Calculation method and system for space charge distribution of high voltage DC extruded insulation cable

Abstract

The invention relates to a method and system for calculating the spatial charge distribution of a high-voltage direct current extruded insulated cable, and belongs to the field of electrical engineering technology. A non-homogeneous structural geometric model of an insulating layer of a high-voltage direct current extruded insulated cable is first constructed, and then a charge transport model of the insulating layer is constructed. Parameters of the charge transport model are respectively set based on the characteristics of a crystalline region and an amorphous region of the insulating layer to obtain a first charge transport model of the crystalline region and a second charge transport model of the amorphous region. Finally, the non-homogeneous structural geometric model, the first charge transport model and the second charge transport model are introduced into simulation software for simulation calculation to obtain a spatial charge distribution result of the insulating layer, so that the spatial charge distribution calculation is performed on the basis of considering the internal non-homogeneous structure of the insulating layer, and a more comprehensive and accurate spatial charge distribution result can be obtained.

Description

Technical Field

[0001] The invention relates to the field of electrical engineering technology, and in particular to a method and system for calculating space charge distribution of a high-voltage direct current extruded insulated cable. Background Art

[0002] As the global climate continues to warm, carbon dioxide emissions reduction has become an important environmental issue that countries around the world have to face. In order to coordinate the relationship between energy environment and economic development, it is imperative to significantly increase the proportion of electric energy in terminal energy consumption.

[0003] As a key power equipment for power transmission, high-voltage cables can be used in extremely cold areas, high terrain, oceans and rivers where it is inconvenient to set up traditional transmission lines. They can also greatly save urban land resources and effectively overcome the inherent drawbacks of traditional overhead lines. The polymer insulation material used in high-voltage DC extruded insulated cables has excellent dielectric properties, so it has been widely used and promoted. However, under the action of the DC electric field, space charge injection and dissociation will occur inside the insulation layer of the extruded insulated cable. This part of the space charge accumulated inside the insulating material will cause local electric field distortion inside the material, causing insulation degradation problems, shortening the normal operating life of the cable, and even causing insulation breakdown in severe cases, affecting the safety and stability of the power grid. Studying the behavioral characteristics of space charge inside the insulating material under the action of an external DC electric field can provide a specific analysis of the above problems and provide corresponding solutions, thereby ensuring the safe and stable transmission of electric energy.

[0004] However, existing studies on the behavior characteristics of space charge inside insulating materials are all based on the analysis and discussion of the behavior of charge inside the insulating materials, which is based on the assumption that the insulating materials are homogeneous materials. Under this approach, the transport behavior of charge in different structures inside the materials is exactly the same. However, the polyolefin insulating material used in extruded insulated cables is itself a semi-crystalline inhomogeneous material. The internal structure of the material is composed of crystalline and amorphous regions. Moreover, due to the obvious differences in the dielectric properties of the two structures of the crystalline and amorphous regions and their interfaces, the transport behavior of charge inside different structures is not the same. Therefore, the calculation results of the space charge distribution of the existing model may be quite different from the actual space charge distribution inside the insulating layer. It is necessary to calculate the distribution of space charge based on the consideration of the inhomogeneous structure inside the insulating layer to obtain a more comprehensive and accurate space charge distribution result.

[0005] Based on this, a new calculation scheme for the spatial charge distribution considering the heterogeneous structure of high-voltage DC extruded insulated cables is urgently needed. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for calculating the spatial charge distribution of a high-voltage DC extruded insulated cable, which can calculate the spatial charge distribution inside the cable insulation layer, thereby providing theoretical guidance and model support for the analysis of the research on the spatial charge characteristics of the high-voltage DC extruded insulated cable.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for calculating the spatial charge distribution of a high-voltage direct current extruded insulated cable, the method comprising:

[0009] Construct the non-homogeneous structural geometric model of the insulation layer of high-voltage DC extruded insulation cable;

[0010] Constructing a charge transport model for the insulating layer, and setting parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model for the crystalline region, and setting parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model for the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression characterizing the injection and extraction processes of electronic charges, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression characterizing the dissociation process of ionic charges, and a transport characteristic mechanism characterizing electronic charges and ionic charges;

[0011] The inhomogeneous structure geometric model, the first charge transport model and the second charge transport model are introduced into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer.

[0012] A calculation system for space charge distribution of a high-voltage direct current extruded insulated cable, the calculation system comprising:

[0013] A geometric model building module is used to build a non-homogeneous structural geometric model of the insulation layer of a high-voltage DC extruded insulated cable;

[0014] A charge transport model construction module, used to construct a charge transport model of the insulating layer, and set the parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model of the crystalline region, and set the parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model of the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression characterizing the injection and extraction process of electronic charge, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression characterizing the dissociation process of ionic charge, and a transport characteristic mechanism characterizing electronic charge and ionic charge;

[0015] The simulation calculation module is used to import the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer.

