A method and system for fast solution of eigenvalues ​​of wind farms based on the ring theorem.

Abstract

This invention belongs to the field of power system stability analysis and control technology, and relates to a method and system for rapid calculation of eigenvalues ​​of wind farms based on the ring theorem. The method includes the following steps: Step S1: online impedance identification; Step S2: constructing the characteristic equations of the wind farm grid-connected system; Step S3: establishing the ring theorem model; Step S4: stability analysis of the wind farm grid-connected system. The technical solution of this application adopts the calculation method of the ring theorem, which can quickly calculate the eigenvalues ​​of high-order wind farm grid-connected systems without reducing the order of the wind farm grid-connected system. It has high solution efficiency and strong ability to capture the main eigenvalues, and can quickly search for the main eigenvalues ​​of the wind farm grid-connected system.

Description

Technical Field

[0001] This invention belongs to the field of power system stability analysis and control technology, specifically relating to a method and system for rapidly solving the characteristic roots of wind farms based on the circular ring theorem. Background Technology

[0002] Wind power is a key force in my country's energy transition, and its stable operation is crucial. Due to fluctuations in wind speed and dispatch commands, wind farm operating points are widely distributed, resulting in diverse small-signal stability characteristics in the high-dimensional parameter space. The stability region can be used for oscillation early warning and can also improve stability by adjusting the operating point.

[0003] Currently, mainstream stability analysis methods include the Nyquist criterion and eigenvalue analysis. While the Nyquist criterion is intuitive, it cannot provide detailed information on each oscillation mode and struggles to identify the frequency and damping characteristics of the dominant mode, thus limiting its application when fine-grained analysis is required. Therefore, current methods primarily employ eigenvalue calculation based on impedance analysis, establishing the system impedance or admittance matrix and solving for eigenvalues ​​to assess stability. However, real-world wind farms are large-scale and topologically complex, resulting in extremely high system matrix orders and the "curse of dimensionality" problem. Traditional eigenvalue solving methods generally employ order reduction, which not only limits accuracy but also leads to slow and inefficient solution speeds due to the high polynomial order, failing to meet real-time analysis requirements. This is a shortcoming of existing technologies.

[0004] In view of this, it is very necessary to provide a method and system for fast solution of wind farm characteristic roots based on the circular ring theorem to solve the above-mentioned defects in the prior art. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by providing a method and system for rapidly solving the characteristic roots of wind farms based on the ring theorem, thereby solving the aforementioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A fast method for solving the eigenvalues ​​of a wind farm based on the ring theorem includes the following steps:

[0008] Step S1, the online impedance identification step, in which:

[0009] A wind farm model is established based on impedance modeling theory. The wind farm is identified online through its grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system.

[0010] Step S2 is the step of constructing the characteristic equations of the wind farm grid-connected system. In this step:

[0011] Based on the identified impedance, the nodal admittance matrix of the entire wind farm grid-connected system is constructed. The small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​(i.e., eigenvalues) of the impedance matrix or admittance matrix of the wind farm grid-connected system.

[0012] Step S3, the step of establishing the model of the circular theorem, in which:

[0013] Define the ring theorem, based on The polynomial coefficients can be calculated numerically to quickly determine the location of the zero point.

[0014] Step S4 is the step in the stability analysis of the wind farm grid-connected system. In this step:

[0015] The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all roots of the characteristic polynomial lie in the left half of the complex plane, the wind farm grid-connected system is stable with minimal disturbances. Considering the computational efficiency of online applications, instead of solving for all eigenvalues, we focus on the key factors determining stability—the dominant eigenvalues ​​near the imaginary axis. Therefore, the stability analysis problem can be transformed into locating the dominant eigenvalues ​​near the imaginary axis based on the rings theorem.

[0016] Preferably, step S1 specifically includes:

[0017] The wind farm grid-connected system collects voltage and current event data at the wind farm grid connection point in real time, and extracts the dynamic response characteristics of the wind farm grid-connected system using the dynamic mode decomposition method. Based on this, the impedance of the wind turbine units and lines is identified online using a piecewise affine model, and the equivalent impedance models of each unit and the aggregated impedance of the wind farm grid-connected system are updated in real time.

[0018] Preferably, step S2 specifically includes:

[0019] Based on the identified impedance of the wind farm grid-connected system, an eigenvalue-based stability analysis method is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the impedance or admittance matrix of the wind farm grid-connected system. Given the current context of deep coupling between wind farms and the power grid, and the complex structure of wind farm grid-connected systems, the eigenvalue-based stability analysis method demonstrates significant advantages.

[0020] Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system.

[0021]

[0022] in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator.

