CN118013844A - Rapid calculation method for current-carrying capacity of power cable bank - Google Patents
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Abstract
The invention discloses a rapid calculation method of the current-carrying capacity of a power cable bank, which comprises the following steps: step 1, determining parameters of a cable rack and a value range of each parameter; step 2, sampling parameters in a parameter feasible interval; step 3, calculating the current-carrying capacity of the cable at the sampling point; step 4, constructing a surface response model based on a support vector machine according to the data obtained in the steps 1 to 3; and 5, rapidly calculating the current-carrying capacity of the cable under any cable arranging pipe parameter by using the constructed surface response model. The invention can rapidly calculate the current-carrying capacity under any cable parameter, and can greatly reduce the calculation time and the calculation cost while guaranteeing the accuracy of the calculation result.
Description
Technical Field
The invention relates to the technical field of cables, in particular to a rapid calculation method of the current-carrying capacity of a power cable bank.
Background
In the existing cable current-carrying capacity calculation method, IEC 60287 cannot provide an accurate calculation formula of cable loss when the distance between cables is short, so that a certain error exists in the cable current-carrying capacity. The traditional current-carrying capacity calculation result based on the electric-thermal-flow coupling model is higher than IEC 60287 in accuracy. However, the basic principle of numerical methods (finite element method, finite difference method, etc.) for calculating multiple physical fields is to convert the problem of the constant solution of the continuous domain partial differential equation into a discrete large algebraic equation set for solving through a certain mathematical process. Because the algebraic equation set of the complex three-dimensional multi-physical field problem is tens of times huge, the analysis and calculation of the algebraic equation set need to occupy huge storage space and a computer CPU. Therefore, it is generally difficult to directly apply the numerical calculation method to effectively solve the analysis and calculation of engineering multi-physical fields, especially multi-physical field calculation under any cable parameters.
The surface response model (RSM) is one method of using statistical knowledge of the physics to build the input-output relationship of a system (device). The basic principle of the surface response model method is as follows: firstly, dispersing a decision variable space into a series of sampling points, and calculating the function values of a target/constraint function at the sampling points by using a numerical calculation method; and reconstructing the target/constraint function by using a certain surface response model according to the function values of the target/constraint function at the sampling points.
The core of the surface response model method is to construct an analytical solution of an input-output relationship by using a certain basis function according to the response of the system on a series of sampling points, so that the key problem to be solved in 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 for RSM models in computational electromagnetics today is the radial basis function (Radial Basis Function, RBF). The RBF has the advantages that: the constructed interpolation function is very simple to process for discrete sampling points of arbitrary dimensions and does not require much computation. 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 sense of "certain"; (2) The model is difficult to process irregular sampling points; (3) the optimal matching of algorithm parameters cannot be automatically realized; (4) When there are many sampling points, the calculation of the reconstruction function still requires a large calculation resource.
Disclosure of Invention
The invention aims to provide a rapid calculation method for the current-carrying capacity of a power cable duct. The invention can rapidly calculate the current-carrying capacity under any cable parameter, and can greatly reduce the calculation time and the calculation cost while guaranteeing the accuracy of the calculation result.
The technical scheme of the invention is as follows: a rapid calculation method of the current-carrying capacity of a power cable bank comprises the following steps:
Step 1, determining parameters of a cable rack and a value range of each parameter;
Step 2, sampling parameters in a parameter feasible interval;
step3, calculating the current-carrying capacity of the cable at the sampling point;
step 4, constructing a surface response model based on a support vector machine according to the data obtained in the steps 1 to 3;
And 5, rapidly calculating the current-carrying capacity of the cable under any cable arranging pipe parameter by using the constructed surface response model.
The above-mentioned power cable calandria current-carrying capacity's quick calculation method, the parameter of cable calandria includes cable calandria external diameter length and left and right soil border to calandria central distance, and the value scope of two is as follows respectively:
x1∈[280,300]；
x2∈[1800,2000]；
Wherein, the units are millimeter.
In the foregoing method for rapidly calculating the current-carrying capacity of the power cable duct, in step 2, uniform sampling is adopted, and the number of points is 100.
According to the rapid calculation method for the current-carrying capacity of the power cable calandria, the current-carrying capacity of the cable at the sampling point is calculated by adopting a magnetic-thermal-flow multi-physical field coupling model, and then the current-carrying capacity of the cable is calculated through an iterative program.
