Impedance automated modeling method for frequency-split offshore wind power system

Abstract

The application discloses an impedance automatic modeling method for a frequency-division offshore wind power system, which comprises the following steps: firstly, constructing a mathematical model of an element and linearizing the mathematical model to obtain a continuous time domain small signal model of the element, and discretizing the continuous time domain small signal model through trapezoidal integration to obtain a discrete time domain small signal model of the element; then, based on a correlation matrix and node analysis, converting the discrete time domain model at the element level to a system level model; finally, through z transformation and bilinear transformation, converting the discrete time domain model at the system level to a continuous frequency domain model at the system level, and realizing the above process through codes in a computer to automatically obtain the impedance of the system. The application replaces traditional manual symbolic derivation with numerical calculation, significantly improves the modeling efficiency, has good flexibility and expansibility, can be suitable for complex systems and new topological structures, provides an efficient stability analysis tool for the design and optimization of offshore wind farms and grid-connected systems, and can be extended to other renewable energy grid-connected systems containing multiple power electronic converters.

Description

Technical Field

[0001] This invention relates to the field of power system impedance modeling and analysis, and in particular to an automated impedance modeling method for frequency-division offshore wind power systems. Background Technology

[0002] Wind energy, as a renewable energy source with large installed capacity and relatively low cost, has become an important direction for global energy transition. Among them, offshore wind energy resources have attracted much attention due to their abundant reserves and great development potential. However, the grid connection process of offshore wind farms is prone to various resonance problems such as subsynchronous oscillations and medium-to-high frequency oscillations, which seriously threaten the safe and stable operation of the power system.

[0003] To address the broadband oscillation problem caused by wind power grid connection, existing research solutions employ small-signal stability analysis methods, including time-domain frequency sweeping, eigenvalue methods, and s-domain impedance analysis. Time-domain frequency sweeping measures impedance by injecting a signal, providing a relatively intuitive physical meaning and facilitating the analysis of oscillation causes. However, for large systems, its sweeping efficiency is very low, and it is significantly affected by the number and values ​​of frequency points. The eigenvalue method analyzes various information about harmonic resonances by solving the eigenvalues ​​of the state matrix, offering relatively accurate results. However, the computational load increases exponentially when dealing with large and complex networks, resulting in long computation times and heavy workloads. S-domain impedance analysis, based on equivalent impedance and port external characteristics, uses the s-transform to quantitatively describe the system's frequency domain characteristics, making it one of the most widely used theoretical methods in the field of stability analysis for new energy grid-connected systems. However, traditional impedance modeling relies on manual derivation. For large offshore wind farms and new transmission topologies (such as frequency-division transmission), manual modeling is cumbersome, inefficient, and prone to errors due to topology complexity or parameter variations, making it difficult to adapt to the demands of rapid technological advancements.

[0004] Furthermore, while existing convergent or reduced-order modeling methods can simplify the calculations of s-domain impedance analysis, they may lose system topology information and lack accuracy in the mid-to-high frequency range. Therefore, there is an urgent need for an automated, universal, and accurate impedance modeling method to address the bottleneck problem in small-signal stability analysis of complex systems. Summary of the Invention

[0005] To address the problems of inefficient and complex impedance modeling of grid-connected wind power systems, which relies on manual derivation, and is difficult to adapt to new topologies, this invention proposes an automated impedance modeling method for frequency-division offshore wind power systems. This method replaces the traditional continuous-time model with a discrete-time small-signal model, reducing computational load and facilitating computer coding. Simultaneously, it utilizes z-transform and bilinear transform to establish a mapping relationship between the continuous frequency domain and the discrete time domain, constructing a complete automated framework for impedance modeling. This method boasts extremely high modeling efficiency, as well as good flexibility and scalability.

