Isothermal design method and system for dry-type hollow current-limiting reactor

Abstract

The invention discloses an isothermal design method of a dry-type hollow current-limiting reactor. The method comprises the following steps: enabling N layers of envelopes of the dry-type hollow current-limiting reactor to be equivalent to coaxial hollow solenoids; calculating mutual inductance between any two coaxial hollow solenoids, and calculating to obtain self-inductance of each hollow solenoid; an equivalent circuit equation is established, according to equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation, current values passing through each layer of encapsulation are calculated, and corresponding active and reactive components are calculated; establishing an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type hollow current-limiting reactor by using a finite element simulation tool in combination with the active component and the reactive component; calculating the electrothermal effect of each layer of encapsulation by combining an equivalent circuit simulation model and an equivalent coil simulation model; and calculating variances of all encapsulated electrothermal effects, comparing the variances with a threshold value, and judging whether electrothermal effect control requirements are met or not. According to the invention, the temperature rise design distribution of the dry-type hollow current-limiting reactor is more uniform.

Description

Technical Field

[0001] The present invention belongs to the technical field of isothermal design of reactors, and particularly relates to an isothermal design method and system for dry-type air-core current-limiting reactors. Background Art

[0002] With the rapid construction and development of AC and DC power grids in China, the problem of excessive short-circuit current in the power grid has gradually emerged. According to calculations, if no measures are taken to limit short-time current in the next few years, the short-circuit current of multiple 500 kV substations will exceed the breaking current of the current circuit breakers, and there are even more substations approaching this current, which will seriously affect the safe and stable operation of the power grid. Installing a series current-limiting reactor is the simplest and most effective way to limit the short-circuit current in the line. This method can effectively reduce the short-circuit current level of the installed line and play a role in isolating dense power source points. Dry-type air-core reactors have excellent electrical characteristics such as good linearity, low loss, low noise, stable parameters, and good fire resistance. Therefore, dry-type reactors are very suitable for use in ultra-high voltage and extra-high voltage lines to limit short-circuit current and ensure the safe and stable operation of the line.

[0003] Existing dry-type air-core reactors have given the relevant principles of the design of air-core reactors by selecting conductors and calculating temperature rise. However, it has limitations if it is used for dry-type air-core current-limiting reactors in 500 kV systems. With the increase in load level, especially the continuous improvement of the capacity of extra-high voltage transmission lines connecting urban loads. In order to limit the short-circuit current of large-capacity transmission lines, it is urgent to design extra-high voltage large-capacity dry-type air-core current-limiting reactors for 500 kV systems. The required current-carrying capacity can reach 4000 A, 5000 A or even more than 6000 A, and its capacity can reach 175 MVar, 225 Mvar or even 252 Mvar. The magnetic field intensity generated by the reactor body is far greater than 3×10 5 A / m, so it is necessary to consider the influence of the magnetic field intensity generated by the reactor body on the conductors of the reactor body. In addition, the eddy current loss of the conductors in large-capacity dry-type air-core current-limiting reactors in 500 kV systems will show non-linear growth. In the case of a strong magnetic field, extremely strong eddy current losses will be generated, resulting in a large amount of heat, and then causing the temperature of the reactor body to rise, affecting the safe and stable operation of the current-limiting reactor. Therefore, it is necessary to consider the influence of the magnetic field intensity generated by the reactor body on the conductors of the reactor body.

[0004] As in the prior art solution, the patent application with the publication number CN116384161A proposed a method for realizing a dry-type air-core reactor. The reactor adopted a traditional fully parallel or series-parallel pancake coil structure, and the current passing through it was limited by a single wire, and the maximum current was determined by a single wire. Therefore, a relatively large current (1000 kA and above) could not be passed. Moreover, this patent solution only adjusted the reactor parameters from the balance of overall temperature / loss, and did not recognize that as the capacity increased, the eddy current loss caused by extremely uneven magnetic field distribution became an important influencing factor in the design and manufacture of large-capacity UHV series compensation reactors. The uneven characteristics of the electromagnetic field distribution and the influence of eddy current loss were not considered in the temperature rise calculation.

