Calculation method, system, equipment and medium for sequence parameters of superconducting cable transmission lines

Abstract

The present invention discloses a method, system, device and medium for calculating sequence parameters of superconducting cable transmission lines, obtaining structural parameters and electrical property parameters of superconducting cables, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance; calculating the induced electric field and induced current density vector of the shielding layer based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; calculating the transmission current of the conductive layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable; and calculating the sequence parameters of the superconducting cable transmission line through the induced electric field and induced current density vector of the shielding layer and the transmission current coupling of the conductive layer and the shielding layer. The present invention establishes an analytical method for calculating the parameters of cold-insulated superconducting transmission lines, which has important theoretical value and practical significance.

Description

Technical Field

[0001] The present invention belongs to the field of superconducting cable power transmission, and in particular relates to a method, system, equipment and medium for calculating sequence parameters of a superconducting cable power transmission line. Background Art

[0002] Superconducting cables are characterized by low loss, compactness and large capacity. They are potential transformative technologies for power grids. A large number of basic research and grid-connected test demonstrations have been carried out at home and abroad. In 2000, the Southern Line Company of the United States connected the world's first 30m long, 12.5kV / 1.25kA three-phase all-in-one cold-insulated high-temperature superconducting cable to the grid. In 2014, Germany put into operation a 1km long, 10kV / 1kA three-phase coaxial superconducting cable. At present, Europe, the United States, Japan and South Korea have intensively carried out dozens of demonstration projects to systematically verify the technical performance of superconducting cables. In China, in 2003, Inna Superconducting connected the grid with a 33.5m, 35kV / 2kA thermal insulation high-temperature superconducting cable, which initially explored the grid-connected technology of thermal insulation superconducting cables; in 2013, Baosteel, where Shangcable is located, put into operation a three-phase split cold-insulated superconducting cable, marking that China has basically mastered the manufacturing technology of superconducting cables; in 2021, the superconducting cable transmission demonstration projects put into operation in Shanghai and Shenzhen respectively marked that superconducting cables have entered the actual grid-connected stage in China.

[0003] A typical cold-insulated superconducting cable includes an inner support, a cable conductor, a cryostat, an electrical insulation layer, a cable shielding layer, and an outer sheath. The biggest difference between a cold-insulated superconducting cable and a conventional cable is its shielding layer, which is generally made of the same superconducting tape as the conductor layer and is coaxially wound. During operation, the shielding layer is also in a low-temperature environment and is called a superconducting shielding layer. The function of the cold-insulated superconducting cable shielding layer is to shield the alternating magnetic field generated when the superconducting cable conductor transmits power. On the one hand, shielding the alternating magnetic field prevents the generation of induced currents in metal conductors such as cryostat, avoids eddy current losses, reduces cooling power, and reduces safety risks; on the other hand, it reduces the spacing between phases, saves the pipe gallery space occupied by cable laying, and improves the utilization efficiency of space.

[0004] Compared with conventional cables, superconducting shielding has two effects. First, under asymmetric faults inside and outside the line, the sum of the three-phase current transmitted is not zero, so the current entering the shielding layer is not zero, such as Figure 1 As shown, this will change the zero-sequence current of the power grid system. Secondly, the resistance of the superconducting shielding layer is very small, and it is well coupled with the conductive layer. In general, the induced current of the superconducting shielding layer is about 90% of the transmission current. The existence of the induced current reduces the cable line reactance. Both of these effects are related to the line sequence parameters of the superconducting cable. Therefore, it is necessary to establish a superconducting cable line sequence parameter analysis method considering the cold insulation superconducting shielding layer structure. Summary of the invention

[0005] The purpose of the present invention is to provide a method, system, equipment and medium for calculating the sequence parameters of a superconducting cable transmission line to overcome the defects of the prior art. The present invention establishes an analytical method for calculating the parameters of a cold-insulated superconducting transmission line, which has important theoretical value and practical significance.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] The calculation method of sequence parameters of superconducting cable transmission lines includes:

[0008] Acquiring structural parameters and electrical property parameters of the superconducting cable, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance;

[0009] The shielding layer induced electric field and induced current density vector are calculated based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; the conductive layer and shielding layer transmission current are calculated based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable;

[0010] The sequence parameters of superconducting cable transmission lines are calculated through the induced electric field and induced current density vector of the shielding layer and the transmission current coupling between the conducting layer and the shielding layer.

[0011] Furthermore, the two-dimensional equivalent magnetic field model of the superconducting cable is shown in formula (1):

[0012]

[0013] Where: μ is the magnetic permeability of the magnetic field; J e is the density vector of the external excitation current; J s is the induced current density vector; A is the vector magnetic potential; Compute the sign for the curl.

[0014] Furthermore, the calculation of the shielding layer induced electric field and induced current density vector based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable is specifically as follows:

[0015] According to the structural parameters of the superconducting cable, the edge finite element method is used to solve the overall interpolation function of the magnetic field region of the two-dimensional equivalent magnetic field model as shown in formula (2):

[0016]

[0017] Where: A is the vector magnetic potential, and the overall interpolation function is used here to represent the vector magnetic potential; N n (x, y, z) is the unit interpolation function; n is the unit number of the nth unit; n1 is the total number of units; A n represents the vector magnetic potential of each cell using an interpolation function;

[0018] According to Green's theorem, equation (2) is solved to obtain the Galerkin weighted residual equation in the corresponding magnetic field region:

[0019]

[0020] Where: N m , N n They represent the unit interpolation functions of the m-th unit and the n-th unit respectively; m represents the unit number of the m-th unit; J is the current density;

[0021] If the current distribution is known in the two-dimensional equivalent magnetic field model, the Galerkin weighted residual equation is discretized into a set of algebraic equations, and the vector magnetic potential A in the cross-sectional space of the superconducting cable is obtained by solving the set of algebraic equations.

