AC submarine cable broadband impedance modeling method

Abstract

The invention discloses an AC submarine cable broadband impedance modeling method, which comprises the steps of complete calculation of unit length sequence impedance and unit length sequence susceptance in a broadband of an AC submarine cable, and consideration of a seawater return path when the unit length sequence impedance in the broadband of the AC submarine cable is calculated, so that the calculation result is more accurate; when the unit length sequence susceptance in the alternating current submarine cable wide frequency band is calculated, different types of submarine cables, different connection modes of the submarine cables and grounding arrangement modes are discussed, and a complete calculation system is established. Finally, the accurate pi model of each sequence of the wide frequency band of the alternating current submarine cable established by the method is different from an alternating current submarine cable wide frequency band impedance model expanded by applying power frequency parameters, the calculation result is more accurate, and a basis is provided for researching the resonance problem of alternating current grid connection of an offshore wind plant.

Description

Technical Field

[0001] The present invention belongs to the technical field of power transmission and distribution of offshore power systems, and in particular relates to a wide-band impedance modeling method for an AC submarine cable. Background Art

[0002] In recent years, offshore wind power has developed rapidly. For many small offshore wind farms, AC power transmission has become the main way to connect offshore wind power to the grid due to its simplicity, economy and mature technology. Electric energy is sent through long-distance AC submarine cables. Compared with the common overhead lines in onshore AC power grids, the positive sequence capacitance of AC cables is 20 to 40 times that of overhead lines of the same length and voltage level, but its series impedance is 50% to 100% of the overhead lines of the same voltage level. Due to the capacitance effect of AC cables, there is generally no serious resonance problem in AC grid connection of onshore wind farms, but it may become very serious in AC grid connection of offshore wind farms. Therefore, establishing a wide-band impedance model of AC submarine cables will help study the resonance problem of AC grid connection of offshore wind farms.

[0003] At present, the method for establishing the wide-band impedance model of AC submarine cables is incomplete. The literature [Qian Jie. Research on electrical parameters and electrical characteristics of power cables [D]. Hangzhou: Zhejiang University, 2013] mainly studies the electrical parameters of single-core cables, and only makes a preliminary analysis of the three-core cables with armored layers that have been widely used in submarine power transmission. For the two widely used types of AC submarine cables, namely three-phase single-core submarine cables with armor layers and three-core submarine cables with armor layers, the literature [Xu Zheng, Li Sixun, Jin Yanqiu. Calculation of electrical parameters of submarine cables in harmonic frequency bands [J]. Automation of Electric Power Systems, 2021, 45(21): 76-84] analyzes the calculation method of electrical parameters in a wide frequency band, but the following problems still exist: ① When calculating each impedance in the series full impedance matrix, the seawater is not considered as the return path, and the earth is still used as the return path; ② The distance between conductor layers in the mutual impedance calculation formula in the series full impedance matrix is ​​not clearly given; ③ A complete system has not been established for the calculation of sequence susceptance per unit length, and there is a lack of discussion on different types of submarine cables, different cable connection methods and grounding arrangements.

[0004] Therefore, it is necessary to propose a broadband impedance modeling method for AC submarine cables, including a complete calculation method for the sequence impedance per unit length and the sequence susceptance per unit length within the broadband band of AC submarine cables, to provide a basis for studying the resonance problem of AC grid-connected offshore wind farms. Summary of the invention

[0005] In order to address the problem of incomplete methods for establishing wide-band impedance models of AC submarine cables, the present invention provides a method for modeling wide-band impedance of AC submarine cables, which includes complete calculation of sequence impedance per unit length and sequence susceptance per unit length within the wide-band of AC submarine cables, providing a basis for studying the resonance problem of AC grid-connected offshore wind farms.

[0006] A wide-band impedance modeling method for an AC submarine cable comprises: calculating the sequence impedance per unit length and the sequence susceptance per unit length within the wide-band of the AC submarine cable; and establishing an accurate π model for each sequence of the wide-band of the AC submarine cable according to the sequence impedance per unit length and the sequence susceptance per unit length.

[0007] Furthermore, the calculation of the sequence impedance per unit length within the wide frequency band of the AC submarine cable includes:

[0008] 1.1 Calculate the DC resistance per unit length of each conductor layer of the AC submarine cable;

[0009] 1.2 Calculate the AC resistance per unit length of each conductor layer of the AC submarine cable based on the DC resistance per unit length of each conductor layer of the AC submarine cable;

[0010] 1.3 Calculate the parameters of the seawater return path;

[0011] 1.4 According to the AC resistance per unit length of each conductor layer of the AC submarine cable and the parameters of the seawater return path, the AC submarine cable series full impedance matrix is ​​constructed;

[0012] 1.5 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable series full impedance matrix is ​​converted into the AC submarine cable series phase impedance matrix;

[0013] 1.6 According to the type of AC submarine cable, the AC submarine cable series phase impedance matrix is ​​transformed through phase sequence to obtain the AC submarine cable series sequence impedance matrix. The elements in this matrix are the unit length sequence impedance of the AC submarine cable in the wide frequency band.

