Broadband equivalent analysis modeling method and system for AC / DC power transmission line

Abstract

The invention discloses an AC / DC power transmission line broadband equivalent analysis modeling method and system, and belongs to the technical field of power system AC / DC power transmission, and the method comprises the steps: obtaining the self-impedance and mutual impedance frequency change parameters of each phase based on a phase domain frequency change model, and converting the self-impedance and mutual impedance into differential mode impedance and common mode impedance; vector fitting is carried out on the impedance data to construct an RL branch parameter solving equation, the cascade number is determined, and an RLC circuit equivalent model corresponding to differential mode impedance and common mode impedance is obtained; a topological form of a differential mode RLC equivalent circuit corresponding to differential mode impedance and a compensation current source is adopted to construct a power transmission line equivalent circuit considering mutual inductance. According to the long-distance AC / DC submarine cable RLC equivalent modeling method, an AC / DC cable port voltage and current relation considering mutual inductance characteristics is deduced based on phase-mode transformation, a cable mutual inductance equivalent circuit based on a differential / common mode RLC circuit and a compensation current source is constructed, and the long-distance AC / DC submarine cable RLC equivalent modeling method capable of accurately reflecting frequency change, time delay, distribution characteristics and mutual inductance effects is provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of AC / DC power transmission in power systems, and in particular relates to a broadband equivalent analytical modeling method and system for AC / DC transmission lines. Background Art

[0002] The statements herein merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Transmission line models are generally categorized into π-type equivalent circuits, Bergeron models, and frequency-variant models in the mode and phase domains. Lumped parameter models, such as the π-type equivalent circuit and Bergeron models, struggle to simulate the frequency-variant and time-delay characteristics of power lines. Frequency-variant line models based on frequency-variant parameters can provide more accurate frequency and time-delay characteristics. However, the analytical expressions of frequency-variant models include time-delay components, making them complex and difficult to convert into state-space models, much less suitable for small-signal stability analysis. Currently, the most widely used models for small-signal stability analysis of transmission lines are single-π or multi-π cascade equivalent models. However, literature research indicates that traditional multi-π cascade equivalent models can cause spurious oscillations in the system, while purely resistive networks that ignore inductance can only accurately simulate dynamic characteristics in the low-frequency range. Furthermore, in practical projects, AC transmission lines employ three-core structures, and DC transmission lines are often laid in parallel. The electrical distances between lines are relatively close, and mutual inductance significantly impacts the characteristics of line ports. Existing line models rarely consider the impact of mutual inductance and no longer meet simulation requirements.

[0004] For example, in the prior art, "Modeling and Simulation of Dynamic Phasor Method for Three-Phase Distributed Parameter Lines" proposes a large-step dynamic phasor model suitable for distributed parameter lines and analyzes the errors generated by it. However, the model relies on historical data from the previous moment and is only applicable to simulation models, making it difficult to perform small-signal modeling. Another example is "Low-Order Fitting Method in Frequency-Varying Transmission Line Model" which proposes a parameter fitting method based on a frequency-variable line model in the model domain. It uses a nonlinear least squares method to reduce the fitting error and achieves accurate fitting of characteristic impedance and propagation coefficient using low-order rational functions. However, this modeling method introduces phase model transformation and inverse transformation, which results in a large amount of calculation and is difficult to use for small-signal modeling. Another example is "Small Signal Modeling of HVDC Systems Considering Frequency-Varying Effects of DC Line Parameters" which proposes a distributed parameter modeling method for overhead lines considering frequency-varying characteristics. It regards the positive and negative line voltages as opposite numbers, eliminates the coupling effect between the positive and negative poles, and uses a multi-π cascade circuit model to simulate the DC line. This method takes the symmetry of the positive and negative voltages and currents as a premise. However, when a DC line has a single-pole fault, the positive and negative currents and voltages are asymmetric, and the model is no longer applicable. In addition, the line model based on the distributed parameter model in this paper involves complex trigonometric function calculations, and the small signal stability modeling requires a large amount of calculation.