[0022] The magnetic induction intensity B is obtained by using the vector magnetic potential A, as shown in formula (4):

[0023]

[0024] The electromagnetic induction law is used to solve the spatial induced electric field E, as shown in formula (5):

[0025]

[0026] The induced current density vector J is obtained by Ohm's law s , as shown in formula (6):

[0027] J s =σE (6)

[0028] Where σ is the electrical conductivity.

[0029] Furthermore, the equivalent circuit model includes three-phase power supplies A, B and C, and the three-phase power supplies A, B and C are connected through resistors R s It forms a loop with the conductive layer of the superconducting cable to form a conductive layer loop with a resistance R s Including power supply internal resistance and load resistance; the shielding layer of phases A, B and C is short-circuited at both ends and connected in series with resistance R g , forming a shielding layer loop, the resistor R g is the ground resistance.

[0030] The circuit equation of the conductive layer loop is shown in formula (7):

[0031]

[0032] Where: E A 、E B and E C are the power supply potentials of the conductive layer loop phases A, B and C respectively; I A ,I Band I C are the transmission currents of phases A, B and C of the conductive layer loops respectively; U A , U B and U C are the voltage drops across the conducting layers of the superconducting cables of phases A, B and C, respectively, obtained by the two-dimensional equivalent magnetic field model;

[0033] The circuit equation of the shielding layer loop is shown in formula (8):

[0034]

[0035] Where: U a , U b and U c They are the three-phase induced electromotive force of the shielding layer circuit a, b and c respectively; I a ,I b and I c are the transmission currents of the three phases of the shielding layer loop a, b and c, obtained from the two-dimensional equivalent magnetic field model; I g is the shielding layer loop ground current, when I a , I b and I c When the three phases are symmetrical, the ground current I g is 0.

[0036] Furthermore, the calculation of the sequence parameters of the superconducting cable transmission line by coupling the induced electric field and induced current density vector of the shielding layer and the transmission current of the conductive layer and the shielding layer specifically includes:

[0037] 1) Given the power supply potential at a certain moment, solve the transmission current of the superconducting cable conductive layer and shielding layer in the equivalent circuit model;

[0038] 2) Substitute the transmission current of the conductive layer and the shielding layer into the two-dimensional equivalent magnetic field model, and obtain the vector magnetic potential A and magnetic induction intensity B of the overall spatial magnetic field by solving equations (1) and (4). Then, the voltage drop U and the induced current density vector J of the conductive layer and the shielding layer are obtained by equations (5) and (6). s ;

[0039] 3) Substitute the voltage drop U of the conductive layer and the shielding layer into the equivalent circuit model, iterate steps 1) and 2) until the conductive layer current and the shielding layer current meet the convergence condition, and then proceed to step 4);

[0040] 4) Fit the conductive layer current and the shielding layer current to obtain the amplitude and phase;

[0041] 5) Dividing the vector values ​​of voltage and current to obtain the order parameter, wherein the vector value is composed of amplitude and phase.

[0042] Further, the superconducting cable transmission line sequence parameter calculation includes zero sequence impedance calculation and positive sequence impedance and negative sequence impedance calculation;

[0043] The calculation method of the positive sequence impedance is as follows:

[0044] Set the excitation power potential E A 、E B and E C The three phases are symmetrical, with a phase difference of 120°. By integrating the current density in the A, B and C phase regions, I A ,I B and I C The curve that changes with time, I A ,I B and I C The curve that changes with time, intercepts the steady-state part, and fits it according to the sine curve, as shown in formula (9):

[0045] I1=a1sin(b1t+c1) (9)

[0046] Where: t is time; a1 represents the positive sequence current amplitude; b1 is the positive sequence angular frequency; c1 is the positive sequence phase, and the I1 obtained by fitting is the transmission current of the conductive layer loop A, B and C phases;

[0047] Assume that the positive sequence impedance of the superconducting cable is:

[0048] Z1=R1+jX1 (10)

[0049] Where, Z1 is the positive sequence impedance; R1 is the positive sequence resistance; X1 is the positive sequence reactance; j is an imaginary number;

[0050] Substituting equation (9) and equation (10) into equation (7), we obtain:

[0051]

[0052] Substituting the fitted formula (9) into formula (11), the positive sequence impedance formula is:

[0053]

[0054] The negative sequence impedance is equal to the positive sequence impedance;

[0055] The calculation method of the zero-sequence impedance is as follows:

[0056] Set the excitation power potential E A 、E B and E C The amplitude and phase of the simulation are equal, and the integral is used to obtain I A ,I B and I CThe curve that changes with time is fitted by intercepting the steady-state part, as shown in formula (13):

[0057] I0=a0sin(b0t+c0) (13)

[0058] In the formula, a0 represents the zero-sequence current amplitude, b0 is the zero-sequence angular frequency, c0 is the zero-sequence phase, and the I0 obtained by fitting is the zero-sequence current of phase A, B or C;

[0059] Let the zero-sequence impedance of the superconducting cable be:

[0060] Z0=R0+jX0 (14)

[0061] In the formula, Z0 is zero-sequence impedance; R0 is zero-sequence resistance; X0 is zero-sequence reactance;

[0062] Assuming that the voltage across the superconducting cable is U0, then:

[0063] U0=E A -I0R s (15)

[0064] The zero-sequence impedance is:

[0065]

[0066] Substitute the fitted formula (13) into formula (16) and combine it with formula (15) to calculate the zero-sequence impedance:

[0067]

[0068] The calculation system of sequence parameters of superconducting cable transmission line includes:

[0069] Parameter acquisition module: used to obtain the structural parameters and electrical property parameters of the superconducting cable, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance;

[0070] Intermediate quantity calculation module: used to calculate the shielding layer induced electric field and induced current density vector based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; calculate the transmission current of the conductive layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable;

[0071] Sequence parameter calculation module: used to calculate the sequence parameters of superconducting cable transmission lines through the induced electric field and induced current density vector of the shielding layer and the transmission current coupling between the conductive layer and the shielding layer.