[0006] The objective of this invention can be achieved through the following technical solutions: An automated impedance modeling method for frequency-division offshore wind power systems is characterized by the following steps: 1) Component Model Construction: Construct a mathematical model in the form of differential-algebraic equations for the wind turbine (WTG) components in the offshore wind power system based on frequency division transmission: (10) In the formula, k opt It is the maximum power tracking factor; ω r It is the rotor speed of the permanent magnet synchronous machine; P ref , P e These are the power reference value and the electromagnetic power, respectively. T m , T e These are mechanical torque and electromagnetic torque, respectively. H r It is the rotor inertial constant of the permanent magnet synchronous machine. / and / These represent the voltage and current along the dq axis of the stator, respectively. ω er It is the base value of the stator angular frequency; R s It is the stator resistance; L sd / L s and q represent the inductances along the d-axis and q-axis of the stator, respectively. ψ r denoted as , where is the magnetic flux of the rotor. z 1, z 2 and z 3 represents a state variable; / and / These are the proportional / integral gains of the outer and inner loop control circuits on the permanent magnet synchronous machine side, respectively. s d and s q Permanent magnet synchronous machine side control target; This indicates the inverter output voltage; L f and R f These are the inductance and resistance of the filter, respectively; ω g Indicates the angular velocity of the power grid; Cdc It is a DC capacitor; u dc This is the DC bus voltage; P vsc This refers to the inverter's output power. P s This refers to the stator output power of the permanent magnet synchronous motor. u ref DC bus voltage reference value; Q ref This is a reference value for reactive power. / and / These represent the grid voltage and current along the d and q axes, respectively. / and / These are the proportional / integral gains of the inner and outer control loops on the power grid side, respectively. g d and g q The target for grid-side control.

[0007] Construct a mathematical model in the form of differential-algebraic equations for the frequency division transmission (FFTS) element in the offshore wind power system based on frequency division transmission: (11) In the formula, ω low This refers to the low-frequency side angle frequency of the frequency division transmission system. L f1 and L f2 For filtering inductors; C f For filtering capacitors; and These represent the low-frequency side voltage and current of the frequency-division power transmission system, respectively. and These represent the voltage output and current output of the filter circuit, respectively. and These represent the voltage and current of the capacitor, respectively. z 4, z 5, z 6 and z 7 is a state variable; and These represent the zero-sequence components of the arm voltage and current in a frequency-division transmission system, respectively. for The reference voltage; / and / These are the proportional / integral gains of the outer and inner loop control circuits, respectively. and It controls the target value.

[0008] The general mathematical model of the two components mentioned above can be expressed as follows: (12) In the formula, x ( t ) represents the state variable of the component. u dq ( t )and i dq ( t ) represent the voltage and current of the component in the dq coordinate system, respectively.

[0009] 2) Initialization Data Acquisition and Linearization: Based on the system parameters, power flow calculations are performed to determine the steady-state operating point of each component. The mathematical model is then linearized around this operating point to obtain the continuous-time small-signal model of each component, typically expressed as: (13) In the formula, A CT , B CT , C CT and D CT The coefficient matrix, x 0 and u dq0 This represents the state variables and dq voltage value at the steady-state operating point.

[0010] 3) Discretization: Introducing a "historical current term" Δ p ( t ): (14) The continuous time-domain small-signal model is discretized using the trapezoidal integral method, transforming the continuous differential equation into a recursive form of the discrete time-domain small-signal model. (15) In the formula, Δ t The step size for discretization, the coefficient matrix A DT , B DT , C DT and D DT It can be calculated using the following formula: (16) 4) System-level model integration: Based on component interconnection relationships, three types of association matrices are defined: node-branch, node-dynamic component, and node-port. K Node-Branch , K Node-Dyn and K Node-Port The connections between elements are represented using 0, 1, or -1. If there is no connection, the corresponding matrix element is 0; if there is a forward connection, the corresponding matrix element is 1; and if there is a reverse connection, the corresponding matrix element is -1. Node analysis couples the discrete-time small-signal models of each component into a unified system-level discrete-time small-signal model. (17) In the formula, and These represent the voltage and current flowing into the subsystem from the external port, respectively. It is a column vector of the discrete state variables of all dynamic elements. (Coefficient matrix) , , and It can be calculated using the following formula: (18) In the formula, the matrix , and All are block diagonal matrices, with the diagonal blocks representing the dynamic elements. A DT , B DT and C DT The matrix is ​​arranged in order. It is also a block diagonal matrix, where the diagonal blocks are composed of all the elements. D DT The matrix is ​​arranged in order.