The magnetic-thermal-flow multi-physical field coupling model comprises a vortex field, a temperature field, a fluid field and boundary conditions;
For the vortex field, the vector magnetic potential control equation under coulomb specification is:
Wherein: Is the current density,/> Is the vector magnetic potential, σ is the conductivity; /(I)Is Laplacian, μ is permeability; j is a complex number unit; omega is the angular frequency;
for the temperature field, the control equation is:
Wherein: ρ is the density of the material, C p is the solid heat capacity at constant pressure, u is the velocity vector of the fluid, k is the thermal conductivity, Q e is the heat generation in the solid, Q is the heat flux density, E is the electric field strength; is a gradient; t is the temperature; j is a current density vector;
for a fluid field, it follows three basic conservation laws:
Wherein: i is an identity matrix, eta is dynamic viscosity, and F is buoyancy force caused by density change;
For boundary conditions, the process is as follows:
Taking the deep soil boundary as a first type boundary, and taking the boundary far away from the left side and the right side of the calandria as a second type boundary; the surface-over-air interface acts as a third type of boundary.
According to the rapid calculation method for the current-carrying capacity of the power cable calandria, the temperature initial value is firstly set in the solving of the magnetic-thermal-flow multi-physical field coupling model, then the conductivity at the current temperature is calculated, then the electromagnetic field equation is solved to obtain the electromagnetic loss, then the heat flow coupling field equation is solved to obtain the temperature value, then whether the temperature difference meets the requirement is judged, if not, the process returns to the conductivity calculation process, the calculation is repeated until the temperature difference meets the requirement, and the temperature field calculation result is output after the temperature difference meets the requirement.
According to the rapid calculation method of the current-carrying capacity of the power cable calandria, the cable current-carrying capacity is solved by adopting a chord cut method, when the highest temperature of a cable conductor reaches 90 ℃, the instantaneous current is defined as the current-carrying capacity of the cable, the corresponding conductor temperature is calculated by solving a temperature field, and the cable current-carrying capacity is calculated by adopting the chord cut method; in the iterative calculation, when the value of |T k -90| is smaller than 0.01 ℃, the conductor temperature of the cable is considered to be stabilized at the highest allowable temperature, and the current flowing through the cable is the current carrying capacity of the cable.
The foregoing method for rapidly calculating the current-carrying capacity of the power cable gauntlet, wherein the surface response model based on the support vector machine is represented as follows:
Wherein: m is the number of support vectors, and x represents the parameters of the cable rack; alpha i For Lagrange multiplier, K (x i, x) represents the kernel function and b is the coefficient.
Compared with the prior art, the invention firstly determines the design parameters of the cable duct and establishes a feasible interval of the parameters of the cable duct on the basis; secondly, uniformly sampling in a parameter feasible interval, and then calculating the current-carrying capacity of the cable at a sampling point; finally, reconstructing an input-output relationship between the cable management parameters and the cable current-carrying capacity by using a surface response model of the support vector machine; therefore, the cable carrying capacity under any cable duct bank parameter can be rapidly calculated by using the constructed surface response model. Further, the uniform sampling of the parameters adopted in the invention ensures that the invention is suitable for calculating the download flow of any parameter in the feasible parameter interval; the accuracy of the current-carrying capacity calculation result at the sampling point is ensured by combining an electromagnetic-thermal-flow multi-field coupling model and a chord cut method; in view of the strong function reconstruction capability of the support vector machine, the numerical matching precision of the reconstruction function and the original function is ensured. In conclusion, the invention has good numerical precision for any parameter in the parameter feasible interval. The invention not only overcomes the defect that the prior method can not calculate the current-carrying capacity of the cable under any cable bank parameters; compared with the existing cable current-carrying capacity calculation method, the method and the device can ensure the accuracy of the current-carrying capacity calculation result, greatly reduce the calculation time and reduce the calculation cost.
Drawings
FIG. 1 is a schematic illustration of a typical dual-loop cable rack layout;
FIG. 2 is a diagram of multiple physical field coupling relationships under gauntlet application;
FIG. 3 is a flow chart of a magnetic-thermal-flow coupling field calculation;
Fig. 4 is a flow chart of the cable current-carrying capacity calculation.
Detailed Description
The invention is further illustrated by the following figures and examples, which are not intended to be limiting.
Examples: a rapid calculation method of the current-carrying capacity of a power cable bank is applied to the laying of a power cable. The power cable duct (fig. 1) is an important way of laying cables, and there are many combinations of laying multi-loop cables in the duct, and arranging the cables at suitable holes helps to improve the current carrying capacity of the cable lines. In addition, the current-carrying capacity of the cable is mainly determined by the long-term maximum temperature of the insulating material used. For example, for the widely used cross-linked polyethylene (XLPE) cables, the long term maximum operating temperature of the cable core conductor cannot exceed 90 degrees celsius.
