An impedance measurement method for power electronic power systems

Abstract

This invention discloses an impedance measurement method for power electronic power systems, comprising: setting a set of frequency points based on a preset impedance measurement frequency range; constructing a disturbance signal set containing multiple sinusoidal signals; constructing and solving an objective function with the initial phase of all sinusoidal signals as the independent variable and the time-domain peak of the superposition of multiple sinusoidal signals as the dependent variable to obtain the sinusoidal disturbance signal with the minimum time-domain peak superposition; for the component under test, analyzing the sampled voltage and current data using a Fast Fourier Transform based on the sinusoidal disturbance signal corresponding to the injection position to obtain the impedance frequency domain information of the component at each frequency point, wherein the impedance frequency domain information includes impedance amplitude and phase information; fitting the impedance frequency domain information at each frequency point to obtain the complete impedance curve of the component in the impedance measurement. The method provided by this invention ensures that the subsequent FFT process for obtaining impedance information accurately identifies the response information of the corresponding frequency.

Description

Technical Field

[0001] This invention belongs to the technical field of impedance measurement of power electronic converters, and particularly relates to an impedance measurement method for power electronic power systems. Background Technology

[0002] With the continuous development of power systems and new energy power generation technologies, more and more new energy power generation technologies such as wind power and photovoltaics, 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 that occur in many parts 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 degree of visualization, and strong research extensibility.

[0003] To achieve 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), making modeling extremely complex and cumbersome.

[0004] The academic literature, *Research on Online Measurement Technology of Grid Impedance for High-Power Grid-Connected Inverters Based on Multi-Sinusoidal Signal Injection* [J / OL], published in the *Proceedings of the Chinese Society for Electrical Engineering*, discloses a method based on multi-sinusoidal signals as voltage disturbances, and optimizes the disturbance signal design by referring to the Gerchberg-Saxton phase retrieval algorithm in spatial optical field theory. However, this method only analyzes grid impedance information and does not mention how to obtain the corresponding impedance curves.

[0005] 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, 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, with over 90% of the energy concentrated within the set band. Within the entire set band, the signal amplitude is essentially consistent, and the crest factor is low, which is beneficial for signal identification and reduces the impact on the system under test. However, injecting a large number of perturbation signals in similar frequency bands inevitably causes mutual interference between signals. Furthermore, these signals contain a significant 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

[0006] The purpose of this invention is to provide an impedance measurement method for power electronic power systems, which can ensure that the FFT process for obtaining subsequent impedance information accurately identifies the response information at the corresponding frequency.

[0007] To achieve the objectives of this invention, the following technical solution is provided: an impedance measurement method for power electronic power systems, comprising the following steps:

[0008] A set of frequency points is set based on the frequency range of the preset impedance measurement, and the frequency values ​​corresponding to the frequency points in the set of frequency points are uniformly distributed in the logarithmic domain within the frequency range.

[0009] The frequency points in the frequency point set are divided according to the number of perturbation signals injected in a single injection to obtain the injection positions of signals in different frequency bands, and different sinusoidal signal amplitudes are assigned to the perturbation signals injected at each injection position to construct a perturbation signal set containing multiple sinusoidal signals.

[0010] Using the initial phase of all sinusoidal signals as independent variables and the time-domain peaks after the superposition of multiple sinusoidal signals as dependent variables, an objective function is constructed and solved to obtain the sinusoidal disturbance signal with the minimum superposition of time-domain peaks.

[0011] For the component under test, based on the sinusoidal disturbance signal corresponding to the injection position, the sampled voltage and current data are analyzed by fast Fourier transform to obtain the impedance frequency domain information of the component at each frequency point. The impedance frequency domain information includes impedance amplitude and phase information.

[0012] Fitting is performed based on impedance frequency domain information at certain frequency points to obtain the complete impedance curve of the component in impedance measurement.

[0013] This invention employs a method of superimposing multiple sinusoidal signals at custom frequency points to synthesize disturbance signals, ensuring targeted measurement of impedance information within the required frequency band with minimal impact on system stability. Simultaneously, the PSO algorithm is used to select the initial phase of the superimposed disturbance signals, effectively reducing the time-domain peaks of the synthesized signal and minimizing its impact on the system. Finally, bilinear mapping and the least squares method are used to perform frequency domain fitting on all acquired impedance information points to obtain the impedance expression in the frequency domain.

