A method for constructing a simulation model of a three-phase high-temperature superconducting cable

Abstract

The application belongs to the technical field of cable simulation, and proposes a three-phase high-temperature superconducting cable simulation model construction method, which firstly establishes a lumped parameter model in PSCAD, and then calculates the temperature field and magnetic field distribution of the three-phase superconducting cable in real time according to the three-phase transmission current in MATLAB through the PSCAD and MATLAB interface. The parameters calculated by MATLAB are returned to PSCAD to realize the thermal-magnetic coupling simulation. The application is suitable for fault simulation verification of the three-phase high-temperature superconducting cable body, can effectively simulate the real thermal-magnetic characteristics of the cable body fault, has high calculation efficiency, balances the fidelity and simplicity, and has high engineering practical significance.

Description

Technical Field

[0001] This invention belongs to the field of cable simulation technology, specifically relating to a method for constructing a simulation model of a three-axis coaxial high-temperature superconducting cable. Background Technology

[0002] With the commercialization of second-generation high-temperature superconducting tapes, they can achieve unobstructed current carrying capacity and extremely low loss in the liquid nitrogen temperature range. Compared with conventional copper-aluminum cables, superconducting cables can increase the current carrying capacity by 3-5 times under the same cross-section, reduce losses by more than 60%, and have no electromagnetic heat leakage, providing a revolutionary solution for high-load-density power supply in cities and capacity expansion of old lines. Several demonstration lines have been put into operation globally, accumulating preliminary experience. However, high-temperature superconducting cables inevitably experience quenching faults due to various reasons during operation. Experimentally studying quenching faults within the cable itself is extremely costly and destructive. It requires pre-fabricating defects inside the cable to trigger quenching, which may lead to permanent damage to the entire cable. More importantly, experiments cannot measure the temperature, current density, and spatiotemporal evolution of the quench propagation front at arbitrary locations within the conductor layer. This "blind information" is precisely the key to understanding the fault mechanism and verifying protection schemes. Summary of the Invention

[0003] To address the aforementioned technical challenges and accurately simulate the precise thermo-magnetic field, magnetic field characteristics, and current distribution of a three-axis coaxial high-temperature superconducting cable during quenching, this invention proposes a method for constructing a simulation model of a three-axis coaxial high-temperature superconducting cable. The three-axis coaxial superconducting cable model established by this method can effectively simulate the true thermo-magnetic characteristics of the cable body during faults, boasts high computational efficiency, and balances fidelity with simplicity, thus possessing significant engineering practical value.

[0004] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0005] A method for constructing a simulation model of a three-axis coaxial high-temperature superconducting cable includes the following steps:

[0006] S1. Based on the dimensions of each phase of the three-phase coaxial superconducting cable and the dielectric constant of the interphase insulation material, obtain the fixed electrical parameters of the three-phase coaxial superconducting cable, including the unit self-inductance of the three phases and the shielding layer, the unit mutual inductance between them, the unit resistance of the shielding layer, and the unit capacitance between phases.

[0007] S2. Establish an electrical parameter model of a three-coaxial high-temperature superconducting cable in PSCAD, including lumped parameters. Each parameter is determined by S1. Write an interface program between PSCAD and MATLAB.

[0008] S3. Based on the coordinate system of the three coaxial superconducting cables, the temperature field matrix is ​​obtained. The cable temperature distribution is obtained in MATLAB from the data transmitted from PSCAD by the interface program in S2 and the temperature rise calculation expression.

[0009] S4. Based on the magnetic field coordinate system of the three coaxial superconducting cables, obtain the magnetic field distribution at the current moment in MATLAB.

[0010] S5. Based on the electrical characteristics of the superconducting tape selected for the cable, obtain the tape characteristic equation at the current moment to assist convergence, and solve it using MATLAB.

[0011] S6. Based on the solution obtained in S5, calculate the temperature, strip lumped resistance, and real-time magnetic field that need to be returned to PSCAD in MATLAB, and proceed to the next moment.

[0012] S7. Repeat steps S3, S4, and S6 in sequence until the last moment of the simulation, at which point the simulation ends.

[0013] The beneficial effects achieved by this invention are as follows:

[0014] (1) The actual heat generation during the operation of the three coaxial high-temperature superconducting cables was accurately quantified, which improved the accuracy of the thermal field in the simulation process;

[0015] (2) This invention uses PSCAD to establish an electrical parameter model and uses MATLAB to calculate the temperature field and magnetic field in real time, thus achieving transient simulation of cable body faults.