[0023] The above equation is essentially about solving for the following characteristic polynomial:

[0024]

[0025] in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

[0026] Preferably, step S3 specifically includes:

[0027] Based on the characteristic polynomial Construct the following n-order matrix:

[0028]

[0029] Characteristic polynomial of matrix A This can be deduced as:

[0030]

[0031] in, Let be the eigenvalue. Therefore, we can obtain the equation... with formula They are equivalent. Therefore, the eigenvalues ​​of matrix A and the wind farm grid-connected system are consistent.

[0032] In summary, the ring theorem under the roots of the characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n... ,in ,but The roots must all lie within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, as expressed by the following formula:

[0033]

[0034]

[0035] in, It is the order of the characteristic polynomial of the wind farm grid-connected system.

[0036] The annulus theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annulus results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annulus interval result with less conservatism. For example, the calculation method using the Frobenius norm of matrix A is as follows:

[0037]

[0038] in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix.

[0039] Preferably, the process of locating the dominant eigenvalues ​​near the imaginary axis based on the annulus theorem in step S4 specifically includes:

[0040] According to the inner circle property of the ring theorem, namely that there are no characteristic roots in the inner circle centered at the origin, in order to study the location of the dominant characteristic roots, the application of the inner circle needs to be extended to the entire complex plane.

[0041] Step S41, coordinate transformation:

[0042] First, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged. Therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle.

[0043] Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, the characteristics of the inner circle are determined, namely, the characteristic that there are no characteristic roots within the inner circle centered at the origin. This determines whether there are characteristic roots within the range of the inner circle of the ring.

[0044] Step S42, the search for the location of the dominant feature root, includes:

[0045] Step S421, virtual axis search:

[0046] fixed Different centers are taken sequentially along the imaginary axis (i.e., scanning oscillation frequencies). The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The radius of the inner circle is calculated from the spectral radius of matrix A. For matrix A and its characteristic polynomial, the constraint is: the compatibility norm of any matrix A in the wind farm grid-connected system. All are not less than the spectral radius of matrix A ,Right now The compatibility matrix norm refers to the matrix satisfying compatibility. The spectral radius is obtained by calculating the maximum modulus of all eigenvalues ​​of matrix A, as shown in the following expression:

[0047]

[0048] Step S422, Real Axis Search:

[0049] At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the starting point, and calculate the radius of the inner circle of the ring multiple times.

[0050] Step S423, determine the dominant eigenvalue:

[0051] If, during the search process, the radius of the inner circle of the ring gradually approaches zero, the dominant eigenvalue is determined to be near the current center. If, during the search along the imaginary axis, the radius of the inner circle of the ring remains unchanged, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant eigenvalue is far from the imaginary axis. If the real part of the dominant eigenvalue is positive and sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway. If such a situation can be ruled out during the online identification phase, it indicates that the current wind farm grid-connected system is operating in a stable region.

[0052] Furthermore, this invention provides a fast solution system for wind farm eigenvalues ​​based on the ring theorem, comprising:

[0053] The impedance online identification module contains:

[0054] A wind farm model is established based on impedance modeling theory. The wind farm is identified online through the grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system.

[0055] Construct a module for the characteristic equations of a wind farm grid-connected system. In this module:

[0056] Based on the identified impedance, the nodal admittance matrix of the entire wind farm grid-connected system is constructed. The small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​(i.e., eigenvalues) of the impedance matrix or admittance matrix of the wind farm grid-connected system.

[0057] Establish a module for modeling the circular theorem, in which:

[0058] Define the ring theorem, based on The polynomial coefficients can be calculated numerically to quickly determine the location of the zero point.

[0059] The stability analysis module for wind farm grid-connected systems includes:

[0060] The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all roots of the characteristic polynomial lie in the left half of the complex plane, the wind farm grid-connected system is stable with minimal disturbances. Considering the computational efficiency of online applications, instead of solving for all eigenvalues, we focus on the key factors determining stability—the dominant eigenvalues ​​near the imaginary axis. Therefore, the stability analysis problem can be transformed into locating the dominant eigenvalues ​​near the imaginary axis based on the rings theorem.

[0061] Preferably, the impedance online identification module specifically includes:

[0062] The wind farm grid-connected system collects voltage and current event data at the wind farm grid connection point in real time, and extracts the dynamic response characteristics of the wind farm grid-connected system using the dynamic mode decomposition method. Based on this, the impedance of the wind turbine units and lines is identified online using a piecewise affine model, and the equivalent impedance models of each unit and the aggregated impedance of the wind farm grid-connected system are updated in real time.

[0063] Preferably, the module for constructing the characteristic equations of the wind farm grid-connected system specifically includes:

[0064] Based on the identified impedance of the wind farm grid-connected system, an eigenvalue-based stability analysis method is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the impedance or admittance matrix of the wind farm grid-connected system. Given the current context of deep coupling between wind farms and the power grid, and the complex structure of wind farm grid-connected systems, the eigenvalue-based stability analysis method demonstrates significant advantages.