[0014] Furthermore, in step 1.3, the parameters of the seawater return path are calculated by the following formula;

[0015]

[0016]

[0017] Where: r sea is the radius of the seawater equivalent conductor, α is the intermediate variable of the external impedance correction term, kei(α) is the external resistance correction term, ker(α) is the external reactance correction term, ρ sea is the resistivity of seawater (generally 0.5Ω·m), f is the harmonic frequency of the power grid, d Phase is the average distance between the submarine cables, kei(α) and ker(α) are the imaginary and real parts of the Kelvin function of α respectively (for the three-core submarine cable with armor layer, the seawater return path is not considered, kei(α)=ker(α)=0).

[0018] Furthermore, in step 1.4, for the three-core submarine cable with an armor layer, the series total impedance matrix expression is as follows:

[0019]

[0020] For a three-phase single-core submarine cable with an armor layer, the series impedance matrix expression is as follows:

[0021]

[0022] Where: Z F is the series full impedance matrix, Z xy represents the impedance matrix between the three-core submarine cable x and y, Z xx represents the impedance matrix of the three-core submarine cable x, Z xmyn represents the mutual impedance between phase m x and phase n y, Z xma =Z axm represents the mutual impedance between the armor layer of the three-core submarine cable and the m-phase x, Z xmxm represents the self-impedance of phase m x, Z aa represents the self-impedance of the armor layer of the three-core submarine cable, Z cs,ca and Z sc,ac It represents the impedance matrix composed of the mutual impedance between the core layer and the sheath layer and the mutual impedance between the core layer and the armor layer. ssaa It represents the impedance matrix composed of the self-impedance of the sheath layer, the self-impedance of the armor layer and the mutual impedance between the sheath layer and the armor layer. x, y = c, s, a correspond to the core layer, sheath layer and armor layer of the submarine cable. m, n = 1, 2, 3 correspond to the three phases ABC. xm≠yn.

[0023] Furthermore, for the core layer, its self-impedance Z cmcm The expression is as follows:

[0024]

[0025] Where: R c,ac is the AC resistance per unit length of the AC submarine cable core layer, r oc and r ic are the outer radius and inner radius of the core layer, μ c is the relative magnetic permeability of the core material, j is an imaginary unit; if r ic = 0, that is, the core layer is a circular conductor, then the function F(r oc ,r ic )=1; if r ic > 0, then the function F(r oc ,r ic ) is as follows:

[0026]

[0027] For the sheath layer, its self-impedance Z smsm The expression is as follows:

[0028]

[0029] Where: R s,ac is the AC resistance per unit length of the AC submarine cable sheath, r os and r is are the outer radius and inner radius of the sheath layer, μ s is the relative magnetic permeability of the sheath material;

[0030] For the armor layer, its self-impedance Z aa and Z amam The expression is as follows:

[0031]

[0032] Where: R a,ac is the AC resistance per unit length of the AC submarine cable armor layer, r oa and r ia are the outer radius and inner radius of the armor layer, μ a is the relative magnetic permeability of the armor material;

[0033] The mutual impedance Z xmyn and Z xma The expression is as follows:

[0034]

[0035] Where: d xmyn represents the distance between the axes of m phase x and n phase y, d xma It represents the axial distance between the m-phase x and the armor layer of the three-core submarine cable. If the m-phase x contains the n-phase y, then d xmyn is the average radius of the m phase x, i.e. d xmyn =(r ox +r ix ) / 2, r ox and r ix are the outer radius and inner radius of x respectively; if n-phase y or the armor layer contains m-phase x, then d xmyn is the average radius of phase n y, d xma is the average radius of the armor layer, then d xmyn =(r oy +r iy ) / 2,d xma =(r oa +r ia ) / 2, r oy and r iy are the outer and inner radius of y respectively.

[0036] Furthermore, in step 1.5, for a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the series phase impedance matrix Z Phase The expression is:

[0037]

[0038] For a three-core submarine cable with an armor layer where the sheath and armor are connected together but grounded at only one point or not grounded at all, the series phase impedance matrix Z Phase =Z cc ;

[0039] For a three-phase single-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the series phase impedance Z Phase The expression is:

[0040]

[0041] For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together but grounded at only one point or not grounded at all, the series phase impedance Z Phase =Z c1c1 .

[0042] Furthermore, the calculation of the sequence susceptance per unit length within the wide frequency band of the AC submarine cable includes:

[0043] 2.1 Constructing an AC submarine cable parallel all-susceptance matrix;

[0044] 2.2 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable parallel full susceptance matrix is ​​converted into the AC submarine cable parallel phase susceptance matrix;

[0045] 2.3 According to the type of AC submarine cable, the AC submarine cable parallel phase susceptance matrix is ​​transformed through phase sequence to obtain the AC submarine cable parallel sequence susceptance matrix. The elements in this matrix are the unit length sequence susceptance of the AC submarine cable within the wide frequency band.

