A low-delay anti-aliasing resampling method for a protection device

Abstract

The application discloses a low-delay anti-aliasing resampling method for a protection device side, and belongs to the technical field of relay protection. First sampling rate sampling value data output by a merging unit is acquired; a preset low-pass response of a target sampling link is established according to design parameters of a front-end analog low-pass loop of a protection device; a linear-phase FIR anti-aliasing resampling filter is determined by determining a second sampling rate, an effective frequency band, an anti-aliasing stop band and a group delay threshold, so that an equivalent low-pass amplitude-frequency response of the filter meets a fundamental wave amplitude error limit, an effective frequency band approximation error limit and a stop band attenuation limit, and meets a group delay constraint; rational resampling is performed according to an interpolation multiple and a decimation multiple; and fixed group delay compensation and time scale correction are performed on output sampling values. The application is used to solve the problems that amplitude-frequency responses of a digital sampling link and a target traditional sampling link are inconsistent at an entrance of a protection algorithm, aliasing is caused by sampling rate conversion, and time scale deviation is caused by fixed group delay.

Description

Technical Field

[0001] This invention relates to a low-delay anti-aliasing resampling method on the protection device side, belonging to the field of relay protection technology. Background Technology

[0002] In existing technologies, the sampling data links of protection devices mainly include two forms: traditional sampling links and digital sampling links. In a traditional sampling link, the analog signals collected by the primary voltage transformer and current transformer are sequentially processed by the protection device's pre-amplifier analog low-pass circuit for anti-aliasing filtering and analog-to-digital conversion to generate a sampling sequence for use by the protection algorithm. In a digital sampling link, the analog signals collected by the primary voltage transformer and current transformer are first sent to the merging unit. After passing through the merging unit's pre-amplifier analog low-pass circuit, the sampled data is output at a first sampling rate. The protection device then converts this sampled data to a second sampling rate required by the protection algorithm for its use. Although both sampling links can provide data at the same sampling rate to the protection algorithm, they differ in terms of pre-amplifier low-pass characteristics, phase characteristics, high-frequency transient retention, and reduction of sampling aliasing risk.

[0003] The aforementioned existing technologies have at least the following drawbacks: First, when the protection device only performs routine resampling without consistency constraints for the protection algorithm, significant amplitude-frequency response differences may occur between the protection algorithm input data output from the digital sampling link and the data from the target traditional sampling link. For protection algorithms that rely on voltage and current amplitudes, phase relationships, transient components, or multi-channel synchronization relationships, this difference may affect the accuracy and criterion margin of the protection calculation. Second, with the increasing proportion of power electronic interface power supplies such as wind power, photovoltaics, and energy storage, the voltage and current signals input to the protection device may contain more complex harmonics, interharmonics, transient impacts, and broadband components caused by control interactions. If anti-aliasing processing is not performed in conjunction with the sampling rate of the protection algorithm during the sampling rate conversion process, these components may fold into the frequency band of interest of the protection algorithm and be superimposed on the differences in the pre-pass low-pass of the two sampling links, further affecting the amplitude, phase relationship, and multi-channel synchronization calculation results. Third, while existing technologies include oversampling anti-aliasing, sample value resampling, sampling rate conversion filtering, and protection action delay optimization, these solutions typically only focus on the sampling rate conversion itself. They do not fully consider how to ensure that the low-pass amplitude-frequency response of the digital sampling link entering the protection algorithm approximates the target traditional sampling link, while simultaneously meeting the requirements of power frequency fundamental frequency fidelity, effective frequency band preservation, downsampling anti-aliasing, protection response speed constraints, and fixed time scale consistency, under the condition that the merging unit cannot be modified. Therefore, a low-delay anti-aliasing resampling scheme suitable for the protection device side is urgently needed to reduce the amplitude-frequency response difference between the digital sampling link and the target traditional sampling link at the protection algorithm entry point and eliminate fixed time scale deviation. Summary of the Invention

[0004] The purpose of this invention is to provide a low-delay anti-aliasing resampling method for protection devices. Under the condition that the merging unit cannot be modified, a preset low-pass response of the target sampling link is established, and a linear phase FIR (Linear Phase Finite Impulse Response Anti-Aliasing Resampling Filter) is determined under the joint constraints of power frequency fundamental frequency fidelity, effective frequency band approximation, anti-aliasing stopband attenuation, and group delay. This solves the problems of inconsistent amplitude-frequency response between the digital sampling link and the target traditional sampling link at the entry point of the protection algorithm, aliasing caused by sampling rate conversion, and time scale deviation caused by fixed group delay in the existing technology. It reduces the difference in amplitude-frequency response between the digital sampling link and the target traditional sampling link at the entry point of the protection algorithm, reduces the risk of sampling aliasing, and reduces fixed time scale deviation.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:

[0006] This invention provides a low-latency anti-aliasing resampling method for protection devices, comprising:

[0007] Obtain the first sampling rate sampled value data output by the merging unit;

[0008] Based on the design parameters of the pre-simulated low-pass circuit of the protection device, a preset low-pass response for the target sampling link is established;

[0009] The target sampling rate of the protection algorithm is used as the second sampling rate to determine the fundamental frequency of the power system, and a preset group delay threshold is set.

[0010] The effective frequency band is determined based on the preset low-pass response;

[0011] The anti-aliasing stopband is determined based on the second sampling rate;

[0012] A linear phase FIR anti-aliasing resampling filter is determined based on the preset group delay threshold.

[0013] Wherein, the equivalent low-pass amplitude-frequency response and the preset low-pass response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm meet the preset fundamental amplitude error limit at the power frequency fundamental frequency, meet the preset frequency band approximation error limit in the effective frequency band, meet the preset stopband attenuation limit in the anti-aliasing stopband, and the group delay of the linear phase FIR anti-aliasing resampling filter is not greater than the preset group delay threshold;

[0014] Using the linear phase FIR anti-aliasing resampling filter, rational resampling is performed on the first sampling rate sampled data at the protection device side according to the interpolation multiple and the decimation multiple, and the second sampling rate sampled value is output. Fixed group delay compensation and time stamp correction are performed on the second sampling rate sampled value, wherein the first sampling rate is higher than the second sampling rate.

[0015] Furthermore, based on the design parameters of the pre-amplifier low-pass circuit of the protection device, a preset low-pass response for the target sampling link is established, including:

[0016] Based on the design parameters of the low-pass circuit in the front-end simulation of the protection device, a set of parameters that can determine the low-pass characteristics of the circuit is extracted.

[0017] Based on the circuit topology of the pre-amplified low-pass loop of the protection device and the parameter set, establish the continuous domain transfer function of the pre-amplified low-pass loop of the protection device.

[0018] Substituting the Laplace domain complex frequency variable into the continuous domain transfer function according to the sinusoidal steady-state frequency mapping relationship, the frequency response of the front-end analog low-pass circuit of the protection device is obtained.

[0019] The amplitude of the frequency response is normalized to establish a preset low-pass response for the target sampling link;

[0020] Wherein, when the front-end analog low-pass circuit of the protection device is an RC low-pass circuit, the design parameters include the cutoff frequency and filter order of the RC low-pass circuit, and / or the cutoff frequency and RC parameters of the RC low-pass circuit.