[0065] Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system.

[0066]

[0067] in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator.

[0068] The above equation is essentially about solving for the following characteristic polynomial:

[0069]

[0070] in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

[0071] Preferably, the module for establishing the circular theorem model specifically includes:

[0072] Based on the characteristic polynomial Construct the following n-order matrix:

[0073]

[0074] Characteristic polynomial of matrix A This can be deduced as:

[0075]

[0076] in, Let be the eigenvalue. Therefore, we can obtain the equation... with formula They are equivalent. Therefore, the eigenvalues ​​of matrix A and the wind farm grid-connected system are consistent.

[0077] In summary, the ring theorem under the roots of the characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n... ,in ,but The roots must all lie within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, as expressed by the following formula:

[0078]

[0079]

[0080] in, It is the order of the characteristic polynomial of the wind farm grid-connected system.

[0081] The annulus theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annulus results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annulus interval result with less conservatism. For example, the calculation method using the Frobenius norm of matrix A is as follows:

[0082]

[0083] in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix.

[0084] Preferably, the localization process of the dominant eigenvalue near the imaginary axis based on the ring theorem in the stability analysis module of the wind farm grid-connected system includes: a coordinate transformation submodule and a dominant eigenvalue location search submodule;

[0085] The coordinate transformation submodule specifically includes:

[0086] First, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged. Therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle.

[0087] Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, based on the characteristics of the inner ring, namely that there are no characteristic roots within the inner circle centered at the origin, it can be determined whether there are characteristic roots within the range of the inner circle of the ring.

[0088] The dominant feature root location search submodule includes: an imaginary axis search unit, a real axis search unit, and a dominant feature root determination unit;

[0089] The virtual axis search unit includes:

[0090] fixed Different centers are taken sequentially along the imaginary axis (i.e., scanning oscillation frequencies). The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The radius of the inner circle is calculated from the spectral radius of matrix A. For matrix A and its characteristic polynomial, the constraint is: the compatibility norm of any matrix A in the wind farm grid-connected system. All are not less than the spectral radius of matrix A ,Right now The compatibility matrix norm refers to the matrix satisfying compatibility. The spectral radius is obtained by calculating the maximum modulus of all eigenvalues ​​of matrix A, as shown in the following expression:

[0091]

[0092] The real axis searching unit includes:

[0093] At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the starting point, and calculate the radius of the inner circle of the ring multiple times.

[0094] The determination of the dominant feature root unit includes:

[0095] If, during the search process, the radius of the inner circle of the ring gradually approaches zero, the dominant eigenvalue is determined to be near the current center. If, during the search along the imaginary axis, the radius of the inner circle of the ring remains unchanged, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant eigenvalue is far from the imaginary axis. If the real part of the dominant eigenvalue is positive and sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway. If such a situation can be ruled out during the online identification phase, it indicates that the current wind farm grid-connected system is operating in a stable region.

[0096] The advantages of this invention lie in its strong ability to capture key eigenvalues, enabling rapid searching of the main eigenvalues ​​of a wind farm grid-connected system. By employing the ring theorem calculation method, it can quickly calculate the eigenvalues ​​of high-order wind farm grid-connected systems without reducing the order of the system, achieving high accuracy, fewer iterations, and computation time reduced to the second level. This results in high solution efficiency while preserving many original modes of the wind farm grid-connected system. The method of this invention can be further applied to real-time online evaluation and monitoring of large-scale power systems.

[0097] Therefore, it is evident that the present invention has outstanding substantive features and significant progress compared with the prior art, and the beneficial effects of its implementation are also obvious. Attached Figure Description

[0098] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0099] Figure 1 This is a flowchart of a method for quickly solving the characteristic roots of a wind farm based on the circular ring theorem, provided by this invention.

[0100] Figure 2 This is a schematic diagram of a system for rapidly solving the characteristic roots of a wind farm based on the circumcircle theorem, provided by this invention.

[0101] Figure 3 This is a schematic diagram of the location of the characteristic roots of the circular ring theorem, which is a method for quickly solving the characteristic roots of wind farms based on the circular ring theorem provided by this invention.

[0102] Figure 4 This is a schematic diagram of coordinate transformation for the application of the circular ring theorem in a method for quickly solving the characteristic roots of a wind farm based on the circular ring theorem, provided by this invention.

[0103] Figure 5This is a schematic diagram of the imaginary axis direction eigenvalue search based on the circular ring theorem, which is a fast solution method for wind farm eigenvalues ​​based on the circular ring theorem provided by this invention.

[0104] Figure 6 This is a schematic diagram of the real axis eigenvalue search based on the circular ring theorem, which is a method for quickly solving the characteristic roots of wind farms based on the circular ring theorem provided by this invention.