In calandria laying, the power cable needs to pass through a conduit laid in advance in the ground. The calandria multiphysics coupling field thus comprises a vortex field, a temperature field, a fluid field. In this multiple physical coupling field, the electromagnetic loss of the cable is the heat source for the temperature field, which is determined by the cable electromagnetic loss and the heat dissipation conditions, which are closely related to the dielectric constant and resistivity of the medium, which in turn are closely related to temperature. And the calandria temperature field is coupled with three heat transfer modes of heat conduction, heat convection and heat radiation. The heat conduction exists between the cable body and the external soil, and the heat radiation exists between the outer surface of the cable and the inner wall of the holes of the calandria. Under the calandria laying mode, the cable body and the calandria inner wall have air gaps, and natural convection process exists in an air domain, and belongs to heat convection heat transfer. The vortex field, the temperature field and the fluid field are coupled, and the coupling relation is shown in figure 2.
In the calculation of the current capacity of the cable, the parameters of the cable duct can be considered as input variables and the current capacity as output variables. 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. Based on the above background description, the flow of the cable-drain fast calculation method provided by the invention is as follows. The method comprises the following steps of 5 steps according to the implementation sequence:
Step 1, determining parameters of a cable rack and a value range of each parameter;
Step 2, sampling parameters in a parameter feasible interval;
step3, calculating the current-carrying capacity of the cable at the sampling point;
step 4, constructing a surface response model based on a support vector machine according to the data obtained in the steps 1 to 3;
step 5, rapidly calculating the current-carrying capacity of the cable under any cable arranging pipe parameter by using the constructed surface response model;
These 5 parts will be explained separately below.
(1) Determining parameters of cable rack and feasible interval of each parameter
In order to calculate the current-carrying capacity under any cable management parameters, the specific parameter composition of the cable management and the value range of each parameter are firstly determined. The invention defines 2 parameters of the cable duct arrangement (the units are millimeter). The method comprises the following steps of:
outer diameter length of cable rack tube: x 1 epsilon [280,300]
Left-right soil border to calandria center distance: x 2. Epsilon. 1800,2000.
(2) Parameter sampling within a parameter feasible interval
In order to construct the surface response model, sampling points need to be set in the cable rack pipe parameter feasible space. The invention adopts uniform sampling. The number of sampling points is 100.
(3) Calculating the current-carrying capacity of the cable at the sampling point
In order to calculate the current carrying capacity of the cable at the sampling point, the invention adopts a magnetic-thermal-flow multi-physical field coupling model to calculate the temperature field of the cable at the sampling point, and then calculates the current carrying capacity of the cable through an iterative program. The following description is specifically directed to vortex fields, temperature fields, fluid fields, boundary conditions, model solutions, and current capacity calculations, respectively.
1. Vortex field:
for a two-dimensional vortex field, the vector magnetic potential control equation under coulomb specification is:
Wherein: Is the current density,/> Is the vector magnetic potential, σ is the conductivity; /(I)Is Laplacian, μ is permeability; j is a complex number unit; omega is the angular frequency;
from equation (1), the magnetic field and eddy current distribution of the analysis domain can be found.
2. And (3) a temperature field:
In cables, the heat source in the solid and fluid heat transfer fields is joule heat generated by the cable current. The length of the cabling can be regarded as infinitely long compared to its diameter. Thus, the temperature field of the cable can also be simplified to be two-dimensional. The control equation is:
Wherein: ρ is the density of the material, C p is the solid heat capacity at constant pressure, u is the velocity vector of the fluid, k is the thermal conductivity, Q e is the heat generation in the solid, Q is the heat flux density, E is the electric field strength; is a gradient; t is the temperature; j is a current density vector;
3. A fluid field:
According to the theory of fluid mechanics, natural convection of air around a cable in a trench will follow three basic conservation laws: law of conservation of mass, law of conservation of momentum and law of conservation of energy:
Wherein: i is an identity matrix, eta is dynamic viscosity, and F is buoyancy force caused by density change;
4. Boundary conditions:
In the above calculation model, the boundary conditions are handled as follows: the deep soil boundary is a first type boundary, and the boundary far away from the left side and the right side of the calandria is a second type boundary; the surface-over air interface is a third type of boundary.
