CN114330164A - Method for rapidly calculating horizontal jacking pipe current-carrying capacity of high-voltage alternating-current cable - Google Patents

Method for rapidly calculating horizontal jacking pipe current-carrying capacity of high-voltage alternating-current cable Download PDF

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CN114330164A
CN114330164A CN202111623973.7A CN202111623973A CN114330164A CN 114330164 A CN114330164 A CN 114330164A CN 202111623973 A CN202111623973 A CN 202111623973A CN 114330164 A CN114330164 A CN 114330164A
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current
cable
carrying capacity
temperature
calculating
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陈赛慧
卞荣
陈科技
孙永军
杨仕友
王宁
诸言涵
张琳琳
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Zhejiang University ZJU
Economic and Technological Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Zhejiang University ZJU
Economic and Technological Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Abstract

The invention discloses a method for quickly calculating the current-carrying capacity of a horizontal jacking pipe of a high-voltage alternating-current cable, which comprises the following steps: s1, acquiring submarine cable parameters and the value range thereof; s2, constructing an adaptive surface response model based on the tightly-supported radial basis function and the electromagnetic-thermal-flow coupling; and S3, rapidly calculating the current carrying capacity of the cable under any submarine cable parameter by using the constructed adaptive surface response model. The method can quickly calculate the current-carrying capacity under any cable parameter, and can greatly reduce the calculation time and the calculation cost while ensuring the accuracy of the calculation result.

Description

Method for rapidly calculating horizontal jacking pipe current-carrying capacity of high-voltage alternating-current cable
Technical Field
The invention relates to the technical field of cables, in particular to a method for quickly calculating the current-carrying capacity of a horizontal jacking pipe of a high-voltage alternating-current cable.
Background
With the continuous development of national economy and power industry, power cables are more and more widely applied to power transmission and distribution lines, the current-carrying capacity of the power cables is accurately calculated, and the method has important significance for improving the utilization rate of the power cables and dynamically adjusting loads. The current carrying capacity of the cable is mainly determined by the long term maximum temperature of the insulation used. For example, for a widely used cross-linked polyethylene (XLPE) cable, the maximum operating temperature of the core conductor cannot exceed 90 degrees celsius for a long period of time.
The horizontal jacking pipe of the cable is a common cable structure form, and the air layer between the cable in the jacking pipe and the pipe wall is coupled by three heat transfer modes, namely heat conduction, heat convection and heat radiation. The current in the cable conductor generates an electromagnetic field, which influences the generation of the heat of the surrounding cables and further influences the temperature field distribution of the cable group. Therefore, the horizontal jacking pipe of the cable needs to be coupled with an electromagnetic field, a thermal field and a fluid field to complete the calculation of the current-carrying capacity of the cable. In the calculation of the current-carrying capacity of the cable, the parameters of the horizontal jacking pipe of the cable can be considered as input variables, and the current-carrying capacity is an output variable. Therefore, the functional relation between the cable parameters and the current-carrying capacity can be reconstructed by adopting the surface response model, so that the calculation efficiency is improved, and the calculation cost is reduced.
Surface response model (RSM) is a method that uses mathematical statistics to establish system (device) input-output relationships. The core of the method is to construct an analytical solution of an input-output relationship by using a certain basis function according to the response of a system on a series of sampling points, so that the key problem to be solved for constructing the RSM model is to determine a proper basis function to construct the relationship between an output variable and an input variable. The most common Basis Function of the RSM model in computational electromagnetics is the Radial Basis Function (RBF) at present. The RBF has the advantages that: the constructed interpolation function is simple to process for discrete sampling points in any dimension and does not need too much calculation. However, the surface response model constructed based on the fully-supported radial function has the following problems: (1) the constructed function is not an "optimal" function in the "one's" sense; (2) the model is difficult to process irregular sampling points; (3) the optimal matching of algorithm parameters cannot be automatically realized; (4) when the number of sampling points is large, the calculation of the reconstruction function still requires large calculation resources.
Disclosure of Invention
The invention aims to provide a method for quickly calculating the horizontal jacking flow capacity of a high-voltage alternating-current cable. The method can quickly calculate the current-carrying capacity of the horizontal jacking pipe of the cable under any cable parameter, and can greatly reduce the calculation time and the calculation cost while ensuring the accuracy of the calculation result.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a method for quickly calculating the horizontal jacking flow of a high-voltage alternating-current cable comprises the following steps:
s1, acquiring parameters of the horizontal jacking pipe of the cable and the value range of each parameter;
s2, sampling parameters in a parameter feasible interval;
s3, calculating the current-carrying capacity of the cable at the sampling point;
s4, constructing a surface response model based on the moving least square approximation;
and S5, rapidly calculating the current-carrying capacity of the cable under any horizontal jacking pipe parameter of the cable by using the constructed surface response model.
