A method, system and storage medium for optimizing the full current imbalance of a superconducting cable

Abstract

The present invention discloses a method, system and storage medium for optimizing the full current imbalance of a superconducting cable. The optimization method includes establishing a three-phase coaxial superconducting cable basic structure according to initial parameters; performing a binary design on the three-phase coaxial superconducting cable basic structure; establishing a mathematical model according to the three-phase coaxial superconducting cable basic structure after the binary design; determining optimization variables according to the mathematical model established by the three-phase coaxial superconducting cable basic structure; calculating the three-phase full current imbalance of the three-phase coaxial superconducting cable, and optimizing the optimization variables according to the target that the three-phase full current imbalance of the three-phase coaxial superconducting cable is less than a set value, so as to optimize the full current imbalance of the three-phase coaxial superconducting cable. The present invention increases the optimization variables by introducing a binary particle swarm optimization algorithm, uses the positive sequence, negative sequence, zero sequence components and shielding layer current of the three-phase current as the optimization objective function, and takes into account the three-phase current vector balance and the reduction of the shielding layer current.

Description

Technical Field

[0001] The invention belongs to the technical field of three-phase coaxial superconducting cable optimization, and in particular relates to a method, a system and a storage medium for optimizing the full current imbalance of a superconducting cable. Background Art

[0002] In recent years, with the development of economy, the load of urban power grids has been increasing, and the space resources in developed cities are in short supply, making it extremely difficult to add or transform transmission lines. Conventional transmission technology is limited by conductive materials, and it is difficult to achieve major breakthroughs in increasing transmission capacity, reducing transmission losses, and reducing transmission corridors and urban land. How to use the existing cable tunnel space to achieve higher capacity power transmission has become a major issue facing the construction of power supply lines in urban load centers.

[0003] YBCO high-temperature superconducting tapes can work in a liquid nitrogen environment at 77K, which greatly reduces the refrigeration cost compared to low-temperature superconducting materials, making the cost of applying high-temperature superconducting tapes to power transmission significantly reduced. At the same time, superconducting materials have high density and unimpeded current carrying capacity when in a superconducting state, which also greatly improves the transmission capacity. Superconducting cables have strong current carrying capacity, and the transmission capacity is 3-5 times that of traditional cables with the same cross-section, and the resistance loss during transmission is almost zero.

[0004] Compared with conventional superconducting cables, three-phase coaxial superconducting cables have a more compact structure and only require one shielding layer for the three phases. In steady-state operation, the three-phase currents are balanced and no superconducting tape is needed to wind the shielding layer. The amount of superconducting tape can be reduced by more than half, and the cost is lower. At present, three-phase coaxial high-temperature superconducting cables are one of the technologies that are expected to solve the problem of urban expansion and reconstruction.

[0005] The three-phase coaxial superconducting cable has different radii of each phase and asymmetric three-phase electromagnetic parameters, which causes unbalanced three-phase current, resulting in increased AC loss and reduced power quality. In addition, the asymmetry of the three-phase electromagnetic parameters may cause a large current in the shielding layer. Since the three-phase coaxial superconducting cable uses a copper shielding layer, the copper loss is large, the heat is serious, and the burden on the refrigeration system is increased.

[0006] The existing impedance balance optimization method of three-phase coaxial superconducting cable realizes the impedance balance optimization design of three-phase coaxial superconducting cable by connecting a reactor in series at the end of each phase or other structural adjustment means to make the impedance amplitude of each phase equal.

[0007] However, the existing three-phase coaxial superconducting cable impedance balance optimization method still has the following problems: it requires additional equipment such as reactors, which has a high investment cost; it only considers the balance of the three-phase current amplitude, and does not reflect the phase imbalance; although it can reduce the imbalance of the three-phase current, the shielding layer current is still large after optimization, resulting in high losses. Summary of the invention

[0008] The purpose of the present invention is to provide a method, system and storage medium for optimizing the total current imbalance of a superconducting cable in view of the problems in the above-mentioned prior art, introduce a binary particle swarm optimization algorithm to increase the optimization variables, use the positive sequence, negative sequence, zero sequence components of the three-phase current and the shielding layer current as the optimization objective function, and take into account the balance of the three-phase current and the reduction of the shielding layer current.

[0009] In order to achieve the above object, the present invention has the following technical solutions:

[0010] In a first aspect, a method for optimizing the full current imbalance of a superconducting cable is provided, comprising:

[0011] Performing a binary design on a three-phase coaxial superconducting cable basic structure pre-established according to initial parameters to obtain a three-phase coaxial superconducting cable basic structure after the binary design;

[0012] A mathematical model is established based on the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0013] Determining optimization variables according to the mathematical model;

[0014] The three-phase full current unbalance of the three-phase coaxial superconducting cable is calculated, and the optimization variables are optimized with the goal of making the three-phase full current unbalance of the three-phase coaxial superconducting cable less than a set value, so as to achieve the optimization of the full current unbalance of the three-phase coaxial superconducting cable.

