Computer automatic construction method of impedance model for multi-terminal vsc-hvdc system

Abstract

A kind of impedance model computer automatic construction method for multi-terminal flexible system.The method first obtains the steady state operating point of each element of system by power flow analysis, then establishes mathematical model for common elements of multi-terminal flexible system, and linearizes, discretizes based on steady state operating point, to establish element small signal state space model;Subsequently, the generalized incidence matrix group compatible with ac-dc hybrid system is used to realize element aggregation, obtain subsystem model and calculate its z domain impedance model, finally generate s domain impedance model by bilinear transformation.The invention realizes the computer-aided automatic construction of multi-terminal flexible system impedance model, supports the impedance fast analysis of any ac / dc port, is flexible and efficient;And the topological sensitivity of system is low, when the structure changes, only the corresponding part of generalized incidence matrix group needs to be modified, and the scalability is high.Example analysis shows that the invention can accurately obtain the ac / dc port impedance of multi-terminal flexible system, and effectively improve the analysis efficiency.

Description

Technical Field

[0001] This invention relates to the field of power system impedance modeling and analysis, and in particular to a computer-automated method for constructing impedance models for multi-terminal flexible DC systems. It is applicable to the automated impedance modeling and stability analysis of AC-DC hybrid systems that include AC power grids, DC networks and modular multilevel converters (MMCs). Background Technology

[0002] With the advancement of the "dual carbon" target, the large-scale integration of new energy sources into the power grid, and the increasingly diverse methods of their collection and transmission, are driving profound changes in the power system's structure. The development and application of flexible DC transmission have made the role of converters in the system more prominent. However, the complex coupling relationship between converters and the power grid has altered the operating characteristics of the grid and also given rise to increasingly prominent new oscillation and stability problems. As the large-scale grid connection of new energy sources, especially wind power and photovoltaics, has become the mainstream direction of power system development, their access and transmission methods are becoming more diversified, further driving profound changes in the structure and operating characteristics of the power system. In this process, the widespread application of flexible DC transmission technology has made the control based on power electronic converters play an increasingly important role in system dynamics; at the same time, the complex coupling relationship between converters and the AC power grid has also brought about new oscillation and stability problems, becoming an increasingly prominent challenge in current research and engineering practice.

[0003] For the assessment and analysis of small-disturbance stability of power systems, existing technologies mainly include mainstream methods such as the eigenvalue method, frequency sweep method, and impedance analysis method. The eigenvalue method determines system stability by establishing a state-space model of the entire system and calculating the eigenvalues ​​of the state matrix. This method requires prior knowledge of all independent state variables in the system, and the results are highly sensitive to component parameters and topology. Therefore, when the system order or scale is large, the modeling and computational complexity of the eigenvalue method increases significantly, limiting its application. The frequency sweep method is suitable for "black box" or difficult-to-model subsystems. It obtains impedance characteristics by applying disturbances and measuring port responses. However, this method usually requires a large number of repeated experiments, resulting in low data acquisition and processing efficiency, making it difficult to meet the needs of large-scale analysis. The impedance analysis method divides the entire system into two subsystems and calculates the port impedances separately before performing stability analysis. It offers good flexibility in port selection and subsystem division, and does not require remodeling the global model when local system structures change. However, the practical application of existing impedance methods often remains at the component level or local equivalent level of impedance expression: in the process of deriving the subsystem port impedance from the component impedance, it is often necessary to perform a series of topological transformations, algebraic elimination, and addition or inversion operations of frequency domain impedance / admittance based on the series and parallel relationships of the components within the subsystem. These steps in current research and engineering practice mostly rely on manual analysis and derivation, which is time-consuming and error-prone, and lacks a systematic and universal automated modeling process.

