CN106897487B - A kind of modeling method of high-temperature superconducting magnet nonlinear analysis - Google Patents
A kind of modeling method of high-temperature superconducting magnet nonlinear analysis Download PDFInfo
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Abstract
The present invention provides a kind of high-temperature superconducting magnet nonlinear analysis modeling methods, according to magnet realistic model, establish the PDE model of electromagnetism Thermal couple analysis, and dynamic inductance, equivalent resistance parameter are calculated according to PDE model solution result, and obtain the key parameters such as critical current of superconducting magnet, maximum temperature rise；According to the mathematical relationship of inductance, resistance parameter and the pressure drop of magnet both ends, using controlled current source come equivalent magnet model, any time in simulations, equivalent inductance, equivalent resistance and the key parameters of magnet are related to magnet current state, have fully considered the non-linear E-J characteristic of superconducting magnet.The present invention can embody influencing each other for system control module and superconducting magnet, and then influence of the analysis control algorithm to superconducting magnet response characteristic.Compared with superconducting magnet is equivalent to the method for pure inductance by tradition, method proposed by the present invention has the characteristics that precision is higher, and modeling process is also and uncomplicated, does not introduce multi-parameter, and can monitor superconducting magnet state in real time.
Description
Technical field
The invention belongs to high-temperature superconducting magnet technologies, and in particular to a kind of modeling side of high-temperature superconducting magnet nonlinear analysis
Method.
Background technique
As the increase of power system capacity, system structure complication and power consumer propose power supply quality requirement
Height, electric system have highlighted several technical problems in terms of electric power safety, high-quality power supply, high efficiency conveying.It is super
Leading power technology is a forward-looking technology by domestic and international extensive concern, and being introduced into electric system will be solution power train
The inherent technology problem of system provides a new technological approaches.Currently, Superconducting Power Technology is to enter high-speed developing period, part
The test run of superconducting power product especially high-temperature superconducting magnet or hanging net operation such as hyperconductive cable, superconducting transformer, surpass
Lead current limiter and superconducting magnetic energy storage system etc..
High temperature superconducting materia from often lead that material is different, and equivalent resistivity can be provided by E-J equation,Wherein, E0=1e-4V/m quenches criterion for superconductor, and J is that electric current is close
Degree, Jc(B, T) is critical current density of the superconductor at magnetic field B and temperature T, by formula (1) it is found that the resistance of superconductor
Characteristic there are nonlinearity, when curent change rapidly caused by changes of magnetic field it is rapid when it is particularly evident, and the characteristic is to temperature
Same sensitive, this is and the place of often leading material there are notable difference.About in the modeling and analysis of superconducting power application, at present
The A.C.power loss of researcher's concern mainly how accurately calculated under given excitation, proposes and perfect H- equation method in succession
And minimum magnetic energy method etc., and calculate the superconducting coil A.C.power loss of ten thousand circle ranks.
In fact, due to the nonlinearity and its temperature dependency of superconductor resistivity, not only in dynamic process
Loss problem merit attention, it is thus non-linear caused by superconductor current density distribution it is uneven caused by inductance
Dynamic change equally be worth research, in traditional analysis method, superconducting magnet is usually equivalent to pure inductance element, is ignored
Its nonlinear characteristic, the magnet for thus causing design to be completed have differences with target, and dynamic performance index not fully accords with
Close design criteria.Therefore, the Nonlinear Modeling of superconducting magnet needs further to be analysed in depth.
Summary of the invention
The purpose of the present invention is to provide a kind of high-temperature superconducting magnet nonlinear analysis modeling methods, it is intended to solve existing super
Magnetizer is simply equivalent to pure inductance element in network analysis, ignores superconduction caused by its inductance and non-linear resistance characteristic
The technical problem of magnet response characteristic inaccuracy, the whole external characteristics of Analysis of Superconducting magnet in systems obtain in dynamic process
Inductance variation, equivalent resistance variation, flux density distribution and the key parameters such as temperature rise, its nonlinear characteristic of primary study is to system
Influence, with to traditional SUPERCONDUCTING MAGNET DESIGN provide amendment reference.
