A method and system for generating a multi-level pseudo-random disturbance signal based on finite field trace

Abstract

The application discloses a kind of multi-level pseudo-random disturbance signal generation method and system based on finite field trace, method includes: according to target level number and expected period, construct extension field;In the extension field, produce extension field element sequence according to selected nonzero base element and coefficient, the extension field element sequence is nonzero extension field element sequence;Extension field element sequence is mapped by applying field trace, so that it is reduced dimension and obtains base field symbol sequence;The base field symbol sequence is converted into symmetric multi-level symbol sequence according to predetermined mapping rule and is expanded into continuous time disturbance signal by zero order, that is, multi-level pseudo-random disturbance signal.This application method can adjust the level number and signal period of disturbance signal as needed, produce spectrum characteristic controllable, cover wide-band disturbance signal, with uniform spectrum line distribution, excellent correlation, simple hardware implementation and the like advantages, facilitate to improve the frequency domain resolution of impedance estimation and reduce injection transient stress.

Description

Technical Field

[0001] This invention belongs to the field of power system measurement and control technology, and in particular relates to a method and system for generating multilevel pseudo-random disturbance signals based on finite domain traces, which can be used for broadband impedance detection, system identification and dynamic characteristic analysis of power grid or power electronic systems. Background Technology

[0002] With the widespread application of new energy power systems and power electronic equipment, the dynamic characteristics of grid impedance in the mid-to-high frequency range have a significant impact on system stability and resonance suppression. Wideband impedance detection technology has become an important tool for studying the electromagnetic stability of power systems and network resonance.

[0003] Existing broadband impedance sensing methods mostly employ multiple sinusoidal signals or binary pseudo-random sequences (PRBS) as perturbation signals. The frequency response function is obtained by injecting these signals and measuring the response signal of the system under test, thus yielding the broadband impedance spectrum. However, existing methods have the following shortcomings:

[0004] (1) Binary sequences can only generate two-level signals (±1), with a fixed spectral distribution and containing even harmonics, which is not good for power systems containing a large number of nonlinear components;

[0005] (2) The generation process of multiple sinusoidal signals is complex and requires comprehensive consideration of peak factor and phase arrangement, which places high demands on hardware implementation cost and software implementation.

[0006] (3) Existing pseudo-random sequence generation methods are mostly based on linear feedback shift registers (LFSRs), whose mathematical basis is limited to the binary base domain GF(2), and it is difficult to extend to multi-level signals;

[0007] (4) For multi-level disturbance signals (e.g. ±2, ±1, 0) often required in power grid or power converter testing, traditional methods lack a systematic generation mechanism and usually rely on empirical design or numerical quantization, resulting in discontinuous test spectrum and low signal-to-noise ratio (SNR). Summary of the Invention

[0008] Purpose of the invention: The purpose of this invention is to provide a method and system for generating multi-level pseudo-random disturbance signals based on finite domain traces, so as to solve the problems of single disturbance signal level and complex hardware implementation in existing broadband impedance detection.

[0009] Technical solution: The method described in this invention includes the following steps:

[0010] The target level number and the extension number are selected according to the predetermined target level number and the desired period, and the generator polynomial of the extension field is constructed based on the target level number and the extension number.

[0011] In the extended field, a non-zero primitive and a coefficient are selected, and an extended field element sequence is generated according to the non-zero primitive and the coefficient according to a predetermined generation rule. The extended field element sequence is a non-zero extended field element sequence.

[0012] The extended field element sequence is reduced in dimension by trace mapping and converted into a base field symbol sequence.

[0013] The base domain symbol sequence is converted into a symmetric multilevel symbol sequence according to a predetermined mapping rule, which includes centering mapping and amplitude normalization.

[0014] The symmetrical multilevel symbol sequence is expanded to obtain a continuous-time perturbation signal, i.e., a multilevel pseudo-random perturbation signal.

[0015] Furthermore, the generator polynomial used to construct the extended field is an irreducible polynomial.