[0015] Preferably, in the step of performing binary design on the three-phase coaxial superconducting cable infrastructure pre-established according to initial parameters, the initial parameters include the rated voltage, rated current, withstand voltage of the insulating material, maximum tolerable field strength, relative dielectric constant, critical current of the superconducting tape, superconducting tape thickness, superconducting tape width and minimum bending radius of the designed three-phase coaxial superconducting cable.

[0016] Preferably, in the step of performing binary design on the three-phase coaxial superconducting cable infrastructure structure pre-established according to the initial parameters, the three-phase coaxial superconducting cable infrastructure structure includes a minimum insulation thickness of the cable and a minimum radius of the cable, and the minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages, and the specific calculation formula is as follows:

[0017] Δ i =r i (exp(U / r i E max )-1)

[0018] In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; Emax is the maximum field strength for each withstand voltage;

[0019] The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows:

[0020] r A =((ω+δ)×n / cosα) / 2π

[0021] In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots;

[0022] The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows:

[0023]

[0024] Where m is the current margin, I r is the rated current of the superconducting cable, I c is the critical current of the superconducting tape.

[0025] Preferably, in the step of bisection designing the three-phase coaxial superconducting cable basic structure pre-established according to the initial parameters, the bisection design step includes: dividing the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions.

[0026] Preferably, the step of establishing a mathematical model according to the three-phase coaxial superconducting cable infrastructure structure after the binary design comprises:

[0027] The voltage-current relationship of the three-phase coaxial superconducting cable is obtained according to the following formula:

[0028] I=([R+jwL] -1 +jwC)·U

[0029] in:

[0030]

[0031]

[0032] In the formula, is the A phase current, is the B phase current, is the C phase current, is the shield current, is the A phase voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, Ra is the phase A resistance, R b is the resistance of phase B, R c is the C phase resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Both are mutual inductance between phases A and B, M ac With M ca Both are mutual inductance between phases A and C, M bc With M cb Both are the mutual inductance between phases B and C, M as With M sa The mutual inductance between phase A and shielding layer, M bs With M sb The mutual inductance between phase B and the shield layer, M cs With M sc The mutual inductance between phase C and shielding layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer;

[0033] The calculation expressions of self-inductance and mutual inductance of three-phase coaxial superconducting cable are as follows:

[0034]

[0035] M ij =0.5μ0πr i 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 P j2 )+μ0ln(D / r j ) / 2π

[0036] Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1; D is taken as 1m.

[0037] Preferably, in the step of determining the optimization variables according to the mathematical model established according to the three-phase coaxial superconducting cable infrastructure, the optimization variables are:

[0038] X=[β a ,β b ,β c1 ,β c2 ,β s1 ,β s2 ,γ a ,γ b ,γ c1 ,γ c2 ,γ s1 ,γ s2 ]

[0039] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2 is the winding angle of the second section of the C-phase superconducting tape, β s1 is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding layer copper tape, γ s2 The winding direction of the second section of the shielding layer copper tape;

[0040] The relationship between the winding angle β and the winding pitch P is:

[0041]

[0042] Preferably, in the step of calculating the three-phase full current unbalance of the three-phase coaxial superconducting cable, the full current unbalance is calculated using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current, and the calculation formula is as follows:

[0043]

[0044] In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current;

[0045] The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are:

[0046]

[0047]

[0048]

[0049] Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the A phase current, is the B phase current, is the C phase current, j is an imaginary unit, j 2 =-1.

[0050] Preferably, in the step of optimizing the optimization variables with the goal of the three-phase full current unbalance degree of the three-phase coaxial superconducting cable being less than a set value, the set value is 5%, and the optimization adopts a particle swarm algorithm, specifically including:

[0051] According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population;

[0052] The constraints of β in the optimization variable are:

[0053] βmin<β<βmax

[0054] Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters;

[0055] The constraints of γ in the optimization variable are:

[0056] γ=1 means clockwise winding, γ=-1 means counterclockwise winding;

[0057] The constraints on the speed of individuals in the population are:

[0058] V min ≤v iq ≤V max

[0059] In the formula, viq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed.

[0060] Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value;

[0061] The velocity update expression is:

[0062]

[0063] In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient;

[0064] The individual update expression is:

[0065]

[0066] Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

[0067] In a second aspect, a superconducting cable full current imbalance optimization system is provided, comprising:

[0068] A binary design module is used to perform binary design on a three-phase coaxial superconducting cable infrastructure structure pre-established according to initial parameters, and obtain the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0069] A mathematical model building module, used to build a mathematical model according to the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0070] An optimization variable determination module, used for determining optimization variables according to the mathematical model;

[0071] The imbalance optimization module is used to calculate the three-phase full current imbalance of the three-phase coaxial superconducting cable, and optimize the optimization variables with the goal of making the three-phase full current imbalance of the three-phase coaxial superconducting cable less than a set value, so as to achieve the optimization of the full current imbalance of the three-phase coaxial superconducting cable.

[0072] Preferably, when the binary design module performs binary design on the three-phase coaxial superconducting cable infrastructure pre-established according to initial parameters, the initial parameters include the rated voltage, rated current, withstand voltage of the insulating material, maximum tolerable field strength, relative dielectric constant, critical current of the superconducting tape, superconducting tape thickness, superconducting tape width and minimum bending radius of the designed three-phase coaxial superconducting cable.