[0004] To alleviate these problems, the academic community has explored several automated modeling approaches. For example, some studies have proposed representing multi-port power components in a unified discretized form and automatically generating the discrete state space of the entire system using the correlation matrix for eigenvalue analysis and factor calculation. Other studies have used the ideas of node shrinkage and component aggregation to construct equivalent models of the system in the discrete domain and obtain continuous frequency domain impedance characteristics through inter-domain mapping. These works have reduced the workload of manual modeling to some extent and improved the modeling efficiency and analytical capabilities for AC systems. However, these methods usually focus on AC systems or treat DC dynamics as known local processes within the converter. In multi-terminal flexible DC systems with complex DC network structures and significant interconnection and coupling between DC-side ports, if the assumption of simplifying the DC side to a constant voltage or treating its dynamics as internalized continues, it is difficult to accurately reflect the impact of the DC network on the AC-side impedance, and it is also impossible to directly obtain the impedance characteristics of the DC-side ports. On the other hand, to accurately introduce DC dynamics, it is often necessary to manually identify independent state loops and establish equations one by one, and loop analysis must be repeated when the topology changes, resulting in insufficient scalability of the method. Summary of the Invention

[0005] To address the problems of existing technologies, such as reliance on manual topology transformations for impedance modeling of multi-terminal flexible DC systems, difficulty in considering AC and DC side dynamics, and poor scalability, this invention provides a computer-automated method for constructing impedance models for multi-terminal flexible DC systems. This method is based on the idea of ​​multiple mappings from continuous time domain to discrete time domain to discrete frequency domain to continuous frequency domain, constructing a unified discrete state-space model for AC components, DC components, and modular multilevel converters (MMCs). It also proposes a generalized correlation matrix set compatible with AC / DC hybrid systems to characterize the system topology and subsystem segmentation port locations, thereby achieving automatic aggregation and generation of subsystem-level admittance / impedance models. The entire process can be automatically executed with computer assistance, avoiding manual topology analysis and circuit simplification, making it flexible and efficient.

[0006] The objective of this invention can be achieved through the following technical solutions: A computer-automated method for constructing impedance models for multi-terminal flexible DC systems includes the following steps: Step 1: Obtain the stable operating point of each component in the multi-terminal flexible DC system based on power flow analysis. The analysis of each AC network in the multi-terminal flexible DC system is performed as an independent power grid. For each AC network, the type of each node is first determined. The different control strategies of each MMC will result in different types of AC nodes connected to it. For example, the AC side nodes of MMCs with PQ control and Vdc / Q control are regarded as PQ nodes, and the AC side nodes of MMCs with V / F and other network-type control are regarded as slack nodes. The power flow is calculated using Newton-Raphson iteration to obtain the steady-state voltage, phase and injected power of each node. Furthermore, the steady-state solutions of the state variables of various converters and nonlinear elements in the whole system can be solved. Step 2: Construct mathematical models of AC / DC transmission lines and components such as MMC: For DC transmission lines, the RL model is used for mathematical description: (1) in, R and L These are the equivalent resistance and inductance values ​​of the circuit; u and i These are the line voltage and current.

[0007] For AC transmission lines, an RL model is established in the dq coordinate system: (2) in, R and L These are the equivalent resistance and inductance values ​​of the circuit; u d and u q These are the dq coordinate components of the voltage at both ends of the line; i d and i q These are the dq coordinate components of the line current.

[0008] For MMC, a 12th-order mathematical model is constructed using the dynamic phasor method: (3) (4) It can be written in the following form: (5) in, . These are the third harmonic, second harmonic, fundamental frequency, and DC component of the total capacitor voltage of the upper bridge arm submodule, respectively. i cirdq2 and i cir0 These are the second harmonic and DC components of the bridge arm circulating current, respectively. i dq This refers to the AC current on the MMC valve side.u d and u q The AC voltage on the MMC valve side; u dc This refers to the DC side voltage of the MMC. M d and M q The modulation ratio of the fundamental frequency voltage signal. M d2 and M q2 This is the modulation ratio of the circulating current suppression signal.

