High-temperature superconducting cable length planning method

Abstract

The invention belongs to the technical field of power system planning, and particularly discloses a high-temperature superconducting cable length planning method, which comprises the following steps: firstly, determining a cable length range, calculating each phase fault current and temperature change curve under fault working conditions for each candidate length, solving the temperature rise time required by each phase temperature rising to the liquid nitrogen evaporation temperature of the cable, and calculating the temperature rise time; comparing the starting time with the starting time required by the power grid protection system to cut off the cable fault to obtain a first length range in which the temperature of each phase of the cable does not reach the evaporation temperature; calculating the maximum fault current of an adjacent cable running in parallel with the cable under the fault condition, comparing the maximum fault current with the bearable fault current of the power grid to obtain a second length range, and determining the target length of the cable through the first length range and the second length range; the method has the following advantages: quantitative correlation of length, temperature rise and fault current is realized, and a target length interval considering thermal safety of the superconducting cable and current safety of an adjacent line is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system planning, in particular to a high-temperature superconducting cable length planning method. BACKGROUND

[0002] Since the high-temperature superconducting cable has a faster electromagnetic response speed and a higher temperature rise rate under fault conditions, its influence on power grid stability, cable inter-phase current distribution and adjacent line fault current is significantly higher than that of ordinary conventional cables. Existing superconducting cable planning mostly focuses on economy, cost constraints and process implementability, and pays insufficient attention to the temperature rise trend changes caused by length changes under fault conditions, the liquid nitrogen evaporation temperature trigger point changes and the fault current response of parallel operation cables, resulting in length selection biased towards engineering feasibility and failing to fully reflect the consideration of safety constraints. Especially in the scene of too short cable or free selection within the process allowable range, the traditional planning method cannot reflect the risks such as rapid temperature rise of superconducting cable under fault, and the protection system may not complete the removal before the evaporation temperature trigger, and the quantitative corresponding relationship between length and adjacent cable fault current is not established, so that the traditional protection system has the problem of insufficient adaptability when facing superconducting cable application.

[0003] Therefore, a high-temperature superconducting cable length planning method is proposed to solve the above problems. SUMMARY

[0004] The present application aims to provide a high-temperature superconducting cable length planning method to solve or improve the above technical problems that the existing planning method cannot quantize the influence of high-temperature superconducting cable length on fault temperature rise and adjacent cable fault current, resulting in the problem of lack of safety constraints in length selection.

[0005] Therefore, the first aspect of the present application is to provide a high-temperature superconducting cable length planning method.

[0006] The second aspect of the present application is to provide a system.

[0007] The third aspect of the present application is to provide an electronic device.

[0008] The fourth aspect of the present application is to provide a computer readable storage medium.

[0009] A first aspect of the present invention provides a method for planning the length of a high-temperature superconducting cable, comprising the following steps: determining a length range of the cable through multiple construction schemes; calculating the fault current of each phase under fault conditions for each candidate length within the length range, and calculating a temperature change curve based on the fault current and resistance parameters; determining, based on the temperature change curve, the heating time required for each phase temperature to rise to the evaporation temperature of liquid nitrogen at the current candidate length; determining a first length range within which the temperature of each phase of the cable does not reach the evaporation temperature based on the temperature rise time and the start-up time required for the power grid protection system to clear the cable fault; calculating the maximum fault current passing through an adjacent cable running parallel to the cable under the fault conditions; obtaining the tolerable fault current of the power grid, and determining a second length range for the cable such that the maximum fault current does not exceed the tolerable fault current; and determining the target length of the cable using the first length range and the second length range.

[0010] A second aspect of the present invention provides a system in which the step of determining a second length range of a cable such that the maximum fault current does not exceed the tolerable fault current includes: obtaining the maximum fault current for all candidate lengths; plotting a second curve of the maximum fault current as a function of the candidate lengths; recording all maximum fault currents higher than the tolerable fault current on the second curve; and determining the second length range by using the candidate lengths corresponding to the recorded maximum fault currents.

[0011] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described high-temperature superconducting cable length planning method.

[0012] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described high-temperature superconducting cable length planning method.

[0013] The beneficial effects of this invention compared to the prior art are as follows: By calculating the fault current of each phase under fault conditions for each candidate length within the length range, and obtaining the corresponding temperature change curve, the time required for each phase temperature to rise from the stable operating temperature to the liquid nitrogen evaporation temperature of the cable is quantitatively extracted from the temperature change curve. This time is then compared with the start-up time required for the power grid protection system to clear the cable fault, and a first length range in which the temperature rise time is greater than the protection start-up time is selected. In this way, a clear quantitative relationship between length, temperature rise time, and protection action time is established at the method level. This ensures that, at any length selected within the first length range, the temperature of each phase of the cable does not reach the liquid nitrogen evaporation temperature before the protection completes the clearing. This avoids the risk mentioned in the background technology that the cable is too short, causing the temperature to rise rapidly and the protection system may not be able to complete the clearing before the evaporation temperature is triggered. In terms of thermal safety, a quantifiable safety margin is reserved between high-temperature superconducting cables and existing protection configurations.

