Method of multi-frequency impedance measurement based on frequency adaptive selection

Abstract

The present application relates to a kind of multi-frequency impedance measurement methods based on frequency adaptive selection, it is related to power electronic converter impedance measurement technical field, including: according to measurement requirement given frequency range, and set iteration number and initial point number, generate initial impedance measurement frequency point set;Adaptive selection impedance measurement frequency point is through interpolation error calculation algorithm and dynamic average threshold method;All new impedance measurement frequency points are grouped according to odd-even, and the multi-sine signal of two groups of sub-frequency band amplitude is injected into the system to be measured;Based on the impedance data corresponding to all iteration cumulative impedance measurement frequency points, impedance curve is fitted by bilinear mapping and least square method.The present application can realize the adaptive selection of measurement frequency point, solve the problem that the peak or valley of impedance cannot be accurately observed in the traditional equal-frequency interval impedance measurement mode, and can provide important standardized tool and research background for system impedance acquisition and stability analysis.

Description

Technical Field

[0001] This invention relates to the field of impedance measurement technology for power electronic converters, and in particular to a multi-frequency impedance measurement method based on frequency adaptive selection. Background Technology

[0002] To address the climate crisis, building a new power system based on new energy sources is a crucial pathway to promoting a clean and low-carbon energy transition. With the continuous development of power systems and new energy generation technologies, more and more wind power, photovoltaic, and other new energy generation technologies, along with power electronic equipment, are being integrated into the power grid, significantly increasing the degree of power electronics in power systems and forming power electronic power systems. However, due to the low inertia of power electronic equipment and the frequent disturbances to many components of the power system, the operating state of the power system can change significantly when subjected to small disturbances such as random load fluctuations and slow changes in system parameters. Furthermore, the dynamic characteristics of power electronic devices make the stability problem of small disturbances more prominent compared to traditional power systems. Among numerous analytical methods, impedance analysis has become a commonly used method for analyzing system instability mechanisms due to its clear physical concepts, high visualization, and strong research extensibility. This method models the source and load converters of a cascaded system as independent subsystems and represents their port characteristics in the form of impedance. Then, it uses impedance-based stability criteria (such as the Nyquist criterion and norm criterion) to analyze the stability of the cascaded system. Therefore, accurately obtaining the impedance information of the source and carrier ends of the cascaded system helps to analyze the operating status of the converter equipment and provides a basis for online improvement of system stability.