In the method for rapidly calculating the horizontal jacking flow of the high-voltage alternating-current cable, in step S1, the parameters of the horizontal jacking pipe of the cable include the inner diameter length of the horizontal jacking pipe of the cable and the outer diameter length of the horizontal jacking pipe of the cable.
In the method for quickly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable, in step S2, the parameter sampling is uniform sampling within a parameter feasible interval, and the number of sampling points is 100.
In step S3, a multi-physical-field coupling model is used to calculate an eddy current field, a temperature field, and a fluid field of a cable at a sampling point, and then an iterative procedure is used to calculate the cable carrying capacity at the sampling point of the cable, specifically including:
s3.1, calculating an eddy current field: for a two-dimensional eddy current field, the vector magnetic potential control equation under the coulomb specification is as follows:
Figure BDA0003439146260000031
in the formula:
Figure BDA0003439146260000032
in order to be the current density,
Figure BDA0003439146260000033
to vector the magnetic potential, σ is the electrical conductivity,
Figure BDA0003439146260000034
vector differential operators, namely gradient operators; mu is magnetic conductivity, j is a complex symbol, and omega is angular frequency;
s3.2, calculating a temperature field: for a two-dimensional temperature field, the governing equation is:
Figure BDA0003439146260000035
in the formula: ρ is density, CpIs the normal pressure heat capacity, u is the velocity vector, k is the thermal conductivity, QeThe heating power of the heat source unit volume is shown, and q is the heat flux density;
Figure BDA0003439146260000036
is the gradient of temperature, J is the current density vector, E is the electric field intensity vector;
s3.3, calculating a fluid field, wherein the fluid field meets the mass conservation law, the momentum conservation law and the energy conservation law:
Figure BDA0003439146260000041
in the formula: i is an identity matrix, mu is dynamic viscosity, T is the temperature of the fluid material, and F is the buoyancy lift force caused by density change;
s3.4, setting boundary conditions including a known boundary temperature condition, a known boundary normal heat flow density condition and a convection boundary condition:
Figure BDA0003439146260000042
in the formula: t iswIs the known pipe wall temperature of the jacking pipe, q is the heat flux density, alpha is the temperature coefficient of the conductor resistivity, TfIs the fluid medium temperature;
s3.5, regarding the temperature field as a two-dimensional steady-state heat conduction problem, the electrical conductivity sigma of the conductor changes with the temperature, and is expressed as:
Figure BDA0003439146260000043
where α is the temperature coefficient of the resistivity of the conductor, ρ0Is the resistivity, T, of the conductor at 20 DEG CrefIs a reference temperature;
s3.6, solving the current-carrying capacity by adopting a chord section method, namely, when the highest temperature of the cable conductor reaches 90 ℃, determining the current at the momentMeaning the current carrying capacity of the cable; calculating the corresponding conductor temperature by solving the temperature field, calculating the current-carrying capacity of the cable by adopting a truncation method, and in iterative calculation, when the absolute value of T iskWhen the value of-90 is less than 0.01 ℃, the conductor temperature of the cable is considered to be stable at the maximum allowable temperature, and the current flowing through the cable is the current-carrying capacity of the cable.
In the method for quickly calculating the horizontal jacking flow capacity of the high-voltage alternating-current cable, in step S4, the step of constructing a surface response model based on the moving least square approximation specifically includes:
for any of f (x)n→ R if known at some column of sample points xi∈RDThe function value of (i-1, 2, …, N) is fiThen at the selected basis function
Figure BDA0003439146260000051
Under the condition, first, local approximate L of MLS is definedxf is:
Figure BDA0003439146260000052
wherein the basis functions
Figure BDA0003439146260000053
Satisfies the following conditions:
1)、b(1)≡1；
2)、b(i)∈Cm(RD)(i＝1,2,…,n)；
3) at a given number n of sample points,
Figure BDA0003439146260000054
independently of each other;
then defining a global projection operator Gf as: for any point x ∈ RD：
Figure BDA0003439146260000055
To determine the coefficients a (x), L is defined by the inner product2Norm, i.e.
