1. A simulation method of a high temperature superconducting cable, characterized by comprising the steps of:

step 1, obtaining a parameter calculation formula of the high-temperature superconducting cable, wherein the parameter comprises critical current density J_cSuperconducting layer resistance R_aSuperconducting layer temperature T;

step 2, building simulation logic of the high-temperature superconducting cable based on the parameter calculation formula obtained in the step 1;

step 3, establishing a high-temperature superconducting cable electrical element model based on PSCAD according to the simulation logic in the step 2;

and 4, constructing a simulation model of the high-temperature superconducting cable in the PSCAD, setting a fault through a fault generator for simulation, and analyzing the transient characteristic of the high-temperature superconducting cable in a fault state.

2. The simulation method of a hts cable according to claim 1,

critical current density J_cComprises the following steps:

where α is a parameter which is evaluated on the basis of different superconducting tapes, T_refIs the reference temperature, J_c(T_ref) Is the critical current density, T, of the superconducting layer at a reference temperature_cIs the critical temperature of the superconducting layer.

3. The simulation method of a hts cable according to claim 2,

superconducting layer resistance R_aComprises the following steps:

where ρ is_HTSThe resistivity of the superconducting tape is l, the length of the high-temperature superconducting cable is l, and the transverse sectional area of the high-temperature superconducting cable is A;

I_c＝J_c(T)×A

wherein I is the actual current, I_cIs critical current, T is superconducting layer temperature; j is the actual current density, J_c(T) is the critical current density at temperature T, E_cIs the critical electric field strength, and the value range of N is 21-30.

4. The simulation method of the hts cable according to claim 3,

the superconducting layer temperature T is:

wherein, t tableDenotes the time, d is the density of the superconducting layer, w is the width of the superconducting layer, T_in70K is the temperature of liquid nitrogen; h is the heat transfer coefficient, c is the heat capacity of the superconducting layer, and 2wl is the contact area of the superconducting layer and the liquid nitrogen layer.

5. The simulation method of the hts cable according to claim 4,

in the step 2, the simulation logic of the high-temperature superconducting cable is as follows:

s1, inputting an initial parameter T_refAnd J_c(T_ref)；

S2, using parameter T_refAnd J_c(T_ref) Initialization temperature T and critical current density J_c；

S3, calculating the current temperature T_n；

S4, according to the current temperature T_nCalculating the current critical current density J_c；

S5, inputting the real-time current density J according to the current temperature T_nCurrent critical current density J_cCalculating the real-time current density J and the resistivity rho_HTSAnd further calculating the superconducting layer resistance R_a；

S6, according to the resistance R of the superconducting layer_aCurrent temperature T_n(ii) a Calculating the temperature T after the time of Deltat_n+1And feeds back to step S3.

6. The simulation method of a hts cable according to claim 5,

in the step S3, the temperature T is fed back according to the step S6_n+1And assigning to obtain the current temperature T_n。

7. The simulation method of a hts cable according to claim 1,

in the step 3, the model of the high temperature superconducting cable electrical component is a control module, which comprises an input quantity and a real-time current I_a(ii) a And two outputs, real-time superconducting layer resistance R_aAnd a real-time superconducting layer temperature T.

8. The simulation method of a hts cable according to claim 7,

in the step 4, the simulation model comprises an input alternating current power supply, a superconducting layer resistor and a copper layer resistor which are connected in parallel, and a fault generator; the superconducting layer resistance is controlled by a control module.

9. The simulation method of the hts cable according to claim 8,

in the control module, a script is written according to the simulation logic using a programming language.

10. The simulation method of the hts cable according to claim 9,

the simulation was performed by setting the point of ground fault and the start time and duration of the fault by the fault generator.