[0003] For the impedance stability analysis methods described above, accurate impedance information of the source and load converters is required. Traditional converter port impedance modeling techniques are complex to derive, especially for multiple converters with input-series-output-parallel (ISOP) or input-parallel-output-series (IPOS) configurations, making modeling extremely complex and tedious. To address this issue, impedance measurement techniques can accurately obtain the port impedances of complex or combined converters, thus avoiding the complex and tedious process of obtaining impedance analytical models. Common impedance measurement schemes are categorized into passive and active techniques based on whether disturbance signals are actively injected. In terms of passive techniques, in grid impedance measurement, passive techniques only require the acquisition and processing of characteristic harmonic signals to achieve impedance estimation. However, this type of scheme is overly dependent on grid events, resulting in lower measurement accuracy. In addition, data-driven impedance measurement technology is gradually emerging. This technology trains artificial intelligence algorithms with a large amount of prior impedance data, then predicts the impedance of converters or power grids at different steady-state operating points, enabling relatively accurate passive impedance information. However, due to the difficulty in acquiring impedance data, it is difficult to generate a large amount of prior impedance data as training data for artificial intelligence algorithms, making the implementation of such methods challenging. In terms of active technologies, research mainly focuses on developing disturbance signal injection devices. To obtain the broadband characteristics of impedance, the injected disturbance signal needs to contain energy information at multiple frequency points. Domestic and international scholars have conducted extensive research and designed a series of disturbance signals that meet this characteristic, such as pseudo-random binary sequences (PRBS), triangular pulse signals, and frequency-varying signals. As research progresses, Discrete Interval Binary Sequences (DIBS), Maximum Length Binary Sequences (MLBS), and Ternary Sequences (TS) have been developed, concentrating energy in specific frequency bands / points and solving the problem of uncontrollable PRBS spectrum. However, these signals contain a large amount of energy from frequencies other than the target frequency band, increasing inter-frequency interference. While frequency-varying signals can limit the spectral distribution range, the problem of insufficient spectral design capability at each frequency point remains unresolved. Compared to the aforementioned signals, the spectral distribution of multiple sinusoidal signals can be flexibly designed and controlled in the time domain, avoiding the complex time-frequency domain conversion process required for other signals, reducing design difficulty, and mitigating signal injection contamination to some extent. These characteristics make them highly applicable to impedance measurement.However, multi-sinusoidal signals with random phases often produce high time-domain peaks. To ensure that the injection of disturbance signals does not affect the steady-state operation of the system, selecting a suitable initial phase set to reduce the signal's time-domain peaks is particularly important. Domestic and international scholars have conducted extensive research on this topic. Considering the large number of independent variables in multi-sinusoidal functions, numerical analytical methods are insufficient to accurately calculate the minimum value of the signal's time-domain peak. Therefore, the Gerchberg-Saxton phase retrieval algorithm from spatial optical field theory was ultimately chosen to map multi-sinusoidal signals with smaller time-domain peaks by searching through frequency-domain phase information. However, the selection criteria for the characteristic harmonic frequencies of multi-sinusoidal signals are not yet clear, the iterative algorithm for the initial phase set has room for improvement, and how to design the synthesized sinusoidal signal requires further research. Furthermore, a significant problem with the traditional principle of equidistant frequency selection for multi-sinusoidal waves is the inability to accurately observe the peak or valley portions of the impedance. In addition, many unnecessary frequency points are measured in relatively flat impedance characteristic regions. Thus, equidistant selection of frequency points leads to poor measurement accuracy and unnecessary resource waste. To improve the accuracy of traditional impedance measurement methods, more measurement points are needed. In other words, for impedance measurement, the two most important indicators, measurement time and measurement accuracy, cannot be improved simultaneously. Patent document CN114520594A discloses a high-power impedance measurement device based on constant-amplitude Chirp perturbation voltage injection. This device injects a constant-amplitude Chirp signal into the circuit, then measures the frequency response of the voltage and current at the corresponding locations, and finally calculates the impedance information of the converter. The Chirp signal allows for freely set frequency bands, and over 90% of the energy is concentrated within the set frequency band. Within the entire set frequency band, the signal amplitude is basically consistent, and the crest factor is low, which is beneficial for signal identification and reduces the impact on the system under test. However, because a large number of perturbation signals in similar frequency bands are injected at once, mutual interference between signals is inevitable. Furthermore, these signals contain a large amount of energy from frequencies other than the measured frequency band, which can affect the stability of the system and consequently compromise the accuracy of the measurement. Summary of the Invention

[0004] To address the technical problems existing in the prior art, the present invention aims to provide a multi-frequency impedance measurement method based on frequency adaptive selection. This method avoids the complex modeling and derivation process in stability analysis, enables adaptive selection of measurement frequency points, and solves the problem that traditional equal-frequency interval impedance measurement methods cannot accurately observe the peak or valley portions of impedance. It provides an important standardized tool and research background for system impedance acquisition and stability analysis.

[0005] To achieve the above-mentioned objectives, this invention provides a multi-frequency impedance measurement method based on frequency adaptive selection, comprising the following steps:

[0006] Step S1: Given the frequency range [f1, f2] according to the measurement requirements, and set the number of iterations N and the number of initial points i to generate the initial impedance measurement frequency point set;

[0007] Step S2: Adaptively select the impedance measurement frequency point using the interpolation error calculation algorithm and the dynamic mean threshold method;

[0008] Step S3: Group all newly added impedance measurement frequency points into odd and even groups, synthesize two groups of multi-sine signals with varying amplitudes in different frequency bands, and inject them into the system under test in stages.

[0009] Step S4: Based on the impedance data corresponding to the impedance measurement frequency points accumulated in all iterations, fit the impedance curve through bilinear mapping and least squares method.