[0016] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0017] The present invention is used to provide a method and system for calculating the spatial charge distribution of a high-voltage DC extruded insulated cable. First, a non-homogeneous structural geometric model of the insulating layer of the high-voltage DC extruded insulated cable is constructed, and then a charge transport model of the insulating layer is constructed. The parameters of the charge transport model are set based on the characteristics of the crystalline region and the amorphous region of the insulating layer, respectively, to obtain a first charge transport model of the crystalline region and a second charge transport model of the amorphous region. Finally, the non-homogeneous structural geometric model, the first charge transport model and the second charge transport model are imported into the simulation software for simulation calculation to understand the distribution of charges at different structures and obtain the actual spatial charge distribution inside the insulating layer with a non-homogeneous structure. This method of calculating the spatial charge distribution based on the consideration of the non-homogeneous structure inside the insulating layer can obtain a more comprehensive and accurate spatial charge distribution result. Among them, the construction of the non-homogeneous structural geometric model visualizes the non-homogeneous structure of the polyolefin insulating material, the construction of the charge transport model stipulates the behavior process of the spatial charge inside the insulating material, and the simulation method calculates the charge distribution law inside the high-voltage cable insulation layer. The calculation method provides theoretical guidance and model support for the study of the spatial charge characteristics of the high-voltage DC extruded insulated cable. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0019] Figure 1 A flow chart of the calculation method provided in Example 1 of the present invention;

[0020] Figure 2 This is a principle block diagram of the calculation method provided in Example 1 of the present invention;

[0021] Figure 3 A schematic diagram of a three-phase model of the internal structure of an insulating material provided in Example 1 of the present invention;

[0022] Figure 4 This is a principle block diagram of the process of constructing a geometric model of a heterogeneous structure provided in Example 1 of the present invention;

[0023] Figure 5 A schematic diagram of the structure of a cable provided in Example 1 of the present invention;

[0024] Figure 6 A schematic diagram of a geometric model of a heterogeneous structure provided in Example 1 of the present invention;

[0025] Figure 7 A schematic diagram of the transport behavior of space charges inside the insulating material provided in Example 1 of the present invention;

[0026] Figure 8 A principle block diagram of the simulation calculation process provided by Embodiment 1 of the present invention;

[0027] Fig. 9 This is a system block diagram of the computing system provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] The purpose of the present invention is to provide a method and system for calculating the spatial charge distribution of a high-voltage DC extruded insulated cable taking into account the heterogeneous structure of a polyolefin insulating material of the extruded insulated cable, which belongs to the technical field of the intersection of electrical engineering, polymer materials and physics. The method and system can calculate the spatial charge distribution inside the cable insulation layer, thereby providing theoretical guidance and model support for the analysis of the research on the spatial charge characteristics of the high-voltage DC extruded insulated cable, and solving the problem of inaccuracy and incompleteness of the existing calculation methods.

[0030] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] Embodiment 1:

[0032] Since the current simulation methods for the space charge characteristics of high-voltage DC extruded insulated cables all treat the insulation layer as a homogeneous structure for simulation calculation, while the insulation layer of extruded insulated cables is a non-homogeneous structure, the accuracy and effectiveness of the existing simulation methods need to be studied, and they cannot accurately evaluate the space charge behavior inside the cable insulation material. Therefore, there is an urgent need for a simulation calculation method for the space charge characteristics of high-voltage DC extruded insulated cables that can be practically applied, has comprehensive calculations and has a certain degree of reliability.

[0033] Based on this, this embodiment is used to provide a method for calculating the spatial charge distribution of a high-voltage DC extruded insulated cable, which can calculate the spatial charge distribution inside the cable insulation layer, provide theoretical guidance and model support for the study of the spatial charge characteristics of high-voltage DC extruded insulated cables, and ensure the stable operation of power equipment. Figure 1 and Figure 2 As shown, the calculation method includes:

[0034] S1: Construct the inhomogeneous structural geometric model of the insulation layer of high-voltage DC extruded insulated cable;

[0035] Specifically, this embodiment is based on the heterogeneous structure of the insulation layer of the actual high-voltage DC extruded insulated cable, and constructs a heterogeneous structural geometric model with a similar structure. Considering that the insulation layer is not a homogeneous material, but a heterogeneous structure with a crystalline region, an amorphous region and an interface between the two phases, its three-phase model is as follows: Figure 3 Based on this, this embodiment constructs a non-homogeneous structural geometric model of insulating materials with similar structures based on the Voronoi network model, such as Figure 4 As shown in Figure 2, the construction process of the inhomogeneous structure geometric model includes:

[0036] (1) Prepare samples of the insulation layer of high-voltage DC extruded insulated cables.

[0037] like Figure 5 As shown, it is a schematic diagram of the cable structure. In this embodiment, a part of the insulation layer of the high-voltage DC extruded insulated cable can be arbitrarily cut off as a sample as needed.

[0038] (2) Testing the sample to determine the size of the sample, the number of spherulites in the sample, and the volume ratio of the crystalline region to the amorphous region in the sample. The size includes length and width.

[0039] In this embodiment, a polarizing microscope may be used to detect the sample, and the width may be understood as the thickness of the insulating layer.

[0040] (3) Draw the boundary of the heterogeneous structure geometric model according to the size, randomly set multiple Voronoi seed points within the boundary, and generate a Voronoi diagram; fill the crystalline region and the amorphous region in each Voronoi polygon in the Voronoi diagram according to the volume ratio to obtain the heterogeneous structure geometric model, the number of Voronoi seed points is the same as the number of spherulites, and the amorphous region filled in the Voronoi polygon is set around the crystalline region filled in the Voronoi polygon.