[0014] For each candidate length within the specified length range, the maximum fault current carried by adjacent cables under fault conditions is calculated. This current is then compared with the grid's tolerable fault current to obtain a second length range that ensures the maximum fault current does not exceed the tolerable fault current. The target cable length is then determined from the intersection of the first and second length ranges. This approach addresses the deficiency in previous technologies that lacked a quantitative relationship between length and adjacent cable fault current, allowing planners to clearly understand the changes in fault current levels experienced by adjacent lines at different lengths. This ensures that the selected cable length naturally meets the current-carrying capacity requirements of adjacent cables and their equipment without altering the existing protection system's setting principles. Furthermore, by superimposing the first and second length ranges, the fault temperature rise safety of the high-temperature superconducting cable itself and the fault current safety of parallel lines are unified under a single length selection rule. This creates a target length range that considers both thermal and current safety, enabling the final selected cable length to be safely connected within the existing grid protection system configuration.

[0015] Additional aspects and advantages of embodiments of the invention will become apparent in the following description or may be learned by practice of embodiments of the invention. Attached Figure Description

[0016] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of the method steps of the present invention; Figure 2 This is a flowchart illustrating a specific implementation of the present invention; Figure 3 This is a flowchart illustrating the process of calculating the time required for each phase temperature to reach the liquid nitrogen evaporation temperature according to the present invention. Figure 4 This is a schematic diagram of the process for determining the length range based on the temperature rise time according to the present invention; Figure 5 This is a schematic diagram of the process for determining the length range based on the fault current according to the present invention; Figure 6 This is a schematic diagram showing the relationship between the temperature rise time of the superconducting cable of the present invention and its length. Figure 7 This is a schematic diagram showing the relationship between the fault current of adjacent cables in the superconducting cable of the present invention and their length. Figure 8 This is a schematic diagram of the cable equivalent circuit model of the present invention. Figure 9 This is a system logic block diagram of the present invention; Figure 10 This is a schematic diagram of the structure of an electronic device according to the present invention. Detailed Implementation

[0017] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0018] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0019] Please see Figures 1-10 The following describes a method, system, electronic device, and computer-readable storage medium for planning the length of a high-temperature superconducting cable according to some embodiments of the present invention.

[0020] An embodiment of the first aspect of the present invention provides a method for planning the length of a high-temperature superconducting cable. In some embodiments of the present invention, such as... Figures 1-2 , Figures 6-8 As shown, the method for planning the length of a high-temperature superconducting cable includes the following steps: S101 determines the cable length range through multiple construction schemes; calculates the fault current of each phase under fault conditions for each candidate length within the length range, and calculates the temperature change curve based on the fault current and resistance parameters.

[0021] Here, the cable length range is determined through multiple construction schemes. That is, during the planning stage, several construction schemes are pre-set according to different engineering requirements and layout methods. For example, for the same power supply area, engineering scenarios such as inter-substation interconnection and radial power supply from substations to load areas are considered. Under each construction scheme, the minimum and maximum achievable cable laying lengths are determined by combining the geographical location of the substations, the distribution of load centers, and the spatial conditions of the cable laying path, thus obtaining the corresponding candidate length ranges. After obtaining the candidate length ranges corresponding to multiple construction schemes, the above ranges are uniformly organized. They can be comprehensively corrected by taking the union, intersection, or according to engineering constraints to form the cable length range used in the subsequent analysis of this method. Within this length range, several discrete candidate lengths are divided with a preset step size, so that each candidate length represents a planning option that is achievable in engineering and can be evaluated separately in subsequent simulations, thus providing a clear length variable basis for subsequent fault current calculation and temperature change analysis.