[0021] Furthermore, the continuous-domain transfer function is expressed as:

[0022] ;

[0023] In the formula, This represents the continuous domain transfer function when the pre-amplifier analog low-pass circuit of the protection device is an RC low-pass circuit. Represents the complex frequency variable in the Laplace domain. Represents complex frequency variable Multiply by the sum of the resistance and capacitance time constants, These represent the resistance values ​​of the first resistor and the second resistor, respectively. These represent the capacitance of the first capacitor and the capacitance of the second capacitor, respectively.

[0024] Further, determining the effective frequency band based on the preset low-pass response includes:

[0025] Based on the frequency range corresponding to the preset low-pass response and protection algorithm, an effective frequency band attenuation limit is set;

[0026] Within the frequency band defined from the fundamental frequency to half of the second sampling rate, the amplitude attenuation of the preset low-pass response is calculated;

[0027] The maximum frequency at which the amplitude attenuation does not exceed the effective frequency band attenuation limit is determined as the upper limit of the effective frequency band, and the upper limit of the effective frequency band is not lower than the fundamental frequency of the power frequency.

[0028] The frequency range from zero frequency to the upper limit of the effective frequency band is defined as the effective frequency band.

[0029] Further, determining the anti-aliasing stopband based on the second sampling rate includes:

[0030] Half of the second sampling rate is defined as the output Nyquist frequency;

[0031] The internal equivalent sampling rate is determined by multiplying the interpolation factor and the first sampling rate, and half of the internal equivalent sampling rate is determined as the upper limit of the stopband.

[0032] The output Nyquist frequency is determined as the stopband start point, and the stopband upper limit is determined as the stopband end point;

[0033] The frequency range between the start and end points of the stopband is defined as the anti-aliasing stopband.

[0034] Further, determining the linear-phase FIR anti-aliasing resampling filter based on the preset group delay threshold includes:

[0035] Calculate the maximum allowed number of odd taps based on the preset group delay threshold and the internal equivalent sampling rate;

[0036] Candidate tap numbers are selected within a range not exceeding the maximum number of odd taps, and linear phase FIR coefficients corresponding to each candidate tap number are designed based on the preset low-pass response and anti-aliasing stopband.

[0037] Calculate the equivalent low-pass amplitude frequency response and group delay of each candidate filter, and verify the power frequency fundamental amplitude error limit, frequency band approximation error limit, anti-aliasing stopband attenuation limit and preset group delay threshold in sequence.

[0038] From the candidate filters that have passed the verification, a linear phase FIR anti-aliasing resampling filter is determined based on the available hardware multiply-accumulate resources and the protection response speed.

[0039] Furthermore, the equivalent low-pass amplitude frequency response of the linear-phase FIR anti-aliasing resampling filter at the input of the protection algorithm satisfies:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] In the formula, Represents the logarithmic function with base 10. Indicates the fundamental frequency of the power frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Indicates the fundamental frequency of the power frequency Preset low-pass response at the target sampling link Indicates the fundamental amplitude error limit. This indicates taking the maximum value. Represents continuous frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Represents continuous frequency In the preset low-pass response of the target sampling link, Indicates the effective frequency band. This indicates the effective frequency band approximation error limit. Indicates the preset passband reference amplitude. Indicates the anti-aliasing stopband attenuation limit. Indicates the first sampling rate. Indicates the second sampling rate. Indicates the internal equivalent sampling rate. Indicates the interpolation factor. Indicates the extraction multiplier. Indicates fixed group delay. This indicates the preset group delay threshold. This indicates taking the absolute value. This indicates the number of taps in a linear-phase FIR anti-aliasing resampling filter. , This indicates the delay order of the symmetric linear-phase FIR anti-aliasing resampling filter. This represents the sampling rate factor when the delay order is converted into group delay.

[0046] Furthermore, using the linear-phase FIR anti-aliasing resampling filter, rational resampling is performed on the first sampling rate sample data at the protection device side based on the multiphase FIR structure, according to the interpolation factor and decimation factor, to output the second sampling rate sample value, and fixed group delay compensation and time scale correction are performed on the second sampling rate sample value, including:

[0047] On the protection device side, the linear phase FIR coefficients corresponding to the linear phase FIR anti-aliasing resampling filter are moduloed by the interpolation factor according to the coefficient number, and then split into sub-filters with the same number of interpolation factors based on the multiphase FIR structure.

[0048] The product of the current output sample number and the decimation factor is modulo the interpolation factor, and the remainder is used to determine the current output phase. The input sampling reference position is determined based on the integer division result of the product and the interpolation factor.

[0049] Based on the current output phase and the input sampling reference position, an input sampling value window and corresponding sub-filter coefficients are selected from the first sampling rate sample data, and multiply-accumulate operations are performed based on the polyphase FIR structure.

[0050] The result of the multiplication and addition operation is rounded and saturated, and the sampled value at the second sampling rate is output.

[0051] Obtain the output sample number and output sampling time base corresponding to the sampled value at the second sampling rate;

[0052] Obtain the fixed group delay and optional hardware processing delay of the linear phase FIR anti-aliasing resampling filter;

[0053] Based on the output sample number, output sampling time base, fixed group delay, and optional hardware processing delay, the equivalent sampling time is calculated, and the equivalent sampling time is written into the output timestamp of the corresponding second sampling rate sample value to obtain the second sampling rate sample value after fixed group delay compensation and timestamp correction.

[0054] Furthermore, the equivalent sampling time is expressed as:

[0055] ;

[0056] In the formula, Indicates the first The equivalent sampling time corresponding to each output sample Indicates the output sampling time reference. This indicates the optional hardware processing delay.

[0057] Furthermore, the multiphase FIR structure includes:

[0058] An input sampling buffer is used to receive the sampled value data of the first sampling rate and store the sequence of input sampled value data participating in the multiply-accumulate operation of the current output phase. The input sampled value data sequence is output to the multiply-accumulate pipeline according to the input sampling buffer read address generated by the output phase scheduler.

[0059] The output phase scheduler is used to take the modulus of the interpolation factor based on the product of the current output sample number and the decimation factor, generate the current output phase with the remainder result, and generate the input sampling buffer read address and coefficient read address with the integer division result.

[0060] The coefficient memory is used to store the fixed-point coefficients of each sub-filter in Q-format signed integers according to the output phase, and synchronously output the current sub-filter coefficients to the multiply-accumulate pipeline according to the coefficient read address.

[0061] A multiply-accumulate pipeline is used to perform multiply-accumulate operations on the input sampled value data sequence and the coefficients of the current sub-filter to obtain the multiply-accumulate operation result; wherein, the pipeline stage number and the number of clock cycles consumed by the multiply-accumulate pipeline are used to calculate the hardware processing delay;

[0062] The rounding saturation unit is used to scale, round, and saturate the multiplication and addition operation result according to the number of decimal places in the Q format, and output the data bit width to the second sampling rate sampling value;

[0063] The three-phase synchronous output interface is used to output the second sampling rate sampled value according to the data bit width of the sampled value at the second sampling rate.