(u,v)x＝uTw(x)v；
Figure BDA0003439146260000056
Wherein z is (z (x)1)z(x2)…z(xN))T(z ═ u, v), w (x) is an N × N diagonal matrix whose diagonal elements are w(i)(x)，w(i)(x) Is a weight function of the MLS;
the MLS is characterized by a weight function w(i)(x) Is a tight-branch function centered at the ith sample point; the least squares approximation by Gf as function f is:
a(x)＝A(x)-1B(x)f；
in the formula: f ═ f1 f2 … fN]T；
Figure BDA0003439146260000061
B(x)＝[w1(x)b(x1) w2(x)b(x2) … wN(x)b(xN)]；
A surface response model based on moving least squares is thus obtained.
The weight function w is calculated according to the method for quickly calculating the horizontal jacking flow of the high-voltage alternating-current cable(i)(x) And correcting to enable the MLS to become an approximate method of an interpolation type, wherein a correction formula is as follows:
Figure BDA0003439146260000062
in the formula, a is a positive number.
In the method for quickly calculating the horizontal jacking flow of the high-voltage alternating-current cable, the weight function w(i)(x) Satisfies the following conditions:
1) in the support domain omegaxInner, w (x-x)i)＞0；
2) In the support domain omegaxOuter, w (x-x)i)＝0；
3) Normality, i.e. [ integral ] nΩw(x-xi)dΩ＝1；
4) The weight function is | | x-xiA monotonically decreasing function of | l;
5) the weight function is continuously derivable.
In the method for quickly calculating the horizontal jacking flow of the high-voltage alternating-current cable, the weight function w(i)(x) Is a gaussian function, a cubic spline function or a quadratic spline function.
In the method for quickly calculating the horizontal jacking flow of the high-voltage alternating-current cable, the weight function w(i)(x) Is a cubic spline function:
Figure BDA0003439146260000071
or a quartic spline function:
Figure BDA0003439146260000072
wherein r | | | x-xi||，
Figure BDA0003439146260000073
rmaxIs the support domain radius of the weight function.
Compared with the prior art, the method comprises the steps of firstly determining parameters of the cable horizontal jacking pipe and the value range of each parameter; secondly, sampling parameters in a parameter feasible interval; then calculating the current-carrying capacity of the cable at the sampling point; and finally, reconstructing the input-output relationship between the horizontal jacking pipe parameters of the cable and the current-carrying capacity of the cable by using a surface response model based on the moving least squares, namely inputting any horizontal jacking pipe parameter of the cable in a feasible interval by using the surface response model constructed by the invention, and calculating and outputting to obtain the current-carrying capacity of the cable. Therefore, the parameter sampling adopted in the invention ensures that the method is suitable for calculating the current-carrying capacity under any parameter in the parameter feasible interval; the accuracy of a current-carrying capacity calculation result at a sampling point is ensured by combining a multi-physical-field coupling model with a truncation method; the numerical matching precision of the reconstruction function and the original function is ensured in view of the strong function reconstruction capability of the mobile least square. In conclusion, the method has good numerical precision for any parameter in the parameter feasible interval. The method can greatly reduce the calculation time and the calculation cost while ensuring the accuracy of the current-carrying capacity calculation result.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of the cable horizontal jacking parameters of the present invention;
fig. 3 is a flow chart of cable ampacity calculation.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the present invention is not limited thereto.
Example (b): a method for rapidly calculating the horizontal jacking flow of a high-voltage alternating-current cable comprises the following steps as shown in figure 1:
s1, acquiring parameters of the horizontal jacking pipe of the cable and the value range of each parameter;
the horizontal jacking parameters of the cable in the embodiment are 2 (unit is millimeter), as shown in fig. 2. Respectively as follows:
inner diameter length of a horizontal jacking pipe of the cable: x is the number of1∈[1500,1600]；
The outer diameter length of the horizontal jacking pipe of the cable is as follows: x is the number of2∈[1800,1900]。
S2, sampling parameters in a parameter feasible interval; the parameter sampling is uniform sampling in a parameter feasible interval, and the number of sampling points is 100.
S3, calculating the current-carrying capacity of the cable at the sampling point; for cables inside the cable top tube, the cable is the only heat source, which includes joule heating generated by the conductive material and dielectric loss of the insulation layer. The heat dissipation in the cable jacking pipe comprises heat conduction between the cable and surrounding media, natural convection of air between the outer surface of the cable and the inner wall of the cable jacking pipe, and heat radiation between the outer surfaces.