[0011] 5) Impedance derivation: Perform a z-transform on the system-level discrete-time small-signal model to obtain the discrete-frequency-domain transfer function matrix. H DF ( z ): (19) The formula for the bilinear transformation is: (20) Mapping the poles and zeros of the discrete frequency domain to the continuous frequency domain yields the continuous frequency domain admittance. G CF ( s ); for admittanceG CF ( s Inverse the equation to obtain the system impedance. Z CF ( s ).

[0012] Finally, based on the aforementioned process, a computer program is developed that only requires manual input of the component mathematical model and system parameters. Subsequent linearization, discretization, system integration, and impedance derivation are all automatically completed by the program, achieving full automation of the process.

[0013] The technical effects of this invention are as follows: The impedance automated modeling method provided by this invention is based on the transformation from "continuous time domain to discrete time domain to discrete frequency domain to continuous frequency domain." It replaces traditional manual symbolic derivation with numerical calculation. Only the construction of the component mathematical model requires manual intervention; the rest of the process is executed automatically by the computer, significantly reducing labor costs and avoiding errors from manual derivation. Compared to the traditional frequency scanning method (which requires multiple time-domain simulations), this method reduces the calculation time from several hours to seconds, improving efficiency by thousands of times. Through trapezoidal integral discretization and rigorous mathematical transformations, the accuracy of the impedance results is guaranteed. When the system topology or parameters change, only the component mathematical model or correlation matrix needs to be updated; the entire modeling framework does not need to be reconstructed. This method is adaptable to new topologies such as frequency division transmission and complex multi-component systems, and can be extended to other renewable energy grid-connected systems. Attached Figure Description

[0014] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the impedance automated modeling algorithm framework for frequency-division offshore wind power systems of the present invention; Figure 2 This is a schematic diagram of the circuit topology and control system of the permanent magnet synchronous wind turbine (WTG) used in the embodiments of the present invention; Figure 3 This is a schematic diagram of the circuit topology and control system of the low-frequency side of the frequency division transmission system in an embodiment of the present invention; Figure 4 This is a schematic diagram of a system composed of a large number of components; Figure 5 This is a diagram of the offshore wind farm structure based on frequency division transmission; Figure 6 This is a schematic diagram comparing the impedance and admittance Bode plots obtained using automated modeling and frequency sweeping methods in an embodiment of the present invention. Detailed Implementation

[0015] The present invention will be further described below with reference to the accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0016] Example This embodiment realizes automated impedance modeling of offshore wind power based on frequency division transmission. Its algorithm framework is as follows: Figure 1 As shown. Includes the following steps: 1. Mathematical Model Establishment. Through analytical derivation or by referring to technical documents, a mathematical model of the wind turbine and frequency-division transmission components in offshore wind power based on frequency division transmission is constructed.

[0017] 2. Initialize data acquisition and linearization. Based on the parameters of the offshore wind power system based on frequency division transmission, perform power flow calculations to determine the steady-state operating point of all components. Linearize the mathematical model at the steady-state operating point to construct a continuous time-domain small-signal model for all components.

[0018] 3. Discretization. The continuous-time-domain small-signal model is transformed into a discrete-time-domain small-signal model using the trapezoidal integral method, obtaining the coefficient matrix. A DT , B DT , C DT and D DT .