The present invention provides a kind of modeling methods of high-temperature superconducting magnet nonlinear analysis, include the following steps:
(1) structure, each component part and the material parameter of superconducting magnet model are determined；
Structure includes coil pattern, the winding method of superconducting conductor, insulation system, support construction and conduction structure, group
Include superconducting conductor, epoxy resins insulation, copper conduction structure at part, the material parameter being related in model include magnetic conductivity,
Resistivity, thermal conductivity and specific heat capacity；
(2) nonlinear PDEs model is established according to the structure of the superconducting magnet model, each component part and material parameter；
The nonlinear PDEs model includes: electromagnetic field PDE equationConduct heat PDE equation
And constraint condition；
The constraint condition includes: the boundary setting of magnetic field and heat transfer, the heat source in heat transfer model, specific to superconducting magnet
The heat source shows as refrigeration work consumption；H is magnetic intensity vector in electromagnetic field PDE equation, and J is current density vectors, ρ1For material
Expect resistivity；The ρ in heat transfer PDE equation2For density of material, Cρ2For material specific heat capacity, k is material thermal conductivity, and u is medium conduction
Velocity vector；
(3) it is loaded into after realizing electromagnetism thermal coupling in PDE model and obtains using the real-time A.C.power loss Q of superconductor as heat source
Revised PDE model is obtained,
(4) it solves revised nonlinear PDEs model and obtains t moment flux density distribution B (t), magnetic field distribution H (t), electricity
Field intensity E (t), current density are distributed J (t), Temperature Distribution T (t), critical current Ic(t) and maximum temperature rise Tmax(t), and according to
PDE calculated result obtains equivalent inductance Leq(t) and equivalent resistance Req(t)；
(5) according to equivalent inductance Leq(t) and equivalent resistance Req(t) transient current of superconducting magnet is obtained:
(6) superconducting magnet mould is constructed according to nonlinear PDEs model, controlled current source, hysteresis module and voltage measurement unit
The input terminal of block, voltage measurement unit connects external power system, and the input terminal of hysteresis module is connected to voltage measurement unit
Output end, the output end of the input terminal connection hysteresis module of nonlinear PDEs model, the input terminal of controlled current source connect external electrical
Force system, the first output end of the control terminal connected nonlinearity PDE model of controlled current source；The first of nonlinear PDEs model is defeated
Outlet is used to export the transient current of superconducting magnet, and the second output terminal of nonlinear PDEs model is for exporting magnet critical current
Ic(t), maximum temperature rise Tmax(t), equivalent inductance Leq(t) and equivalent resistance Req(t)。
Further, in step (2), nonlinear PDEs model is established in finite element software.
Further, in step (3), revised nonlinear PDEs model includes:Wherein, A.C.power loss Q=E × J E is electric field strength, and J is that electric current is close
Degree.
Further, in step (4), the equivalent inductanceThe equivalent electricity
Resistance
Further, in step (5), the transient currentIts
Middle i1For last moment current value, it is seen that nonlinear PDEs model can be by a controlled current flow source-representation, and inputting is the module two
The electric current of the pressure drop at end, controlled current source determines by real-time voltage and equivalent inductance, resistance parameter, the superconducting magnetic fully considered
The nonlinear characteristic of body.
To sum up, superconducting magnet non-linear modeling method proposed by the present invention have it is following the utility model has the advantages that
(1) nonlinear characteristic that superconducting magnet can be simulated while system emulation, avoids previous pure inductance element
Simple equivalent bring response characteristic error；In addition, the nonlinear characteristic of superconducting magnet has been also in different system models
Difference, the model adapt to various condition calculatings；
(2) the key state parameter of output superconducting magnet is supported in the encapsulation of PDE module, makes magnet state in simulation process
It can be monitored in real-time, facilitate comprehensive Analysis of Superconducting magnet dynamic response performance；
(3) influencing each other for system control module and superconducting magnet can be embodied, thus can analyze control algolithm to super
The nonlinear influence of magnetizer；
(4) this method modeling process is simple, does not need additional complexity parameter, pure with being equivalent to fix by superconducting magnet in the past
The mode of inductance is compared to more accurate.