[0072] Furthermore, the two-dimensional equivalent magnetic field model of the superconducting cable is shown in formula (1):

[0073]

[0074] Where: μ is the magnetic permeability of the magnetic field; J e is the density vector of the external excitation current; J s is the induced current density vector; A is the vector magnetic potential; Compute the sign for the curl.

[0075] Furthermore, the calculation of the shielding layer induced electric field and induced current density vector based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable is specifically as follows:

[0076] According to the structural parameters of the superconducting cable, the edge finite element method is used to solve the overall interpolation function of the magnetic field region of the two-dimensional equivalent magnetic field model as shown in formula (2):

[0077]

[0078] Where: A is the vector magnetic potential, and the overall interpolation function is used here to represent the vector magnetic potential; N n (x, y, z) is the unit interpolation function; n is the unit number of the nth unit; n1 is the total number of units; A n represents the vector magnetic potential of each cell using an interpolation function;

[0079] According to Green's theorem, equation (2) is solved to obtain the Galerkin weighted residual equation in the corresponding magnetic field region:

[0080]

[0081] Where: N m , N n They represent the unit interpolation functions of the m-th unit and the n-th unit respectively; m represents the unit number of the m-th unit; J is the current density;

[0082] If the current distribution is known in the two-dimensional equivalent magnetic field model, the Galerkin weighted residual equation is discretized into a set of algebraic equations, and the vector magnetic potential A in the cross-sectional space of the superconducting cable is obtained by solving the set of algebraic equations.

[0083] The magnetic induction intensity B is obtained by using the vector magnetic potential A, as shown in formula (4):

[0084]

[0085] The electromagnetic induction law is used to solve the spatial induced electric field E, as shown in formula (5):

[0086]

[0087] The induced current density vector J is obtained by Ohm's law s , as shown in formula (6):

[0088] Js =σE (6)

[0089] Where σ is the electrical conductivity.

[0090] Furthermore, the equivalent circuit model includes three-phase power supplies A, B and C, and the three-phase power supplies A, B and C are connected through resistors R s It forms a loop with the conductive layer of the superconducting cable to form a conductive layer loop with a resistance R s Including power supply internal resistance and load resistance; the shielding layer of phases A, B and C is short-circuited at both ends and connected in series with resistance R g , forming a shielding layer loop, the resistor R g is the ground resistance.

[0091] Furthermore, the circuit equation of the conductive layer loop is shown in formula (7):

[0092]

[0093] Where: E A 、E B and E C are the power supply potentials of the conductive layer loop phases A, B and C respectively; I A ,I B and I C are the transmission currents of phases A, B and C of the conductive layer loops respectively; U A , U B and U C are the voltage drops across the conducting layers of the superconducting cables of phases A, B and C, respectively, obtained by the two-dimensional equivalent magnetic field model;

[0094] The circuit equation of the shielding layer loop is shown in formula (8):

[0095]

[0096] Where: U a , U b and U c They are the three-phase induced electromotive force of the shielding layer circuit a, b and c respectively; I a ,I b and I c are the transmission currents of the three phases of the shielding layer loop a, b and c, obtained from the two-dimensional equivalent magnetic field model; I g is the shielding layer loop ground current, when I a , I b and I c When the three phases are symmetrical, the ground current I g is 0.

[0097] Furthermore, the calculation of the sequence parameters of the superconducting cable transmission line by coupling the induced electric field and induced current density vector of the shielding layer and the transmission current of the conductive layer and the shielding layer specifically includes:

[0098] 1) Given the power supply potential at a certain moment, solve the transmission current of the superconducting cable conductive layer and shielding layer in the equivalent circuit model;

[0099] 2) Substitute the transmission current of the conductive layer and the shielding layer into the two-dimensional equivalent magnetic field model, and obtain the vector magnetic potential A and magnetic induction intensity B of the overall spatial magnetic field by solving equations (1) and (4). Then, the voltage drop U and the induced current density vector J of the conductive layer and the shielding layer are obtained by equations (5) and (6). s ;

[0100] 3) Substitute the voltage drop U of the conductive layer and the shielding layer into the equivalent circuit model, iterate steps 1) and 2) until the conductive layer current and the shielding layer current meet the convergence condition, and then proceed to step 4);

[0101] 4) Fit the conductive layer current and the shielding layer current to obtain the amplitude and phase;

[0102] 5) Dividing the vector values ​​of voltage and current to obtain the order parameter, wherein the vector value is composed of amplitude and phase.