[0010] According to one technical solution of the present invention, the interpolation error calculation algorithm includes:

[0011] Arrange the current set of impedance measurement frequency points in order and divide them into multiple groups of three consecutive points using a sliding window;

[0012] The interpolation error S for each group is calculated using the triangle rule and expressed as follows:

[0013]

[0014] Where d is the frequency interval within the group, x t ,x t+1 For adjacent impedance measurement frequency points within the group, f(·) is the impedance amplitude corresponding to that frequency point.

[0015] According to one technical solution of the present invention, the dynamic mean threshold method includes:

[0016] Calculate the mean interpolation error for all groups;

[0017] Select all groups whose interpolation errors are greater than the mean interpolation error, and insert new impedance measurement frequency points.

[0018] According to one technical solution of the present invention, in step S3, the odd-even grouping includes:

[0019] Number the newly added impedance measurement frequency points according to the generation sequence;

[0020] All odd-numbered points are combined to form the first group of multi-sine signals, and even-numbered points are combined to form the second group of multi-sine signals.

[0021] The first set of multi-sine signals was used for the first measurement, and the second set of multi-sine signals was used for the second measurement.

[0022] According to one technical solution of the present invention, the frequency band amplitude value M n Determined by the following formula:

[0023] M n =M ref ×(1%+n×0.2%)

[0024] Among them, M n M represents the amplitude of the disturbance signal at the nth frequency point. ref is the reference value for the disturbance signal, and n is the number of the nth disturbance signal.

[0025] According to one technical solution of the present invention, in step S4, impedance curve fitting includes:

[0026] The frequency domain data corresponding to the impedance measurement frequency point is converted to the unit circle through bilinear mapping.

[0027] The continuous transfer function is solved using the SK iterative algorithm, and is expressed as:

[0028]

[0029] Where W is the specified frequency-related weight, D is the denominator of the transfer function model to be estimated, Ni is the numerator corresponding to the i-th input, y and u are the measured output and input data, respectively, and n f and n u It represents the frequency and the number of inputs, where ω is the frequency.

[0030] According to one technical solution of the present invention, the SK iteration algorithm includes:

[0031] Initialize the denominator D0(ω) = 1;

[0032] The parameters are updated iteratively based on rational basis functions, which are expressed as follows:

[0033]

[0034] Where, λ j,m-1 It is the j-th pole determined in the previous iteration m-1, where (λ) is the pole. j,m-1 )* is λ j,m-1 The complex conjugate of q, where q is a frequency domain variable on the unit circle;

[0035] The process terminates when the rate of change of the loss function is less than 0.001 or the number of iterations is greater than or equal to 20.

[0036] According to one aspect of the present invention, a multi-frequency impedance measurement system based on frequency adaptive selection is proposed, comprising:

[0037] The initialization module is used to specify the frequency range [f1, f2] according to the measurement requirements, and set the number of iterations N and the number of initial points i to generate the initial impedance measurement frequency point set;

[0038] An adaptive selection module is used to adaptively select the impedance measurement frequency point through an interpolation error calculation algorithm and a dynamic mean threshold method.

[0039] The signal synthesis module is used to group all newly added impedance measurement frequency points into odd and even groups, synthesize two groups of multi-sinusoidal signals with varying amplitudes in different frequency bands, and inject them into the system under test in stages.

[0040] The impedance fitting module is used to fit the impedance curve based on the impedance data corresponding to the impedance measurement frequency points accumulated over all iterations, using bilinear mapping and the least squares method.

[0041] According to one aspect of the present invention, an electronic device is provided, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory, and when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any of the above technical solutions.

[0042] According to one aspect of the present invention, a computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any of the above technical solutions.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] This invention proposes a multi-frequency impedance measurement method based on adaptive frequency selection. Addressing the problem that traditional equidistant frequency selection principles using multiple sinusoidal waves cannot accurately observe the peak or valley portions of impedance, this method employs a dynamic mean threshold method for adaptive frequency selection. This ensures that more frequency points are used for measurement at impedance peaks or valleys, and fewer points are used in areas where impedance is relatively flat. The algorithm exhibits high measurement accuracy and reliability. Furthermore, this method reduces mutual interference from multiple sinusoidal signal injections by dividing frequency points into odd and even numbers to obtain sinusoidal composite waves with larger frequency intervals and by providing different voltage amplitudes, thereby increasing measurement accuracy. Finally, through bilinear mapping and the least squares method, frequency domain fitting is performed on all acquired impedance information points to obtain the impedance expression in the frequency domain.

