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

Abstract

An isothermal design method for a dry-type hollow current-limiting reactor comprises the following steps: equating N layers of dry-type hollow current-limiting reactor envelopes to coaxial hollow solenoids; calculating the mutual inductance between any two coaxial hollow solenoids and the self-inductance of each hollow solenoid; establishing an equivalent circuit equation, and calculating the current value passing through each layer of envelope based on the equivalent resistance, equivalent mutual inductance, and equivalent self-inductance in the equation, and calculating the corresponding active and reactive components; combining the active and reactive components, using a finite element simulation tool to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type hollow current-limiting reactor; combining the equivalent circuit simulation model and the equivalent coil simulation model, calculating the electrothermal effect of each layer of envelope; calculating the variance of the electrothermal effects of all envelopes, comparing the variance with a threshold value, and determining whether the electrothermal effect control requirement is met. The present invention can make the temperature rise design distribution of the dry-type hollow current-limiting reactor more uniform.

Description

Technical Field

[0001] The present invention belongs to the technical field of isothermal design of reactors, and in particular relates to an isothermal design method and system for a dry-type hollow current-limiting reactor. Background Art

[0002] With the rapid construction and development of my country's AC and DC power grids, the problem of excessive short-circuit currents has gradually emerged. According to estimates, if no measures are taken to limit short-time currents in the next few years, the short-circuit currents at many 500kV substations will exceed the current circuit breaker interruption current, and even more substations will approach this current limit, seriously impacting the safe and stable operation of the power grid. Installing series current-limiting reactors is the simplest and most effective way to limit line short-circuit currents. This method can effectively reduce the short-circuit current level of the installed line and isolate dense power supply points. Dry-type air-core reactors offer excellent electrical characteristics such as good linearity, low losses, low noise, stable parameters, and excellent fire resistance. Therefore, dry-type reactors are ideally suited for limiting short-circuit currents in ultra-high voltage (UHV) lines and ensuring their safe and stable operation.

[0003] Existing dry-type air-core reactors provide relevant principles for the design of air-core reactors by selecting conductors and calculating temperature rise. However, dry-type air-core current-limiting reactors used in 500kV systems are limited. With the increase in load levels, especially the continuous increase in the capacity of ultra-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 ultra-high voltage and large-capacity dry-type air-core current-limiting reactors for 500kV systems. The required flow current can reach 4000A, 5000A or even 6000A, and its capacity can reach 175MVar, 225Mvar or even 252Mvar. The magnetic field strength generated by the reactor body is much greater than 3×10 5 A / m, which requires consideration of the impact of the magnetic field strength generated by the reactor body on the reactor body conductors. Furthermore, the eddy current losses in the conductors of large-capacity dry-type air-core current-limiting reactors in 500kV systems show a nonlinear growth. In the presence of a strong magnetic field, these losses are extremely strong, generating a large amount of heat. This in turn causes the reactor body temperature to rise, affecting the safe and stable operation of the current-limiting reactor. Therefore, it is necessary to consider the impact of the magnetic field strength generated by the reactor body on the reactor body conductors.

[0004] For example, in the prior art, patent application CN116384161A proposes a method for implementing a dry-type air-core reactor. This reactor utilizes a traditional fully parallel or series-parallel pancake coil structure. The current flowing through it is limited to a single conductor, with the maximum current determined by that single conductor. Therefore, it cannot carry high currents (1000kA and above). Furthermore, this patent solution adjusts the reactor parameters solely based on the overall temperature / loss balance, failing to recognize that as capacity increases, eddy current losses caused by the extremely uneven magnetic field distribution become a significant factor in the design and manufacture of high-capacity UHV series-compensated reactors. The uneven electromagnetic field distribution and the impact of eddy current losses are not considered in the temperature rise calculation.

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

[0006] In order to address the deficiencies in the prior art, the present invention provides an isothermal design method and system for a dry-type hollow current-limiting reactor, which takes into account the uneven characteristics of the electromagnetic field distribution of the dry-type hollow reactor and the eddy current loss of the reactor body wire, thereby making the temperature rise design distribution of the dry-type hollow 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 hollow current-limiting reactor, comprising:

[0009] S1, encapsulating N layers of a dry-type hollow current-limiting reactor into a coaxial hollow solenoid; calculating the mutual inductance between any two coaxial hollow solenoids, and calculating the self-inductance of each hollow solenoid, wherein the dry-type hollow current-limiting reactor adopts a multi-layer multi-spiral parallel winding method;