[0022] For a given candidate length, an equivalent circuit model of the cable is first constructed based on parameters such as the self-inductance of each phase conductor layer, the mutual inductance between conductor layers, and the conductor resistance at the current length. In this model, the candidate length is used as a key parameter affecting conductor resistance and equivalent impedance, ensuring the model accurately reflects the electromagnetic characteristics of the cable under fault conditions at that length. Then, under a preset fault condition, the equivalent power source from the grid and the fault point conditions are applied to the cable's equivalent circuit model. By solving this model, the waveforms or data sequences of the fault currents of each phase during the fault are obtained, thus revealing the magnitude and temporal evolution of the fault currents at the candidate length. After obtaining the fault currents, the power or energy of each phase fault current is calculated by combining it with the cable's resistance parameters at the current candidate length. Based on the specific heat capacity, mass, and other thermal characteristics of the cable material, the temperature rise of each phase per unit time during the fault is calculated. By accumulating over time steps, the temperature at each moment is updated to the starting temperature for the next moment, gradually obtaining a continuous curve of the cable's temperature changing over time—the temperature change curve at the candidate length.

[0023] As can be seen above, by repeatedly calculating the fault current and generating the temperature change curve for each candidate length within the aforementioned length range, a fault response and temperature response database covering the entire length range can be formed, providing a complete data foundation for determining the heating time based on the temperature change curve and further screening the first and second length ranges.

[0024] Specifically, the steps for calculating the fault current of each phase under fault conditions for each candidate length within the length range include: An equivalent circuit model of the cable is constructed based on the self-inductance of the conductor layers in each phase, the mutual inductance between the conductor layers, and the conductor resistance.

[0025] The fault current of each phase is calculated based on the equivalent circuit model of the cable under the set fault conditions.

[0026] Based on the specific description above, an equivalent circuit model of the cable is constructed according to the self-inductance of each phase conductor layer, the mutual inductance between conductor layers, and the conductor resistance. That is, at the candidate length, the electrical distributed parameters of the high-temperature superconducting cable are abstracted into an equivalent circuit structure composed of self-inductance elements of each phase conductor layer, mutual inductance elements between phases and layers, and series resistance elements. Among them, self-inductance is used to characterize the self-induced voltage generated by each phase conductor when the current changes, mutual inductance is used to characterize the mutual inductance effect between different conductor layers due to magnetic field coupling, and conductor resistance is used to characterize the active power loss and voltage drop of the conductor itself under the action of fault current. By reasonably connecting the above parameters in the equivalent circuit according to the topological relationship of the actual physical structure of the cable, the cable equivalent circuit model can accurately reflect the electromagnetic coupling relationship and overall impedance characteristics between each phase conductor layer under the current candidate length condition. After the cable equivalent circuit model is constructed, the fault current of each phase is calculated according to the cable equivalent circuit model under the set fault conditions. That is, under the fault type, fault location, and power grid operation mode selected in the planning stage, the equivalent power source, system impedance, and fault point conditions of the power grid side are applied to the cable equivalent circuit model.

[0027] As described above, by solving the response equation of the equivalent circuit during the fault, the current waveforms of the three phases of the cable after the fault occurs or the current values ​​at critical moments are obtained. This allows the fault current of each phase to be quantitatively characterized based on the comprehensive influence of self-inductance, mutual inductance, and conductor resistance, thereby forming the calculation results of the fault current of each phase under the current candidate length. After repeating the above modeling and solving process for all candidate lengths, a one-to-one correspondence between the length and the fault current of each phase is established, providing reliable electrical foundation data for further calculation of temperature change curves and determination of temperature rise time based on fault current and resistance parameters.

[0028] Specifically, based on the structure of the superconducting cable, the corresponding equivalent parameter model is determined. The established model is as follows: Figure 8 As shown in the figure, each parameter is determined according to the formula: The formula for calculating the self-inductance of the i-th conductor layer is:

[0029] In the formula, di For the first i The radius of the layer, Pi For the first i The pitch of the layered conductor, μ0Let H be the permeability in vacuum, with a value of 4π × 10⁻⁷ H / m, and D be the geometric mean distance. In a three-coaxial cable, i =1, 2, 3 represent phases A, B, and C, respectively.

[0030] No. i Layer and First j The mutual inductance between the conductor layers is:

[0031] In the formula, ai and aj They represent the first i Layer and First j The coefficient for the winding direction of the conductor layer is taken as -1 or 1 depending on whether the winding direction is clockwise or counterclockwise. di and dj For the first i Layer and first j The diameter of the layer, Pi and Pj The first i Layer and First j The pitch of the layered conductor, μ0 The magnetic permeability in vacuum is 4π × 10⁻⁷ H / m. D This is the geometric mean distance. In a three-coaxial cable, i , j =1, 2, 3 represent phases A, B, and C, respectively.

[0032] Specifically, the magnitude of the fault current in each phase is calculated, and the temperature change curve is calculated from the fault current. The magnitude of the fault current in each phase is calculated using the following formula:

[0033]

[0034]

[0035] In the formula, R i For the first i The resistance of the layer conductor, I For the first i The current flowing through the conductor layer, U For voltage, ω It is related to the frequency of the voltage.