[0005] Therefore, there is an urgent need for a temperature rise calculation method for a large-capacity UHV dry-type air-core current-limiting reactor that takes into account both the uneven characteristics of the electromagnetic field distribution of the dry-type air-core reactor and the eddy current loss of the wires of the reactor body. Summary of the Invention

[0006] To solve the deficiencies in the prior art, the present invention provides an isothermal design method and system for a dry-type air-core current-limiting reactor, which takes into account the uneven characteristics of the electromagnetic field distribution of the dry-type air-core reactor and the eddy current loss of the wires of the reactor body, so as to make the temperature rise design distribution of the dry-type air-core current-limiting reactor more uniform.

[0007] The present invention adopts the following technical solutions.

[0008] The present invention proposes an isothermal design method for a dry-type air-core current-limiting reactor, including: S1, equivalent the N-layer windings of the dry-type air-core current-limiting reactor into coaxial air-core solenoids; calculate the mutual inductance between any two coaxial air-core solenoids, and calculate the self-inductance of each air-core solenoid, where the dry-type air-core current-limiting reactor adopts a multi-layer and multi-spiral parallel winding method; S2, establish an equivalent circuit equation of the dry-type air-core current-limiting reactor, and calculate the current values passing through each layer of windings according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation; S3, calculate the corresponding active and reactive components according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance of each layer of winding; S4, combine the active and reactive components, and use a finite element simulation tool to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor; S5, combine the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model, and calculate the electrothermal effect of each layer of winding of the dry-type air-core current-limiting reactor; calculate the variance of the electrothermal effects of all windings, compare the variance with a threshold value, and judge whether to change the wire usage parameters and recalculate the electrothermal effect until the variance is less than the threshold value.

[0009] Further, in S1, each encapsulation layer in the dry-type air-core current-limiting reactor is numbered, with a total of N layers; The N encapsulation layers of the dry-type air-core current-limiting reactor are equivalent to coaxial air-core solenoids; any two coaxial air-core solenoids are respectively defined as the first solenoid and the second solenoid; calculate the mutual inductance of the single-turn coil at x' on the first solenoid with respect to the single-turn coil at x'' on the second solenoid ; According to the mutual inductance of the single-turn coil on the first solenoid with respect to the entire second solenoid calculate the mutual inductance between the first solenoid and the second solenoid ; Further, based on the mutual inductance , obtain the self-inductance of each solenoid.

[0010] Further, let the number of turns per unit length of the first solenoid and the second solenoid be n 1 and n 2 respectively. According to the integral principle, the mutual inductance x' of the single-turn coil at x'' on the first solenoid with respect to the single-turn coil at on the second solenoid is: ; where represents the radius of the first single-turn coil, represents the radius of the second single-turn coil, represents the height of the first single-turn coil, represents the height of the second single-turn coil, represents the angle between the point x' on the single-turn coil and the axis, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the vacuum permeability.

[0011] Further, according to the mutual inductance of the single-turn coil on the first solenoid with respect to the entire second solenoid calculate the mutual inductance between the first solenoid and the second solenoid : ; where the function is related to the geometric parameters and relative positions of the solenoids; represents the radius of the first single-turn coil, represents the radius of the second single-turn coil; n 1 and n 2 are respectively the number of turns per unit length of the first solenoid and the second solenoid; is the vacuum permeability; , , and are four corresponding positions on the Z-axis; For the i th encapsulation height is h , the number of turns per unit length is n , and the coil radius is r of the thin-walled solenoid, where i = 1,..., N, and N is the total number of encapsulations. It can be considered that , , then the self-inductance of the coil is: ; Through the iteration of the function , the equivalent self-inductance and mutual inductance of each layer of encapsulation are obtained.