[0010] S2, establish the equivalent circuit equation of the dry-type hollow current-limiting reactor, and calculate the current value passing through each layer of the envelope based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation;

[0011] S3, calculate the corresponding active and reactive components based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance of each layer of encapsulation;

[0012] S4, combining active and reactive components, using finite element simulation tools to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor;

[0013] S5, combining the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model, calculate the electrothermal effect of each layer of the dry-type air-core current-limiting reactor; calculate the variance of the electrothermal effects of all the envelopes, compare the variance with the threshold, and determine whether to change the use parameters of the wires. If the variance does not exceed the threshold, the electrothermal effect control requirements are met. If the variance exceeds the threshold, change the use parameters of the coils in each layer of the envelope, and recalculate the electrothermal effect of each layer of the envelope until the variance is less than the threshold.

[0014] Furthermore, in S1, each encapsulation layer in the dry-type hollow current-limiting reactor is numbered, with a total of N layers;

[0015] Equivalently equate the N-layer envelope of a dry-type hollow current-limiting reactor to a coaxial hollow solenoid. Define any two coaxial hollow solenoids as the first solenoid and the second solenoid, respectively. Calculate 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.

[0016] According to the mutual inductance of the first single-turn coil to the entire second solenoid Calculate the mutual inductance between the first solenoid and the second solenoid ; Further based on mutual induction , and get the self-inductance of each solenoid.

[0017] Furthermore, suppose the number of turns per unit length of the first solenoid and the second solenoid are respectively n 1 and n 2. According to the principle of integration, the first solenoid x' The mutual inductance of the single-turn coil at the second solenoid for:

[0018] ;

[0019] in, x'' Indicates that the second solenoid x'' A single-turn coil at 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, Indicates the point x' on the single-turn coil and The angle between the axes, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the magnetic permeability of vacuum.

[0020] Furthermore, according to the mutual inductance of the first single-turn coil to the entire second solenoid Calculate the mutual inductance between the first solenoid and the second solenoid :

[0021] ;

[0022] Among them, the function is defined as follows:

[0023] ;

[0024] function middle, 、 、 and The meanings are as follows:

[0025] ;

[0026] in, represents the radius of the first single-turn coil, represents the radius of the second single-turn coil; n 1 and n 2 is the number of turns per unit length of the first solenoid and the second solenoid respectively; is the vacuum permeability; 、 、 and The four corresponding positions on the Z axis; represents the height of the first single-turn coil, represents the height of the second single-turn coil, Indicates the point x' on the single-turn coil and The angle between the axes, is the relative distance between the centers of the first single-turn coil and the second single-turn coil;

[0027] For the i The envelope height is h , the number of turns per unit length is n , the coil radius is r The self-inductance of a thin-walled solenoid, where i = 1, ..., N, N is the total number of envelopes, , , then the coil self-inductance is:

[0028] ;

[0029] Through the function By iteration, the equivalent self-inductance and mutual inductance of each layer of encapsulation are obtained.

[0030] Furthermore, in S2, the equivalent circuit equation of the dry-type air-core current-limiting reactor is established as follows:

[0031] ;

[0032] in, 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 the envelope; is the voltage applied to each layer of the envelope.

[0033] Furthermore, in S4, a finite element simulation tool is used to establish an equivalent circuit simulation model corresponding to the topological structure of the dry-type air-core current-limiting reactor based on the mutual inductance between different encapsulation layers, the self-inductance and resistance of each encapsulation layer, and the active and reactive components of each encapsulation layer; based on the equivalent circuit simulation model, the current distribution of each encapsulation layer is obtained. I 1e 、 I 2e 、 I 3e ....、 I Ne ;

[0034] Using finite element simulation tools, an equivalent coil simulation model is created based on the parameters of the coaxial hollow solenoid, including the number of turns, height, and radius of each layer of encapsulation. Based on the equivalent coil simulation model, the magnetic induction intensity at the location of each layer of encapsulation is obtained.

[0035] Furthermore, in S5, the electrothermal effects of the dry-type air-core current limiting reactor layers 1 to N are calculated by combining the current distribution of the equivalent circuit simulation model and the magnetic induction intensity of the equivalent coil simulation model, which are marked as Q 1. Q 2. Q 3....、 Q N :

[0036] ;

[0037] in, is the electrocaloric effect of the i-th layer of encapsulation, i=1,...,N, For the i Eddy current loss heat dissipation coefficient of layer encapsulation, For the i Layer encapsulation through-flow loss heat dissipation coefficient, and According to the experience value setting, For the i The resistivity of the layer envelope, B i For the iThe magnetic induction intensity at the location of the layer envelope, V i For the i The volume enclosed by the layer, I i For the i The layer encapsulates the current flowing through, R i For the i Layer encapsulated resistor.