In this embodiment, a multi-physical-field coupling model is used to calculate an eddy current field, a temperature field, and a fluid field of a cable at a sampling point, and then a cable current-carrying capacity at the sampling point of the cable is calculated through an iterative procedure, which specifically includes:
s3.1, calculating an eddy current field: for a two-dimensional eddy current field, the vector magnetic potential control equation under the coulomb specification is as follows:
Figure BDA0003439146260000091
in the formula:
Figure BDA0003439146260000092
in order to be the current density,
Figure BDA0003439146260000093
to vector the magnetic potential, σ is the electrical conductivity,
Figure BDA0003439146260000094
vector differential operators, namely gradient operators; mu is magnetic conductivity, j is a complex symbol, and omega is angular frequency;
s3.2, calculating a temperature field: in cables, the heat source in solid and fluid heat transfer fields is joule heat generated by the cable current. The length of the cabling can be considered to be infinitely long compared to its diameter. Therefore, the temperature field of the cable arranged in the header can also be simplified to two dimensions, for which the control equation is:
Figure BDA0003439146260000095
in the formula: ρ is density, CpIs the normal pressure heat capacity, u is the velocity vector, k is the thermal conductivity, QeThe heating power of the heat source unit volume is shown, and q is the heat flux density;
Figure BDA0003439146260000096
is the gradient of temperature, J is the currentDensity vector, E is the electric field intensity vector;
s3.3, calculating a fluid field, wherein the fluid field meets the mass conservation law, the momentum conservation law and the energy conservation law:
Figure BDA0003439146260000097
in the formula: i is an identity matrix, mu is dynamic viscosity, T is the temperature of the fluid material, and F is the buoyancy lift force caused by density change;
s3.4, setting boundary conditions: in order to solve the temperature field and the current-carrying capacity of the horizontal jacking pipe of the cable, the boundary conditions of the cable heat transfer problem can be summarized into three types: the first type is the known boundary temperature; the second type is the known boundary normal heat flux density; the third category is convective boundary conditions, i.e., convective heat transfer coefficient and fluid temperature within a known boundary. These three types of boundaries are expressed as:
Figure BDA0003439146260000101
in the formula: t iswIs the known pipe wall temperature of the jacking pipe, q is the heat flux density, alpha is the temperature coefficient of the conductor resistivity, TfIs the fluid medium temperature;
and S3.5, in the process of cable laying, the on-site cable laying conditions are extremely complicated. Therefore, in order to reduce the complexity of the model and further ensure the smooth operation of the heat transfer finite element analysis, the following simplification is performed:
the cable inside the cable top tube is assumed to be of infinite length, without considering the effect of axial heat transfer. The three-dimensional model is simplified into a two-dimensional model, that is, the temperature field is regarded as a two-dimensional steady-state heat conduction problem, and the electrical conductivity σ of the conductor changes along with the temperature, which is expressed as:
Figure BDA0003439146260000102
where α is the temperature coefficient of the resistivity of the conductor, ρ0Is the resistivity, T, of the conductor at 20 DEG CrefIs a reference temperature; the natural convection velocity of the enclosed air region within the cable trench is relatively low and the trench air can be considered an incompressible fluid.
S3.6, calculating the cable jacking flow based on the temperature field, and performing the inverse process of the calculation of the electromagnetic field and the temperature field. In the embodiment, a current-carrying capacity is solved by adopting a chord-section method, namely when the highest temperature of a cable conductor reaches 90 ℃, the current at the moment is defined as the current-carrying capacity of the cable; as shown in fig. 3, the initial value of the current may be calculated by IEC60287 standard. Calculating the corresponding conductor temperature by solving the temperature field, calculating the current-carrying capacity of the cable by adopting a truncation method, and in iterative calculation, when the absolute value of T iskWhen the value of-90 is less than 0.01 ℃, the conductor temperature of the cable is considered to be stable at the maximum allowable temperature, and the current flowing through the cable is the current-carrying capacity of the cable.
S4, constructing a surface response model based on the moving least square approximation;
in order to quickly calculate the current-carrying capacity of the cable jacking pipe, the invention adopts a surface response model based on moving least square approximation to reconstruct the input-output relation between an input variable (cable horizontal jacking pipe parameter) and an output variable (cable current-carrying capacity).