[0073] Preferably, when the binary design module performs binary design on the three-phase coaxial superconducting cable infrastructure structure pre-established according to the initial parameters, the three-phase coaxial superconducting cable infrastructure structure includes the minimum insulation thickness of the cable and the minimum radius of the cable. The minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages. The specific calculation formula is as follows:

[0074] Δ i =r i (exp(U / r i E max )-1)

[0075] In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; E max is the maximum field strength for each withstand voltage;

[0076] The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows:

[0077] r A =((ω+δ)×n / cosα) / 2π

[0078] In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots;

[0079] The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows:

[0080] n=(1+m)I r / I c

[0081] Where m is the current margin, I r is the rated current of the superconducting cable, I cis the critical current of the superconducting tape.

[0082] Preferably, the binary design module divides the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions.

[0083] Preferably, the mathematical model building module obtains the voltage-current relationship of the three-phase coaxial superconducting cable according to the following formula:

[0084] I=([R+jwL] -1 +jwC)·U

[0085] in:

[0086]

[0087]

[0088] In the formula, is the A phase current, is the B phase current, is the C phase current, is the shield current, is the A phase voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, R a is the phase A resistance, R b is the resistance of phase B, R c is the phase C resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Equal to the mutual inductance between phases A and B, M ac With M ca Equal to the mutual inductance between phases A and C, M bc With M cb Equal to the mutual inductance between phases B and C, M as With M sa Equal to the mutual inductance between phase A and the shielding layer, M bs With M sb Equal to the mutual inductance between phase B and the shielding layer, M cs With M sc Equal to the mutual inductance between phase C and the shield layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer;

[0089] The calculation expressions of self-inductance and mutual inductance of three-phase coaxial superconducting cable are as follows:

[0090]

[0091] M ij =0.5μ0πr i 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 P j2 )+μ0ln(D / r j ) / 2π

[0092] Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1 is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1; D is taken as 1m.

[0093] Preferably, the optimization variables determined by the optimization variable determination module are:

[0094] X=[β a ,β b ,β c1 ,β c2 ,β s1 ,β s2 ,γ a ,γ b ,γ c1 ,γ c2 ,γ s1 ,γ s2 ]

[0095] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2is the winding angle of the second section of the C-phase superconducting tape, β s1 is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding layer copper tape, γ s2 The winding direction of the second section of the shielding layer copper tape;

[0096] The relationship between the winding angle β and the winding pitch P is:

[0097]

[0098] Preferably, when the imbalance degree optimization module calculates the three-phase full current imbalance degree of the three-phase coaxial superconducting cable, the full current imbalance degree is calculated by using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current, and the calculation formula is as follows:

[0099]

[0100] In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current;

[0101] The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are:

[0102]

[0103]

[0104]

[0105] Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the A phase current, is the B phase current, is the C phase current, j is an imaginary unit, j 2 =-1.

[0106] Preferably, when the imbalance optimization module optimizes the optimization variable, the set value is 5%, and the optimization adopts a particle swarm algorithm, specifically including:

[0107] According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population;

[0108] The constraints of β in the optimization variable are:

[0109] βmin<β<βmax

[0110] Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters;

[0111] The constraints of γ in the optimization variable are:

[0112] γ=1 means clockwise winding, γ=-1 means counterclockwise winding;

[0113] The constraints on the speed of individuals in the population are:

[0114] V min ≤v iq ≤V max

[0115] In the formula, v iq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed.

[0116] Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value;

[0117] The velocity update expression is:

[0118]

[0119] In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient;

[0120] The individual update expression is:

[0121]

[0122] Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

[0123] In a third aspect, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for optimizing the total current imbalance of a superconducting cable as described in the first aspect is implemented.

[0124] Compared with the prior art, the first aspect of the present invention has at least the following beneficial effects:

[0125] The full current imbalance of a three-phase coaxial superconducting cable refers to the difference between the amplitude and phase of the three-phase current flowing through the cable and the standard three-phase sinusoidal current. The present invention uses input initial parameters to establish the basic structure of the three-phase coaxial superconducting cable, and performs a binary design on the basic structure of the three-phase coaxial superconducting cable. The binary design refers to dividing the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions, and then determining the optimization variables based on the mathematical model established according to the basic structure of the three-phase coaxial superconducting cable. Compared with the traditional three-phase coaxial superconducting cable impedance balance optimization method, the present invention increases the optimization variables, can comprehensively consider the amplitude and phase balance of the three-phase current, does not need to add additional equipment such as reactors, so the investment cost is small, and optimizes the optimization variables based on the goal of the full three-phase current imbalance of the three-phase coaxial superconducting cable being less than the set value, taking into account the three-phase current balance and reducing the shielding layer current, thereby improving the power quality and reducing the loss of the shielding layer.