[0103] Further, the superconducting cable transmission line sequence parameter calculation includes zero sequence impedance calculation and positive sequence impedance and negative sequence impedance calculation;

[0104] The calculation method of the positive sequence impedance is as follows:

[0105] Set the excitation power potential E A 、E B and E C The three phases are symmetrical, with a phase difference of 120°. By integrating the current density in the A, B and C phase regions, I A ,I B and I C The curve that changes with time, I A ,I B and I C The curve that changes with time, intercepts the steady-state part, and fits it according to the sine curve, as shown in formula (9):

[0106] I1=a1sin(b1t+c1) (9)

[0107] Where: t is time; a1 represents the positive sequence current amplitude; b1 is the positive sequence angular frequency; c1 is the positive sequence phase, and the I1 obtained by fitting is the transmission current of the conductive layer loop A, B and C phases;

[0108] Assume that the positive sequence impedance of the superconducting cable is:

[0109] Z1=R1+jX1 (10)

[0110] Where, Z1 is the positive sequence impedance; R1 is the positive sequence resistance; X1 is the positive sequence reactance; j is an imaginary number;

[0111] Substituting equation (9) and equation (10) into equation (7), we obtain:

[0112]

[0113] Substituting the fitted formula (9) into formula (11), the positive sequence impedance formula is:

[0114]

[0115] The negative sequence impedance is equal to the positive sequence impedance;

[0116] The calculation method of the zero-sequence impedance is as follows:

[0117] Set the excitation power potential E A 、E B and E C The amplitude and phase of the simulation are equal, and the integral is used to obtain I A ,I B and I C The curve that changes with time is fitted by intercepting the steady-state part, as shown in formula (13):

[0118] I0=a0sin(b0t+c0) (13)

[0119] In the formula, a0 represents the zero-sequence current amplitude, b0 is the zero-sequence angular frequency, c0 is the zero-sequence phase, and the I0 obtained by fitting is the zero-sequence current of phase A, B or C;

[0120] Let the zero-sequence impedance of the superconducting cable be:

[0121] Z0=R0+jX0 (14)

[0122] In the formula, Z0 is zero-sequence impedance; R0 is zero-sequence resistance; X0 is zero-sequence reactance;

[0123] Assuming that the voltage across the superconducting cable is U0, then:

[0124] U0=E A -I0R s (15)

[0125] The zero-sequence impedance is:

[0126]

[0127] Substitute the fitted formula (13) into formula (16) and combine it with formula (15) to calculate the zero-sequence impedance:

[0128]

[0129] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for calculating the sequence parameters of a superconducting cable transmission line when executing the computer program.

[0130] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for calculating the sequence parameters of a superconducting cable transmission line.

[0131] Compared with the prior art, the present invention has the following beneficial technical effects:

[0132] Different from conventional cables, the zero resistance characteristics of superconducting power transmission and the strong coupling characteristics of the conductive layer / shielding layer make the line parameter characteristics of superconducting power transmission have new features. The present invention calculates the induced electric field and induced current density vector of the shielding layer based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; calculates the transmission current of the conductive layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable, and then calculates the positive sequence, negative sequence and zero sequence line parameters of the superconducting transmission line through the induced electric field and induced current density vector of the shielding layer and the transmission current coupling of the conductive layer and the shielding layer. It can provide an important basis for calculating system short-circuit current, relay protection setting, power system flow calculation and selecting a reasonable operation mode, etc., and has important theoretical value and practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] The drawings in the specification are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0134] Figure 1 This is a wiring diagram of a three-core superconducting cable system;

[0135] Figure 2 It is a schematic diagram of the process of the present invention;

[0136] Figure 3 It is a schematic diagram of the system structure of the present invention;

[0137] Figure 4 This is a schematic diagram of the magnetic field calculation model for cold-insulated three-phase superconducting cables;

[0138] Figure 5 It is a schematic diagram of the circuit model of a three-phase superconducting cable;

[0139] Figure 6 This is the relationship diagram between the positive sequence reactance of the cable and the shield resistance;

[0140] Figure 7 This is the relationship diagram between the cable zero-sequence reactance and the shield resistance. DETAILED DESCRIPTION

[0141] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0142] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0143] The present invention calculates and analyzes line sequence parameters based on the superconducting cable time-domain field-circuit coupling electromagnetic model, such as Figure 2 The equivalent circuit model calculates the transmission current of the conductive layer and the shielding layer, the two-dimensional equivalent magnetic field model calculates the induced electric field and the induced current density vector of the shielding layer, and the line sequence parameters of the superconducting cable are calculated by coupling the induced electric field and the induced current density vector of the shielding layer and the transmission current of the conductive layer and the shielding layer.

[0144] The present invention has the following assumptions for the time-domain field-path coupled electromagnetic model of superconducting cables:

[0145] 1) The time-domain field-circuit coupled electromagnetic model of the present invention does not consider the influence of the nonlinear resistance of the superconductor on the line impedance, but focuses on the reactance analysis method of the line.

[0146] 2) Ignore the magnetic field effect of the ground current, that is, do not consider the mutual inductance between the ground current and the superconducting conductive layer and the superconducting shielding layer.

[0147] 3) Ignore the influence of superconducting cable winding parameters and use the two-dimensional model of the cable cross section as the magnetic field simulation object.

[0148] Two-dimensional equivalent magnetic field model

[0149] The electromagnetic induction relationship between the conductive layer and the shielding layer of the superconducting cable is analyzed based on the two-dimensional equivalent magnetic field model. Figure 4 As shown, the edge finite element method and vector magnetic potential A are used to establish a two-dimensional equivalent magnetic field model of the superconducting cable:

[0150]

[0151] Where: μ is the magnetic permeability of the magnetic field, which characterizes the magnetic properties of the medium; J e is the density vector of the external excitation current, which represents the magnitude and direction of the excitation current; J s is the induced current density vector, which represents the magnitude and direction of the induced current; Compute the sign for the curl.

