter detected in the current period can be set to f. new The reference parameter used in the previous cycle was f. old Then the updated reference parameter f ref = β·f new + (1-β)·f old β is a smoothing factor, ranging from 0 to 1. When β is close to 1, the reference parameter quickly follows the current detection result, suitable for scenarios with drastic changes in system operating conditions; when β is close to 0, the reference parameter changes slowly, helping to filter out random noise and transient disturbances during the detection process. This weighted smoothing avoids output jumps in boundary parameters due to noise interference or transient events in a single detection, thus ensuring the stability of subsequent adaptive dual-channel sampling and frequency domain fusion. Next, when constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated centered on the updated reference parameter. For example, if the switching frequency reference value determined in the previous cycle is f... ref Then the candidate frequency set for the next period can be set as [f ref - Δ, f refThe search radius is defined as a dense frequency sequence within the range of +Δ, where Δ is the search radius, which can be set according to the maximum possible drift of the switching frequency (e.g., ±5% of the switching frequency variation range). This strategy of generating a candidate set centered on historical reference parameters significantly reduces the search space and computational overhead. Furthermore, since the actual switching frequency changes are usually continuous and relatively slow, searching centered on historical reference values ​​can cover the true values ​​with a high probability. In addition, when the system starts up or has been idle for a long time resulting in the absence of historical parameters, a wider default search range can be used as the initial candidate set. After the reference parameters are calculated in the first cycle, subsequent cycles switch to a narrowband search centered on the reference parameters. This example enhances the anti-interference capability and continuity of the boundary parameters through temporal smoothing, avoiding the impact of parameter abrupt changes on subsequent sampling. By adaptively narrowing the search range of the candidate frequency set, the computational efficiency and real-time performance of the detection phase are greatly improved, enabling the entire high-frequency harmonic detection method to operate stably for a long period while maintaining a low demand for computational resources.

[0050] In some implementations, the adaptive dual-channel parallel sampling and frequency domain fusion of the two channels' sampled data for the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal includes: A synchronous analog-to-digital converter is used to synchronously sample the electrical signals of the flexible DC transmission system. The synchronously sampled data is then input into a low-pass filter to obtain the sampled low-frequency components. A asynchronous analog-to-digital converter is used to asynchronously sample the electrical signals of the flexible DC transmission system. The asynchronous sampled data is then input into a high-pass filter to obtain the sampled high-frequency components. The full-band digital signal is reconstructed by time-domain superposition of the sampled low-frequency component and the sampled high-frequency component. The synchronous analog-to-digital converter (ADC) and the asynchronous ADC operate in parallel. The sampling frequency of the synchronous ADC tracks the fundamental frequency of the power grid. The sampling frequency of the asynchronous ADC is determined based on the frequency domain boundary parameter. The cutoff frequencies of the low-pass filter and the high-pass filter are both configured to use the frequency domain boundary parameter.

[0051] In this example implementation, two ADCs (Analog-to-Digital Converters) are used for parallel sampling. Specifically, a synchronous ADC is used to synchronously sample the electrical signals (current / voltage signals) of the flexible DC transmission system. The synchronously sampled data is input into a low-pass filter to obtain the sampled low-frequency components. A synchronous ADC means that its sampling clock is strictly synchronized with the fundamental frequency of the power grid. Typically, a phase-locked loop (PLL) is used to lock the zero-crossing point or phase of the fundamental frequency, ensuring that the sampling window length is exactly an integer multiple of the fundamental frequency period. Synchronous sampling can fundamentally eliminate spectral leakage caused by non-integer period truncation, ensuring the accuracy of amplitude and phase measurements of power frequency and low-order harmonics. The synchronously sampled data is processed by a low-pass filter. The cutoff frequency of the low-pass filter is configured to the aforementioned dynamically determined frequency domain boundary parameter (e.g., 2-9kHz), thereby filtering out high-frequency components above this cutoff frequency and retaining only low-frequency components from DC to the boundary frequency range. Simultaneously, an asynchronous ADC is used to asynchronously sample the electrical signals (current / voltage signals) of the flexible DC transmission system. The asynchronously sampled data is input into a high-pass filter to obtain the sampled high-frequency components. Asynchronous sampling does not require tracking the fundamental frequency. Its sampling frequency is determined based on the frequency domain boundary parameter, typically set to 2.56 times or higher to satisfy the Nyquist theorem, ensuring the acquisition of high-frequency harmonic components above the boundary parameter without aliasing. The asynchronous sampled data is processed by a high-pass filter, whose cutoff frequency is also configured to the boundary parameter, thus filtering out low-frequency components below the cutoff frequency and retaining only the high-frequency components from the boundary frequency to the Nyquist frequency of the analog-to-digital converter (ADC). Importantly, the synchronous and asynchronous ADCs operate in parallel, meaning both continuously sample the same electrical signal simultaneously, ensuring alignment of low-frequency and high-frequency components on the time axis. Finally, the sampled low-frequency and high-frequency components are time-domain superimposed to reconstruct the full-band digital signal. Because the low-pass and high-pass filters are complementary in design (e.g., using linear-phase filters so that the sum of their amplitude-frequency responses is close to 1 across the entire frequency band), the time-domain superposition can recover all components of the original signal from DC to the highest analysis frequency without distortion. This dual-channel parallel sampling and frequency domain fusion scheme balances the trade-off between synchronization accuracy and high-frequency bandwidth. Based on the aforementioned determined switching threshold... The synchronous-asynchronous sampling sequence is reconstructed by a digital filter bank to obtain a full-band discrete digital signal sequence. Set a low-pass filter With high-pass filter Their cutoff frequencies are all Furthermore, satisfying the complementary property, this sequence serves as input data for subsequent spectral analysis, providing a high-quality input signal for subsequent frequency band differentiation analysis.

[0052] In some implementations, dividing the full frequency band into at least three sub-bands includes: The entire frequency band is divided into the first sub-band, the second sub-band, and the third sub-band; The first sub-band is a frequency band from 2kHz to 9kHz, the second sub-band is a frequency band from 9kHz to 150kHz, and the third sub-band is a frequency band above 150kHz.

[0053] In this example implementation, based on the differences in the physical characteristics, propagation laws, and impacts on equipment of harmonics in different frequency bands within a flexible DC transmission system, the entire frequency band is divided into a first sub-band, a second sub-band, and a third sub-band. The first sub-band is from 2kHz to 9kHz, the second sub-band is from 9kHz to 150kHz, and the third sub-band is above 150kHz. The first sub-band (2kHz-9kHz) is near the upper limit of the human ear's audible range and is often referred to as "high-frequency harmonics" or "higher harmonics." Its main source is the switching operation of the converter and its sideband modulation. Harmonics in this band are characterized by concentrated energy in continuous spectral clusters; that is, energy tends to accumulate within a narrow bandwidth centered on the switching frequency and its harmonics, forming a series of clustered distributions. The second sub-band (9kHz-150kHz) is defined as the "superharmonics" band in the International Electrotechnical Commission standards IEC 61000-4-7 and IEC 61000-4-30. Superharmonic waves (SOHs) are primarily generated by the switching frequencies (typically within this range) of modern power electronic equipment and their harmonics. They are characterized by high frequencies and wavelengths comparable to the size of the equipment, thus exhibiting significant transmission line effects and radiation characteristics during propagation. Furthermore, traditional electromagnetic compatibility (EMC) standards for this frequency band are not yet fully developed. The third sub-band (above 150kHz) typically falls under the category of high-frequency conducted emissions in the EMC field. Precisely dividing the entire frequency band into these three sub-bands allows subsequent spectrum aggregation strategies to be customized for the unique properties of each band: for the first sub-band, due to its clustered spectrum, an equivalent method based on energy aggregation is suitable; for the second sub-band, with its large frequency span and numerous non-integer multiples of switching frequencies, a balance between frequency resolution and computational efficiency is required; for the third sub-band, due to its extremely high frequency and rapid signal attenuation, it is often only necessary to focus on the presence of peaks exceeding a threshold, allowing for coarser-grained aggregation. This hierarchical and segmented division method not only aligns with international standards (9kHz and 150kHz are commonly used dividing points for EMC testing) but also fully considers the actual distribution characteristics of high-frequency harmonics in flexible DC transmission systems, laying a frequency domain foundation for subsequent targeted analysis algorithms. In some implementations, the high-frequency harmonic analysis employs a spectrum aggregation strategy for each sub-band, including: A first spectrum aggregation strategy is used to perform harmonic analysis on the first sub-band. The first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. A second spectrum aggregation strategy is adopted to perform harmonic analysis on the second and third sub-bands. The second spectrum aggregation strategy is used to balance transient feature capture and data compression efficiency.