[0046] Furthermore, in step 2.1, for the three-core submarine cable with an armor layer, the parallel full susceptance matrix expression is as follows:

[0047]

[0048] For a three-phase single-core submarine cable with an armor layer, the parallel full susceptance matrix expression is as follows:

[0049]

[0050] Among them: B F is a parallel full susceptance matrix, B xy represents the susceptance matrix between the three-core submarine cable x and y, B xxrepresents the susceptance matrix of the three-core submarine cable x, B smsn It represents the susceptance between the m-phase sheath layer and the n-phase sheath layer of the three-core submarine cable, B cmsm It represents the susceptance between the m-phase core layer and the m-phase sheath layer, B sma It represents the susceptance between the armor layer and the m-phase sheath layer of the three-core submarine cable, B smam It represents the susceptance between the m-phase armor layer and the m-phase sheath layer of the three-phase single-core submarine cable, B amg It represents the susceptance between the m-phase armor layer of the three-phase single-core submarine cable and the seawater, B ag represents the susceptance between the armor layer of the three-core submarine cable and the seawater, B cs,ca and B sc,ac It represents the susceptance matrix composed of the susceptance between the core layer and the sheath layer and the susceptance between the core layer and the armor layer. ss,aa It represents the susceptance matrix composed of the susceptance between the sheath layer and the armor layer, and between the armor layer and the seawater. x, y = c, s, a correspond to the core layer, sheath layer and armor layer of the submarine cable, and m, n = 1, 2, 3 correspond to the three phases ABC.

[0051] Furthermore, the susceptance B smsn , B cmsm , B sma , B smam , B amg , B ag The expression is as follows:

[0052]

[0053]

[0054] Where: f is the harmonic frequency of the power grid, r oc is the outer radius of the core layer, r oa and r ia are the outer radius and inner radius of the armor layer, r os and r is are the outer radius and inner radius of the sheath layer, respectively, sm is the axial distance between the m-phase sheath layer and the armor layer of the three-core submarine cable, ε cs is the relative dielectric constant of the insulation layer between the core layer and the sheath layer, ε sa is the relative dielectric constant of the insulating layer between the sheath layer and the armor layer, ε ag is the relative dielectric constant of the outer insulation layer of the three-core submarine cable armor layer, ε amg is the relative dielectric constant of the outer insulation layer of the m-phase armor layer of the three-phase single-core submarine cable, d smsn It is the axial distance between the m-phase sheath layer and the n-phase sheath layer of the three-core submarine cable.

[0055] Furthermore, in step 2.2, for a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together but grounded at only one point or not grounded at all, the parallel phase susceptance matrix B Phase The expression is:

[0056]

[0057] For a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance matrix B Phase =B cc ;

[0058] For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together but only grounded at one point or not grounded at all, the parallel phase susceptance B Phase The expression is:

[0059]

[0060] For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance B Phase =B c1s1 .

[0061] In a second aspect, the present invention provides an AC submarine cable broadband impedance modeling system, comprising:

[0062] Impedance calculation unit, used to calculate the sequence impedance per unit length in the wide frequency band of AC submarine cable;

[0063] Susceptance calculation unit, used to calculate the sequence susceptance per unit length in the wide frequency band of AC submarine cable;

[0064] The modeling unit establishes an accurate π model of each sequence in the wide-band AC submarine cable according to the sequence impedance per unit length and the sequence susceptance per unit length in the wide-band AC submarine cable.

[0065] In a third aspect, the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor is used to execute the computer program to implement the above-mentioned AC submarine cable wide-band impedance modeling method.

[0066] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the above-mentioned AC submarine cable wide-band impedance modeling method.

[0067] Compared with the prior art, the present invention has the following beneficial technical effects:

[0068] 1. Different from the method for calculating the sequence impedance per unit length of a submarine cable that takes the earth as the return path, the present invention takes the seawater return path into consideration when calculating the sequence impedance per unit length in a wide frequency band of a submarine cable, and approximates the complex Kelvin function to a simple elementary function when calculating the external impedance correction term, thereby reducing the amount of calculation while ensuring the accuracy of the result.

[0069] 2. Different from the calculation method which only considers the grounding arrangement at both ends of the sheath layer and the armor layer and directly uses the core layer susceptance as the unit length susceptance, the present invention discusses different types of submarine cables, different connection methods of submarine cables and grounding arrangements when calculating the unit length sequence susceptance within the wide frequency band of the submarine cable, establishes a complete calculation system, and improves the flexibility of submarine cable modeling.

[0070] 3. Different from the wide-band impedance model of AC submarine cables expanded by using industrial frequency parameters, the wide-band accurate π model of AC submarine cables established by the present invention takes into account the frequency variation effect of unit length parameters, and the calculation results are more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The figure is a flow chart of the AC submarine cable wide-band impedance modeling method of the present invention.

[0072] Figure 2 This is a schematic diagram of the cross section of a three-phase single-core submarine cable with an armor layer.

[0073] Figure 3 This is a schematic diagram of the cross section of a three-core submarine cable with an armor layer.

[0074] Figure 4 Schematic diagram of the equivalent capacitance of a three-core submarine cable with an armor layer.

[0075] Figure 5 Schematic diagram of single-phase equivalent capacitance of three-phase single-core submarine cable with armor layer.

[0076] Figure 6 Schematic diagram of the precise π model of each sequence in the wide-band AC submarine cable.

[0077] Figure 7 The structure block diagram of the AC submarine cable wide-band impedance modeling system of the present invention.

[0078] Figure 8 The present invention is a schematic diagram of the structure of an electronic device implemented according to the method of the present invention. DETAILED DESCRIPTION

[0079] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0080] like Figure 1 As shown, the AC submarine cable wide-band impedance modeling method of the present invention comprises the following steps:

[0081] Step 1: Calculate the sequence impedance per unit length of the AC submarine cable in the wide frequency band.

