Converter multi-working-condition admittance identification method

Abstract

The invention discloses a converter multi-working-condition admittance identification method, which relates to the technical field of converter admittance identification, and comprises the following steps of: carrying out dimensionality reduction decomposition on admittance prior physical knowledge of a general control type and structural parameter converter; carrying out dimensionality reduction decomposition on the high-dimensional admittance into a combination of one-dimensional mapping functions through a Coriolgov-Arnod representation theorem; according to the method, a multi-working-condition admittance model is established based on a Coriolgov-Arnod network, a sparse connection KAN model with strict physical constraints is designed according to a dimensionality reduction decomposition result, and the problem that in engineering practice, due to the fact that the admittance measurement sample size is insufficient, a deep learning model cannot be effectively trained can be solved; and moreover, the small sample generalization ability of the multi-working-condition admittance model is also improved, the system stability is judged by the obtained multi-working-condition admittance through an impedance analysis method, and the method can be used for multi-operation-mode small-interference stability rapid and robust verification before grid connection of the new energy converter.

Description

Technical Field

[0001] This invention relates to the field of converter admittance identification technology, specifically a method for identifying the admittance of converters under multiple operating conditions. Background Technology

[0002] Impedance analysis can effectively evaluate the grid-connected stability of new energy sources using power electronic converters as interfaces. Therefore, conducting port multi-condition admittance modeling of converters is beneficial for quickly verifying the small-disturbance stability of new energy grid-connected operation modes.

[0003] Impedance analysis requires obtaining the small-signal impedance / admittance model of the converter to construct an equivalent negative feedback loop, and then analyzing the system stability using the Nyquist criterion. However, due to factors such as commercial confidentiality, converter control schemes are often provided as encapsulated dynamic link libraries in the form of digital programs, making it difficult to obtain their control information and parameter configurations. Therefore, it is difficult to theoretically derive the analytical model of the converter admittance.

[0004] In engineering, the frequency sweep method based on port disturbances has become an effective way to obtain converter admittance. This method treats the equipment as a "black box," calculating impedance only by injecting small disturbances into the ports at the steady-state operating point and extracting the response, without requiring internal information. However, the frequency sweep method can only obtain admittance under specific operating conditions. Converters operate under a vast number of conditions, and the admittance characteristics vary significantly across these conditions. The mapping relationship between operating conditions and admittance is essentially a complex, high-dimensional nonlinear function. It is impossible to analyze the stability of the equipment under multiple operating conditions using admittance under a single condition; a comprehensive measurement of all potential operating conditions is necessary to reliably assess the converter's grid-connected stability, which is time-consuming and impractical. Furthermore, continuously injecting disturbance signals into the grid will cause severe harmonic pollution, affecting the safe operation of the power system.

[0005] To address the challenge of acquiring impedance / admittance models for converters under multiple operating conditions, existing research has incorporated machine learning methods to conduct data-driven modeling of converters based on partial operating condition admittance samples. While deep learning-based multi-condition admittance modeling methods for converters avoid the need to traverse the entire operating condition set to some extent, deep learning models suffer from complex structures and a large number of parameters. A common problem is their reliance on a vast amount of admittance measurement data under various operating conditions for model training. However, in practical engineering, the amount of admittance measurement sample data is limited, making it insufficient to support effective training of deep learning models. Summary of the Invention

[0006] The purpose of this invention is to address the problems mentioned in the background section by proposing a multi-condition admittance identification method for converters. Regarding the rapid and stable verification of small-interference operation of grid-connected new energy converters under multiple operating modes, the stability of the operating modes is evaluated through impedance analysis of the converter grid-connected system.

[0007] The objective of this invention can be achieved through the following technical solution: a method for identifying the admittance of a converter under multiple operating conditions, comprising:

[0008] S1: Based on the Kolmogorov-Arnold representation theorem, the dimension reduction decomposition form of the general modular admittance function of the converter port admittance is derived, and the high-dimensional admittance function is decomposed into a combination of finite one-dimensional functions.

[0009] S2: Based on the dimensionality reduction decomposition results of the converter admittance in step S1, construct a multi-condition admittance KAN model with concise sparse connectivity.

[0010] S3: Based on Chebyshev polynomial design, a low-parameter dynamic learnable activation function is designed to achieve the best consistent approximation of the one-dimensional mapping function of admittance in step S1, and to learn the essential characteristics of admittance from small sample data.