[0054] In this example implementation, the first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. Since harmonics within the first sub-band (2kHz-9kHz) typically form multiple continuous spectrum clusters centered around the switching frequency and its harmonics, each cluster contains dense spectral lines, and the spacing between adjacent spectral lines may be equal to the fundamental frequency or a fraction thereof. The first spectrum aggregation strategy employs a cluster energy capture method, for example, by performing energy integration or root-mean-square aggregation on all spectral lines within a preset bandwidth (such as 1% of the switching frequency or a fixed 200Hz) to obtain an equivalent amplitude representing the total energy of the spectrum cluster. This method can stably reflect the overall energy level of harmonics in the frequency band, ignoring fine structures within clusters, thereby reducing the amount of data and improving measurement repeatability. For the second sub-band (9kHz-150kHz) and the third sub-band (above 150kHz), the signal characteristics differ from the first sub-band: in addition to the possible presence of higher harmonics at the switching frequency, this band may also exhibit broadband noise and time-varying transient components generated by mechanisms such as resonance and reflection. Meanwhile, this frequency band has a wide frequency range (from 9kHz to several MHz), and high-resolution point-by-point analysis would generate massive amounts of data. Therefore, the second spectrum aggregation strategy emphasizes balancing transient feature capture with data compression efficiency. Specifically, this strategy may dynamically adjust the analysis window length and aggregation bandwidth according to the time-varying nature of the signal: when the signal is relatively stable, a longer analysis window and a coarser aggregation bandwidth are used to compress the amount of data; when transient disturbances are detected, it automatically switches to a short time window and high time resolution mode to capture the start and end times and peak values ​​of the transient waveform. This balanced strategy enables the entire detection system to operate stably for a long time with limited storage and communication bandwidth, while maintaining sensitivity to key transient features.

[0055] In some implementations, a first spectrum aggregation strategy is used to perform harmonic analysis on the first sub-band, including: The full-band digital signal is subjected to Fourier transform using a rectangular window of the first cycle to obtain the first amplitude spectrum; The first sub-band is divided into multiple consecutive first bandwidths according to the first bandwidth interval. The energy of the spectral lines in each first bandwidth in the first amplitude spectrum is aggregated to obtain the aggregated amplitude corresponding to each first bandwidth. The amplitude of each harmonic in the first sub-band is determined based on the center frequency and aggregate amplitude corresponding to each first bandwidth.

[0056] In this example implementation, a rectangular window of the first cycle is used to perform a Fourier transform on the full-band digital signal to obtain a first amplitude spectrum. The first cycle typically refers to an integer multiple of a fundamental frequency period, such as 10 cycles. A rectangular window is used because, under synchronous sampling conditions (where the low-frequency components in the full-band digital signal come from the synchronous sampling channel, ensuring full-cycle truncation), the rectangular window does not introduce additional spectral leakage and has the highest frequency resolution. The first amplitude spectrum obtained after the Fourier transform contains amplitude information for all frequency points from DC to the Nyquist frequency. Then, the first sub-band (e.g., 2kHz to 9kHz) is divided into multiple consecutive first bandwidths according to a first bandwidth interval. The first bandwidth interval can be set according to the typical width of the spectral clusters within the sub-band, for example, 100Hz, 200Hz, or a value related to the fundamental component interval of the switching frequency. Each first bandwidth is a continuous frequency interval, and adjacent bandwidths can be non-overlapping and gapless, thus completely covering the entire first sub-band. Next, energy aggregation is performed on the spectral lines within each first bandwidth in the first amplitude spectrum to obtain the aggregated amplitude corresponding to each first bandwidth. Energy aggregation can be performed using the root mean square (RMS) method, which is the square root of the sum of the squares of the amplitudes at all frequency points within a bandwidth. Alternatively, it can be achieved through summation or taking the maximum value. RMS aggregation reflects the total energy within the bandwidth and is suitable for assessing the contribution of harmonics to the thermal effects of equipment. Finally, the amplitudes of each harmonic within the first sub-band are determined based on the center frequency and aggregated amplitude corresponding to each first bandwidth. The center frequency of each first bandwidth can be approximated as the characteristic frequency of the spectral cluster, and the corresponding aggregated amplitude represents the equivalent amplitude of the spectral cluster. For example, in the 2kHz-9kHz frequency band, using a Fourier algorithm based on a 10-cycle rectangular window (spectral resolution 5Hz), the proposed aggregation method divides the analysis band into several continuous 200Hz interval spectral lines, with the center frequency starting at 2100Hz and increasing in 200Hz steps to 8900Hz. The frequency band, its aggregate amplitude for:

[0057] in, For frequency The amplitude of the spectral lines. In this way, the originally messy and dense hundreds of spectral lines are compressed into dozens to hundreds of bandwidth aggregation values, which greatly reduces the complexity of subsequent storage, transmission and evaluation, while retaining the necessary information to determine whether harmonics exceed the limit.

[0058] In some implementations, a second spectrum aggregation strategy is used to perform harmonic analysis on the second and third sub-bands, including: Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands.

[0059] In this example implementation, different processing methods are adaptively switched based on the actual time-varying nature of the signal. Signals in the second sub-band (9kHz-150kHz) and the third sub-band (above 150kHz) have higher frequencies and stronger time-varying characteristics. For example, when a converter in a flexible DC transmission system undergoes a transient process (such as startup, shutdown, fault ride-through, or modulation strategy switching), the harmonic amplitude in this band may fluctuate drastically within milliseconds. This example assesses the time-varying characteristics of the full-band digital signal in real time, such as calculating the envelope variability, variance, or kurtosis of high-frequency components, to determine whether the current signal is in a stationary state or undergoing rapid changes. When the time variability exceeds a certain threshold, it indicates the presence of transient disturbances or non-stationary processes. In this case, the first aggregation scheme is selected—this scheme sacrifices some frequency resolution for higher time resolution, clearly depicting the trajectory of harmonic amplitude changes over time. Conversely, when the time variability is below the threshold, the signal is in a relatively stable state. In this case, the second aggregation scheme is selected—this scheme uses a longer time window, which can obtain higher frequency resolution, thereby distinguishing harmonic components with similar frequencies. At the same time, data compression is achieved through coarser frequency aggregation, reducing the burden on storage and transmission. This dynamic selection mechanism can adaptively balance the two conflicting needs of capturing transients and data compression, and is especially suitable for long-term online monitoring scenarios.

[0060] In some implementations, based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands, including: The full-band digital signal is high-pass filtered to extract the high-frequency components of the signal; Perform Hilbert transform on the high-frequency components of the signal to extract the envelope sequence; The envelope sequence is divided into time periods, and the volatility index for each time period is calculated; the time-varying index of the full-band digital signal is determined based on the volatility index for each time period. Harmonic analysis is performed by dynamically selecting either the first aggregation scheme or the second aggregation scheme based on the time-varying index.

[0061] In this example implementation, a high-pass filter is applied to the full-band digital signal to extract its high-frequency components. The cutoff frequency of the high-pass filter can be set to the upper limit of the first sub-band (i.e., 9kHz) or the lower limit of the second sub-band to ensure that the extracted high-frequency components mainly contain elements of the second and third sub-bands, filtering out interference from low-frequency, high-energy signals. The high-pass filter can be a digital high-pass filter (such as a Butterworth or Chebyshev filter), and its design must ensure a flat passband and linear phase to avoid distortion. Then, a Hilbert transform is performed on the high-frequency components to extract the envelope sequence. The envelope sequence reflects the slow variation trend of high-frequency harmonic energy, such as amplitude modulation of the switching frequency or energy fluctuations during transient processes. Next, the envelope sequence is divided into time periods, and volatility indices are calculated for each time period. Time period division can be achieved by dividing the continuous envelope sequence into multiple time periods with a fixed duration (e.g., 10ms, 20ms, or 1s), or by using a sliding window method. Within each time period, volatility indices are calculated, such as standard deviation, variance, integral of absolute deviation, or peak factor. The volatility index quantifies the degree of variation in high-frequency harmonic energy within a given time period—greater volatility indicates greater harmonic instability and the potential for transient events. Then, based on the volatility index for each time period, a time-varying index for the full-band digital signal is determined. This time-varying index can be the average, maximum, or the value of the most recent time period's volatility index. Finally, based on this time-varying index, either a first aggregation scheme or a second aggregation scheme is dynamically selected for harmonic analysis.

[0062] For example, for frequency bands above 9kHz (the second and third sub-bands), two different technical solutions are proposed based on the time-varying characteristics and spectral sparsity of the measured signal. The first aggregation solution can capture the amplitude changes of the transient process while compressing the data, while the second aggregation solution can utilize data conforming to the current IEEE harmonic detection standard, thus having higher frequency resolution. This example proposes a method based on time-domain waveform analysis, which enables dynamic selection of the solution.