[0012] Furthermore, in S2, an equivalent circuit equation of the dry-type air-core current-limiting reactor is established as follows: ; Among them, is the power frequency angular frequency; and are the resistance and self-inductance of each layer of encapsulation respectively; is the mutual inductance between every two layers of encapsulation; is the current passing through each layer of encapsulation; is the voltage applied to each layer of encapsulation.

[0013] Furthermore, in S4, using a finite element simulation tool, an equivalent circuit simulation model corresponding to the topological structure in the dry-type air-core current-limiting reactor is established according to the mutual inductance between different encapsulation layers, the self-inductance and resistance of each encapsulation layer, and the active and reactive components of each layer of encapsulation; according to the equivalent circuit simulation model, the current distribution of each layer of encapsulation is obtained I 1e , I 2e , I 3e ...., I Ne ; Using a finite element simulation tool, based on the parameters of the coaxial air-core solenoid, the parameters including the number of turns, height, and radius of the coils of each layer of encapsulation, an equivalent coil simulation model is created; according to the equivalent coil simulation model, the magnetic induction intensity at the position of each layer of encapsulation is obtained.

[0014] Furthermore, in S5, combining the current distribution of the equivalent circuit simulation model and the magnetic induction intensity of the equivalent coil simulation model, the electro-thermal effects of the 1st to Nth layers of the dry-type air-core current-limiting reactor are calculated and marked as Q 1, Q 2, Q 3...., QN : ; Wherein, is the electro-thermal effect of the i-th layer of encapsulation, i = 1,..., N, is the eddy current loss heat dissipation coefficient of the i th layer of encapsulation, is the through-flow loss heat dissipation coefficient related to the i th layer of encapsulation, and are set according to empirical values, is the resistivity of the i th layer of encapsulation, B i is the magnetic induction intensity at the position where the i th layer of encapsulation is located, V i is the volume of the i th layer of encapsulation, I i is the current flowing through the i th layer of encapsulation, R i is the resistance of the i th layer of encapsulation.

[0015] Furthermore, calculate the Q 1, Q 2, Q 3...., Q N variance of. If the variance does not exceed the threshold, the electro-thermal effect control requirements are met; if the variance exceeds the threshold, change the usage parameters of the coils in each layer of encapsulation, recalculate the electro-thermal effect of each layer of encapsulation until the variance is less than the threshold.

[0016] The present invention also proposes an isothermal design system for a dry-type air-core current-limiting reactor, including an inductance calculation module, a model establishment and component calculation module, a simulation model construction module, and an electro-thermal effect evaluation and optimization module: The inductance calculation module equates the N layers of encapsulation of the dry-type air-core current-limiting reactor to coaxial air-core solenoids; calculates the mutual inductance between any two coaxial air-core solenoids, and calculates the self-inductance of each air-core solenoid; The model establishment and component calculation module establishes the equivalent circuit equation of the dry-type air-core current-limiting reactor, and calculates the current values passing through each layer of encapsulation according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance of each layer of encapsulation; The simulation model construction module combines the active and reactive components and uses a finite element simulation tool to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor; The electrothermal effect evaluation and optimization module calculates the electrothermal effect of each layer of the dry-type air-core current-limiting reactor by combining the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model; calculates the variance of the electrothermal effects of all the windings, compares the variance with a threshold value, and determines whether to change the usage parameters of the wire and recalculate the electrothermal effect until the variance is less than the threshold value.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By equating the reactor winding to a coaxial air-core solenoid to calculate the mutual inductance and self-inductance, establishing an equivalent circuit equation to solve the current value, and then analyzing the active and reactive components, the present invention comprehensively and accurately simulates the operating state of the reactor, making the design more in line with the actual situation and improving the accuracy of the design.

[0018] 2. The present invention uses a finite element simulation tool to establish an equivalent circuit and an equivalent coil simulation model, and calculates the electrothermal effect in combination with the model parameters. By calculating the variance of the electrothermal effect and comparing it with the threshold value, and adjusting the usage parameters of the wire, the temperature rise distribution of each layer of the reactor can be effectively optimized. This method can avoid local overheating, ensure the safe and stable operation of the reactor, and extend the service life of the equipment.