[0045] This invention avoids the complex modeling and derivation process in stability analysis, enables adaptive selection of measurement frequency points, solves the problem that traditional equal-frequency interval impedance measurement methods cannot accurately observe the peak or valley parts of impedance, and provides an important standardized tool and research background for system impedance acquisition and stability analysis. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating the steps of the multi-frequency impedance measurement method based on frequency adaptive selection in an embodiment of the present invention.

[0048] Figure 2 This is a geometric description diagram of linear interpolation at three frequency points provided in an embodiment of the present invention;

[0049] Figure 3 A geometric description diagram of linear interpolation at five frequency points provided in an embodiment of the present invention;

[0050] Figure 4 This is a diagram illustrating the multi-sine signal synthesis rules provided in an embodiment of the present invention;

[0051] Figure 5 This is a graph showing the output impedance test results of an EMI filter provided in an embodiment of the present invention;

[0052] Figure 6 The graph shows the input impedance test results of the Buck converter provided in an embodiment of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] like Figures 1 to 6 As shown, a multi-frequency impedance measurement method based on frequency adaptive selection according to the present invention includes the following steps:

[0055] Step S1: Based on the measurement requirements, specify the frequency range [f1, f2], and set the iteration count N and the number of initial points i to generate the initial impedance measurement frequency point set, specifically including:

[0056] Step S11: Specify the frequency range [f1~f2] for impedance measurement of the power electronic device according to the required measurement frequency range.

[0057] Step S12: Based on the time and measurement accuracy requirements, the iteration number N of the frequency adaptive selection algorithm and the number of initial frequency measurement points i are given to generate the initial impedance measurement frequency point set.

[0058] Step S2: Adaptively select the impedance measurement frequency point using the interpolation error calculation algorithm and the dynamic mean threshold method, specifically including:

[0059] Step S21: According to the interpolation error calculation principle, the impedance frequency point of each iteration is used as the interpolation point. Then, based on the sliding principle, the points are divided into groups of three, and the interpolation error of each group is calculated according to the triangle rule. Mathematically, port impedance measurement involves finding a piecewise linear interpolation function g(x) to approximate the original function f(x). Figure 2 In the diagram, the solid black line represents f(x), and the dashed red line represents g(x). Figure 3 China init (x) represents the result of linear interpolation fitting using 5 points. It can be seen that the more data points used, the more accurate the fitting result. Therefore, if a relationship can be established between the measurement error and the number of data points, the measurement frequency points can be selected iteratively and adaptively. The interpolation error calculation process is as follows:

[0060] Depend on Figure 2 and Figure 3 It can be seen that when f(x) and g(x) satisfy the error requirement, i.e., f(x)≈g(x), the green shaded area in the graph is smaller, and vice versa. Assume x t (t=1,2…,n) are n points distributed at equal frequency intervals, satisfying a≤x1 <x2…<x n ≤b, according to the above description, the frequency interval d between any two of these n equally spaced points can be expressed by the following formula:

[0061]

[0062] With [x t-1 ,x t Taking the interval as an example, the area S of the green shaded region f equal:

[0063]

[0064] If there are enough linear interpolation points, i.e., the area |S f If |<ε, and the value of ε approaches 0, then the current linear interpolation method has achieved a good fit. According to numerical theory, the interpolation error can be calculated as:

[0065]

[0066] Because the system is unknown, the expression for f(x) is also unknown. Therefore, the interpolation error described above cannot be obtained directly. Therefore, the interpolation error will be estimated through the following steps. Figure 3 In the interval [x t-1 ,x t Insert a new point at the midpoint of the first three interpolation points. The error between these three interpolation points can be expressed as S. f1 +S f2 S f1 [x] t-1 ,(x t +x t-1 The shaded area S in ) / 2] f2 It means [(x t +x t-1 ) / 2,x t The shaded area in ] . By analogy with the above formula (3), the interpolation error of the three points can be calculated as:

[0067]

[0068] If f(x) 」 is in [x t-1 ,x t Since f(ξ1)″ is almost a constant, then f(ξ2)″ ≈ f(ξ2)″. From equations (3) and (4), we can obtain the following equation:

[0069]

[0070] According to the trapezoidal rule, the integral of g(x) can be calculated:

[0071]

[0072] g1(x) and g2(x) can also be calculated by analogy with equation (6). Therefore, the interpolation error S of these three points can be estimated by the following equation:

[0073]

[0074] Where d is the frequency interval within the group, x t ,x t+1 For adjacent impedance measurement frequency points within the group, f(·) is the impedance amplitude corresponding to that frequency point.