[0009] Step 3: Linearize the mathematical model of the component to obtain the small-signal continuous-time state-space model of the component. Near the steady-state operating point obtained in step 1, the mathematical models of each component established in step 2 are linearized to obtain a unified small-signal continuous-time state-space model: The mathematical model of the DC transmission line RL is linearized by differentiation, resulting in... (6) Similarly, by linearizing the AC transmission lines, we obtain... (7) For MMC, due to the modulation signal M d , M q , M d2 and M q2 Determined by state variables and port voltages, the MMC dynamic phasor model can be further simplified as follows: (8) in, x It includes all state variables of the circuit and control loop. u acdc It is the AC / DC port voltage. i acdc It is the AC / DC port current. After linearization, we obtain... (9) Among them, each coefficient matrix is (10) Step 4. Discretize the continuous-time state-space model to obtain the discrete-time state-space model of the component. The continuous time-domain state-space model obtained in step 3 is discretized using the trapezoidal integral method to obtain the discrete time-domain state-space model of each component.

[0010] For DC RL transmission lines, discretization is achieved using trapezoidal integrals. (11) make g 1= t / (2 L ),Will t - t The item is recorded as a historical item. h ( t Thus, its discrete-time state-space model is obtained: (12) For an AC RL transmission line, the trapezoidal integral yields: (13) Among them, matrix T 1. T 2 and T 3 is (14) Will t - t The item is recorded as a historical item. h ( t Thus, its discrete-time state-space model is obtained: (15) For MMC, following the same method as for RL transmission lines, its discrete-time state-space model can be obtained: (16) Step 5. Construct a generalized correlation matrix group compatible with AC / DC hybrid systems to achieve component aggregation within subsystems. First, we define three types of generalized correlation matrices: Define the generalized node-branch association matrix P nb For any node in the subsystem i and branch road j ,matrix( i , j The positional elements describe the connection relationships and correspond to a sub-matrix. If the branch... j Current outflow node i ,but( i , j The element should be I 2×2 Or 1, or conversely - I2×2 The matrix dimension can be -1 or 0, and the remaining matrix dimension is determined by the AC / DC characteristics of the branches and nodes.

[0011] Define the generalized node-dynamic branch association matrix P ndy Its construction method and P nb Similarly, you only need to remove purely resistive / conductive components from it.

[0012] Define a generalized node-port association matrix P np If port p If the characteristic is communication, then it is represented as: (17) If port q If the characteristic is DC, then it is represented as: (18) Based on the aforementioned generalized correlation matrix set, the KCL equations for the internal nodes of the subsystem are written using nodal analysis. By simultaneously solving these equations to eliminate internal node voltages, the relationship between subsystem port currents, port voltages, and historical current sources is obtained, forming a discrete-time state-space model at the subsystem level. This model maintains the same Norton circuit structure as individual components, achieving recursive aggregation from the component level to the subsystem level. The entire process requires no manual topological transformation or circuit equivalence simplification within the subsystem. Specifically: Component Subsystem AC / DC Hybrid Node Admittance Matrix Y HVDC The calculation formula is (19) in D diag It consists of various components D d A block diagonal matrix composed of matrices.

[0013] The following equations can be combined to eliminate the parameters of nodes within a subsystem, thus achieving the aggregation of internal components: (20) Where Δ i inj It is the node injection current; Δ u node It is the node voltage; Δ u port It is the subsystem port voltage; Δ i port It is the current flowing into the subsystem port.

[0014] Finally, the discrete-time state-space model of the subsystem-level port is obtained: (twenty one) Step 6: Based on the discrete-time state-space model of the subsystem, derive its z-domain admittance / impedance transfer function. For the AC port, the z-domain admittance is a 2 2 matrices, each element having zeros, poles, and gain in the form of... (twenty two) For the DC port, the z-domain admittance is a one-dimensional transfer function, and its zero-pole-gain form is: (twenty three) Step 7: Transform the z-domain admittance / impedance model into the s-domain admittance / impedance model using a bilinear transformation to obtain the required subsystem port admittance / impedance characteristics: Using the bilinear transform, the zero-pole-gain form of each element of the AC port s-domain admittance matrix is: (twenty four) DC port admittance zero pole gain form is (25) The s-domain admittance zero-pole-gain is obtained by the bilinear transformation of the z-domain zero-pole-gain.