[0016] Furthermore, the generator polynomial used to construct the extended field is a primitive polynomial, and the non-zero primitives of the extended field are primitives.

[0017] Furthermore, the pre-generation rules are as follows:

[0018] ;

[0019] in, For the first element in the extended field sequence One non-zero element, For non-zero primitives, For coefficients, The sequence length is related to the desired period. , For the target level number, This refers to the number of times the domain has been expanded.

[0020] Furthermore, the trace mapping is represented as:

[0021] ;

[0022] in, For trace mapping function, For the first element in the extended field sequence One non-zero element, The sequence length is related to the desired period. , For the target level number, This refers to the number of times the domain has been expanded.

[0023] The result of the trace mapping function is used as the base domain symbol sequence. Base field symbol sequence The values ​​of all belong to the set. .

[0024] Furthermore, the pre-defined mapping rule is expressed as follows:

[0025] ;

[0026] in, It is a symmetrical multilevel symbol sequence. For the base field symbol sequence, For the target level number, It is the modulo operator.

[0027] Furthermore, the symmetrical multi-level symbol sequence is expanded to obtain a continuous-time perturbation signal, i.e., a multi-level pseudo-random perturbation signal, including:

[0028] The symmetric multilevel symbol sequence is expanded using zero-order hold, that is, the expansion is repeated for each symbol. The output is achieved through a digital sampling point and a digital-to-analog converter and hold circuit, where:

[0029] ;

[0030] in, For digital sampling rate, The duration of each symbol, Let be the integer function, and the total number of sampling points after expansion is . .

[0031] The present invention also provides a broadband impedance testing method based on the aforementioned method, comprising:

[0032] The generated multi-level pseudo-random disturbance signal is injected into the object under test, and the response signal of the object under test to the disturbance signal is acquired simultaneously.

[0033] The frequency response of the object under test is calculated based on the response signal, and the broadband impedance spectrum is calculated therefrom for use in broadband impedance detection or system identification.

[0034] Furthermore, based on the response signal, the frequency response of the object under test is calculated using the following formula to calculate the impedance spectrum, which is used for broadband impedance detection or system identification:

[0035] ;

[0036] in, It is a complex-valued function, and its value is given at frequency. The impedance magnitude and phase response of the system, including all frequencies. The result obtained is the broadband impedance spectrum. and These represent the transformation of the synchronously acquired voltage and current time-domain sequences, that is, the Fourier transform of the response signal to obtain the frequency response.

[0037] The present invention also provides a multi-level pseudo-random perturbation signal generation system based on finite domain traces, comprising:

[0038] An extended-domain generator polynomial construction unit is used to select a target level number and an extended-domain degree according to a predetermined target level number and a desired period, and to construct an extended-domain generator polynomial based on the target level number and the extended-domain degree.

[0039] An extended field element sequence generation unit is used to select a non-zero primitive and a coefficient in the extended field, and generate an extended field element sequence according to the non-zero primitive and the coefficient according to a predetermined generation rule. The extended field element sequence is a non-zero extended field element sequence.

[0040] A base field symbol sequence generation unit is used to convert the extended field element sequence into a base field symbol sequence through trace mapping for dimensionality reduction.

[0041] A symmetrical multilevel symbol sequence generation unit is used to convert the base domain symbol sequence into a symmetrical multilevel symbol sequence according to a predetermined mapping rule, the predetermined mapping rule including centering mapping and amplitude normalization;

[0042] A multi-level pseudo-random perturbation signal generation unit is used to expand the symmetrical multi-level symbol sequence to obtain a continuous-time perturbation signal, that is, a multi-level pseudo-random perturbation signal.