[0005] In summary, the inventors found that the phase-domain frequency-varying model is the most accurate cable equivalent model at present, but this model is only applicable to electromagnetic transient simulation, and it is difficult to establish an analytical small-signal stability analysis model; the existing cable small-signal stability analysis model is based on a lumped parameter model with a single-π or multi-π structure, which does not consider the frequency-varying characteristics of the line, and the analysis results are different from the actual situation; and when the existing model considers the coupling mutual inductance characteristics between lines, it is only based on the symmetry of the voltage and current of each phase, and is no longer applicable when simulating asymmetric faults. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and provide a broadband equivalent analytical modeling method and system for AC / DC transmission lines. Based on phase mode transformation, the voltage-current relationship at the AC / DC cable port is derived considering the mutual inductance characteristics, and a cable mutual inductance equivalent circuit based on differential / common mode RLC circuits and compensation current sources is constructed. A long-distance AC / DC submarine cable RLC equivalent modeling method is proposed that can accurately reflect the frequency variation, time delay and distribution characteristics as well as the mutual inductance effect.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions: On the one hand, the technical solution of the present invention provides a broadband equivalent analytical modeling method for AC and DC transmission lines, comprising: Obtain the frequency-varying parameters of self-impedance and mutual impedance of each phase based on the phase-domain frequency-varying model, and transform the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance; Perform vector fitting on the impedance data to construct the RL branch parameter solution equation, determine the cascade number, and obtain the RLC circuit equivalent model corresponding to the differential mode impedance and common mode impedance; The topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source is used to construct an equivalent circuit of the transmission line considering mutual inductance.

[0008] In at least one embodiment, the obtaining of frequency-varying parameters of self-impedance and mutual impedance of each phase based on the phase-domain frequency-varying model is specifically as follows: building a phase-domain frequency-varying model in PSCAD and deriving frequency-varying data of self-impedance and mutual impedance of the positive and negative lines.

[0009] In at least one embodiment, the self-impedance and mutual impedance are converted into differential-mode impedance and common-mode impedance, specifically: the differential-mode impedance of the DC transmission line is the difference between the positive and negative self-impedance and the mutual impedance, and the common-mode impedance is the sum of the positive and negative self-impedance and the mutual impedance; The differential mode impedance of an AC transmission line is the difference between the self-impedance and the mutual impedance, and the common mode impedance is the sum of the single-phase self-impedance and twice the mutual impedance.

[0010] In at least one embodiment, performing vector fitting on the impedance data to construct an RL branch parameter solution equation specifically includes: Perform vector fitting on the original impedance data and determine the number of RL branches based on the order of the fitting function ; Select Frequency points and their corresponding impedance data are used to construct the RL branch parameter solution equation; The amplitude-frequency characteristics of multi-π-type circuits with multiple RL parallel branches and phase-domain frequency-varying models with different cascade numbers are compared to determine the cascade number. Each cascade part is equivalent to a π-type structure in the form of lumped parameters, and the equivalent RLC circuit model corresponding to the differential-mode impedance and common-mode impedance is obtained.

[0011] In at least one embodiment, the RL branch parameter solution equation is specifically expressed as: ; Where, is the fitting function, is the number of RL branches, is the frequency point The corresponding impedance data.

[0012] In at least one embodiment, the parameters of the π-type structure are specifically expressed as: ; Where, the cable length simulated by a single π-shaped structure is , The cable length simulated for N π-shaped structures.

[0013] In at least one embodiment, a differential-mode RLC equivalent circuit corresponding to differential-mode impedance and a compensation current source topology are used to construct a transmission line equivalent circuit that takes mutual inductance into account, specifically including: Based on the differential-mode RLC circuit, the difference between the current at the differential-mode circuit port and the actual current is calculated to obtain the current value of the compensation current source; the compensation current is obtained by calculating the electrical quantities of the differential-mode circuit and the common-mode circuit, and is compensated at the differential-mode circuit port in the form of a current source.