[0075] Step S22: Based on the interpolation errors of all groups calculated in Step 3, calculate the mean interpolation error, and then select all groups whose interpolation errors are greater than the mean interpolation error to insert new frequency points.

[0076] Step S3: Group all newly added impedance measurement frequency points into odd and even groups, synthesize two sets of multi-sine signals with varying amplitudes in different frequency bands, and inject them into the system under test in stages. Specifically, this includes:

[0077] Number the newly added impedance measurement frequency points according to the generation sequence;

[0078] All odd-numbered points are combined to form the first group of multi-sine signals, and even-numbered points are combined to form the second group of multi-sine signals.

[0079] The first set of multi-sinusoidal signals was used for the first measurement, and the second set of multi-sinusoidal signals was used for the second measurement.

[0080] Based on all the newly inserted frequency points obtained in step S2, the multi-frequency signals in each frequency measurement iteration are divided according to the multi-frequency signal division principle. All newly added impedance measurement frequency points are numbered in the order of generation. Odd-numbered points are combined into the first group of signals, and even-numbered points are combined into the second group of signals to ensure that there is a large interval between different frequency points of multi-frequency synthesis and to reduce the measurement inaccuracy caused by the decomposition of signals with similar frequencies.

[0081] The principles for dividing numbers into even and odd are as follows:

[0082] For the first measurement, starting from the first new frequency point, the next point after the first point is selected as the second point, and this rule is followed until all selections are completed. This means that all odd-order frequency points are selected for the first measurement, and all odd-order frequency points are selected for the second measurement. Figure 4 This is a geometric description of the pattern. The red and green dots are new frequency points, representing the combined points of the first and second measurements, respectively.

[0083] Step S4: Based on the impedance data corresponding to the impedance measurement frequency points accumulated over all iterations, fit the impedance curve using bilinear mapping and the least squares method, specifically including:

[0084] Step S41: Based on the two injected disturbance signals obtained in step S3, different amplitudes are assigned to signals in different frequency bands to reduce mutual interference between them. The amplitude is set at 1% of the reference value and gradually increases from low frequency to high frequency. The amplitude can be obtained by the following formula:

[0085] M n =M ref ×(1%+n×0.2%)

[0086] Among them, M n M represents the amplitude of the disturbance signal at the nth frequency point. ref is the reference value for the disturbance signal (if a voltage signal is injected, the reference value is the node's rated voltage value), and n is the number of the nth disturbance signal.

[0087] Step S42: The disturbance signal obtained in step S41 is injected into the test location in an invasive manner. The sampled voltage and current data are decomposed using fast Fourier transform, and the frequency domain impedance of the converter at each frequency is calculated.

[0088] Step S43: Based on the number of iterations set in step S1, execute steps 3 to 7 to obtain the amplitude and phase frequency domain information of the impedance of the system port.

[0089] Step S44: Perform transfer function fitting on all acquired impedance information points. The transfer function fitting uses bilinear mapping and least squares method for parameter estimation. An optimization algorithm is then used to select the optimal model structure and parameters, finally returning an estimated continuous transfer function model. The specific calculation process is as follows:

[0090] The process of solving continuous transfer functions using bilinear mapping and the SK iterative algorithm:

[0091] (1) Perform a bilinear mapping to transform the domain (frequency grid) of the transfer function. For continuous-time models, the imaginary axis is transformed into the unit circle;

[0092] (2) Solve the nonlinear least squares problem by performing SK iterations—consider a multi-input single-output system. The nonlinear least squares problem is to minimize the following loss function:

[0093]

[0094] Where W is the specified frequency-related weight. D is the denominator of the transfer function model to be estimated, and N... i Let be the molecule corresponding to the i-th input. y and u are the output and input data of the measurement, respectively. f and n u Here, ω represents the frequency and the number of inputs. Rearranging the above equation yields the following:

[0095]

[0096] To perform the SK iteration, the algorithm iteratively solves the problem:

[0097]

[0098] Where m is the current iteration number, D m-1 (ω) represents the denominator response determined in the previous iteration. Each step of the current iteration is now a linear least squares problem, where the determined parameters capture the response D. m (ω) and N i,m (ω) for i = 1, 2, ..., n u The iteration is initialized by choosing D0(ω) = 1.