[0152] According to the structural parameters of the superconducting cable, the edge finite element method is used to solve the overall interpolation function of the magnetic field region of the two-dimensional equivalent magnetic field model:

[0153]

[0154] Where: A is the vector magnetic potential, and the overall interpolation function is used here to represent the vector magnetic potential; N n (x, y, z) is the unit interpolation function; n is the unit number of the nth unit; n1 is the total number of units; A n Represents the vector magnetic potential of each cell using an interpolation function.

[0155] Solving equation (2) according to Green's theorem, we can obtain the Galerkin weighted residual equation in the corresponding magnetic field region:

[0156]

[0157] Where: N m , N n They represent the unit interpolation functions of the m-th unit and the n-th unit respectively; m represents the unit number of the m-th unit; and J is the current density.

[0158] If the current distribution is known in the two-dimensional equivalent magnetic field model, the Galerkin weighted residual equation is discretized into a set of algebraic equations, and the vector magnetic potential A in the cross-sectional space of the superconducting cable can be obtained by solving it.

[0159] The magnetic induction intensity B is obtained by using the vector magnetic potential A:

[0160]

[0161] Using the law of electromagnetic induction to solve the spatial induced electric field E

[0162]

[0163] After obtaining the induced electric field E of the shielding layer, the induced current density vector J can be obtained by Ohm's law. s ;

[0164] J s =σE (6)

[0165] Where σ is the conductivity.

[0166] Equivalent circuit model

[0167] The equivalent circuit model is as follows Figure 5 As shown, the three-phase power supply passes through the resistor R s The conductive layer of the superconducting cable forms a loop, called a conductive layer loop, with a resistance R s Including power supply internal resistance and load resistance; the shielding layer of phases A, B and C is short-circuited at both ends and connected in series with resistance R g , called the shielding layer loop, resistance R g Mainly including ground resistance. In the simulation calculation of the present invention, the cable length l is 1 km.

[0168] The circuit equation of the conductive layer loop is

[0169]

[0170] Where: E A 、E B and E C are the power supply potentials of the conductive layer loop phases A, B and C respectively; I A ,I B and I C are the transmission currents of phase A, B and C respectively; U A , U B and U C They are the voltage drops across the conducting layers of the superconducting cables of phases A, B and C, obtained by the two-dimensional equivalent magnetic field model.

[0171] Similarly, the circuit equation of the shielding layer loop is

[0172]

[0173] Where: U a , U b and U c They are the three-phase induced electromotive force of the shielding layer circuit a, b and c respectively; I a ,I b and I care the transmission currents of the three phases of the shielding layer loop a, b and c, obtained through the magnetic field model; I g is the current entering the ground of the shielding layer loop. Obviously, when I a , I b and I c When the three phases are symmetrical, the ground current I g is 0.

[0174] The solution of the time-domain field-circuit coupled electromagnetic model includes the following steps:

[0175] 1) Given the power supply potential at a certain moment, solve the transmission current of the superconducting cable conductive layer and shielding layer in the equivalent circuit model.

[0176] 2) Substitute the transmission current of the conductive layer and the shielding layer into the two-dimensional equivalent magnetic field model, and obtain the vector magnetic potential A and magnetic induction intensity B of the overall spatial magnetic field by solving equations (1) and (4). Then, the voltage drop U (which is equal to the spatial induced electric field E per unit length) and the induced current density vector J of the conductive layer and the shielding layer are obtained by equations (5) and (6). s .

[0177] 3) Substitute the voltage drop U of the conductive layer and the shielding layer into the equivalent circuit model, iterate steps 1) and 2) until the conductive layer current and the shielding layer current meet the convergence condition, and then proceed to step 4);

[0178] 4) Fit the conductive layer current and the shielding layer current to obtain the amplitude and phase;

[0179] 5) Dividing the vector values ​​of voltage and current to obtain the order parameter, wherein the vector value is composed of amplitude and phase.

[0180] Positive sequence parameter calculation method

[0181] The extraction method of superconducting cable sequence parameters refers to the actual measurement method of line sequence parameters in engineering. In engineering, the line sequence parameters are obtained by short-circuiting the A, B and C phases at one end of the line, injecting a three-phase voltage source at the other end, and measuring the voltage, current and power of the line.

[0182] In the time-domain field-circuit coupled electromagnetic model, the basic idea is to obtain the currents of phases A, B, and C of the superconducting cable through the excitation of a three-phase voltage source, and then calculate the equivalent positive and negative sequence and equivalent zero-sequence parameters of the superconducting cable.

[0183] For cables, the positive-sequence impedance is equal to the negative-sequence impedance, and the positive-sequence impedance is used as an example to explain below.

[0184] In the calculation of positive sequence parameters, the excitation power supply potential E is set A 、E B and E CThe three phases are symmetrical, with a phase difference of 120°. The magnetic field distribution is obtained after the field-circuit coupling model simulation calculation. By integrating the current density in the A, B and C phase regions, I A ,I B and I C The curve changes with time. A ,I B and I C The curve over time, intercepting the steady-state part, is fitted according to the sine curve:

[0185] I1=a1sin(b1t+c1) (9)

[0186] Where: t is time; a1 represents the positive sequence current amplitude; b1 is the positive sequence angular frequency; c1 is the positive sequence phase, and the I1 obtained by fitting is the transmission current of the conductive layer loop A, B and C phases.

[0187] Assume that the positive sequence impedance of the superconducting cable is

[0188] Z1=R1+jX1 (10)

[0189] Where, Z1 is the positive-sequence impedance; R1 is the positive-sequence resistance; X1 is the positive-sequence reactance; j is an imaginary number.