[0036] In any of the above embodiments, the cable equivalent circuit model is associated with the cable at the current candidate length.

[0037] In this embodiment, given the cable's structural form, material properties, and cross-sectional dimensions, the self-inductance, mutual inductance, and resistance values ​​per unit length can be obtained in advance based on the electrical parameter information per unit length. When constructing the equivalent circuit model, the aforementioned unit length parameters are amplified or converted according to the corresponding length based on the current candidate length, thereby obtaining the total self-inductance, total mutual inductance, and total resistance corresponding to the candidate length. This ensures that the cable equivalent circuit model can accurately reflect the overall impedance characteristics and electromagnetic coupling relationship of the cable under the given length condition. Through this method, a matching cable equivalent circuit model is generated for each candidate length within the length range. This ensures that when calculating the fault current of each phase based on the model under the set fault conditions, the obtained current results can truly reflect the cable's response characteristics under the fault at the candidate length, thus guaranteeing that the correspondence between length and fault current has physical meaning and engineering credibility.

[0038] S102, based on the temperature change curve, determine the heating time required for each phase temperature to rise to the evaporation temperature of the liquid nitrogen where the cable is located at the current candidate length.

[0039] Here, after calculating the evolution of temperature changes of each phase over time for the current candidate length, the evaporation temperature of liquid nitrogen is first determined by combining the actual operating conditions of liquid nitrogen during cable operation. A correspondence is then established between the operating pressure of liquid nitrogen and its corresponding boiling point. For example, the boiling point of liquid nitrogen at atmospheric pressure is approximately... At 196.56℃, the boiling point increases accordingly under higher pressure, allowing this method to uniquely determine an evaporation temperature for judgment based on the liquid nitrogen pressure used in cable operation. Based on this, the stable operating temperature of the cable under liquid nitrogen cooling before the fault occurs is used as the starting point of the temperature change curve. The temperature change curve calculated using fault current and resistance parameters is considered as the trajectory of each phase's temperature gradually increasing over time. For each phase at the current candidate length, the process is performed point-by-point or step-by-step along the time axis of its corresponding temperature change curve. When the temperature of that phase first reaches or exceeds the liquid nitrogen evaporation temperature, [the process is complete]. Record the time value corresponding to this moment, and subtract the fault initiation time from this time value to obtain the heating time of this phase from the stable operating temperature to the liquid nitrogen evaporation temperature under the current candidate length. For a three-phase coaxial cable, the above search and recording process can be performed on phases A, B and C respectively to obtain the corresponding heating time. Alternatively, when needed, the maximum heating time, minimum heating time or representative heating time selected according to preset principles among the three phases can be used as the heating time index corresponding to the candidate length for subsequent comparison with the start time required for the power grid protection system to disconnect the cable fault.

[0040] As can be seen above, by using the obtained temperature change curve and the above criterion of liquid nitrogen evaporation temperature, the abstract temperature rise process is quantified into a time parameter that can be directly used for length screening. This allows for the construction of a first length range that satisfies the safety constraint that the temperature of each phase does not reach the liquid nitrogen evaporation temperature before the protection action is completed, based on the relative relationship between the heating time and the protection start time among all candidate lengths.

[0041] Specifically, the steps for determining the heating time required for each phase temperature to rise to the evaporation temperature of the liquid nitrogen at the current candidate length include: The evaporation temperature of liquid nitrogen is determined based on the pressure of liquid nitrogen during cable operation, as well as the stable temperature of liquid nitrogen during cable operation at the current candidate length.

[0042] Determine the corresponding points of the evaporation temperature and the steady-state temperature on the temperature change curve, and determine the heating time based on the horizontal coordinate of the corresponding points on the temperature change curve.