[0064] The output time stamp compensation unit is used to obtain the fixed group delay of the linear phase FIR anti-aliasing resampling filter and the hardware processing delay of the multiply-accumulate pipeline, and calculate the equivalent sampling time according to the current output sample number, the output sampling time reference, the fixed group delay and the hardware processing delay, and write the equivalent sampling time into the output time stamp of the corresponding second sampling rate sample value.

[0065] The output phase scheduler is connected to the input sampling buffer, the coefficient memory, and the multiply-accumulate pipeline, respectively. The output terminals of the input sampling buffer and the coefficient memory are connected to the input terminal of the multiply-accumulate pipeline. The multiply-accumulate pipeline, the rounding saturation unit, the output time scale compensation unit, and the three-phase synchronous output interface are connected in sequence.

[0066] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0067] 1. This invention constrains the equivalent low-pass amplitude-frequency response of the linear-phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm to meet a preset frequency band approximation error limit within the effective frequency band, based on a preset low-pass response. This ensures that the amplitude-frequency characteristics of the digital filtering stage match the amplitude-frequency characteristics of the preceding analog low-pass circuit, avoiding amplitude-frequency response distortion within the effective frequency band caused by the independent design of the digital filter. Simultaneously, by jointly constraining the filter coefficients through preset fundamental amplitude error limits, preset stopband attenuation limits, and preset group delay thresholds, the filter group delay is limited to the acceptable range of the protection algorithm while ensuring the accuracy of fundamental measurement and anti-aliasing performance. Combined with fixed group delay compensation and time scale correction for the resampled output sample value, this invention achieves coordinated amplitude-frequency matching between the analog and digital links and accurate positioning of the output time scale during low-delay rational resampling on the protection device side.

[0068] 2. This invention approximates the target by using the preset low-pass response of the pre-amplitude analog low-pass circuit of the protection device as the amplitude-frequency response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm. The preset low-pass response is normalized to establish the preset low-pass response of the target sampling link. This enables the digital resampling link and the pre-amplitude analog low-pass circuit to form a cooperative amplitude-frequency match within the effective frequency band, reducing the amplitude-frequency response difference between the two types of sampling links at the entry point of the protection algorithm and avoiding amplitude-frequency response distortion within the effective frequency band caused by the independent design of the digital filter.

[0069] 3. This invention defines half of the second sampling rate as the output Nyquist frequency and uses it as the stopband start point. The internal equivalent sampling rate is determined by the product of the interpolation factor and the first sampling rate, and half of the internal equivalent sampling rate is used as the upper limit of the stopband. The frequency range between the stopband start point and the stopband end point is defined as the anti-aliasing stopband. The number of taps of the linear phase FIR anti-aliasing resampling filter is jointly constrained by the preset group delay threshold. A verifiable engineering constraint is formed between the fundamental wave measurement accuracy, the anti-aliasing stopband attenuation and the protection response speed, which overcomes the aliasing risk caused by the mismatch between the analog low-pass fixed cutoff frequency and the digital resampling stopband when the protection device focuses on resampling.

[0070] 4. This invention employs a multiphase FIR structure to split the linear phase FIR coefficients into sub-filter banks by taking the modulus of the interpolation multiple according to the coefficient number. Rational resampling is performed based on the current output phase and the input sampling reference position. The fixed group delay and hardware processing delay of the linear phase FIR anti-aliasing resampling filter are obtained, and the output sample value is time-stamped. The equivalent sampling time is written into the output timestamp of the corresponding second sampling rate sample value. The resampling process eliminates the measurement error caused by the inconsistency of the sampling timestamps between phases. Attached Figure Description

[0071] Figure 1This is a flowchart illustrating a low-delay anti-aliasing resampling method for the protection device side provided in an embodiment of the present invention;

[0072] Figure 2 This is a flowchart comparing the traditional sampling link and the target sampling link provided in the embodiments of the present invention;

[0073] Figure 3 This is a schematic diagram of the equivalent structure of rational resampling provided in an embodiment of the present invention;

[0074] Figure 4 This is a schematic diagram showing the comparison results of the amplitude-frequency characteristics of the FIR anti-aliasing resampling filter under different preset group delay thresholds provided in the embodiments of the present invention. Detailed Implementation

[0075] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0076] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0077] Example 1

[0078] like Figure 1 As shown in the figure, this embodiment introduces a low-delay anti-aliasing resampling method on the protection device side, including:

[0079] Step 1: Obtain the first sampling rate sampled data output by the merging unit.

[0080] This embodiment directly obtains the first sampling rate sampled value data output by the merging unit, eliminating the need for an additional analog sampling pre-circuit on the protection device side, avoiding additional amplitude-frequency distortion and delay introduced by secondary signal conditioning, maintaining the integrity of the original sampling timing, and providing an original data reference consistent with the timing of the merging unit output for resampling.

[0081] Step 2: Based on the design parameters of the pre-simulated low-pass circuit of the protection device, establish the preset low-pass response of the target sampling link.

[0082] In this embodiment, the preset low-pass response is used as the amplitude-frequency response approximation target of the digital resampling filter at the entry point of the protection algorithm. This enables the digital resampling stage and the pre-amplifier analog low-pass circuit to form a cooperative amplitude-frequency match within the effective frequency band, reducing the amplitude-frequency response difference between the two types of sampling links at the entry point of the protection algorithm and avoiding amplitude-frequency response distortion within the effective frequency band caused by the independent design of the digital filter.

[0083] Step 3: Use the target sampling rate of the protection algorithm as the second sampling rate to determine the fundamental frequency of the power system and set a preset group delay threshold.

[0084] This embodiment provides fundamental frequency accuracy constraints and group delay boundary conditions for the design of a linear phase FIR anti-aliasing resampling filter, enabling the filter design to limit the group delay to an acceptable range for the protection response speed while meeting the fundamental frequency measurement accuracy requirements of the protection algorithm.

[0085] Step 4: Determine the effective frequency band based on the preset low-pass response.

[0086] This embodiment sets an effective bandwidth attenuation limit based on the frequency range corresponding to the preset low-pass response and protection algorithm. The amplitude attenuation of the preset low-pass response is calculated within the bandwidth defined by the fundamental frequency to half of the second sampling rate. The maximum frequency at which the amplitude attenuation does not exceed the effective bandwidth attenuation limit is determined as the upper limit of the effective bandwidth, and the upper limit of the effective bandwidth is not lower than the fundamental frequency. The frequency range between zero frequency and the upper limit of the effective bandwidth is determined as the effective bandwidth. This ensures that the definition of the effective bandwidth is related to the actual amplitude-frequency characteristics of the front-end analog low-pass circuit, and that the effective bandwidth range meets both the bandwidth requirements of the protection algorithm and the actual passband capability of the analog channel.

[0087] Step 5: Determine the anti-aliasing stopband based on the second sampling rate.

