Three-core power cable high-frequency transient model of refined frequency-dependent mutual impedance

Abstract

The invention relates to a refined frequency-dependent mutual impedance three-core power cable high-frequency transient model, and belongs to the field of power disturbance analysis of power systems. The model is composed of a plurality of distributed cable units (ReCABLE units), each ReCABLE unit represents a three-core power cable section with the unit length of 10, a plurality of three-core power cable sections with the unit length of 10 are built into a complete three-core power cable, and the distributed cable units with the corresponding number are selected for the complete three-core power cable according to the total length of the complete three-core power cable; and each ReCABLE unit comprises three refined frequency-varying mutual impedance modules Mcs (f), three frequency-varying admittance modules Yin (f), three frequency-varying wire core impedance modules Zc (f) and one frequency-varying metal sheath impedance module Zs (f). According to the method, a high-precision model is established through a vector fitting-circuit synthesis-passive optimization method based on mutual impedance frequency change data calculated through experimental measurement, so that the defect of an existing cable model in mutual impedance parameter simulation precision is effectively overcome; and a more reliable model basis is provided for transient analysis research and engineering application of the three-core power cable.

Description

Technical Field

[0001] The present invention relates to a high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance, belonging to the field of power disturbance analysis in power systems. Background Art

[0002] Due to the coaxial multi-layer metal conductors and the dielectric properties of the insulating materials of the three-core power cable, the model parameters have high-frequency frequency-varying characteristics. Among them, the high-frequency frequency-varying characteristics of the cable metal core impedance, insulation admittance, and metal shielding layer impedance have been relatively fully revealed, and corresponding simulation analysis models can be constructed through the derived theoretical analytical formulas. However, the frequency-varying mutual impedance parameter that determines the electromagnetic induction effect between the cable core and the metal shielding layer is often ignored or simplified.

[0003] In fact, the frequency-varying mutual impedance parameter between the cable core and the metal shielding layer is an important parameter in the related application research of power cables. For example, in the analysis of various cable transient faults involving grounding circuits, such as partial discharge, arc fault, grounding fault, etc., when calculating the distribution characteristics of transient fault voltages and fault currents, the frequency-varying mutual impedance of the cable needs to be carefully considered. When studying problems such as the propagation, suppression, and traceability of electromagnetic disturbance waveforms in power cables, the frequency-varying mutual impedance is the most critical influencing factor and calculation basis. Monitoring the insulation state of the cable using the induced current of the metal shielding layer, evaluating the transient current-carrying capacity of the cable, and calculating the transient loss of the cable also depend on the accuracy of the frequency-varying mutual impedance parameter.

[0004] However, in existing simulation software, the cable transient model and its simulation of electromagnetic induction effects are still not accurate enough. In the commonly used electromagnetic transient simulation software PSCAD (Power System Computer Aided Design), the cable transient models Frequency Dependent (Phase) Model and Bergeron model are the most widely used. The Bergeron model considers the distributed parameter characteristics of the cable line, but usually assumes that the transmission line characteristics are linear within a certain frequency range, and cannot provide accurate responses under high-frequency and complex dynamic conditions, with insufficient accuracy. The frequency-domain frequency-varying model Frequency Dependent (Phase) Model uses a frequency-varying transformation matrix and considers the changes in line parameters at all frequencies. It is a relatively accurate model at present, but its frequency-varying mutual impedance parameter has not been fully explained and verified, and its modeling calculation and simulation accuracy still need to be improved. Summary of the Invention

[0005] The purpose of the present invention is to solve the deficiencies of the prior art, and provide a high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance and a construction method thereof. Using this model can improve the analysis accuracy of the frequency-varying model of the three-core power cable.