[0063] Let the waveform recording signal after the aforementioned adaptive sampling be... n is the sampling point number, and the sampling frequency is To extract high-frequency components above 9kHz, a Butterworth high-pass filter is used. Its amplitude-frequency response is flat within the passband, making it suitable for broadband signal processing. The filter order is... 3dB cutoff frequency Set as The analog filter is mapped to a digital filter through a bilinear transform. To eliminate the phase delay introduced by the filter, a zero-phase filtering technique is used: the signal is passed through the filter in the forward direction, then the output sequence is time-reversed and passed through the same filter twice, and finally time-reversed again to obtain high-frequency components without phase distortion. .

[0064] To quantify the time-varying amplitude characteristics of a high-frequency signal, its envelope needs to be extracted. The envelope reflects the slow variation trend of the signal amplitude and is crucial for the filtered signal. Perform a Hilbert transform to obtain the analytic signal. :

[0065] in, Imaginary number sign; Hilbert transform Defined as:

[0066] in, The impulse response is the Hilbert transform.

[0067] In the frequency domain, the Hilbert transform is equivalent to shifting the phase of the positive frequency components. Phase shift of negative frequency components The magnitude of the analytic signal is the envelope of the original signal.

[0068] Envelope sequence As a non-negative real number, its amplitude change over time directly reflects the fluctuation level of the high-frequency signal. The envelope sequence is divided into... There are several equal-length time intervals, each with a length of [missing information]. The sampling point. For the first sampling point. Envelope signal of time period Calculate its mean with standard deviation :

[0069]

[0070] Define the wave qualitative index for this period. for:

[0071] Volatility Indicators It is a normalized measure of volatility, which is independent of the absolute amplitude of the signal and only reflects the degree of relative volatility. The larger the value, the more drastic the amplitude fluctuation during that period, and the stronger the time-varying nature of the signal. The median of the coefficient of variation for each period is taken. As a global time-varying indicator of the entire signal, the median has the characteristic of resisting outlier interference and can avoid misjudgment due to sudden disturbances. In some implementations, considering that the actual control frequency of the flexible DC converter valve in actual operation is generally less than 50kHz, and the main harmonic energy in its frequency domain is concentrated within twice the control frequency, a single sub-band division of 9kHz to 150kHz, if its frequency band span is large, will make it difficult for the spectrum aggregation strategy to take into account both the dense modes in the low-frequency band and the sparse noise in the high-frequency band within the bandwidth. Therefore, the entire frequency band can be further divided into four sub-bands. Among them, the first sub-band: 2kHz to 9kHz, this band still mainly contains continuous spectrum clusters near the switching frequency, and its physical characteristics are mainly characterized by the energy concentration of continuous spectrum clusters. The second sub-band: 9kHz to 50kHz, this band is the core area of ​​concern for conducted interference. The higher-order switching harmonics and sideband effects of the converter are still significant in this range, and a high frequency resolution needs to be maintained to distinguish different resonance peaks. The third sub-band: 50kHz to 150kHz. In this band, harmonic energy typically decreases exponentially with increasing frequency, and the signal characteristics transition from a dense clustered distribution to a sparse discrete spectrum. The fourth sub-band: above 150kHz. Its physical characteristics and aggregation strategy are consistent with the third sub-band in Example 1. Corresponding spectrum aggregation strategy adjustments: For the second sub-band (9kHz-50kHz), due to the potential presence of multiple discontinuous resonant peaks, the second bandwidth interval in the second spectrum aggregation strategy needs to be narrowed accordingly (e.g., adjusted from 2kHz to 1kHz) to enhance the frequency resolution of adjacent resonant peaks. For the third sub-band (50kHz-150kHz), due to energy attenuation and sparse spectral lines, the third bandwidth interval in the second spectrum aggregation strategy can be appropriately widened (e.g., adjusted from 2kHz to 5kHz) to further compress redundant data and reduce the communication and storage load of the real-time monitoring system.

[0072] Furthermore, in flexible DC transmission systems with multiple converter topologies (such as cascaded modular multilevel converters (MMCs) and two-level converters) or multi-timescale control interactions, the high-frequency harmonic spectrum structure becomes more complex. To accurately assess the differentiated impacts of different frequency bands on equipment insulation and communication channels, the entire frequency band can be further subdivided into more sub-bands. The specific sub-band division strategy can be determined based on the actual scenario and engineering practice.

[0073] In some implementations, the process of determining the time-varying index further includes: The quantile of the volatility index within the preset sliding window is used as the reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying volatility index.

[0074] In this example implementation, a sliding window-based quantile reference and dynamic update mechanism is introduced. Specifically, the quantile of the volatility index within a preset sliding window is used as a reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as a dynamically updated time-varying index. The preset sliding window is a buffer that moves along the time axis, storing volatility index values ​​for several past periods (e.g., the most recent 100 periods). The quantile (e.g., the 75th quantile, 90th quantile, or median) is a statistic extracted from the numerical distribution within this sliding window, representing the typical level of the volatility index within that period. Compared to directly using a fixed threshold, using quantiles as the reference volatility coefficient can automatically adapt to the normal fluctuation range of the system during long-term operation. This adaptive reference system design avoids the problem of fixed thresholds failing under different operating conditions. Then, the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying index. By setting a preset threshold, when the time-varying index is greater than or equal to this threshold, the signal is considered to have significant time-varying non-stationary characteristics, thus triggering the first aggregation scheme; otherwise, the signal is considered stationary, and the second aggregation scheme is adopted. This time-varying index is dynamically updated. After each detection cycle, the volatility index of the current cycle is added to the sliding window, and the quantiles within the window are updated, allowing the reference volatility coefficient to track the slow changes in the long-term characteristics of the system (such as seasonal variations, noise baseline drift caused by equipment aging, etc.). For example, defining a time-varying index... The ratio of the volatility indicator to the reference value:

[0075] in, The reference fluctuation coefficient is a pre-calibrated value, typically taken as a typical value during the steady-state operation of the system. For example, Based on 1: This indicates that the signal fluctuation exceeds the steady-state level and has strong time-varying characteristics; This indicates that the signal is relatively stable and has weak time-varying characteristics.

[0076] In some implementations, if the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis. The first aggregation scheme includes: The full-band digital signal is subjected to a short-time window Fourier transform using a Hanning window to obtain a second amplitude spectrum, and the amplitude results of integer multiples of the first frequency in the second amplitude spectrum are extracted. The statistical characteristic values ​​of the amplitude results extracted within the first time period are calculated as the harmonic detection results for the second and third sub-bands.

[0077] In this example implementation, when the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis. At this time, because the detected signal exhibits strong time-varying non-stationary characteristics (e.g., converter modulation strategy switching, DC voltage fluctuations, or external disturbances), a high-time-resolution analysis method capable of capturing transient changes is required. The first aggregation scheme is: using a Hanning window to perform a short-time-window Fourier transform on the full-band digital signal to obtain the second amplitude spectrum. The Hanning window is chosen instead of a rectangular window because, under short-time-window conditions (window length much shorter than one fundamental period), the spectral leakage of a rectangular window is very severe, while the Hanning window has better sidelobe suppression capabilities, reducing interference between adjacent frequency bands. The length of the "short-time window" in the short-time-window Fourier transform is usually set much smaller than the traditional harmonic analysis window (e.g., 1ms to 5ms) to ensure a time resolution in the sub-millisecond or millisecond range. By sliding this short-time window, a series of spectra on time slices can be obtained, each spectrum corresponding to a frequency domain snapshot at a specific moment. Then, the amplitude results at integer multiples of the first frequency in the second amplitude spectrum are extracted. Here, the "first frequency" can be the switching frequency, the fundamental frequency, or a user-specified characteristic frequency. Extracting the amplitude at its integer multiples of the frequency is equivalent to focusing only on harmonic components closely related to the system's operating state, rather than all frequency points across the entire frequency band, thus significantly reducing the amount of data. For example, if the switching frequency is 10kHz, only the amplitude variation curves of frequencies such as 10kHz, 20kHz, and 30kHz over time need to be extracted. Next, the statistical characteristic values ​​of the extracted amplitude results within the first time period are calculated as the harmonic detection results for the second and third sub-bands. The first time period can be a fundamental frequency period (20ms) or a fixed short time period (e.g., 1s). The statistical characteristic values ​​include the maximum, minimum, average, root mean square (RMS) value, and 95% probability maximum value of the amplitude at each multiple of the frequency within that time period. For example, using a short-time Fourier algorithm based on a 0.5ms Hanning window, the amplitude calculation results for integer multiples of the 10kHz frequency are extracted, and the maximum and RMS values ​​within a 200ms time period are calculated and stored. In this way, the first aggregation scheme retains the temporal information of transient events (through the position of short time windows) and compresses the data in the form of statistical feature values. This makes the final output detection results reflect the rapid changes of harmonics without generating an explosive amount of data, achieving a good balance between transient capture and data compression.