[0105] Figure 7 This is a schematic diagram illustrating the eigenvalue search of a complex wind farm grid-connected system based on the cyclic theorem, which is a method for rapidly solving the eigenvalues ​​of a wind farm based on the cyclic theorem provided by this invention. Detailed Implementation

[0106] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following implementation methods.

[0107] Example 1:

[0108] like Figure 1 As shown in the figure, this embodiment provides a fast solution method for wind farm characteristic roots based on the circular ring theorem, which includes the following steps:

[0109] Step S1, the online impedance identification step, in which:

[0110] A wind farm model is established based on impedance modeling theory. The wind farm is identified online through the grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system.

[0111] Step S2 is the step of constructing the characteristic equations of the wind farm grid-connected system. In this step:

[0112] Based on the identified impedance, the nodal admittance matrix of the entire wind farm grid-connected system is constructed. The small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​(i.e., eigenvalues) of the impedance matrix or admittance matrix of the wind farm grid-connected system.

[0113] Step S3, the step of establishing the model of the circular theorem, in which:

[0114] Define the ring theorem, based on The polynomial coefficients can be calculated numerically to quickly determine the location of the zero point.

[0115] Step S4 is the step in the stability analysis of the wind farm grid-connected system. In this step:

[0116] The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all roots of the characteristic polynomial lie in the left half of the complex plane, the wind farm grid-connected system is stable with minimal disturbances. Considering the computational efficiency of online applications, instead of solving for all eigenvalues, we focus on the key factors determining stability—the dominant eigenvalues ​​near the imaginary axis. Therefore, the stability analysis problem can be transformed into locating the dominant eigenvalues ​​near the imaginary axis based on the rings theorem.

[0117] Step S1 specifically includes:

[0118] The wind farm grid-connected system collects voltage and current event data at the wind farm grid connection point in real time, and extracts the dynamic response characteristics of the wind farm grid-connected system using the dynamic mode decomposition method. Based on this, the impedance of the wind turbine units and lines is identified online using a piecewise affine model, and the equivalent impedance models of each unit and the aggregated impedance of the wind farm grid-connected system are updated in real time.

[0119] Step S2 specifically includes:

[0120] Based on the identified impedance of the wind farm grid-connected system, an eigenvalue-based stability analysis method is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the impedance or admittance matrix of the wind farm grid-connected system. Given the current context of deep coupling between wind farms and the power grid, and the complex structure of wind farm grid-connected systems, the eigenvalue-based stability analysis method demonstrates significant advantages.

[0121] Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system.

[0122]

[0123] in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator.

[0124] The above equation is essentially about solving for the following characteristic polynomial:

[0125]

[0126] in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

[0127] Step S3 specifically includes:

[0128] Based on the characteristic polynomial Construct the following n-order matrix:

[0129]

[0130] Characteristic polynomial of matrix A This can be deduced as:

[0131]

[0132] in, Let be the eigenvalue. Therefore, we can obtain the equation... with formula They are equivalent. Therefore, the eigenvalues ​​of matrix A and the wind farm grid-connected system are consistent.

[0133] In summary, the ring theorem under the roots of the characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n... ,in ,but The root must lie entirely within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, such as... Figure 3 As shown, the formula is as follows:

[0134]

[0135]

[0136] in, It is the order of the characteristic polynomial of the wind farm grid-connected system.

[0137] The annulus theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annulus results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annulus interval result with less conservatism. For example, the calculation method using the Frobenius norm of matrix A is as follows:

[0138]

[0139] in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix.

[0140] The process of locating the dominant eigenvalues ​​near the imaginary axis based on the annulus theorem in step S4 specifically includes:

[0141] According to the inner circle property of the ring theorem, namely that there are no characteristic roots in the inner circle centered at the origin, in order to study the location of the dominant characteristic roots, the application of the inner circle needs to be extended to the entire complex plane.

[0142] Step S41, coordinate transformation:

[0143] like Figure 4 As shown, firstly, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged. Therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle.

[0144] Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, based on the characteristics of the inner ring, namely that there are no characteristic roots within the inner circle centered at the origin, it can be determined whether there are characteristic roots within the range of the inner circle of the ring.

[0145] Step S42, the search for the location of the dominant feature root, includes:

[0146] Step S421, virtual axis search:

[0147] fixed Different centers are taken sequentially along the imaginary axis (i.e., scanning oscillation frequencies). The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The radius of the inner circle is calculated from the spectral radius of matrix A. For matrix A and its characteristic polynomial, the constraint is: the compatibility norm of any matrix A in the wind farm grid-connected system. All are not less than the spectral radius of matrix A ,Right now The compatibility matrix norm refers to the matrix satisfying compatibility. The spectral radius is obtained by calculating the maximum modulus of all eigenvalues ​​of matrix A, as shown in the following expression:

[0148]

[0149] Step S422, Real Axis Search:

[0150] At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the starting point, and calculate the radius of the inner circle of the ring multiple times.