Background

The superconducting transmission technology is one of advanced power grid technologies, and by utilizing the resistance-free characteristic of a superconducting material in a superconducting state, the superconducting material can replace conventional metal materials such as copper, aluminum and the like to serve as a current-carrying conductor, so that the high-density and large-capacity transmission requirements of a modern power grid are met. Compared with the conventional transmission cable, the High-temperature superconducting cable (HTS) has the advantages of large capacity, small area, low loss, environmental friendliness, no electromagnetic radiation, optimized electric energy structure and the like, and can generate huge technical and economic benefits. Therefore, the high-temperature superconducting cable is one of the key technologies for solving the problem of high-density power transmission, and the research on the superconducting power transmission technology has great significance.

The YBCO high-temperature superconducting cable is a superconducting material which enables the superconducting temperature to be more than 77K and is a cooling medium by using liquid nitrogen with relatively low price, so that the YBCO high-temperature superconducting cable is a key research object of the high-temperature superconducting material since discovery.

The high temperature superconducting cable is composed of a plurality of YBCO tapes spirally wound on a cylindrical copper layer to form a multilayer structure to achieve high current carrying capacity. Under normal operating conditions, the resistivity of the superconducting layer of the high-temperature superconducting cable is negligible, and at the moment rho_HTS0. However, since the resistivity of the superconducting layer is greatly affected by current density and temperature, and the thermal capacity of the superconducting tape of the YBCO high-temperature superconducting cable is much smaller than that of a conventional conductor, the transient response of the high-temperature superconducting cable becomes complicated when a fault current occurs.

In a fault state, the resistance of a superconducting layer in a high-temperature superconducting cable is characterized by being a function of current density and temperature, the current density can be changed along with the occurrence of faults, the temperature is changed due to the change of the current density, the resistance is changed due to the change of the temperature, and finally the current density is influenced, so that the resistance changes depending on the resistance in a cyclic process.

Therefore, it is necessary to simulate the transient response of the high temperature superconducting cable, and a superconducting cable model related to current density and temperature is established in the PSCAD. The model can simulate the transient response of temperature and current of the superconducting layer and the copper resistance layer when the high-temperature superconducting cable encounters a short-circuit fault.

Disclosure of Invention

In order to solve the defects in the prior art, the invention aims to provide a simulation method of a high-temperature superconducting cable, which constructs a high-temperature superconducting cable electric element model in PSCAD and carries out simulation by applying faults, thereby simulating the transient response characteristic of the high-temperature superconducting cable in a fault state in real time.

The invention adopts the following technical scheme.

A simulation method of a high temperature superconducting cable includes the steps:

step 1, obtaining a parameter calculation formula of the high-temperature superconducting cable, wherein the parameter comprises critical current density J_cSuperconducting layer resistance R_aSuperconducting layer temperature T;

step 2, building simulation logic of the high-temperature superconducting cable based on the parameter calculation formula obtained in the step 1;

step 3, establishing a high-temperature superconducting cable electrical element model based on PSCAD according to the simulation logic in the step 2;

and 4, constructing a simulation model of the high-temperature superconducting cable in the PSCAD, setting a fault through a fault generator for simulation, and analyzing the transient characteristic of the high-temperature superconducting cable in a fault state.

Further, critical current density J_cComprises the following steps:

where α is a parameter which is evaluated on the basis of different superconducting tapes, T_refIs the reference temperature, J_c(T_ref) Is the critical current density, T, of the superconducting layer at a reference temperature_cIs the critical temperature of the superconducting layer.

Further, superconducting layer resistance R_aComprises the following steps:

where ρ is_HTSThe resistivity of the superconducting tape is l, the length of the high-temperature superconducting cable is l, and the transverse sectional area of the high-temperature superconducting cable is A;

I_c＝J_c(T)×A

wherein I isCurrent, I_cIs critical current, T is superconducting layer temperature; j is the actual current density, J_c(T) is the critical current density at temperature T, E_cIs the critical electric field strength, and the value range of N is 21-30.

Further, the superconducting layer temperature T is:

where T represents time, d is the density of the superconducting layer, w is the width of the superconducting layer, T_in70K is the temperature of liquid nitrogen; h is the heat transfer coefficient, c is the heat capacity of the superconducting layer, and 2wl is the contact area of the superconducting layer and the liquid nitrogen layer.