[0078] In some implementations, if the time-varying index is less than a preset threshold, the second aggregation scheme is selected for harmonic analysis. The second aggregation scheme includes: The full-band digital signal is subjected to a long-time window Fourier transform using a second-cycle rectangular window to obtain the third amplitude spectrum; The second sub-band is divided into multiple consecutive second bandwidths according to the second bandwidth interval. The spectral lines in each second bandwidth in the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each second bandwidth. The amplitude of each harmonic in the second sub-band is determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The third sub-band is divided into multiple consecutive third bandwidths according to the third bandwidth interval. The spectral lines in each third bandwidth of the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each third bandwidth. The amplitude of each harmonic in the third sub-band is determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth.

[0079] In this example implementation, when the time-varying index is less than a preset threshold, the second aggregation scheme is selected for harmonic analysis. At this time, the signal is in a relatively stable state without drastic time-varying disturbances, so a longer time window can be used to obtain higher frequency resolution, and the data volume is compressed through frequency domain aggregation. The second aggregation scheme: A long-time-window Fourier transform is performed on the full-band digital signal using a second-cycle rectangular window to obtain the third amplitude spectrum. The second cycle typically refers to multiple fundamental frequency cycles (e.g., 10 cycles, 16 cycles, or the standard-recommended 200ms window). The use of a rectangular window is predicated on the low-frequency components in the full-band digital signal originating from a synchronous sampling channel, ensuring full-cycle truncation; therefore, the rectangular window will not cause spectral leakage. While high-frequency components originate from asynchronous sampling channels, the long-time-window Fourier transform still provides stable spectral estimates due to the signal's stability. The use of a long time window results in very high frequency resolution; for example, a 200ms window corresponds to a 5Hz frequency resolution, sufficient to distinguish closely spaced harmonic components. Then, the second sub-band (9kHz-150kHz) is divided into multiple consecutive second bandwidths according to the second bandwidth interval. Energy aggregation is performed on the spectral lines within each second bandwidth of the third amplitude spectrum to obtain the aggregated amplitude corresponding to each second bandwidth. The harmonic amplitudes within the second sub-band are determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The second bandwidth interval can be wider than the bandwidth in the first spectrum aggregation strategy, for example, set to 1kHz or wider, because fine-grained frequency domain information is not needed in a steady state, and coarse-grained aggregation can effectively compress the data. Simultaneously, the third sub-band (above 150kHz) is divided into multiple consecutive third bandwidths according to the third bandwidth interval. Energy aggregation is performed on the spectral lines within each third bandwidth of the third amplitude spectrum to obtain the aggregated amplitude corresponding to each third bandwidth. The harmonic amplitudes within the third sub-band are determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth. The third bandwidth interval can typically be coarser than the second bandwidth interval, for example, set to 10kHz or divided by logarithmic intervals, because harmonic energy in extremely high frequency bands usually decays rapidly with increasing frequency; it is only necessary to focus on whether abnormal energy accumulation occurs in certain wider frequency bands. For example, using a Fourier algorithm based on a 10-cycle rectangular window, the calculation results are aggregated using a multi-level aggregation method. Spectral lines are aggregated with a 2kHz bandwidth in the 9kHz–150kHz frequency band, and with a 10kHz bandwidth above 150kHz, achieving data compression and feature preservation. Through this two-layer aggregation strategy, the second aggregation scheme compresses the originally millions of fine spectral lines into tens to hundreds of bandwidth aggregated values, greatly reducing the data storage and transmission pressure. Simultaneously, due to the use of a long-time-window Fourier transform, each aggregated value has high frequency stability and will not fluctuate due to short-term noise, making it very suitable for long-term trend analysis and threshold alarms. This scheme complements the first aggregation scheme.

[0080] For example, based on time-varying indicators Set threshold To achieve adaptive selection of solutions:

[0081] when When the signal exhibits strong time-varying characteristics and significant amplitude fluctuations, a shorter window width can capture the time-varying characteristics of high-frequency harmonics while quantifying the harmonic content. Therefore, the first aggregation scheme with a short time window is adopted. When the signal is relatively stable, it indicates that the time-varying nature of the signal is weak and the amplitude is relatively stable. Therefore, a longer window width can be used, i.e., the second aggregation scheme with a long time window can be adopted.

[0082] For the second aggregation scheme with a long time window, the calculation results can be aggregated in a multi-stage manner. For example, the first-stage aggregation for the second sub-band (9kHz – 150kHz) in the second aggregation scheme is as follows: a rectangular window Fourier analysis algorithm with uniform sampling and 10 power frequency cycles is used to obtain a 5Hz resolution spectrum, and a 200Hz spectrum is formed by referring to the aforementioned 2-9kHz aggregation method. These spectrums are then aggregated with a 2kHz bandwidth to generate a center frequency of 150kHz. The spectral lines, the amplitude of the aggregated spectral lines for:

[0083] in, It is the center frequency after aggregation at 2kHz.

[0084] The second aggregation scheme for the third sub-band (above 150kHz) involves a secondary aggregation approach: For frequencies above 150kHz, due to the sparser signal energy characteristics, the aggregation range is further expanded, starting from 160kHz. The spectrum is divided and aggregated in 10kHz intervals. For example, [the following is an example of an aggregation scheme]. The energy of all spectral lines within the frequency band is aggregated to form the representative frequency. One value. The aggregation formula is:

[0085] in, It could be the aforementioned 200Hz resolution spectral line or the result of the previous aggregation. It is the center frequency after the spectral lines are converged through a 10kHz bandwidth. yes Amplitude after spectral convergence.

[0086] In some implementations, it also includes: Based on the spectrum aggregation results of the first sub-band, the high-frequency harmonic voltage content rate and the total high-frequency harmonic distortion rate of the voltage are calculated. Based on the spectrum aggregation results of the second sub-band, the over-frequency harmonic voltage content and the voltage over-frequency harmonic total distortion rate are calculated. Based on the spectrum aggregation results of the third sub-band, the voltage content of ultra-high frequency harmonics and the total voltage ultra-high frequency harmonic distortion rate are calculated. The high-frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the first sub-frequency band; the super harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the second sub-frequency band; and the ultra-high frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the third sub-frequency band. The total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the first sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the second sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of ultra-high frequency is used to characterize the ratio of the root mean square value of each harmonic voltage in the third sub-frequency band to the effective value of the fundamental voltage.

[0087] In this example implementation, based on the spectral aggregation results of the aforementioned three sub-bands, a series of evaluation indicators with clear physical meaning and engineering application value are calculated. The high-frequency harmonic voltage content ratio characterizes the ratio of a single harmonic voltage to the fundamental voltage within the first sub-band. A single harmonic does not refer to a single frequency point, but rather to the equivalent harmonic component corresponding to each bandwidth after energy aggregation. The total high-frequency harmonic distortion rate is the ratio of the root mean square value of each harmonic voltage within the first sub-band to the effective value of the fundamental voltage. That is, it is calculated by summing the squares of the aggregated amplitudes of all bandwidths, taking the square root, and then dividing by the fundamental voltage, thus characterizing the overall harmonic pollution level of the entire first sub-band. Similarly, the over-frequency harmonic voltage content ratio characterizes the ratio of the harmonic voltage to the fundamental voltage corresponding to each aggregated bandwidth within the second sub-band; the total over-frequency harmonic distortion rate is the ratio of the root mean square value of all aggregated bandwidths within the second sub-band to the effective value of the fundamental voltage. The definition of UHF harmonic voltage content and total UHF voltage harmonic distortion rate in the third sub-band (above 150kHz) is similar to that of the first two sub-bands. These indicators provide operation and maintenance personnel with intuitive and quantitative high-frequency harmonic assessment parameters. By outputting these standardized indicators, this method not only completes the detection of high-frequency harmonics but also directly provides evaluation results that conform to engineering practices, enabling seamless integration with existing power quality monitoring systems and alarm threshold systems.

[0088] For example, the high-frequency harmonic quantization characterization index is defined as follows: First, define... This is the effective value of the fundamental voltage. For the first RMS value of subharmonic voltage For harmonic order, This refers to the harmonic frequency.