[0126] It can be understood that the beneficial effects of the second to third aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0128] Figure 1 Flow chart of a method for optimizing the total current imbalance of a superconducting cable according to an embodiment of the present invention;

[0129] Figure 2 Schematic diagram of an equivalent circuit model of a coaxial superconducting cable according to a third embodiment of the present invention;

[0130] Figure 3 Current waveform after optimization using conventional optimization methods;

[0131] Figure 4 The current waveform diagram after optimization by the method of the present invention. DETAILED DESCRIPTION

[0132] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0133] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0134] See also Figure 1 , a method for optimizing the full current imbalance of a superconducting cable proposed in an embodiment of the present invention comprises:

[0135] S1. Performing a binary design on a three-phase coaxial superconducting cable infrastructure structure pre-established according to initial parameters to obtain a three-phase coaxial superconducting cable infrastructure structure after the binary design;

[0136] S2. Establishing a mathematical model based on the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0137] S3, determining optimization variables according to the mathematical model;

[0138] S4. Calculate the three-phase full current unbalance of the three-phase coaxial superconducting cable, and optimize the optimization variables with the goal of making the three-phase full current unbalance of the three-phase coaxial superconducting cable less than the set value, so as to achieve the optimization of the full current unbalance of the three-phase coaxial superconducting cable.

[0139] In a possible implementation, when step S1 establishes a three-phase coaxial superconducting cable infrastructure according to initial parameters, first input the initial parameters, and then Figure 2 The three-phase coaxial superconducting cable equivalent circuit model structure shown in the figure, the initial parameters input into the embodiment of the method of the present invention include the rated voltage and rated current of the designed three-phase coaxial superconducting cable, the withstand voltage of the insulating material, the maximum field strength that can be tolerated, the relative dielectric constant, the critical current of the superconducting tape, the thickness of the superconducting tape, the width of the superconducting tape and the minimum bending radius.

[0140] In a possible implementation manner, the three-phase coaxial superconducting cable infrastructure established in step S1 includes a minimum insulation thickness of the cable and a minimum radius of the cable. The minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages. The specific calculation formula is as follows:

[0141] Δ i =r i (exp(U / r i E max )-1)

[0142] In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; E max is the maximum field strength for each withstand voltage;

[0143] The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows:

[0144] r A =((ω+δ)×n / cosα) / 2π

[0145] In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots;

[0146] The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows:

[0147] n=(1+m)I r / I c

[0148] Where m is the current margin, generally 20% to 50%, I r is the rated current of the superconducting cable, I c is the critical current of the superconducting tape.

[0149] In a possible implementation, step S1 performs a binary design on the three-phase coaxial superconducting cable infrastructure by dividing the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions. Here, the C-phase conductor layer and the copper shielding layer of the three-phase coaxial superconducting cable are binary-processed.

[0150] In a possible implementation manner, step S2 establishes a mathematical model of a three-phase coaxial superconducting cable according to the three-phase coaxial superconducting cable structure after being divided into two, and obtains its voltage-current relationship. The specific formula is as follows:

[0151] I=([R+jwL] -1 +jwC)·U

[0152] in:

[0153]

[0154]

[0155] In the formula, is the A phase current, is the B phase current, is the C phase current, is the shield current, is the A phase voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, R a is the phase A resistance, R b is the resistance of phase B, R c is the phase C resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Both are mutual inductance between phases A and B, M ac With M ca Both are mutual inductance between phases A and C, M bc With M cb Both are the mutual inductance between phases B and C, M as With M sa The mutual inductance between phase A and shielding layer, M bs With M sb The mutual inductance between phase B and the shield layer, M cs With M sc The mutual inductance between phase C and shielding layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer;

[0156] The resistance of a three-phase coaxial superconducting cable is almost zero in the superconducting state, and the phase-to-phase capacitance is much smaller than the values ​​of self-inductance and mutual inductance, so the three-phase current balance depends on the self-inductance of each phase of the cable and the mutual inductance between phases.

[0157] The calculation formulas for self-inductance and mutual inductance are related to the strip winding pitch, conductor layer radius and winding direction. The calculation formulas are as follows:

[0158]

[0159] M ij =0.5μ0πri 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 P j2 )+μ0ln(D / r j ) / 2π

[0160] Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1 is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1; D is taken as 1m.

[0161] According to the mathematical model of the three-phase coaxial superconducting cable obtained in step S2, it can be known that the three-phase current balance is related to the self-inductance of each phase and the mutual inductance between phases. The calculation of self-inductance and mutual inductance depends on the strip winding pitch, winding direction and conductor layer radius. The conductor layer radius is affected by the insulation thickness and cannot be changed at will, so step S3 determines the optimization variables in the optimization method as:

[0162] X=[β a ,β b ,β c1 ,β c2 ,β s1 ,β s2 ,γ a ,γ b ,γ c1 ,γ c2 ,γ s1 ,γ s2 ]

[0163] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2 is the winding angle of the second section of the C-phase superconducting tape, β s1is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding layer copper tape, γ s2 This is the winding direction of the second section of the shielding layer copper tape.

[0164] The relationship between the winding angle β and the winding pitch P is:

[0165]

[0166] In a possible implementation, the total current unbalance degree in step S4 is calculated using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current. The calculation formula is as follows:

[0167]

[0168] In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current;

[0169] The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are:

[0170]

[0171]

[0172]

[0173] Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the A phase current, is the B phase current, is the C phase current, j is an imaginary unit, j 2 =-1.

