Rapid submarine cable temperature calculation method based on intrinsic orthogonal decomposition

Abstract

The invention discloses a submarine cable temperature rapid calculation method based on intrinsic orthogonal decomposition, and the method comprises the steps: S1, determining a sample space of submarine cable temperature, and obtaining a sample working condition data set; s2, node temperature column vectors of all sample working conditions are calculated based on the submarine cable simulation calculation model, a snapshot matrix is formed, and a base vector and a modal coefficient matrix of the submarine cable temperature field reduced-order model are obtained according to the snapshot matrix; s3, constructing a polynomial response surface model corresponding to the modal coefficient matrix and the sample working condition, and calculating a corresponding modal coefficient according to the input test working condition; and S4, reconstructing a submarine cable temperature field reduced-order model according to the basis vector and the modal coefficient. Compared with a finite element multi-physics field coupling calculation method for the submarine cable temperature, the calculation speed of the submarine cable temperature field reduced-order model is increased by about 800 times, the real-time requirement of cable temperature calculation in digital twin application can be met, and the accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of calculating the temperature distribution of submarine cables, and specifically relates to a method for quickly calculating the temperature of submarine cables based on proper orthogonal decomposition. Background Technique

[0002] Submarine cables are the power collection systems and transmission channels for offshore wind power, and are also widely used in island power supply, independent grid connection, power supply for offshore oil platforms, and short-distance power transmission across rivers and straits. The temperature of submarine cables is closely related to the operating state of submarine cables. How to more quickly and accurately determine the temperature distribution of submarine cables and then evaluate the operating state of submarine cables has become an urgent problem to be solved. At present, the research on solving the calculation problem of the electrothermal field of submarine cables by relying on traditional numerical simulation methods (such as the finite element method, the finite volume method, etc.) has been relatively mature. However, due to the high degree of freedom of traditional finite element models and the need to discretize both the spatial domain and the time domain simultaneously, the calculation amount is huge and the calculation time is up to the hour level, which is not applicable to digital twin models.

[0003] In order to further improve the calculation efficiency on the basis of ensuring the accuracy of traditional numerical calculation methods, scholars at home and abroad have proposed a method for constructing a reduced-order model of the electrothermal field of electrical equipment based on the proper orthogonal decomposition method. However, at present, the research on the reduced-order model of the electrothermal field of power equipment is still in its infancy, and the research on the reduced-order model of the temperature of submarine cables is still very scarce. Summary of the Invention

[0004] The purpose of the invention is to overcome the disadvantages and deficiencies existing in the prior art, and provide a method for quickly calculating the temperature of submarine cables based on proper orthogonal decomposition, which can realize the quick calculation of the temperature of submarine cables, and the method has good calculation accuracy and efficiency.

[0005] The purpose of the present invention is achieved by the following technical solutions:

[0006] A method for quickly calculating the temperature of submarine cables based on proper orthogonal decomposition includes the steps of:

[0007] S1. Determine the sample space of the temperature of the submarine cable and obtain the sample working condition data set of the temperature of the submarine cable;

[0008] S2. Calculate the column vector of the node temperature of each sample working condition based on the submarine cable simulation calculation model, form a snapshot matrix with the column vectors of the node temperature, and obtain the basis vector U' and the modal coefficient matrix α of the reduced-order model of the submarine cable temperature field according to the snapshot matrix;

[0009] S3. Construct a polynomial response surface model corresponding to the modal coefficient matrix α and the sample working condition, and calculate the corresponding modal coefficient α' according to the input test working condition based on the polynomial response surface model;

[0010] S4. Reconstruct the reduced-order model of the submarine cable temperature field based on the basis vectors U' obtained in step S2 and the modal coefficients α' obtained in step S3.

[0011] Preferably, step S1 specifically includes: selecting the three most significant factors affecting the temperature of the submarine cable, including the current-carrying capacity, seawater temperature, and seawater velocity, presetting the value ranges of each factor to form a sample space, and then obtaining a sample working condition data set through the Latin hypercube sampling method.