[0089] 1) High-frequency harmonic voltage content This value, used to characterize the percentage ratio of single harmonic voltage to fundamental voltage in the 2 kHz to 9 kHz frequency band, is calculated using the following formula:

[0090] 2) Superharmonic voltage content This is used to characterize the percentage ratio of single harmonic voltage to fundamental voltage in the 9 kHz to 150 kHz frequency band. The calculation formula is:

[0091] 3) Ultra-high frequency harmonic voltage content The ratio of single harmonic voltage to fundamental voltage in frequency bands above 150 kHz is used to characterize the ratio of single harmonic voltage to fundamental voltage. The formula is as follows:

[0092] 4) Total harmonic distortion of voltage high frequencies The root mean square (RMS) value of each harmonic voltage in the 2 kHz to 9 kHz frequency band is used to characterize the percentage ratio of the RMS value of the fundamental voltage. The formula is as follows:

[0093] 5) Voltage superharmonic total distortion rate The root mean square (RMS) value of each harmonic voltage in the frequency band from 9 kHz to 150 kHz is used to characterize the percentage ratio of the RMS value of the fundamental voltage. The formula is as follows:

[0094] 6) Total harmonic distortion of ultra-high frequency waves The root mean square value of harmonic voltage above 150 kHz is used to characterize the percentage ratio of the effective value of fundamental voltage. The formula is as follows:

[0095] For the frequency domain characteristics of flexible DC converter stations, low-frequency signal energy is concentrated in the fundamental wave and its harmonics, requiring synchronous sampling to ensure periodic consistency; high-frequency signal energy is distributed across a continuous spectrum and is related to the frequency of the power electronic devices themselves, where asynchronous sampling simplifies sampling control and avoids period truncation errors. This method proposes an adaptive sampling strategy, utilizing a synchronous-asynchronous sampling dual-ADC architecture to perform non-power frequency periodicity analysis in the frequency domain, thereby deriving the sampling switching threshold. .right The following frequency bands employ synchronous sampling, with the sampling frequency tracking the fundamental frequency of the power grid to reduce spectrum leakage; The above frequency bands employ asynchronous sampling to avoid high-frequency component spectral leakage caused by power frequency cycle truncation, thus adapting to the frequency characteristics of power electronic devices.

[0096] This invention addresses the monitoring problem of high-frequency harmonics (above 2kHz) with wide spectrum and strong time-varying characteristics generated by power electronic switching in flexible DC transmission systems, proposing a detection method and device. First, an adaptive synchronous sampling and multi-level spectrum aggregation algorithm is proposed. This algorithm dynamically adjusts the detection strategy according to the signal characteristics of different frequency bands, ensuring the accuracy of traditional harmonic measurements below 2kHz while efficiently capturing and compressing high-frequency non-stationary signals. This effectively overcomes the shortcomings of traditional Fourier methods in wideband asynchronous scenarios, such as spectral leakage and insufficient resolution. This method has been integrated into a dedicated detection device and completed in engineering testing, verifying its ability to perform online monitoring and feature extraction of high-frequency harmonics in flexible DC systems. Furthermore, a frequency-band-specific high-frequency harmonic quantification index system is proposed, solving the problem of the lack of standardized quantification indicators in this field.

[0097] The technology of this invention has broad application prospects. With the rapid development of new power systems based on new energy sources, flexible DC transmission technology is experiencing rapid expansion in construction and renovation due to its unique advantages in long-distance, large-capacity transmission and asynchronous grid interconnection. As a power quality monitoring method to ensure the safe and stable operation of such systems, the technology of this invention can be widely applied to power quality monitoring scenarios for sensitive power users, such as newly built flexible DC converter stations, intelligent transformation of existing DC projects, and offshore wind power flexible DC transmission platforms, providing technical support for the high-quality operation of power systems.

[0098] Example 2 Based on the same inventive concept, the present invention also provides a high-frequency harmonic detection device for a flexible DC transmission system, comprising: The detection module is used to perform probing sampling on the flexible DC transmission system to obtain detection data; to perform frequency domain analysis on the detection data for power frequency harmonics and switching frequency harmonics, and to dynamically determine the frequency domain boundary parameters based on the frequency domain analysis results; An adaptive sampling module is used to perform adaptive dual-channel parallel sampling and frequency domain fusion of the two channel sampling data on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal. The high-frequency harmonic analysis module is used to divide the entire frequency band into at least three sub-bands based on the physical characteristics of different frequency components; and to perform high-frequency harmonic analysis on the digital signal of the entire frequency band using a spectrum aggregation strategy for each sub-band. The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

[0099] In one possible implementation, the detection module includes: The sampling submodule is used to asynchronously sample electrical signals from target monitoring points within the flexible DC transmission system to obtain detection data. The parameter determination submodule is used to perform a fast Fourier transform on the detection data to obtain the corresponding detection amplitude spectrum; identify the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detection amplitude spectrum, and then dynamically determine the frequency domain boundary parameters.

[0100] In one possible implementation, the parameter determining submodule is specifically used for: Construct a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring points; For each candidate frequency in the candidate frequency set, construct the spectrum template corresponding to that candidate frequency; Based on the amplitude spectrum data, the detected amplitude spectrum is aggregated at each octave point to obtain the aggregated amplitude at each octave point; For each candidate frequency, the matching score of the candidate frequency is obtained by weighted summing of the spectral template corresponding to the candidate frequency and the corresponding aggregate amplitude. The matching score is penalized and corrected based on the number of octaves of the candidate frequency; the frequency domain boundary parameter is selected from the candidate frequency set based on the corrected matching score. The spectral template takes a non-zero value at integer multiples of the candidate frequency, and a zero value at all other frequency points.

[0101] In one possible implementation, the matching score of the candidate frequencies is as follows:

[0102]

[0103] in, Candidate frequency Match score, For the first Weighting coefficients for subharmonics Candidate frequency The maximum harmonic order, For aggregated amplitude, For harmonic order index, The attenuation compensation index, For a set of frequency indexes within a preset aggregation range, Let be the amplitude of the j-th spectral line of the detected amplitude spectrum.

[0104] In one possible implementation, the parameter determination submodule is further configured to: The frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters of the previous period to obtain the updated reference parameters. When constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated with the updated reference parameters as the center.

[0105] In one possible implementation, the adaptive sampling module includes: The first sampling submodule is used to synchronously sample the electrical signals of the flexible DC transmission system using a synchronous analog-to-digital converter, and input the synchronous sampling data into a low-pass filter to obtain the sampled low-frequency components. The second sampling submodule is used to perform asynchronous sampling of the electrical signals of the flexible DC transmission system using an asynchronous analog-to-digital converter, and inputs the asynchronous sampling data into a high-pass filter to obtain the sampled high-frequency components. The signal reconstruction submodule is used to perform time-domain superposition of the sampled low-frequency component and the sampled high-frequency component to reconstruct the full-band digital signal. The synchronous analog-to-digital converter (ADC) and the asynchronous ADC operate in parallel. The sampling frequency of the synchronous ADC tracks the fundamental frequency of the power grid. The sampling frequency of the asynchronous ADC is determined based on the frequency domain boundary parameter. The cutoff frequencies of the low-pass filter and the high-pass filter are both configured to use the frequency domain boundary parameter.

[0106] In one possible implementation, the high-frequency harmonic analysis module includes: The frequency band division submodule is used to divide the entire frequency band into the first sub-band, the second sub-band, and the third sub-band. The first sub-band is a frequency band from 2kHz to 9kHz, the second sub-band is a frequency band from 9kHz to 150kHz, and the third sub-band is a frequency band above 150kHz.

[0107] In one possible implementation, the high-frequency harmonic analysis module includes: The first harmonic analysis submodule is used to perform harmonic analysis on the first sub-frequency band using a first spectrum aggregation strategy, wherein the first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. The second harmonic analysis submodule is used to perform harmonic analysis on the second and third sub-frequency bands using a second spectrum aggregation strategy. The second spectrum aggregation strategy is used to balance transient feature capture and data compression efficiency.

[0108] In one possible implementation, the first harmonic analysis submodule is specifically used for: The full-band digital signal is subjected to Fourier transform using a rectangular window of the first cycle to obtain the first amplitude spectrum; The first sub-band is divided into multiple consecutive first bandwidths according to the first bandwidth interval. The energy of the spectral lines in each first bandwidth in the first amplitude spectrum is aggregated to obtain the aggregated amplitude corresponding to each first bandwidth. The amplitude of each harmonic in the first sub-band is determined based on the center frequency and aggregate amplitude corresponding to each first bandwidth.

[0109] In one possible implementation, the second harmonic analysis submodule is specifically used for: Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands.

[0110] In one possible implementation, the second harmonic analysis submodule includes: The index calculation subunit is used to perform high-pass filtering on the full-band digital signal to extract the high-frequency components of the signal; perform Hilbert transform on the high-frequency components of the signal to extract the envelope sequence; divide the envelope sequence into time periods and calculate the volatility index for each time period; and determine the time-varying index of the full-band digital signal based on the volatility index for each time period. The analysis subunit is used to dynamically select either the first aggregation scheme or the second aggregation scheme for harmonic analysis based on the time-varying index.