[0043] Based on the above specific description, and having already obtained the temperature change curves of each phase temperature over time at the current candidate length, the evaporation temperature of liquid nitrogen is first determined according to the liquid nitrogen pressure during cable operation, and the stable temperature of liquid nitrogen during cable operation at the current candidate length. This is the stable operating temperature of the cable under long-term continuous operation under liquid nitrogen cooling conditions before the fault occurs. The evaporation temperature of liquid nitrogen is uniquely determined by the liquid nitrogen operating pressure; the higher the operating pressure, the higher the corresponding evaporation temperature. Therefore, this step obtains the corresponding evaporation temperature by reading the liquid nitrogen pressure under the current operating conditions and substituting this pressure into the pre-established pressure-evaporation temperature correspondence. Combining the design parameters of the cooling system, the refrigeration temperature, and the heat balance calculation results at the current candidate length, the stable temperature of the cable under normal operating conditions is determined. The evaporation temperature and the stable temperature are then used as two types of key temperature nodes and mapped onto the obtained temperature change curves. As mentioned above, determining the corresponding points of the evaporation temperature and the stable temperature on the temperature change curve involves finding the initial temperature point corresponding to the stable temperature and the target temperature point corresponding to the evaporation temperature on the temperature change curve. The horizontal coordinates of these two corresponding points on the temperature change curve are then read, and the horizontal coordinates are interpreted as the cumulative time from the start of the fault. The difference between the horizontal coordinates of the evaporation temperature point and the stable temperature point is then calculated and used as the heating time required for each phase temperature to rise from the stable temperature to the liquid nitrogen evaporation temperature under the current candidate length. This allows the quantitative index of heating time to be directly derived from the relative positions of the two typical temperature points on the time axis in the temperature change curve. This enables subsequent comparison and screening based on the magnitude of the heating time among different candidate lengths, providing an accurate time parameter basis for determining the first length range within which the phase temperature does not reach the evaporation temperature during the protection activation time.

[0044] S103, based on the temperature rise time and the start-up time required for the power grid protection system to disconnect the cable fault, determine the first length range within which the temperature of each phase of the cable does not reach the evaporation temperature.

[0045] Here, the heating time corresponding to each candidate length is summarized, so that each candidate length corresponds to the amount of time required for the temperature to rise from the stable operating temperature to the liquid nitrogen evaporation temperature of the cable. Based on this, the start time required to disconnect the high-temperature superconducting cable fault under the current power grid protection configuration is obtained. This start time can be understood as the time from the fault being detected, the protection device completing the judgment and issuing the disconnection command until the cable is actually disconnected. It is a fixed time scale determined by the existing protection device and setting parameters and used as a constraint condition in this method.

[0046] Using the heating time as the vertical axis and the candidate length as the horizontal axis, a curve showing the change of heating time with the candidate length can be generated in the planning calculation. Alternatively, a one-to-one correspondence between length and heating time can be established directly at the data level without plotting. Then, the heating time for each candidate length is compared with the start-up time. When the heating time corresponding to a certain candidate length is greater than the start-up time, under this length condition, even if a fault occurs and the entire protection start-up process is completed, the temperature of each phase of the cable will not rise to the evaporation temperature of liquid nitrogen before the protection action is completed. This will not trigger a large amount of liquid nitrogen vaporization and a sudden decrease in cooling capacity. Therefore, this candidate length can be regarded as an acceptable length under the temperature rise constraint. Conversely, when the heating time corresponding to a certain candidate length is less than or equal to the start-up time, it indicates that before the protection is completed and the cable phases are cleared, the temperature of each phase may have reached or exceeded the liquid nitrogen evaporation temperature. There are risks such as premature boiling of liquid nitrogen, cooling failure, and degradation of the superconducting tape from the superconducting state to the normal conducting state. This candidate length should not be included in the selection range from the perspective of temperature rise safety.

[0047] As mentioned above, by comparing time scales, the set of lengths whose heating time is greater than the start-up time is selected from all candidate lengths. The continuous interval or discrete point set of the candidate lengths corresponding to this set is defined as the first length range of the cable. This ensures that any length within the first length range meets the safety condition that the temperature of each phase of the cable does not reach the evaporation temperature before the power grid protection device completes fault clearing. This provides a preliminary length selection result with thermal safety as the core for further convergence by combining the fault current constraints of adjacent cables.

[0048] Specifically, the steps for determining a first length range in which the temperature of each phase of the cable does not reach the evaporation temperature include: Obtain the heating time for all candidate lengths and plot the first curve showing the change in heating time with the candidate length.

[0049] On the first curve, record all heating times that are longer than the start-up time.

[0050] The first length range is determined by the candidate lengths corresponding to the recorded heating times.

[0051] Based on the specific descriptions above, the heating times for all candidate lengths are summarized and organized, so that each candidate length corresponds one-to-one with the heating time required for the temperature of each phase of the cable to rise from its stable temperature to the evaporation temperature of the liquid nitrogen at the cable location. Using candidate length as the independent variable and heating time as the dependent variable, a first curve is plotted to show the change in heating time versus candidate length. This allows for a visual representation of the differences in cable temperature rise rates under different lengths through a continuous or segmented continuous curve, enabling a comparative analysis of the safety margin of each candidate length in terms of temperature rise behavior within the same coordinate system. After obtaining this first curve, the activation time required for the power grid protection system to clear cable faults is introduced as a reference benchmark on the time axis. This activation time is compared with... The heating times corresponding to each point on the first curve are compared. When the heating time corresponding to a certain point is higher than the start-up time, under the candidate length corresponding to that point, the time it takes for the temperature of each phase of the cable to rise from the stable temperature to the evaporation temperature is longer than the time required for the protection system to complete fault detection and disconnection. From a thermal safety perspective, the temperature of each phase of the cable will not reach the evaporation temperature of liquid nitrogen before the protection action is completed. Therefore, the heating time corresponding to that point can be recorded as a heating time higher than the start-up time. Conversely, for points on the first curve where the heating time is lower than or equal to the start-up time, it indicates that under the corresponding candidate length, there is a risk that the temperature of each phase of the cable has reached or is close to the evaporation temperature of liquid nitrogen before the protection system completes disconnection. This part of the candidate length is not adopted.