[0190] Substituting equation (9) and equation (10) into equation (7), we can obtain:

[0191]

[0192] Substituting the fitted formula (9) into formula (11), the impedance formula is:

[0193]

[0194] Zero sequence parameter calculation method

[0195] In the zero-sequence parameter calculation, set the excitation power supply potential E A 、E B and E C For equal amplitude and same phase, simulation calculation is performed and I is obtained by integration. A ,I B and I C The curve that changes with time is fitted after intercepting the steady-state part:

[0196] I0=a0sin(b0t+c0) (13)

[0197] Similarly, a0 represents the zero-sequence current amplitude, b0 is the zero-sequence angular frequency, c0 is the zero-sequence phase, and the I0 obtained by fitting is the zero-sequence current of phase A, B or C.

[0198] Let the zero-sequence impedance of the superconducting cable be

[0199] Z0=R0+jX0 (14)

[0200] In the formula, Z0 is zero-sequence impedance; R0 is zero-sequence resistance; X0 is zero-sequence reactance;

[0201] Assuming that the voltage across the superconducting cable is U0, then

[0202] U0=E A -I0R s (15)

[0203] The zero sequence parameter is

[0204]

[0205] Substituting the fitted formula (13) into formula (16) and combining it with formula (15), the zero-sequence impedance is calculated as

[0206]

[0207] The present invention also provides a system for calculating sequence parameters of a superconducting cable transmission line, such as Figure 3 ,include:

[0208] Parameter acquisition module: used to obtain the structural parameters and electrical property parameters of the superconducting cable, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance;

[0209] Intermediate quantity calculation module: used to calculate the shielding layer induced electric field and induced current density vector based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; calculate the transmission current of the conductive layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable;

[0210] Sequence parameter calculation module: used to calculate the sequence parameters of superconducting cable transmission lines through the induced electric field and induced current density vector of the shielding layer and the transmission current coupling between the conductive layer and the shielding layer.

[0211] Example

[0212] Based on the method of the present invention, the sequence parameters of the superconducting transmission line can be calculated according to the parameters in Table 1 combined with the finite element analysis method and the circuit analysis method, as shown in Table 2.

[0213] Table 1 Structural parameters and electrical properties of superconducting cables

[0214]

[0215]

[0216] Table 2 Sequence parameters of superconducting transmission lines

[0217]

[0218] When the shielding layer resistance is 0, the sequence parameter of the superconducting transmission line is obtained, and then the relationship between the positive sequence reactance of the cable and the shielding layer resistance is obtained by changing the shielding layer resistance value (such as Figure 6 ) and the relationship between the cable zero-sequence reactance and the shield resistance (such as Figure 7 ).

[0219] The accuracy of the positive-sequence impedance parameters and zero-sequence impedance parameters of superconducting cables is related to the safe and stable operation of the power grid, and is the basis for calculating system short-circuit current, relay protection setting, power system flow calculation and selecting a reasonable operation mode. The present invention can provide an important basis for calculating system short-circuit current, relay protection setting, power system flow calculation and selecting a reasonable operation mode by calculating the positive-sequence, negative-sequence and zero-sequence line parameters of superconducting transmission lines, and has important theoretical value and practical significance.

[0220] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0221] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0222] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0223] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit its protection scope. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that after reading the present invention, those skilled in the art can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the pending claims of the invention.