[0014] Specifically, the expression for the set of disturbance signals is as follows:

[0015]

[0016] Where i is the number of characteristic harmonic frequency points in the multi-sinusoidal signal, and M i f i θ i These represent the amplitude, frequency, and initial phase angle of the i-th sinusoidal characteristic harmonic frequency, respectively.

[0017] Specifically, the differentiation rules for the injection sites are as follows:

[0018]

[0019] In the formula, f Kn The frequency of the Kn-th injected signal is where K represents the number of sinusoidal signals to be injected in a single operation, and n represents the number of injections.

[0020] Specifically, the amplitude is gradually increased from low frequency to high frequency, using one percent of the preset amplitude as a standard, to assign different sinusoidal signal amplitudes to the injected disturbance signal.

[0021] Specifically, the amplitude of the sinusoidal signal is selected as follows:

[0022] M n =M ref ×(1%+n×0.2%)

[0023] In the formula, M ref M is the preset amplitude of the injection point signal. n This represents the amplitude of the nth sine wave of the single-injection disturbance signal.

[0024] Specifically, the PSO algorithm is used to solve the objective function.

[0025] Specifically, the expression for the objective function is as follows:

[0026] M obj = f(θ1,θ2,...,θ) n )

[0027] In the formula, Mobj θ represents the peak value in the time domain of a single injected signal. n The initial phase value of the nth sinusoidal component of the single-injection signal.

[0028] Specifically, the fitting includes bilinear mapping and least squares method.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] To address the issue that signals such as PRBS and Chirp contain a large amount of energy from frequencies other than those being measured, signal synthesis is performed by rationally dividing the low, medium, and high frequency bands. This minimizes the signal aliasing effect and ensures that the subsequent FFT process for obtaining impedance information accurately identifies the response information of the corresponding frequency. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the impedance measurement method for power electronic power systems provided in this embodiment.

[0032] Figure 2 This is a schematic diagram of the superposition and synthesis of multiple sine waves provided in this embodiment;

[0033] Figure 3 This embodiment provides a comparison of the input impedance measurement and analytical model of a two-point flat Buck converter under certain circuit parameters.

[0034] Figure 4 The results of the measurement and analytical model comparison of the input impedance of the two-point flat Buck converter under another circuit parameter provided in this embodiment are presented. Detailed Implementation

[0035] 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, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0036] like Figure 1 As shown in this embodiment, an impedance measurement method for power electronic power systems is provided, and its specific process is as follows:

[0037] The frequency range [f1~f2] for impedance measurement of power electronic devices is given according to the measurement frequency range requirements, and the number of frequency points K for measurement is given according to the time and measurement accuracy requirements, wherein the corresponding frequency values ​​are uniformly distributed in the logarithmic domain within the selected frequency range.

[0038] The frequency points in the frequency point set are divided according to the number of perturbation signals injected in a single injection to obtain the injection positions of signals in different frequency bands. Different sinusoidal signal amplitudes are assigned to the perturbation signals injected at each injection position to construct a perturbation signal set containing multiple sinusoidal signals, i.e., a multi-sinusoidal signal D. signal It has the ability to simultaneously inject harmonic disturbances at any finite number of frequency points within a unit of time, and its expression is:

[0039]

[0040] Where i is the number of characteristic harmonic frequency points in the multi-sinusoidal signal, and M i f i θ i These represent the amplitude, frequency, and initial phase angle of the i-th sinusoidal characteristic harmonic frequency, respectively.

[0041] Based on the acquired multi-sine signal D signal K sine waves are injected in a single injection. The injected sine waves are then divided into different frequency bands according to the following rules:

[0042]

[0043] This is to avoid mutual interference caused by the similar frequencies of the sine waves injected in a single operation, which would result in obtaining incorrect port impedance information.

[0044] Given composition D signal The sinusoidal signal has different amplitudes, with the amplitude set at 1% of the reference value, gradually increasing from low frequency to high frequency.