[0082] The AC submarine cable types studied in this embodiment include three-phase single-core submarine cable with armor layer and three-core submarine cable with armor layer, and their cross-sectional views are as follows: Figure 2 and Figure 3 As shown, the wide frequency band ranges from 1 to 2500 Hz.

[0083] 1.1 Calculate the DC resistance per unit length of each conductor layer of the AC submarine cable, including the DC resistance per unit length of the core layer, the DC resistance per unit length of the sheath layer, and the DC resistance per unit length of the armor layer.

[0084] The DC resistance per unit length of each conductor layer of the AC submarine cable (unit Ω / km) is calculated as follows:

[0085]

[0086] Where: subscript x is the conductor layer symbol, x = c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer; ρ x is the resistivity of each conductor layer material, in Ω·m; r ox is the outer radius of each conductor layer, in m; r ix is the inner radius of each conductor layer, in m; α x,20 is the temperature coefficient of resistance, in °C -1 ; T0 = 20°C.

[0087] 1.2 According to the DC resistance per unit length of each conductor layer of the AC submarine cable, calculate the AC resistance per unit length of each conductor layer of the AC submarine cable, including the AC resistance per unit length of the core layer, the AC resistance per unit length of the sheath layer and the AC resistance per unit length of the armor layer.

[0088] The AC resistance per unit length of each conductor layer of the AC submarine cable (unit Ω / km) is calculated as follows:

[0089] R x,ac =R x,dc (1+k x,s +k x,p )

[0090] Where: k x,s is the skin effect coefficient, k x,p is the proximity effect coefficient.

[0091] Skin effect coefficient k x,s The calculation method is as follows:

[0092] (1) Calculate the conductor skin effect constant a x,s , when the conductor is a circular or fan-shaped conductor, ax,s =1; when the conductor is a segmented or Milliken conductor, a x,s =0.43; when the conductor is a ring conductor, a x,s =[(r ox -r ix ) / (r ox +r ix )][(r ox +2r ix ) / (r ox +r ix )] 2 .

[0093] (2) Calculate the intermediate variable s x , the formula is as follows:

[0094]

[0095] Where: f is the grid harmonic frequency, unit is Hz.

[0096] (3) Calculation of skin effect coefficient k x,s , the formula is as follows:

[0097]

[0098] Proximity effect coefficient k x,p The calculation method is as follows:

[0099] (1) For all conductor layers of the three-phase single-core submarine cable with armor layer, the proximity effect is not considered, that is, k x,p =0; For three-core submarine cables with armor layers, the proximity effect is only considered between conductor layers of the same type, that is, the core layer only takes into account the proximity effect of the adjacent core layer, and the sheath layer only takes into account the proximity effect of the adjacent sheath layer.

[0100] (2) Calculate the conductor proximity effect constant a x,p , when the conductor is circular, sector-shaped or ring-shaped, a x,p =0.8; when the conductor is a segmented conductor, a x,p =0.37.

[0101] (3) Calculate the intermediate variable p x Its function F(p x ), the formula is as follows:

[0102]

[0103] (4) Calculate the proximity effect coefficient k x,p , the formula is as follows:

[0104]

[0105] Where: S xmxn It is the interaxial distance of the same type of conductor layers in different phases, in meters. The subscripts m and n are phase symbols, m, n = 1, 2, 3, m ≠ n.

[0106] 1.3 Calculate the parameters of the seawater return path, including the equivalent conductor radius r sea , the external impedance correction term intermediate variable α, the external resistance correction term kei(α) and the external reactance correction term ker(α).

[0107] (1) Equivalent conductor radius r of the seawater return path sea (Unit: m), calculated as follows:

[0108]

[0109] Where: sea is the resistivity of seawater, in Ω·m. If not given, ρ is generally used. sea =0.5Ω·m.

[0110] (2) Taking into account the external impedance correction term of the seawater return path, the intermediate variable α is calculated as follows:

[0111]

[0112] Where: d Phase It is the average distance between submarine cables, in meters.

[0113] (3) Taking into account the external resistance correction term kei(α) of the seawater return path, calculate as follows:

[0114]

[0115] Where: kei(α) is essentially the imaginary part of the Kelvin function of α; for the three-core submarine cable with armor layer, the external resistance correction term of the seawater return path is not considered, that is, kei(α) = 0.

[0116] (4) Taking into account the external reactance correction term ker(α) of the seawater return path, calculate as follows:

[0117]

[0118] Where: ker(α) is essentially the real part of the Kelvin function of α; for the three-core submarine cable with armor layer, the external reactance correction term of the seawater return path is not considered, that is, ker(α) = 0.

[0119] 1.4 Based on the AC resistance per unit length of each conductor layer of the AC submarine cable and the parameters of the seawater return path, a full impedance matrix of the AC submarine cable series connection is constructed.