[0015] The port impedance can be derived by exchanging the input and output of its state-space model.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Based on the idea of ​​multiple mappings between continuous time domain, discrete time domain, discrete frequency domain and continuous frequency domain, this invention establishes a computer-aided system-level impedance modeling framework. Compared with the traditional impedance analysis method with simple mapping between continuous time domain and continuous frequency domain, this invention does not require topological transformation and circuit simplification of internal system components. It only needs to rely on the generalized correlation matrix group generated by the computer to eliminate the parameters of internal nodes, which greatly reduces the degree of human intervention, simplifies the analysis process and reduces human error. Compared with the frequency sweep method, it does not require repeated simulation loops, which greatly reduces the analysis time. (2) This invention establishes a unified discrete equivalent model for AC components, DC components and flexible DC converter components, and constructs a generalized correlation matrix group compatible with AC / DC hybrid systems, realizing a general representation of the topological relationship between any AC / DC node and component in a multi-terminal flexible DC system. Compared with the common analysis methods that simplify the DC network or treat it as the internal structure of AC components, this invention can accurately describe the AC / DC coupling characteristics of converter components and realize automatic impedance modeling of any AC / DC port, which is highly flexible. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to the present invention. Figure 2 A schematic diagram illustrating the discretization of each component into a Norton equivalent circuit using trapezoidal integral; Figure 3 A schematic diagram of a four-terminal ring network structure offshore wind power flexible DC system used to verify the method of the present invention; Figure 4 The diagrams show a comparison of the AC / DC port impedance characteristics obtained by the method of the present invention and the frequency sweep method. (a) is a comparison of the Bode plots of the AC port impedance at subsystem segment 1, and (b) is a comparison of the Bode plots of the DC port impedance at subsystem segment 2. Detailed Implementation

[0018] 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.

[0019] This invention provides a computer-automated method for constructing impedance models for multi-terminal flexible DC systems, the process of which is as follows: Figure 1 As shown, a unified state-space model of AC components, DC components, and flexible DC converter components is first established. This model is then discretized to form the equivalent circuit of a multi-terminal flexible DC system. A generalized correlation matrix set applicable to AC / DC hybrid connection systems is introduced to aggregate components within the subsystem. Based on this, the admittance / impedance expressions for the AC and DC ports can be derived and used for stability analysis.

[0020] This embodiment provides a computer-automated method for constructing impedance models for multi-terminal flexible DC systems, including the following steps: Step 1. Obtain the stable operating points of each component in the system based on power flow analysis: In a multi-terminal flexible DC system, each AC network is treated as an independent power grid for separate power flow analysis. For each AC network, the node type is first determined based on the control strategy of the MMC it connects to: for MMCs using PQ control and Vdc / Q control, their AC-side nodes are considered PQ nodes; for MMCs using V / F network configuration control, their AC-side nodes are considered slack nodes. After determining the node type, Newton-Raphson iteration is used for power flow calculation to obtain the steady-state voltage amplitude, phase, and injected power of each node. Based on this, combined with the mathematical models of each component, the steady-state solutions of the state variables of all types of converters and nonlinear components in the entire system are further solved. These steady-state solutions serve as the operating point inputs for subsequent linearization processing.

[0021] Step 2. Construct mathematical models of AC / DC transmission lines and components such as MMC: For DC transmission lines, taking the RL model as an example, its mathematical expression is: (1) in, R and L These are the equivalent resistance and inductance values ​​of the circuit, respectively. u and i These are the line voltage and current, respectively.

[0022] For AC transmission lines, an RL model is established in the synchronous rotating dq coordinate system, and its mathematical expression is: (2) in, R and L These are the equivalent resistance and inductance values ​​of the circuit; u d and u q These are the dq coordinate components of the voltage at both ends of the line; i d and i q These are the dq coordinate components of the line current. This is the fundamental angular frequency of the system.

[0023] For MMC, its 12th-order mathematical model is constructed using the dynamic phasor method: (3) (4) It can be written in the following form: (5) in, . These are the third harmonic, second harmonic, fundamental frequency, and DC component of the total capacitor voltage of the upper bridge arm submodule, respectively. i cirdq2 and i cir0 These are the second harmonic and DC components of the bridge arm circulating current, respectively. i dq This refers to the AC current on the MMC valve side. u d and u q The AC voltage on the MMC valve side; u dc This refers to the DC side voltage of the MMC. M d and M q The modulation ratio of the fundamental frequency voltage signal. M d2 and M q2 This is the modulation ratio of the circulating current suppression signal.