[0012] Preferably, step S2 specifically includes:

[0013] S21. Compose the snapshot matrix from the column vectors of each node temperature:

[0014] X = [x1, x2,..., x n , Equation (1),

[0015] where X is the snapshot matrix, and let x i be the column vector of node temperature, i ∈ [1, n];

[0016] S22. Perform singular value decomposition on the snapshot matrix:

[0017] X = U·Σ·V T , Equation (2),

[0018] where U = (ψ1, ψ2,... ψ n ), Σ = diag(λ1, λ2,... λ n ),

[0019] In the formula, U is the eigenvector matrix, ψ i is the eigenvector, Σ is the diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, and V T is the right orthogonal matrix;

[0020] S23. Arrange the eigenvalues λ i from largest to smallest, and select the eigenvectors corresponding to the first m eigenvalues to form the basis vectors U' of the reduced-order model of the submarine cable temperature field, where m ≤ n:

[0021] U' = (ψ1, ψ2,... ψ m ), Equation (3);

[0022] S24. Select the first m-order diagonal matrix ∑' and the first m-order right orthogonal matrix V' and obtain the modal coefficient matrix α:

[0023] α = V'·∑', Equation (4).

[0024] Preferably, in step S3, the polynomial response surface model takes the modal coefficient matrix as the output variable and the sample working conditions as the input variables, and fits the relationship between the modal coefficients and the sample working conditions with a polynomial function:

[0025]

[0026] where z i and z j are the i-th and j-th input variables, β0, β i , β ii , β ij are the coefficients to be determined, represents the modal coefficient matrix α.

[0027] Preferably, the expression for reconstructing the reduced-order model of the submarine cable temperature field in step S4 is:

[0028] x = U′α′, Equation (6),

[0029] where x represents the column vector of the submarine cable temperature under the input test working conditions.

[0030] Preferably, the construction of the submarine cable simulation calculation model specifically includes:

[0031] Modeling the 35kV three-core submarine cable using the finite element method and considering the influence of the submarine soil and seawater; the geometric model dimensions of the 35kV three-core submarine cable include a core diameter of 26.2mm, an insulation layer thickness of 24.0mm, a shielding layer thickness of 2.9mm, an armor thickness of 5.6mm, an inner sheath thickness of 2.9mm, and an outer sheath thickness of 3.5mm; the length of the submarine cable simulation calculation model is 5m, the width is 2m, and the height is 6m, where the water layer height is 2m and the soil layer height is 4m; the 35kV three-core submarine cable is buried, and the burial depth is 2m; the initial temperature of each layer of the cable and the environment is set to 25°C, and the geometric model boundary is set to thermal insulation with a normal heat flux density of 0.

[0032] Preferably, the first m eigenvalues need to satisfy:

[0033]

[0034] Preferably, the specific value range includes: the current-carrying capacity I ∈ [200, 700] A, the seawater temperature T ∈ [3, 30] °C, and the seawater velocity V ∈ [0, 1] m / s.

[0035] Preferably, the specific process of obtaining the sample working condition data set by the Latin hypercube sampling method is as follows: evenly divide the sample space intervals of the three dimensions of current-carrying capacity, seawater temperature, and seawater velocity into N layers, randomly take values in each layer, and then randomly match the values taken in each layer from each dimension to form N three-dimensional sample sampling points.

[0036] The present invention has the following advantages and effects compared with the prior art:

[0037] (1) The present invention provides a fast calculation method for the temperature of submarine cables based on proper orthogonal decomposition. First, a reduced-order model of the submarine cable temperature field is constructed based on the proper orthogonal decomposition method, and then the polynomial response surface method is used to establish the relationship between the modal coefficients of the reduced-order model and the sample working conditions of the submarine cable temperature, that is, a polynomial response surface model is obtained. The temperature of the submarine cable can be quickly calculated by inputting the sample working conditions of the submarine cable temperature. This method does not require solving the finite element equations with high degrees of freedom. Compared with the finite element multi-physics field coupling calculation method for the submarine cable temperature, the calculation speed of the reduced-order model of the submarine cable temperature field is increased by about 800 times, which can meet the real-time requirements of cable temperature calculation in digital twin applications and improve the accuracy.