[0019] 4. System Model Construction. Based on the principle of interconnection data and port equivalence between components, the system-level discrete-time small-signal model matrix is ​​obtained. , , and 5. Impedance Derivation. The system-level discrete-time small-signal model is subjected to z-transform and bilinear transform to obtain the continuous frequency domain admittance. G CF ( s ); for the admittance G CF ( s Inverse the equation to obtain the system impedance. Z CF ( s ).

[0020] The following will provide a more detailed explanation of the steps involved in the automated impedance modeling of this embodiment.

[0021] I. Detailed Explanation of Mathematical Model Establishment Figure 2The circuit composition and control system of the permanent magnet synchronous wind turbine in the embodiment of the present invention are shown. Based on the connection and control relationship of the circuit composition and control system of the permanent magnet synchronous wind turbine, a mathematical model of the permanent magnet synchronous wind turbine is constructed.

[0022] Based on the characteristics of permanent magnet synchronous machines, the following relationship exists: (twenty one) In the formula, k opt It is the maximum power tracking factor; ω r It is the rotor speed of the permanent magnet synchronous machine; P ref , P e These are the power reference value and the electromagnetic power, respectively. T m , T e These are mechanical torque and electromagnetic torque, respectively. H r It is the rotor inertial constant of the permanent magnet synchronous machine. / and / These represent the voltage and current along the dq axis of the stator, respectively. ω er It is the base value of the stator angular frequency; R s It is the stator resistance; / These are the inductances along the d-axis and q-axis of the stator, respectively. ψ r denoted as , where is the magnetic flux of the rotor.

[0023] Based on the circuit composition and control system, the following relationship exists: (twenty two) In the formula, z 1, z 2 and z 3 represents a state variable; / and / These are the proportional / integral gains of the outer and inner loop control circuits on the permanent magnet synchronous machine side, respectively. s d and s q Permanent magnet synchronous machine side control target; This indicates the inverter output voltage; L f and R f These are the inductance and resistance of the filter, respectively; ω g Indicates the angular velocity of the power grid; C dc It is a DC capacitor; u dc This is the DC bus voltage; P vsc This refers to the inverter's output power. P s This refers to the stator output power of the permanent magnet synchronous motor. u ref DC bus voltage reference value; Q ref This is a reference value for reactive power. / and / These represent the grid voltage and current along the d and q axes, respectively. / and / These are the proportional / integral gains of the inner and outer control loops on the power grid side, respectively. g d and g q The target for grid-side control.

[0024] Combining the two formulas above, we can obtain the mathematical model of the permanent magnet synchronous wind turbine.

[0025] Figure 3 The circuit composition and control system of the low-frequency side of the frequency-division power transmission system in this embodiment of the invention are shown. Based on the connection and control relationship of the circuit composition and control system of the low-frequency side of the frequency-division power transmission system, a mathematical model of the low-frequency side of the frequency-division power transmission system is constructed.

[0026] Based on the circuit composition of the low-frequency side of the frequency division transmission system, the following relationship exists: (twenty three) In the formula, ω low This refers to the low-frequency side angle frequency of the frequency division transmission system. L f1 and L f2 For filtering inductors; C f For filtering capacitors; and These represent the low-frequency side voltage and current of the frequency-division power transmission system, respectively. and These represent the voltage output and current output of the filter circuit, respectively. and These represent the voltage and current of the capacitor, respectively.

[0027] According to the control system on the low-frequency side of the frequency-division transmission system, the following relationship exists: (twenty four) In the formula, z 4, z 5, z 6 and z 7 is a state variable; and These represent the zero-sequence components of the arm voltage and current in a frequency-division transmission system, respectively. for The reference voltage; / and / These are the proportional / integral gains of the outer and inner loop control circuits, respectively. and It controls the target value.

[0028] Combining the two formulas, we can obtain the mathematical model of the low-frequency side of the frequency division transmission system.