[0006] To achieve the above-mentioned invention object, the technical solution adopted by the present invention is as follows:

[0007] A high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance, which is composed of distributed cable units. Each distributed cable unit represents a three-core power cable segment with a unit length of l0, and a corresponding number of distributed cable units are taken according to the total length of a cable; each distributed cable unit internally contains 3 refined frequency-varying mutual impedance modules M cs (f), 3 frequency-varying admittance modules Y in (f), 3 frequency-varying core impedance modules Z c (f), and 1 frequency-varying metal sheath impedance module Z s (f).

[0008] The modeling method of the refined frequency-varying mutual impedance module M cs (f) is as follows:

[0009] Step1: Calculate the frequency-varying mutual impedance data. Use a signal generator, a three-core power cable, and an oscilloscope to build a measurement circuit. Inject a 0-100 kHz sinusoidal sweep current signal into the cores of the three-core power cable, measure the induced voltage signal of the metal shield layer, and after Fourier transform of the collected sinusoidal sweep current signal and the induced voltage signal, calculate the frequency-varying mutual impedance data of the three-core power cable;

[0010] Step2: Vector fitting. Perform vector fitting on the frequency-varying mutual impedance data obtained in Step1 to obtain a rational fitting formula of the frequency-varying mutual impedance data The rational fitting formula contains and three decomposition terms:

[0011]

[0012] In the formula, s represents a complex variable; N represents all the pole numbers, including real poles and conjugate complex poles; M represents the number of real poles;

[0013] The decomposition term is the constant term and the first-order term of the rational fitting formula , including the parameters k and b obtained by vector fitting calculation, where k is the coefficient of the first-order term and b is the constant term;

[0014] The decomposition term is the real pole and its residue part of the rational fitting formula , including the parameters a j , c j , j, where aj is a real pole, c j is the residue corresponding to the real pole, j ∈ [1, 2,..., M];

[0015] Decomposition term is a rational expression the conjugate complex poles and their residue parts, including the parameters a obtained by vector fitting calculation j1 、c j1 、a j2 、c j2 、j1, j2, where a j1 and a j2 represent a pair of conjugate complex poles, c j1 and c j2 represent the residues corresponding to a pair of conjugate complex poles, the subscripts 1 and 2 indicate adjacent, j = M + 1, M + 2,..., (N + M) / 2;

[0016] Step3. Circuit synthesis. Using the circuit synthesis method, according to the rational fitting formula obtained in Step2 and the three decomposition terms and the parameters obtained by vector fitting calculation of each item, convert each decomposition term into a circuit combination conversion formula of resistance R, inductance L, capacitance C, and conductance G to achieve physical circuit equivalence;

[0017] In each circuit combination conversion formula, the subscripts of the corresponding R, L, C, G are a;

[0018] When the c in j is a negative real number, the subscripts of the corresponding R, L, C, G are b1;

[0019] When the c in j is a positive real number, the subscripts of the corresponding R, L, C, G are b2;

[0020] the subscripts of the corresponding R, L, C, G are c;

[0021]

[0022] Step4. Passive optimization of the equivalent physical model. Use the pattern search algorithm to perform passive optimization on the calculation results of the resistances R, inductances L, capacitances C, and conductances G obtained in Step3. The objective function F and the constraint conditions of the pattern search algorithm for passive optimization are shown in Equation (5):

[0023]

[0024] In the formula, Z RLCGrepresents the calculated value of the frequency-dependent mutual impedance of the built model; Z measure represents the measured value of the frequency-dependent mutual impedance, m represents the number of calculation points of the mutual impedance of the three-core power cable, and the constraint condition for realizing passivation is that the values of the R, L, C, and G elements are all greater than zero;

[0025] Step5. Model construction: Connect the equivalent circuit elements R, L, C, and G obtained from the passive optimization in Step4 according to the circuit combination transformation formula in Eqs. (2)-(4) to connect the equivalent elements and build a refined frequency-dependent mutual impedance module M cs (f).