[0174] In a possible implementation, step S4 performs variable optimization on the three-phase coaxial superconducting cable with the goal of less than 5% of the three-phase full current imbalance of the three-phase coaxial superconducting cable. The optimization adopts a particle swarm algorithm, which is a global optimization method based on groups and individuals. The specific steps are as follows:

[0175] According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population;

[0176] The constraints of β in the optimization variable are:

[0177] βmin<β<βmax

[0178] Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters;

[0179] The constraints of γ in the optimization variable are:

[0180] γ=1 means clockwise winding, γ=-1 means counterclockwise winding;

[0181] The constraints on the speed of individuals in the population are:

[0182] V min ≤v iq ≤V max

[0183] In the formula, v iq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed.

[0184] Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value;

[0185] The velocity update expression is:

[0186]

[0187] In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient;

[0188] The individual update expression is:

[0189]

[0190] Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

[0191] See also Figure 3 and Figure 4 According to the test results, in the current waveform optimized by the conventional optimization method, the three-phase current imbalance is 41%, and the shielding layer current amplitude is 750A. In the current waveform optimized by the method of the present invention, the three-phase current imbalance is 1.2%, and the shielding layer current amplitude is 1A. It can be seen that the three-phase current imbalance of the three-phase coaxial superconducting cable after optimization by the present invention is significantly reduced, and the shielding layer current is significantly reduced after optimization, resulting in reduced losses.

[0192] Another embodiment of the present invention further provides a superconducting cable full current imbalance optimization system, comprising:

[0193] A binary design module is used to perform binary design on a three-phase coaxial superconducting cable infrastructure structure pre-established according to initial parameters, and obtain the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0194] A mathematical model building module, used to build a mathematical model according to the three-phase coaxial superconducting cable infrastructure structure after binary design;

[0195] An optimization variable determination module, used for determining optimization variables according to the mathematical model;

[0196] The imbalance optimization module is used to calculate the three-phase full current imbalance of the three-phase coaxial superconducting cable, and optimize the optimization variables with the goal of making the three-phase full current imbalance of the three-phase coaxial superconducting cable less than a set value, so as to achieve the optimization of the full current imbalance of the three-phase coaxial superconducting cable.

[0197] In one possible implementation, when the binary design module performs binary design on a three-phase coaxial superconducting cable infrastructure pre-established according to initial parameters, the initial parameters include the rated voltage and rated current of the designed three-phase coaxial superconducting cable, the withstand voltage of the insulating material, the maximum field strength that can be tolerated, the relative dielectric constant, the critical current of the superconducting tape, the thickness of the superconducting tape, the width of the superconducting tape and the minimum bending radius.

[0198] In a possible implementation, when the binary design module performs binary design on the three-phase coaxial superconducting cable infrastructure structure pre-established according to the initial parameters, the three-phase coaxial superconducting cable infrastructure structure includes a minimum insulation thickness of the cable and a minimum radius of the cable. The minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages. The specific calculation formula is as follows:

[0199] Δ i =r i (exp(U / r i E max )-1)

[0200] In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; E max is the maximum field strength for each withstand voltage;

[0201] The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows:

[0202] r A =((ω+δ)×n / cosα) / 2π

[0203] In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots;

[0204] The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows:

[0205] n=(1+m)I r / I c

[0206] Where m is the current margin, I r is the rated current of the superconducting cable, I c is the critical current of the superconducting tape.

[0207] In a possible implementation, when the binary design module performs binary design on the three-phase coaxial superconducting cable infrastructure structure, the conductor layer and the shielding layer of the three-phase coaxial superconducting cable are divided into two sections with the same radius but different pitches and winding directions.

[0208] In a possible implementation, the mathematical model building module obtains the voltage-current relationship of the three-phase coaxial superconducting cable according to the following formula:

[0209] I=([R+jwL] -1 +jwC)·U

[0210] in:

[0211]

[0212]

[0213] In the formula, is the A phase current, is the B phase current, is the C phase current, is the shield current, is the A phase voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, R a is the phase A resistance, R b is the resistance of phase B, R c is the phase C resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Both are mutual inductance between phases A and B, M ac With M ca Both are mutual inductance between phases A and C, M bc With M cb Both are the mutual inductance between phases B and C, M as With M sa The mutual inductance between phase A and shielding layer, M bs With M sb The mutual inductance between phase B and the shield layer, M cs With M sc The mutual inductance between phase C and shielding layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer;

[0214] The calculation expressions of self-inductance and mutual inductance of three-phase coaxial superconducting cable are as follows:

[0215]

[0216] M ij =0.5μ0πr i 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 Pj2 )+μ0ln(D / r j ) / 2π

[0217] Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1 is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1; D is taken as 1m.