[0099] The first iteration of the algorithm determines the denominator response of D1(ω). D1(ω) and N i,1 (ω) polynomials are represented by monomial basis functions.

[0100] The second and subsequent iterations use orthogonal rational basis functions on the unit circle to represent the polynomial D. m (ω) and N i,m (ω). These rational basis functions are as follows:

[0101]

[0102] Where, λ j,m-1 It is the j-th pole determined in the previous iteration m-1, which is iterated m times. (λ) j,m-1 )* is λ j,m-1 The complex conjugate of , where q is a frequency domain variable on the unit circle.

[0103] The algorithm runs for a maximum of 20 iterations. If the relative change in the loss function value is less than 0.001 in the last three iterations, the iteration will terminate prematurely.

[0104] (3) Perform linear optimization (SK iterations), but even if they converge, they do not always produce local optima. To find the critical point in the optimization problem that can produce a local optimum, a second set of iterations is performed. The critical point is a solution to a set of nonlinear equations. The algorithm searches for a critical point by constructing a linear approximation of the nonlinear equations one by one and solving the resulting linear equations in the least-squares sense. The equations are as follows:

[0105] The j-th denominator parametric equation:

[0106]

[0107] Input the equation for the j-th molecular parameter corresponding to l:

[0108]

[0109] The first iteration uses SK to determine the molecule N. i The process begins with finding the optimal solution for the denominator D parameters. Unlike the SK iteration, the basis function B... j (ω) remains unchanged in each iteration; iterations are performed using the basis functions that produce the optimal solution in the SK iterations. As before, the algorithm runs for a maximum of 20 iterations. If the relative change in the loss function value is less than 0.001 in the last three iterations, the iteration terminates prematurely.

[0110] If bounds are specified for the transfer function coefficients, these bounds are incorporated into the necessary optimality conditions using generalized Lagrange multipliers. The resulting constrained linear least squares problem is solved using the same method explained in the SK iteration steps.

[0111] (4) Return the transfer function parameters corresponding to the optimal solution.

[0112] According to one aspect of the present invention, an electronic device is provided, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory, and when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any of the above technical solutions.

[0113] According to one aspect of the present invention, a computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any of the above technical solutions.

[0114] Figure 5 and Figure 6 To verify the application of the scheme proposed in this invention through experiments, wherein... Figure 5 This demonstrates the output impedance measurement of an EMI filter. Figure 6 The diagram demonstrates the input impedance measurement of a Buck converter. The theoretical and actual measured values ​​in the figure are in good agreement, and the method of this invention can identify impedance peaks and valleys, demonstrating the measurement accuracy of the method.

[0115] This invention discloses a multi-frequency impedance measurement method based on adaptive frequency selection, comprising: generating an initial impedance measurement frequency point set by specifying a frequency range according to measurement requirements, setting the number of iterations and the number of initial points; adaptively selecting impedance measurement frequency points using an interpolation error calculation algorithm and a dynamic mean threshold method; grouping all newly added impedance measurement frequency points into odd and even groups, synthesizing two sets of multi-sine signals with varying amplitudes in different frequency bands, and injecting them into the system under test in stages; and fitting the impedance curve based on the impedance data corresponding to all iteratively accumulated impedance measurement frequency points using bilinear mapping and the least squares method. This invention enables adaptive selection of measurement frequency points, solving the problem of inaccurately observing the peak or valley portions of impedance in traditional equal-frequency interval impedance measurement methods, and providing an important standardized tool and research background for system impedance acquisition and stability analysis.