[0011] In a preferred embodiment of the present invention, in step S1, by decomposing the general prior knowledge of the modular admittance of the converter port into a dimensionless form, a layer-by-layer decomposition matrix and a one-dimensional mapping function of the admittance are obtained, thereby obtaining a combination of one-dimensional mapping functions of the high-dimensional admittance function, including:

[0012] S11: Express the prior physical knowledge of converter port admittance as a modular admittance transfer function, and then use the positive-sequence self-admittance Y... pp (s), positive-sequence transitive admittance Y pn (s), negative-order self-admittance Y nn (s), Negative-order transit admittance Y np (s) Characterize the port admittance properties and form the admittance matrix:

[0013]

[0014] Among them, positive-order self-admittance Y pp (s) and positive-order transitive admittance Y pn (s) can be composed of functional sub-modules related to the electrical and control parts of the converter, expressed as:

[0015]

[0016] Where H c0 (s) represents the current controller transfer function module, G θ (s) represents the phase-locked loop transfer function module, G L (s) represents the filter transfer function module, Y1 is defined as the steady-state fundamental waveguide admittance, and s is the Laplace operator;

[0017] S12: According to the Kolmogorov-Arnold representation theorem, for a high-dimensional nonlinear continuous function F(x) with port admittance, through a multi-level decomposition matrix Ψ... lThe composite form is decomposed into a dimension reduction form with respect to the operating condition variable I. d I q The combination of V1 and a one-dimensional function related to frequency f is expressed as:

[0018]

[0019] in Represents the Hadamard product, s = j2πf; decompose matrix Ψ l The one-dimensional mapping function is represented as:

[0020]

[0021] in Represents a one-dimensional mapping function to the input, decomposing the matrix Ψ. l It consists of one-dimensional mapping functions.

[0022] In a preferred embodiment of the present invention, in step S2, based on the sparse dimensionality reduction decomposition matrix of the port admittance obtained in step S1, a concise sparsely connected multi-condition admittance KAN model with physical structural constraints is designed, including:

[0023] S21: Using the real and imaginary parts of the converter's admittance as output variables, the converter is represented in the form of conductance and susceptance. Y is extracted through a 2×(M+N) dimensional decomposition matrix Y2. pp The real and imaginary parts are represented as follows:

[0024]

[0025] S22: Based on the layer-by-layer decomposition matrix Ψ l In the form of designing each KAN layer Φ l The relationship between the number of neurons and sparse connections; the first KAN layer Φ1 is used to obtain working condition I. d I q The first layer, Φ2, corresponds to the decomposition matrix Ψ2, used to perform power function transformation on the one-dimensional function polynomial; the second layer, Φ3, corresponds to the decomposition matrix Ψ3, used to extract the real and imaginary parts of the admittance; based on the decomposition matrix Ψ... l Dimension setting of KAN layer Φ l The number of input and output neurons and their connections.

[0026] In a preferred embodiment of the present invention, in step S3, Chebyshev dynamic learnable activation functions are embedded on the edges of the KAN model designed in S2 using Chebyshev polynomials, thereby achieving the best consistent approximation of the one-dimensional admittance mapping function, including:

[0027] S31: The explicit expression for the Chebyshev polynomial function is:

[0028] T k (x) = cos(k arccosx)

[0029] Chebyshev polynomials, composed of decoupled orthogonal basis functions, have low parameter redundancy and can efficiently capture the characteristics of one-dimensional admittance mapping functions with a low number of parameters, improving approximation accuracy and stability. Chebyshev polynomials can achieve the best uniform approximation of any continuous function by minimizing the maximum error. Specifically, for any one-dimensional mapping function... There exists a set of weight parameters The following relationship must be satisfied:

[0030]

[0031] Among them, T1 k For Chebyshev polynomial sum, T2 k Let k be a polynomial space of degree k, ||·|| ∞ It is the infinite norm (i.e., the maximum absolute error).