[0038] (2) The present invention uses the polynomial response surface method to establish the relationship between the modal coefficients of the reduced-order model and the working conditions of the submarine cable, avoiding the bottleneck of still needing to solve the stiffness matrix in the traditional reduced-order algorithm and further improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a schematic flow chart of a fast calculation method for the temperature of submarine cables based on proper orthogonal decomposition of the present invention.

[0040] Figure 2 is a schematic structural diagram of a 35kV three-core submarine cable finite element model of the present invention.

[0041] Figure 3 is a schematic diagram of a finite element model of multi-physics field coupling of a 35kV three-core submarine cable in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The present invention will be further described in detail below with reference to the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0043] Embodiment 1

[0044] As Figure 1 shown is a schematic flow chart of a fast calculation method for the temperature of submarine cables based on proper orthogonal decomposition, including the steps:

[0045] S1. Determine the sample space of the submarine cable temperature and obtain the sample working condition data set of the submarine cable temperature;

[0046] Step S1 specifically includes: Selecting the three most significant factors affecting the temperature of the submarine cable, including the current-carrying capacity, seawater temperature, and seawater velocity, presetting the value ranges of each factor to form a sample space, and then obtaining a sample working condition data set through the Latin hypercube sampling method.

[0047] The specific value ranges include: the current-carrying capacity I ∈ [200, 700] A, the seawater temperature T ∈ [3, 30] °C, and the seawater velocity V ∈ [0, 1] m / s.

[0048] S2. Calculate the nodal temperature column vector of each sample working condition based on the submarine cable simulation calculation model, form a snapshot matrix with the nodal temperature column vectors, and obtain the basis vector U' and the modal coefficient matrix α of the reduced-order model of the submarine cable temperature field according to the snapshot matrix;

[0049] Step S2 specifically includes:

[0050] S21. Form a snapshot matrix with each nodal temperature column vector:

[0051] X = [x1, x2,..., x n , Equation (1),

[0052] where X is the snapshot matrix, and let x i be the nodal temperature column vector, i ∈ [1, n];

[0053] S22. Perform singular value decomposition on the snapshot matrix:

[0054] X = U·Σ·V T , Equation (2),

[0055] where U = (ψ1, ψ2,... ψ n ), Σ = diag(λ1, λ2,... λ n ),

[0056] In the formula, U is the eigenvector matrix, ψ i is the eigenvector, Σ is the diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, and V T is the right orthogonal matrix;

[0057] S23. Arrange the eigenvalues λ i from largest to smallest, and select the eigenvectors corresponding to the first m eigenvalues to form the basis vector U' of the reduced-order model of the submarine cable temperature field, where m ≤ n:

[0058] U' = (ψ1, ψ2,... ψ m ), Equation (3);

[0059] S24. Select the first m-order diagonal matrix ∑′ and the first m-order right orthogonal matrix V′, and obtain the modal coefficient matrix α:

[0060] α = V′·∑′, Equation (4).

[0061] Specifically, in this embodiment, in order to meet the requirement of reduced calculation accuracy, the first m eigenvalues need to satisfy:

[0062]

[0063] S3. Construct a polynomial response surface model corresponding to the modal coefficient matrix and the sample working conditions, and based on the polynomial response surface model, calculate the corresponding modal coefficient α′ according to the input test working conditions;

[0064] In step S3, the polynomial response surface model uses the modal coefficient matrix as the output variable and the sample working conditions as the input variable, and fits the relationship between the modal coefficient and the sample working conditions with a polynomial function:

[0065]

[0066] where z i 、z j are the i-th and j-th input variables, namely the current-carrying capacity, seawater temperature, and seawater velocity, β0, β i 、β ii 、β ij are the coefficients to be determined, represents the modal coefficient matrix α.

[0067] Specifically, in this embodiment, a response surface model of the three factors of the current-carrying capacity, seawater temperature, and seawater velocity and the modal coefficient is established as shown in Equation (5). Then, the input test working conditions are selected from the sample working condition dataset, and the corresponding modal coefficient α′ is output using this response surface model. The polynomial response surface method uses a mathematically simple polynomial function to describe the relationship between the input variables and the output variables, which is easy to understand and interpret. By adjusting the order of the polynomial, the complexity of the model can be flexibly adjusted to adapt to different degrees of non-linear relationships. Compared with other complex surrogate models, the polynomial response surface method has a lower computational cost, and combining it with the proper orthogonal decomposition method will improve the computational efficiency of the reduced-order model.