[0043] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) Continuous spectral lines and uniform power distribution: By generating extended domain elements in a finite domain and using trace mapping for dimensionality reduction, the multi-level pseudo-random signal obtained by the present invention has an approximately flat power spectral density throughout the entire frequency band of interest, uniform spectral line distribution and no even harmonic components, which can effectively cover a wide frequency range and improve the accuracy of impedance spectrum estimation; (2) Flexible configuration of multi-level structure: The number of sequence levels in the present invention is determined by the base domain parameter p, and the number of levels can be flexibly selected within the hardware capability limit, such as three levels (p=3) or five levels (p=5), to adapt to measurement scenarios with different power levels and injection amplitude limitations; (3) Rigorous mathematical construction and good correlation characteristics: The sequence generation process is based entirely on the algebraic properties of finite fields, which is deterministic and repeatable. The autocorrelation of the resulting sequence is superior, significantly better than the empirically designed multi-level disturbance signal; (4) The hardware implementation is simple: the sequence generation of this invention only relies on finite field addition and multiplication, which can be achieved by table lookup or simple register operation. It is suitable for microcontroller, DSP and FPGA platforms, and can realize high-performance wideband disturbance signal generation under limited resource conditions; (5) It is suitable for wideband impedance detection of power grid and power converter: the multi-level disturbance signal is injected into the system under test through the output interface and the response signal is collected. The frequency response function and impedance spectrum of the system can be obtained quickly. It is widely applicable to the analysis and system identification of power systems, power electronic devices, energy storage interfaces, etc. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention;

[0045] Figure 2 This is a waveform diagram of Embodiment 1 of the present invention;

[0046] Figure 3 The spectrum diagram of Embodiment 1 of the present invention ( =1 ms);

[0047] Figure 4 This is a waveform diagram of Embodiment 2 of the present invention;

[0048] Figure 5 The spectrum diagram of Embodiment 2 of the present invention ( =1 ms). Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present application will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowcharts, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0050] like Figure 1 As shown, the method of the present invention includes the following steps:

[0051] S1. Select parameters based on the predetermined target level and desired period. With the number of domain expansions and based on the and Construct extended domain The generator polynomial;

[0052] The parameters The target level number is a prime number. It is a positive integer greater than 1.

[0053] Used to construct extended domain The generator polynomial is an irreducible polynomial; preferably, the generator polynomial is a primitive polynomial.

[0054] S2, in the extended domain A non-zero primitive and a coefficient are selected; preferably, the non-zero primitive is a primitive, thereby giving the extended field element sequence the maximum periodicity. And generate an extended field element sequence according to the non-zero primitives and the coefficients according to a predetermined generation rule, wherein the extended field element sequence is a non-zero extended field element sequence;

[0055] The extended field element sequence is formed by the extended field. Selected non-zero primitives With coefficient Generate according to the following relationship;

[0056] ;

[0057] in, For the first element in the extended field sequence One non-zero element, , That is, the sequence length, which is related to the expected period.

[0058] S3. Convert the extended field element sequence into a base field symbol sequence by dimensionality reduction through trace mapping;

[0059] The trace mapping is defined as being derived from the extended field. to base domain mapping That is, for any extended field element ,calculate:

[0060] ;

[0061] in, The trace mapping function is used as the result of the trace mapping function as the base field symbol sequence. Base field symbol sequence The values ​​of all belong to the set. .

[0062] S4. Convert the base domain symbol sequence into a symmetric multilevel symbol sequence according to a predetermined mapping rule;

[0063] The predetermined mapping rules include centering mapping and amplitude normalization. The preferred mapping expression is:

[0064] ;

[0065] in, The base field symbol sequence obtained in step S3, It is the modulo operator, which converts the base field symbol sequence into a modulo operation. Mapped to the symmetric multilevel symbol sequence, i.e. The It can be further scaled by peak value or root mean square (RMS) to meet injection amplitude or power limits.

[0066] S5. Expand the symmetrical multi-level symbol sequence to obtain a continuous-time perturbation signal, that is, a multi-level pseudo-random perturbation signal;

[0067] The symmetrical multilevel symbol sequence is expanded using a zero-order hold (ZOH) to generate a continuous-time perturbation signal, i.e., a multilevel pseudo-random perturbation signal. In digital implementation, the ZOH expansion is preferably performed by repeating the process for each symbol. The output is achieved through a digital sampling point and a digital-to-analog converter (DAC) with a hold circuit, where:

[0068] ;

[0069] in, For digital sampling rate, The duration of each symbol, Let be the integer function, and the total number of sampling points after expansion is . .