[0041] like Figure 6As shown, the length of the dimension is equal to the length of the two-dimensional boundary of the non-homogeneous structural geometric model, and the width of the dimension is equal to the width of the two-dimensional boundary of the non-homogeneous structural geometric model, so as to draw the two-dimensional boundary of the non-homogeneous structural geometric model, and the shape of the two-dimensional boundary is generally a rectangle. Within the two-dimensional boundary range, the same number of Voronoi seed points are set according to the number of spherulites, and the perpendicular bisectors of the connecting lines of adjacent seed points intersect to form a Voronoi diagram including multiple Voronoi polygons. The process of generating the Voronoi diagram from the Voronoi seed points can adopt the existing technology, which will not be repeated here. According to the crystallization characteristics of the insulating layer itself, the area proportion of the two in the Voronoi diagram is set in proportion with reference to the volume ratio of the crystalline region and the amorphous region in the insulating layer. Specifically, the crystalline region and the amorphous region are filled in proportion in each Voronoi polygon according to the volume ratio, and the amorphous region is arranged around the crystalline region to obtain the non-homogeneous structural geometric model of the insulating layer. Figure 6 In the figure, the black lines are Voronoi polygons, the gray parts are crystalline areas, and the white parts are amorphous areas.

[0042] Traditional research models for the internal electric field distribution characteristics of cable insulation materials regard them as homogeneous structures, ignoring the differences between crystalline and amorphous regions. The inhomogeneous structural geometric model of the insulation material described in this embodiment provides an analytical approach and specific method for the electric field distribution of the microstructure of the insulation material.

[0043] S2: constructing a charge transport model for the insulating layer, and setting parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model for the crystalline region, and setting parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model for the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression for characterizing the injection and extraction processes of electronic charges, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression for characterizing the dissociation process of ionic charges, and a transport characteristic mechanism for characterizing electronic charges and ionic charges;

[0044] After constructing the charge transport model of the cable insulation layer in this embodiment, when an external DC electric field acts on the cable insulation layer, considering that the energy band parameters and dielectric properties of the crystalline region, amorphous region and interface inside the insulation layer are not completely the same, the relevant parameters of the space charge transport process in the above-mentioned different structures are also different and need to be defined separately. Therefore, in this embodiment, according to the difference in dielectric properties at different structures in the insulation layer, the parameters of the charge transport model of the crystalline region and the amorphous region are set respectively, so that the first charge transport model of the crystalline region and the second charge transport model of the amorphous region can be obtained. That is, in this embodiment, the first charge transport model of the crystalline region and the second charge transport model of the amorphous region have only different values ​​of some parameters.

[0045] like Figure 7 As shown, when considering the spatial charge behavior inside the insulating layer, this embodiment simultaneously considers the injection and extraction process of the electron charge, the dissociation process of the ion charge, and the charge transport process. The electron charge injection and extraction process includes the Schottky injection current density expression of the injection process and the extraction current density expression of the extraction process. The ion charge dissociation process includes the impurity molecule dissociation rate expression and the impurity molecule concentration change expression. The charge transport process includes the transport characteristic mechanism of the electron charge and the ion charge. In the formula definition of the spatial charge behavior, both the crystalline region and the amorphous region can be expressed by the same formula, but due to the differences in their structures, the selection of some related parameters in the formula is not the same. Therefore, after defining the relevant formulas, the relevant parameters of the crystalline region and the amorphous region are set respectively, and the parameters of the crystalline region are set as follows: x' , the parameters of the amorphous region are set as x'' .

[0046] Specifically, the expressions are as follows:

[0047] The Schottky injection current density expression of the first charge transport model, that is, the Schottky injection current density expression of the crystal region is as follows:

[0048]

[0049] in, is the hole injection current density of the crystal region, in A / m 2 ; r represents the radius, r 0 is the inner radius of the insulation layer; t is the time, in seconds; A is the Richardson constant; T ( r 0 , t )for t Time along the radius r 0 The temperature at different positions in the direction, in K; is the hole injection barrier in the crystal region, in eV; k is the Boltzmann constant, also known as the Boltzmann constant; e is the basic charge; E ( r 0 , t )for t Time along the radius r 0 The local electric field at different positions in the direction is expressed in V / m; is the dielectric constant of the insulation layer of the high voltage DC cable; is the electron injection current density of the crystal region, in A / m 2 ; r d is the outer radius of the insulation layer; T ( r d , t )for t Time along the radius r d The temperature at different positions in the direction, in K; is the electron injection barrier in the crystal region, in eV; E ( r d , t )for t Time along the radius r d The local electric field at different positions in the direction is expressed in V / m.

[0050] The expression of the Schottky injection current density of the second charge transport model, that is, the expression of the Schottky injection current density of the amorphous region, is as follows:

[0051]

[0052] in, is the hole injection current density of the amorphous region, in A / m 2 ; is the hole injection barrier in the amorphous region, in eV; is the electron injection current density of the amorphous region, in A / m 2 ; is the electron injection barrier of the amorphous region, in eV.

[0053] During the injection of electronic charges, the molecular chains in the crystalline region are arranged relatively regularly and tightly relative to the amorphous region, making charge injection more difficult. However, the molecular chains in the amorphous region are arranged relatively disordered and sparsely, and the free volume accounts for a high proportion, making charge injection more likely to occur. Therefore, in this embodiment, the injection barrier in the crystalline region at the interface between the two electrodes is set to be higher than the injection barrier in the amorphous region.

[0054] The extraction current density expression of the first charge transport model, that is, the equation satisfied by the electron charge extraction process in the crystal region is as follows:

[0055]

[0056] in, is the hole extraction current density of the crystal region, in A / m 2 ;r d is the outer radius of the insulation layer; t For time; is the extraction coefficient of holes in the crystal region; is the mobility of holes in the crystal region, in m 2 / (V·s); n hμ ( r d , t ) is the density of holes outside the insulating layer, in C / m 3 ; E ( r d , t )for t Time along the radius r d The local electric field at different positions in the direction; is the electron extraction current density of the crystal region, in A / m 2 ; r 0 is the inner radius of the insulation layer; is the electron extraction coefficient of the crystal region; is the electron mobility in the crystal region, in m 2 / (V·s); n eμ ( r 0 , t ) is the density of electrons inside the insulating layer, in C / m 3 ; E ( r 0 , t )for t Time along the radius r 0 The local electric field at different locations in the direction.