[0038] The present invention also proposes an isothermal design system for dry-type hollow current-limiting reactors, 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:

[0039] The inductance calculation module converts the N-layer package of the dry-type hollow current-limiting reactor into a coaxial hollow solenoid. It calculates the mutual inductance between any two coaxial hollow solenoids and the self-inductance of each hollow solenoid.

[0040] The model establishment and component calculation module establishes the equivalent circuit equation of the dry-type hollow current-limiting reactor and calculates the current value passing through each layer of the envelope based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance of each layer of the envelope;

[0041] The simulation model building module combines active and reactive components and uses finite element simulation tools to establish an equivalent circuit simulation model and an equivalent coil simulation model for a dry-type air-core current-limiting reactor;

[0042] The electrothermal effect evaluation and optimization module combines the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model to calculate the electrothermal effect of each layer of the dry-type air-core current-limiting reactor; calculates the variance of the electrothermal effect of all envelopes, compares the variance with the threshold, and determines whether to change the operating parameters of the conductors. If the variance does not exceed the threshold, the electrothermal effect control requirements are met. If the variance exceeds the threshold, the operating parameters of the coils in each layer of the envelope are changed, and the electrothermal effect of each layer of the envelope is recalculated until the variance is less than the threshold.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. The present invention calculates the mutual inductance and self-inductance by encapsulating the reactor as a coaxial hollow solenoid, establishes an equivalent circuit equation to solve the current value, and then analyzes the active and reactive components, comprehensively and accurately simulating the operating state of the reactor, making the design more practical and improving the accuracy of the design.

[0045] 2. This invention uses finite element simulation tools to create equivalent circuit and equivalent coil simulation models, and calculates the electrothermal effect based on model parameters. By calculating the variance of the electrothermal effect and comparing it with a threshold, the conductor parameters are adjusted to effectively optimize the temperature rise distribution within each layer of the reactor envelope. This approach prevents local overheating, ensures safe and stable operation of the reactor, and extends the equipment's service life.

[0046] 3. The isothermal design method and system provided by the present invention are applicable to large-capacity dry-type hollow current-limiting reactors, which enhances the adaptability of reactors in ultra-high voltage lines and is of great significance to the safe and stable operation of power grids. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of an isothermal design method for a dry-type hollow current-limiting reactor according to the present invention;

[0048] Figure 2 It is a coaxial hollow solenoid equivalent diagram of an isothermal design method for a dry-type hollow current-limiting reactor of the present invention;

[0049] Figure 3 The present invention discloses a circuit model diagram of a dry-type air-core reactor according to an isothermal design method of the dry-type air-core current-limiting reactor. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0051] The present invention proposes a method for calculating the temperature rise of a dry-type hollow current limiting reactor. Figure 1 As shown, a flow chart of the method of the present invention is shown, and the specific steps are as follows.

[0052] Step 1: The dry-type hollow current-limiting reactor adopts a multi-layer multi-spiral parallel winding method; each encapsulation layer in the dry-type hollow current-limiting reactor is numbered, with a total of N layers;

[0053] Step 2: Equivalently encapsulate the N layers of the dry-type hollow current-limiting reactor into a coaxial hollow solenoid; define any two coaxial hollow solenoids as the first solenoid and the second solenoid respectively; let the number of turns per unit length of the first solenoid and the second solenoid be n 1 and n 2. According to the principle of integration, the first solenoid x' The mutual inductance of the first single-turn coil to the second solenoid for:

[0054] ;

[0055] in, 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, Indicates the point x' on the single-turn coil and The angle between the axes, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the magnetic permeability of vacuum.

[0056] The mutual inductance between the first solenoid and the second solenoid is obtained as:

[0057] ;

[0058] Among them, the function It is related to the geometric parameters and relative position 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 is the number of turns per unit length of the first solenoid and the second solenoid respectively; is the vacuum permeability; 、 、 and The four corresponding positions on the Z axis;

[0059] function is defined as follows:

[0060] ;

[0061] function middle, 、 、 and The meanings are as follows:

[0062] ;

[0063] function It can be rewritten as follows:

[0064] ;

[0065] Where,

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] For the self-inductance of a thin-walled solenoid with an envelope height of h, a number of turns per unit length of n, and a coil radius of r, where i = 1, ..., N, where N is the total number of envelopes, it can be considered that , , then the coil self-inductance is:

[0073] ;

[0074] exist z =0, A =1 / 3, B =0, so , then rewrite it as:

[0075] ;

[0076] After rewriting, the function It is converted into the standard form of Bartky transformation, and the self-inductance and mutual inductance of each layer of coil encapsulation are obtained through iteration.