5. Model solving
In the calculation of the temperature field of the power cable, the distribution of the temperature field of the power cable is determined by the electromagnetic loss of the power cable, and the electromagnetic loss of the power cable is closely related to the conductivity, which is closely related to the temperature; under the calandria laying mode, the calculation of the temperature field of the power cable comprises three heat transfer modes of conduction, natural convection and radiation, and the three heat transfer modes need to be subjected to coupling solution. Therefore, the calculation of the calandria laid power cable temperature field is a magnetic-thermal-flow coupling field calculation process, the implementation flow is shown in fig. 3, namely, the initial temperature value is set firstly, then the conductivity at the current temperature is calculated, then the electromagnetic field equation is solved to obtain the electromagnetic loss, then the thermal flow coupling field equation is solved to obtain the temperature value, then whether the temperature difference meets the requirement is judged, if not, the electrical conductivity calculation process is returned, the calculation is repeated until the temperature difference meets the requirement, and after the temperature difference meets the requirement, the temperature field calculation result is output.
6. And (3) current-carrying capacity calculation:
The calculation of the current-carrying capacity of the cable duct is based on the calculation of a temperature field, and is the inverse process of the calculation of an electromagnetic field and the temperature field. The invention adopts a chord cut method to solve the current carrying capacity of the cable, namely when the highest temperature of the cable conductor reaches 90 ℃, the instantaneous current is defined as the current carrying capacity of the cable. The initial value of the current can be calculated by IEC60287 standard. And calculating the corresponding conductor temperature by solving the temperature field, and calculating the current-carrying capacity of the cable by adopting a chord cut method. In the iterative calculation, when the value of |T k -90| is smaller than 0.01 ℃, the conductor temperature of the cable is considered to be stabilized at the highest allowable temperature, and the current flowing through the cable is the current carrying capacity of the cable. The current-carrying capacity calculation flow chart is shown in fig. 4.
(4) Constructing a surface response model based on a support vector machine
In order to quickly calculate the current-carrying capacity of the cable duct, the invention adopts a surface response model based on a support vector machine to reconstruct the input-output relationship between an input variable (cable duct parameter) and an output variable (cable current-carrying capacity).
The function value y i of the function f at a series of sample point function values x i is known, thereby forming a data pair { (x 1,y1),(x2,y2),…,(xn,yn)}(x∈Rd, y ε R). The function f is based on the general approximation of SVMs:
f(x)＝f(x,w)＝<x,w>+b； (4)
Where </and > -represents the dot product of the two vectors.
To determine the coefficients w and b, the following ε -insensitive loss function is generally defined:
unlike other forms of loss functions, the solution of SV based on the above equation is sparse. From the epsilon-insensitive loss function, the parameters w and b are typically obtained by taking the extremum from the following equation:
A relaxation variable xi i is introduced which, The original data space original form 'private form' of SVM approximation is obtained by mathematical operation:
since the ill-posed problem usually occurs with this formula for numerical calculations, the following dual form corresponding to the feature space with formula (6) is defined and applied:
wherein alpha i and Is Lagrange multiplier.
According to mathematical theory, the solution of the quadratic programming problem corresponding to equation (8) is unique and can be obtained by means of any quadratic programming optimization algorithm. Therefore, formula (4) becomes:
according to Karush-Kuhn-Tucker conditions, only a small fraction of alpha i and Is not zero. Alpha i and/>, which are different from those of zeroThe corresponding data points are referred to as support vectors. Furthermore, as can be seen from mathematical theory, there must be a kernel function K (x i, x) in the input space corresponding to the inner product in the feature space. So by means of a kernel function, equation (9) can be further expressed as:
Wherein m is the number of support vectors, and x represents the cable bank parameters.
Thus, the function f is based on the approximate interpolation expression of the SVM: and (5) a surface response model.
Finally, inputting any cable arranging pipe parameter in a feasible interval by using the constructed surface response model, and rapidly calculating the cable carrying capacity under any cable arranging pipe parameter;
In summary, the invention firstly determines the design parameters of the cable duct and establishes a feasible interval of the parameters of the cable duct on the basis; secondly, uniformly sampling in a parameter feasible interval; thirdly, calculating the current-carrying capacity of the cable calandria at the sampling point by utilizing an electromagnetic-thermal-flow multi-field coupling model and combining a chord cut method; fourthly, reconstructing an input-output relationship between the cable management parameters and the cable current-carrying capacity by using a surface response model of the support vector machine; fifthly, substituting the design parameters of the cable duct in the new feasible interval into the reconstruction function, and calculating to obtain the current-carrying capacity under the new parameters. Therefore, the uniform sampling of the parameters adopted in the invention ensures that the invention is suitable for calculating the download flow of any parameter in the feasible parameter interval; the accuracy of the current-carrying capacity calculation result at the sampling point is ensured by combining an electromagnetic-thermal-flow multi-field coupling model and a chord cut method; in view of the strong function reconstruction capability of the support vector machine, the numerical matching precision of the reconstruction function and the original function is ensured. Therefore, the invention has good numerical precision for any parameter in a parameter feasible interval. The invention not only overcomes the defect that the prior method can not calculate the current-carrying capacity of the cable under any cable bank parameters; compared with the existing cable current-carrying capacity calculation method, the method and the device can ensure the accuracy of the current-carrying capacity calculation result, greatly reduce the calculation time and reduce the calculation cost.