The Moving Least Squares (MLS) method was originally proposed by Shepard for the fitting of low dimensional curves, and later Lancaster and Salkauskas generalize it to high dimensional problems. Because the fitting capability of the method is very strong, the method is widely applied to the fields of curve and curved surface fitting, non-grid algorithm and the like in recent years.
For any of f (x)n→ R if known at some column of sample points xi∈RDThe function value of (i-1, 2, …, N) is fiThen at the selected basis function
Figure BDA0003439146260000111
Under the condition, first, local approximate L of MLS is definedxf is:
Figure BDA0003439146260000112
wherein the basis functions
Figure BDA0003439146260000113
Satisfies the following conditions:
1)、b(1)≡1；
2)、b(i)∈Cm(RD)(i＝1,2,…,n)；
3) at a given number n of sample points,
Figure BDA0003439146260000114
independently of each other;
then defining a global projection operator Gf as: for any point x ∈ RD：
Figure BDA0003439146260000121
To determine the coefficients a (x), L is defined by the inner product2Norm, i.e.
(u,v)x＝uTw(x)v；
Figure BDA0003439146260000122
Wherein z is (z (x)1)z(x2)…z(xN))T(z ═ u, v), w (x) is an N × N diagonal matrix whose diagonal elements are w(i)(x)，w(i)(x) Is a weight function of the MLS;
one of the features of MLS is the weight function w(i)(x) Is a tight-branch function centered at the ith sample point; thus, the MLS approximation is a local approximation, the least-squares approximation of the function f by Gf, having:
a(x)＝A(x)-1B(x)f；
in the formula: f ═ f1 f2 … fN]T；
Figure BDA0003439146260000123
B(x)＝[w1(x)b(x1) w2(x)b(x2) … wN(x)b(xN)]；
A surface response model based on moving least squares is thus obtained. Generally, MLS is not an interpolation-type fitting method, and in order to make MLS an interpolation-type approximation method, the weight function is modified as follows:
Figure BDA0003439146260000124
in the formula, a is a positive number. The MLS in this case is called interpolation-type moving least square approximation (IMLS).
The weight function plays a very important role in the moving least square method, and the weight function has a great influence on the calculation result. In general, the weight function w(i)(x) Satisfies the following conditions:
1) in the support domain omegaxInner, w (x-x)i)＞0；
2) In the support domain omegaxOuter, w (x-x)i)＝0；
3) Normality, i.e. [ integral ] nΩw(x-xi)dΩ＝1；
4) The weight function is | | x-xiA monotonically decreasing function of | l;
5) the weight function is continuously derivable.
Where condition 2) is crucial, it can guarantee that the MLS is a local approximation with tight support, i.e. the approximation solution depends only on nodes within the area of influence, and not on other nodes.
The weight function is a Gaussian function, a cubic spline function or a quartic spline function, wherein when the weight function is the cubic spline function:
Figure BDA0003439146260000131
when the weight function is a quartic spline:
Figure BDA0003439146260000132
wherein r | | | x-xi||，
Figure BDA0003439146260000133
rmaxIs the support domain radius of the weight function.
In general, the support radius (domain of influence) of the weight function has a large influence on the performance of the MLS. Under the condition that the sampling point is unchanged, the larger the support radius of the weight function is, the higher the accuracy of the reconstruction function is, but the locality of the MLS is poor at the moment; under the limit condition that the influence domain of the weight function covers all sampling points, the MLS becomes a fully-supported surface response model; conversely, if the support radius is small, the locality of the MLS becomes good, but the accuracy of the reconstruction function becomes poor. In addition, in practical applications, the area of influence should contain enough sampling points so that the formula a (x) ═ a (x)-1B (x) in f A (x) is reversible.
According to the invention, the function relation between the horizontal jacking pipe parameters of the cable and the current-carrying capacity of the cable is reconstructed by applying the mobile least square method according to 100 sampling points and the objective function value (the current-carrying capacity of the cable). During reconstruction, the basis function is a quadratic basis function, and the weight function is a three-spline function.
S5, the cable ampacity under any cable horizontal jacking parameter can be quickly calculated by using the surface response model constructed in the steps, namely the cable ampacity can be quickly and accurately calculated and output by inputting any cable horizontal jacking parameter in a feasible interval by using the surface response model constructed in the invention.