[0077] Seek The iterative method is as follows:

[0078] ;

[0079] ;

[0080] ;

[0081] Step 3: Establish the equivalent circuit of dry-type air-core current limiting reactor, as shown in Figure 3 The dry-type air-core reactor winding of the present invention is a multi-layer cylindrical parallel connection, and each layer of winding has a self-inductance. L 11 、 L 22 、...... L ii , there is mutual induction between layers M 12 、 M13 、 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 each layer of encapsulated reactance. The equivalent circuit equation of the dry-type hollow current limiting reactor is as follows:

[0082] ;

[0083] For the power frequency angular frequency , there is the following relationship:

[0084] ;

[0085] According to the equivalent circuit equation of the dry-type air-core current limiting reactor, the resistance matrix can be obtained: , inductance matrix and voltage matrix :

[0086] ;

[0087] Generally, the harmonic current flowing through the dry-type air-core current limiting reactor is a known quantity, considering:

[0088] ,in ;

[0089] Multiply both sides of the above equation by the vector get:

[0090] ;

[0091] The synthetic admittance of the dry-type air-core current-limiting reactor is:

[0092] ;

[0093] The synthetic impedance is ,but Substitute this formula into The current value in each layer of coil envelope can be obtained.

[0094] Step 4: Calculate the active and reactive components based on the equivalent resistance and equivalent inductance in each layer of the envelope; use the finite element simulation tool to establish the equivalent circuit and equivalent coil of the dry-type hollow current limiting reactor, and calculate the electrothermal effects of the reactor layers 1 to N, which are marked as Q 2. Q 3....、Q N .

[0095] The specific steps are:

[0096] Using the finite element simulation tool, the self-inductance of each winding layer obtained in step 3 is L 11 、 L 22 、...... L ii , the mutual inductance between layers M 12 、 M 13 、 M 14 , ...etc., and the different DC resistance of each layer of winding R 1. R 2. R 3....... R i , combined with the active and reactive components of each layer of envelope, the equivalent circuit is constructed according to the topological structure of the parallel circuit, and the reactance of each layer of envelope is simulated as a component in the circuit to construct an equivalent circuit simulation model corresponding to the actual reactor winding structure. According to the equivalent circuit simulation model, the current distribution of each layer of envelope can be obtained I 1e 、 I 2e 、 I 3e ....、 I Ne .

[0097] Using finite element simulation tools, we created an equivalent coil simulation model based on the parameters of the coaxial hollow solenoid, including the number of turns, height, and radius of each encapsulated coil layer. Leveraging the tool's modeling capabilities, we simulated the actual electromagnetic characteristics of the coil and created this model to simulate the actual reactor coil conditions. This model provided the magnetic induction intensity at each encapsulated coil layer.

[0098] The reactor itself is constructed from layers of enclosures connected in parallel from the inside out. Each layer of enclosure flows a certain current, with varying current values, resistance values, and enclosure lengths. Because each layer of enclosure is located in a , it experiences a different electromagnetic field strength. Furthermore, because each layer of enclosure itself flows through an alternating current, it generates different eddy current losses. The thermal effects of the enclosure itself include eddy current losses and the conduction losses of the enclosure itself. The conduction losses are related to the resistance and current values of the enclosure, while the eddy current losses are related to the magnetic induction strength felt by the enclosure and the volume of the enclosure. Therefore, the thermal effects of each layer can vary significantly if not adjusted.

[0099] According to the parameter values in the equivalent circuit and equivalent coil, the electrothermal effects of reactor layers 1 to N are calculated and marked as Q 2. Q 3....、 Q N :

[0100] ;

[0101] in, is the electrocaloric effect of the i-th layer of encapsulation, i=1,...,N, For the i Eddy current loss heat dissipation coefficient of layer encapsulation, For the i Layer encapsulation through-flow loss heat dissipation coefficient, and According to the experience value setting, For the i The resistivity of the layer envelope, B i For the i The magnetic induction intensity at the location of the layer envelope, V i For the i The volume enclosed by the layer, I i For the i The layer encapsulates the current flowing through, R i For the i Layer encapsulated resistor.