[0111] In one possible implementation, the analysis subunit is specifically used for: If the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis. The first aggregation scheme includes: The full-band digital signal is subjected to a short-time window Fourier transform using a Hanning window to obtain a second amplitude spectrum, and the amplitude results of integer multiples of the first frequency in the second amplitude spectrum are extracted. The statistical characteristic values ​​of the amplitude results extracted within the first time period are calculated as the harmonic detection results for the second and third sub-frequency bands.

[0112] In one possible implementation, the analysis subunit is further configured to: if the time-varying index is less than a preset threshold, select the second aggregation scheme for harmonic analysis, wherein the second aggregation scheme includes: The full-band digital signal is subjected to a long-time window Fourier transform using a second-cycle rectangular window to obtain the third amplitude spectrum; The second sub-band is divided into multiple consecutive second bandwidths according to the second bandwidth interval. The spectral lines in each second bandwidth in the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each second bandwidth. The amplitude of each harmonic in the second sub-band is determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The third sub-band is divided into multiple consecutive third bandwidths according to the third bandwidth interval. The spectral lines in each third bandwidth of the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each third bandwidth. The amplitude of each harmonic in the third sub-band is determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth.

[0113] In one possible implementation, the index calculation subunit is further configured to: The quantile of the volatility index within the preset sliding window is used as the reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying volatility index.

[0114] In one possible implementation, it further includes: a quantitative indicator calculation module, which is used for: Based on the spectrum aggregation results of the first sub-band, the high-frequency harmonic voltage content rate and the total high-frequency harmonic distortion rate of the voltage are calculated. Based on the spectrum aggregation results of the second sub-band, the over-frequency harmonic voltage content and the voltage over-frequency harmonic total distortion rate are calculated. Based on the spectrum aggregation results of the third sub-band, the voltage content of ultra-high frequency harmonics and the total voltage ultra-high frequency harmonic distortion rate are calculated. The high-frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the first sub-frequency band; the super harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the second sub-frequency band; and the ultra-high frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the third sub-frequency band. The total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the first sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the second sub-frequency band to the effective value of the fundamental voltage; the total harmonic distortion rate of ultra-high frequency is used to characterize the ratio of the root mean square value of each harmonic voltage in the third sub-frequency band to the effective value of the fundamental voltage.

[0115] Verification Experiment A monitoring point was selected at a flexible DC converter station, such as... Figure 2 As shown, the high-frequency harmonic detection device of this invention was used to collect on-site data of the current and voltage transformer signals of the end screen of the through-wall bushing of the entire bridge arm at a sampling rate of 100MHz. The acquisition principle is as follows: Figure 2 As shown, the specific parameters acquired are as follows: Current signal of the end screen of the bridge arm through-wall bushing, with a current sensor ratio of 10A / 5V; Voltage signal of the valve-side capacitive voltage transformer, with a terminal ratio of... The capacitive voltage transformer is located between the transformer and the bridge arm reactor.

[0116] Adaptive sampling was performed on the flexible DC system, and the resulting primary voltage waveform is as follows: Figure 3 As shown, the current time-domain waveform is as follows: Figure 4 As shown, after preprocessing, the acquired voltage / current signals are used to calculate the spectrum data for different frequency bands using an adaptive multi-level spectrum aggregation method.

[0117] Based on the high-frequency harmonic quantification index system proposed in this invention, the harmonic content and total distortion rate of each sub-frequency band are calculated. The calculation results demonstrate the high-frequency harmonic quantification characterization indexes obtained by the high-frequency harmonic detection method described in this invention for the monitored converter station under different operating conditions. Figure 5-7 As shown, the high-frequency harmonic level of the flexible DC converter station can be observed to change with the station's operating power. The final results are output and stored via a human-machine interface or data interface, supporting real-time monitoring and historical querying. Figure 5 The curve shows the total harmonic distortion (THDU) of the monitored converter station as a function of operating power in the range of 2kHz to 9kHz (first sub-band). Figure 4 It can be seen that as the operating power of the converter station increases, the total harmonic distortion rate of this frequency band fluctuates significantly (fluctuating between 1% and 2%), indicating that the harmonic energy of this frequency band has a complex relationship with the transmission power of the converter station. Figure 6 The curves showing the total harmonic distortion (THD) of the voltage at the monitored converter station in the range of 9kHz to 150kHz (second sub-band) as a function of power show a slight fluctuation trend in the operating power range of 540-920MW, and the fluctuation amplitude (fluctuating between 1.4% and 1.6%) is significantly smaller than that of the first sub-band. Figure 7 The graph shows the total harmonic distortion (THD) of the voltage at the monitored converter station in the frequency band above 150kHz (the third sub-band) as a function of power. The distortion rate in this band fluctuates between 2% and 2.7%. Distortion rate decreases at certain power points in each sub-band. The distortion rate-power graphs for the three sub-bands show significant differences in how harmonics change with operating power across different frequency bands.

[0118] Currently, flexible DC transmission systems lack methods for characterizing high-frequency harmonics. Existing methods are mainly designed for lower-frequency harmonics and are ill-suited to the non-stationary, wide-bandwidth, and highly time-varying characteristics of high-frequency signals, resulting in low accuracy in the quantitative assessment of high-frequency harmonics. This invention proposes a high-frequency harmonic detection scheme and successfully characterizes the ultra-high-frequency harmonic level of a flexible DC converter station using a flexible DC high-frequency harmonic detection device with adaptive sampling and adaptive spectrum aggregation. Its beneficial effects are mainly reflected in the following aspects: First, this invention proposes quantitative characterization indices for high-frequency harmonics, covering harmonic voltage content and total harmonic voltage distortion in three frequency bands: 2kHz to 9kHz, 9kHz to 150kHz, and above 150kHz. This system enables hierarchical quantitative evaluation of high-frequency harmonics in flexible DC systems.

[0119] Secondly, this invention proposes an adaptive sampling-aggregation detection method to address the characteristics of signals in different frequency bands.

[0120] Regarding sampling, the switching threshold is determined based on an adaptive sampling strategy. The entire frequency band is divided into low-frequency bands ( ) and high frequency band ( The low-frequency band uses synchronous sampling to ensure the measurement accuracy of integer multiples of the power frequency harmonics; the high-frequency band uses asynchronous sampling to avoid periodic truncation errors and fully preserve the original frequency characteristics of the high-frequency components. The data acquired in parallel by the dual ADCs are fused in the frequency domain by a digital filter bank to form a full-band discrete digital signal sequence.

[0121] In terms of spectrum aggregation, harmonic / interharmonic classification aggregation is used in the frequency band below 2kHz to improve the quantization capability of low-frequency components; in the frequency band from 2kHz to 9kHz, 200Hz band aggregation is used to characterize the cluster energy centered on the switching frequency harmonics; for the ultra-high frequency band above 9kHz, uniform sampling is adopted and two feasible aggregation schemes are provided: 10-cycle data storage for the 10kHz harmonics through a short-time Hanning window or feature extraction through further hierarchical aggregation. This adaptive analysis framework achieves a balance between measurement accuracy and computational efficiency, providing a reference for the signal processing flow of broadband disturbance monitoring.

[0122] The ultra-high frequency harmonic characterization method involved in this invention has been successfully applied to pilot monitoring of a specific flexible DC transmission project, verifying its effectiveness in actual complex electromagnetic environments.

[0123] Example 3 like Figure 8 As shown, the present invention also provides an electronic device, which may be a computer device, a microcontroller device, a smart mobile device, etc. The electronic device in this embodiment may include a processor, a memory, a transceiver component, etc. The memory, processor, and transceiver component are connected via a bus; the memory can be used to store executable programs, and an exemplary executable program may include instructions; the processor is used to execute the instructions stored in the memory. The memory can also be used to store data, which can be accessed and / or modified when instructions are executed.

[0124] The processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and it is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions in the storage medium to realize the corresponding method flow or corresponding function, so as to realize the steps of the high-frequency harmonic detection method of a flexible DC transmission system in the above embodiments.

[0125] Example 4 Based on the same inventive concept, this invention also provides a readable storage medium, specifically an electronic device readable storage medium (Memory). An electronic device readable storage medium is a memory device within an electronic device used to store programs and data. It is understood that the storage medium here can include both built-in storage media within the electronic device and extended storage media supported by the electronic device. The storage medium provides storage space, which stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more executable programs (including program code). It should be noted that the storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. Loading and executing one or more instructions stored in the storage medium by the processor can implement the steps of the high-frequency harmonic detection method for a flexible DC transmission system described in the above embodiments.

[0126] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0127] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0128] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0129] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the application, but these changes, modifications or equivalent substitutions are all within the scope of protection of the claims pending approval.