Detailed description of the invention
Fig. 1 is the PDE illustraton of model in COMSOLMultiphysics；
Fig. 2 be PDE model encapsulation at system can calling module inner topology figure；
Fig. 3 is exciter control system topology diagram in Matlab/Simulink；
Fig. 4 is current-order and superconducting magnet actual current waveform diagram in Dynamic Regulating Process；
Critical current and maximum temperature rise variation diagram in Fig. 5 Dynamic Regulating Process；
Equivalent inductance and equivalent resistance variation diagram in Fig. 6 Dynamic Regulating Process.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
The present invention provides a kind of high-temperature superconducting magnet nonlinear analysis modeling method, comprising: is based on actual magnet model, builds
The PDE model encapsulation is the variable parameter modulator that Softwares of System Simulation can call directly by vertical Coupled Electromagnetic-Thermal PDE model.It should
The equivalent inductance and equivalent resistance of module measure distribution by real-time field and calculate acquisition, while exporting magnet state parameter, such as critical
Electric current Ic, maximum temperature rise TmaxData-interface Deng, packaging model supports coordinated control, can be according to system emulation and PDE model meter
The related setting of calculation carries out customized, the nonlinear dynamic response characteristic of realization acquisition superconducting magnet in system emulation.
Wherein, the establishment step of superconducting magnet module specifically:
Step 1, superconducting magnet structure, and each composition some materials parameter are determined；Superconducting magnet structure includes coil form
Formula, the winding method of superconducting conductor, insulation system, support construction and conduction structure etc., component part include superconducting conductor,
Epoxy resins insulation, copper conduction structure, the material parameter being related in model includes magnetic conductivity, resistivity, thermal conductivity, specific heat
Hold.
Step 2, nonlinear PDEs model is established in finite element software, the nonlinear PDEs model includes: Formula (2) and (3) are respectively electromagnetic field PDE equation and heat transfer
PDE equation, the constraint condition of above-mentioned model include the boundary setting of magnetic field and heat transfer, the heat source in heat transfer model, specific to super
The magnetizer heat source shows as refrigeration work consumption；H is magnetic intensity vector in formula (2), and J is current density vectors, ρ1For material
Resistivity；The ρ in formula (3)2For density of material,For material specific heat capacity, k is material thermal conductivity, and u is medium conduction of velocity arrow
Amount；
Step 3, real-time A.C.power loss Q=E × J of superconductor is loaded into PDE model as heat source, realizes electromagnetism
Thermal coupling, E are electric field strength, and J is current density；
Step 4, nonlinear PDEs model is solved, t moment flux density is obtained and is distributed B (t), magnetic field distribution H (t), electric-field strength
Spend E (t), current density is distributed J (t), Temperature Distribution T (t), critical current Ic(t) and maximum temperature rise Tmax(t), and according to PDE
Calculated result obtains equivalent inductance Leq(t) and equivalent resistance Req(t)。
Step 5, according to equivalent inductance Leq(t) and equivalent resistance Req(t) transient current of superconducting magnet is obtained:Wherein i1For last moment current value, it is seen that nonlinear PDEs model can
By a controlled current flow source-representation, input is the pressure drop at the module both ends, the electric current of controlled current source by real-time voltage and
Equivalent inductance, resistance parameter decision, the nonlinear characteristic of the superconducting magnet fully considered.
Step 6, superconducting magnet is constructed according to nonlinear PDEs model, controlled current source, hysteresis module and voltage measurement unit
The input terminal of module, voltage measurement unit connects external power system, and the input terminal of hysteresis module is connected to voltage measurement unit
Output end, the output end of the input terminal connection hysteresis module of nonlinear PDEs model, the input terminal of controlled current source connects external
Electric system, the first output end of the control terminal connected nonlinearity PDE model of controlled current source；The first of nonlinear PDEs model
Output end is used to export the transient current of superconducting magnet, and the second output terminal of nonlinear PDEs model is for exporting the critical electricity of magnet
Flow Ic(t), maximum temperature rise Tmax(t), equivalent inductance Leq(t) and equivalent resistance Req(t).Calculating obtained in step 4,5 is public
Formula is incorporated into custom block, generates package module using the custom block tool that system carries.
After the completion of module encapsulation, system model is built in Softwares of System Simulation, customized packaging model is accessed, carry out
System emulation can realize that the synchronous of superconducting magnet non-linear response characteristic calculates.
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
Zhong row of the present invention is further described.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention.
This embodiment is small with superconduction list cake (singlepancakecoil, the SPC) composition of one three each 108 circles
Type magnet illustrates a kind of modeling side of high-temperature superconducting magnet nonlinear analysis for the response characteristic under variable-current excitation
Method.PDE module realizes that system emulation part is by Matlab/ by COMSOL Multiphysics simulation software in the example
Simulink realizes that specific implementation step is as follows.