[0102] Step 5: Calculate the corresponding envelope of each layer Q 2. Q 3....、 Q N If the variance does not exceed the threshold, the electrothermal effect control requirement is met; if the variance exceeds the threshold, the use parameters of the wire are changed, including the thickness, length, number of strands, number of parallel roots, etc., and steps 2-4 are repeated to make the Q 2. Q 3....、 Q N The variance of does not exceed the threshold. In this embodiment, the threshold is set to 0.1.

[0103] The present invention also proposes an isothermal design system for dry-type hollow current-limiting reactors, 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:

[0104] The inductance calculation module converts the N-layer package of the dry-type hollow current-limiting reactor into a coaxial hollow solenoid. It calculates the mutual inductance between any two coaxial hollow solenoids and the self-inductance of each hollow solenoid.

[0105] The model establishment and component calculation module establishes the equivalent circuit equation of the dry-type hollow current-limiting reactor and calculates the current value passing through each layer of the envelope based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance of each layer of the envelope;

[0106] The simulation model building module combines active and reactive components and uses finite element simulation tools to establish an equivalent circuit simulation model and an equivalent coil simulation model for a dry-type air-core current-limiting reactor;

[0107] The electrothermal effect evaluation and optimization module combines the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model to calculate the electrothermal effect of each layer of the dry-type air-core current-limiting reactor. It also calculates the variance of the electrothermal effects of all the envelopes and compares the variance with the threshold to determine whether to change the operating parameters of the conductors. If the variance exceeds the threshold, the operating parameters of the coils in each layer of the envelope are changed and the electrothermal effect of each layer of the envelope is recalculated until the variance is less than the threshold.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. An isothermal design method for a dry-type hollow current-limiting reactor, characterized in that: include: S1, the N-layer encapsulation of the dry-type hollow current-limiting reactor is equivalent to a coaxial hollow solenoid; Calculate the mutual inductance between any two coaxial hollow solenoids and calculate the self-inductance of each hollow solenoid, wherein the dry-type hollow current-limiting reactor adopts a multi-layer multi-spiral parallel winding method; S2, establish the equivalent circuit equation of the dry-type hollow current-limiting reactor, and calculate the current value passing through each layer of the envelope based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation; S3, calculate the corresponding active and reactive components based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance of each layer of encapsulation; S4, combining active and reactive components, using finite element simulation tools to establish an equivalent circuit simulation model and an equivalent coil simulation model of the dry-type air-core current-limiting reactor; S5, combining the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model, calculate the electrothermal effect of each layer of the dry-type air-core current-limiting reactor; calculate the variance of the electrothermal effects of all the envelopes, compare the variance with the threshold, and determine whether to change the use parameters of the wires. If the variance does not exceed the threshold, the electrothermal effect control requirements are met. If the variance exceeds the threshold, change the use parameters of the coils in each layer of the envelope, and recalculate the electrothermal effect of each layer of the envelope until the variance is less than the threshold.

2. The isothermal design method for a dry-type hollow current-limiting reactor according to claim 1, characterized in that: In S1, each encapsulation layer in the dry-type hollow current-limiting reactor is numbered, with a total of N layers; Equivalently equate the N-layer envelope of a dry-type hollow current-limiting reactor to a coaxial hollow solenoid. Define any two coaxial hollow solenoids as the first solenoid and the second solenoid, respectively. Calculate 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. According to the mutual inductance of the first single-turn coil to the entire second solenoid Calculate the mutual inductance between the first solenoid and the second solenoid ; Further based on mutual induction , and get the self-inductance of each solenoid.

3. The isothermal design method for a dry-type hollow current-limiting reactor according to claim 2, characterized in that: Assume that the number of turns per unit length of the first solenoid and the second solenoid are n 1 and n 2. According to the principle of integration, the first solenoid x' The mutual inductance of the single-turn coil at for: ； in, x'' Indicates that the second solenoid x'' A single-turn coil at 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, Indicates the point x' on the single-turn coil and The angle between the axes, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; is the magnetic permeability of vacuum.