[0057] The extraction current density expression of the second charge transport model, that is, the equation satisfied by the electron charge extraction process in the amorphous region, is as follows:

[0058]

[0059] in, is the hole extraction current density of the amorphous region, in A / m 2 ; is the extraction coefficient of holes in the amorphous region; is the mobility of holes in the amorphous region, in m 2 / (V·s); is the electron extraction current density of the amorphous region, in A / m 2 ; is the electron extraction coefficient of the amorphous region; is the electron mobility in the amorphous region, in m 2 / (V·s).

[0060] Similar to the injection process, the molecular chain structure with a higher density in the crystalline region limits the migration of charges, so it is more difficult to extract charges from the interior than from the amorphous region. Therefore, in this embodiment, the extraction coefficient of the crystalline region is set to be lower than that of the amorphous region.

[0061] The expression of the impurity molecule dissociation rate of the first charge transport model, that is, the formula satisfied by the dissociation rate of impurity molecules in the crystal region is as follows:

[0062]

[0063] in, is the dissociation rate of impurity molecules in the crystal region; v To try to escape the frequency; It is the dissociation barrier height when the impurity molecules in the crystal region dissociate into positive ions and negative ions; k is the Boltzmann constant; T is temperature; e is the basic charge; E is the local electric field; is the dielectric constant of the insulation layer of the high voltage DC cable.

[0064] The expression of the impurity molecule dissociation rate of the second charge transport model, that is, the dissociation rate of the impurity molecules in the amorphous region satisfies the following formula:

[0065] ;

[0066] in, is the dissociation rate of impurity molecules in the amorphous region; It is the dissociation barrier height when the impurity molecules in the amorphous region dissociate into positive ions and negative ions.

[0067] The expression of the impurity molecule concentration change in the first charge transport model, that is, the formula satisfied by the impurity molecule concentration change in the crystal region is as follows:

[0068] ;

[0069] in, is the change in the concentration of impurity molecules in the crystal region; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; n ptis the density of trapped positive ions; n nμ is the density of free negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n pμ is the density of free positive ions; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; n nt is the density of trapped negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; is the dissociation rate of impurity molecules in the crystal region; is the concentration of impurity molecules in the crystal region.

[0070] The expression of the impurity molecule concentration change in the second charge transport model, that is, the formula satisfied by the impurity molecule concentration change in the amorphous region is as follows:

[0071]

[0072] in, is the concentration change of impurity molecules in the amorphous region; is the dissociation rate of impurity molecules in the amorphous region; is the concentration of impurity molecules in the amorphous region.

[0073] There is no significant difference in the dissociation rate between the crystalline region and the amorphous region, but there is a significant difference in the concentration of impurity molecules inside them. The amorphous region is concentrated with impurity molecules such as crosslinking byproducts and antioxidants, and the concentration is significantly higher than that of the crystalline region. Therefore, in this embodiment, the impurity concentration of the crystalline region is set lower than that of the amorphous region.

[0074] The charge mobility expressions of the transport characteristic mechanism, that is, the expressions of charge mobility in the crystalline and amorphous regions inside the insulating layer, are as follows:

[0075]

[0076] Among them, the subscript a represents the type of charge, For the a The mobility of the charges, including free holes h , trapped holes ht , free electrons eμ , Trapped Electrons et , free negative ions nμ , trapped negative ions nt , free positive ions pμ and trapped cations pt ,n , p They represent negative ions and positive ions respectively; δ a is the average jump distance of negative and positive ions; v To try to escape the frequency; E ( r , t )for t Time along the radius r The local electric field at different positions in the direction; r is the insulation layer radius; t For time; ΔU ta It is the migration barrier for negative and positive ions; k is the Boltzmann constant; T is temperature; ΔU na is the change in the migration barrier of negative ions and positive ions under the action of the electric field.

[0077] Changes in the migration potential barriers of negative and positive ions under the action of an electric field ΔU na It can be obtained by the following formula:

[0078]

[0079] in, q is the unit charge of the ion.

[0080] In the transport characteristic mechanism of homopolar space charge carriers, the expression equation of the current density of homopolar space charge carriers, that is, the charge transport process can also be described by the conduction equation, Poisson's equation and current continuity equation:

[0081]

[0082]

[0083]

[0084] Among them, the subscript a represents the charge type, i.e. a for h and ht represents free holes and trapped holes, a for eμ and et represents free electrons and trapped electrons, a for nμ and nt When represents free anions and trapped anions, a for pμ and ptrepresents free positive ions and trapped positive ions. j a ( r , t ) is the charge type a hour, t Time along the radius r The current density at different positions in the direction; Space charge a Mobility within the insulating layer; n a ( r , t ) is the charge type a hour, t Time along the radius r The charge density at different positions in the direction; E ( r , t )for t Time along the radius r The electric field strength at different positions in the direction; D f is the diffusion coefficient; ▽ is the differential operator; ρ 1 ( r , t )for t Time along the radius r The space charge density of the same polarity injected in the direction, ρ 1 = n ht +n hμ -n et -n eμ , n ht is the density of trapped holes, n hμ is the density of free holes, n et is the density of trapped electrons, n eμ is the density of free electrons; ρ 2 ( r , t )for t Time along the radius r The heteropolar space charge density generated by the dissociation of impurities in the direction, ρ 2 = n pt +n pμ-n nt -n nμ , n pt is the density of trapped positive ions, n pμ is the density of free positive ions, n nt is the density of trapped negative ions, n nμ is the density of free negative ions; is the dielectric constant of the insulation layer of the high voltage DC cable; s a ( r , t ) represents the source term, representing t Time along the radius r The source term describes the local change of the charge density in the direction. The source term describes the transport behavior of eight types of space charges in the medium. The source term is expressed as:

[0085] ;

[0086] in, S eμ is the source term representing the local variation of the free electron density; S hteμ is the recombination coefficient of trapped holes and free electrons; n ht is the density of trapped holes; n eμ is the density of free electrons; S hμeμ is the recombination coefficient of free holes and free electrons; n hμ is the density of free holes; B e is the electron trap coefficient; n et is the density of trapped electrons; n oet is the electron trap density; D e is the electron desorption coefficient.

[0087] ;

[0088] in, S pt is the source term representing the local variation of the trapped positive ion density; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; npt is the density of trapped positive ions; n nμ is the density of free negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; n nt is the density of trapped negative ions; B p is the trapping coefficient of the positive ion; n pμ is the density of free positive ions; n opt is the trap density of positive ions; D p is the desorption coefficient of the positive ion.

[0089] ;

[0090] in, S pμ is the source term representing the local variation of the free positive ion density; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; n pμ is the density of free positive ions; n nt is the density of trapped negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n nμ is the density of free negative ions; B p is the trapping coefficient of the positive ion; n pt is the density of trapped positive ions; n opt is the trap density of positive ions; D p is the trapping coefficient of the positive ion; D e is the electron trap coefficient; N 0 is the concentration of impurity molecules.

[0091] ;

[0092] in, S nt is the source term representing the local variation of the trapped anion density; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; npμ is the density of free positive ions; n nt is the density of trapped negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; n pt is the density of trapped positive ions; B n is the trapping coefficient of negative ions; n nμ is the density of free negative ions; n ont is the trap density of negative ions; D n is the trapping coefficient of negative ions.

[0093] ;

[0094] in, S nμ is the source term representing the local variation of the free anion density; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; n pt is the density of trapped positive ions; n nμ is the density of free negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n pμ is the density of free positive ions; B n is the trapping coefficient of negative ions; n nt is the density of trapped negative ions; n ont is the trap density of negative ions; D n is the trapping coefficient of negative ions; D d is the dissociation rate of impurity molecules; N 0 is the concentration of impurity molecules.

[0095] ;

[0096] in, S ht is the source term representing the local variation of the trapped hole density; S hteμ is the recombination coefficient of trapped holes and free electrons; nht is the density of trapped holes; n eμ is the density of free electrons; S htet is the recombination coefficient of trapped holes and trapped electrons; n et is the density of trapped electrons; B h is the cavity trap coefficient; n hμ is the density of free holes; n oht is the hole trap density; D h is the hole trapping coefficient.

[0097] ;

[0098] in, S hμ is the source term representing the local variation of the free hole density; S hμet is the recombination coefficient of free holes and trapped electrons; n hμ is the density of free holes; n et is the density of trapped electrons; S hμeμ is the recombination coefficient of free holes and free electrons; n eμ is the density of free electrons; B h is the cavity trap coefficient; n ht is the density of trapped holes; n oht is the hole trap density; D h is the hole trapping coefficient.

[0099] ;

[0100] in, S et is the source term representing the local variation of the trapped electron density; S hμet is the recombination coefficient of free holes and trapped electrons; n hμ is the density of free holes; n et is the density of trapped electrons; S htetis the recombination coefficient of trapped holes and trapped electrons; n ht is the density of trapped holes; B e is the electron trap coefficient; n eμ is the density of free electrons; n oet is the electron trap density; D e is the electron desorption coefficient.

[0101] In the expressions of the above 8 source terms, B a is the sinking coefficient, n oat is the trap density, D a is the escape coefficient related to the trap depth, and the specific expression is:

[0102] ;

[0103] in, is the depth of the charge trap.

[0104] S hteμ is the recombination coefficient of trapped holes and free electrons, and its specific expression is:

[0105]

[0106] in, express t Time along the radius r The mobility of free electrons in one direction.

[0107] S hμet is the recombination coefficient of free holes and trapped electrons, expressed as:

[0108]

[0109] in, express t Time along the radius r The mobility of free holes in the direction.

[0110] S htet is the recombination coefficient of trapped holes and trapped electrons, and its specific value is:

[0111]

[0112] S hμeμis the recombination coefficient of free holes and free electrons, and its specific expression is:

[0113]

[0114] S ptnμ is the recombination coefficient of trapped positive ions and free negative ions, and its specific expression is:

[0115]

[0116] in, express t Time along the radius r The mobility of free anions in the direction.

[0117] S pμnt is the recombination coefficient of free positive ions and trapped negative ions, and the specific expression is:

[0118]

[0119] in, express t Time along the radius r The mobility of free positive ions in one direction.