[0151] Step S423, determine the dominant eigenvalue:

[0152] If, during the search process, the radius of the inner circle of the ring gradually approaches zero, the dominant eigenvalue is determined to be near the current center. If, during the search along the imaginary axis, the radius of the inner circle of the ring remains unchanged, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant eigenvalue is far from the imaginary axis. If the real part of the dominant eigenvalue is positive and sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway. If such a situation can be ruled out during the online identification phase, it indicates that the current wind farm grid-connected system is operating in a stable region.

[0153] Example 2:

[0154] like Figure 2 As shown in the figure, this embodiment provides a fast solution system for wind farm characteristic roots based on the rings theorem, including:

[0155] Impedance online identification module 1, in which:

[0156] A wind farm model is established based on impedance modeling theory. The wind farm is identified online through the grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system.

[0157] Module 2, which constructs the characteristic equations of a wind farm grid-connected system, includes:

[0158] Based on the identified impedance, the nodal admittance matrix of the entire wind farm grid-connected system is constructed. The small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​(i.e., eigenvalues) of the impedance matrix or admittance matrix of the wind farm grid-connected system.

[0159] Module 3 establishes the model for the circular theorem. In this module:

[0160] Define the ring theorem, based on The polynomial coefficients can be calculated numerically to quickly determine the location of the zero point.

[0161] Module 4, Stability Analysis of Wind Farm Grid-Connected System, contains:

[0162] The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all roots of the characteristic polynomial lie in the left half of the complex plane, the wind farm grid-connected system is stable with minimal disturbances. Considering the computational efficiency of online applications, instead of solving for all eigenvalues, we focus on the key factors determining stability—the dominant eigenvalues ​​near the imaginary axis. Therefore, the stability analysis problem can be transformed into locating the dominant eigenvalues ​​near the imaginary axis based on the rings theorem.

[0163] The impedance online identification module 1 specifically includes:

[0164] The wind farm grid-connected system collects voltage and current event data at the wind farm grid connection point in real time, and extracts the dynamic response characteristics of the wind farm grid-connected system using the dynamic mode decomposition method. Based on this, the impedance of the wind turbine units and lines is identified online using a piecewise affine model, and the equivalent impedance models of each unit and the aggregated impedance of the wind farm grid-connected system are updated in real time.

[0165] The aforementioned module 2 for constructing the characteristic equations of a wind farm grid-connected system specifically includes:

[0166] Based on the identified impedance of the wind farm grid-connected system, an eigenvalue-based stability analysis method is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the impedance or admittance matrix of the wind farm grid-connected system. Given the current context of deep coupling between wind farms and the power grid, and the complex structure of wind farm grid-connected systems, the eigenvalue-based stability analysis method demonstrates significant advantages.

[0167] Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system.

[0168]

[0169] in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator.

[0170] The above equation is essentially about solving for the following characteristic polynomial:

[0171]

[0172] in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

[0173] The aforementioned module 3 for establishing the circular theorem model specifically includes:

[0174] Based on the characteristic polynomial Construct the following n-order matrix:

[0175]

[0176] Characteristic polynomial of matrix A This can be deduced as:

[0177]

[0178] in, Let be the eigenvalue. Therefore, we can obtain the equation... with formula They are equivalent. Therefore, the eigenvalues ​​of matrix A and the wind farm grid-connected system are consistent.

[0179] In summary, the ring theorem under the roots of the characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n... ,in ,but The roots must all lie within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, as expressed by the following formula:

[0180]

[0181]

[0182] in, It is the order of the characteristic polynomial of the wind farm grid-connected system.

[0183] The annulus theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annulus results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annulus interval result with less conservatism. For example, the calculation method using the Frobenius norm of matrix A is as follows:

[0184]

[0185] in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix.

[0186] The process of locating the dominant eigenvalue near the imaginary axis based on the circular theorem in the stability analysis module 4 of the wind farm grid-connected system includes: a coordinate transformation submodule and a dominant eigenvalue location search submodule;

[0187] According to the inner circle property of the ring theorem, namely that there are no characteristic roots in the inner circle centered at the origin, in order to study the location of the dominant characteristic roots, the application of the inner circle needs to be extended to the entire complex plane.

[0188] The coordinate transformation submodule specifically includes:

[0189] First, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged. Therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle.

[0190] Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, based on the characteristics of the inner ring, namely that there are no characteristic roots within the inner circle centered at the origin, it can be determined whether there are characteristic roots within the range of the inner circle of the ring.