[0026] The frequency-dependent admittance module Y in (f), the frequency-dependent core impedance module Z c (f), and the frequency-dependent metal sheath impedance module Z s (f) are modeled as follows:

[0027] First, calculate the frequency-dependent core impedance Z c data using Eq. (6), calculate the frequency-dependent metal sheath impedance Z s data using Eq. (7), and calculate the frequency-dependent admittance Y in data using Eq. (8);

[0028]

[0029] where r c , r in , r s are the radii of the core, insulation layer, and metal shielding layer of the three-core power cable respectively, ρ c , ρ s are the conductivities of the core and metal shielding layer of the three-core power cable respectively, μ0 is the vacuum permeability, ε0 is the vacuum permittivity, ε r is the relative complex permittivity of the insulation layer of the three-core power cable, including the real part ε r ' and the imaginary part ε r ";

[0030] Then, use the methods in Steps Step2-Step4 to construct the model to obtain the frequency-dependent admittance module Y in (f), the frequency-dependent core impedance module Z c (f), and the frequency-dependent metal sheath impedance module Z s (f).

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. Revealed the unique frequency-varying characteristics of mutual impedance and promoted technological innovation: The present invention discovered for the first time through experiments that the mutual impedance of three-core power cables has unique frequency-varying characteristics in the frequency range of 0-100kHz. This discovery provides a new breakthrough and innovative direction for the refined modeling of three-core power cable models, filling the technical gap in this field.

[0033] 2. It makes up for the accuracy defects of the existing models: Based on the mutual impedance frequency-varying data calculated by experimental measurement, the present invention establishes a high-precision model through the method of vector fitting-circuit synthesis-passive optimization, which effectively solves the shortcomings of the existing cable model in the simulation accuracy of mutual impedance parameters and provides a more reliable model basis for the transient analysis research and engineering application of three-core power cables.

[0034] 3. Significantly improved the transient analysis capability and practicality of existing models: Compared with the cable model that comes with PSCAD, a commonly used electromagnetic transient simulation software for power systems, the refined frequency-variable mutual impedance model proposed in the present invention has significant improvements in capturing subtle features of transient signals, while also having the advantages of clear physical meaning and easy simulation modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the implementation steps, results or existing technical solutions of the present invention, the following will briefly introduce the techniques or drawings required for use in the implementation process or technical description. Obviously, the drawings described below are only some specific implementation processes of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without carrying out creative work.

[0036] Figure 1 It is the modeling process and model of the high-frequency transient model of three-core power cable with refined frequency-dependent mutual impedance;

[0037] Figure 2 This is the experimental measurement circuit diagram of the frequency-variable mutual impedance of three-core power cables;

[0038] Figure 3 is the frequency-dependent mutual impedance spectrum of the three-core power cable, where: Figure 3 (a) is the imaginary part of the mutual impedance spectrum, Figure 3 (b) is the real part of the mutual impedance spectrum;

[0039] Figure 4 is the comparison between the real and imaginary parts of the mutual impedance after the model is passive and the real and imaginary parts of the measured mutual impedance, where: Figure 4 (a) is the comparison between the imaginary part of the model mutual impedance and the imaginary part of the measured mutual impedance. Figure 4 (b) is the comparison between the real part of the model mutual impedance and the real part of the measured mutual impedance;

[0040] Figure 5It is a comparison of the induced voltages of four models under different transient disturbance conditions. Among them, Figure 5 (a) is the comparison of the induced voltages of the four models during a single-phase-to-ground fault on phase C, Figure 5 (b) is the comparison of the induced voltages of the four models during a two-phase-to-ground fault on phases AB, Figure 5 (c) is the comparison of the induced voltages of the four models during a two-phase-to-ground fault on phases BC, Figure 5 (d) is the comparison of the induced voltages of the four models during single-phase open-circuit operation;