Claims

1. A method for detecting high-frequency harmonics in a flexible DC transmission system, characterized in that, include: Detection data was obtained by probing the flexible DC transmission system. The detection data is subjected to frequency domain analysis for power frequency harmonics and switching frequency harmonics, and the frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results. Based on the frequency domain boundary parameters, the flexible DC transmission system is subjected to adaptive dual-channel parallel sampling and frequency domain fusion of the sampling data from the two channels to obtain a full-band digital signal. Based on the physical characteristics of different frequency components, the entire frequency band is divided into at least three sub-bands; A spectrum aggregation strategy targeting each sub-band is used to perform high-frequency harmonic analysis on the full-band digital signal; The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

2. The method according to claim 1, characterized in that, Probing data was obtained by probing the flexible DC transmission system, including: Asynchronous sampling of electrical signals is performed on target monitoring points within the flexible DC transmission system to obtain detection data; The detection data is subjected to frequency domain analysis, and frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results, including: Perform a fast Fourier transform on the detection data to obtain the corresponding detection amplitude spectrum; The frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum are identified, and then the frequency domain boundary parameters are dynamically determined.

3. The method according to claim 2, characterized in that, The process of identifying the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detected amplitude spectrum, and then dynamically determining the frequency domain boundary parameters, includes: Construct a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring points; For each candidate frequency in the candidate frequency set, construct the spectrum template corresponding to that candidate frequency; Based on the amplitude spectrum data, the detected amplitude spectrum is aggregated at each octave point to obtain the aggregated amplitude at each octave point; For each candidate frequency, the matching score of the candidate frequency is obtained by weighted summing of the spectral template corresponding to the candidate frequency and the corresponding aggregate amplitude. The matching score is penalized and corrected based on the number of octaves of the candidate frequency; the frequency domain boundary parameter is selected from the candidate frequency set based on the corrected matching score. The spectral template takes a non-zero value at integer multiples of the candidate frequency, and a zero value at all other frequency points.

4. The method according to claim 3, characterized in that, The matching scores of the candidate frequencies are as follows: in, Candidate frequency Match score, For the first Weighting coefficients for subharmonics Candidate frequency The maximum harmonic order, For aggregated amplitude, For harmonic order index, The attenuation compensation index, For a set of frequency indexes within a preset aggregation range, Let be the amplitude of the j-th spectral line of the detected amplitude spectrum.

5. The method according to claim 3, characterized in that, The dynamic determination of frequency domain boundary parameters also includes: The frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters of the previous period to obtain the updated reference parameters. When constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated with the updated reference parameters as the center.

6. The method according to claim 1, characterized in that, The adaptive dual-channel parallel sampling and frequency domain fusion of the two channel sampled data for the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal includes: A synchronous analog-to-digital converter is used to synchronously sample the electrical signals of the flexible DC transmission system. The synchronously sampled data is then input into a low-pass filter to obtain the sampled low-frequency components. A asynchronous analog-to-digital converter is used to asynchronously sample the electrical signals of the flexible DC transmission system. The asynchronous sampled data is then input into a high-pass filter to obtain the sampled high-frequency components. The full-band digital signal is reconstructed by time-domain superposition of the sampled low-frequency component and the sampled high-frequency component. The synchronous analog-to-digital converter (ADC) and the asynchronous ADC operate in parallel. The sampling frequency of the synchronous ADC tracks the fundamental frequency of the power grid. The sampling frequency of the asynchronous ADC is determined based on the frequency domain boundary parameter. The cutoff frequencies of the low-pass filter and the high-pass filter are both configured to use the frequency domain boundary parameter.

7. The method according to claim 1, characterized in that, The division of the full frequency band into at least three sub-bands includes: The entire frequency band is divided into the first sub-band, the second sub-band, and the third sub-band; The first sub-band is a frequency band from 2kHz to 9kHz, the second sub-band is a frequency band from 9kHz to 150kHz, and the third sub-band is a frequency band above 150kHz.

8. The method according to claim 7, characterized in that, The high-frequency harmonic analysis employs a spectrum aggregation strategy for each sub-band, including: A first spectrum aggregation strategy is used to perform harmonic analysis on the first sub-band. The first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. A second spectrum aggregation strategy is adopted to perform harmonic analysis on the second and third sub-bands. The second spectrum aggregation strategy is used to balance transient feature capture and data compression efficiency.

9. The method according to claim 8, characterized in that, Harmonic analysis is performed on the first sub-frequency band using a first spectrum aggregation strategy, including: The full-band digital signal is subjected to Fourier transform using a rectangular window of the first cycle to obtain the first amplitude spectrum; The first sub-band is divided into multiple consecutive first bandwidths according to the first bandwidth interval. The energy of the spectral lines in each first bandwidth in the first amplitude spectrum is aggregated to obtain the aggregated amplitude corresponding to each first bandwidth. The amplitude of each harmonic in the first sub-band is determined based on the center frequency and aggregate amplitude corresponding to each first bandwidth.

10. The method according to claim 7, characterized in that, A second spectrum aggregation strategy is used to perform harmonic analysis on the second and third sub-bands, including: Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands.

11. The method according to claim 10, characterized in that, Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands, including: The full-band digital signal is high-pass filtered to extract the high-frequency components of the signal; Perform Hilbert transform on the high-frequency components of the signal to extract the envelope sequence; The envelope sequence is divided into time periods, and the volatility index for each time period is calculated; the time-varying index of the full-band digital signal is determined based on the volatility index for each time period. Harmonic analysis is performed by dynamically selecting either the first aggregation scheme or the second aggregation scheme based on the time-varying index.

12. The method according to claim 11, characterized in that, If the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis. The first aggregation scheme includes: The full-band digital signal is subjected to a short-time window Fourier transform using a Hanning window to obtain a second amplitude spectrum, and the amplitude results of integer multiples of the first frequency in the second amplitude spectrum are extracted. The statistical characteristic values ​​of the amplitude results extracted within the first time period are calculated as the harmonic detection results for the second and third sub-bands.

13. The method according to claim 11, characterized in that, If the time-varying index is less than a preset threshold, the second aggregation scheme is selected for harmonic analysis. The second aggregation scheme includes: The full-band digital signal is subjected to a long-time window Fourier transform using a second-cycle rectangular window to obtain the third amplitude spectrum; The second sub-band is divided into multiple consecutive second bandwidths according to the second bandwidth interval. The spectral lines in each second bandwidth in the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each second bandwidth. The amplitude of each harmonic in the second sub-band is determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The third sub-band is divided into multiple consecutive third bandwidths according to the third bandwidth interval. The spectral lines in each third bandwidth of the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each third bandwidth. The amplitude of each harmonic in the third sub-band is determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth.

14. The method according to claim 11, characterized in that, The process of determining the time-varying index also includes: The quantile of the volatility index within the preset sliding window is used as the reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying volatility index.

15. The method according to claim 7, characterized in that, Also includes: Based on the spectrum aggregation results of the first sub-band, the high-frequency harmonic voltage content rate and the total high-frequency harmonic distortion rate of the voltage are calculated. Based on the spectrum aggregation results of the second sub-band, the over-frequency harmonic voltage content and the voltage over-frequency harmonic total distortion rate are calculated. Based on the spectrum aggregation results of the third sub-band, the voltage content of ultra-high frequency harmonics and the total voltage ultra-high frequency harmonic distortion rate are calculated. The high-frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the first sub-frequency band; the super harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the second sub-frequency band; and the ultra-high frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the third sub-frequency band. The total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the first sub-band to the effective value of the fundamental voltage; the total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the second sub-band to the effective value of the fundamental voltage; the total harmonic distortion rate of ultra-high frequency is used to characterize the ratio of the root mean square value of each harmonic voltage in the third sub-band to the effective value of the fundamental voltage.

16. A high-frequency harmonic detection device for a flexible DC transmission system, characterized in that, include: The detection module is used to perform probing sampling on the flexible DC transmission system to obtain detection data; The detection data is subjected to frequency domain analysis for power frequency harmonics and switching frequency harmonics, and the frequency domain boundary parameters are dynamically determined based on the frequency domain analysis results. An adaptive sampling module is used to perform adaptive dual-channel parallel sampling and frequency domain fusion of the two channel sampling data on the flexible DC transmission system based on the frequency domain boundary parameters to obtain a full-band digital signal. The high-frequency harmonic analysis module is used to divide the entire frequency band into at least three sub-bands based on the physical characteristics of different frequency components; and to perform high-frequency harmonic analysis on the digital signal of the entire frequency band using a spectrum aggregation strategy for each sub-band. The spectrum aggregation strategy for each sub-band is determined based on the signal characteristics of that sub-band, including the energy concentration characteristics of continuous spectrum clusters and / or time-varying non-stationary characteristics.