[0191] The dominant feature root location search submodule includes: an imaginary axis search unit, a real axis search unit, and a dominant feature root determination unit;

[0192] The virtual axis search unit includes:

[0193] fixed Different centers are taken sequentially along the imaginary axis (i.e., scanning oscillation frequencies). The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The radius of the inner circle is calculated from the spectral radius of matrix A. For matrix A and its characteristic polynomial, the constraint is: the compatibility norm of any matrix A in the wind farm grid-connected system. All are not less than the spectral radius of matrix A ,Right now The compatibility matrix norm refers to the matrix satisfying compatibility. The spectral radius is obtained by calculating the maximum modulus of all eigenvalues ​​of matrix A, as shown in the following expression:

[0194]

[0195] The real axis searching unit includes:

[0196] At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the starting point, and calculate the radius of the inner circle of the ring multiple times.

[0197] The determination of the dominant feature root unit includes:

[0198] If, during the search process, the radius of the inner circle of the ring gradually approaches zero, the dominant eigenvalue is determined to be near the current center. If, during the search along the imaginary axis, the radius of the inner circle of the ring remains unchanged, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant eigenvalue is far from the imaginary axis. If the real part of the dominant eigenvalue is positive and sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway. If such a situation can be ruled out during the online identification phase, it indicates that the current wind farm grid-connected system is operating in a stable region.

[0199] Example 3:

[0200] Based on experiments conducted in simulation software on a single wind turbine generator model, the coefficients of the univariate nth-degree polynomial were obtained. .

[0201] Calculate the annulus at the origin using the Frobenius norm, 1-norm, and ∞-norm, respectively, where the radius of the largest inner circle is... For 1-norm:

[0202]

[0203] Secondly, translate the coordinate system along the imaginary axis, and draw annular circles with centers at intervals of 0.5. The interval between the centers can also be adjusted according to the size of the inner circle of the annulus. The result is as follows. Figure 5 As shown in (a). Inner circle radius , , The gradual increase in radius values ​​indicates that all eigenvalues ​​are far from the imaginary axis. For a grid-connected wind farm operating online, the eigenvalues ​​will not undergo large-scale abrupt changes, and the system can be considered stable at present. The calculated eigenvalues ​​are marked with "X" in the graph, and the distribution of the eigenvalues ​​proves that the search results of the ring theorem are correct.

[0204] When changes occur in the wind farm grid-connected system, the dominant eigenvalues ​​tend towards critical stability or instability, yielding the coefficients of a univariate nth-degree polynomial. Consider the following grid connection system for this wind farm:

[0205] First, calculate the annulus at the origin using the Frobenius norm, 1-norm, and ∞-norm, respectively, where the radius of the largest inner circle is... For 1-norm:

[0206]

[0207] Secondly, draw a ring along the same imaginary axis, and the result is as follows. Figure 5 As shown in (b), it can be seen that... The radius of the annulus is very small, and the center of the annulus is (0, 1j). This indicates that there is a dominant eigenvalue near the current frequency close to the imaginary axis. Therefore, it is necessary to further determine the location of the dominant eigenvalue to assess stability.

[0208] Finally, at the imaginary part 1j, draw an annulus along the real axis, and the result is as follows. Figure 6 As shown in (a), it can be seen that as the search proceeds along the positive real axis, the inner circle gradually increases, indicating that there are no characteristic roots along the positive real axis. Based on... Figure 6As shown in (b), the search proceeds along the negative real axis, with the inner circle gradually decreasing in size. The search stops when the radius is less than 0.05. The smallest annular radius is 0.023, and its center is located at (…). 0.15, 1j). Considering the conservatism of the ring theorem and retaining a certain stability margin, the estimated position of the eigenvalues ​​is ( ). 0.173,1j). The calculated eigenvalues ​​are marked with the symbol "X" in the figure, and the dominant eigenvalues ​​are located at ( (0.2,1j). The search results and calculation results are very close, proving that the search results based on the annulus theorem are correct and retain a certain margin. To further improve the accuracy of the eigenvalues, the number of iterations of the search along the imaginary and real axes of the annulus can be increased, or a numerical method can be used to solve the problem in a small neighborhood of the final annulus.

[0209] For higher-order and more complex wind farm systems, a schematic diagram of the search using the ring theorem is shown below. Figure 7 As shown, using the method provided in this embodiment, the solution time is only 1.61 seconds, which is a significant improvement in speed and efficiency compared to other methods.

[0210] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The methods disclosed in the embodiments are described simply because they correspond to the systems disclosed in the embodiments; relevant details can be found in the method section.

[0211] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0212] In the embodiments provided by this invention, it should be understood that the disclosed systems, methods, and approaches can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or units may be electrical, mechanical, or other forms.

[0213] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0214] In addition, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit.

[0215] Similarly, in the various embodiments of the present invention, each processing unit can be integrated into a functional module, or each processing unit can exist physically, or two or more processing units can be integrated into a functional module.