[0032] S32: T1 k To be a Chebyshev-learnable activation function, the one-dimensional mapping function of the actual admittance is expressed as a Chebyshev decomposition. The one-dimensional mapping function of admittance typically includes proportional, integral, inertial, trigonometric, power, and inverse proportional functions, and can be represented as:

[0033]

[0034] Among them, parameter set By dynamically learning and adjusting based on input data, adaptive optimal approximation of one-dimensional mapping functions of varying complexity can be achieved.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. A method for dimensionality reduction decomposition of admittance prior physical knowledge for general converters is proposed, which maps high-dimensional admittance functions to a linear combination of a finite number of one-dimensional functions, and constructs a multi-condition admittance KAN network with a simple sparse connection structure based strictly on this mapping relationship, thereby realizing the full embedding of finite physical knowledge and further reducing the dependence on measurement samples.

[0037] 2. A low-parameter learnable activation function based on Chebyshev polynomials was designed, which breaks through the limitations of traditional fixed activation functions. It can dynamically learn and effectively capture the general essential features of high-dimensional admittance functions through small sample data, thereby improving the identification accuracy of multi-condition admittance models and the generalization ability of small sample multi-condition models. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of the method of the present invention;

[0040] Figure 2 This is a schematic diagram of the training process of the KAN model for working condition admittance in this invention;

[0041] Figure 3 This is a training convergence plot of the multi-condition admittance model of the present invention;

[0042] Figure 4 This is a generalization error diagram of the multi-condition admittance model for converters used in this invention;

[0043] Figure 5 This is a graph showing the variation of the training loss of the multi-condition admittance model for converters in this invention with the sample size.

[0044] Figure 6 This is a graph showing the goodness of fit of the multi-condition admittance model for converters in this invention as a function of sample size;

[0045] Figure 7 This is the Bode plot of the amplitude and phase of the admittance model for a specific operating condition of a converter, as used in this invention. Detailed Implementation

[0046] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0047] Please see Figures 1-6 As shown, a method for identifying the admittance of a converter under multiple operating conditions includes:

[0048] S1: Based on the Kolmogorov-Arnold representation theorem, the dimension reduction decomposition form of the general modular admittance function of the converter port admittance is derived, and the high-dimensional admittance function is decomposed into a combination of finite one-dimensional functions.

[0049] S2: Based on the dimensionality reduction decomposition results of the converter admittance in step S1, construct a multi-condition admittance KAN model with concise sparse connectivity.

[0050] S3: Based on Chebyshev polynomial design, a low-parameter dynamic learnable activation function is designed to achieve the best consistent approximation of the one-dimensional mapping function of admittance in step S1, and to learn the essential characteristics of admittance from small sample data.

[0051] One possible implementation of this application embodiment is that, in step S1, by decomposing the general prior knowledge of the converter port modular admittance into a dimensionless form, a layer-by-layer decomposition matrix and a one-dimensional mapping function of admittance are obtained, thereby obtaining a combination of one-dimensional mapping functions of the high-dimensional admittance function, including:

[0052] S11: Express the prior physical knowledge of converter port admittance as a modular admittance transfer function, and then use the positive-sequence self-admittance Y... pp (s), positive-sequence transitive admittance Y pn (s), negative-order self-admittance Y nn (s), Negative-order transit admittance Y np (s) Characterize the port admittance properties and form the admittance matrix:

[0053]

[0054] Among them, positive-order self-admittance Y pp (s) and positive-order transitive admittance Y pn (s) can be composed of functional sub-modules related to the electrical and control parts of the converter, expressed as:

[0055]

[0056] Where H c0 (s) represents the current controller transfer function module, G θ (s) represents the phase-locked loop transfer function module, G L (s) represents the filter transfer function module, Y1 is defined as the steady-state fundamental waveguide admittance, and s is the Laplace operator;

[0057] S12: According to the Kolmogorov-Arnold representation theorem, for a high-dimensional nonlinear continuous function F(x) with port admittance, through a multi-level decomposition matrix Ψ... l The composite form is decomposed into a dimension reduction form with respect to the operating condition variable I. d I q The combination of V1 and a one-dimensional function related to frequency f is expressed as:

[0058]

[0059] in Represents the Hadamard product, s = j2πf; decompose matrix Ψ l The one-dimensional mapping function is represented as:

[0060]

[0061] in Represents a one-dimensional mapping function to the input, decomposing the matrix Ψ. l It consists of one-dimensional mapping functions.