[0120] S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions, and its specific value is:

[0121]

[0122] S pμnμ is the recombination coefficient of free positive ions and free negative ions, and the specific expression is:

[0123]

[0124] In terms of mobility, in general, the molecular chain structure in the crystalline region is closely arranged, and the charge is not easily transferred in the crystalline region, while the molecular chain arrangement in the amorphous region is loose and disordered, which is conducive to the transfer of charge. h , ht , e μ , et , nμ , nt , pμ and pt The mobility of various carriers in the crystalline region is lower than that in the amorphous region.

[0125] As far as the trap characteristics are concerned, due to the complex microstructure of insulating materials, various physical and chemical defects are inevitably present, and these defects will form trap centers in the energy level structure of the material. The type of traps that are more distributed in the crystalline region are chemical defects. This type of trap is caused by the disorder of the chemical structure of the material itself, and is concentrated in the crystalline region and at the interface between the crystalline region and the amorphous region. These defects have higher energy levels. The type of traps that are more distributed in the amorphous region are physical defects. This type of defect is formed by the disorder of the topological structure caused by the irregular arrangement of molecular chains inside the structure, and has a lower energy level. Therefore, this embodiment sets the trap depth of the crystalline region to be higher than the trap depth of the amorphous region.

[0126] In this embodiment, the injection barrier in the first charge transport model is higher than the injection barrier in the second charge transport model, the extraction coefficient in the first charge transport model is lower than the extraction coefficient in the second charge transport model, the impurity molecule concentration in the first charge transport model is lower than the impurity molecule concentration in the second charge transport model, the charge mobility in the first charge transport model is lower than the charge mobility in the second charge transport model, and the trap depth in the first charge transport model is higher than the trap depth in the second charge transport model. The specific parameter settings of the charge transport model parameters of the crystalline region and the amorphous region are shown in Table 1 below:

[0127] Table 1

[0128]

[0129] S3: Importing the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer.

[0130] In this embodiment, the non-homogeneous structural geometric model and charge transport model of the insulating layer are imported into COMSOL multi-physics simulation software for simulation calculation, and the distribution result of the space charge inside the insulating layer of the high-voltage DC extruded insulated cable can be obtained. The space charge distribution result is a graph that can reflect the size of the space charge at each position inside the insulating layer.

[0131] like Figure 8 As shown, S3 can include: import Figure 5 The structure and Figure 6 The non-homogeneous structural geometric model shown in the figure is used to obtain a cable with a non-homogeneous structural geometric model for the insulation layer, and the first charge transport model and the second charge transport model are introduced; boundary conditions are set, and the insulation layer of the cable with a non-homogeneous structural geometric model for the insulation layer is meshed; simulation calculations are performed to obtain the spatial charge distribution results inside the insulation layer of the cable under a DC field. The meshing process can be automatically completed by multi-physics field simulation software.

[0132] Among them, the boundary conditions include electric potential and temperature. Setting the boundary conditions may include: setting the inner side of the insulation layer of the cable whose insulation layer adopts a non-homogeneous structural geometric model to a high voltage and the outer side to ground, setting the temperature of the insulation layer of the cable whose insulation layer adopts a non-homogeneous structural geometric model to the same value, that is, setting the temperature of each part of the cable whose insulation layer adopts a non-homogeneous structural geometric model to a uniform value.

[0133] Based on the heterogeneous structure of the high-voltage DC cable insulation material, this embodiment constructs a heterogeneous structural geometric model with a similar structure, constructs charge transport models of the crystalline region and the amorphous region of the cable insulation material, and sets the charge transport model parameters of the crystalline region and the amorphous region respectively according to the difference in dielectric properties at different structures in the insulation material. The heterogeneous structural geometric model and the charge transport model are imported into the multi-physics field simulation software for simulation calculation to obtain the distribution result of the internal space charge of the high-voltage DC extruded insulation cable. The construction of the heterogeneous structural geometric model visualizes the heterogeneous structure of the polyolefin insulation material, and the construction of the charge transport model specifies the behavior process of the internal space charge of the insulation material. The simulation method calculates the charge distribution law inside the high-voltage cable insulation layer. This method provides theoretical guidance and model support for the study of the space charge characteristics of the high-voltage DC extruded insulation cable.

[0134] Embodiment 2:

[0135] This embodiment is used to provide a system for calculating the spatial charge distribution of a high-voltage DC extruded insulated cable. Fig. 9 As shown, the computing system includes:

[0136] A geometric model building module M1 is used to build a non-homogeneous structural geometric model of the insulation layer of a high-voltage DC extruded insulated cable;

[0137] A charge transport model construction module M2 is used to construct a charge transport model of the insulating layer, and to set parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model of the crystalline region, and to set parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model of the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression characterizing the injection and extraction processes of electronic charges, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression characterizing the dissociation process of ionic charges, and a transport characteristic mechanism characterizing electronic charges and ionic charges;

[0138] The simulation calculation module M3 is used to import the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer.

[0139] Each embodiment in this specification focuses on the differences from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0140] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for calculating the spatial charge distribution of high-voltage DC extruded insulated cables. It is characterized in that The calculation method includes: Construct the non-homogeneous structural geometric model of the insulation layer of high-voltage DC extruded insulation cable; Constructing a charge transport model for the insulating layer, and setting parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model for the crystalline region, and setting parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model for the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression characterizing the injection and extraction processes of electronic charges, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression characterizing the dissociation process of ionic charges, and a transport characteristic mechanism characterizing electronic charges and ionic charges; Importing the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer; The construction of the non-homogeneous structural geometric model of the insulation layer of the high-voltage DC extruded insulated cable specifically includes: Make samples of insulation layer of high voltage DC extruded insulated cable; Testing the sample to determine the size of the sample, the number of spherulites in the sample, and the volume ratio of the crystalline region to the amorphous region in the sample; the size includes length and width; The boundary of the non-homogeneous structure geometric model is drawn according to the size, and a plurality of Voronoi seed points are randomly set within the boundary to generate a Voronoi diagram; the crystalline region and the amorphous region are filled in each Voronoi polygon in the Voronoi diagram according to the volume ratio to obtain the non-homogeneous structure geometric model; the number of the Voronoi seed points is the same as the number of the spherulites; the amorphous region filled in the Voronoi polygon is arranged around the crystalline region filled in the Voronoi polygon.