17. The apparatus according to claim 16, characterized in that, The detection module includes: The sampling submodule is used to perform asynchronous sampling of electrical signals at target monitoring points within the flexible DC transmission system to obtain detection data. The parameter determination submodule is used to perform a fast Fourier transform on the detection data to obtain the corresponding detection amplitude spectrum; identify the frequency domain distribution characteristics of power frequency harmonics and switching frequency harmonics in the detection amplitude spectrum, and then dynamically determine the frequency domain boundary parameters.

18. The apparatus according to claim 17, characterized in that, The parameter determination submodule is specifically used for: Construct a candidate frequency set covering the high-frequency harmonic fundamental frequency range of the target monitoring points; For each candidate frequency in the candidate frequency set, construct the spectrum template corresponding to that candidate frequency; Based on the amplitude spectrum data, the detected amplitude spectrum is aggregated at each octave point to obtain the aggregated amplitude at each octave point; For each candidate frequency, the matching score of the candidate frequency is obtained by weighted summing of the spectral template corresponding to the candidate frequency and the corresponding aggregate amplitude. The matching score is penalized and corrected based on the number of octaves of the candidate frequency; the frequency domain boundary parameter is selected from the candidate frequency set based on the corrected matching score. The spectral template takes a non-zero value at integer multiples of the candidate frequency, and a zero value at all other frequency points.

19. The apparatus according to claim 18, characterized in that, The matching scores of the candidate frequencies are as follows: in, Candidate frequency Match score, For the first Weighting coefficients for subharmonics Candidate frequency The maximum harmonic order, For aggregated amplitude, For harmonic order index, The attenuation compensation index, For a set of frequency indexes within a preset aggregation range, Let be the amplitude of the j-th spectral line of the detected amplitude spectrum.

20. The apparatus according to claim 18, characterized in that, The parameter determination submodule is also used for: The frequency domain boundary parameters determined in the current detection period are weighted and smoothed with the historical parameters of the previous period to obtain the updated reference parameters. When constructing the candidate frequency set in the next detection cycle, the candidate frequency set is generated with the updated reference parameters as the center.

21. The apparatus according to claim 16, characterized in that, The adaptive sampling module includes: The first sampling submodule is used to synchronously sample the electrical signals of the flexible DC transmission system using a synchronous analog-to-digital converter, and input the synchronous sampling data into a low-pass filter to obtain the sampled low-frequency components. The second sampling submodule is used to perform asynchronous sampling of the electrical signals of the flexible DC transmission system using an asynchronous analog-to-digital converter, and inputs the asynchronous sampling data into a high-pass filter to obtain the sampled high-frequency components. The signal reconstruction submodule is used to perform time-domain superposition of the sampled low-frequency component and the sampled high-frequency component to reconstruct the full-band digital signal. The synchronous analog-to-digital converter (ADC) and the asynchronous ADC operate in parallel. The sampling frequency of the synchronous ADC tracks the fundamental frequency of the power grid. The sampling frequency of the asynchronous ADC is determined based on the frequency domain boundary parameter. The cutoff frequencies of the low-pass filter and the high-pass filter are both configured to use the frequency domain boundary parameter.

22. The apparatus according to claim 16, characterized in that, The high-frequency harmonic analysis module includes: The frequency band division submodule is used to divide the entire frequency band into the first sub-band, the second sub-band, and the third sub-band; The first sub-band is a frequency band from 2kHz to 9kHz, the second sub-band is a frequency band from 9kHz to 150kHz, and the third sub-band is a frequency band above 150kHz.

23. The apparatus according to claim 22, characterized in that, The high-frequency harmonic analysis module includes: The first harmonic analysis submodule is used to perform harmonic analysis on the first sub-frequency band using a first spectrum aggregation strategy, wherein the first spectrum aggregation strategy is used to capture the cluster energy of continuous spectrum clusters. The second harmonic analysis submodule is used to perform harmonic analysis on the second and third sub-frequency bands using a second spectrum aggregation strategy. The second spectrum aggregation strategy is used to balance transient feature capture and data compression efficiency.

24. The apparatus according to claim 23, characterized in that, The first harmonic analysis submodule is specifically used for: The full-band digital signal is subjected to Fourier transform using a rectangular window of the first cycle to obtain the first amplitude spectrum; The first sub-band is divided into multiple consecutive first bandwidths according to the first bandwidth interval. The energy of the spectral lines in each first bandwidth in the first amplitude spectrum is aggregated to obtain the aggregated amplitude corresponding to each first bandwidth. The amplitude of each harmonic in the first sub-band is determined based on the center frequency and aggregate amplitude corresponding to each first bandwidth.

25. The apparatus according to claim 22, characterized in that, The second harmonic analysis submodule is specifically used for: Based on the time-varying characteristics of the full-band digital signal, a first aggregation scheme or a second aggregation scheme is dynamically selected to perform harmonic analysis on the second and third sub-bands.

26. The apparatus according to claim 25, characterized in that, The second harmonic analysis submodule includes: The index calculation subunit is used to perform high-pass filtering on the full-band digital signal to extract the high-frequency components of the signal; perform Hilbert transform on the high-frequency components of the signal to extract the envelope sequence; divide the envelope sequence into time periods and calculate the volatility index for each time period; and determine the time-varying index of the full-band digital signal based on the volatility index for each time period. The analysis subunit is used to dynamically select either the first aggregation scheme or the second aggregation scheme for harmonic analysis based on the time-varying index.

27. The apparatus according to claim 26, characterized in that, The analysis subunit is specifically used for: If the time-varying index is greater than or equal to a preset threshold, the first aggregation scheme is selected for harmonic analysis. The first aggregation scheme includes: The full-band digital signal is subjected to a short-time window Fourier transform using a Hanning window to obtain a second amplitude spectrum, and the amplitude results of integer multiples of the first frequency in the second amplitude spectrum are extracted. The statistical characteristic values ​​of the amplitude results extracted within the first time period are calculated as the harmonic detection results for the second and third sub-bands.

28. The apparatus according to claim 26, characterized in that, The analysis subunit is further configured to: if the time-varying index is less than a preset threshold, select the second aggregation scheme for harmonic analysis, wherein the second aggregation scheme includes: The full-band digital signal is subjected to a long-time window Fourier transform using a second-cycle rectangular window to obtain the third amplitude spectrum; The second sub-band is divided into multiple consecutive second bandwidths according to the second bandwidth interval. The spectral lines in each second bandwidth in the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each second bandwidth. The amplitude of each harmonic in the second sub-band is determined based on the center frequency and aggregated amplitude corresponding to each second bandwidth. The third sub-band is divided into multiple consecutive third bandwidths according to the third bandwidth interval. The spectral lines in each third bandwidth of the third amplitude spectrum are aggregated to obtain the aggregated amplitude corresponding to each third bandwidth. The amplitude of each harmonic in the third sub-band is determined based on the center frequency and aggregated amplitude corresponding to each third bandwidth.

29. The apparatus according to claim 26, characterized in that, The index calculation subunit is also used for: The quantile of the volatility index within the preset sliding window is used as the reference volatility coefficient, and the ratio of the volatility index of the current period to the reference volatility coefficient is used as the dynamically updated time-varying volatility index.

30. The apparatus according to claim 22, characterized in that, Also includes: The quantitative indicator calculation module is used for: Based on the spectrum aggregation results of the first sub-band, the high-frequency harmonic voltage content rate and the total high-frequency harmonic distortion rate of the voltage are calculated. Based on the spectrum aggregation results of the second sub-band, the over-frequency harmonic voltage content and the voltage over-frequency harmonic total distortion rate are calculated. Based on the spectrum aggregation results of the third sub-band, the voltage content of ultra-high frequency harmonics and the total voltage ultra-high frequency harmonic distortion rate are calculated. The high-frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the first sub-frequency band; the super harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the second sub-frequency band; and the ultra-high frequency harmonic voltage content rate is used to characterize the ratio of single harmonic voltage to fundamental voltage in the third sub-frequency band. The total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the first sub-band to the effective value of the fundamental voltage; the total harmonic distortion rate of voltage is used to characterize the ratio of the root mean square value of each harmonic voltage in the second sub-band to the effective value of the fundamental voltage; the total harmonic distortion rate of ultra-high frequency is used to characterize the ratio of the root mean square value of each harmonic voltage in the third sub-band to the effective value of the fundamental voltage.

31. An electronic device, characterized in that, include: At least one processor and memory; The memory and processor are connected via a bus; The memory is used to store one or more programs; When the one or more programs are executed by the at least one processor, the method as described in any one of claims 1 to 15 is implemented.

32. A readable storage medium, characterized in that, It contains an executable program, which, when executed, implements the method as described in any one of claims 1 to 15.

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