[0062] One possible implementation of this application embodiment is that, in step S2, based on the sparse dimensionality reduction decomposition matrix of the port admittance obtained in step S1, a concise sparsely connected multi-condition admittance KAN model with physical structural constraints is designed, including:

[0063] S21: Using the real and imaginary parts of the converter's admittance as output variables, the converter is represented in the form of conductance and susceptance. Y is extracted through a 2×(M+N) dimensional decomposition matrix Y2. pp The real and imaginary parts are represented as follows:

[0064]

[0065] S22: Based on the layer-by-layer decomposition matrix Ψ l In the form of designing each KAN layer Φ l The relationship between the number of neurons and sparse connections; the first KAN layer Φ1 is used to obtain working condition I. d I q The first layer, Φ2, corresponds to the decomposition matrix Ψ2, used to perform power function transformation on the one-dimensional function polynomial; the second layer, Φ3, corresponds to the decomposition matrix Ψ3, used to extract the real and imaginary parts of the admittance; based on the decomposition matrix Ψ... l Dimension setting of KAN layer Φ l The number of input and output neurons and their connections.

[0066] One possible implementation of this application embodiment is that, in step S3, Chebyshev dynamically learnable activation functions are embedded on the edges of the KAN model designed in S2 using Chebyshev polynomials, thereby achieving the best consistent approximation of the one-dimensional admittance mapping function, including:

[0067] S31: The explicit expression for the Chebyshev polynomial function is:

[0068] T k (x) = cos(k arccosx)

[0069] Chebyshev polynomials, composed of decoupled orthogonal basis functions, have low parameter redundancy and can efficiently capture the characteristics of one-dimensional admittance mapping functions with a low number of parameters, improving approximation accuracy and stability. Chebyshev polynomials can achieve the best uniform approximation of any continuous function by minimizing the maximum error. Specifically, for any one-dimensional mapping function... There exists a set of weight parameters Let the set of real numbers satisfy the following relation:

[0070]

[0071] Among them, T1 k For Chebyshev polynomial sum, T2 k Let k be a polynomial space of degree k, ||·|| ∞ It is the infinite norm (i.e., the maximum absolute error).

[0072] S32: T1 k To be a Chebyshev-learnable activation function, the one-dimensional mapping function of the actual admittance is expressed as a Chebyshev decomposition. The one-dimensional mapping function of admittance typically includes proportional, integral, inertial, trigonometric, power, and inverse proportional functions, and can be represented as:

[0073]

[0074] Among them, parameter set By dynamically learning and adjusting based on input data, adaptive optimal approximation of one-dimensional mapping functions of varying complexity can be achieved.

[0075] This invention innovatively proposes a multi-condition admittance identification method for converters based on Kolmogorov-Arnold networks for rapid verification of stability under small disturbances in multiple operating modes before grid connection of new energy converters. This method fully utilizes the limited physical knowledge of converters, designing a multi-condition admittance KAN network with sparse connections and simple relationships based on prior physical knowledge, greatly compressing the network architecture and parameters. Simultaneously, a Chebyshev learnable activation function is designed to extract the general essential features of admittance from small sample data, thereby enhancing the network's expressive power for high-dimensional admittance functions and its small-sample generalization ability. This invention solves the problem of insufficient admittance measurement samples in engineering practice, which leads to the ineffective training of deep learning models. It also improves the small-sample generalization ability of multi-condition admittance models. The obtained multi-condition admittances are used to determine system stability through impedance analysis, and can be used for rapid and robust verification of stability under small disturbances in multiple operating modes before grid connection of new energy converters.

[0076] To verify the effectiveness of this invention, the method of this invention is now applied to a converter grid-connected test case. The KAN network training process for the converter's multi-condition admittance in this embodiment is as follows: Figure 2 As shown, Figure 3 The loss after training the KAN model is shown. Figure 4 The generalization errors of existing ANN and PINN methods and the proposed KAN method for the multi-condition admittance model of converters were compared. Figure 5The training loss of ANN, PINN, and KAN methods for converter multi-condition admittance was compared with the sample size. Figure 6 The goodness-of-fit R-values ​​of ANN, PINN, and KAN methods were compared. 2 Changes in sample size.

[0077] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for identifying the admittance of a converter under multiple operating conditions, characterized in that, include: S1: Based on the Kolmogorov-Arnold representation theorem, the dimension reduction decomposition form of the general modular admittance function of the converter port admittance is derived, and the high-dimensional admittance function is decomposed into a combination of finite one-dimensional functions. S2: Based on the dimensionality reduction decomposition results of the converter admittance in step S1, construct a multi-condition admittance KAN model with concise sparse connectivity. S3: Based on Chebyshev polynomial design, a low-parameter dynamic learnable activation function is designed to achieve the best consistent approximation of the one-dimensional mapping function of admittance in step S1, and to learn the essential characteristics of admittance from small sample data.