[0019] 3. The isothermal design method and system provided by the present invention are applicable to large-capacity dry-type air-core current-limiting reactors, enhance the application adaptability of the reactors in ultra-high voltage and extra-high voltage lines, and are of great significance to the safe and stable operation of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flowchart of a method for isothermal design of a dry-type air-core current-limiting reactor according to the present invention; Figure 2 is an equivalent diagram of a coaxial air-core solenoid of a method for isothermal design of a dry-type air-core current-limiting reactor according to the present invention; Figure 3 is a circuit model diagram of a dry-type air-core reactor of a method for isothermal design of a dry-type air-core current-limiting reactor according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the spirit of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0022] The present invention proposes a method for calculating the temperature rise of a dry-type air-core current-limiting reactor, as Figure 1As shown, the method flow chart of the present invention is presented, and the specific steps are as follows.

[0023] Step 1, the dry-type air-core current-limiting reactor adopts a multi-layer and multi-spiral parallel winding method; number each package layer in the dry-type air-core current-limiting reactor, with a total of N layers; Step 2, equivalent the N package layers of the dry-type air-core current-limiting reactor into coaxial air-core solenoids; define any two coaxial air-core solenoids as the first solenoid and the second solenoid respectively; assume that the number of turns per unit length of the first solenoid and the second solenoid are n 1 and n 2 respectively. According to the integral principle, the mutual inductance of the first single-turn coil at x' on the first solenoid to the single-turn coil at x'' on the second solenoid is: ; Among them, represents the radius of the first single-turn coil, represents the radius of the second single-turn coil, represents the height of the first single-turn coil, represents the height of the second single-turn coil, represents the angle between the x' point on the single-turn coil and the axis, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the vacuum permeability.

[0024] The mutual inductance between the first solenoid and the second solenoid is obtained as: ; Among them, the function is related to the geometric parameters and relative positions of the solenoids; represents the radius of the first single-turn coil, represents the radius of the second single-turn coil; n 1 and n 2 are the number of turns per unit length of the first solenoid and the second solenoid respectively; is the vacuum permeability; , , and are the four corresponding positions on the Z axis; The definition of the function is as follows: ; In the function , , , and The meaning is as follows: ; The function can be rewritten in the following form: ; In the formula, ; ; ; ; ; ; For the self - inductance of the thin - walled solenoid with the height of the i - th envelope being h, the number of turns per unit length being n, and the coil radius being r, where i = 1,..., N and N is the total number of envelopes, it can be considered that , , then the self - inductance of the coil is: ; In the case of z = 0, A = 1 / 3, B = 0, so , then it is rewritten as: ; After rewriting, the function is transformed into the standard form of the Bartky transformation. By iteration, the self - inductance and mutual inductance of each layer of the coil envelope are obtained.

[0025] The iterative method for obtaining is as follows: ; ; ; Step 3, establish the equivalent circuit of the dry - type air - core current - limiting reactor, as shown in Figure 3 . The winding of the dry - type air - core reactor of the present invention is a multi - layer cylindrical parallel connection. Each layer of the winding has a self - inductance L 11 , L 22 ,...... L ii , and there are mutual inductances M 12 , M 13 , M 14, etc., and each layer of winding has a different DC resistance R 1、 R 2、 R 3、...... R i , the DC resistance value changes with temperature. The circuit topology of the reactor is equivalent to a parallel circuit between the reactances of each layer of encapsulation. The equivalent circuit equation of the dry-type air-core current-limiting reactor is as follows: ; For the power frequency angular frequency , there is the following relationship: ; According to the equivalent circuit equation of the dry-type air-core current-limiting reactor, the resistance matrix , inductance matrix and voltage matrix can be obtained: ; Usually, the harmonic current flowing through the dry-type air-core current-limiting reactor is a known quantity. Considering that: , where ; Multiply both sides of the above equation by the vector to get: ; Then the combined admittance of the dry-type air-core current-limiting reactor is: ; The combined impedance is , then . Substitute this equation into to calculate the current values in each layer of coil encapsulation.