[0120] For a three-core submarine cable with an armored layer, the series impedance matrix is:

[0121]

[0122] For a three-phase single-core submarine cable with an armor layer, since the phases are far apart, the mutual impedance of the conductor layer between phases is not considered. The series impedance matrix can be simply expressed as a single-phase series impedance matrix. Taking the first phase series impedance matrix as an example, that is:

[0123]

[0124] The method for constructing the AC submarine cable series full impedance matrix comprises the following steps:

[0125] (1) Calculate the core self-impedance Z taking into account the seawater return path cmcm (Unit: Ω / km), including the internal impedance of the core layer and the external impedance of the seawater return path, calculated as follows:

[0126]

[0127] Where: μ c is the relative magnetic permeability of the core material; if r ic =0, that is, the core layer is a circular conductor, then:

[0128] F(r oc ,r ic )=1

[0129] If r ic >0, that is, the core layer is a ring conductor, then:

[0130]

[0131] (2) Calculate the sheath self-impedance Z taking into account the seawater return path smsm (Unit: Ω / km), including the internal impedance of the sheath layer and the external impedance of the seawater return path, calculated as follows:

[0132]

[0133] Where: μ s is the relative magnetic permeability of the sheath material.

[0134]

[0135] (3) Calculate the armor layer self-impedance Z taking into account the seawater return path amam (Unit: Ω / km), including the internal impedance of the armor layer and the external impedance of the seawater return path, calculated as follows:

[0136]

[0137] Where: μ a is the relative magnetic permeability of the sheath material.

[0138]

[0139] (4) Calculate the mutual impedance Z between the conductor layers taking into account the return path xmyn (Unit: Ω / km), that is, taking into account the external impedance of the seawater return path, it is calculated as follows:

[0140]

[0141] Where: subscript y is the conductor layer mark, y = c, s, a, c represents the core layer, s represents the sheath layer, a represents the armor layer, xm ≠ yn; if the conductor layer xm and the conductor layer yn do not contain each other, then d xmyn is the interaxial distance between the conductor layer xm and the conductor layer yn, in meters; if the conductor layer xm includes the conductor layer yn, then d xmyn is the average radius of the outer conductor layer xm, i.e. d xmyn =(r ox +r ix ) / 2; if the conductor layer yn includes the conductor layer xm, then d xmyn is the average radius of the outer conductor layer yn, i.e. d xmyn =(r oy +r iy ) / 2.

[0142] 1.5 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable series full impedance matrix is ​​converted into the AC submarine cable series phase impedance matrix, and the following cases are discussed:

[0143] (1) For a three-core submarine cable with armored layer where the sheath and armor are connected together and grounded at both ends, the series phase impedance matrix is ​​calculated as follows:

[0144]

[0145] (2) For a three-core submarine cable with an armor layer where the sheath and armor are connected together but grounded only at one point or not grounded at all, the series phase impedance matrix is ​​calculated as follows:

[0146] Z Phase =Z cc

[0147] (3) For a three-phase single-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the series phase impedance is calculated as follows:

[0148]

[0149] (4) For a three-phase single-core submarine cable in which the sheath and armor are connected together but grounded at only one point or not grounded at all, the series phase impedance is calculated as follows:

[0150] Z Phase =Z c1c1

[0151] 1.6 According to the type of AC submarine cable, the AC submarine cable series phase impedance matrix is ​​converted into the AC submarine cable series sequence impedance matrix through phase sequence transformation, and the following cases are discussed:

[0152] (1) For a three-core submarine cable with an armor layer, the AC submarine cable series phase impedance matrix is ​​converted into an AC submarine cable series sequence impedance matrix through phase sequence transformation, as follows:

[0153]

[0154] Where: A is the phase sequence transformation matrix, where the complex operator a = e j120° ; Z Z Z is the AC submarine cable series zero-sequence impedance; P Z is the positive sequence impedance of the AC submarine cable in series; N It is the negative sequence impedance in series with the AC submarine cable.

[0155] (2) For a three-phase single-core submarine cable with an armor layer, the series phase impedance is the series sequence impedance, and the series sequence impedances are equal, that is:

[0156] Z Z =Z P =Z N =Z Phase

[0157] Step 2: Calculate the sequence susceptance per unit length of the AC submarine cable within the wide frequency band.

[0158] 2.1 Construct an AC submarine cable parallel all-electric susceptance matrix.

[0159] For a three-core submarine cable with an armor layer, due to the shielding effect of the sheath layer, there is no capacitance between the core layers of different phases, but there is still capacitance between the sheath layers of different phases. The equivalent capacitance is as follows: Figure 4 As shown, the parallel full susceptance matrix is:

[0160]

[0161] For a three-phase single-core submarine cable with an armor layer, due to the shielding effect of the sheath layer, there is no capacitance between the conductor layers of different phases. The single-phase equivalent capacitance is as follows: Figure 5 As shown, the parallel full susceptance matrix can be simply expressed as a single-phase parallel full susceptance matrix. Taking the first phase parallel full susceptance matrix as an example, that is:

[0162]

[0163] For three-core submarine cables with armored layer:

[0164] (1) Susceptance B between the core layer and the sheath layer of the same phase line cmsm (Unit: μS / km) is calculated as follows:

[0165]

[0166] Where: ε cs It is the relative dielectric constant of the insulation layer between the core layer and the sheath layer.

[0167] (2) Susceptance B between different phase line core layers smsn (Unit: μS / km) is calculated as follows:

[0168]

[0169] Where: ε sa is the relative dielectric constant of the insulation layer between the sheath layer and the armor layer.