[0029] II. Detailed Explanation of Initial Data Acquisition and Linearization The mathematical model obtained in step one is usually expressed in the following form: (25) In the formula, x ( t ) represents the state variable of the component. u dq ( t )and i dq ( t ) represent the voltage and current of the component in the dq coordinate system, respectively.

[0030] Based on the input component parameters, power flow calculations can be performed to determine the steady-state operating points of all components. The mathematical models of all components are then linearized at these steady-state operating points to obtain the continuous-time small-signal models of the components, typically expressed as follows: (26) In the formula, A CT , B CT , C CT and D CT The coefficient matrix, x 0 and u dq0 This represents the state variables and dq voltage value at the steady-state operating point.

[0031] III. Detailed Explanation of Discretization According to the rule of trapezoidal integrals, Δ i ( t The value Δ can be obtained from the previous moment. i ( t- Δ t The integral increment of the current step is added together with the integral increment of the current step, that is: (27) Substitute the aforementioned formula into the continuous-time small-signal model of the component, and simultaneously define the "historical current term" Δ. p ( t ): (28) We can obtain a recursive form of the discrete-time small-signal model of the components: (29) In the formula, Δ t The step size for discretization, the coefficient matrix A DT , B DT , C DT and D DT It can be calculated using the following formula: (30) IV. Detailed Explanation of System Model Construction Figure 4 This demonstrates a system consisting of numerous components. (Port selection) l The entire system is divided into two subsystems. Focusing on the left subsystem, assume it contains... M Each component and N Each node (excluding the grounding node). M Among the components, i One is a resistive element. j Each of these is a dynamic element (i.e., all non-resistive elements).

[0032] An association matrix is ​​defined to describe the interconnection relationships between branches, nodes, and ports, where, K Node-Branch This indicates the connection relationship between nodes and branches; K Node-Dyn This indicates the connection relationship between nodes and dynamic elements; K Node-Port This indicates the mapping relationship between nodes and ports.

[0033] Based on Kirchhoff's laws, the following relationship can be established: (31) In the formula, the superscripts "Node", "Port", and "Branch" represent column vectors composed of electrical quantities of nodes, ports, and branches, respectively. Since each dynamic component operates independently, the following equation exists: (32) In the formula, the superscript "Dyn" represents the dynamic component within the subsystem, Δ p Dyn ( t ) = [Δ p (1) ( t ), Δ p (2) ( t ),…, Δ p (j) ( t )] T ;Δ u Dyn dq( t ) = [Δ u (1) dq( t ), Δ u (2) dq( t ), …, Δ u ( j ) dq( t )] T ; A Dyn DT = diag( A (1) DT, A (2) DT, …, A ( j ) DT); B Dyn DT = diag( B (1) DT, B (2) DT,…, B ( j ) DT).

[0034] Using node analysis, It can be represented as: (33) In the formula, D Branch DT = diag( D (1) DT,…, D ( j ) DT, D ( j +1) DT, …, D ( j+i ) DT).

[0035] In addition, Δ i Node dq( t It can also be obtained through an equivalent current source (representing the "historical current term" Δ of each dynamic element). p Dyn ( t The injection current and port current Δ i Node dq( t They jointly stated: (34) In the formula, C Dyn DT = diag( C (1) DT, C (2) DT, …, C ( j ) DT).

[0036] By eliminating internal nodes and variables, we can obtain only Δ p Dyn ( t ), Δ u Port dq( t ) and Δ i Port dq( t The system discrete-time small-signal model with variables as follows: (35) coefficient matrix , , and It can be calculated using the following formula: (36) V. Detailed Explanation of Impedance Derivation Perform a z-transform on the system-level discrete-time small-signal model to obtain the discrete-frequency-domain transfer function matrix. H DF ( z ): (37) Due to Δ u Port dq( t ) and Δ i Port dq( t Let ) represent the voltage and current in the dq coordinate system, therefore H DF ( z () is a 2×2 matrix: (38) H DF ( zEach element in ) can be viewed as four sets of single-input, single-output transfer functions. H DF,dd For example, this quantity is only related to the electrical quantity of the d-axis, so the change in the q-axis voltage can be set to 0 in equation (37) to obtain: (39) (40) In the formula, B Port DT,d indicates B The row vector in Port DT corresponding to the d-axis voltage. C Port DT,d indicates C The row vector that affects the d-axis current in Port DT. D Port DT,dd indicates D scalar elements along the d-axis in Port DT.