[0088] In this embodiment, half of the second sampling rate is defined as the output Nyquist frequency. The internal equivalent sampling rate is determined by multiplying the interpolation factor and the first sampling rate. Half of the internal equivalent sampling rate is defined as the upper limit of the stopband. The output Nyquist frequency is defined as the start point of the stopband, and the upper limit of the stopband is defined as the end point of the stopband. The frequency range between the start point and the end point of the stopband is defined as the anti-aliasing stopband. The definition of the anti-aliasing stopband is associated with the interpolation factor and decimation factor of rational resampling. The frequency range that high-frequency components may fold into the frequency band of interest of the protection algorithm during downsampling is constrained as the stopband, reducing the risk of high-frequency components folding into the effective frequency band during downsampling.

[0089] Step 6: Determine the linear phase FIR anti-aliasing resampling filter based on the preset group delay threshold.

[0090] In this embodiment, the equivalent low-pass amplitude-frequency response and the preset low-pass response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm meet the preset fundamental amplitude error limit at the power frequency fundamental frequency, meet the preset frequency band approximation error limit within the effective frequency band, meet the preset stopband attenuation limit within the anti-aliasing stopband, and the group delay of the linear phase FIR anti-aliasing resampling filter is not greater than the preset group delay threshold.

[0091] This embodiment calculates the maximum allowable number of odd taps based on a preset group delay threshold and an internal equivalent sampling rate. Candidate tap numbers are selected within a range not exceeding this maximum. Linear phase FIR coefficients corresponding to each candidate tap number are designed based on a preset low-pass response and anti-aliasing stopband. The equivalent low-pass amplitude-frequency response and group delay of each candidate filter are calculated. The fundamental frequency amplitude error limit, band approximation error limit, stopband attenuation limit, and preset group delay threshold are verified sequentially. From the verified candidate filters, a linear phase FIR anti-aliasing resampling filter is determined based on available hardware multiply-accumulate resources and protection response speed. This ensures that the filter coefficients form progressively verifiable engineering constraints between fundamental frequency measurement accuracy, effective band amplitude-frequency approximation, anti-aliasing stopband attenuation, and protection response speed, guaranteeing that the filter meets the comprehensive requirements of the protection algorithm for amplitude-frequency characteristics and delay under all constraints.

[0092] Step 7: Using the linear phase FIR anti-aliasing resampling filter, rational resampling is performed on the first sampling rate sampled data at the protection device side according to the interpolation multiple and the decimation multiple, and the second sampling rate sampled value is output. Fixed group delay compensation and time stamp correction are then performed on the second sampling rate sampled value.

[0093] In this embodiment, the first sampling rate is higher than the second sampling rate. This embodiment ensures that the sampled values ​​output by resampling are precisely aligned to the original sampling time axis in terms of timing, eliminating the impact of fixed group delay and hardware processing delay on the offset of sampling time, and providing time-stamped sampled data for the protection algorithm.

[0094] Example 2

[0095] Similar to the inventive concept of Embodiment 1, this invention introduces the implementation steps of a low-delay anti-aliasing resampling method on the protection device side. The method is set between the output sampled data of the merging unit and the input of the protection algorithm, and performs the following steps without changing the pre-amplified analog low-pass loop of the merging unit and the main criterion of the protection algorithm:

[0096] like Figure 2As shown, this embodiment can compensate for the difference in the pre-pass low-pass of the traditional sampling link and the target sampling link on the protection device side without changing the merging unit and the main criterion of the protection algorithm, and suppress high-frequency components that may fold into the frequency band of interest of the protection algorithm before downsampling.

[0097] Step 1: Obtain the first sampling rate sampled data output by the merging unit.

[0098] Step 2: Based on the design parameters of the pre-simulated low-pass circuit of the protection device, establish the preset low-pass response of the target sampling link.

[0099] Step 2.1: Based on the design parameters of the low-pass circuit of the protection device's front-end simulation, extract the parameter set that can determine the low-pass characteristics of the circuit.

[0100] Step 2.2: Based on the circuit topology of the pre-amplified low-pass loop of the protection device and the parameter set, establish the continuous domain transfer function of the pre-amplified low-pass loop of the protection device.

[0101] In this embodiment, the pre-amplified low-pass circuit of the protection device is configured as being composed of... , , and The constructed second-order RC ladder network has an output stage input impedance relative to... Large enough. The continuous-domain transfer function, established based on the node voltage relationships, is expressed as:

[0102] ;

[0103] In the formula, This represents the continuous domain transfer function when the pre-amplifier analog low-pass circuit of the protection device is an RC low-pass circuit. Represents the complex frequency variable in the Laplace domain. Represents complex frequency variable Multiply by the sum of the resistance and capacitance time constants, These represent the resistance values ​​of the first resistor and the second resistor, respectively. These represent the capacitance of the first capacitor and the capacitance of the second capacitor, respectively.

[0104] Step 2.3: Substitute the Laplace domain complex frequency variable into the continuous domain transfer function according to the sinusoidal steady-state frequency mapping relationship to obtain the frequency response of the front-end simulated low-pass circuit of the protection device.

[0105] Step 2.4: Normalize the amplitude of the frequency response to establish the preset low-pass response of the target sampling link.

[0106] This embodiment makes The preset low-pass response of the target sampling link is obtained by normalizing the DC amplitude, where, Represents the imaginary unit. The preset low-pass response of the target sampling link, representing a continuous frequency in Hertz, is expressed as:

[0107] ;

[0108] In the formula, Represents continuous frequency In the preset low-pass response of the target sampling link, This represents the complex frequency response obtained by substituting the sinusoidal steady-state frequency mapping relationship into the continuous domain transfer function. This represents the DC response of the continuous-domain transfer function at zero frequency. This indicates taking a complex value.

[0109] In this embodiment, a traditional pre-pass low-pass response with a cutoff frequency of approximately 275Hz can be used as a reference; this value is only for specific implementation configurations. For different orders or other RC network topologies, this embodiment establishes a continuous domain transfer function according to the corresponding circuit node relationships and performs the same complex frequency variable substitution and amplitude normalization processing. Therefore, the preset low-pass response of the target sampling link is determined by a verifiable circuit topology and parameter set, rather than simply replacing the complete amplitude-frequency response with the cutoff frequency parameter.

[0110] In this embodiment, when the front-end analog low-pass circuit of the protection device is an RC low-pass circuit, the design parameters include the cutoff frequency and filter order of the RC low-pass circuit, and / or the cutoff frequency and RC parameters of the RC low-pass circuit.

[0111] Step 3: Use the target sampling rate of the protection algorithm as the second sampling rate to determine the fundamental frequency of the power system and set a preset group delay threshold.

[0112] In this embodiment, the first sampling rate is higher than the second sampling rate. The first sampling rate is 4kHz, the second sampling rate is 1.2kHz, the interpolation factor is 3, the decimation factor is 10, the internal equivalent sampling rate is 12kHz, and the power frequency fundamental frequency is 50Hz. The processing on the protection device side is equivalent to performing linear phase FIR low-pass filtering at the 12kHz internal equivalent sampling rate, and then outputting a set of sampled values ​​every 10 internal equivalent sampling intervals.

[0113] Step 4: Determine the effective frequency band based on the preset low-pass response.

[0114] Step 4.1: Set the effective frequency band attenuation limit according to the frequency range corresponding to the preset low-pass response and protection algorithm.