Further, in the step 2, the simulation logic of the high temperature superconducting cable is:

s1, inputting an initial parameter T_refAnd J_c(T_ref)；

S2, using parameter T_refAnd J_c(T_ref) Initialization temperature T and critical current density J_c；

S3, calculating the current temperature T_n；

S4, according to the current temperature T_nCalculating the current critical current density J_c；

S5, inputting the real-time current density J according to the current temperature T_nCurrent critical current density J_cCalculating the real-time current density J and the resistivity rho_HTSAnd further calculating the superconducting layer resistance R_a；

S6, according to the resistance R of the superconducting layer_aCurrent temperature T_n(ii) a Calculating the temperature T after the time of Deltat_n+1And feeds back to step S3.

Further, in the step S3, the temperature T is fed back according to the step S6_n+1And assigning to obtain the current temperature T_n。

Further, in step 3, the model of the electrical component of the hts cable is a control module, which includes an input, real-time current I_a(ii) a Two outputsReal-time superconducting layer resistance R_aAnd a real-time superconducting layer temperature T.

Further, in the step 4, the simulation model includes an input ac power supply, a superconducting layer resistor and a copper layer resistor connected in parallel, and a fault generator; the superconducting layer resistance is controlled by a control module.

Further, in the control module, scripts are written according to the simulation logic using a programming language.

Further, the simulation was performed by setting the point of ground fault and the start time and duration of the fault by the fault generator.

Compared with the prior art, the core influence factor of the mathematical model of the dynamic characteristic of the high-temperature superconducting cable is the temperature of the superconducting layer of the superconducting cable, and the change of the temperature can bring the change of the critical current density and the resistance of the superconducting layer, further influence the change of the temperature, and circulate in this way. The invention constructs the high-temperature superconducting cable electric element model in the PSCAD, and can simulate the transient response characteristic of the high-temperature superconducting cable in a fault state in real time by applying fault simulation. The mathematical model of the superconducting cable obtained by the simulation method is more accurate, the electrical characteristics of the superconducting cable can be more accurately represented, and the further application and analysis of the superconducting cable are facilitated.

Drawings

Fig. 1 is a flowchart of a simulation method of a hts cable according to the present invention;

FIG. 2 is a logic block diagram of a simulation model of the HTC cable;

FIG. 3 is a high temperature superconducting cable equivalent control module;

fig. 4 is a circuit diagram of a simulation of the PSCAD high-temperature superconducting cable.

Detailed Description

The present application is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present application is not limited thereby.

As shown in fig. 1, the simulation method of the hts cable according to the present invention includes the steps of:

(1) obtaining a parameter calculation formula of the high-temperature superconducting cable for simulation, wherein the parameter comprises critical current density J_cSuperconducting layer resistance R_aSuperconducting layer temperature T;

(1.1) Critical Current Density J_c；

The critical current density and critical temperature are two important parameters that directly affect the resistivity of the superconducting layer. Critical current density J of superconducting layer of YBCO high-temperature superconducting cable_cIn relation to the temperature T, the expression is:

wherein alpha is a parameter which is taken as a value according to different superconducting tapes, and the value of alpha of the YBCO superconducting tape adopted by the invention is 1.5; t is_refThe unit of the reference temperature is Kelvin (K), and the operation temperature 70K of the high-temperature superconducting cable is used as the reference temperature; j. the design is a square_c(T_ref) Is the critical current density, J, at the reference temperature of the YBCO superconductive layer_c(T_ref)＝3.5×10¹⁰A/m²；T_cIs the critical temperature, T, of the YBCO superconductive layer_c＝89K。

Critical current I_cThe expression of (a) is:

I_c＝J_c(T)×A (2)

wherein A is the transverse cross-sectional area of the high-temperature superconducting cable and the unit is mm²。

(1.2) superconducting layer resistance R_a；

For YBCO high temperature superconducting cables, the superconducting layer is connected in parallel with the copper layer. If the current of the superconducting layer is less than the critical current, the resistivity of the superconducting layer is 0, and the current can flow through the superconducting layer; however, when the current in the superconducting layer exceeds the critical current, the resistivity of the superconducting layer abruptly increases, causing most of the current to flow through the copper layer.