[0116] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0117] Finally, it should be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A multi-frequency impedance measurement method based on frequency adaptive selection, characterized in that, Includes the following steps: Step S1: Given the frequency range [f1, f2] according to the measurement requirements, and set the number of iterations N and the number of initial points i to generate the initial impedance measurement frequency point set; Step S2: Adaptively select the impedance measurement frequency point using the interpolation error calculation algorithm and the dynamic mean threshold method; Step S3: Group all newly added impedance measurement frequency points into odd and even groups, synthesize two groups of multi-sine signals with varying amplitudes in different frequency bands, and inject them into the system under test in stages. Step S4: Based on the impedance data corresponding to the impedance measurement frequency points accumulated in all iterations, fit the impedance curve through bilinear mapping and least squares method. The interpolation error calculation algorithm includes: Arrange the current set of impedance measurement frequency points in order and divide them into multiple groups of three consecutive points using a sliding window; The interpolation error S for each group is calculated using the triangle rule and expressed as follows: Where d is the frequency interval within the group, x t ,x t+1 For adjacent impedance measurement frequency points within the group, f(⋅) is the impedance amplitude corresponding to that frequency point; The dynamic mean threshold method includes: Calculate the mean interpolation error for all groups; Select all groups whose interpolation errors are greater than the mean interpolation error, and insert new impedance measurement frequency points.

2. The multi-frequency impedance measurement method based on frequency adaptive selection according to claim 1, characterized in that, In step S3, the odd-even grouping includes: Number the newly added impedance measurement frequency points according to the generation sequence; All odd-numbered points are combined to form the first group of multi-sine signals, and even-numbered points are combined to form the second group of multi-sine signals. The first set of multi-sine signals was used for the first measurement, and the second set of multi-sine signals was used for the second measurement.

3. The multi-frequency impedance measurement method based on frequency adaptive selection according to claim 2, characterized in that, The frequency band amplitude value M n Determined by the following formula: Among them, M n M represents the amplitude of the disturbance signal at the nth frequency point. ref is the reference value for the disturbance signal, and n is the number of the nth disturbance signal.

4. The multi-frequency impedance measurement method based on frequency adaptive selection according to claim 1, characterized in that, In step S4, impedance curve fitting includes: The frequency domain data corresponding to the impedance measurement frequency point is converted to the unit circle through bilinear mapping. The continuous transfer function is solved using the SK iterative algorithm, and is expressed as: Where W is the specified frequency-related weight, D is the denominator of the transfer function model to be estimated, Ni is the numerator corresponding to the i-th input, y and u are the measured output and input data, respectively, and n f and n u It represents the frequency and the number of inputs, where ω is the frequency.

5. The multi-frequency impedance measurement method based on frequency adaptive selection according to claim 4, characterized in that, The SK iteration algorithm includes: Initialize the denominator D0(ω) = 1; The parameters are updated iteratively based on rational basis functions, which are expressed as follows: Where, λ j,m-1 It is the j-th pole determined in the previous iteration m-1, where (λ) is the pole. j,m-1 )* is λ j,m-1 The complex conjugate of q, where q is a frequency domain variable on the unit circle; The process terminates when the rate of change of the loss function is less than 0.001 or the number of iterations is greater than or equal to 20.

6. A multi-frequency impedance measurement system based on frequency adaptive selection, used to implement the multi-frequency impedance measurement method based on frequency adaptive selection as described in any one of claims 1 to 5, characterized in that, include: The initialization module is used to specify the frequency range [f1, f2] according to the measurement requirements, and set the number of iterations N and the number of initial points i to generate the initial impedance measurement frequency point set; An adaptive selection module is used to adaptively select the impedance measurement frequency point through an interpolation error calculation algorithm and a dynamic mean threshold method. The signal synthesis module is used to group all newly added impedance measurement frequency points into odd and even groups, synthesize two groups of multi-sinusoidal signals with varying amplitudes in different frequency bands, and inject them into the system under test in stages. The impedance fitting module is used to fit the impedance curve based on the impedance data corresponding to the impedance measurement frequency points accumulated over all iterations, using bilinear mapping and the least squares method.

7. An electronic device, characterized in that, include: One or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory, and when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, implement the frequency-adaptive selection-based multi-frequency impedance measurement method as described in any one of claims 1 to 5.

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