[0041] Figure 1 In the model, it consists of several distributed cable units (ReCABLE units). Each ReCABLE unit represents a three-core power cable section with a unit length of l0. Several three-core power cable sections with a unit length of l0 are built into a complete three-core power cable. The complete three-core power cable takes the corresponding number of distributed cable units according to its total length. Each ReCABLE unit contains 3 refined frequency-varying mutual impedance modules M cs (f), 3 frequency-varying admittance modules Y in (f), 3 frequency-varying core impedance modules Z c (f), and 1 frequency-varying metallic sheath impedance module Z s (f). Each module is connected by an equivalent circuit resistance R, inductance L, capacitance C, and conductance G according to the modeling method of the present invention. Detailed implementation mode

[0042] The present invention is described through specific implementation processes. Without departing from the scope of the present invention, various transformations and equivalent substitutions can also be made to the present invention. Therefore, the present invention is not limited to the disclosed specific implementation processes, but should include all implementation schemes falling within the scope of the claims of the present invention.

[0043] Example 1

[0044] The following will make a detailed description of the specific implementation mode of the present invention with reference to the accompanying drawings. However, the present invention is not limited to the above implementation modes. Within the knowledge scope of those of ordinary skill in the art, various changes can also be made without departing from the gist of the present invention.

[0045] As Figure 1 shown, a high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance. The model consists of several distributed cable units (ReCABLE units). Each ReCABLE unit represents a three-core power cable section with a unit length of l0. Several three-core power cable sections with a unit length of l0 are built into a complete three-core power cable. The complete three-core power cable takes the corresponding number of distributed cable units according to its total length. Each ReCABLE unit contains 3 refined frequency-varying mutual impedance modules Mcs (f), 3 frequency-variable admittance modules Y in (f), 3 frequency-variable core impedance modules Z c (f), 1 frequency-variable metal sheath impedance module Z s (f), and each module is formed by connecting an equivalent circuit resistance R, an inductor L, a capacitor C, and a conductance G according to the modeling method of the present invention.

[0046] The refined frequency-variable mutual impedance module M cs (f) has the following modeling method:

[0047] Step1. Calculate the frequency-variable mutual impedance data. Use a signal generator, a three-core power cable, and an oscilloscope to build a measurement circuit. Inject a 0 - 100 kHz sinusoidal sweep current signal into the cores of the three-core power cable, and measure the induced voltage signal on the metal shield layer. The experimental platform is built as Figure 2 shown; after Fourier transforming the collected sinusoidal sweep current signal and the induced voltage signal, calculate the frequency-variable mutual impedance data of the three-core power cable. The real and imaginary parts of its variation in the range of 0 - 100 kHz are as Figure 3 shown;

[0048] Step2. Vector fitting. Perform vector fitting on the frequency-variable mutual impedance data obtained in Step1 to obtain the rational fitting formula of the frequency-variable mutual impedance data Rational fitting formula contains and three decomposition terms:

[0049]

[0050] In the formula, s represents a complex variable; N represents all the pole numbers, including real poles and conjugate complex poles; M represents the number of real poles;

[0051] Decomposition term is the constant term and the first-order term of the rational fitting formula , including the parameters k and b obtained by vector fitting calculation, where k is the coefficient of the first-order term and b is the constant term;

[0052] Decomposition term is the real pole and its residue part of the rational fitting formula , including the parameters a j , c j , j, where a j is the real pole, c j is the residue corresponding to the real pole, and j ∈ [1, 2,..., M];

[0053] Decomposition term is a rational expression The conjugate complex poles and their residue parts, including the parameters a obtained by vector fitting calculation j1 , c j1 , a j2 , c j2 , j1, j2, where a j1 and a j2 represent a pair of conjugate complex poles, c j1 and c j2 represent the residues corresponding to a pair of conjugate complex poles, the subscripts 1 and 2 indicate adjacency, j = M + 1, M + 2,...,(N + M) / 2; Fit the frequency-varying mutual impedance data of the three-core power cable obtained in Step1, and the poles and their corresponding residues obtained by fitting are shown in Table 1:

[0054] Table 1 Poles and Residues

[0055]