As can be seen from equation (1), the critical current density of the superconducting layer is 0 after the temperature exceeds the critical temperature. Thus, the resistivity of the YBCO superconducting layer can be viewed as a piecewise function of the actual current and the actual temperature.

a. When the actual current I is less than the critical current I_cThe temperature T of the superconducting layer is less than the critical temperature T_cWhen the current is over;

when the superconducting cable is in a superconducting state, the resistivity of the superconducting layer is rho_HTS＝0。

b. When the actual current I is larger than the critical current I_cThe temperature T of the superconducting layer is less than the critical temperature T_cWhen the current is over;

at this time, the YBCO superconducting layer quenches, and the resistivity of the superconducting layer is increased. Resistivity p of superconducting layer_HTsNon-linearly related to temperature T and current density J:

wherein E is_cIs the critical electric field intensity, for the YBCO superconducting cable of the present invention, E_c1 μ V/cm. For the YBCO strip, the value range of N is 21-30, N in the invention is 30, and J is the actual current density; j. the design is a square_c(T) is the critical current density at that temperature, in units of A/m²。

When the actual current is larger than the critical current, the thermal effect causes the resistivity of the superconducting layer to increase exponentially, thereby causing the temperature of the superconducting layer to increase.

c. When the temperature T of the superconducting layer is greater than the critical temperature T_cWhen the current is over;

the YBCO superconducting layer will lose its superconducting properties completely and turn into the normal state. At this point, current flows through the copper layer in parallel with the superconducting layer. In this case, assuming that the resistance of the superconducting layer is equal to that of the copper layer, the resistivity of the superconducting layer is:

ρ_HTS＝(0.0084T-0.4603)×10^-8 77K<T<250K (4)

wherein the empirical parameters are calculated according to the resistivity of the copper and taking into account the temperature variation characteristics.

Thus, the resistivity ρ of the superconductive layer in three states_HTS：

Knowing the resistivity of the superconductive layer in three states, it is readily possible to obtain a superconductive layer with a resistance of:

where ρ is_HTSThe above has been obtained for the resistivity of the superconducting tape; l is the length of the superconducting cable in meters; and A is the transverse cross-sectional area of the superconducting cable, and the unit is square millimeter.

(1.3) superconducting layer temperature T;

when the high-temperature superconducting cable operates in a normal state, the temperature of the high-temperature superconducting cable is kept unchanged. When a short circuit occurs, the temperature of the superconducting layer increases, and the temperature characteristics of the superconducting cable change, thereby causing a change in the resistance of the superconducting layer. Therefore, it is necessary to study the heat transfer of the high temperature superconducting cable.

The temperature difference of the liquid nitrogen in the axial direction depends on the heat leakage which is negligible, and therefore, the temperature of the liquid nitrogen is almost constant when the superconducting cable length is less than 1 km. In the following analysis, only the heat transfer of the transverse cross-section of the cable is considered. The temperature of the superconducting layer may be expressed as a piecewise function related to the short circuit current.

a. When a short-circuit fault occurs, the actual current I>Critical current I_c；

According to the law of conservation of energy, assuming that the superconducting cable does not exchange heat with the external environment, the heat generated by the superconducting layer is absorbed by the superconductor itself and the outer shell of liquid nitrogen. Since the time for the short-circuit failure is short, the superconducting layer temperature changes depending on the amount of heat absorbed by the superconducting layer, assuming that there is no temperature change in the liquid nitrogen enclosure.

Heat Q generated by superconducting layer_jComprises the following steps:

Q_j＝I²R_at (7)

wherein t represents time in seconds; i is the current actually flowing through the superconducting layer, and the unit is ampere; r_aThe superconducting layer resistance is given in ohms.