[0170] (3) Susceptance B between the core layer and the armor layer sma (Unit: μS / km) is calculated as follows:

[0171]

[0172] Where: d sm It is the axial distance between the m-phase sheath layer and the armor layer, in meters.

[0173] (4) Susceptance B between armor layer and seawater ag (Unit: μS / km) is calculated as follows:

[0174]

[0175] Where: ε ag is the relative dielectric constant of the outer insulation layer of the armor layer; t ps It is the thickness of the outer insulation layer of the armor layer, in m.

[0176] For three-phase single-core submarine cables with armored layer:

[0177] (5) Susceptance B between the core layer and the sheath layer of the single-phase line cmsm The susceptance B between the armor layer and the seawater amg The calculation method is the same as that of the three-core cable with armor layer.

[0178] (6) Susceptance B between single-phase sheath layer and armor layer smam (Unit: μS / km) is calculated as follows:

[0179]

[0180] 2.2 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable parallel full susceptance matrix is ​​converted into the AC submarine cable parallel phase susceptance matrix, and the following cases are discussed:

[0181] (1) For a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance matrix is ​​calculated as follows:

[0182] B Phase =B cc

[0183] (2) For a three-core submarine cable with an armor layer where the sheath and armor are connected together but grounded at only one point or not grounded at all, the parallel phase susceptance matrix is ​​calculated as follows:

[0184]

[0185] (3) For a three-phase single-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance is calculated as follows:

[0186] B Phase =B c1s1

[0187] (4) For a three-phase single-core submarine cable in which the sheath and armor are connected together but grounded at only one point or not grounded at all, the parallel phase impedance is calculated as follows:

[0188]

[0189] 2.3 According to the type of AC submarine cable, the AC submarine cable parallel phase susceptance matrix is ​​converted into the AC submarine cable parallel sequence susceptance matrix through phase sequence transformation, and the following cases are discussed:

[0190] (1) For a three-core submarine cable with an armor layer, the AC submarine cable parallel sequence susceptance matrix is ​​converted into the AC submarine cable parallel sequence susceptance matrix through phase sequence transformation, as follows:

[0191]

[0192] Where: B Z B is the parallel zero-sequence susceptance of the AC submarine cable; P B is the positive sequence susceptance of the AC submarine cable in parallel; N It is the negative sequence susceptance in parallel with the AC submarine cable.

[0193] (2) For a three-phase single-core submarine cable with an armor layer, the parallel phase susceptance is the parallel sequence susceptance, and the parallel sequence susceptances are equal, that is:

[0194] B Z=B P =B N =B Phase

[0195] Step 3: According to the sequence impedance per unit length and the sequence susceptance per unit length in the wide-frequency band of the AC submarine cable, establish an accurate π model for each sequence in the wide-frequency band of the AC submarine cable.

[0196] The accurate π model of each sequence in the wide frequency band of AC submarine cable is composed of a whole line series impedance Z s And 2 full line parallel admittance Y p Composition, such as Figure 6 shown.

[0197] The series impedance of the whole line is Z s And the whole line parallel admittance Y p Calculate as follows:

[0198]

[0199] Where: l is the length of the AC submarine cable, in km; z is the sequence impedance per unit length in the wide frequency band of the AC submarine cable. For the positive sequence accurate π model, z = Z P ; For the negative sequence exact π model, z = Z N ; For the zero-sequence accurate π model, z = Z Z ; b is the sequence susceptance per unit length in the wide frequency band of the AC submarine cable. For the positive sequence accurate π model, b = B P ; For the negative sequence exact π model, b = B N ; For the zero-sequence accurate π model, b = B Z ; K Z and K Y are the correction coefficients for series impedance and parallel admittance respectively; Z c and γ are characteristic impedance and propagation coefficient respectively, which are calculated as follows:

[0200]

[0201] The following is an example of a three-phase single-core submarine cable with an armored layer. The cable is 10 km long and laid horizontally. The distance between adjacent submarine cables is 200 m. The specific geometric parameters are shown in Table 1:

[0202] Table 1

[0203] Structure Name Outer radius / mm Resistivity / Ω·m Relative dielectric constant Core layer (round conductor) 17.1 <![CDATA[1.7241×10 -8 ]]> / Insulation layer 1 46.4 / 2.25 Sheath layer 50.3 <![CDATA[2.14×10 -7 ]]> / Insulation layer 2 62.2 / 2.25 Armor layer 68.2 <![CDATA[1.38×10 -7 ]]> / Insulation layer 3 72.2 / 2.25

[0204] The broadband impedance model of the submarine cable is established by this embodiment, the frequency band is selected as 1-8000 Hz, and the impedance model parameters of the three-phase single-core submarine cable are obtained by analysis as shown in Table 2:

[0205] Table 2

[0206]

[0207]

[0208] like Figure 7 As shown, an embodiment of the present invention further provides an AC submarine cable wide-band impedance modeling system, comprising:

[0209] Impedance calculation unit, used to calculate the sequence impedance per unit length in the wide frequency band of AC submarine cable;

[0210] Susceptance calculation unit, used to calculate the sequence susceptance per unit length in the wide frequency band of AC submarine cable;

[0211] The modeling unit establishes an accurate π model of each sequence in the wide-band AC submarine cable according to the sequence impedance per unit length and the sequence susceptance per unit length in the wide-band AC submarine cable.