[0026] Step 4, calculate the active and reactive components based on the equivalent resistance and equivalent inductance in each layer of encapsulation; use the finite element simulation tool to establish the equivalent circuit and equivalent coil of the dry-type air-core current-limiting reactor, and calculate the electrothermal effects of the reactor from layer 1 to layer N, which are respectively marked as Q 2、 Q 3....、 Q N .

[0027] The specific steps are: Use the finite element simulation tool, according to the self-inductance of each layer of winding obtained in step 3 L 11 、 L 22 、...... L ii , the mutual inductance between layersM 12 , M 13 , M 14 , ...... etc., and the different DC resistances of each layer of winding R 1. R 2. R 3, ...... R i , combining the active and reactive components of each layer of encapsulation, constructing an equivalent circuit according to the topological structure of the parallel circuit, simulating the reactance of each layer of encapsulation as an element in the circuit, and building an equivalent circuit simulation model corresponding to the actual reactor winding structure. The current distribution of each layer of encapsulation can be obtained according to the equivalent circuit simulation model I 1e , I 2e , I 3e .... , I Ne .

[0028] Using a finite element simulation tool, based on the parameters of the coaxial hollow solenoid, including the number of turns, height, radius, etc. of each layer of encapsulation, using the modeling function in the tool to create an equivalent coil simulation model of the actual coil electromagnetic characteristics, simulating the actual situation of the reactor coil. According to the equivalent coil simulation model, the magnetic induction intensity at the position where each layer of encapsulation is located can be obtained.

[0029] The reactor body is composed of layers of encapsulations in parallel from the inside to the outside. A certain current will flow through each layer of encapsulation, and the current values, resistance values, and encapsulation lengths of each layer of encapsulation are different. Since each layer of encapsulation is in, the electromagnetic field intensity felt by each layer of encapsulation is different. Also, since an alternating current flows through each layer of encapsulation itself, the eddy current losses generated by each layer of encapsulation are different. The thermal effect of the encapsulation itself includes eddy current losses and the current-carrying losses of the encapsulation itself. Among them, the current-carrying losses are related to the resistance value and current value of the current layer of encapsulation, and the eddy current losses are related to the magnetic induction intensity felt by the encapsulation and the volume of the encapsulation layer. Therefore, if not adjusted, the thermal effects of each layer will vary greatly.

[0030] According to the parameter values in the equivalent circuit and equivalent coil, calculate the electrothermal effects of the 1st to Nth layers of the reactor, and mark them respectively as Q 2. Q 3 .... , Q N : ; Among them, is the electrothermal effect of the i-th layer of encapsulation, i = 1, ..., N, is thei Eddy current loss heat dissipation coefficient of the layer encapsulation, is the i heat dissipation coefficient of the current-carrying loss of the layer encapsulation, and is set according to empirical values, is the i resistivity of the layer encapsulation, B i is the i magnetic induction intensity at the position where the layer encapsulation is located, V i is the i volume of the layer encapsulation, I i is the i current flowing through the layer encapsulation, R i is the i resistance of the layer encapsulation.

[0031] Step 5, calculate the Q 2, Q 3...., Q N variance of. If the variance does not exceed the threshold, the requirements for electrothermal effect control are met; if the variance exceeds the threshold, by changing the usage parameters of the wire, including multiple forms such as changing the thickness, length, number of strands, and number of parallel strands of the wire, repeat Steps 2-4 to make the Q 2, Q 3...., Q N variance of does not exceed the threshold. In this embodiment, the threshold is set to 0.1.