The amount of heat absorbed by the superconducting layer depends on its heat capacity c and the mass m of the superconducting tape:

Q_HTS＝cmΔT＝cdAl(T_n+1-T_n)(8)

wherein d is the density of the superconductor; Δ T is the superconducting layer temperature increment, and T is used in each iteration step_n+1-T_nTo represent; l is the length of the superconducting cable; and A is the transverse cross-sectional area of the superconducting cable.

The heat dissipated by the liquid nitrogen is:

Q_LN2＝2hwlt(T_n+1-T_in)(9)

wherein w is the width of the superconducting layer in millimeters; 2wl is the contact area of the superconducting layer and the liquid nitrogen layer; t is_in70K is the temperature of liquid nitrogen; h is a heat transfer coefficient representing the efficiency of heat transfer from the superconducting layer to the liquid nitrogen layer, and in the invention, the value of h is 1.5W-cm^-2·K^-1。

Assuming no heat leak, the equation for transfer between the heat quantities is, according to the law of conservation of energy:

Q_j＝Q_HTS+Q_LN2 (10)

after each iteration of Δ T time, T_n+1A new value is generated, and T can be derived by the equations (6) - (10)_n+1Expression (c):

b. when the fault is over, the actual current I<Critical current I_c；

After the fault current is over, if the superconducting tape is not permanently damaged, the resistance of the superconducting layer begins to be gradually reduced and is converted into the superconducting state again. At this point, the superconducting layer no longer generates heat, which previously would be slowly dissipated through the liquid nitrogen layer, and a new T_n+1The expression of (a) is:

therefore, superconducting layer temperature T:

the parameter values used by the formulas (1) to (13) in the embodiment of the invention take values: the width w of the YBCO superconducting layer is 0.0048 m; the transverse sectional area A of the YBCO superconducting layer is 59.52mm²(ii) a The length l of the superconducting cable is 1.15 km; the thermal capacity c of the YBCO superconducting layer takes 390J/kg.K; the density d of YBCO superconducting layer is 5.7 x 10³kg/m³。

(2) Constructing a simulation logic of the high-temperature superconducting cable based on the parameter calculation formula obtained in the step 1;

as shown in fig. 2, the logic flow of the simulation model of the YBCO high-temperature superconducting cable includes the steps of:

s1, inputting initial parameters: high-temperature superconducting cable operation reference temperature T_ref(ii) a Critical current density J of YBCO superconductive layer at reference temperature_c(T_ref)；

S2, using parameter T_refAnd J_c(T_ref) Initialization temperature T and critical current density J_c；

S3, calculating the current temperature T_n；

Temperature T fed back according to step S6_n+1And assigning to obtain the current temperature T_n. Current temperature T_nInitial value of T_ref。

S4, according to the current temperature T_nCalculating the current critical current density J by adopting the formula (1) in the step (1.1)_c；

S5, inputting the real-time current density J according to the current temperature T_nCurrent critical current density J_cAnd (3) calculating the resistivity rho by adopting a formula (5) in the step (1.2) according to the real-time current density J_HTSGo to further lead toCalculating the resistance R of the superconducting layer by the formula (6)_a；

S6, according to the resistance R of the superconducting layer_aCurrent temperature T_n(ii) a Calculating the temperature T after the time of delta T by adopting the formula (13) in the step (1.3)_n+1And feeds back to step S3.

The insulation layer of the cold insulation high temperature superconducting cable considered by the invention is designed outside the shielding layer, when the coaxially designed cold insulation high temperature superconducting cable runs at the temperature of liquid nitrogen, and the shielding layer passes the reverse current with the same current value as the current value of the superconducting layer, no magnetic field exists outside the shielding layer of the superconducting cable. The problems that when the cold insulation high-temperature superconducting cable is used for a three-phase power transmission system, one phase of the superconducting cable generates an electromagnetic induction effect on the metal layer of the adjacent phase of the superconducting cable, and the critical current of the conductor is degraded due to the action of a vertical external magnetic field on the adjacent superconducting cable conductor are solved. Therefore, the influence of the magnetic field on the operating state of the superconducting cable can be not considered in the modeling.