[0070] A broadband impedance testing method, comprising:

[0071] (1) The multi-level pseudo-random disturbance signal is injected into the object under test through the output interface and the response signal of the object under test to the multi-level pseudo-random disturbance signal is collected synchronously.

[0072] The multi-level pseudo-random disturbance signal is injected into the object under test through the output interface. The output interface is driven in the form of a voltage source or current source and includes an amplitude conditioning unit, an isolation converter, and a protection unit to meet electrical coupling and safety requirements. The synchronous acquisition shares a clock with the output interface to ensure that the multi-level pseudo-random disturbance signal and the response signal are accurately sampled in time, thereby facilitating the calculation of the frequency response of the object under test based on frequency domain or time domain methods, so as to obtain the impedance spectrum.

[0073] (2) Calculate the frequency response of the object under test based on the response signal and thereby calculate the impedance spectrum for use in broadband impedance detection or system identification;

[0074] Based on the response signal, the frequency response of the object under test is calculated using the following formula to calculate the impedance spectrum, which is used for broadband impedance detection or system identification:

[0075] ;

[0076] in, It is a complex-valued function, with units of ohms, and its value is given at frequency. The impedance magnitude and phase response of the system, including all frequencies. The result obtained is the broadband impedance spectrum. and These represent the transformation of the synchronously acquired voltage and current time-domain sequences, that is, the Fourier transform of the response signal to obtain the frequency response.

[0077] Furthermore, the multi-cycle measurement results can be optionally superimposed and averaged or segmented to improve the signal-to-noise ratio (SNR) and estimation accuracy.

[0078] The present invention discloses a multi-level pseudo-random perturbation signal generation system based on finite domain traces, comprising:

[0079] An extended-domain generator polynomial construction unit is used to select a target level number and an extended-domain degree according to a predetermined target level number and a desired period, and to construct an extended-domain generator polynomial based on the target level number and the extended-domain degree.

[0080] An extended field element sequence generation unit is used to select a non-zero primitive and a coefficient in the extended field, and generate an extended field element sequence according to the non-zero primitive and the coefficient according to a predetermined generation rule. The extended field element sequence is a non-zero extended field element sequence.

[0081] A base field symbol sequence generation unit is used to convert the extended field element sequence into a base field symbol sequence through trace mapping for dimensionality reduction.

[0082] A symmetrical multilevel symbol sequence generation unit is used to convert the base domain symbol sequence into a symmetrical multilevel symbol sequence according to a predetermined mapping rule, the predetermined mapping rule including centering mapping and amplitude normalization;

[0083] A multi-level pseudo-random perturbation signal generation unit is used to expand the symmetrical multi-level symbol sequence to obtain a continuous-time perturbation signal, that is, a multi-level pseudo-random perturbation signal.

[0084] Example Verification 1: Generation of a Three-Level Fourth-Order Pseudo-Random Perturbation Signal ( , ).

[0085] 1. Based on step S1, construct the extended domain according to the selected parameters. If the field contains zero elements, then the total number of elements in the field is [number missing]. There are n elements, and both addition and multiplication are performed modulo 3. The number of selections is 1. primitive polynomial As a generating polynomial, then we have The polynomial in the base field It is irreducible, therefore it can be used as the generator polynomial of the extended field.

[0086] 2. According to step S2, take non-zero primitives. If the root of this generating polynomial is , then we have Take the coefficient Then the generated extended field element sequence is That is, the sequence of non-zero extended field elements contains 80 elements.