[0068] S4. Reconstruct the reduced-order model of the submarine cable temperature field according to the basis vector U‘ obtained in step S2 and the modal coefficient α′ obtained in step S3.

[0069] The expression for reconstructing the reduced-order model of the submarine cable temperature field in step S4 is:

[0070] x = U′α′, Equation (6),

[0071] Among them, \(x\) represents the column vector of the submarine cable temperature under the input test conditions.

[0072] Specifically, after reconstructing the reduced-order model of the submarine cable temperature field with the basis vector \(U'\) obtained in step S2 and the modal coefficient \(\alpha'\) obtained in step S3, that is, according to formula (6), the column vector of the submarine cable temperature corresponding to the input test conditions of the modal coefficient \(\alpha'\) is obtained, realizing the rapid calculation of the submarine cable temperature.

[0073] The specific process of obtaining the sample condition data set by the Latin hypercube sampling method includes: evenly dividing the sample space intervals of the three dimensions of current-carrying capacity, seawater temperature, and seawater velocity into \(N\) layers, randomly taking values in each layer, and then randomly matching the values taken in each layer from each dimension to form \(N\) three-dimensional sample sampling points.

[0074] The construction of the submarine cable simulation calculation model specifically includes:

[0075] Modeling the 35kV three-core submarine cable using the finite element method and considering the influence of the seabed soil and seawater; the geometric model dimensions of the 35kV three-core submarine cable include a cable core diameter of 26.2mm, an insulation layer thickness of 24.0mm, a shielding layer thickness of 2.9mm, an armor thickness of 5.6mm, an inner sheath thickness of 2.9mm, and an outer sheath thickness of 3.5mm; the length of the submarine cable simulation calculation model is 5m, the width is 2m, and the height is 6m, where the water layer height is 2m and the soil layer height is 4m; the 35kV three-core submarine cable is buried, and the burial depth is 2m; the initial temperature of each layer of the cable and the environment is set to 25°C, and the geometric model boundary is set to thermal insulation, with a normal heat flux density of 0.

[0076] Specifically, in this embodiment, the cable used is of the model

[0077] HYJYF41-F26 / 35ky3×70mm 2 +2×36B1, as Figure 2 shown in the structural schematic diagram of the 35kV three-core submarine cable finite element model. As Figure 3 shown in the schematic diagram of the 35kV three-core submarine cable multi-physical field coupling finite element model.

[0078] In summary, the present invention provides a method for rapidly calculating the temperature of submarine cables based on proper orthogonal decomposition. First, a reduced-order model of the submarine cable temperature field is constructed based on the proper orthogonal decomposition method, and then the polynomial response surface method is used to establish the relationship between the modal coefficients of the reduced-order model and the sample conditions of the submarine cable temperature, that is, a polynomial response surface model is obtained. The temperature of the submarine cable can be rapidly calculated by inputting the sample conditions of the submarine cable temperature. The traditional finite element model of multi-physical field coupling of submarine cables contains 271,526 degrees of freedom, and the time required to solve one simulation is 6,977 seconds. The time required for one calculation of the reduced-order model of the submarine cable temperature field of the present invention is 8.7 seconds, and the calculation efficiency is increased by about 800 times, which can meet the real-time requirements of cable temperature calculation in digital twin applications and improve the accuracy.

[0079] The above embodiments are preferred embodiments of the present invention and cannot limit the present invention. Any other changes or other equivalent replacement methods made without departing from the technical solutions of the present invention are included in the protection scope of the present invention.