[0052] As described above, through the comparison and recording process, candidate lengths corresponding to all heating times higher than the start-up time on the first curve are extracted. Based on the distribution of these candidate lengths on the number axis, one or more continuous length intervals or several discrete length point sets can be formed. The set composed of these candidate lengths is defined as the first length range of the cable. This ensures that any candidate length within the first length range satisfies the condition that after a fault occurs and the complete protection start-up process is completed, the temperature of each phase of the cable does not reach the evaporation temperature of the liquid nitrogen where the cable is located. This provides a preliminary length screening result with temperature rise safety as the core for determining the target length in a comprehensive sense by combining the maximum fault current constraint of adjacent cables.

[0053] S104, calculate the maximum fault current passing through an adjacent cable running in parallel with the cable under fault conditions; obtain the tolerable fault current of the power grid, and determine a second length range of the cable that ensures the maximum fault current does not exceed the tolerable fault current.

[0054] Here, based on the established candidate length range of the cable and the analysis of its own fault current and temperature rise behavior under each candidate length, the focus is extended to adjacent cables laid in parallel with the cable in the same corridor and affected by electromagnetic coupling under the same fault condition. For each candidate length within the length range, a fault current calculation model for the adjacent cable is established under a pre-set fault condition, taking into account the voltage level, line resistance parameters, and equivalent impedance parameters of the load carried by the adjacent cable in the power grid. This ensures that the current response of the adjacent cable under the fault condition matches the fault state of the high-temperature superconducting cable corresponding to the current candidate length. Based on the above model, the change of the three-phase current of the adjacent cable with time during the fault is solved, and the peak current carried by the adjacent cable during the entire fault process is extracted. This peak value is taken as the maximum fault current of the adjacent cable under the current candidate length condition. The above calculation process is repeated for all candidate lengths within the length range to obtain a one-to-one correspondence between the candidate length and the maximum fault current of the adjacent cable.

[0055] After obtaining the maximum fault current corresponding to each candidate length, the grid-acceptable fault current is further obtained. This acceptable fault current can be understood as the upper limit of the fault current that adjacent cables and their connected equipment can withstand in terms of thermal and electrodynamic stability under existing equipment configuration, conductor cross-section, and related protection settings. This acceptable fault current is used as a criterion to compare with the maximum fault current under different candidate lengths. When the maximum fault current of the adjacent cable corresponding to a certain candidate length does not exceed the acceptable fault current, it means that under this length condition, even if a fault occurs, the current level borne by the adjacent cable is still within the acceptable safety range of the grid. It will not cause conductor overheating, insulation damage, or mechanical stress exceeding the limit due to excessive current. Therefore, this candidate length can be regarded as an acceptable length under the fault current constraint. Conversely, when the maximum fault current corresponding to a certain candidate length exceeds the acceptable fault current, it indicates that under this length condition, the adjacent cable will withstand a current surge exceeding its allowable range during the fault process. This candidate length should not be selected from the perspective of current safety.

[0056] As described above, by comparing and analyzing all candidate lengths, all candidate lengths that ensure the maximum fault current does not exceed the tolerable fault current are organized into a length set, or correspond to one or more continuous length intervals. This set or interval is defined as the second length range of the cable, so that any length within the second length range can ensure that the fault current of adjacent cables does not exceed the power grid's pre-set tolerable capacity under fault conditions. This provides a length selection basis centered on fault current constraints for selecting the final target length from the intersection of the first and second length ranges.

[0057] Specifically, the steps for calculating the maximum fault current carried by an adjacent cable operating in parallel with the existing cable under fault conditions include: Based on the voltage, resistance, and load parameters of the cable, calculate the fault current range of adjacent cables operating in parallel with the cable under fault conditions; take the maximum value within the fault current range as the maximum fault current.