[0087] 3. Based on step S3, calculate the trace mapping:

[0088] ;

[0089] For ease of explanation, only the base field symbol sequence will be calculated below. The first three items are from We can obtain:

[0090] ;

[0091] Then according to the trace mapping function ,get

[0092] ;

[0093] ;

[0094] ;

[0095] That is, to obtain The first three items By calculating in sequence, a base field symbol sequence of length 80 can be obtained. ;

[0096] 4. Based on step S4, obtain the mapping from the predetermined rules. Obtain a symmetric three-level fourth-order symbol sequence ;

[0097] 5. Following step S5, expand the symmetrical three-level fourth-order symbol sequence into a continuous-time perturbation signal, such as... Figure 2 As shown ( Figure 2 After normalizing the peak value to 1), its frequency characteristics are as follows: Figure 3 As shown, there are no even-order harmonic components, and a continuous perturbation voltage or current signal can be generated through the output interface for wideband impedance testing.

[0098] Example Verification 2: Generation of a Five-Level Third-Order Pseudo-Random Perturbation Sequence ( , ).

[0099] 1. Based on step S1, construct the extended domain according to the selected parameters. If the field contains zero elements, then the total number of elements in the field is [number missing]. There are n elements, and both addition and multiplication are performed modulo 5. The number of selections is 1. primitive polynomial As a generating polynomial, then we have The polynomial in the extended field It is irreducible, therefore it can be used as the generator polynomial of the extended field.

[0100] 2. According to step S2, take non-zero primitives. If the root of this generating polynomial is , then we have Take the coefficient Then the generated extended field element sequence is That is, the sequence of non-zero extended field elements contains 124 elements.

[0101] 3. Based on step S3, calculate the trace mapping:

[0102] ;

[0103] For ease of explanation, only the base field symbol sequence will be calculated below. The first three items are from We can obtain:

[0104] ;

[0105] Then according to the trace mapping function ,get

[0106] ;

[0107] ;

[0108] ;

[0109] That is, to obtain The first three items By calculating in sequence, a base field symbol sequence of length 124 can be obtained. ;

[0110] 4. Based on step S4, obtain the mapping from the predetermined rules. Obtain a symmetric five-level third-order symbol sequence ;

[0111] 5. Following step S5, expand the symmetrical five-level third-order symbol sequence into a continuous-time perturbation signal, such as... Figure 4 As shown ( Figure 4 After normalizing the peak value to 1), its frequency domain characteristics are as follows: Figure 5 As shown, there are no even-order harmonic components, and a continuous perturbation voltage or current signal can be generated through the output interface for wideband impedance testing.

[0112] This invention utilizes the extended finite field structure and its trace mapping characteristics to mathematically construct a multi-level pseudo-random sequence with strict uniformity and good autocorrelation properties. It enables efficient generation of multi-level signals under limited hardware resources, making it suitable for applications such as broadband impedance detection in power grids, power converter modeling, and system identification. It can generate signals with ideal broadband spectral characteristics under limited hardware resources, while also considering signal amplitude control and multi-level output characteristics to meet the application requirements of broadband impedance detection and system identification in power grids. This method is used for broadband impedance detection and system identification in power grids and power electronic systems. It can adjust the number of levels and the signal period of the disturbance signal as needed, generating a disturbance signal with controllable spectral characteristics and covering a wide frequency band. It has advantages such as uniform spectral distribution, excellent correlation, and simple hardware implementation, which facilitates improving the frequency domain resolution of impedance estimation and reducing injected transient stress. It is suitable for online broadband impedance measurement and system identification scenarios in power systems.

Claims

1. A method for generating multi-level pseudo-random perturbation signals based on finite domain traces, characterized in that, Includes the following steps: The target level number and the extension number are selected according to the predetermined target level number and the desired period, and the generator polynomial of the extension field is constructed based on the target level number and the extension number. In the extended field, a non-zero primitive and a coefficient are selected, and a sequence of extended field elements is generated according to the non-zero primitive and the coefficient based on a predetermined generation rule. The extended field element sequence is a sequence of non-zero extended field elements. The predetermined generation rule is: ； in, For the first element in the extended field sequence One non-zero element, For non-zero primitives, For coefficients, The sequence length is related to the desired period. , For the target level number, For the number of domain expansions; The extended field element sequence is reduced in dimension by trace mapping and converted into a base field symbol sequence. The base domain symbol sequence is converted into a symmetric multilevel symbol sequence according to a predetermined mapping rule, which includes centering mapping and amplitude normalization; the predetermined mapping rule is expressed as follows: ； in, It is a symmetrical multilevel symbol sequence. For the base field symbol sequence, For the target level number, It is the modulo operator; The symmetrical multilevel symbol sequence is expanded to obtain a continuous-time perturbation signal, i.e., a multilevel pseudo-random perturbation signal.