[0212] Regarding the system in the above embodiment, the specific manner in which each unit performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0213] Accordingly, the present invention also provides an electronic device, including a processor and a memory, wherein the memory is used to store a computer program, and the processor is used to execute the computer program to implement the above-mentioned AC submarine cable wide-band impedance modeling method. Figure 8 The figure shows a hardware structure of any electronic device with data processing capability in which the AC submarine cable wide-band impedance modeling system provided by the embodiment of the present invention is located. Figure 8 In addition to the processor, memory and network interface shown, the electronic device with data processing capability in which the system in the embodiment is located may also include other hardware according to the actual function of the electronic device, which will not be described in detail.

[0214] Accordingly, the present invention also provides a computer-readable storage medium on which computer instructions are stored, and when the instructions are executed by a processor, the AC submarine cable wide-band impedance modeling method as described above is implemented. The computer-readable storage medium can be an internal storage unit of the aforementioned electronic device with data processing capability, such as a hard disk or memory; or it can be other external storage devices, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. The computer-readable storage medium can also include both an internal storage unit of an electronic device with data processing capability and an external storage device, which is used to store the computer program and other programs and data required by the electronic device with data processing capability, and can also be used to temporarily store data that has been output or is to be output.

[0215] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A method for modeling wide-band impedance of an AC submarine cable, characterized in that: Calculate the sequence impedance and susceptance per unit length in the wide frequency band of AC submarine cables; According to the sequence impedance per unit length and the sequence susceptance per unit length, an accurate π model of each sequence in a wide frequency band of the AC submarine cable is established.

2. The AC submarine cable broadband impedance modeling method according to claim 1, characterized in that: The calculation of the sequence impedance per unit length within the wide frequency band of the AC submarine cable comprises: 1.1 Calculate the DC resistance per unit length of each conductor layer of the AC submarine cable; 1.2 Calculate the AC resistance per unit length of each conductor layer of the AC submarine cable based on the DC resistance per unit length of each conductor layer of the AC submarine cable; 1.3 Calculate the parameters of the seawater return path; 1.4 According to the AC resistance per unit length of each conductor layer of the AC submarine cable and the parameters of the seawater return path, the AC submarine cable series full impedance matrix is ​​constructed; 1.5 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable series full impedance matrix is ​​converted into the AC submarine cable series phase impedance matrix; 1.6 According to the type of AC submarine cable, the AC submarine cable series phase impedance matrix is ​​transformed through phase sequence to obtain the AC submarine cable series sequence impedance matrix. The elements in this matrix are the unit length sequence impedance of the AC submarine cable in the wide frequency band.

3. The AC submarine cable broadband impedance modeling method according to claim 2, characterized in that: In step 1.3, the parameters of the seawater return path are calculated by the following formula; Where: r sea is the radius of the seawater equivalent conductor, α is the intermediate variable of the external impedance correction term, kei(α) is the external resistance correction term, ker(α) is the external reactance correction term, ρ sea is the resistivity of seawater, f is the harmonic frequency of the power grid, d Phase is the average distance between submarine cables.

4. The AC submarine cable broadband impedance modeling method according to claim 2, characterized in that: In step 1.4, for the three-core submarine cable with armor layer, the series impedance matrix expression is as follows: For a three-phase single-core submarine cable with an armor layer, the series impedance matrix expression is as follows: Where: Z F is the series full impedance matrix, Z xy represents the impedance matrix between the three-core submarine cable x and y, Z xx represents the impedance matrix of the three-core submarine cable x, Z xmyn represents the mutual impedance between phase m x and phase n y, Z xma =Z axm represents the mutual impedance between the armor layer of the three-core submarine cable and the m-phase x, Z xmxm represents the self-impedance of phase m x, Z aa represents the self-impedance of the armor layer of the three-core submarine cable, Z cs,ca and Z sc,ac It represents the impedance matrix composed of the mutual impedance between the core layer and the sheath layer and the mutual impedance between the core layer and the armor layer. ss,aa It represents the impedance matrix composed of the self-impedance of the sheath layer, the self-impedance of the armor layer and the mutual impedance between the sheath layer and the armor layer. x, y = c, s, a correspond to the core layer, sheath layer and armor layer of the submarine cable. m, n = 1, 2, 3 correspond to the three phases ABC. xm≠yn.

5. The AC submarine cable broadband impedance modeling method according to claim 4, characterized in that: For the core layer, its self-impedance Z cmcm The expression is as follows: Where: R c,ac is the AC resistance per unit length of the AC submarine cable core layer, r oc and r ic are the outer radius and inner radius of the core layer, μ c is the relative magnetic permeability of the core material, j is the imaginary unit, f is the harmonic frequency of the power grid, r sea is the radius of the seawater equivalent conductor, α is the intermediate variable of the external impedance correction term, kei(α) is the external resistance correction term, and ker(α) is the external reactance correction term; if r ic = 0, that is, the core layer is a circular conductor, then the function F(r oc ,r ic )=1; if r ic > 0, then the function F(r oc ,r ic ) is as follows: For the sheath layer, its self-impedance Z smsm The expression is as follows: Where: R s,ac is the AC resistance per unit length of the AC submarine cable sheath, r os and r is are the outer radius and inner radius of the sheath layer, μ s is the relative magnetic permeability of the sheath material; For the armor layer, its self-impedance Z aa and Z amam The expression is as follows: Where: R a,ac is the AC resistance per unit length of the AC submarine cable armor layer, r oa and r ia are the outer radius and inner radius of the armor layer, μ a is the relative magnetic permeability of the armor material; The mutual impedance Z xmyn and Z xma The expression is as follows: Where: d xmyn represents the distance between the axes of phase m x and phase n y, d xma It represents the axial distance between the m-phase x and the armor layer of the three-core submarine cable. If the m-phase x contains the n-phase y, then d xmyn is the average radius of the m phase x, i.e. d xmyn =(r ox +r ix ) / 2, r ox and r ix are the outer radius and inner radius of x respectively; if n-phase y or the armor layer contains m-phase x, then d xmyn is the average radius of phase n y, d xma is the average radius of the armor layer, then d xmyn =(r oy +r iy ) / 2,d xma =(r oa +r ia ) / 2, r oy and r iy are the outer and inner radius of y respectively.