[0058] Based on the voltage, resistance, and load parameters of the cable, the fault current range of adjacent cables operating in parallel with the existing cable under fault conditions is calculated. This involves using the voltage levels connected to both ends of the adjacent cables as the power supply boundary conditions, the resistance parameters of the adjacent cables as the line impedance basis, and the equivalent impedance parameters of the loads carried by the adjacent cables to construct the electrical path. Furthermore, depending on whether the fault occurs on the cable itself, the busbar side, or the load side, the voltage, resistance, and load parameters are combined accordingly. Circuit analysis methods are used to solve for various fault current values ​​that may occur in the adjacent cables during the fault period, thus forming a fault current range composed of fault currents under multiple operating conditions or at multiple times. This fault current range can be understood as the upper and lower bounds or a set of discrete current values ​​that the adjacent cables may withstand under the stated fault conditions and current parameter configuration.

[0059] As can be seen above, by comparing the above current values, the maximum value is identified and taken as the maximum fault current. That is, it is assumed that in the most unfavorable fault situation or at the fault time, the fault current borne by the adjacent cable will not exceed the above maximum value. Thus, the above maximum fault current is used to characterize the severity of the current impact on the adjacent cable under the fault condition, providing a quantitative basis for subsequently comparing the maximum fault current with the fault current that the power grid can withstand and determining the second length range of the cable accordingly.

[0060] Specifically, calculate the current flowing through each phase of the adjacent cables when a fault occurs:

[0061] In the formula, U C This refers to the voltage across the adjacent cables. R C The resistance of the adjacent cables, I C The current flowing through the adjacent cable. Z For the load carried by the cable, ω It is related to the frequency of the voltage.

[0062] Specifically, the steps for determining a second length range of the cable that ensures the maximum fault current does not exceed the tolerable fault current include: Obtain the maximum fault current for all candidate lengths and plot a second curve showing the maximum fault current as a function of the candidate length.

[0063] On the second curve, record all the maximum fault currents that are higher than the tolerable fault current.

[0064] The second length range is determined by the candidate length corresponding to the recorded maximum fault current.

[0065] Based on the specific description above, the maximum fault current for all candidate lengths is obtained, so that each candidate length corresponds one-to-one with the maximum fault current borne by an adjacent cable under the fault condition. A second curve is plotted with the candidate length as the abscissa and the maximum fault current as the ordinate, so that the trend of the fault current level of adjacent cables under different length conditions is intuitively presented in the same coordinate system through the second curve. After obtaining the second curve, the grid's tolerable fault current is added to the same coordinate system as a reference benchmark parallel to the ordinate. By comparing the magnitude relationship between the maximum fault current corresponding to each point on the second curve and the tolerable fault current, all maximum fault currents higher than the tolerable fault current are recorded on the second curve. The recorded maximum fault currents are regarded as the part that does not meet the requirements under the current safety constraint, and the corresponding candidate length represents the current surge that the adjacent cable will bear during the fault process that exceeds the grid's allowable upper limit.

[0066] As described above, based on the distribution of the recorded maximum fault current on the second curve, the position of the corresponding candidate length on the length axis is used as the dividing point to divide the entire candidate length range: on the one hand, candidate lengths whose corresponding maximum fault current is higher than the tolerable fault current are marked as length intervals or length points to be eliminated; on the other hand, the remaining length intervals after removing the candidate lengths that do not meet the above conditions are regarded as the set of lengths acceptable from the perspective of current safety. Thus, by using the positional relationship of the candidate lengths corresponding to the recorded maximum fault current on the length axis, the second length range is determined, so that the maximum fault current borne by any candidate length within the second length range under fault conditions does not exceed the tolerable fault current of the power grid. This provides a length screening result based on current safety for selecting the target length of the cable under the premise of simultaneously satisfying the temperature rise constraint and the fault current constraint.

[0067] S105, determine the target length of the cable by using the first length range and the second length range.

[0068] Here, after obtaining the first length range based on the temperature rise time constraint and the second length range based on the maximum fault current constraint of adjacent cables, the two length ranges are used as the screening results of the same cable length parameter under different physical constraint dimensions for comprehensive comparison and unified processing. First, the first length range is regarded as the set of lengths acceptable from the perspective of thermal safety, that is, any length in it can ensure that the temperature of each phase of the cable does not reach the evaporation temperature of the liquid nitrogen where the cable is located before the power grid protection system completes fault clearing under the corresponding fault condition. The second length range is regarded as the set of lengths acceptable from the perspective of current safety, that is, any length in it can ensure that the maximum fault current borne by the adjacent cable running in parallel with the cable does not exceed the fault current that the power grid can withstand during the fault condition. On this basis, a set operation is performed on the first length range and the second length range, preferably determining the intersection of the two. The length intervals or discrete candidate lengths contained in the intersection are regarded as the comprehensive feasible length set that simultaneously satisfies the temperature rise constraint and the fault current constraint. That is, any cable length selected within this set can take into account both the temperature rise safety of the cable itself and the current safety of the adjacent cables without changing the existing protection system configuration.