[0056] Step3, Circuit synthesis, using the circuit synthesis method, according to the rational fitting formula obtained in Step2 and the three decomposition terms The various parameters obtained by vector fitting calculation, convert each decomposition term into a circuit combination conversion formula of resistance R, inductance L, capacitance C, and conductance G to achieve physical circuit equivalence;

[0057] In each circuit combination conversion formula, the subscripts of the corresponding R, L, C, G are a;

[0058] When the c in j is a negative real number, the subscripts of the corresponding R, L, C, G are b1;

[0059] When the c in j is a positive real number, the subscripts of the corresponding R, L, C, G are b2;

[0060] the subscripts of the corresponding R, L, C, G are c;

[0061]

[0062]

[0063] Using the circuit synthesis theory of formulas (2)-(4) in the present invention, combined with the calculation of poles and residues, the mutual impedance R, L, C, G equivalent circuit elements of the three-core power cable can be obtained, and their values are shown in Table 2. It can be seen from the table that there is a "negative value" problem with the equivalent circuit elements before passive optimization, and passive optimization is required.

[0064] Table 2 Initial equivalent circuit element values for circuit synthesis

[0065]

[0066] In Table 2, a1 represents the values of one corresponding R, L, C, and G components; b21 represents the value of one c in j When it is a positive real number, the values of the corresponding R, L, C, and G components; b11 represents the value of one c in j When it is a negative real number, the values of the corresponding R, L, C, and G components; c1 - c2 represent the values of two corresponding R, L, C, and G components.

[0067] Step 4, Passive optimization of the equivalent physical model. Use the pattern search algorithm to perform passive optimization on the calculation results of the resistances R, inductances L, capacitances C, and conductances G obtained in Step 3. The objective function F and the constraint conditions of the pattern search algorithm for passive optimization are shown in Equation (5):

[0068]

[0069] In the formula, Z RLCG represents the calculated value of the refined frequency - varying mutual impedance; Z measure represents the measured value of the frequency - varying mutual impedance, m represents the number of calculation points of the mutual impedance of the three - core power cable. The constraint condition for realizing passivity is that the values of the R, L, C, and G components are all greater than zero; after the passive optimization by the pattern search algorithm, the equivalent circuit element values of the refined frequency - varying mutual impedance are shown in Table 3, and its accuracy verification and comparison are as Figure 4 shown. After passivation, the real and imaginary parts of the refined frequency - varying mutual impedance model are relatively close to the real and imaginary parts of the measured frequency - varying mutual impedance, and can meet the accuracy requirements.

[0070] Table 3 Equivalent circuit element values of the refined frequency - varying mutual impedance after passive implementation

[0071]

[0072] In Table 3, c1 - c5 represent the values of five corresponding R, L, C, and G components.

[0073] It can be seen from Table 3 that the equivalent circuit element values after passivation are all greater than zero, solving the problem of "negative values" existing in the equivalent circuit element values in Step 3.

[0074] Step 5, Model construction. Arrange the circuit equivalent components R, L, C, and G obtained from the passive optimization in Step 4 according to the formulas (2) - (4) Connect the equivalent components according to the circuit combination transformation formula to build the refined frequency-variable mutual impedance module M cs (f), as shown in Figure 1 .

[0075] The frequency-variable admittance module Y in (f), the frequency-variable core impedance module Z c (f) and the frequency-variable metal sheath impedance module Z s (f) are modeled as follows:

[0076] First, use Equation (6) to calculate the frequency-variable core impedance Z c data, use Equation (7) to calculate the frequency-variable metal sheath impedance Z s data, and use Equation (8) to calculate the frequency-variable admittance Y in data;

[0077]

[0078] In the formula, r c , r in , r s are the radii of the core, insulation layer, and metal shielding layer of the three-core power cable respectively, ρ c , ρ s are the conductivities of the core and metal shielding layer of the three-core power cable respectively, μ0 is the vacuum permeability, ε0 is the vacuum permittivity, and ε r is the relative complex permittivity of the insulation layer of the three-core power cable, including the real part ε r ' and the imaginary part ε r ";

[0079] Then, use the methods in Steps Step2 - Step4 to build the model to obtain the Figure 1 shown frequency-variable admittance module Y in (f), the frequency-variable core impedance module Z c (f) and the frequency-variable metal sheath impedance module Z s (f). The values of the corresponding equivalent circuit elements in each module are shown in Tables 4 - 6.