(1) 9 Cr 2 steel using electromagnetic heating coupling model is built in COMSOL Multiphysics, establishes magnet PDE model, magnet structure
As shown in Figure 1, superconduction list cake has 4050 band coiling of Superpower to form, self-fields critical current 192A, winding inner diameter is
50mm, single cake thickness 36.5mm, cake height are 5.3mm, cake spacing 3mm.
(2) PDE model is exported as to the model of Matlab sentence pattern, and is embedded in customized S- in Simulink
In function, it is named as PDE_Model module, further includes a voltage measurement module, for taking superconducting magnet in addition to this
Input of the both end voltage as custom block, a hysteresis module, for eliminating the algebraic loop in emulation, output includes electricity
Stream, equivalent inductance L, equivalent resistance R, critical current Ic, maximum temperature rise Tmax, wherein output current value is as controlled current source
Signal, packaging effect are as shown in Figure 2；
(3) exciter control system is made of a voltage inverter (VSC) and a Buck-Boost inverter, VSC's
Input is three-phase alternating current, voltage 380V, for maintaining the voltage of DC bus；Buck-Boost inverter is used to according to control
Instruction control exciting current size, establishes whole system topological structure, as shown in figure 3, in Fig. 3 in Matlab/Simulink
FEM model be encapsulation after superconducting magnet module, [Vabc] be three-phase alternating voltage signal, [Iabc] be three-phase alternating current
Signal, [Udc] are VSC output voltage signal, and [Ir] controls output current signal, and [Uc1] controls output voltage signal.
Emulation duration is set as 6s, as a result as follows:
(1) as shown in figure 4, compared to control instruction value, actual current value fluctuation is more obvious, especially in curent change
More prominent when rate is higher, due to the presence of loss, simulated current value is lower than instruction value, using nonlinear block than former traditional mould
Block dynamic property is more accurate.
(2) in simulation process on the outside of magnet the critical current of cake and inside cake and temperature rise variation as shown in figure 5, according to
Formula (1) is it is found that superconductor critical current and Distribution of Magnetic Field are closely related, and outside cake magnetic field is larger, and critical current is lower, therefore
Loss is more concentrated, and temperature rise is also more obvious compared with inside cake.
(3) Fig. 6 is that the equivalent resistance of magnet and equivalent inductance change, inside and outside since E-J characteristic is exponentially non-linear
The equivalent resistance of side cake changes greatly, and instantaneous maximum value is more than 0.1 Ω of line impedance, will no longer be ignored, and outside cake is equivalent
Resistance is greater than inside cake, comparison diagram 4 and Fig. 6 it is found that non-linear being also more obvious of the more violent inductance of current fluctuation, fluctuation are more than
10%.
In conclusion the modeling method is realized simply, known magnet model and system model are only needed, magnet model is encapsulated
Combined calculation is carried out in system model, without other cumbersome data transfers, simulation result is than traditional pure electricity
Feel equivalent superconducting magnet to compare, simulation result is more accurate, can reflect the nonlinear characteristic of superconducting magnet, has centainly feasible
Property.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (2)
1. a kind of modeling method of high-temperature superconducting magnet nonlinear analysis, which is characterized in that include the following steps:
(1) structure, each component part and the material parameter of superconducting magnet model are determined；
Structure includes coil pattern, the winding method of superconducting conductor, insulation system, support construction and conduction structure, composition portion
Dividing includes superconducting conductor, epoxy resins insulation, copper conduction structure, and the material parameter being related in model includes magnetic conductivity, resistance
Rate, thermal conductivity and specific heat capacity；
(2) nonlinear PDEs model is established according to the structure of the superconducting magnet model, each component part and material parameter；Having
Nonlinear PDEs model is established in limit meta software；
The nonlinear PDEs model includes: electromagnetic field PDE equation
Conduct heat PDE equationAnd constraint condition；
The constraint condition includes: the boundary setting of magnetic field and heat transfer, the heat source in heat transfer model, specific to the superconducting magnet heat