[0218] In a possible implementation manner, the optimization variable determined by the optimization variable determination module is:

[0219] X=[β a ,β b ,β c1 ,β c2 ,β s1 ,β s2 ,γ a ,γ b ,γ c1 ,γ c2 ,γ s1 ,γ s2 ]

[0220] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2 is the winding angle of the second section of the C-phase superconducting tape, β s1 is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding layer copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding layer copper tape, γ s2 The winding direction of the second section of the shielding layer copper tape;

[0221] The relationship between the winding angle β and the winding pitch P is:

[0222]

[0223] In a possible implementation, when the imbalance optimization module calculates the three-phase full current imbalance of the three-phase coaxial superconducting cable, the full current imbalance is calculated using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current, and the calculation formula is as follows:

[0224]

[0225] In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current;

[0226] The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are:

[0227]

[0228]

[0229]

[0230] Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the A phase current, is the B phase current, is the C phase current, j is an imaginary unit, j 2 =-1.

[0231] In a possible implementation, when the imbalance optimization module optimizes the optimization variable, the setting value is 5%, and the optimization adopts the particle swarm algorithm. The specific steps of optimizing by the particle swarm algorithm include:

[0232] According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population;

[0233] The constraints of β in the optimization variable are:

[0234] βmin<β<βmax

[0235] Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters;

[0236] The constraints of γ in the optimization variable are:

[0237] γ=1 means clockwise winding, γ=-1 means counterclockwise winding;

[0238] The constraints on the speed of individuals in the population are:

[0239] V min ≤v iq ≤V max

[0240] In the formula, v iq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed.

[0241] Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value;

[0242] The velocity update expression is:

[0243]

[0244] In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient;

[0245] The individual update expression is:

[0246]

[0247] Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

[0248] The present invention introduces a binary particle swarm optimization algorithm, increases optimization variables, uses the positive sequence, negative sequence, zero sequence components of the three-phase current and the shielding layer current as the optimization objective function, comprehensively considers the amplitude and phase balance of the three-phase current, ensures that the imbalance of the three-phase full current is below 5% while making the shielding layer current 0, improves the power quality, and reduces the loss of the shielding layer.

[0249] The embodiment of the present invention also provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the superconducting cable full current imbalance optimization method is implemented. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable storage medium may include: any entity or device, medium, USB flash drive, mobile hard disk, disk, optical disk, computer memory, read-only memory, random access memory, electric carrier signal, telecommunication signal and software distribution medium that can carry the computer program code. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals. For ease of explanation, the above content only shows the part related to the embodiment of the present invention. For specific technical details not disclosed, please refer to the method part of the embodiment of the present invention. The computer-readable storage medium is non-temporary and can be stored in a storage device formed by various electronic devices, which can implement the execution process recorded in the method of the embodiment of the present invention.

[0250] 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.

[0251] 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 process in the flowchart. Figure 1A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0252] 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.

[0253] 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.

[0254] 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 it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the total current imbalance of a superconducting cable, characterized in that: include: Performing binary design on a three-phase coaxial superconducting cable infrastructure structure pre-established according to initial parameters to obtain a three-phase coaxial superconducting cable infrastructure structure after binary design; the initial parameters include the rated voltage, rated current, withstand voltage of the insulating material, maximum tolerable field strength, relative dielectric constant, critical current of the superconducting tape, thickness of the superconducting tape, width of the superconducting tape and minimum bending radius of the designed three-phase coaxial superconducting cable; A mathematical model is established based on the three-phase coaxial superconducting cable infrastructure after binary design, including: The voltage-current relationship of the three-phase coaxial superconducting cable is obtained according to the following formula: I=([R+jwL] -1 +jwC)·U in: In the formula, is the phase A current, is the B phase current, is the C phase current, is the shield current, is the phase A voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, R a is the phase A resistance, R b is the resistance of phase B, R c is the C phase resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Both are mutual inductance between phases A and B, M ac With M ca Both are mutual inductance between phases A and C, M bc With M cb Both are the mutual inductance between phases B and C, M as With M sa The mutual inductance between phase A and shielding layer, M bs With M sb The mutual inductance between phase B and the shield layer, M cs With M sc The mutual inductance between phase C and shielding layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer; The calculation expressions of self-inductance and mutual inductance of three-phase coaxial superconducting cable are as follows: M ij =0.5μ0πr i 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 P j2 )+μ0ln(D / r j ) / 2π Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1 is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1. D is taken as 1m. Determine the optimization variables according to the mathematical model; the determined optimization variables are: X=[β a ,b b ,b c1 ,b c2 ,b s1 ,b s2 ,c a ,c b ,c c1 ,c c2 ,c s1 ,c s2 ] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2 is the winding angle of the second section of the C-phase superconducting tape, β s1 is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding layer copper tape, γ s2 The winding direction of the second section of the shielding layer copper tape; The relationship between the winding angle β and the winding pitch P is: The three-phase full current unbalance of the three-phase coaxial superconducting cable is calculated, and the optimization variables are optimized with the goal of making the three-phase full current unbalance of the three-phase coaxial superconducting cable less than a set value, so as to achieve the optimization of the full current unbalance of the three-phase coaxial superconducting cable.