[0032] The present invention also proposes an isothermal design system for a dry-type air-core current-limiting reactor, including an inductance calculation module, a model establishment and component calculation module, a simulation model construction module, and an electrothermal effect evaluation and optimization module: Inductance calculation module, which equivalent the N-layer encapsulation of the dry-type air-core current-limiting reactor into coaxial air-core solenoids; calculates the mutual inductance between any two coaxial air-core solenoids, and calculates the self-inductance of each air-core solenoid; Model establishment and component calculation module, which establishes the equivalent circuit equation of the dry-type air-core current-limiting reactor, and calculates the current values passing through each layer encapsulation according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance of each layer encapsulation; Simulation model construction module, which combines the active and reactive components and uses a finite element simulation tool to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor; The electrothermal effect evaluation and optimization module calculates the electrothermal effect of each layer of the dry-type air-core current-limiting reactor by combining the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model; calculates the variance of the electrothermal effects of all the windings, compares the variance with a threshold value, and determines whether to change the usage parameters of the wire and recalculate the electrothermal effect until the variance is less than the threshold value.

[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement without departing from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. An isothermal design method for a dry-type air-core current-limiting reactor, characterized in that, Including: S1. Equivalent the N layers of the dry-type air-core current-limiting reactor into coaxial air-core solenoids; Calculate the mutual inductance between any two coaxial air-core solenoids, and calculate the self-inductance of each air-core solenoid, where the dry-type air-core current-limiting reactor adopts a multi-layer and multi-spiral parallel winding method; S2. Establish an equivalent circuit equation of the dry-type air-core current-limiting reactor, and calculate the current values passing through each layer of the package according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation; S3. Calculate the corresponding active and reactive components according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance of each layer of the package; S4. Combine the active and reactive components, and use a finite element simulation tool to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor; S5. Combine the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model, and calculate the electro-thermal effect of each layer of the dry-type air-core current-limiting reactor; calculate the variance of the electro-thermal effects of all the packages, compare the variance with a threshold value, and determine whether to change the usage parameters of the wire and recalculate the electro-thermal effect until the variance is less than the threshold value.

2. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 1, characterized in that: In S1, number each layer of the package in the dry-type air-core current-limiting reactor, with a total of N layers; The N-layer windings of the dry-type air-core current-limiting reactor are equivalent to coaxial air-core solenoids; any two coaxial air-core solenoids are respectively defined as the first solenoid and the second solenoid; calculate the mutual inductance of the single-turn coil at x' on the first solenoid with respect to the single-turn coil at x'' on the second solenoid ; According to the mutual inductance of the first single-turn coil with respect to the entire second solenoid The mutual inductance between the first solenoid and the second solenoid is calculated ; Further, based on the mutual inductance , the self-inductance of each solenoid is obtained.

3. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 2, characterized in that: Let the number of turns per unit length of the first solenoid and the second solenoid be n 1 and n 2 respectively. According to the integral principle, the mutual inductance of a single-turn coil at x' on the first solenoid with respect to a single-turn coil at x'' on the second solenoid is: ； Among them, represents the radius of the first single-turn coil, represents the radius of the second single-turn coil, represents the height of the first single-turn coil, represents the height of the second single-turn coil, represents the angle between the x' point on the single-turn coil and the axis, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the vacuum permeability.

4. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 3, characterized in that: According to the mutual inductance of the first single-turn coil with respect to the entire second solenoid The mutual inductance between the first solenoid and the second solenoid is calculated : ； Among them, the function is related to the geometric parameters and relative positions of the solenoid; represents the radius of the first single-turn coil, represents the radius of the second single-turn coil; n 1 and n 2 are the number of turns per unit length of the first solenoid and the second solenoid, respectively; is the vacuum permeability; , , and are the four corresponding positions on the Z-axis; For the i th envelope height of h , the number of turns per unit length is n , and the coil radius is r of the thin-walled solenoid, where i = 1,..., N, N is the total number of envelopes, and it can be considered that , , then the self-inductance of the coil is: ； By means of the function Through iteration, the equivalent self-inductance and mutual inductance of each layer of encapsulation are obtained.

5. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 1 or 4, characterized in that: In S2, establish an equivalent circuit equation of the dry-type air-core current-limiting reactor as follows: ； Among them, is the power frequency angular frequency; and are the resistance and self-inductance of each layer of the encapsulation respectively; is the mutual inductance between every two layers of the encapsulation; is the current passing through each layer of the encapsulation; is the voltage applied to each layer of the encapsulation.

6. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 5, characterized in that: According to the equivalent circuit equation of the dry-type air-core current-limiting reactor, the resistance matrix , inductance matrix and voltage matrix can be obtained as follows: ； Considering the current matrix , being the admittance matrix, the current values in each layer of coil encapsulation are obtained.

7. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 1, characterized in that: In S4, using a finite element simulation tool, an equivalent circuit simulation model corresponding to the topology in the dry-type air-core current-limiting reactor is established according to the mutual inductance between different encapsulation layers, the self-inductance and resistance of each encapsulation layer, and the active and reactive components of each layer of the encapsulation; according to the equivalent circuit simulation model, the current distribution of each layer of the encapsulation is obtained. I 1e 、 I 2e 、 I 3e ....、 I Ne ; Use a finite element simulation tool to create an equivalent coil simulation model based on the parameters of the coaxial air-core solenoid, where the parameters include the number of turns, height, and radius of the coil of each layer of the package; according to the equivalent coil simulation model, obtain the magnetic induction intensity at the position of each layer of the package.

8. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 7, characterized in that: In S5, by combining the current distribution of the equivalent circuit simulation model and the magnetic induction intensity of the equivalent coil simulation model, the electrothermal effects of the 1st to Nth layers of the dry-type air-core current-limiting reactor are calculated and respectively labeled as Q 1、 Q 2、 Q 3....、 Q N : ； Among them, is the electrothermal effect of the i-th layer of encapsulation, where i = 1, ..., N, is the eddy current loss heat dissipation coefficient of the i -th layer of encapsulation, is the through-current loss heat dissipation coefficient related to the i -th layer of encapsulation, and are set according to empirical values, is the resistivity of the i -th layer of encapsulation, B i is the magnetic induction intensity at the position where the i -th layer of encapsulation is located, V i is the volume of the i -th layer of encapsulation, I i is the current flowing through the i -th layer of encapsulation, R i is the resistance of the i -th layer of encapsulation.

9. An isothermal design method for a dry-type air-core current-limiting reactor according to claim 8, characterized in that: Calculate the Q 1. Q 2. Q 3.... Q N variance. If the variance does not exceed the threshold, the electrothermal effect control requirements are met; if the variance exceeds the threshold, change the usage parameters of the coils in each layer of the encapsulation, recalculate the electrothermal effect of each layer of the encapsulation until the variance is less than the threshold.

10. An isothermal design system for a dry-type air-core current-limiting reactor, using the method described in any one of claims 1-9, including an inductance calculation module, a model establishment and component calculation module, a simulation model construction module, and an electro-thermal effect evaluation and optimization module, characterized in that: The inductance calculation module equivalent the N layers of the dry-type air-core current-limiting reactor into coaxial air-core solenoids; calculate the mutual inductance between any two coaxial air-core solenoids, and calculate the self-inductance of each air-core solenoid; Model establishment and component calculation module, establish the equivalent circuit equation of the dry-type air-core current-limiting reactor, and calculate the current values passing through each layer of winding according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components according to the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance of each layer of winding; Simulation model construction module, combine the active and reactive components, and use the finite element simulation tool to establish the equivalent circuit simulation model and equivalent coil simulation model of the dry-type air-core current-limiting reactor; Electro-thermal effect evaluation and optimization module, combine the parameter values in the equivalent circuit simulation model and equivalent coil simulation model, and calculate the electro-thermal effect of each layer of winding of the dry-type air-core current-limiting reactor; Calculate the variance of the electro-thermal effects of all windings, compare the variance with the threshold, and judge whether to change the use parameters of the wire and recalculate the electro-thermal effect until the variance is less than the threshold.

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