[0080] Table 4 Equivalent circuit element values of the frequency-variable core impedance module

[0081]

[0082]

[0083] In Table 4, a1 represents the values of the R, L, C, and G components corresponding to 1 ; b21 - b26 represent the c in 6 j ​When it is a positive real number, the values of the corresponding R, L, C, and G components.

[0084] Table 5 Equivalent Circuit Element Values of Frequency-Variable Metal Sheath Impedance Module

[0085]

[0086] In Table 5, a1 represents 1 The values of the corresponding R, L, C, and G components; b21 - b24 represent 4 c in j When it is a positive real number, the values of the corresponding R, L, C, and G components.

[0087] Table 6 Equivalent Circuit Element Values of Frequency-Variable Admittance Module

[0088]

[0089] In Table 6, a1 represents 1 The values of the corresponding R, L, C, and G components; b21 - b23 represent 3 c in j When it is a positive real number, the values of the corresponding R, L, C, and G components; b11 - b13 represent 3 c in j When it is a negative real number, the values of the corresponding R, L, C, and G components.

[0090] Finally, the effectiveness and accuracy of the present invention are further verified through model comparison. Using the Frequency Dependent(Phase)Model and Bergeron Model cable models built into the currently mainstream electromagnetic transient simulation software PSCAD, a simulation model is built based on the actual cable size and parameters, and its induced voltage is measured and compared with the measured induced voltage; at the same time, the induced voltage is calculated using the refined frequency-variable mutual impedance three-core power cable high-frequency transient model proposed by the present invention and compared and analyzed with the measured induced voltage. The comparison results are as Figure 5 shown. In the figure, u s_test is the measured induced voltage of the metal shield of the three-core power cable, u passive is the induced voltage of the model of the present invention, u PSCADFre is the induced voltage of the Frequency Dependent(Phase)model model, and u PSCADBer is the induced voltage of the Bergeron model model.

[0091] Figure 5The comparison results show that under the excitation of the same transient disturbance current, the calculation results of the model of the present invention can more truly reflect the pulse and fluctuation details of the transient disturbance induced voltage. In contrast, the calculation results based on the Frequency Dependent (Phase) Model and Bergeron Model cable models built in PSCAD have relatively large errors, and it is impossible to accurately capture the detailed characteristics of the transient induced voltage, making it difficult to meet the accurate analysis requirements of cable transient disturbance induction. This comparison result fully demonstrates the effectiveness and engineering application value of the present invention in high-frequency transient analysis.

Claims

1. A high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance, characterized in that, The model consists of distributed cable units. Each distributed cable unit represents a three-core power cable section with a unit length of l0. For a cable, the corresponding number of distributed cable units is taken according to its total length. Each distributed cable unit contains 3 refined frequency-varying mutual impedance modules M cs (f), 3 frequency-varying admittance modules Y in (f), 3 frequency-varying core impedance modules Z c (f), 1 frequency-varying metal sheath impedance module Z s (f).