[0216] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0217] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus 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 apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0218] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for rapidly solving the eigenvalues ​​of a wind farm based on the circular ring theorem, characterized in that, Includes the following steps: Step S1, the online impedance identification step, in which: A wind farm model is established based on impedance modeling theory; the wind farm is identified online through the grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system; Step S2 is the step of constructing the characteristic equations of the wind farm grid-connected system. In this step: Based on the identified impedance, the node admittance matrix of the entire wind farm grid-connected system is constructed; the small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​of the impedance matrix or admittance matrix of the wind farm grid-connected system. Step S3, the step of establishing the model of the circular theorem, in which: Define the ring theorem based on the Laplace operator. The polynomial coefficients can be used to quickly determine the location of the zero point through numerical calculation; Step S4 is the step in the stability analysis of the wind farm grid-connected system. In this step: The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all the roots of the characteristic polynomial are located in the left half of the complex plane, then the wind farm grid-connected system is stable with minimal disturbances. Step S3 specifically includes: Based on the characteristic polynomial Construct the following n-order matrix: in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem. Characteristic polynomial of matrix A This can be deduced as: in, For eigenvalues; Equation with formula Equivalent, matrix A and the eigenvalues ​​of the wind farm grid-connected system are the same; The circular theorem under the roots of a characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n ,in , The roots must all lie within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, as expressed by the following formula: in, It is the order of the characteristic polynomial of the wind farm grid-connected system; The annular theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annular results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annular interval result with less conservatism. The calculation method based on the Frobenius norm of matrix A is as follows: in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix; The process of locating the dominant eigenvalues ​​near the imaginary axis based on the annulus theorem in step S4 specifically includes: Step S41, coordinate transformation: First, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged; therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle. Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, based on the characteristics of the inner ring, namely that there are no characteristic roots within the inner circle centered at the origin, it can be determined whether there are characteristic roots within the range of the inner circle of the ring. Step S42, the search for the location of the dominant feature root, includes: Step S421, virtual axis search: fixed By taking different centers along the imaginary axis, the oscillation frequency is scanned. The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The inner circle radius is calculated from the spectral radius of matrix A. The spectral radius is obtained by calculating the maximum value of the modulus of all eigenvalues ​​of matrix A, as shown in the following expression: Step S422, Real Axis Search: At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the point, and calculate the radius of the inner circle of the annulus multiple times; Step S423, determine the dominant eigenvalue: If, during the search process, the radius of the inner circle of the ring gradually approaches zero, it is determined that the dominant characteristic root is located near the current center of the ring. If, during the search along the imaginary axis, the radius of the inner circle of the ring does not change, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant characteristic root is far from the imaginary axis. If the real part of the dominant characteristic root is positive and its value is sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway.

2. The method for rapidly solving the characteristic roots of a wind farm based on the circular ring theorem according to claim 1, characterized in that, Step S1 specifically includes: The wind farm grid connection system collects voltage and current event data at the wind farm grid connection point in real time, extracts the dynamic response characteristics of the wind farm grid connection system through dynamic mode decomposition, and identifies the impedance of wind turbine units and lines online based on a piecewise affine model, and updates the equivalent impedance model of each unit and the aggregated impedance of the wind farm grid connection system in real time.

3. The method for rapidly solving the characteristic roots of a wind farm based on the circular ring theorem according to claim 2, characterized in that, Step S2 specifically includes: Based on the identified wind farm grid-connected system impedance, the method based on eigenvalue calculation is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the wind farm grid-connected system impedance or admittance matrix. Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system: in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator; The above equation is essentially about solving for the following characteristic polynomial: in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