[0014] In at least one embodiment, the DC line equivalent circuit compensation current source is obtained by a common mode circuit and a differential mode circuit, which is specifically expressed as: Differential mode RLC circuit at port k Apply positive voltage Corresponding current for: ; port k Positive compensation current source The expression is: ; port k Negative compensation current source The expression is: ; Where, and Port k Corresponding differential mode voltage and common mode voltage; For differential mode RLC circuit at port k Apply negative voltage The corresponding current; 、 The common mode RLC circuit is at the port k The current corresponding to the positive and negative voltages applied.

[0015] In at least one embodiment, the AC line equivalent circuit compensation current source can be obtained by a common mode circuit and a differential mode circuit, which can be specifically expressed as follows: AC line A phase port k compensation current source The expression is: ; AC line phase B and C ports k Compensation current source 、 The expression is: ; Where, The currents corresponding to the A, B, and C phase voltages applied to port k by the differential-mode RLC circuit are respectively; The currents corresponding to the A, B, and C phase voltages are applied to the port k of the common-mode RLC circuit respectively.

[0016] On the other hand, the technical solution of the present invention also provides a broadband equivalent analytical modeling system for AC and DC transmission lines, comprising: The impedance transformation module is configured to: obtain frequency-varying parameters of self-impedance and mutual impedance of each phase based on a phase-domain frequency-varying model, and transform the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance; An RLC circuit equivalent model building module is configured to: perform vector fitting on impedance data to build an RL branch parameter solution equation, determine the number of cascades, and obtain an RLC circuit equivalent model corresponding to the differential mode impedance and the common mode impedance; The transmission line equivalent circuit construction module is configured to: use the topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source to construct the transmission line equivalent circuit considering the mutual inductance.

[0017] The beneficial effects of the technical solution of the present invention are as follows: 1) The broadband equivalent analytical modeling method for AC / DC transmission lines of the present invention takes into account the phase coupling of the transmission lines. Based on the idea of ​​phase-mode transformation, it achieves phase decoupling by solving differential-mode circuits and common-mode circuits separately. It also constructs an equivalent circuit in the form of a differential-mode RLC circuit and a compensating current source, solving the problem that the time delay characteristics, frequency variation characteristics, and phase mutual inductance characteristics of the transmission lines cannot be described analytically.

[0018] 2) The broadband equivalent analytical modeling method for AC and DC transmission lines of the present invention uses RLC circuits to perform equivalent modeling of the lines, which can realize impedance simulation of the transmission lines over a wide frequency band, facilitate the writing of state-space models, and further derive small-signal models of the transmission lines, providing a model basis for stability analysis.

[0019] 3) The broadband equivalent analytical modeling method for AC / DC transmission lines of the present invention introduces a compensating current source, so that the equivalent model can simulate the electrical characteristics of the port under asymmetric faults taking into account the line mutual inductance effect, which can provide a model basis for fault analysis calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0021] Figure 1 This is a flow chart of the broadband equivalent analytical modeling method for AC and DC transmission lines disclosed in Example 1 of the present invention; Figure 2 is a schematic diagram of an AC / DC circuit with coupling effect disclosed in Example 1 of the present invention; wherein, Figure 2 (a) is a schematic diagram of the cable topology structure of the phase domain frequency-variable model built in PSCAD. Figure 2 (b) is a schematic diagram of the topological structure of the equivalent circuit of the transmission line considering mutual inductance; Figure 3 This is a schematic diagram of a multi-RL parallel branch multi-π cascade circuit disclosed in Example 1 of the present invention; Figure 4 Schematic diagram of an equivalent RLC circuit of a DC line considering mutual inductance disclosed in Example 1 of the present invention; Figure 5 This is a schematic diagram of an equivalent RLC circuit of an AC line considering mutual inductance disclosed in Example 1 of the present invention. DETAILED DESCRIPTION