[0037] According to the properties of rational functions, the zero-pole form of equation (37) is: (41) Combining equations (40) and (41), H DF,dd ( z extreme points v j for The characteristic roots of . In order to solve w i For this single-input single-output system, swapping the input and output results in the poles of the resulting transfer function being the zeros of the original transfer function. Transforming equation (39) allows Δ... u Port d( t As an output variable, Δ i Port d( t As input variables: (42) Similarly, H DF,dd ( z The zero point w i yes[ A Port DT- B Port DT,d( D Port DT,dd) -1 C The eigenvalues ​​of Port DT,d].

[0038] Assumption H DF,dd ( zThe corresponding s-domain transfer function G CF,dd ( s )for: (43) In the formula, q j and p i They are respectively G CF,dd ( s The zeros and poles of ) K dd For gain. Based on the relationship between the continuous domain s-transform and the discrete domain z-transform: (44) The zero-pole relationship of the transfer function in the continuous domain and the discrete domain can be obtained: (45) In the formula, z 0 can take any value that satisfies the condition. Combining the above relationships, we can obtain... H DF,dd ( z ) continuous frequency domain G CF,dd ( s The expression for the transfer function of the system can be obtained by analogy; similarly, the expressions for the transfer functions of the other three terms can be derived, ultimately yielding the overall continuous frequency domain admittance of the system. (46) The continuous impedance of the system is, i.e. G CF ( s The inverse of ) is, G -1 CF( s ). The following simulation examples further illustrate the effectiveness of the automated impedance modeling proposed in this invention. The offshore wind farm based on frequency division transmission is as follows: Figure 5 As shown, it includes frequency-division power transmission, wind farms, transformers, and transmission lines.

[0039] Table 1 shows the relevant parameters of wind turbines and transmission lines, and Table 2 shows the relevant parameters of the low-frequency side of the frequency-division transmission system.

[0040] Table 1 Parameters of Wind Turbine Units and Transmission Lines Table 2 Parameters of the Low-Frequency Side of the Frequency Division Transmission System Based on the parameters, initialization can be performed, power flow calculations can be conducted, and the steady-state values ​​of each component can be determined. Subsequently, the models of each component are linearized and transformed into discrete-time small-signal models. A discrete-time small-signal model of the multi-component system is established through port equivalence. Finally, using z-transform and bilinear transform, the continuous frequency domain admittance / impedance matrix of the system on both sides of the port is established, and the admittance / impedance characteristic curves are plotted on the Bode plot.

[0041] like Figure 6 As shown, the results obtained using the automated method of this invention are compared with those obtained using the frequency sweep method. Both methods yield admittance and impedance with extremely high accuracy. These results verify the correctness of the automated impedance modeling method proposed in this invention.

[0042] Table 3 Computation time required for automated methods and traditional frequency sweeping methods Table 3 shows the computation time required to obtain impedance using the automated method of this invention and the traditional frequency sweep method on the same computer. It can be seen that this invention significantly improves the efficiency of impedance modeling compared to the traditional method.