2. The method according to claim 1, characterized in that, The generator polynomial used to construct the extended field is an irreducible polynomial.

3. The method according to claim 1, characterized in that, The generator polynomial used to construct the extended field is the primitive polynomial, and the non-zero primitives of the extended field are primitives.

4. The method according to claim 1, characterized in that, The trace mapping is represented as: ； in, For trace mapping function, For the first element in the extended field sequence One non-zero element, The sequence length is related to the desired period. , For the target level number, For the number of domain expansions; The result of the trace mapping function is used as the base domain symbol sequence. Base field symbol sequence The values ​​of all belong to the set. .

5. The method according to claim 1, characterized in that, Expanding the symmetrical multi-level symbol sequence to obtain a continuous-time perturbation signal, i.e., a multi-level pseudo-random perturbation signal, includes: The symmetric multilevel symbol sequence is expanded using zero-order hold, that is, the expansion is repeated for each symbol. The output is achieved through a digital sampling point and a digital-to-analog converter and hold circuit, where: ； in, For digital sampling rate, The duration of each symbol, Let be the integer function, and the total number of sampling points after expansion is . .

6. A broadband impedance testing method based on any one of claims 1-5, characterized in that, include: The generated multi-level pseudo-random disturbance signal is injected into the object under test, and the response signal of the object under test to the disturbance signal is acquired simultaneously. The frequency response of the object under test is calculated based on the multi-level pseudo-random disturbance signal and the response signal, and the broadband impedance spectrum is calculated from it for broadband impedance detection or system identification.

7. The broadband impedance testing method according to claim 6, characterized in that, Based on the response signal, the frequency response of the object under test is calculated using the following formula to calculate the impedance spectrum, which is used for broadband impedance detection or system identification: ； in, It is a complex-valued function, and its value is given at frequency. The impedance magnitude and phase response of the system, including all frequencies. The result obtained is the broadband impedance spectrum. and These represent the transformation of the synchronously acquired voltage and current time-domain sequences, that is, the Fourier transform of the response signal to obtain the frequency response.

8. A multi-level pseudo-random perturbation signal generation system based on finite domain traces, characterized in that, include: An extended-domain generator polynomial construction unit is used to select a target level number and an extended-domain degree according to a predetermined target level number and a desired period, and to construct an extended-domain generator polynomial based on the target level number and the extended-domain degree. An extended field element sequence generation unit is configured to select a non-zero primitive and a coefficient in the extended field, and generate an extended field element sequence according to the non-zero primitive and the coefficient based on a predetermined generation rule. The extended field element sequence is a sequence of non-zero extended field elements. The predetermined generation rule is as follows: ； in, For the first element in the extended field sequence One non-zero element, For non-zero primitives, For coefficients, The sequence length is related to the desired period. , For the target level number, For the number of domain expansions; A base field symbol sequence generation unit is used to convert the extended field element sequence into a base field symbol sequence through trace mapping for dimensionality reduction. A symmetric multilevel symbol sequence generation unit is used to convert the base domain symbol sequence into a symmetric multilevel symbol sequence according to a predetermined mapping rule. The predetermined mapping rule includes centering mapping and amplitude normalization; the predetermined mapping rule is expressed as follows: ； in, It is a symmetrical multilevel symbol sequence. For the base field symbol sequence, For the target level number, It is the modulo operator; A multi-level pseudo-random perturbation signal generation unit is used to expand the symmetrical multi-level symbol sequence to obtain a continuous-time perturbation signal, that is, a multi-level pseudo-random perturbation signal.

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