Claims

1. A method for calculating sequence parameters of a superconducting cable transmission line, characterized in that: include: Acquiring structural parameters and electrical property parameters of the superconducting cable, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance; The shielding layer induced electric field and induced current density vector are calculated based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; Calculate the transmission current of the conducting layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable; The two-dimensional equivalent magnetic field model of the superconducting cable is shown in formula (1): Where: μ is the magnetic permeability of the magnetic field; J e is the density vector of the external excitation current; J s is the induced current density vector; A is the vector magnetic potential; Compute the sign for the curl; The shielding layer induced electric field and induced current density vector are calculated based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable, specifically: According to the structural parameters of the superconducting cable, the edge finite element method is used to solve the overall interpolation function of the magnetic field region of the two-dimensional equivalent magnetic field model as shown in formula (2): Where: A is the vector magnetic potential, and the overall interpolation function is used here to represent the vector magnetic potential; N n (x, y, z) is the unit interpolation function; n is the unit number of the nth unit; n1 is the total number of units; A n represents the vector magnetic potential of each cell using an interpolation function; According to Green's theorem, equation (2) is solved to obtain the Galerkin weighted residual equation in the corresponding magnetic field region: Where: N m， N n They represent the unit interpolation functions of the m-th unit and the n-th unit respectively; m represents the unit number of the m-th unit; J is the current density; If the current distribution is known in the two-dimensional equivalent magnetic field model, the Galerkin weighted residual equation is discretized into a set of algebraic equations, and the vector magnetic potential A in the cross-sectional space of the superconducting cable is obtained by solving the set of algebraic equations. The magnetic induction intensity B is obtained by using the vector magnetic potential A, as shown in formula (4): The electromagnetic induction law is used to solve the spatial induced electric field E, as shown in formula (5): The induced current density vector J is obtained by Ohm's law s , as shown in formula (6): J s =σE (6) Where σ is the conductivity; The equivalent circuit model includes three-phase power supplies A, B and C, and the three-phase power supplies A, B and C are connected through resistors R s It forms a loop with the conductive layer of the superconducting cable to form a conductive layer loop with a resistance R s Including power supply internal resistance and load resistance; the shielding layer of phases A, B and C is short-circuited at both ends and connected in series with resistance R g , forming a shielding layer loop, the resistor R g is the grounding resistance; The circuit equation of the conductive layer loop is shown in formula (7): Where: E A 、E B and E C are the power supply potentials of the conductive layer loop phases A, B and C respectively; I A ,I B and I C are the transmission currents of phases A, B and C of the conductive layer loops respectively; U A , U B and U C are the voltage drops across the conducting layers of the superconducting cables of phases A, B and C, respectively, obtained by the two-dimensional equivalent magnetic field model; The circuit equation of the shielding layer loop is shown in formula (8): Where: U a , U b and U c They are the three-phase induced electromotive force of the shield layer circuit a, b and c respectively; I a ,I b and I c are the transmission currents of the three phases of the shielding layer loop a, b and c, obtained from the two-dimensional equivalent magnetic field model; I g is the shielding layer loop ground current, when I a , I b and I c When the three phases are symmetrical, the ground current I g is 0; The sequence parameters of the superconducting cable transmission line are calculated by coupling the induced electric field and induced current density vector of the shielding layer and the transmission current of the conductive layer and the shielding layer, including: 1) Given the power supply potential at a certain moment, solve the transmission current of the superconducting cable conductive layer and shielding layer in the equivalent circuit model; 2) Substitute the transmission current of the conductive layer and the shielding layer into the two-dimensional equivalent magnetic field model, and obtain the vector magnetic potential A and magnetic induction intensity B of the overall spatial magnetic field by solving equations (1) and (4). Then, the voltage drop U and the induced current density vector J of the conductive layer and the shielding layer are obtained by equations (5) and (6). s ; 3) Substitute the voltage drop U of the conductive layer and the shielding layer into the equivalent circuit model, iterate steps 1) and 2) until the conductive layer current and the shielding layer current meet the convergence condition, and then proceed to step 4); 4) Fit the conductive layer current and the shielding layer current to obtain the amplitude and phase; 5) Dividing the vector values ​​of voltage and current to obtain an order parameter, wherein the vector value is composed of an amplitude and a phase; The superconducting cable transmission line sequence parameter calculation includes zero sequence impedance calculation and positive sequence impedance and negative sequence impedance calculation; The calculation method of the positive sequence impedance is as follows: Set the excitation power potential E A 、E B and E C The three phases are symmetrical, with a phase difference of 120°. By integrating the current density in the A, B and C phase regions, I A ,I B and I C The curve that changes with time, I A ,I B and I C The curve that changes with time, intercepts the steady-state part, and fits it according to the sine curve, as shown in formula (9): I1=a1sin(b1t+c1) (9) Where: t is time; a1 represents the positive sequence current amplitude; b1 is the positive sequence angular frequency; c1 is the positive sequence phase, and the I1 obtained by fitting is the transmission current of the conductive layer loop A, B and C phases; Assume that the positive sequence impedance of the superconducting cable is: Z1=R1+jX1 (10) Where, Z1 is the positive sequence impedance; R1 is the positive sequence resistance; X1 is the positive sequence reactance; j is an imaginary number; Substituting equation (9) and equation (10) into equation (7), we obtain: Substituting the fitted formula (9) into formula (11), the positive sequence impedance formula is: The negative sequence impedance is equal to the positive sequence impedance; The calculation method of the zero-sequence impedance is as follows: Set the excitation power potential E A 、E B and E C The amplitude and phase of the simulation are equal, and the integral is used to obtain I A ,I B and I C The curve that changes with time is fitted by intercepting the steady-state part, as shown in formula (13): I0=a0sin(b0t+c0) (13) In the formula, a0 represents the zero-sequence current amplitude, b0 is the zero-sequence angular frequency, c0 is the zero-sequence phase, and the I0 obtained by fitting is the zero-sequence current of phase A, B or C; Let the zero-sequence impedance of the superconducting cable be: Z0=R0+jX0 (14) In the formula, Z0 is zero-sequence impedance; R0 is zero-sequence resistance; X0 is zero-sequence reactance; Assuming that the voltage across the superconducting cable is U0, then: U0=E A -I0R s (15) The zero-sequence impedance is: Substitute the fitted formula (13) into formula (16) and combine it with formula (15) to calculate the zero-sequence impedance:

2. A system for calculating sequence parameters of a superconducting cable transmission line, characterized in that: include: Parameter acquisition module: used to obtain the structural parameters and electrical property parameters of the superconducting cable, wherein the electrical property parameters include magnetic permeability, electrical conductivity and resistance; Intermediate quantity calculation module: used to calculate the shielding layer induced electric field and induced current density vector based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable; Calculate the transmission current of the conducting layer and the shielding layer based on the equivalent circuit model of the superconducting cable and the resistance of the superconducting cable; The two-dimensional equivalent magnetic field model of the superconducting cable is shown in formula (1): Where: μ is the magnetic permeability of the magnetic field; J e is the density vector of the external excitation current; J s is the induced current density vector; A is the vector magnetic potential; Compute the sign for the curl; The shielding layer induced electric field and induced current density vector are calculated based on the two-dimensional equivalent magnetic field model of the superconducting cable and the structural parameters, magnetic permeability and electrical conductivity of the superconducting cable, specifically: According to the structural parameters of the superconducting cable, the edge finite element method is used to solve the overall interpolation function of the magnetic field region of the two-dimensional equivalent magnetic field model as shown in formula (2): Where: A is the vector magnetic potential, and the overall interpolation function is used here to represent the vector magnetic potential; N n (x, y, z) is the unit interpolation function; n is the unit number of the nth unit; n1 is the total number of units; A n represents the vector magnetic potential of each cell using an interpolation function; According to Green's theorem, equation (2) is solved to obtain the Galerkin weighted residual equation in the corresponding magnetic field region: Where: N m , N n They represent the unit interpolation functions of the m-th unit and the n-th unit respectively; m represents the unit number of the m-th unit; J is the current density; If the current distribution is known in the two-dimensional equivalent magnetic field model, the Galerkin weighted residual equation is discretized into a set of algebraic equations, and the vector magnetic potential A in the cross-sectional space of the superconducting cable is obtained by solving the set of algebraic equations. The magnetic induction intensity B is obtained by using the vector magnetic potential A, as shown in formula (4): The electromagnetic induction law is used to solve the spatial induced electric field E, as shown in formula (5): The induced current density vector J is obtained by Ohm's law s , as shown in formula (6): J s =σE (6) Where σ is the conductivity; The equivalent circuit model includes three-phase power supplies A, B and C, and the three-phase power supplies A, B and C are connected through resistors R s It forms a loop with the conductive layer of the superconducting cable to form a conductive layer loop with a resistance R s Including power supply internal resistance and load resistance; the shielding layer of phases A, B and C is short-circuited at both ends and connected in series with resistance R g , forming a shielding layer loop, the resistor R g is the grounding resistance; The circuit equation of the conductive layer loop is shown in formula (7): Where: E A 、E B and E C are the power supply potentials of the conductive layer loop phases A, B and C respectively; I A ,I B and I C are the transmission currents of phases A, B and C of the conductive layer loops respectively; U A , U B and U C are the voltage drops across the conducting layers of the superconducting cables of phases A, B and C, respectively, obtained by the two-dimensional equivalent magnetic field model; The circuit equation of the shielding layer loop is shown in formula (8): Where: U a , U b and U c They are the three-phase induced electromotive force of the shield layer circuit a, b and c respectively; I a ,I b and I c are the transmission currents of the three phases of the shielding layer loop a, b and c, obtained from the two-dimensional equivalent magnetic field model; I g is the shielding layer loop ground current, when I a , I b and I c When the three phases are symmetrical, the ground current I g is 0; Sequence parameter calculation module: used to calculate the sequence parameters of superconducting cable transmission lines through the shielding layer induced electric field and induced current density vector and the conductive layer and shielding layer transmission current coupling, including: 1) Given the power supply potential at a certain moment, solve the transmission current of the superconducting cable conductive layer and shielding layer in the equivalent circuit model; 2) Substitute the transmission current of the conductive layer and the shielding layer into the two-dimensional equivalent magnetic field model, and obtain the vector magnetic potential A and magnetic induction intensity B of the overall spatial magnetic field by solving equations (1) and (4). Then, the voltage drop U and the induced current density vector J of the conductive layer and the shielding layer are obtained by equations (5) and (6). s ; 3) Substitute the voltage drop U of the conductive layer and the shielding layer into the equivalent circuit model, iterate steps 1) and 2) until the conductive layer current and the shielding layer current meet the convergence condition, and then proceed to step 4); 4) Fit the conductive layer current and the shielding layer current to obtain the amplitude and phase; 5) Dividing the vector values ​​of voltage and current to obtain an order parameter, wherein the vector value is composed of an amplitude and a phase; The superconducting cable transmission line sequence parameter calculation includes zero sequence impedance calculation and positive sequence impedance and negative sequence impedance calculation; The calculation method of the positive sequence impedance is as follows: Set the excitation power potential E A 、E B and E C The three phases are symmetrical, with a phase difference of 120°. By integrating the current density in the A, B and C phase regions, I A ,I B and I C The curve that changes with time, I A ,I B and I C The curve that changes with time, intercepts the steady-state part, and fits it according to the sine curve, as shown in formula (9): I1=a1sin(b1t+c1) (9) Where: t is time; a1 represents the positive sequence current amplitude; b1 is the positive sequence angular frequency; c1 is the positive sequence phase, and the I1 obtained by fitting is the transmission current of the conductive layer loop A, B and C phases; Assume that the positive sequence impedance of the superconducting cable is: Z1=R1+jX1 (10) Where, Z1 is the positive sequence impedance; R1 is the positive sequence resistance; X1 is the positive sequence reactance; j is an imaginary number; Substituting equation (9) and equation (10) into equation (7), we obtain: Substituting the fitted formula (9) into formula (11), the positive sequence impedance formula is: The negative sequence impedance is equal to the positive sequence impedance; The calculation method of the zero-sequence impedance is as follows: Set the excitation power potential E A 、E B and E C The amplitude and phase of the simulation are equal, and the integral is used to obtain I A ,I B and I C The curve that changes with time is fitted by intercepting the steady-state part, as shown in formula (13): I0=a0sin(b0t+c0) (13) In the formula, a0 represents the zero-sequence current amplitude, b0 is the zero-sequence angular frequency, c0 is the zero-sequence phase, and the I0 obtained by fitting is the zero-sequence current of phase A, B or C; Let the zero-sequence impedance of the superconducting cable be: Z0=R0+jX0 (14) In the formula, Z0 is zero-sequence impedance; R0 is zero-sequence resistance; X0 is zero-sequence reactance; Assuming that the voltage across the superconducting cable is U0, then: U0=E A -I0R s (15) The zero-sequence impedance is: Substitute the fitted formula (13) into formula (16) and combine it with formula (15) to calculate the zero-sequence impedance:

3. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for calculating the sequence parameters of a superconducting cable transmission line as claimed in claim 1 are implemented.

4. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for calculating the sequence parameters of a superconducting cable transmission line as claimed in claim 1 are implemented.

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