Claims (8)
1. A rapid calculation method for the current-carrying capacity of a power cable bank is characterized by comprising the following steps: the method comprises the following steps:
Step 1, determining parameters of a cable rack and a value range of each parameter;
Step 2, sampling parameters in a parameter feasible interval;
step3, calculating the current-carrying capacity of the cable at the sampling point;
step 4, constructing a surface response model based on a support vector machine according to the data obtained in the steps 1 to 3;
And 5, rapidly calculating the current-carrying capacity of the cable under any cable arranging pipe parameter by using the constructed surface response model.
2. The rapid calculation method of power cable duct bank current capacity according to claim 1, wherein: the parameters of the cable duct comprise the outer diameter length of the cable duct and the distance from the left soil boundary and the right soil boundary to the center of the duct, and the values of the parameters are respectively as follows:
x1∈[280,300]；
x2∈[1800,2000]；
Wherein, the units are millimeter.
3. The rapid calculation method of power cable duct bank current capacity according to claim 1, wherein: in step 2, uniform sampling is adopted, and the number of adopted points is 100.
4. The rapid calculation method of power cable duct bank current capacity according to claim 1, wherein: the calculation of the current carrying capacity of the cable at the sampling point is to calculate the temperature field of the cable at the sampling point by adopting a magnetic-thermal-flow multi-physical field coupling model, and then calculate the current carrying capacity of the cable by an iterative procedure.
5. The method for quickly calculating the current-carrying capacity of the power cable duct according to claim 4, wherein: the magneto-thermal-flow multi-physical field coupling model comprises a vortex field, a temperature field, a fluid field and boundary conditions;
For the vortex field, the vector magnetic potential control equation under coulomb specification is:
Wherein: Is the current density,/> Is the vector magnetic potential, σ is the conductivity; /(I)Is Laplacian, μ is permeability; j is a complex number unit; omega is the angular frequency;
for the temperature field, the control equation is:
Wherein: ρ is the density of the material, C p is the solid heat capacity at constant pressure, u is the velocity vector of the fluid, k is the thermal conductivity, Q e is the heat generation in the solid, Q is the heat flux density, E is the electric field strength; is a gradient; t is the temperature; j is a current density vector;
for a fluid field, it follows three basic conservation laws:
Wherein: i is an identity matrix, eta is dynamic viscosity, and F is buoyancy force caused by density change;
For boundary conditions, the process is as follows:
Taking the deep soil boundary as a first type boundary, and taking the boundary far away from the left side and the right side of the calandria as a second type boundary; the surface-over-air interface acts as a third type of boundary.
6. The method for quickly calculating the current-carrying capacity of the power cable duct according to claim 5, wherein: the method comprises the steps of firstly setting a temperature initial value, then calculating conductivity at the current temperature, then solving an electromagnetic field equation to obtain electromagnetic loss, then solving a heat flow coupling field equation to obtain a temperature value, judging whether the temperature difference meets the requirement, returning to a conductivity calculation process if the temperature difference does not meet the requirement, repeatedly calculating until the temperature difference meets the requirement, and outputting a temperature field calculation result after the temperature difference meets the requirement.
7. The method for quickly calculating the current-carrying capacity of the power cable duct according to claim 6, wherein: solving the current carrying capacity of the cable by adopting a chord cut method, defining the instantaneous current 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 a temperature field, and calculating the current carrying capacity of the cable by adopting the chord cut method; in the iterative calculation, when the value of |T k -90| is smaller than 0.01 ℃, the conductor temperature of the cable is considered to be stabilized at the highest allowable temperature, and the current flowing through the cable is the current carrying capacity of the cable.
8. The rapid calculation method of power cable duct bank current capacity according to claim 1, wherein: the surface response model based on the support vector machine is expressed as follows:
Wherein: m is the number of support vectors, and x represents the parameters of the cable rack; alpha i For Lagrange multiplier, K (x i, x) represents the kernel function and b is the coefficient.
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