[0022] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0023] As introduced in the background technology, the purpose of the present invention is to overcome the shortcomings of the above-mentioned existing technologies and provide a broadband equivalent analytical modeling method and system for AC / DC transmission lines. Based on phase mode transformation, the voltage-current relationship at the AC / DC cable port considering the mutual inductance characteristics is derived, and a cable mutual inductance equivalent circuit based on differential / common mode RLC circuit and compensation current source is constructed. A long-distance AC / DC submarine cable RLC equivalent modeling method is proposed that can accurately reflect the frequency variation, time delay and distribution characteristics as well as the mutual inductance effect.

[0024] Example 1 In a typical embodiment of the present invention, Figure 1 As shown, this embodiment discloses a broadband equivalent analytical modeling method for AC / DC transmission lines, including: S1. Obtain frequency-varying parameters of self-impedance and mutual impedance of each phase based on the phase-domain frequency-varying model, and convert the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance; S2. Perform vector fitting on the impedance data to construct an RL branch parameter solution equation, determine the number of cascades, and obtain an RLC circuit equivalent model corresponding to the differential mode impedance and the common mode impedance; S3. Using the topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source, an equivalent circuit of the transmission line considering mutual inductance is constructed.

[0025] The above-mentioned broadband equivalent analytical modeling method for AC / DC transmission lines is described in detail below with reference to specific implementation methods.

[0026] This embodiment is based on the most accurate phase-domain frequency-variable model currently available, uses PSCAD to obtain line frequency-variable parameters, and simulates line frequency-variable and mutual inductance characteristics by superimposing an RLC circuit with a current source.

[0027] S1. Obtain the frequency-varying parameters of self-impedance and mutual impedance of each phase based on the phase-domain frequency-varying model, and transform the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance.

[0028] In this embodiment, by building a phase domain frequency-variable model in PSCAD, the cable topology is as follows: Figure 2 As shown in (a), the frequency-varying data of the self-impedance and mutual impedance of the positive and negative lines are derived. Taking the DC transmission circuit as an example, based on the phase domain frequency-varying model, the frequency-varying parameters of the self-impedance and mutual impedance of each phase are obtained. The impedance frequency-varying parameters include the series impedance With parallel admittance ,in, , Generally, the insulation of the cable is good and the parallel conductance can be ignored. , and the parallel capacitor The change with frequency is not obvious, and the capacitance value can be directly obtained through the frequency variation data. Therefore, the frequency variation characteristics of the cable are mainly aimed at the series impedance. and Solve it.

[0029] The impedance matrix composed of self-impedance and mutual impedance is transformed into differential mode and common mode forms to achieve decoupling between the positive and negative poles of the DC line. Specifically, assuming that the positive and negative currents of the DC bipolar line are Positive and negative voltage per unit length , then the DC transmission line impedance matrix is ​​as follows: (1); This can be used to measure the positive and negative currents of the DC bipolar line Positive and negative voltage per unit length The relationship is expressed as: (2); in, is the positive cable self-impedance, is the negative cable self-impedance, is the mutual impedance between the positive and negative cables.

[0030] Since the positive and negative cable parameters are symmetrical, we have: (3); Adding and subtracting the two equations (2) yields: (4); make: (5); Substituting formula (4) into formula (5) yields: (6); Where, are the differential mode voltage and common mode voltage of the DC cable respectively; are the differential mode current and common mode current of the DC cable respectively; are the differential mode impedance and common mode impedance of the DC cable respectively. The differential mode impedance of the DC transmission line is the difference between the positive and negative poles’ self-impedance and the mutual impedance, and the common mode impedance is the sum of the positive and negative poles’ self-impedance and the mutual impedance.