Claims

1. An automated impedance modeling method for frequency-division offshore wind power systems, characterized in that, Includes the following steps: Step 1) Component mathematical model construction: For the wind turbine and frequency division transmission components in the frequency division offshore wind power system, construct a nonlinear mathematical model in the form of a differential-algebraic equation system for each component in the dq coordinate system; Step 2) System initialization and linearization: Based on the topology connection table of the frequency-division offshore wind power system, the electrical parameters and operating settings of each component are used to perform power flow calculation, determine the steady-state operating point of the system, and use the steady-state operating point as a reference to linearize the nonlinear mathematical model of each component to obtain the small-signal state-space model of each component in the continuous time domain. Step 3) Discrete-time domain transformation: Using the trapezoidal integral method, the small-signal state-space model of each component in the continuous time domain is transformed into a discrete-time recursive model, and the discrete-time small-signal model of each component is established by introducing the historical current term. A DT , B DT , C DT and D DT ; Step 4) System-level model construction: Based on the interconnection relationships of the components in the system, three types of correlation matrices describing the topology are defined: node-branch correlation matrix, node-dynamic component correlation matrix, and node-port correlation matrix. Using the node analysis method, the discrete-time small-signal models of each component obtained in S3 are automatically coupled and combined using the three types of correlation matrices. By eliminating internal node variables, a unified system-level discrete-time small-signal model is constructed with the voltage and current disturbances of the specified external observation port and the internal discrete state variables of all dynamic components in the system as variables. , , and ; Step 5) Automatic Derivation of Frequency Domain Impedance: Perform a z-transform on the system-level discrete-time small-signal model obtained in Step 4 to obtain the discrete frequency domain transfer function matrix. Then, use a bilinear transform to map it to the continuous frequency domain to obtain the continuous frequency domain admittance matrix. G CF ( s Finally, the inverse continuous frequency domain admittance matrix is ​​obtained. G CF ( s This allows us to obtain the continuous frequency domain impedance matrix of the system at a specified observation port. Z CF ( s ).

2. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The mathematical model in the form of a system of differential-algebraic equations in step 1) is expressed as follows: (1) In the formula, x ( t ) represents the state variable of the component. u dq ( t )and i dq ( t ) represent the voltage and current of the component in the dq coordinate system, respectively.

3. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The continuous time-domain small-signal model of each element in step 2) is expressed as follows: (2) In the formula, A CT , B CT , C CT and D CT The coefficient matrix, x 0 and u dq0 This represents the state variables and dq voltage value at the steady-state operating point.

4. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, In step 3), the historical current term Δ p ( t The formula is as follows: (3) In the formula, I is the identity matrix, Δ t To discretize the step size, x ( t ) represents the state variable of the component. u dq ( t ) represents the voltage of the component in the dq coordinate system.

5. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The discrete-time recursive model in step 3) is as follows: (4) In the formula, Δ t The step size for discretization, the coefficient matrix A DT , B DT , C DT and D DT It can be calculated using the following formula: (5)。 6. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The node-branch association matrix in step 4) K Node-Branch Node-Dynamic Component Association Matrix K Node-Dyn and node-port association matrix K Node-Port , Unified system-level discrete-time small-signal model: (6) In the formula, Δ u Port dq( t ) and Δ i Port dq( t ) represent the voltage and current flowing into the subsystem from the external port, respectively, Δ p Dyn ( t () is a column vector of the discrete state variables of all dynamic elements; coefficient matrix , , and Calculate using the following formula: (7) In the formula, the matrix , and All are block diagonal matrices, with the diagonal blocks representing the dynamic elements. A DT , B DT and C DT The matrix is ​​arranged in order. It is also a block diagonal matrix, where the diagonal blocks are composed of all the elements. D DT The matrix is ​​arranged in order.

7. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The discrete frequency domain transfer function matrix in step 5) H DF ( z The formula is as follows: (8) In the formula, z for z Transformation operator, where I is the identity matrix.

8. The impedance automated modeling method for frequency-division offshore wind power systems according to claim 1, characterized in that, The formula for the bilinear transformation in step 5) is: (9) In the formula, z for z Transformation operator, s For the Laplace complex transform operator.

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