[0115] Step 4.2: Calculate the amplitude attenuation of the preset low-pass response within the frequency band defined by the fundamental frequency to half of the second sampling rate.

[0116] Step 4.3: Determine the maximum frequency at which the amplitude attenuation does not exceed the effective frequency band attenuation limit as the upper limit of the effective frequency band, and the upper limit of the effective frequency band shall not be lower than the fundamental frequency of the power frequency.

[0117] Step 4.4: Determine the frequency range from zero frequency to the upper limit of the effective frequency band as the effective frequency band.

[0118] In this embodiment, the upper limit of the effective frequency band and the effective frequency band are respectively represented as:

[0119] ;

[0120] ;

[0121] In the formula, Indicates the upper limit of the effective frequency band. Represents the maximum value function. Indicates continuous frequency. Indicates the fundamental frequency of the power frequency. Indicates the second sampling rate. Represents the logarithmic function with base 10. Represents continuous frequency In the preset low-pass response of the target sampling link, Indicates the effective frequency band. Indicates the effective bandwidth attenuation limit. Indicates the effective frequency band.

[0122] In this embodiment, if the upper limit of the frequency range of interest of the protection algorithm is lower than the upper limit of the effective frequency band determined according to the preset low-pass response, the upper limit of the frequency range of interest of the protection algorithm can be used as the upper limit of the effective frequency band; after determining the upper limit of the effective frequency band in the selected manner, it is confirmed that the power frequency fundamental frequency is included in the effective frequency band.

[0123] Step 5: Determine the anti-aliasing stopband based on the second sampling rate.

[0124] Step 5.1: Define half of the second sampling rate as the output Nyquist frequency.

[0125] Step 5.2: Determine the internal equivalent sampling rate based on the product of the interpolation factor and the first sampling rate, and determine half of the internal equivalent sampling rate as the upper limit of the stopband.

[0126] Step 5.3: Determine the output Nyquist frequency as the stopband start point and the stopband upper limit as the stopband end point.

[0127] Step 5.4: Determine the frequency range between the start and end points of the stopband as the anti-aliasing stopband.

[0128] In this embodiment, the anti-aliasing stopband is represented as:

[0129] ;

[0130] In the formula, Indicates anti-aliasing stopband. Indicates the second sampling rate. Indicates the internal equivalent sampling rate. Indicates the interpolation factor. This indicates the first sampling rate. In this embodiment, the internal equivalent sampling rate is 12kHz, the output Nyquist frequency is 600Hz, the upper limit of the stopband is 6kHz, and the anti-aliasing stopband is [600Hz, 6kHz].

[0131] In this embodiment, the maximum stopband gain of the candidate linear phase FIR anti-aliasing resampling filter is constrained within the anti-aliasing stopband, so that high-frequency components in the first sampling rate sampled data that cannot be characterized by the second sampling rate are suppressed before downsampling.

[0132] Step 6: Determine the linear phase FIR anti-aliasing resampling filter based on the preset group delay threshold.

[0133] Step 6.1: Calculate the maximum allowed number of odd taps based on the preset group delay threshold and the internal equivalent sampling rate.

[0134] Step 6.2: Select candidate tap numbers within a range not exceeding the maximum number of odd taps, and design the linear phase FIR coefficients corresponding to each candidate tap number based on the preset low-pass response and anti-aliasing stopband.

[0135] Step 6.3: Calculate the equivalent low-pass amplitude frequency response and group delay of each candidate filter, and verify the power frequency fundamental amplitude error limit, frequency band approximation error limit, anti-aliasing stopband attenuation limit and preset group delay threshold in sequence.

[0136] Step 6.4: From the candidate filters that have passed the verification, determine the linear phase FIR anti-aliasing resampling filter based on the available hardware multiply-accumulate resources and protection response speed.

[0137] like Figure 4As shown, under different preset group delay thresholds given in this embodiment, each candidate FIR anti-aliasing resampling filter approximates the preset low-pass response of the target conventional sampling link within the effective frequency band; as the number of allowed taps increases, the anti-aliasing stopband attenuation is enhanced, enabling the fixed engineering configuration to be selected based on the protection response speed, available multiply-accumulate resources, and stopband attenuation requirements.

[0138] This embodiment uses the number of taps of the linear-phase FIR anti-aliasing resampling filter as a design variable and applies symmetric constraints to the linear-phase FIR coefficients. The zero-phase amplitude-frequency function is used to represent the amplitude design variable of the candidate linear-phase FIR anti-aliasing resampling filter. Specifically, the number of taps is set... and apply Given the symmetric constraints, the amplitude design variable of the candidate filter is represented by a zero-phase amplitude-frequency function, where... This indicates the number of taps in a linear-phase FIR anti-aliasing resampling filter. This represents the half-order of a symmetric linear-phase FIR filter, and its value is [value missing]. , This represents the linear phase FIR coefficient corresponding to the current coefficient index. Indicates and Linear phase FIR coefficients symmetrical about the center tap.

[0139] In this embodiment, the zero-phase amplitude-frequency function is expressed as:

[0140] ;

[0141] In the formula, Represents the zero-phase amplitude-frequency function. Indicates the center tap coefficient. The symmetry coefficient, which is determined by the summation index, represents the distance from the center tap. This represents the index of the summation of positive integers from 1 to half-order. This represents the cosine function.

[0142] In this embodiment, the desired response is the preset low-pass response within the effective frequency band and zero within the anti-aliasing stopband. A weighted squared error objective function is constructed according to the preset frequency band weights, and the linear phase FIR coefficients that minimize the objective function are solved. This ensures that the actual amplitude-frequency response of the candidate linear phase FIR anti-aliasing resampling filter approaches the preset low-pass response within the effective frequency band and approaches zero response within the anti-aliasing stopband.

[0143] In this embodiment, the weighted squared error objective function is expressed as:

[0144] ;

[0145] ;

[0146] In the formula, This represents the operation on the coefficient vector that minimizes the weighted squared error within the parentheses. This represents a coefficient vector consisting of mutually independent symmetric linear phase FIR coefficients. Indicates the first Discrete frequency sampling points, Indicates the first frequency band within the effective frequency band Non-negative weights for each discrete frequency sampling point Indicates the first frequency band within the effective frequency band The target response approximation error at discrete frequency points Indicates the first anti-aliasing stopband within the band. Non-negative weights for each discrete frequency sampling point Indicates the first anti-aliasing stopband within the band. Zero-phase amplitude of candidate filters at discrete frequency points Indicates the candidate filter in the th Zero-phase amplitude-frequency response at discrete frequency sampling points Indicates the target sampling link in the th order. Preset low-pass amplitude frequency response at each discrete frequency sampling point.

[0147] In this embodiment, the equivalent low-pass amplitude-frequency response and the preset low-pass response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm meet the preset fundamental amplitude error limit at the power frequency fundamental frequency, meet the preset frequency band approximation error limit within the effective frequency band, meet the preset stopband attenuation limit within the anti-aliasing stopband, and the group delay of the linear phase FIR anti-aliasing resampling filter is not greater than the preset group delay threshold.