[0045] Its amplitude can be obtained by the following formula:

[0046] M n =M ref ×(1%+n×0.2%)

[0047] In the formula, M ref The reference value for the injection point signal can be voltage, current, etc., M n This represents the amplitude of the nth sine wave of the single-injection disturbance signal.

[0048] like Figure 2As shown, using the initial phases of all sinusoidal signals as independent variables and the time-domain peaks of the superimposed sinusoidal signals as dependent variables, an objective function is constructed and solved to obtain the sinusoidal perturbation signal with the minimum superposition of time-domain peaks. That is, based on the perturbation signal injected in a single instance, an objective function is formed with the initial phases of all sinusoidal signals as independent variables and the time-domain peaks of the superimposed sinusoidal signals as dependent variables. The expression of the objective function is:

[0049] M obj = f(θ1,θ2,...,θ) n )

[0050] In the formula, M obj θ represents the peak value in the time domain of a single injected signal. n The initial phase value of the nth sinusoidal component of the single-injection signal.

[0051] The objective function is solved using the PSO algorithm to obtain the sinusoidal perturbation signal with the minimum time-domain peak superposition. The specific process is as follows:

[0052] (1) Parameter initialization. Determine the particle dimension D, population size N, number of iterations M, learning factors c1 and c2, and inertia weight w.

[0053] (2) Initialize the particle's velocity v and position x, and randomly generate a population of particles x = (θ1, θ2, ..., θ). n ).

[0054] (3) Take the objective function obtained in step 6 as the fitness value of the particle, and calculate the initial individual extreme value p based on the fitness value of the particle. ij and global extremum p gi :

[0055] fitness = M obj = f(θ1,θ2,...,θ) n ).

[0056] (4) Update the particle position (x) according to equation (3). ij ) and velocity (v) ij Then, based on the new location, calculate the fitness value and update the individual extreme values ​​and the global extreme values:

[0057]

[0058] In the formula, r1 and r2 are random numbers between [0,1], and the update of x is determined by the result of the previous iteration and the velocity of the particle.

[0059] Determine if the termination condition is met. If it is, output the optimization result x. best =(θ1,θ2,…,θ) nOtherwise, return (3).

[0060] The resulting disturbance, a superposition of multiple sinusoidal signals, is injected into the system. Voltage and current data are collected at corresponding locations. The sampled voltage and current data are decomposed using a Fast Fourier Transform, and the impedance at each frequency is calculated based on the following formula:

[0061]

[0062] In the formula, This represents the voltage value at the corresponding disturbance frequency. This represents the current value at the corresponding disturbance frequency.

[0063] Transfer function fitting is performed 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 process is as follows:

[0064] (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;

[0065] (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:

[0066]

[0067] 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 represent 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:

[0068]

[0069] To perform the SK iteration, the algorithm iteratively solves the problem:

[0070]

[0071] Where m is the current iteration number, and Dm⁻¹(ω) is the denominator response determined in the previous iteration. Each step of the iteration is now a linear least squares problem, where the determined parameters capture responses Dm(ω) and Ni,m(ω) for i = 1, 2, ..., nu. The iteration is initialized by choosing D0(ω) = 1.

[0072] The first iteration of the algorithm determines the denominator response of D1(ω). The D1(ω) and Ni,1(ω) polynomials are represented by monomial basis functions.

[0073] The second and subsequent iterations use orthogonal rational basis functions on the unit circle to represent the polynomials Dm(ω) and Ni,m(ω). These rational basis functions are as follows:

[0074]

[0075] Where λj,m-1 is the j-th pole determined in the previous iteration m-1, which is iterated m times. (λj,m-1)* is the complex conjugate of λj,m-1, and q is the frequency domain variable on the unit circle.

[0076] 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.

[0077] Linear optimization (SK iterations) are performed, 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 successively constructing linear approximations of the nonlinear equations and solving the resulting linear equations in a least-squares sense. The equations are as follows:

[0078] The j-th denominator parametric equation:

[0079]

[0080] Input the equation for the j-th molecular parameter corresponding to l:

[0081]

[0082] The first iteration begins with the optimal solution for the numerator Ni and denominator D parameters from the SK iteration. Unlike the SK iteration, the basis function Bj(ω) remains unchanged in each iteration; the iteration is performed using the basis function that produced the optimal solution in the SK iteration. 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.