2. The calculation method according to claim 1, It is characterized in that The injection barrier in the first charge transport model is higher than the injection barrier in the second charge transport model; the extraction coefficient in the first charge transport model is lower than the extraction coefficient in the second charge transport model; the concentration of impurity molecules in the first charge transport model is lower than the concentration of impurity molecules in the second charge transport model; the charge mobility in the first charge transport model is lower than the charge mobility in the second charge transport model; the trap depth in the first charge transport model is higher than the trap depth in the second charge transport model.

3. The calculation method according to claim 1, It is characterized in that The extraction current density expression of the first charge transport model is as follows: in, is the hole extraction current density of the crystal region; r d is the outer radius of the insulation layer; t For time; is the extraction coefficient of holes in the crystal region; is the mobility of holes in the crystal region; n hμ ( r d , t ) is the density of holes outside the insulating layer; E ( r d , t ) is the local electric field; is the electron extraction current density of the crystal region; r 0 is the inner radius of the insulation layer; is the electron extraction coefficient of the crystal region; is the electron mobility in the crystal region; n eμ ( r 0 , t ) is the electron density inside the insulating layer; E ( r 0 , t ) is the local electric field; The extraction current density expression of the second charge transport model is as follows: in, is the extraction current density of holes in the amorphous region; is the extraction coefficient of holes in the amorphous region; is the mobility of holes in the amorphous region; is the electron extraction current density of the amorphous region; is the electron extraction coefficient of the amorphous region; is the electron mobility in the amorphous region.

4. The calculation method according to claim 1, It is characterized in that The expression for the change of impurity molecule concentration in the first charge transport model is as follows: ； in, is the change in the concentration of impurity molecules in the crystal region; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; n pt is the density of trapped positive ions; n nμ is the density of free negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n pμ is the density of free positive ions; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; n nt is the density of trapped negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; is the dissociation rate of impurity molecules in the crystal region; is the concentration of impurity molecules in the crystal region; The expression for the change of impurity molecule concentration in the second charge transport model is as follows: in, is the concentration change of impurity molecules in the amorphous region; is the dissociation rate of impurity molecules in the amorphous region; is the concentration of impurity molecules in the amorphous region.

5. The calculation method according to claim 1, It is characterized in that The charge mobility expression for the transport property mechanism is as follows: in, For the a The mobility of the charges includes free holes, trapped holes, free electrons, trapped electrons, free negative ions, trapped negative ions, free positive ions and trapped positive ions; δ a is the average jump distance of negative and positive ions; v To try to escape the frequency; E ( r , t ) is the local electric field; r is the insulation layer radius; t For time; ΔU ta It is the migration barrier for negative and positive ions; k is the Boltzmann constant; T is temperature; ΔU na is the change in the migration barrier of negative ions and positive ions under the action of the electric field.