Source shows as refrigeration work consumption；H is magnetic intensity vector in electromagnetic field PDE equation, and J is current density vectors, ρ1For material electricity
Resistance rate；The ρ in heat transfer PDE equation2For density of material,For material specific heat capacity, k is material thermal conductivity, and u is medium conduction speed
Spend vector；
(3) it is loaded into after realizing electromagnetism thermal coupling in PDE model and is repaired using the real-time A.C.power loss Q of superconductor as heat source
Nonlinear PDEs model after just, revised nonlinear PDEs model include:Wherein, A.C.power loss Q=E × J E is electric field strength, and J is electric current
Density；
(4) it solves revised nonlinear PDEs model and obtains the distribution of t moment flux density B (t), magnetic field distribution H (t), electric-field strength
Spend E (t), current density is distributed J (t), Temperature Distribution T (t), critical current Ic(t) and maximum temperature rise Tmax(t), and according to PDE
Calculated result obtains equivalent inductance Leq(t) and equivalent resistance Req(t)；The equivalent inductance
The equivalent resistance
(5) according to equivalent inductance Leq(t) and equivalent resistance Req(t) transient current of superconducting magnet is obtained:
(6) superconducting magnet module, electricity are constructed according to nonlinear PDEs model, controlled current source, hysteresis module and voltage measurement unit
The input terminal of measuring unit is pressed to connect external power system, the input terminal of hysteresis module is connected to the output of voltage measurement unit
End, the output end of the input terminal connection hysteresis module of nonlinear PDEs model, the input terminal of controlled current source connect external power system
System, the first output end of the control terminal connected nonlinearity PDE model of controlled current source；First output end of nonlinear PDEs model
For exporting the transient current of superconducting magnet, the second output terminal of nonlinear PDEs model is for exporting magnet critical current Ic
(t), maximum temperature rise Tmax(t), equivalent inductance Leq(t) and equivalent resistance Req(t)。
2. modeling method as described in claim 1, which is characterized in that in step (5), the transient currentWherein i1For last moment current value, it is seen that nonlinear PDEs model can be by one
A controlled current flow source-representation, input are the pressure drop at the module both ends, and the electric current of controlled current source is by real-time voltage, equivalent electricity
Sense, resistance parameter determine.
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| CN108763712B (en) * | 2018-05-22 | 2020-02-18 | 深圳供电局有限公司 | High-temperature superconducting CORC simulation modeling method |
| CN108845187B (en) * | 2018-06-13 | 2019-09-13 | 华中科技大学 | A kind of acquisition methods of the A.C.power loss of high-temperature superconducting magnet containing iron core |
| CN108959755B (en) * | 2018-06-27 | 2020-07-24 | 华中科技大学 | Simulation modeling method for spiral winding high-temperature superconducting through-current conductor |
| CN109884402B (en) * | 2018-12-20 | 2020-02-14 | 华中科技大学 | Method for acquiring alternating current loss of high-temperature superconducting magnet with three-dimensional asymmetric structure |
| CN111241676A (en) * | 2020-01-08 | 2020-06-05 | 广东电网有限责任公司电力科学研究院 | Modeling method, device and equipment based on current limiting type superconducting cable and storage medium |
| CN113496077B (en) * | 2020-04-07 | 2024-05-03 | 中国航天科工飞航技术研究院（中国航天海鹰机电技术研究院） | Method for calculating induced voltage of superconducting magnet under alternating magnetic field |
| CN112307655B (en) * | 2020-10-21 | 2023-12-05 | 江苏省送变电有限公司 | Composite insulator pollution risk level assessment method and system based on temperature detection |
| CN112462149B (en) * | 2020-11-19 | 2022-12-09 | 天津大学 | Superconducting coil electrical sensing method |
| CN113191033B (en) * | 2021-04-21 | 2023-03-28 | 上海工程技术大学 | Inductance simulation method for BOOST circuit inductance device |
| CN114156916B (en) * | 2021-11-02 | 2023-07-25 | 华中科技大学 | Superconducting energy storage system control method and device based on magnet state prediction |
| CN115659767A (en) * | 2022-12-29 | 2023-01-31 | 中国科学技术大学先进技术研究院 | Magnetic resonance radio frequency coil design method, device, equipment and readable storage medium |
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| US6480728B1 (en) * | 1999-12-13 | 2002-11-12 | Com Dev Ltd. | Superconductive non-linear transmission lines and method of construction |
| CN102945321A (en) * | 2012-10-29 | 2013-02-27 | 哈尔滨工业大学 | Modeling method for equivalent magnetic circuit model of strip-type nonlinear permanent magnet |
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