[0148] In this embodiment, after solving the weighted squared error objective function to obtain candidate coefficients, the zero-phase amplitude-frequency response of the candidate filter at zero frequency is first calculated. All candidate coefficients are then uniformly scaled according to this response value to make the normalized zero-frequency response equal to 1. The fundamental frequency amplitude error, the maximum effective bandwidth approximation error, and the minimum anti-aliasing stopband attenuation are calculated on an independent dense frequency grid. Only when the fundamental frequency amplitude error, the maximum effective bandwidth approximation error, the minimum anti-aliasing stopband attenuation, and the group delay all meet their respective preset limits are the corresponding tap number and linear phase FIR coefficients determined as candidate configurations.

[0149] In this embodiment, the equivalent low-pass amplitude frequency response of the linear-phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm satisfies:

[0150] ;

[0151] ;

[0152] ;

[0153] ;

[0154] ;

[0155] In the formula, Represents the logarithmic function with base 10. Indicates the fundamental frequency of the power frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Indicates the fundamental frequency of the power frequency Preset low-pass response at the target sampling link Indicates the fundamental amplitude error limit. This indicates taking the maximum value. Represents continuous frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Represents continuous frequency In the preset low-pass response of the target sampling link, Indicates the effective frequency band. This indicates the effective frequency band approximation error limit. Indicates the preset passband reference amplitude. Indicates the anti-aliasing stopband attenuation limit. Indicates the first sampling rate. Indicates the second sampling rate. Indicates the internal equivalent sampling rate. Indicates the interpolation factor. Indicates the extraction multiplier. Indicates fixed group delay. This indicates the preset group delay threshold. This indicates taking the absolute value. This indicates the number of taps in a linear-phase FIR anti-aliasing resampling filter. , This indicates the delay order of the symmetric linear-phase FIR anti-aliasing resampling filter. This represents the sampling rate factor when the delay order is converted into group delay.

[0156] Step 7: Using the linear phase FIR anti-aliasing resampling filter, rational resampling is performed on the first sampling rate sampled data at the protection device side according to the interpolation multiple and the decimation multiple, and the second sampling rate sampled value is output. Fixed group delay compensation and time scale correction are then performed on the second sampling rate sampled value.

[0157] This embodiment establishes the multiphase calculation relationship according to the order of coefficient phase separation, output phase determination, input sampling reference position determination, and sub-filter multiplication and addition. Let the normalized linear phase FIR coefficients be... The actual interpolation filter coefficients are Establish a sub-filter for phase r. For the m-th output sample, according to Determine the output phase based on the input sampling reference position corresponding to the current output sample. Determine the input sampling reference position. This indicates rounding down, where the sampled value at the second sampling rate is represented as:

[0158] ;

[0159] In the formula, This indicates the output sample value at the second sampling rate. This represents the product of the sub-filter coefficients corresponding to the current output phase and the corresponding input sample values. This represents the coefficient of the sub-filter corresponding to the current output phase at the current summation index. This represents the sampled value of the input sampling sequence at the current input index. Represents a discrete sequence index.

[0160] In this embodiment, L=3, M=10, the number of sub-filters is 3, and each output sample is obtained by multiplying and adding the sub-filter corresponding to the current output phase with the input sample value window.

[0161] Step 7.1: On the protection device side, the linear phase FIR coefficients corresponding to the linear phase FIR anti-aliasing resampling filter are moduloed by the interpolation factor according to the coefficient number, and the filter is split into sub-filters with the same number of interpolation factors based on the multiphase FIR structure.

[0162] In this embodiment, the multiphase FIR structure includes: an input sampling buffer, used to receive sampled value data at the first sampling rate and store the input sampled value data sequence participating in the current output phase multiplication and addition operation, and output the input sampled value data sequence to the multiply-add pipeline according to the input sampling buffer read address generated by the output phase scheduler; an output phase scheduler, used to take the modulo of the interpolation factor based on the product of the current output sample number and the decimation factor, generate the current output phase with the remainder result, and generate the input sampling buffer read address and coefficient read address with the integer division result; a coefficient memory, used to store the fixed-point coefficients of each sub-filter according to the output phase using Q-format signed integers, and synchronously output the current sub-filter coefficients to the multiply-add pipeline according to the coefficient read address; and a multiply-add pipeline, used to process the input sampled value data sequence and the current sub-filter... The filter coefficients are used to perform multiply-accumulate operations to obtain the result. The pipeline stage number and clock cycles consumed by the multiply-accumulate pipeline are used to calculate the hardware processing delay. A rounding saturation unit is used to scale, round, and saturate the result according to the Q-format decimal places, outputting the data bit width to the second sampling rate sample value. A three-phase synchronous output interface is used to output the second sampling rate sample value according to the data bit width of the second sampling rate sample value. An output time stamp compensation unit is used to obtain the fixed group delay of the linear phase FIR anti-aliasing resampling filter and the hardware processing delay of the multiply-accumulate pipeline, calculate the equivalent sampling time based on the current output sample number, output sampling time reference, the fixed group delay, and the hardware processing delay, and write the equivalent sampling time into the output time stamp of the corresponding second sampling rate sample value.

[0163] The output phase scheduler is connected to the input sampling buffer, the coefficient memory, and the multiply-accumulate pipeline, respectively. The output terminals of the input sampling buffer and the coefficient memory are connected to the input terminal of the multiply-accumulate pipeline. The multiply-accumulate pipeline, the rounding saturation unit, the output time scale compensation unit, and the three-phase synchronous output interface are connected in sequence.

[0164] Step 7.2: Take the modulo of the product of the current output sample number and the decimation factor with the interpolation factor, and determine the current output phase based on the remainder result. Then, determine the input sampling reference position based on the integer division result of the product and the interpolation factor.

[0165] Step 7.3: Based on the current output phase and the input sampling reference position, select the input sampling value window and the corresponding sub-filter coefficients from the first sampling rate sample data, and perform multiply-accumulate operations based on the polyphase FIR structure.

[0166] Figure 3 This is a schematic diagram of the equivalent structure of rational resampling provided in an embodiment of the present invention, as shown below. Figure 3As shown, the multiphase FIR structure only calls the sub-filter corresponding to the current output phase and directly calculates the required input sampling reference position according to the output sampling time, without explicitly generating the internal equivalent sampling sequence after zero-placing. This reduces invalid zero-value multiplication and intermediate data shifting, and keeps the computation path and processing delay of each output sample determined.

[0167] Step 7.4: Round and saturate the result of the multiplication and addition operation, and output the sampled value at the second sampling rate.

[0168] Step 7.5: Obtain the output sample number and output sampling time reference corresponding to the sampled value at the second sampling rate.

[0169] Step 7.6: Obtain the fixed group delay and optional hardware processing delay of the linear phase FIR anti-aliasing resampling filter.

[0170] Step 7.7: Calculate the equivalent sampling time based on the output sample number, output sampling time base, fixed group delay and optional hardware processing delay, and write the equivalent sampling time into the output timestamp of the corresponding second sampling rate sample value to obtain the second sampling rate sample value after fixed group delay compensation and timestamp correction.