[0031] Three-phase AC cable current Voltage The impedance matrix can be expressed as: (7); in, is the phase-to-phase mutual impedance, ; is the self-impedance of each phase, In actual projects, in order to save the construction cost of AC submarine cables, three-phase AC submarine cables often use three-core structures. The distances between the three-phase cables are the same, so the mutual inductance characteristics between the phases are consistent. ; The three-core cable has the same structure and the self-impedance of each phase is equal. .

[0032] Based on the DC cable transformation idea, Equation (7) is transformed into differential mode impedance and common mode impedance, which can be expressed as: (8); (9); in, is the common-mode voltage of the AC cable; the differential-mode impedance of the AC transmission line is the difference between the self-impedance and the mutual impedance, and the common-mode impedance is the sum of the single-phase self-impedance and twice the mutual impedance.

[0033] S2. Perform vector fitting on the impedance data to construct the RL branch parameter solution equation, determine the cascade number, and obtain the RLC circuit equivalent model corresponding to the differential mode impedance and common mode impedance.

[0034] In this embodiment, the topology is constructed as follows Figure 3 The multi-RL branch multi-π cascade model corresponding to the differential mode impedance and common mode impedance shown in the figure is shown in the figure. Specifically, the impedance original data of the real cable data (i.e. the series impedance and parallel admittance values ​​corresponding to the unit length line at different frequencies derived from the phase domain frequency-varying model of the PSCAD simulation software) are vector fitted. The fitting target is the sum of N rational fractions. According to the fitting function The order determines the number of RL branches To determine the impedance parameters of multiple RL branches, select frequency points And its corresponding impedance data According to the principle that the original impedance frequency-varying parameters of the differential mode and common mode forms are the same as the RLC fitting data at the fitting point, the RL branch parameter solution equation is constructed, which is expressed as: (10); Where, is the fitting function, is the number of RL branches, is the frequency point The corresponding impedance data is solved The impedance parameters of the RL strip.

[0035] In this embodiment, a long-distance submarine cable can be viewed as a series of countless infinitesimal elements. To simplify the topological complexity, the long-distance submarine cable is divided into N equal parts, each of which is equivalent to a π-type structure in the form of lumped parameters. To determine the number of cascades, the amplitude-frequency characteristics of multi-RL parallel branch multi-π-type circuits with different cascade numbers are compared with the phase-domain frequency-variant model. The number of cascades N is determined based on the simulation accuracy and efficiency in the frequency band of interest. The parameters of each π-type structure are specifically expressed as: (11); Where, the cable length simulated by a single π-shaped structure is , The cable length simulated for N π-shaped structures.

[0036] S3. Using the topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source, an equivalent circuit of the transmission line considering mutual inductance is constructed.

[0037] In this step, based on the differential mode RLC circuit, the compensation current is obtained by calculating the electrical quantities of the differential mode circuit and the common mode circuit, and the compensation current is applied in the form of a current source at the differential mode circuit port to construct an equivalent circuit of the transmission line considering mutual inductance. The specific topology is as follows: Figure 2 (b)

[0038] Specifically, the differential mode RLC circuit is at port k Apply positive voltage Corresponding current Expressed as: (12); Where, and Port k The corresponding differential mode voltage and common mode voltage.

[0039] According to formula (12), the port k Positive compensation current source The expression is: (13); Where, For differential mode RLC circuit at port k Apply negative voltage The corresponding current; 、 The common mode RLC circuit is at the port k The current corresponding to the positive and negative voltages applied.

[0040] Similarly, ports k Negative compensation current source The expression is: (14); As shown in equations (13) and (14), the DC line equivalent circuit compensation current source can be obtained by the common mode circuit and the differential mode circuit, as shown in Figure 4 The DC line equivalent RLC circuit structure considering mutual inductance is shown in the figure. The main circuit of the DC cable equivalent model has a positive and negative pole topology, and the topology of each pole is the same. It consists of an RLC circuit corresponding to the differential mode impedance and a compensation current source. The auxiliary circuit has a positive and negative pole topology, and the topology of each pole is the same. It consists of a positive and negative pole voltage source and an RLC circuit corresponding to the common mode impedance. The main circuit is directly connected to the system, and the given value of the auxiliary circuit voltage source is obtained by measuring the voltage at the main circuit port. The given current value of the compensation current source is calculated using the current values ​​of the main circuit and the auxiliary circuit.