2. The high-frequency transient model of a three-core power cable with refined frequency-variable mutual impedance according to claim 1, wherein The described refined frequency-variable mutual impedance module M cs (f) is modeled as follows: Step 1. Calculate the frequency-varying mutual impedance data. Build a measurement circuit using a signal generator, a three-core power cable, and an oscilloscope. Inject a sinusoidal swept-frequency current signal of 0 - 100 kHz into the cores of the three-core power cable, measure the induced voltage signal on the metal shielding layer. After performing Fourier transform on the collected sinusoidal swept-frequency current signal and the induced voltage signal, calculate the frequency-varying mutual impedance data of the three-core power cable; Step 2. Vector fitting: perform vector fitting on the frequency-varying mutual impedance data obtained in Step 1 to obtain a rational fitting formula for the frequency-varying mutual impedance data Rational fitting formula Contain And Three decomposition terms: In the formula, s represents a complex variable; N represents the total number of poles, including real poles and conjugate complex poles; M represents the number of real poles; Decomposition term is the rational fitting formula of the constant term and the first-order term, including the parameters k and b obtained from the vector fitting calculation, where k is the coefficient of the first-order term and b is the constant term; Decomposition term is a rational fitting formula of the real poles and their residue parts, including the parameters a j , c j , j, where a j is a real pole, c j is the residue corresponding to the real pole, j ∈ [1, 2,..., M]; Decomposition term is a rational expression conjugate complex poles and their residue parts, including the parameters a obtained by vector fitting calculation j1 , c j1 , a j2 , c j2 , j1, j2, where a j1 and a j2 represent a pair of conjugate complex poles, c j1 and c j2 represent the residues corresponding to a pair of conjugate complex poles, the subscripts 1 and 2 indicate adjacent, j = M + 1, M + 2,..., (N + M) / 2; Step 3, circuit synthesis. Using the circuit synthesis method, according to the rational fitting formula obtained in Step 2 and the three decomposed terms and the parameters obtained by vector fitting calculation, convert each decomposed term into a circuit combination conversion formula of resistance R, inductance L, capacitance C, and conductance G to achieve the equivalent of the physical circuit; In each circuit combination transformation formula, the subscripts of the corresponding R, L, C, and G are a; When c in j is a negative real number, the subscripts of the corresponding R, L, C, and G are b1; When the c in j is a positive real number, the subscripts of the corresponding R, L, C, and G are b2; The subscripts of the corresponding R, L, C, and G are c; Step 4. Passive optimization of the equivalent physical model. Use the pattern search algorithm to perform passive optimization on the calculation results of the resistances R, inductances L, capacitances C, and conductances G calculated in Step 3. The objective function F and the constraint conditions of the pattern search algorithm for passive optimization are shown in Equation (5): where Z RLCG represents the calculated value of the frequency-dependent mutual impedance of the established model; Z measure represents the measured value of the frequency-dependent mutual impedance, m represents the number of calculation points of the mutual impedance of the three-core power cable, and the constraint condition for realizing passivation is that the values of R, L, C, and G elements are all greater than zero; Step 5. Model construction: Connect the equivalent circuit elements R, L, C, and G obtained from the passive optimization in Step 4 according to the circuit combination transformation formula in Equations (2)-(4). Build the refined frequency-variable mutual impedance module M cs (f).

3. The high-frequency transient model of a three-core power cable with refined frequency-varying mutual impedance according to claim 2, characterized in that, The frequency-variable admittance module Y in (f), the frequency-variable core impedance module Z c (f) and the frequency-variable metal sheath impedance module Z s (f) are modeled as follows: First, calculate the frequency-variable core impedance \(Z\) using Equation (6) c data, and calculate the frequency-variable metal sheath impedance \(Z\) using Equation (7) s data, and calculate the frequency-variable admittance \(Y\) using Equation (8) in data; where r c , r in , r s are the radii of the conductor, insulation layer, and metal shielding layer of the three-core power cable respectively, ρ c , ρ s are the conductivities of the conductor and metal shielding layer of the three-core power cable respectively, μ0 is the permeability of free space, ε0 is the permittivity of free space, and ε r is the relative complex permittivity of the insulation layer of the three-core power cable, including the real part ε r ' and the imaginary part ε r "; Then, the method in Steps Step2 - Step4 is adopted to construct the model, and the frequency - varying admittance module Y is obtained. in (f), the frequency - varying core impedance module Z c (f) and the frequency - varying metallic sheath impedance module Z s (f).

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