[0171] When the protection algorithm adopts the point-by-point sampling mode, the calculated equivalent sampling time is written into the timestamp field of the corresponding second sampling rate sampling value; when the protection algorithm adopts the fixed-cycle data block mode, the fixed group delay and the hardware processing delay are used as a unified delay parameter for aligning the sampling timestamps between the voltage channel and the current channel. The compensation only corrects the fixed timestamp deviation and does not change the amplitude-frequency response of the linear phase FIR anti-aliasing resampling filter.

[0172] In this embodiment, the equivalent sampling time is represented as:

[0173] ;

[0174] In the formula, Indicates the first The equivalent sampling time corresponding to each output sample Indicates the output sampling time reference. This indicates the optional hardware processing delay.

[0175] Example 3

[0176] Based on the same inventive concept as other embodiments, this embodiment describes a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the methods of Embodiment 1 or 2 described above.

[0177] Example 4

[0178] Based on the same inventive concept as other embodiments, this embodiment introduces a computer program product, including computer instructions that, when executed by a processor, implement the steps of the methods described in Embodiment 1 or 2 above.

[0179] In summary, this invention constrains the equivalent low-pass amplitude-frequency response of the linear-phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm to meet a preset frequency band approximation error limit within the effective frequency band, based on a preset low-pass response. This ensures that the amplitude-frequency characteristics of the digital filtering stage match the amplitude-frequency characteristics of the preceding analog low-pass circuit, avoiding amplitude-frequency response distortion within the effective frequency band caused by the independent design of the digital filter. Simultaneously, by jointly constraining the filter coefficients through preset fundamental amplitude error limits, preset stopband attenuation limits, and preset group delay thresholds, the filter group delay is limited to an acceptable range for the protection algorithm while ensuring fundamental measurement accuracy and anti-aliasing performance. Combined with fixed group delay compensation and timescale correction for the resampled output sample value, this invention achieves coordinated amplitude-frequency matching between the analog and digital links and accurate positioning of the output timescale during low-delay rational resampling on the protection device side.

[0180] This invention approximates the target by using the preset low-pass response of the analog low-pass circuit before the protection device as the amplitude-frequency response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm. The preset low-pass response is normalized to establish the preset low-pass response of the target sampling link. This enables the digital resampling link and the analog low-pass circuit before the protection device to form a cooperative amplitude-frequency match within the effective frequency band, reducing the difference in amplitude-frequency response between the two types of sampling links at the entry point of the protection algorithm and avoiding amplitude-frequency response distortion within the effective frequency band caused by the independent design of the digital filter.

[0181] This invention defines half of the second sampling rate as the output Nyquist frequency and uses it as the stopband start point. The internal equivalent sampling rate is determined by the product of the interpolation factor and the first sampling rate, and half of the internal equivalent sampling rate is used as the upper limit of the stopband. The frequency range between the stopband start point and the stopband end point is defined as the anti-aliasing stopband. The number of taps of the linear phase FIR anti-aliasing resampling filter is jointly constrained by a preset group delay threshold. A verifiable engineering constraint is formed between the fundamental wave measurement accuracy, the anti-aliasing stopband attenuation, and the protection response speed. This overcomes the aliasing risk caused by the mismatch between the analog low-pass fixed cutoff frequency and the digital resampling stopband when the protection device focuses on resampling.

[0182] This invention employs a multiphase FIR structure to split the linear-phase FIR coefficients into sub-filter banks by taking the modulus of the interpolation multiple according to the coefficient index. Rational resampling is performed based on the current output phase and the input sampling reference position. The fixed group delay and hardware processing delay of the linear-phase FIR anti-aliasing resampling filter are obtained, and the output sample value is time-stamped. The equivalent sampling time is written into the output timestamp of the corresponding second sampling rate sample value. The resampling process eliminates the measurement error caused by the inconsistency of the sampling timestamps between phases.

[0183] 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.

[0184] 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.

[0185] 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.

[0186] 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.

[0187] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A low-delay anti-aliasing resampling method for protection devices, characterized in that, include: Obtain the first sampling rate sampled value data output by the merging unit; Based on the design parameters of the pre-simulated low-pass circuit of the protection device, a preset low-pass response for the target sampling link is established; The target sampling rate of the protection algorithm is used as the second sampling rate to determine the fundamental frequency of the power system, and a preset group delay threshold is set. The effective frequency band is determined based on the preset low-pass response; The anti-aliasing stopband is determined based on the second sampling rate; A linear phase FIR anti-aliasing resampling filter is determined based on the preset group delay threshold. Wherein, the equivalent low-pass amplitude-frequency response and the preset low-pass response of the linear phase FIR anti-aliasing resampling filter at the entry point of the protection algorithm meet the preset fundamental amplitude error limit at the power frequency fundamental frequency, meet the preset frequency band approximation error limit in the effective frequency band, meet the preset stopband attenuation limit in the anti-aliasing stopband, and the group delay of the linear phase FIR anti-aliasing resampling filter is not greater than the preset group delay threshold; Using the linear phase FIR anti-aliasing resampling filter, rational resampling is performed on the first sampling rate sampled data at the protection device side according to the interpolation multiple and the decimation multiple, and the second sampling rate sampled value is output. Fixed group delay compensation and time stamp correction are performed on the second sampling rate sampled value, wherein the first sampling rate is higher than the second sampling rate.

2. The low-delay anti-aliasing resampling method for the protection device side according to claim 1, characterized in that, Based on the design parameters of the pre-simulated low-pass loop of the protection device, a preset low-pass response for the target sampling link is established, including: Based on the design parameters of the low-pass circuit in the front-end simulation of the protection device, a set of parameters that can determine the low-pass characteristics of the circuit is extracted. Based on the circuit topology of the pre-amplified low-pass loop of the protection device and the parameter set, establish the continuous domain transfer function of the pre-amplified low-pass loop of the protection device. Substituting the Laplace domain complex frequency variable into the continuous domain transfer function according to the sinusoidal steady-state frequency mapping relationship, the frequency response of the front-end analog low-pass circuit of the protection device is obtained. The amplitude of the frequency response is normalized to establish a preset low-pass response for the target sampling link; Wherein, when the front-end analog low-pass circuit of the protection device is an RC low-pass circuit, the design parameters include the cutoff frequency and filter order of the RC low-pass circuit, and / or the cutoff frequency and RC parameters of the RC low-pass circuit.

3. The low-delay anti-aliasing resampling method for the protection device side according to claim 2, characterized in that, The continuous domain transfer function is expressed as: ； In the formula, This represents the continuous domain transfer function when the pre-amplifier analog low-pass circuit of the protection device is an RC low-pass circuit. Represents the complex frequency variable in the Laplace domain. Represents complex frequency variable Multiply by the sum of the resistance and capacitance time constants, These represent the resistance values ​​of the first resistor and the second resistor, respectively. These represent the capacitance of the first capacitor and the capacitance of the second capacitor, respectively.

4. The low-delay anti-aliasing resampling method for the protection device side according to claim 2, characterized in that, Determining the effective frequency band based on the preset low-pass response includes: Based on the frequency range corresponding to the preset low-pass response and protection algorithm, an effective frequency band attenuation limit is set; Within the frequency band defined from the fundamental frequency to half of the second sampling rate, the amplitude attenuation of the preset low-pass response is calculated; The maximum frequency at which the amplitude attenuation does not exceed the effective frequency band attenuation limit is determined as the upper limit of the effective frequency band, and the upper limit of the effective frequency band is not lower than the fundamental frequency of the power frequency. The frequency range from zero frequency to the upper limit of the effective frequency band is defined as the effective frequency band.