[0024] Step 3. Linearize the mathematical model of the component: Near the steady-state operating point obtained in step 1, the mathematical models of each component established in step 2 are linearized to obtain the small-signal continuous time-domain state-space model of the component.

[0025] By performing differential linearization on the mathematical model of a DC RL transmission line, we obtain... (6) Linearizing the AC RL transmission line yields a small-signal model in the dq coordinate system: (7) For MMC, due to the modulation signal M d , M q , M d2 and M q2 Determined by both state variables and port voltages, its dynamic phasor model can be further simplified as follows: (8) in, x It includes all state variables of the circuit and control loop. u acdc It is the AC / DC port voltage. i acdc This is the AC / DC port current. Linearizing it near the steady-state operating point, we get: (9) Among them, each coefficient matrix is (10) Step 4. Discretize the continuous time-domain state-space model. The continuous-time state-space model of each component is discretized using the trapezoidal integral method, resulting in a discrete-time state-space model. This model can be equivalent to a Norton circuit with an impedance and a current source in parallel, such as... Figure 2 As shown.

[0026] For a DC RL transmission line, after discretization using trapezoidal integral, we obtain: (11) make g 1= t / (2 L ),Will t - t The item is recorded as a historical item. h ( t Thus, its discrete-time state-space model is obtained: (12) For an AC RL transmission line, the trapezoidal integral discretized is obtained as follows: (13) Among them, matrix T 1. T 2 and T 3 is (14) Will t - t The item is recorded as a historical item. h ( t Thus, its discrete-time state-space model is obtained: (15) For MMC, following the same method as for RL transmission lines, its discrete-time state-space model can be obtained: (16) like Figure 2 As shown, the final component model can be equivalent to a Norton structure with impedance and current source in parallel.

[0027] Step 5. Construct a generalized correlation matrix set for the AC / DC hybrid system to characterize the topology of the multi-terminal flexible DC system and the subsystem segmentation port locations; wherein, the subsystem refers to the two parts obtained after splitting the multi-terminal flexible DC system according to the specified ports. Further, aggregate the internal components of the subsystem to obtain the discrete-time state-space model of the subsystem: First, we define three types of generalized node-branch associations: (1) Generalized node-branch correlation matrix P nb For any node in the subsystem i and branch road j ,matrix( i , j The positional elements describe the connection relationships and correspond to a sub-matrix. If the branch... j Current outflow node i ,but( i , j The element should be I 2×2 Or 1, or conversely - I 2×2 The matrix dimension can be -1 or 0, and the remaining matrix dimension is determined by the AC / DC characteristics of the branches and nodes.

[0028] (2) Generalized node-dynamic branch association matrix P ndy Its construction method and P nb Similarly, you only need to remove purely resistive / conductive components from it.

[0029] (3) Generalized node-port association matrix P np : Used to characterize the connection relationship between a subsystem port and its internal nodes. If the port... p If the characteristic is communication, then it is represented as: (17) If port q If the characteristic is DC, then it is represented as: (18) Based on the definition of the generalized correlation matrix group above, and drawing on the ideas of nodal analysis, component aggregation can be achieved. The component subsystem AC / DC hybrid nodal admittance matrix. Y HVDC The calculation formula is (19) in D diag It consists of various components D d A block diagonal matrix composed of matrices. The following equations can be combined to eliminate the parameters of nodes within the subsystem, achieving aggregation of internal components: (20) Where Δ i inj It is the node injection current; Δ u node It is the node voltage; Δ u port This refers to the subsystem port voltage; ultimately, the discrete-time state-space model of the subsystem-level ports is obtained: (twenty one) Step 6. Derive the z-domain admittance / impedance transfer function of the subsystem. Based on the discrete-time state-space model of the subsystem obtained in step 5, its z-domain admittance / impedance transfer function is derived. The transfer function is expressed using zero-point, pole-point, and gain forms. For the AC port, the z-domain admittance is a 2 2 matrices, each element having zeros, poles, and gain in the form of... (twenty two) For the DC port, the z-domain admittance is a one-dimensional transfer function, and its zero-pole-gain form is: (twenty three) Step 7. Obtain the s-domain admittance / impedance model using bilinear transformation. The z-domain admittance / impedance model is transformed into the s-domain admittance / impedance model using a bilinear transformation, thus obtaining the desired subsystem port admittance / impedance characteristics. The z-domain admittance is converted to the s-domain admittance using a bilinear transformation.