2. The converter multi-condition admittance identification method according to claim 1, characterized in that, In step S1, by reducing the dimensionality of the general prior knowledge of the modular admittance of the converter port through decomposition, a one-dimensional mapping function between the layer-by-layer decomposition matrix and the admittance is obtained, thus yielding a combination of one-dimensional mapping functions for the high-dimensional admittance function, including: S11: Express the prior physical knowledge of converter port admittance as a modular admittance transfer function, and then use the positive-sequence self-admittance Y... pp (s), positive-sequence transitive admittance Y pn (s), negative-order self-admittance Y nn (s), Negative-order transit admittance Y np (s) Characterize the port admittance properties and form the admittance matrix: Among them, positive-order self-admittance Y pp (s) and positive-order transitive admittance Y pn (s) consists of functional sub-modules related to the electrical and control parts of the converter, expressed as: Where H c0 (s) represents the current controller transfer function module, G θ (s) represents the phase-locked loop transfer function module, G L (s) represents the filter transfer function module, Y1 is defined as the steady-state fundamental waveguide admittance, and s is the Laplace operator; S12: According to the Kolmogorov-Arnold representation theorem, for a high-dimensional nonlinear continuous function F(x) with port admittance, through a multi-level decomposition matrix Ψ... l The composite form is decomposed into a dimension reduction form with respect to the operating condition variable I. d I q The combination of V1 and a one-dimensional function related to frequency f is expressed as: in Represents the Hadamard product, s = j2πf; decomposes the matrix Ψ. l The one-dimensional mapping function is represented as: in Represents a one-dimensional mapping function to the input, decomposing the matrix Ψ. l It consists of one-dimensional mapping functions.

3. The converter multi-condition admittance identification method according to claim 2, characterized in that, In step S2, based on the sparse dimensionality reduction decomposition matrix of the port admittance obtained in step S1, a concise sparsely connected multi-condition admittance KAN model with physical structural constraints is designed, including: S21: Using the real and imaginary parts of the converter's admittance as output variables, the converter is represented in the form of conductance and susceptance. Y is extracted through a 2×(M+N) dimensional decomposition matrix Y2. pp The real and imaginary parts are represented as follows: S22: Based on the layer-by-layer decomposition matrix Ψ l In the form of designing each KAN layer Φ l The relationship between the number of neurons and sparse connections; the first KAN layer Φ1 is used to obtain working condition I. d I q The first layer, Φ2, corresponds to the decomposition matrix Ψ2, used to perform power function transformation on the one-dimensional function polynomial; the second layer, Φ3, corresponds to the decomposition matrix Ψ3, used to extract the real and imaginary parts of the admittance; based on the decomposition matrix Ψ... l Dimension setting of KAN layer Φ l The number of input and output neurons and their connections.

4. The converter multi-condition admittance identification method according to claim 3, characterized in that, In step S3, Chebyshev polynomials are used to embed Chebyshev dynamically learnable activation functions on the edges of the KAN model designed in S2, thereby achieving the best consistent approximation of the one-dimensional admittance mapping function, including: S31: The explicit expression for the Chebyshev polynomial function is: T k (x)=cos(k arccosx) Chebyshev polynomials consist of decoupled orthogonal basis functions, exhibiting low parameter redundancy and efficiently capturing the characteristics of one-dimensional admittance mapping functions with a low parameter count. Chebyshev polynomials achieve optimal uniform approximation of arbitrary continuous functions by minimizing the maximum error. For any one-dimensional mapping function... There exists a set of weight parameters The following relationship must be satisfied: Among them, T1 k For Chebyshev polynomial sum, T2 k Let k be a polynomial space of degree k, ||·|| ∞ It is an infinite norm; S32: T1 k To be a Chebyshev-learnable activation function, the one-dimensional mapping function of the actual admittance is expressed as a Chebyshev decomposition, as follows: Among them, parameter set By dynamically learning and adjusting based on input data, adaptive optimal approximation of one-dimensional mapping functions of varying complexity can be achieved.

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