5. The low-delay anti-aliasing resampling method for the protection device side according to claim 4, characterized in that, Determining the anti-aliasing stopband based on the second sampling rate includes: Half of the second sampling rate is defined as the output Nyquist frequency; The internal equivalent sampling rate is determined by multiplying the interpolation factor and the first sampling rate, and half of the internal equivalent sampling rate is determined as the upper limit of the stopband. The output Nyquist frequency is determined as the stopband start point, and the stopband upper limit is determined as the stopband end point; The frequency range between the start and end points of the stopband is defined as the anti-aliasing stopband.

6. The low-delay anti-aliasing resampling method for the protection device side according to claim 5, characterized in that, Determining a linear-phase FIR anti-aliasing resampling filter based on the preset group delay threshold includes: Calculate the maximum allowed number of odd taps based on the preset group delay threshold and the internal equivalent sampling rate; Candidate tap numbers are selected within a range not exceeding the maximum number of odd taps, and linear phase FIR coefficients corresponding to each candidate tap number are designed based on the preset low-pass response and anti-aliasing stopband. Calculate the equivalent low-pass amplitude frequency response and group delay of each candidate filter, and verify the power frequency fundamental amplitude error limit, frequency band approximation error limit, anti-aliasing stopband attenuation limit and preset group delay threshold in sequence. From the candidate filters that have passed the verification, a linear phase FIR anti-aliasing resampling filter is determined based on the available hardware multiply-accumulate resources and the protection response speed.

7. The low-delay anti-aliasing resampling method for the protection device side according to claim 6, characterized in that, The equivalent low-pass amplitude frequency response of the linear-phase FIR anti-aliasing resampling filter at the input of the protection algorithm satisfies: ； ； ； ； ； In the formula, Represents the logarithmic function with base 10. Indicates the fundamental frequency of the power frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Indicates the fundamental frequency of the power frequency Preset low-pass response at the target sampling link Indicates the fundamental amplitude error limit. This indicates taking the maximum value. Represents continuous frequency The equivalent low-pass amplitude frequency response at the entry point of the protection algorithm Represents continuous frequency In the preset low-pass response of the target sampling link, Indicates the effective frequency band. This indicates the effective frequency band approximation error limit. Indicates the preset passband reference amplitude. Indicates the anti-aliasing stopband attenuation limit. Indicates the first sampling rate. Indicates the second sampling rate. Indicates the internal equivalent sampling rate. Indicates the interpolation factor. Indicates the extraction multiplier. Indicates fixed group delay. This indicates the preset group delay threshold. This indicates taking the absolute value. This indicates the number of taps in a linear-phase FIR anti-aliasing resampling filter. , This indicates the delay order of the symmetric linear-phase FIR anti-aliasing resampling filter. This represents the sampling rate factor when the delay order is converted into group delay.

8. The low-delay anti-aliasing resampling method for the protection device side according to claim 7, characterized in that, The linear-phase FIR anti-aliasing resampling filter, based on a multiphase FIR structure, performs rational resampling on the first sampling rate sample data at the protection device side according to the interpolation factor and decimation factor, outputs the second sampling rate sample value, and performs fixed group delay compensation and time-scale correction on the second sampling rate sample value, including: On the protection device side, the linear phase FIR coefficients corresponding to the linear phase FIR anti-aliasing resampling filter are moduloed by the interpolation factor according to the coefficient number, and then split into sub-filters with the same number of interpolation factors based on the multiphase FIR structure. The product of the current output sample number and the decimation factor is modulo the interpolation factor, and the remainder is used to determine the current output phase. The input sampling reference position is determined based on the integer division result of the product and the interpolation factor. Based on the current output phase and the input sampling reference position, an input sampling value window and corresponding sub-filter coefficients are selected from the first sampling rate sample data, and multiply-accumulate operations are performed based on the polyphase FIR structure. The result of the multiplication and addition operation is rounded and saturated, and the sampled value at the second sampling rate is output. Obtain the output sample number and output sampling time base corresponding to the sampled value at the second sampling rate; Obtain the fixed group delay and optional hardware processing delay of the linear phase FIR anti-aliasing resampling filter; Based on the output sample number, output sampling time base, fixed group delay, and optional hardware processing delay, the equivalent sampling time is calculated, and the equivalent sampling time is written into the output timestamp of the corresponding second sampling rate sample value to obtain the second sampling rate sample value after fixed group delay compensation and timestamp correction.

9. The low-delay anti-aliasing resampling method for the protection device side according to claim 8, characterized in that, The equivalent sampling time is expressed as: ； In the formula, Indicates the first The equivalent sampling time corresponding to each output sample Indicates the output sampling time reference. This indicates the optional hardware processing delay.

10. The low-delay anti-aliasing resampling method for the protection device side according to claim 9, characterized in that, The multiphase FIR structure includes: An input sampling buffer is used to receive the sampled value data of the first sampling rate and store the sequence of input sampled value data participating in the multiply-accumulate operation of the current output phase. The input sampled value data sequence is output to the multiply-accumulate pipeline according to the input sampling buffer read address generated by the output phase scheduler. The output phase scheduler is used to take the modulus of the interpolation factor based on the product of the current output sample number and the decimation factor, generate the current output phase with the remainder result, and generate the input sampling buffer read address and coefficient read address with the integer division result. The coefficient memory is used to store the fixed-point coefficients of each sub-filter in Q-format signed integers according to the output phase, and synchronously output the current sub-filter coefficients to the multiply-accumulate pipeline according to the coefficient read address. A multiply-accumulate pipeline is used to perform multiply-accumulate operations on the input sampled value data sequence and the coefficients of the current sub-filter to obtain the multiply-accumulate operation result; wherein, the pipeline stage number and the number of clock cycles consumed by the multiply-accumulate pipeline are used to calculate the hardware processing delay; The rounding saturation unit is used to scale, round, and saturate the multiplication and addition operation result according to the number of decimal places in the Q format, and output the data bit width to the second sampling rate sampling value; The three-phase synchronous output interface is used to output the second sampling rate sampled value according to the data bit width of the sampled value at the second sampling rate. The output time stamp compensation unit is used to obtain the fixed group delay of the linear phase FIR anti-aliasing resampling filter and the hardware processing delay of the multiply-accumulate pipeline, and calculate the equivalent sampling time according to the current output sample number, the output sampling time reference, the fixed group delay and the hardware processing delay, and write the equivalent sampling time into the output time stamp of the corresponding second sampling rate sample value. The output phase scheduler is connected to the input sampling buffer, the coefficient memory, and the multiply-accumulate pipeline, respectively. The output terminals of the input sampling buffer and the coefficient memory are connected to the input terminal of the multiply-accumulate pipeline. The multiply-accumulate pipeline, the rounding saturation unit, the output time scale compensation unit, and the three-phase synchronous output interface are connected in sequence.

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