[0016] (3) This invention is applicable to the fault simulation verification of three coaxial high temperature superconducting cables. It can effectively simulate the real thermomagnetic characteristics when the cable body is faulty, with high calculation efficiency and a balance between fidelity and simplicity, and has high engineering practical significance. Attached Figure Description

[0017] Figure 1 This is a flowchart of a specific embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of the electrical parameter model of a three-coaxial high-temperature superconducting cable in a simulation of a specific embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of a three-axis coaxial high-temperature superconducting cable in a simulation of a specific embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram of the temperature rise at a certain point in phase C after a short-circuit fault occurs in the cable during a simulation in a specific embodiment of the present invention.

[0021] Figure 5This is a schematic diagram of the change in resistance of the C-phase superconducting layer after a short-circuit fault occurs in a cable during a simulation in a specific embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram showing the changes in phase voltage and phase current of each phase after a short-circuit fault occurs in a cable during a simulation in a specific embodiment of the present invention.

[0023] Figure 7 This is a schematic diagram of the current distribution of each layer of phase C after a short-circuit fault occurs in the cable in a specific embodiment of the present invention.

[0024] Figure 8 This is a schematic diagram of the magnetic field distribution of a superconducting tape at a certain point in phase C after a short-circuit fault occurs in a cable during a simulation in a specific embodiment of the present invention.

[0025] Figure 9 This is a schematic diagram of the change in lumped parameter resistance after a short-circuit fault occurs in a cable during a simulation in a specific embodiment of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0027] The electrical parameter model of the three coaxial high-temperature superconducting cables in the simulation is as follows: Figure 2 As shown, the electromagnetic coupling between conductors is represented by self-inductance and mutual inductance. Mutual inductance consists of the self-inductance of a certain phase conductor, the mutual inductance between conductors of different phases, and the mutual inductance of corresponding phase conductors and the shielding layer. Similarly, capacitance consists of the capacitance between adjacent phases. The lumped parameter resistance is composed of the resistance of the superconducting tape and the resistance of the copper stabilizing layer connected in parallel. A schematic diagram of the power grid structure where the three coaxial superconducting cables are located in the simulation is shown below. Figure 3 As shown, the total length L of the cable is 0.4 km.

[0028] like Figure 1 As shown, the present invention provides a method for constructing a simulation model of a three-coaxial high-temperature superconducting cable, comprising the following steps:

[0029] S1. Based on the dimensions of each phase of the three-phase coaxial superconducting cable and the dielectric constant of the interphase insulation material, obtain the fixed electrical parameters of the three-phase coaxial superconducting cable, including the unit self-inductance of the three phases and the shielding layer, the unit mutual inductance between them, the unit resistance of the shielding layer, and the unit capacitance between phases.

[0030] S2. Establish an electrical parameter model of a triaxial high-temperature superconducting cable in PSCAD, including lumped parameters or distributed parameters. A lumped parameter model is as follows: Figure 2 As shown, each parameter is determined by step S1. Write the interface program between PSCAD and MATLAB; this interface program is written in Fortran in PSCAD, defining the transfer matrix and return matrix.

[0031] S3. Based on the coordinate system of the three coaxial superconducting cables, the temperature field matrix is ​​obtained. Using data transmitted from PSCAD by the interface program in S2, and based on the temperature rise calculation expression, the cable temperature distribution is obtained in MATLAB; the m×n order temperature field matrix T is:

[0032]

[0033]

[0034] Where: subscript r0 is the radius of the three coaxial superconducting cables; superscript t0 is the total simulation duration; subscript r represents the radius of any point on the cable; and subscript t represents time t in the simulation. r t Let represent the temperature at a point with radius r at time t. Δt and Δr are the simulation step size and difference radius, respectively. The expression for temperature rise calculation is:

[0035]

[0036]

[0037] Where: ω t Let be the temperature field distribution vector at time t. For ω t-1 The first element of the vector, For ω t-1 The last element of the vector, element , and the actual temperature at that point , The relationship is:

[0038]

[0039] λ=(αΔt) / (Δr) 2 α is the thermal diffusivity of the cable material, ω t The temperature field distribution vector at time t is given by the elements of the L and U matrices:

[0040]

[0041] Where j = 1, 2, 3…n, when a current flows through a point on the radius, the heat generated is added as a heat source term to the temperature field vector for updating. The calculation expression is as follows:

[0042]

[0043] Where: i represents the differential point through which current flows on the radial axis, and N represents the number of differential points through which current flows; I iThis represents the equivalent current value flowing through the differential point, in A. i Let be the equivalent cross-sectional area at that point; ε(·) represents the step function, and k is the thermal conductivity of the material at that point. i This represents the radius of the differential point through which current flows;

[0044] The first and last columns of the temperature field matrix T cannot be calculated using the above formula; they must be calculated separately using the following expression:

[0045]

[0046] Where: h is the heat transfer coefficient with liquid nitrogen; T f K represents the temperature of the circulating liquid nitrogen. f The thermal conductivity of the material in contact with liquid nitrogen.

[0047] S4. Based on the magnetic field coordinate system of the three coaxial superconducting cables, obtain the current magnetic field distribution in MATLAB; the real-time magnetic field calculation expression is:

[0048]

[0049] Among them: B x For a magnetic field parallel to the superconducting tape, B y The magnetic field is perpendicular to the superconducting tape. (B) a For the axial magnetic field of the superconducting tape, B r Let θ be the circumferential magnetic field of the superconducting tape. θ is the winding angle of the tape. The circumferential magnetic field B on the inner surface of the i-th layer of the superconducting tape, counting from the inside out. r-in-i and axial magnetic field B a-in-i They are respectively:

[0050]

[0051]

[0052] Where: μ0 is the free permeability; r in-i Let I be the inner radius of the i-th superconducting tape layer; k Let r be the current flowing through the k-th layer of the superconducting tape. pk-i Let be the midpoint radius of the i-th layer of superconducting tape.

[0053] Circular magnetic field B on the outer surface of the i-th layer of superconducting tape counting from the inside out r-out-i and axial magnetic field B a-out-i They are respectively:

[0054]

[0055]

[0056] Where: r out-iLet be the outer radius of the i-th layer of superconducting tape.

[0057] S5. Based on the electrical characteristics of the superconducting tape used in the cable, the tape characteristic equation for the current moment used to assist convergence is obtained, and solved using MATLAB; the higher-order equation used to assist convergence is:

[0058]

[0059] Where: E0 is a constant representing the quench criterion, and b is a constant depending on the strip characteristics. C-A I C-B I C-C These represent the critical currents of the A, B, and C phases of the superconducting tape at the previous simulation step; I y-A I y-B I y-C These represent the currents flowing through the A, B, and C phases of the superconducting tape at the previous simulation step; R Cu-A R Cu-B R Cu-C These represent the resistances of the three-phase copper stabilization layers A, B, and C respectively, for the previous simulation step; I A I B I C These represent the currents flowing through phases A, B, and C respectively in the previous simulation step; the convergence equation solution for phase A must satisfy the following conditions:

[0060]

[0061] Where: Re(·) represents taking the real part of the complex number, Im(·) represents taking the imaginary part of the complex number; min(·) represents taking the minimum value. δ is a very small number, generally set to 10. -6 ~10 -8 q = 1, 2, 3…b represents b solutions to the above equation. The solutions selected for the B-phase convergent equation must satisfy the following conditions:

[0062]

[0063] The solution selected for the C-phase convergence equation must satisfy the following conditions:

[0064]

[0065] S6. Based on the solution obtained in S5, calculate the temperature, strip lumped resistance, and real-time magnetic field in MATLAB, which need to be returned to PSCAD. Obtain the current distribution at that moment in PSCAD, return to MATLAB, and repeat step 3 until the last moment of the simulation. The simulation ends here.

[0066] S7. Repeat steps S3, S4, and S6 in sequence until the last moment of the simulation, at which point the simulation ends.

[0067] To verify the effectiveness and reliability of this invention, a simulation model was built on PSCAD / EMDTC, an interface program was written, and programs for temperature rise and magnetic field distribution were written in MATLAB. Here, a short-circuit fault between the C phase and the shielding layer is used as an example to verify the performance of the simulation model. In the simulation, the liquid nitrogen temperature was 70K, the simulation step size was 1e-4 s, the fault start time was 0.06 s, and the fault duration was 0.1 s.

[0068] Simulation results are as follows Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 As shown, the present invention can realistically simulate the actual thermomagnetic characteristics and electrical characteristics of a three-coaxial high-temperature superconducting cable after a fault.