4. A system for rapidly solving the eigenvalues ​​of a wind farm based on the ring theorem, characterized in that, include: The impedance online identification module contains: A wind farm model is established based on impedance modeling theory. The wind farm is identified online through the grid connection point and the wind farm grid connection system to obtain the dynamic impedance characteristics of the current operating point of the wind farm grid connection system. Construct a module for the characteristic equations of a wind farm grid-connected system. In this module: Based on the identified impedance, the node admittance matrix of the entire wind farm grid-connected system is constructed; the small-signal stability analysis problem of the wind farm grid-connected system is transformed into the problem of solving the eigenvalues ​​of the impedance matrix or admittance matrix of the wind farm grid-connected system. Establish a module for modeling the circular theorem, in which: Define the ring theorem based on the Laplace operator. The polynomial coefficients can be used to quickly determine the location of the zero point through numerical calculation; The stability analysis module for wind farm grid-connected systems includes: The stability of a wind farm grid-connected system is determined by the characteristic polynomial of matrix A: if all the roots of the characteristic polynomial are located in the left half of the complex plane, then the wind farm grid-connected system is stable with minimal disturbances. The module for establishing the circular theorem model specifically includes: Based on the characteristic polynomial Construct the following n-order matrix: in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem. Characteristic polynomial of matrix A This can be deduced as: in, For the eigenvalues; therefore, we can obtain the equation with formula They are equivalent; therefore, the eigenvalues ​​of matrix A and the wind farm grid-connected system are consistent. The circular theorem under the roots of a characteristic polynomial with complex coefficients is defined as: a univariate polynomial of degree n ,in ,but The roots must all lie within the annulus of the complex plane, that is, between the inner side of the outer circle and the outer side of the inner circle, as expressed by the following formula: in, It is the order of the characteristic polynomial of the wind farm grid-connected system; The annular theorem is calculated using the Frobenius norm, 1-norm, or ∞-norm of matrix A. Different norms yield different annular results. By comparing all norms, the largest inner ring value and the smallest outer ring value are found, thus obtaining the annular interval result with less conservatism. The calculation method based on the Frobenius norm of matrix A is as follows: in, It is the matrix norm, F is an abbreviation for Frobenius, and m represents the number of rows in the matrix; The process of locating the dominant eigenvalue near the imaginary axis based on the ring theorem in the stability analysis module of the wind farm grid-connected system includes: a coordinate transformation submodule and a dominant eigenvalue location search submodule; The coordinate transformation submodule specifically includes: First, the original equation The inner circle of the annulus can be obtained using the annulus theorem. Then, through coordinate transformation, Replace with , Using the imaginary unit, reconstruct the univariate polynomial of degree n, and then analyze the inner circle of the annulus again based on the annulus theorem. and the inner circle the center of the circle As the origin in the complex plane, the radius of the inner circle remains unchanged; therefore, by applying the original equation... Coordinate transformation changes the position of the center of the inner circle. Based on the above process, an inner circle can be constructed at any position in the complex plane. Then, based on the characteristics of the inner ring, namely that there are no characteristic roots within the inner circle centered at the origin, it can be determined whether there are characteristic roots within the range of the inner circle of the ring. The dominant feature root location search submodule includes: an imaginary axis search unit, a real axis search unit, and a dominant feature root determination unit; The virtual axis search unit includes: fixed By taking different centers along the imaginary axis, the oscillation frequency is scanned. The radius of the inner circle of the annulus is calculated multiple times. If the radius decreases at a certain frequency, it indicates the presence of a dominant eigenvalue in the vicinity. The inner circle radius is calculated from the spectral radius of matrix A. The spectral radius is obtained by calculating the maximum value of the modulus of all eigenvalues ​​of matrix A, as shown in the following expression: The real axis searching unit includes: At the detected oscillation frequency Nearby, adjust the position of the inner circle along the real axis direction, from Start searching to the left or right from the point, and calculate the radius of the inner circle of the annulus multiple times; The determination of the dominant feature root unit includes: If, during the search process, the radius of the inner circle of the ring gradually approaches zero, it is determined that the dominant characteristic root is located near the current center of the ring. If, during the search along the imaginary axis, the radius of the inner circle of the ring does not change, and all the inner circles of the ring can cover the imaginary axis and its surrounding complex plane region, it indicates that the current dominant characteristic root is far from the imaginary axis. If the real part of the dominant characteristic root is positive and its value is sufficiently large, it indicates that the wind farm grid-connected system has already entered an unstable state, manifested as rapidly diverging oscillations or voltage and current runaway.

5. The system for rapidly solving the eigenvalues ​​of a wind farm based on the ring theorem according to claim 4, characterized in that, The aforementioned online impedance identification module specifically includes: The wind farm grid connection system collects voltage and current event data at the wind farm grid connection point in real time, extracts the dynamic response characteristics of the wind farm grid connection system through dynamic mode decomposition, and identifies the impedance of wind turbine units and lines online based on a piecewise affine model, and updates the equivalent impedance model of each unit and the aggregated impedance of the wind farm grid connection system in real time.

6. The system for rapidly solving the eigenvalues ​​of a wind farm based on the circular ring theorem according to claim 5, characterized in that, The module for constructing the characteristic equations of a wind farm grid-connected system specifically includes: Based on the identified wind farm grid-connected system impedance, the method based on eigenvalue calculation is used to directly obtain all small-signal dynamic information of the wind farm grid-connected system by solving its eigenvalues, starting from the wind farm grid-connected system impedance or admittance matrix. Solving for the zeros of the determinant of the impedance matrix yields the characteristic roots of the wind farm grid-connected system: in, The characteristic polynomial of the wind farm grid-connected system is obtained through stability analysis. For the Laplace operator; The above equation is essentially about solving for the following characteristic polynomial: in, ,..., , The coefficients are complex, and the coefficients differ depending on the region of the complex plane corresponding to the annulus theorem.

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