(3) Establishing a high-temperature superconducting cable electrical element model based on PSCAD according to the simulation logic in the step (2);

as can be seen from FIG. 2, the superconducting layer temperature T is the critical current density J of the superconducting resistor, which is the core part of the whole electrical model_cAnd resistivity ρ_HTSAll affected by the temperature change, calculating the temperature change in a fixed time interval delta T to obtain the real-time temperature T of the next moment_n+1Then through the real-time temperature T_n+1And calculating the real-time current density J to obtain resistivity rho_HTSFinally, the resistance R of the superconducting layer is calculated_a。

A new component of high temperature superconducting cable is built in PSCAD, as shown in FIG. 3, the superconducting resistance R_aIs controlled by a "Control mode". I is_aAs an input quantity of a Control module (Control mode), a real-time current flowing through the superconducting resistor is used; r_aAnd T is two outputs of the control module, representing the real-time resistance and the real-time temperature of the superconducting cable, respectively. The control module is used for controlling the current I flowing through the superconducting layer according to the real-time current_aTo control the resistance R of the superconducting layer_aAnd a temperature T.

In the control module, the high temperature is defined firstAll parameter variable values related to the superconducting cable are written according to the simulation logic flow calculation method in the step (2) by using Fortran language, and the real-time temperature T and the resistance R of the superconducting cable are finally obtained_a。

(4) Constructing a simulation model of the high-temperature superconducting cable in the PSCAD; setting a fault through a fault generator for simulation, and analyzing the transient characteristics of the temperature, the resistance and the current of the superconducting cable in a fault state;

as shown in FIG. 4, a simulation model of a high temperature superconducting cable is constructed in PSCAD, including an input AC power source, and a parallel superconducting layer resistor R_aResistance with copper layer R_cuAnd a fault generator. The fault generator can conveniently set single-phase earth fault and fault starting time and duration.

The Variable RLC components in the component library are used to define a Variable resistance to represent the superconducting layer resistance R of the high temperature superconducting cable_a. Resistance R of superconducting layer_aResistance with copper layer R_cuIn parallel, when the superconducting cable is quenched, current will flow through the resistance of the copper layer.

Variable superconducting resistance R_aIs controlled by the Control module (Control mode) in fig. 3.

The earth fault is set by the fault generator, the fault point, the fault start time and duration, etc. are set. When a fault occurs, the resistance of the superconducting layer gradually rises, so that the current flowing through the resistance of the superconducting layer generates heat, the temperature of the superconducting layer rises, the critical current density is influenced, the resistance changes continuously, new heat is generated by the change of the resistance, the process is an iterative process, and each parameter is influenced by other parameters and changes continuously. Therefore, the transient characteristics of temperature, resistance and current of the superconducting cable in a fault state can be analyzed by setting a fault and carrying out simulation.

Compared with the prior art, the method has the advantages that a mathematical model of the dynamic characteristics of the high-temperature superconducting cable is researched, the core influence factor of the whole mathematical model is the temperature of the superconducting layer of the superconducting cable, the change of the temperature can bring the change of the critical current density and the resistance of the superconducting layer, the change of the temperature is further influenced, and the steps are repeated. The invention constructs the high-temperature superconducting cable electric element model in the PSCAD, and can simulate the transient response characteristic of the high-temperature superconducting cable in a fault state in real time by applying fault simulation. The mathematical model of the superconducting cable obtained by the simulation method is more accurate, the electrical characteristics of the superconducting cable can be more accurately represented, and the further application and analysis of the superconducting cable are facilitated.

The present applicant has described and illustrated embodiments of the present invention in detail with reference to the accompanying drawings, but it should be understood by those skilled in the art that the above embodiments are merely preferred embodiments of the present invention, and the detailed description is only for the purpose of helping the reader to better understand the spirit of the present invention, and not for limiting the scope of the present invention, and on the contrary, any improvement or modification made based on the spirit of the present invention should fall within the scope of the present invention.