[0083] 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.

[0084] Returns the transfer function parameters corresponding to the optimal solution.

[0085] To better illustrate the effectiveness of the method provided in this embodiment, a comparison of the input impedance measurement and analytical model of the two-level Buck converter under different circuit parameters is presented, such as... Figure 3 and Figure 4 As shown.

[0086] in Figure 3 L = 2.45 μH, while Figure 4 L = 1.45 μH.

[0087] like Figure 3 As can be seen, the measurement results of the method provided in this embodiment are basically consistent with the results of the existing analytical model. This method can avoid the complex impedance modeling and derivation process in the stability analysis process, realize the online measurement of converter port impedance characteristics, and verify the high accuracy of the method through experiments. It can provide an important standardized tool and research background for system impedance acquisition and stability analysis.

[0088] Furthermore, the terms "upper," "lower," "inner," "outer," "front," and "rear" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0089] Of course, the above description is only a specific embodiment of the present invention and is not intended to limit the scope of the present invention. All equivalent changes or modifications made to the structure, features and principles described in the claims of the present invention should be included in the scope of the claims of the present invention.

[0090] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An impedance measurement method for power electronic power systems, characterized in that, Includes the following steps: A set of frequency points is set based on the frequency range of the preset impedance measurement, and the frequency values ​​corresponding to the frequency points in the set of frequency points are uniformly distributed in the logarithmic domain within the frequency range. The frequency points in the frequency point set are divided according to the number of perturbation signals injected in a single injection to obtain the injection positions of signals in different frequency bands, and different sinusoidal signal amplitudes are assigned to the perturbation signals injected at each injection position to construct a perturbation signal set containing multiple sinusoidal signals. Using the initial phase of all sinusoidal signals as independent variables and the time-domain peaks after the superposition of multiple sinusoidal signals as dependent variables, an objective function is constructed and solved to obtain the sinusoidal disturbance signal with the minimum superposition of time-domain peaks. For the component under test, based on the sinusoidal disturbance signal corresponding to the injection position, the sampled voltage and current data are analyzed by fast Fourier transform to obtain the impedance frequency domain information of the component at each frequency point. The impedance frequency domain information includes impedance amplitude and phase information. Fitting is performed based on impedance frequency domain information at certain frequency points to obtain the complete impedance curve of the component in impedance measurement.

2. The impedance measurement method for power electronic power systems according to claim 1, characterized in that, The expression for the set of disturbance signals is as follows: Where i is the number of characteristic harmonic frequency points in the multi-sinusoidal signal, and M i f i θ i These represent the amplitude, frequency, and initial phase angle of the i-th sinusoidal characteristic harmonic frequency, respectively.

3. The impedance measurement method for power electronic power systems according to claim 1, characterized in that, The differentiation rules for the injection sites are as follows: In the formula, f Kn The frequency of the Kn-th injected signal is where K represents the number of sinusoidal signals to be injected in a single operation, and n represents the number of injections.

4. The impedance measurement method for power electronic power systems according to claim 1, characterized in that, The amplitude is gradually increased from low frequency to high frequency, using one percent of the preset amplitude as a standard, to assign different sinusoidal signal amplitudes to the injected disturbance signal.

5. The impedance measurement method for power electronic power systems according to claim 4, characterized in that, The method for selecting the amplitude of the sinusoidal signal is as follows: M n =M ref ×(1%+n×0.2%) In the formula, M ref M is the preset amplitude of the injection point signal. n This represents the amplitude of the nth sine wave of the single-injection disturbance signal.

6. The impedance measurement method for power electronic power systems according to claim 1, characterized in that, The PSO algorithm is used to solve the objective function.

7. The impedance measurement method for power electronic power systems according to claim 1 or 6, characterized in that, The expression for the objective function is as follows: M obj =f(θ1,θ2,...,θ n ) In the formula, M obj θ represents the peak value of the time-domain signal from a single injection. n The initial phase value of the nth sinusoidal component of the single-injection signal.

8. The impedance measurement method for power electronic power systems according to claim 1, characterized in that, The fitting process includes bilinear mapping and least squares method.

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