Claims

1. A method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition, characterized in that: Includes steps: S1. Determine the sample space of the submarine cable temperature and obtain a sample operating condition data set of the submarine cable temperature; S2. Calculate the node temperature column vectors of each sample working condition based on the submarine cable simulation calculation model, form the node temperature column vectors into a snapshot matrix, and obtain the basis vector U′ and the modal coefficient matrix α of the submarine cable temperature field reduction model according to the snapshot matrix; S3, constructing a polynomial response surface model corresponding to the modal coefficient matrix α and the sample working condition, and calculating the corresponding modal coefficient α′ according to the input test working condition based on the polynomial response surface model; S4. Reconstruct the reduced-order model of the temperature field of the submarine cable according to the basis vector U' obtained in step S2 and the modal coefficient α' obtained in step S3.

2. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 1 is characterized in that: Step S1 specifically includes: selecting the three most significant factors affecting the temperature of the submarine cable, including current carrying capacity, seawater temperature and seawater velocity, and presetting the value range of each factor to form a sample space, and then obtaining a sample operating condition data set through the Latin hypercube sampling method.

3. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 1 is characterized in that: Step S2 specifically includes: S21. The temperature column vectors of each node are combined into a snapshot matrix: X=[x1,x2,…,x n ], formula (1), Where X is the snapshot matrix, let x i is the node temperature column vector, i∈[1,n]; S22. Perform singular value decomposition on the snapshot matrix: X = U Σ V T , Equation (2), Where, U=(ψ1,ψ2,…ψ n ),Σ=diag(λ1,λ2,…λ n ), Where U is the eigenvector matrix, ψ i is the eigenvector, Σ is a diagonal matrix, λ i is the eigenvalue corresponding to the eigenvector, v T is a right orthogonal matrix; S23, the eigenvalue λ i Arrange from large to small, and select the eigenvectors corresponding to the first m eigenvalues ​​to form the basis vector U' of the reduced-order model of the submarine cable temperature field, where m≤n: U'=(ψ1,ψ2,…ψ m ), expression(3); S24, select the first m-order diagonal matrix ∑′ and the first m-order right orthogonal matrix V′ and obtain the modal coefficient matrix α: α=V′·∑′, formula (4).

4. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 1 is characterized in that: In step S3, the polynomial response surface model uses the modal coefficient matrix as the output variable and the sample working condition as the input variable, and expresses the relationship between the modal coefficient and the sample working condition by fitting a polynomial function: Among them, z i 、z j are the i-th and j-th input variables, β0, β i , β ii , β ij is the coefficient to be determined, represents the modal coefficient matrix α.

5. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 1 is characterized in that: The expression of the reduced-order model of the submarine cable temperature field reconstructed in step S4 is: x=U′α′, formula (6), Where x represents the column vector of the temperature of the submarine cable under the input test conditions.

6. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 1 is characterized in that: The construction of the submarine cable simulation calculation model specifically includes: The finite element method is used to model the 35kV three-core submarine cable, and the influence of submarine soil and seawater is considered; the geometric model dimensions of the 35kV three-core submarine cable include cable core diameter 26.2mm, insulation layer thickness 24.0mm, shielding layer thickness 2.9mm, armor thickness 5.6mm, inner sheath thickness 2.9mm and outer sheath thickness 3.5mm; the length of the submarine cable simulation calculation model is 5m, the width is 2m, and the height is 6m, of which the water layer height is 2m and the soil layer height is 4m; the 35kV three-core submarine cable is buried with a burial depth of 2m; the initial temperature of each layer of the cable and the environment is set to 25℃, the boundary of the geometric model is set to thermal insulation, and the normal heat flux density is 0.

7. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 3 is characterized in that: The first m eigenvalues ​​must satisfy:

8. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 2 is characterized in that: The value range specifically includes: current carrying capacity I∈[200,700]A, seawater temperature T∈[3,30]℃, and seawater velocity V∈[0,1]m / s.

9. The method for rapid calculation of submarine cable temperature based on intrinsic orthogonal decomposition according to claim 2 is characterized in that: The method of obtaining the sample operating condition data set by the Latin hypercube sampling method specifically includes: evenly dividing the sample space intervals of the three dimensions of current carrying capacity, seawater temperature, and seawater velocity into N layers, randomly taking values ​​in each layer, and then randomly matching the randomly taken values ​​in each layer from each dimension to form N three-dimensional sample sampling points.

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