In summary, the present invention first determines the parameters of the cable horizontal jacking pipes and the value range of each parameter; secondly, sampling parameters in a parameter feasible interval; then calculating the current-carrying capacity of the cable at the sampling point; and finally, reconstructing the input-output relationship between the horizontal jacking pipe parameters of the cable and the current-carrying capacity of the cable by using a surface response model based on the moving least squares, namely inputting any horizontal jacking pipe parameter of the cable in a feasible interval by using the surface response model constructed by the invention, and calculating and outputting to obtain the current-carrying capacity of the cable. Therefore, the parameter sampling adopted in the invention ensures that the method is suitable for calculating the current-carrying capacity under any parameter in the parameter feasible interval; the accuracy of a current-carrying capacity calculation result at a sampling point is ensured by combining a multi-physical-field coupling model with a truncation method; the numerical matching precision of the reconstruction function and the original function is ensured in view of the strong function reconstruction capability of the mobile least square. The method has good numerical precision for any parameter in the parameter feasible interval. The method can greatly reduce the calculation time and the calculation cost while ensuring the accuracy of the current-carrying capacity calculation result.

Claims (9)

1. A method for quickly calculating the horizontal jacking flow capacity of a high-voltage alternating-current cable is characterized by comprising the following steps: the method comprises the following steps:
s1, acquiring parameters of the cable pipe and the value range of each parameter;
s2, sampling parameters in a parameter feasible interval;
s3, calculating the current-carrying capacity of the cable at the sampling point;
s4, constructing a surface response model based on the moving least square approximation;
and S5, rapidly calculating the current-carrying capacity of the cable under any horizontal jacking pipe parameter of the cable by using the constructed surface response model.
2. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 1, which is characterized in that: in step S1, the parameters of the horizontal jacking pipe of the cable include the inner diameter length of the horizontal jacking pipe of the cable and the outer diameter length of the horizontal jacking pipe of the cable.
3. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 1, which is characterized in that: in step S2, the parameter sampling is uniform sampling within the parameter feasible interval, and the number of sampling points is 100.
4. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 1, which is characterized in that: in step S3, a multi-physical-field coupling model is used to calculate an eddy current field, a temperature field, and a fluid field of the cable at the sampling point, and then an iterative procedure is used to calculate the current-carrying capacity of the cable at the sampling point, specifically including:
s3.1, calculating an eddy current field: for a two-dimensional eddy current field, the vector magnetic potential control equation under the coulomb specification is as follows:
Figure FDA0003439146250000021
in the formula:
Figure FDA0003439146250000022
in order to be the current density,
Figure FDA0003439146250000023
to vector the magnetic potential, σ is the electrical conductivity,
Figure FDA0003439146250000024
vector differential operators, namely gradient operators; mu is magnetic conductivity, j is a complex symbol, and omega is angular frequency;
s3.2, calculating a temperature field: for a two-dimensional temperature field, the governing equation is:
Figure FDA0003439146250000025
in the formula: ρ is density, CpIs the normal pressure heat capacity, u is the velocity vector, k is the thermal conductivity, QeThe heating power of the heat source unit volume is shown, and q is the heat flux density;
Figure FDA0003439146250000026
is the gradient of temperature, J is the current density vector, E is the electric field intensity vector;
s3.3, calculating a fluid field, wherein the fluid field meets the mass conservation law, the momentum conservation law and the energy conservation law:
Figure FDA0003439146250000027
in the formula: i is an identity matrix, mu is dynamic viscosity, T is the temperature of the fluid material, and F is the buoyancy lift force caused by density change;
s3.4, setting boundary conditions, wherein the boundary conditions comprise a known boundary temperature condition, a known boundary normal heat flow density condition and a convection boundary condition:
Figure FDA0003439146250000028
in the formula: t iswIs the known pipe wall temperature of the jacking pipe, q is the heat flux density, alpha is the temperature coefficient of the conductor resistivity, TfIs the fluid medium temperature;
s3.5, regarding the temperature field as a two-dimensional steady-state heat conduction problem, the electrical conductivity sigma of the conductor changes with the temperature, and is expressed as:
Figure FDA0003439146250000031
where α is the temperature coefficient of the resistivity of the conductor, ρ0Is the resistivity, T, of the conductor at 20 DEG CrefIs a reference temperature;
s3.6, solving the current-carrying capacity by adopting a chord section method, namely defining the current at the moment as the current-carrying capacity of the cable when the highest temperature of the cable conductor reaches 90 ℃; calculating the corresponding conductor temperature by solving the temperature field, calculating the current-carrying capacity of the cable by adopting a truncation method, and in iterative calculation, when the absolute value of T iskWhen the value of-90 is less than 0.01 ℃, the conductor temperature of the cable is considered to be stable at the maximum allowable temperature, and the current flowing through the cable is the current-carrying capacity of the cable.
5. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 1, which is characterized in that: in step S4, the step of constructing the surface response model based on the moving least squares approximation specifically includes:
for any of f (x)n→ R if known at some column of sample points xi∈RDThe function value of (i-1, 2, …, N) is fiThen at the selected basis function
Figure FDA0003439146250000032
Under the condition, first, local approximate L of MLS is definedxf is:
Figure FDA0003439146250000033
wherein the basis functions
Figure FDA0003439146250000034
Satisfies the following conditions:
1)、b(1)≡1；
2)、b(i)∈Cm(RD)(i＝1,2,…,n)；
3) at a given number n of sample points,
Figure FDA0003439146250000041
independently of each other;
then defining a global projection operator Gf as: for any point x ∈ RD：
Figure FDA0003439146250000042
To determine the coefficients a (x), L is defined by the inner product2Norm, i.e.
(u,v)x＝uTw(x)v；
Figure FDA0003439146250000043
Wherein z is (z (x)1) z(x2) … z(xN))T(z ═ u, v), w (x) is an N × N diagonal matrix whose diagonal elements are w(i)(x)，w(i)(x) Is a weight function of the MLS;
the MLS is characterized by a weight function w(i)(x) Is a tight-branch function centered at the ith sample point; the least squares approximation by Gf as function f is:
a(x)＝A(x)-1B(x)f；
in the formula: f ═ f1 f2 … fN]T；
Figure FDA0003439146250000044
B(x)＝[w1(x)b(x1) w2(x)b(x2) … wN(x)b(xN)]；
A surface response model based on moving least squares is thus obtained.
6. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 5, which is characterized in that: to weight function w(i)(x) And correcting to enable the MLS to become an approximate method of an interpolation type, wherein a correction formula is as follows:
Figure FDA0003439146250000051
in the formula, a is a positive number.
7. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 5, which is characterized in that: the weight function w(i)(x) Satisfies the following conditions:
1) in the support domain omegaxInner, w (x-x)i)＞0；
2) In the support domain omegaxOuter, w (x-x)i)＝0；
3) Normality, i.e. [ integral ] nΩw(x-xi)dΩ＝1；
4) The weight function is | | x-xiA monotonically decreasing function of | l;
5) the weight function is continuously derivable.
8. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 5, which is characterized in that: the weight function w(i)(x) Is a gaussian function, a cubic spline function or a quadratic spline function.
9. The method for rapidly calculating the horizontal jacking current-carrying capacity of the high-voltage alternating-current cable according to claim 8, which is characterized in that: the weight function w(i)(x) Is a cubic spline function:
Figure FDA0003439146250000052
or a quartic spline function:
Figure FDA0003439146250000053
wherein r | | | x-xi||，
Figure FDA0003439146250000054
rmaxIs the support domain radius of the weight function.
CN202111623973.7A 2021-12-28 2021-12-28 Method for rapidly calculating horizontal jacking pipe current-carrying capacity of high-voltage alternating-current cable Pending CN114330164A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115186422A (en) * 2022-09-09 2022-10-14 特变电工山东鲁能泰山电缆有限公司 Simulation analysis method, device and medium for operating characteristics of in-phase parallel cables
CN117574472A (en) * 2024-01-19 2024-02-20 中国石油大学(华东) Umbilical cable temperature field and current-carrying capacity analysis method based on coupling effect

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115186422A (en) * 2022-09-09 2022-10-14 特变电工山东鲁能泰山电缆有限公司 Simulation analysis method, device and medium for operating characteristics of in-phase parallel cables
CN115186422B (en) * 2022-09-09 2022-12-27 特变电工山东鲁能泰山电缆有限公司 Simulation analysis method, device and medium for operating characteristics of in-phase parallel cables
CN117574472A (en) * 2024-01-19 2024-02-20 中国石油大学(华东) Umbilical cable temperature field and current-carrying capacity analysis method based on coupling effect
CN117574472B (en) * 2024-01-19 2024-05-31 中国石油大学(华东) Umbilical cable temperature field and current-carrying capacity analysis method based on coupling effect

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