2. The method for optimizing the total current imbalance of a superconducting cable according to claim 1, characterized in that: In the step of performing binary design on the three-phase coaxial superconducting cable infrastructure structure pre-established according to the initial parameters, the three-phase coaxial superconducting cable infrastructure structure includes a minimum insulation thickness of the cable and a minimum radius of the cable. The minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages. The specific calculation formula is as follows: Δ i =r i (exp(U / r i E max )-1) In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; E max is the maximum field strength for each withstand voltage; The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows: r A =((ω+δ)×n / cosα) / 2π In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots; The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows: Where m is the current margin, I r is the rated current of the superconducting cable, I c is the critical current of the superconducting tape.

3. The method for optimizing the total current imbalance of a superconducting cable according to claim 1, characterized in that: In the step of bisection designing the three-phase coaxial superconducting cable basic structure pre-established according to initial parameters, the bisection design step includes: dividing the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions.

4. The method for optimizing the total current imbalance of a superconducting cable according to claim 1, characterized in that: In the step of calculating the three-phase full current unbalance of the three-phase coaxial superconducting cable, the full current unbalance is calculated using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current, and the calculation formula is as follows: In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current; The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are: Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the phase A current, is the B phase current, is the C phase current, j is the imaginary unit, j 2 =-1.

5. The method for optimizing the total current imbalance of a superconducting cable according to claim 1, characterized in that: In the step of optimizing the optimization variables with the goal of the three-phase full current unbalance degree of the three-phase coaxial superconducting cable being less than a set value, the set value is 5%, and the optimization adopts a particle swarm algorithm, specifically including: According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population; The constraints of β in the optimization variable are: βmin<β<βmax Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters; The constraints of γ in the optimization variable are: γ=1 means clockwise winding, γ=-1 means counterclockwise winding; The constraints on the speed of individuals in the population are: In min ≤in iq ≤V max In the formula, v iq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed. Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value; The velocity update expression is: In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient; The individual update expression is: Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

6. A superconducting cable full current imbalance optimization system, characterized in that: include: A binary design module is used to perform binary design on a three-phase coaxial superconducting cable infrastructure structure pre-established according to initial parameters, and obtain the three-phase coaxial superconducting cable infrastructure structure after binary design; the initial parameters include the rated voltage, rated current, withstand voltage of the insulating material, maximum field strength that can be tolerated, relative dielectric constant, critical current of the superconducting tape, thickness of the superconducting tape, width of the superconducting tape and minimum bending radius of the designed three-phase coaxial superconducting cable; The mathematical model building module is used to build a mathematical model according to the three-phase coaxial superconducting cable basic structure after the binary design; the mathematical model building module obtains the voltage and current relationship of the three-phase coaxial superconducting cable according to the following formula: I=([R+jwL]- 1 +jwC)·U in: In the formula, is the A phase current, is the B phase current, is the C phase current, is the shield current, is the A phase voltage, is the B phase voltage, is the C phase voltage, is the shield voltage, R a is the phase A resistance, R b is the resistance of phase B, R c is the phase C resistance, R s is the shielding layer resistance, L a is the self-inductance of phase A, L b is the self-inductance of phase B, L c is the self-inductance of phase C, L s is the shielding layer self-inductance, M ab With M ba Equal to the mutual inductance between phases A and B, M ac With M ca Equal to the mutual inductance between phases A and C, M bc With M cb Equal to the mutual inductance between phases B and C, M as With M sa Equal to the mutual inductance between phase A and the shielding layer, M bs With M sb Equal to the mutual inductance between phase B and the shield layer, M cs With M sc Equal to the mutual inductance between phase C and the shield layer, C ab is the capacitance between phases A and B, C bc is the capacitance between phases B and C, C cs is the capacitance between phase C and shielding layer; The calculation expressions of self-inductance and mutual inductance of three-phase coaxial superconducting cable are as follows: M ij =0.5μ0πr i 2 (k i1 k j1 / P i1 P j1 +k i2 k j2 / P i2 P j2 )+μ0ln(D / r j ) / 2π Where P i1 is the winding pitch of the first section of the i-layer superconducting tape with the shielding layer being a copper tape, P i2 is the winding pitch of the second section of the i-layer superconducting tape with the shielding layer being a copper tape, P j1 is the winding pitch of the first section of the j-layer superconducting tape with the shielding layer being copper tape, P j2 is the winding pitch of the second section of the j-layer superconducting tape with the shielding layer being a copper tape; r i is the radius of the conductor in layer i; k i1 is the winding direction of the first section of the i-layer conductor, k i2 is the winding direction of the second section of the i-layer conductor, k j1 is the winding direction of the first section of the j-layer conductor, k j2 is the winding direction of the second section of the j-layer conductor. If clockwise is taken as 1, then counterclockwise is -1. D is taken as 1m. An optimization variable determination module, used for determining optimization variables according to the mathematical model; The optimization variables determined by the optimization variable determination module are: X=[β a ,b b ,b c1 ,b c2 ,b s1 ,b s2 ,c a ,c b ,c c1 ,c c2 ,c s1 ,c s2 ] In the formula, β a is the winding angle of the A-phase superconducting tape, β b is the winding angle of the B-phase superconducting tape, β c1 is the winding angle of the first section of the C-phase superconducting tape, β c2 is the winding angle of the second section of the C-phase superconducting tape, β s1 is the winding angle of the first section of the shielding copper tape, β s2 is the winding angle of the second section of the shielding layer copper tape, γ a is the winding direction of phase A superconducting tape, γ b is the winding direction of the B-phase superconducting tape, γ c1 is the winding direction of the first section of the C-phase superconducting tape, γ c2 is the winding direction of the second section of the C-phase superconducting tape, γ s1 is the winding direction of the first section of the shielding copper tape, γ s2 The winding direction of the second section of the shielding layer copper tape; The relationship between the winding angle β and the winding pitch P is: The imbalance optimization module is used to calculate the three-phase full current imbalance of the three-phase coaxial superconducting cable, and optimize the optimization variables with the goal of making the three-phase full current imbalance of the three-phase coaxial superconducting cable less than a set value, so as to achieve the optimization of the full current imbalance of the three-phase coaxial superconducting cable.