6. The calculation method according to claim 5, It is characterized in that The transport characteristic mechanism also includes: Among them, the subscript a represents the charge type, i.e. a for h and ht represents free holes and trapped holes, a for eμ and et represents free electrons and trapped electrons, a for nμ and nt When represents free anions and trapped anions, a for pμ and pt When represents free positive ions and trapped positive ions; j a ( r , t ) is the charge type a hour, t Time along the radius r The current density at different positions in the direction; Space charge a Mobility within the insulating layer; n a ( r , t ) is the charge type a hour, t Time along the radius r The charge density at different positions in the direction; E ( r , t )for t Time along the radius r The electric field strength at different positions in the direction; D f is the diffusion coefficient; ▽ is the differential operator; ρ 1 ( r , t )for t Time along the radius r The space charge density of the same polarity injected in the direction; ρ 2 ( r , t )for t Time along the radius r The heteropolar space charge density generated by the dissociation of impurities in the direction; is the dielectric constant of the insulation layer of the high voltage DC cable; s a ( r , t ) represents the source term, representing t Time along the radius r The local change of the charge density in the direction, the source term is expressed as: ； in, S eμ is the source term representing the local variation of the free electron density; S hteμ is the recombination coefficient of trapped holes and free electrons; n ht is the density of trapped holes; n eμ is the density of free electrons; S hμeμ is the recombination coefficient of free holes and free electrons; n hμ is the density of free holes; B e is the electron trap coefficient; n et is the density of trapped electrons; n oet is the electron trap density; D e is the electron trap coefficient; ； in, S pt is the source term representing the local variation of the trapped positive ion density; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; n pt is the density of trapped positive ions; n nμ is the density of free negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; n nt is the density of trapped negative ions; B p is the trapping coefficient of the positive ion; n pμ is the density of free positive ions; n opt is the trap density of positive ions; D p is the trapping coefficient of the positive ion; ； in, S pμ is the source term representing the local variation of the free positive ion density; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; n pμ is the density of free positive ions; n nt is the density of trapped negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n nμ is the density of free negative ions; B p is the trapping coefficient of the positive ion; n pt is the density of trapped positive ions; n opt is the trap density of positive ions; D p is the trapping coefficient of the positive ion; D e is the electron trap coefficient; N 0 is the concentration of impurity molecules; ； in, S nt is the source term representing the local variation of the trapped anion density; S pμnt is the recombination coefficient of free positive ions and trapped negative ions; n pμ is the density of free positive ions; n nt is the density of trapped negative ions; S ptnt is the recombination coefficient of trapped positive ions and trapped negative ions; n pt is the density of trapped positive ions; B n is the trapping coefficient of negative ions; n nμ is the density of free negative ions; n ont is the trap density of negative ions; D n is the trapping coefficient of negative ions; ； in, S nμ is the source term representing the local variation of the free anion density; S ptnμ is the recombination coefficient of trapped positive ions and free negative ions; n pt is the density of trapped positive ions; n nμ is the density of free negative ions; S pμnμ is the recombination coefficient of free positive ions and free negative ions; n pμ is the density of free positive ions; B n is the trapping coefficient of negative ions; n nt is the density of trapped negative ions; n ont is the trap density of negative ions; D n is the trapping coefficient of negative ions; D d is the dissociation rate of impurity molecules; N 0 is the concentration of impurity molecules; ； in, S ht is the source term representing the local variation of the trapped hole density; S hteμ is the recombination coefficient of trapped holes and free electrons; n ht is the density of trapped holes; n eμ is the density of free electrons; S htet is the recombination coefficient of trapped holes and trapped electrons; n et is the density of trapped electrons; B h is the cavity trap coefficient; n hμ is the density of free holes; n oht is the hole trap density; D h is the trapping coefficient of the hole; ； wherein, S hμ is a source term representing the local variation of the free hole density; S hμet is the recombination coefficient of free holes and trapped electrons; n hμ is the density of free holes; n et is the density of trapped electrons; S hμeμ is the recombination coefficient of free holes and free electrons; n eμ is the density of free electrons; B h is the trapping coefficient of holes; n ht is the density of trapped holes; n oht is the trap density of holes; D h is the detrapping coefficient of holes; ； in, S et is the source term representing the local variation of the trapped electron density; S hμet is the recombination coefficient of free holes and trapped electrons; n hμ is the density of free holes; n et is the density of trapped electrons; S htet is the recombination coefficient of trapped holes and trapped electrons; n ht is the density of trapped holes; B e is the electron trap coefficient; n eμ is the density of free electrons; n oet is the electron trap density; D e is the electron trap coefficient; in, express t Time along the radius r The mobility of free electrons in the direction; is the dielectric constant of the insulation layer of the high voltage DC cable; in, express t Time along the radius r The mobility of free holes in the direction; in, express t Time along the radius r The mobility of free anions in the direction; in, express t Time along the radius r The mobility of free positive ions in the direction; 。 7. The calculation method according to claim 1, It is characterized in that The step of importing the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain the spatial charge distribution result of the insulating layer specifically includes: Importing the structure of the high-voltage direct current extruded insulated cable and the non-homogeneous structural geometric model to obtain a cable whose insulating layer adopts the non-homogeneous structural geometric model; importing the first charge transport model and the second charge transport model; Setting boundary conditions and meshing the insulation layer of the cable; A simulation calculation is performed to obtain the spatial charge distribution result of the insulating layer.

8. The calculation method according to claim 7, It is characterized in that The boundary conditions are specifically set as follows: The inner side of the insulation layer of the cable is set to high voltage and the outer side is grounded; The temperatures of the insulation layers of the cables were set to the same value.

9. A calculation system for the spatial charge distribution of high-voltage DC extruded insulation cables. It is characterized in that The computing system comprises: A geometric model building module is used to build a non-homogeneous structural geometric model of the insulation layer of a high-voltage DC extruded insulated cable; A charge transport model construction module, used to construct a charge transport model of the insulating layer, and set the parameters of the charge transport model based on the characteristics of the crystalline region of the insulating layer to obtain a first charge transport model of the crystalline region, and set the parameters of the charge transport model based on the characteristics of the amorphous region of the insulating layer to obtain a second charge transport model of the amorphous region; the charge transport model includes a Schottky injection current density expression and an extraction current density expression characterizing the injection and extraction process of electronic charge, an impurity molecule dissociation rate expression and an impurity molecule concentration change expression characterizing the dissociation process of ionic charge, and a transport characteristic mechanism characterizing electronic charge and ionic charge; A simulation calculation module, used for importing the inhomogeneous structure geometric model, the first charge transport model and the second charge transport model into simulation software for simulation calculation to obtain a spatial charge distribution result of the insulating layer; The construction of the non-homogeneous structural geometric model of the insulation layer of the high-voltage DC extruded insulated cable specifically includes: Make samples of insulation layer of high voltage DC extruded insulated cable; Testing the sample to determine the size of the sample, the number of spherulites in the sample, and the volume ratio of the crystalline region to the amorphous region in the sample; the size includes length and width; The boundary of the non-homogeneous structure geometric model is drawn according to the size, and a plurality of Voronoi seed points are randomly set within the boundary to generate a Voronoi diagram; the crystalline region and the amorphous region are filled in each Voronoi polygon in the Voronoi diagram according to the volume ratio to obtain the non-homogeneous structure geometric model; the number of the Voronoi seed points is the same as the number of the spherulites; the amorphous region filled in the Voronoi polygon is arranged around the crystalline region filled in the Voronoi polygon.

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