6. The AC submarine cable broadband impedance modeling method according to claim 4, characterized in that: In step 1.5, for a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the series phase impedance matrix Z Phase The expression is: For a three-core submarine cable with an armor layer where the sheath and armor are connected together but grounded at only one point or not grounded at all, the series phase impedance matrix Z Phase =Z cc ; For a three-phase single-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the series phase impedance Z Phase The expression is: For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together but grounded at only one point or not grounded at all, the series phase impedance Z Phase =Z c1c1 .

7. The AC submarine cable broadband impedance modeling method according to claim 1, characterized in that: The calculation of the sequence susceptance per unit length within the wide frequency band of the AC submarine cable comprises: 2.1 Constructing an AC submarine cable parallel all-susceptance matrix; 2.2 According to the AC submarine cable connection mode and grounding arrangement mode, the AC submarine cable parallel full susceptance matrix is ​​converted into the AC submarine cable parallel phase susceptance matrix; 2.3 According to the type of AC submarine cable, the AC submarine cable parallel phase susceptance matrix is ​​transformed through phase sequence to obtain the AC submarine cable parallel sequence susceptance matrix. The elements in this matrix are the unit length sequence susceptance of the AC submarine cable within the wide frequency band.

8. The AC submarine cable broadband impedance modeling method according to claim 7, characterized in that: In step 2.1, for the three-core submarine cable with armor layer, the parallel full susceptance matrix expression is as follows: For a three-phase single-core submarine cable with an armor layer, the parallel full susceptance matrix expression is as follows: Among them: B F is a parallel full susceptance matrix, B xy represents the susceptance matrix between the three-core submarine cable x and y, B xx represents the susceptance matrix of the three-core submarine cable x, B smsn It represents the susceptance between the m-phase sheath layer and the n-phase sheath layer of the three-core submarine cable, B cmsm It represents the susceptance between the m-phase core layer and the m-phase sheath layer, B sma It represents the susceptance between the armor layer and the m-phase sheath layer of the three-core submarine cable, B smam It represents the susceptance between the m-phase armor layer and the m-phase sheath layer of the three-phase single-core submarine cable, B amg It represents the susceptance between the m-phase armor layer of the three-phase single-core submarine cable and the seawater, B ag represents the susceptance between the armor layer of the three-core submarine cable and the seawater, B cs,ca and B sc,ac It represents the susceptance matrix composed of the susceptance between the core layer and the sheath layer and the susceptance between the core layer and the armor layer. ss,aa It represents the susceptance matrix composed of the susceptance between the sheath layer and the armor layer, and between the armor layer and the seawater. x, y = c, s, a correspond to the core layer, sheath layer and armor layer of the submarine cable, and m, n = 1, 2, 3 correspond to the three phases ABC.

9. The AC submarine cable broadband impedance modeling method according to claim 8, characterized in that: The electrical susceptance B smsn , B cmsm , B sma , B smam , B amg , B ag The expression is as follows: Where: f is the harmonic frequency of the power grid, r oc is the outer radius of the core layer, r oa and r ia are the outer radius and inner radius of the armor layer, r os and r is are the outer radius and inner radius of the sheath layer, respectively, sm is the axial distance between the m-phase sheath layer and the armor layer of the three-core submarine cable, ε cs is the relative dielectric constant of the insulation layer between the core layer and the sheath layer, ε sa is the relative dielectric constant of the insulating layer between the sheath layer and the armor layer, ε ag is the relative dielectric constant of the outer insulation layer of the three-core submarine cable armor layer, ε amg is the relative dielectric constant of the outer insulation layer of the m-phase armor layer of the three-phase single-core submarine cable, d smsn It is the axial distance between the m-phase sheath layer and the n-phase sheath layer of the three-core submarine cable.

10. The AC submarine cable broadband impedance modeling method according to claim 8, characterized in that: In step 2.2, for a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together but grounded at only one point or not grounded at all, the parallel phase susceptance matrix B Phase The expression is: For a three-core submarine cable with an armor layer in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance matrix B Phase =B cc ; For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together but only grounded at one point or not grounded at all, the parallel phase susceptance B Phase The expression is: For a three-phase single-core submarine cable with an armor layer, in which the sheath layer and the armor layer are connected together and grounded at both ends, the parallel phase susceptance B Phase =B c1s1 .

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