[0041] AC line A phase port k compensation current source The expression is: (15); Similarly, the AC line B and C phase ports k Compensation current source 、 The expression is: (16); Where, The currents corresponding to the A, B, and C phase voltages applied to port k by the differential-mode RLC circuit are respectively; The currents corresponding to the A, B, and C phase voltages are applied to the port k of the common-mode RLC circuit respectively.

[0042] As shown in Equations (15) and (16), the compensation current source of the AC line equivalent circuit can be obtained by the common mode circuit and the differential mode circuit, as shown in Figure 5 The AC line equivalent RLC circuit structure considering mutual inductance is shown in the figure. The main circuit of the AC cable equivalent model is a three-phase topology with the same topology for each phase, consisting of an RLC circuit corresponding to the differential-mode impedance and a compensation current source. The auxiliary circuit is a three-phase topology with the same topology for each phase, consisting of A-phase, B-phase, and C-phase voltage sources and an RLC circuit corresponding to the common-mode impedance. The main circuit is directly connected to the system, and the given value of the auxiliary circuit voltage source is obtained by measuring the voltage at the main circuit port. The given current value of the compensation current source is calculated using the current values ​​of the main circuit and the auxiliary circuit.

[0043] In this step, the introduction of the compensation current source enables the equivalent model to simulate the port electrical characteristics considering the line mutual inductance effect under asymmetric faults, which can provide a model basis for fault analysis calculations.

[0044] Example 2 In a typical embodiment of the present invention, this embodiment discloses a broadband equivalent analytical modeling system for AC and DC transmission lines, comprising: The impedance transformation module is configured to: obtain frequency-varying parameters of self-impedance and mutual impedance of each phase based on a phase-domain frequency-varying model, and transform the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance; An RLC circuit equivalent model building module is configured to: perform vector fitting on impedance data to build an RL branch parameter solution equation, determine the number of cascades, and obtain an RLC circuit equivalent model corresponding to the differential mode impedance and the common mode impedance; The transmission line equivalent circuit construction module is configured to: use the topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source to construct the transmission line equivalent circuit considering the mutual inductance.

[0045] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A broadband equivalent analytical modeling method for AC / DC transmission lines, characterized by: include: Obtain the frequency-varying parameters of self-impedance and mutual-impedance of each phase based on the phase-domain frequency-varying model, and transform the self-impedance and mutual-impedance into differential-mode impedance and common-mode impedance; Perform vector fitting on the impedance data to construct the RL branch parameter solution equation, determine the cascade number, and obtain the RLC circuit equivalent model corresponding to the differential mode impedance and common mode impedance; The topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source is used to construct an equivalent circuit of the transmission line considering mutual inductance.

2. The method for broadband equivalent analytical modeling of AC / DC transmission lines according to claim 1, characterized in that: The method of obtaining the frequency-varying parameters of the self-impedance and mutual-impedance of each phase based on the phase-domain frequency-varying model specifically includes: building a phase-domain frequency-varying model in PSCAD, and deriving the frequency-varying data of the self-impedance and mutual-impedance of the positive and negative lines.

3. The method for broadband equivalent analytical modeling of AC / DC transmission lines according to claim 1, characterized in that: The self-impedance and mutual impedance are converted into differential-mode impedance and common-mode impedance, specifically: the differential-mode impedance of the DC transmission line is the difference between the positive and negative self-impedance and the mutual impedance, and the common-mode impedance is the sum of the positive and negative self-impedance and the mutual impedance; The differential mode impedance of an AC transmission line is the difference between the self-impedance and the mutual impedance, and the common mode impedance is the sum of the single-phase self-impedance and twice the mutual impedance.