[0069] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A method for constructing a simulation model of a three-coaxial high-temperature superconducting cable, characterized in that: The method for constructing the simulation model of the three-axis coaxial high-temperature superconducting cable includes the following steps: S1. Based on the dimensions of each phase of the three-phase coaxial superconducting cable and the dielectric constant of the interphase insulation material, obtain the fixed electrical parameters of the three phases and the shield layer of the three-phase coaxial superconducting cable, as well as the unit self-inductance, the unit mutual inductance, the unit resistance of the shield layer, and the unit capacitance between phases. S2. Based on the parameters in S1, establish a lumped parameter electrical model of a three-coaxial high-temperature superconducting cable in PSCAD; write an interface program between PSCAD and MATLAB. S3. Based on the coordinate system of the three coaxial superconducting cables, the temperature field matrix is ​​obtained. The cable temperature distribution is obtained in MATLAB from the data transmitted from PSCAD by the interface program in S2 and the temperature rise calculation expression. S4. Based on the magnetic field coordinate system of the three coaxial superconducting cables, obtain the magnetic field distribution at the current moment in MATLAB. S5. Based on the electrical characteristics of the superconducting tape selected for the cable, obtain the tape characteristic equation at the current moment to assist convergence, and solve it using MATLAB. S6. Based on the solution obtained in S5, calculate the temperature, strip lumped resistance, and real-time magnetic field that need to be returned to PSCAD in MATLAB, and proceed to the next moment. S7. Repeat steps S3, S4, and S6 in sequence until the last moment of the simulation, at which point the simulation ends.

2. The method for constructing a simulation model of a three-coaxial high-temperature superconducting cable according to claim 1, characterized in that: In step S3, the temperature field matrix T of order m×n is: Where: r0 is the radius of the three coaxial superconducting cables; t0 is the total simulation duration; the subscript r represents the radius of any point on the cable, and t represents time t in the simulation; T r t Let represent the temperature at a point with radius r at time t; Δt and Δr are the simulation step size and the difference radius, respectively.

3. The method for constructing a simulation model of a three-coaxial high-temperature superconducting cable according to claim 2, characterized in that: The expression for calculating the temperature rise in step S3 is: Where: ω t Let be the temperature field distribution vector at time t; For ω t-1 The first element of the vector, For ω t-1 The last element of the vector, element , and the actual temperature at that point , The relationship is: λ=(αΔt) / (Δr) 2 α is the thermal diffusivity of the cable material; the elements in the L and U matrices are: Where j = 1, 2, 3…n, when a current flows through a point on the radius, the heat generated is added as a heat source term to the temperature field vector for updating. The calculation expression is as follows: Where: i represents the differential point through which current flows on the radial axis, and N represents the number of differential points through which current flows; I i This represents the equivalent current value flowing through the differential point, in A. i The equivalent cross-sectional area at that point; ε(·) represents the step function, k is the thermal conductivity of the material at that point; r i This represents the radius of the differential point through which current flows; The first and last columns of the temperature field matrix T are calculated separately, and the calculation expressions are as follows: Where: h is the heat transfer coefficient with liquid nitrogen; T f K represents the temperature of the circulating liquid nitrogen. f The thermal conductivity of the material in contact with liquid nitrogen.

4. The method for constructing a simulation model of a three-coaxial high-temperature superconducting cable according to claim 3, characterized in that: The higher-order equation used to aid convergence in step S5 is: Where: E0 is the quench criterion, which is a constant; b is a constant that depends on the strip characteristics; I C-A I C-B I C-C These represent the critical currents of the A, B, and C phases of the superconducting tape at the previous simulation step; I y-A I y-B I y-C These represent the currents flowing through the A, B, and C phases of the superconducting tape at the previous simulation step; R Cu-A R Cu-B R Cu-C These represent the resistances of the three-phase copper stabilization layers A, B, and C respectively, for the previous simulation step; I A I B I C These represent the currents flowing through phases A, B, and C respectively in the previous simulation step; the convergence equation solution for phase A must satisfy the following conditions: Where: Re(·) represents taking the real part of the complex number, Im(·) represents taking the imaginary part of the complex number; min(·) represents taking the minimum value; δ is set to 10. -6 ~10 -8 q = 1, 2, 3…b, representing b solutions to the above equation; the solutions selected for the phase B convergence equation must satisfy the following conditions: The solution selected for the C-phase convergence equation must satisfy the following conditions: 。

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