7. The superconducting cable full current imbalance optimization system according to claim 6, characterized in that: When the binary design module performs binary design on the three-phase coaxial superconducting cable infrastructure structure pre-established according to the initial parameters, the three-phase coaxial superconducting cable infrastructure structure includes the minimum insulation thickness of the cable and the minimum radius of the cable. The minimum insulation thickness of the cable is calculated according to the maximum value of the electric field strength under different withstand voltages. The specific calculation formula is as follows: Δ i =r i (exp(U / r i E max )-1) In the formula, r i is the radius of the insulating layer; U is the withstand voltage of the insulating material, which is AC voltage, impulse voltage or partial discharge voltage; E max is the maximum field strength for each withstand voltage; The minimum cable radius is calculated based on the minimum number of strips required to meet the current margin. The specific calculation formula is as follows: r A =((ω+δ)×n / cosα) / 2π In the formula, r A is the minimum radius of the A-phase conductor layer, ω is the width of the superconducting tape, δ is the thickness of the superconducting tape, α is the initial A-phase conductor winding phase angle, and n is the minimum number of tape roots; The minimum number of strips is determined by the strip critical current and the cable rated current, and the calculation formula is as follows: n=(1+m)I r / I c Where m is the current margin, I r is the rated current of the superconducting cable, I c is the critical current of the superconducting tape.

8. The superconducting cable full current imbalance optimization system according to claim 6, characterized in that: The binary design module divides the conductor layer and the shielding layer of the three-phase coaxial superconducting cable into two sections with the same radius but different pitches and winding directions.

9. The superconducting cable full current imbalance optimization system according to claim 6, characterized in that: When the imbalance optimization module calculates the three-phase full current imbalance of the three-phase coaxial superconducting cable, the full current imbalance is calculated by using the effective values ​​of the positive sequence current, negative sequence current, zero sequence current and shielding layer current obtained by decomposing the unbalanced current. The calculation formula is as follows: In the formula, I0 is the zero-sequence current, I1 is the positive-sequence current, I2 is the negative-sequence current, and I s is the shield layer current; The calculation formulas for zero-sequence current, positive-sequence current and negative-sequence current are: Among them, I a ,I b ,I c They are phase A current, phase B current and phase C current respectively; is the zero sequence current, is the positive sequence current, is the negative sequence current, is the phase A current, is the B phase current, is the C phase current, j is the imaginary unit, j 2 =-1.

10. The superconducting cable full current imbalance optimization system according to claim 6, characterized in that: When the imbalance optimization module optimizes the optimization variable, the setting value is 5%, and the optimization adopts the particle swarm algorithm, which specifically includes: According to the constraints, set an initial value for the optimization variables β, γ and speed v of the individuals in the population; The constraints of β in the optimization variable are: βmin<β<βmax Where, βmin is the minimum winding angle of the superconducting tape, βmax is the maximum winding angle of the superconducting tape, and the size of βmin and βmax is related to the tape parameters; The constraints of γ in the optimization variable are: γ=1 means clockwise winding, γ=-1 means counterclockwise winding; The constraints on the speed of individuals in the population are: In min ≤in iq ≤V max In the formula, v iq is the velocity of the ith particle in the q dimension; V min is the minimum flying speed of the particle, V max The maximum flying speed of particles. Their values ​​are set by the user and are related to the convergence speed. Substitute the initial values ​​of all individuals into the total current imbalance calculation formula, find the individual extreme value and group extreme value in the population, that is, the minimum total current imbalance, and update the speed and individuals according to the group extreme value; The velocity update expression is: In the formula, x iq is the position of the ith particle in the q dimension, with a flying speed of v iq , the optimal position currently searched by the i-th particle is p iq , the current optimal position of the entire particle swarm is p gq ; r1 and r2 are random numbers that obey the U(0,1) distribution; c1 and c2 are learning factors, and w is the inertia coefficient; The individual update expression is: Substitute the updated individual into the optimization objective function, and calculate the individual extreme value and the group extreme value again. If the minimum three-phase full current imbalance reaches below 5% required by the optimization design, the best individual value and the obtained minimum three-phase current imbalance are output and the optimization is terminated. If it does not reach below 5%, continue the individual update and speed update.

11. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for optimizing the total current imbalance of a superconducting cable according to any one of claims 1 to 5 is implemented.

Images