4. The method for broadband equivalent analytical modeling of AC / DC transmission lines according to claim 1, characterized in that: The vector fitting of the impedance data to construct the RL branch parameter solution equation specifically includes: Perform vector fitting on the original impedance data and determine the number of RL branches based on the order of the fitting function ; Select Frequency points and their corresponding impedance data are used to construct the RL branch parameter solution equation; The amplitude-frequency characteristics of multi-π-type circuits with multiple RL parallel branches and phase-domain frequency-varying models with different cascade numbers are compared to determine the cascade number. Each cascade part is equivalent to a π-type structure in the form of lumped parameters, and the equivalent RLC circuit model corresponding to the differential-mode impedance and common-mode impedance is obtained.

5. A broadband equivalent analytical modeling method for AC / DC transmission lines according to claim 4, characterized in that: The RL branch parameter solution equation is specifically expressed as: ； Where, is the fitting function, is the number of RL branches, is the frequency point The corresponding impedance data.

6. A broadband equivalent analytical modeling method for AC / DC transmission lines according to claim 4, characterized in that: The parameters of the π-type structure are specifically expressed as: ； Where, the cable length simulated by a single π-shaped structure is , The cable length simulated for N π-shaped structures.

7. The method for broadband equivalent analytical modeling of AC / DC transmission lines according to claim 1, characterized in that: Using the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the topology of the compensation current source, an equivalent circuit of the transmission line considering mutual inductance is constructed, specifically including: Based on the differential-mode RLC circuit, the difference between the current at the differential-mode circuit port and the actual current is calculated to obtain the current value of the compensation current source; the compensation current is obtained by calculating the electrical quantities of the differential-mode circuit and the common-mode circuit, and is compensated at the differential-mode circuit port in the form of a current source.

8. A broadband equivalent analytical modeling method for AC / DC transmission lines according to claim 7, characterized in that: The compensation current source of the DC line equivalent circuit is obtained by the common mode circuit and the differential mode circuit, which can be expressed as follows: Differential mode RLC circuit at port k Apply positive voltage Corresponding current for: ； port k Positive compensation current source The expression is: ； port k Negative compensation current source The expression is: ； Where, and Port k Corresponding differential mode voltage and common mode voltage; For differential mode RLC circuit at port k Apply negative voltage The corresponding current; 、 The common mode RLC circuit is at the port k The current corresponding to the positive and negative voltages applied.

9. The method for broadband equivalent analytical modeling of AC / DC transmission lines according to claim 7, characterized in that: The compensation current source of the AC line equivalent circuit can be obtained from the common mode circuit and the differential mode circuit, which can be expressed as follows: AC line A phase port k compensation current source The expression is: ； AC line phase B and C ports k Compensation current source 、 The expression is: ； Where, The currents corresponding to the A, B, and C phase voltages applied to port k by the differential-mode RLC circuit are respectively; The currents corresponding to the A, B, and C phase voltages are applied to the port k of the common-mode RLC circuit respectively.

10. A broadband equivalent analytical modeling system for AC and DC transmission lines, characterized by: include: The impedance transformation module is configured to: obtain frequency-varying parameters of self-impedance and mutual impedance of each phase based on a phase-domain frequency-varying model, and transform the self-impedance and mutual impedance into differential-mode impedance and common-mode impedance; An RLC circuit equivalent model building module is configured to: perform vector fitting on impedance data to build an RL branch parameter solution equation, determine the number of cascades, and obtain an RLC circuit equivalent model corresponding to the differential mode impedance and the common mode impedance; The transmission line equivalent circuit construction module is configured to: use the topology of the differential-mode RLC equivalent circuit corresponding to the differential-mode impedance and the compensation current source to construct the transmission line equivalent circuit considering the mutual inductance.

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