4. The isothermal design method for a dry-type hollow current-limiting reactor according to claim 3, characterized in that: According to the mutual inductance of the first single-turn coil to the entire second solenoid Calculate the mutual inductance between the first solenoid and the second solenoid : ； Among them, the function is defined as follows: ； function middle, 、 、 and The meanings are as follows: ； in, represents the radius of the first single-turn coil, represents the radius of the second single-turn coil; n 1 and n 2 is the number of turns per unit length of the first solenoid and the second solenoid respectively; is the vacuum permeability; 、 、 and The four corresponding positions on the Z axis; represents the height of the first single-turn coil, represents the height of the second single-turn coil, Indicates the point x' on the single-turn coil and The angle between the axes, is the relative distance between the centers of the first single-turn coil and the second single-turn coil; For the i The envelope height is h , the number of turns per unit length is n , the coil radius is r The self-inductance of a thin-walled solenoid, where i = 1, ..., N, N is the total number of envelopes, , , then the coil self-inductance is: ； Through the function By iteration, the equivalent self-inductance and mutual inductance of each layer of encapsulation are obtained.

5. The isothermal design method for a dry-type hollow current-limiting reactor according to claim 1 or 4, characterized in that: In S2, the equivalent circuit equation of the dry-type air-core current-limiting reactor is established as follows: ； in, 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 the envelope; is the voltage applied to each layer of the envelope.

6. The 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 can be obtained: , inductance matrix and voltage matrix : ； Current Matrix , For the admittance matrix, find the current value in each layer of coil envelope.

7. The isothermal design method for a dry-type air-core current-limiting reactor according to claim 1, characterized in that: In S4, using finite element simulation tools, an equivalent circuit simulation model corresponding to the topological structure of the dry-type air-core current-limiting reactor is established based on the mutual inductance between different envelope layers, the self-inductance and resistance of each envelope layer, and the active and reactive components of each envelope layer; based on the equivalent circuit simulation model, the current distribution of each envelope layer is obtained. I 1e 、 I 2e 、 I 3e ....、 I Ne ; Using finite element simulation tools, an equivalent coil simulation model is created based on the parameters of the coaxial hollow solenoid, including the number of turns, height, and radius of each layer of encapsulation. Based on the equivalent coil simulation model, the magnetic induction intensity at the location of each layer of encapsulation is obtained.

8. The isothermal design method for a dry-type hollow current-limiting reactor according to claim 7, characterized in that: In S5, the electrothermal effects of layers 1 to N of the dry-type air-core current-limiting reactor are calculated by combining the current distribution of the equivalent circuit simulation model and the magnetic induction intensity of the equivalent coil simulation model, which are marked as Q 1. Q 2. Q 3....、 Q N : ； in, is the electrocaloric effect of the i-th layer of encapsulation, i=1,...,N, For the i Eddy current loss heat dissipation coefficient of layer encapsulation, For the i Layer encapsulation through-flow loss heat dissipation coefficient, and According to the experience value setting, For the i The resistivity of the layer envelope, B i For the i The magnetic induction intensity at the location of the layer envelope, V i For the i The volume enclosed by the layer, I i For the i The layer encapsulates the current flowing through it, R i For the i Layer encapsulated resistor.

9. An isothermal design system for a dry-type hollow current-limiting reactor, utilizing the method according to any one of claims 1 to 8, comprising an inductance calculation module, a model establishment and component calculation module, a simulation model construction module, and an electrothermal effect evaluation and optimization module, characterized in that: The inductance calculation module converts the N-layer package of the dry-type hollow current-limiting reactor into a coaxial hollow solenoid. It calculates the mutual inductance between any two coaxial hollow solenoids and the self-inductance of each hollow solenoid. The model establishment and component calculation module establishes the equivalent circuit equation of the dry-type hollow current-limiting reactor and calculates the current value passing through each layer of the envelope based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance in the equation; the module calculates the corresponding active and reactive components based on the equivalent resistance, equivalent mutual inductance and equivalent self-inductance of each layer of the envelope; The simulation model building module combines active and reactive components and uses finite element simulation tools to establish an equivalent circuit simulation model and an equivalent coil simulation model for a dry-type air-core current-limiting reactor; The electrothermal effect evaluation and optimization module combines the parameter values in the equivalent circuit simulation model and the equivalent coil simulation model to calculate the electrothermal effect of each layer of the dry-type air-core current-limiting reactor; The variance of the electrothermal effect of all envelopes is calculated and compared with the threshold to determine whether the use parameters of the wire need to be changed. If the variance does not exceed the threshold, the electrothermal effect control requirements are met. If the variance exceeds the threshold, the use parameters of the coil in each layer of envelope are changed and the electrothermal effect of each layer of envelope is recalculated until the variance is less than the threshold.

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