[0030] For the AC port, the admittance zero-pole-gain form is: (twenty four) For the DC port, the admittance zero-pole-gain form is: (25) The s-domain admittance zero-pole-gain is obtained by the bilinear transformation of the z-domain zero-pole-gain.

[0031] The port impedance can be derived by exchanging the input and output of its state-space model.

[0032] The following simulation examples further illustrate the effectiveness of the computer-automated impedance model construction method proposed in this invention. The four-terminal ring network structure of the offshore wind power flexible DC system is as follows: Figure 3 As shown, the system comprises two sending-end systems, two receiving-end systems, and a DC system. Each wind farm is aggregated and equivalent to a wind power converter. WFMMC1 and WFMMC2 use V / F control; GSMMC1 uses Vdc / Q control; and GSMMC2 uses P / Q control. Specific parameters are shown in Table 1 below.

[0033] Table 1 Simulation Example Parameters Build in MATLAB / Simulink Figure 3 The system shown verifies the universality and accuracy of this invention for arbitrary AC / DC ports of multi-terminal flexible DC systems. The simulation step size is 10 μs, and the results are as follows. Figure 4 As shown, it includes: (1) with Figure 3 The neutron system split port 1 is used as the verification point for AC port impedance modeling. The results obtained using this invention are compared with the results obtained from frequency sweep simulation. The right side of split port 1 is designated as subsystem 1, and the left side as subsystem 2. Bode plots of the subsystem port AC impedance within the 1-4000Hz range are plotted using the proposed method, and frequency sweep impedance Bode plots at 25 frequency points are also plotted. The results of the two methods are shown below. Figure 4As shown in (a), the impedance analysis results obtained by the theoretical method within the studied frequency band are in good agreement with the simulation results obtained by the frequency sweep method, verifying the correctness of the proposed method in AC impedance modeling of multi-terminal flexible DC systems.

[0034] (2) with Figure 3 The split port 2 of the neutron system is used as the DC port impedance modeling verification point. The left side of split port 2 is denoted as subsystem 1, and the right side as subsystem 2. Impedance Bode plots are then drawn again using both methods, and the results are as follows. Figure 4 As shown in (b), the results of the two methods are still in agreement, proving that the proposed method is also correct in modeling the DC impedance of multi-terminal flexible DC systems.

Claims

1. A computer-automated method for constructing impedance models for multi-terminal flexible DC systems, characterized in that, Includes the following steps: Step 1. Obtain the stable operating point of each component in the multi-terminal flexible DC system based on power flow analysis; Step 2. Construct familiar models of each component in the multi-terminal flexible DC system, including at least AC transmission lines, DC transmission lines, and modular multilevel converters; Step 3. Linearize the mathematical model of the component at the stable operating point to obtain the small-signal continuous-time state-space model of each component; Step 4. Discretize the small-signal continuous-time state-space model using the trapezoidal integral method to obtain the discrete-time state-space model of each component. The discrete-time state-space model is uniformly represented as a Norton circuit in which the equivalent admittance matrix and the historical current source are connected in parallel, thereby realizing a unified equivalent expression of AC components, DC components and modular multilevel converters in the discrete domain. Step 5. Construct a generalized correlation matrix set compatible with AC / DC hybrid systems. The generalized correlation matrix set includes a generalized node-branch correlation matrix, a generalized node-dynamic branch correlation matrix, and a generalized node-port correlation matrix. It is used to uniformly represent the topological connection relationship between AC nodes, DC nodes, AC / DC hybrid nodes, and each component branch and port in the multi-terminal flexible DC subsystem. The subsystem is decomposed into a multi-terminal flexible DC system according to a specified port. Based on the generalized correlation matrix set, the discrete-time state-space model of each component in the subsystem is aggregated using the node analysis method to obtain the discrete-time state-space model of the subsystem. Step 6. Based on the discrete-time state-space model of the subsystem, derive the admittance or impedance transfer function of the subsystem port in the z-domain, and express the transfer function in the form of zeros, poles, and gain; Step 7. Convert the z-domain admittance or impedance transfer function into the s-domain admittance or impedance transfer function through bilinear transformation to obtain the desired subsystem port admittance or impedance characteristics.

2. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1, characterized in that, Step 1. The power flow analysis described in the step 1 obtains the steady-state operating points of each component in the multi-terminal flexible DC system, specifically including: In a multi-terminal flexible DC system, each AC network is treated as an independent power grid. The node type of each AC node is determined according to the control strategy of the modular multilevel converter. The power flow is calculated using Newton-Raphson iteration to obtain the steady-state voltage, phase, and injected power of each node. Then, the steady-state solution of the state variables of each component in the multi-terminal flexible DC system is solved.

3. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1, characterized in that, Step 2 involves constructing mathematical models for each component, specifically including: For DC transmission lines, the RL model is used for description, and the mathematical expression is: (1) in, R and L These are the equivalent resistance and inductance values ​​of the circuit; u and i These are the line voltage and current; For AC transmission lines, an RL model is established in the dq coordinate system, and the mathematical expression is: (2) in, R and L These are the equivalent resistance and inductance values ​​of the circuit; u d and u q These are the dq coordinate components of the voltage at both ends of the line; i d and i q These are the dq coordinate components of the line current; For modular multilevel converters, a 12th-order mathematical model is constructed using the dynamic phasor method. The state variables of the 12th-order mathematical model include the third harmonic, second harmonic, fundamental frequency, and DC component of the total capacitor voltage of the upper arm submodule, the second harmonic and DC component of the arm circulating current, and the valve-side AC current.

4. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1, characterized in that, The specific definition of the generalized correlation matrix group in step 5 is as follows: In the generalized node-branch correlation matrix, for any node and branch in the subsystem, the matrix elements are taken as identity matrix or 1, negative identity matrix or -1, or zero matrix according to the branch current direction and AC / DC characteristics of the branch. The method for constructing the generalized node-dynamic branch correlation matrix is ​​the same as that for the generalized node-branch correlation matrix, but it only includes dynamic element branches and excludes pure resistive or conductive branches. The generalized node-port correlation matrix is ​​used to characterize the connection relationship between subsystem ports and internal nodes, and is taken as an identity matrix or 1 according to the AC / DC characteristics of the ports.

5. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1 or 4, characterized in that, Step 5, which involves aggregating the discrete-time state-space models of each component within the subsystem, specifically includes: based on the generalized correlation matrix group, using the node analysis method to write the KCL equations for the nodes within the subsystem; simultaneously solving the equations to eliminate the internal node voltages; obtaining the relationship between the subsystem port current, port voltage, and historical current sources; and forming a discrete-time state-space model at the subsystem level. This model maintains the same Norton circuit structure as a single component, thereby achieving recursive aggregation from the component level to the subsystem level.

6. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1, characterized in that, The admittance or impedance transfer function in the z-domain mentioned in step 6, for AC ports of 2... The two matrices are in one-dimensional transfer function form for the DC port, expressed as zeros, poles, and gains to support the analytical calculation of the subsequent bilinear transformation.

7. The computer-automated method for constructing impedance models for multi-terminal flexible DC systems according to claim 1, characterized in that, The multi-terminal flexible DC system includes an AC / DC hybrid system consisting of an AC power grid, a DC network, and a modular multilevel converter; the subsystem ports include AC ports and DC ports; when the system topology changes, only the corresponding part of the generalized correlation matrix group needs to be modified, without having to rebuild the entire system model.

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