[0069] As mentioned above, for the obtained set of intersection lengths, in engineering applications, one or more length values ​​can be selected as the target length for final implementation based on specific construction plans, corridor conditions, and process constraints. For example, when the intersection is a continuous interval, the length closest to the expected laying distance can be selected based on the actual route. When the intersection is multiple discrete segments, the length of one segment can be selected as the preferred solution based on construction convenience and equipment configuration conditions. Thus, this method provides a clear target range and a feasible length value for the selection of the length of high-temperature superconducting cables under the premise of ensuring quantitative safety constraints, and realizes parameter coordination and adaptation between the cable length planning results and the existing power grid protection system.

[0070] In any of the above embodiments, as Figure 3 As shown, the calculation of the time required for each phase to reach the liquid nitrogen evaporation temperature is broken down into steps, specifically including: The evaporation temperature of liquid nitrogen varies with operating pressure. For example, the boiling point of liquid nitrogen is -196.56℃ at atmospheric pressure, -185.10℃ at three standard atmospheres, and -169.20℃ at ten standard atmospheres. Under normal circumstances, the liquid nitrogen pressure is higher than atmospheric pressure but lower than ten atmospheres when superconducting cables are in operation.

[0071] Based on the current and temperature of the superconducting cable, it can be determined whether it is in a superconducting state. In the superconducting state, the resistance of the superconducting cable is zero; otherwise, its resistance is approximately equal to the resistance of the metal plating.

[0072] After obtaining the current in each phase, the temperature change per unit time can be calculated as follows:

[0073] In the formula, C HTS It is the specific heat capacity of the superconducting cable. m HTS It is the weight of the superconducting cable. I HTS This represents the current flowing through the strip. t For time increments, T HTS For temperature changes on the superconducting cable, R HTS The resistance of the superconducting tape is given.

[0074] Assuming the current temperature of the superconducting cable is T i Calculate the temperature of the superconducting cable at the next moment using the following formula:

[0075] In the formula, T i+1 The temperature at the next moment.

[0076] Once the temperature of the superconducting cable reaches the temperature required for evaporation, record the time elapsed.

[0077] In any of the above embodiments, as Figure 4 As shown, determining the length range based on the temperature rise time involves several steps, specifically including: Determine the length of the superconducting cable for all options, and calculate the time required for the temperature of the superconducting cable to rise to the liquid nitrogen evaporation temperature for each length using the method described in the preceding steps. t .

[0078] Based on the time required for the temperature of the superconducting cable to rise to the liquid nitrogen evaporation temperature for each length t and the corresponding superconducting cable length L ,draw t along with L The changing curve, i.e. t - L curve.

[0079] Based on the current configuration of the power grid's protection system, determine the time required from fault detection to cable disconnection. t 0.

[0080] Find the match in the curve t > t The length range of superconducting cables under zero conditions.

[0081] In any of the above embodiments, as Figure 5 As shown, determining the length range based on the fault current involves several steps, specifically including: Determine the length of the superconducting cable in all schemes, and calculate the fault current of the cable adjacent to the superconducting cable for each length according to the method in step S5.

[0082] Based on the maximum fault current of adjacent cables of the superconducting cable at each length I f and the corresponding superconducting cable length L ,draw I f along with L The changing curve, i.e. I f - L curve.

[0083] Determine the range of fault currents that the power grid can withstand based on the current configuration of the power grid's protection system.

[0084] Based on the previously calculated length range and the principle of minimizing fault current, the final length range of the superconducting cable is determined.

[0085] A second aspect of the present invention provides a system 2. In some embodiments of the present invention, such as... Figure 9 As shown, system 2 includes: The length determination module 201 is used to determine the length range of the cable through multiple construction schemes.

[0086] The fault calculation module 202 is used to calculate the fault current of each phase under fault conditions for each candidate length within the length range, and to calculate the temperature change curve based on the fault current and resistance parameters.

[0087] The temperature rise judgment module 203 is used to determine the heating time required for the temperature of each phase to rise to the evaporation temperature of the liquid nitrogen where the cable is located, based on the temperature change curve, and to obtain the first length range.

[0088] The current judgment module 204 is used to calculate the maximum fault current passing through adjacent cables under fault conditions, obtain the fault current that the power grid can withstand, and obtain the second length range.

[0089] The target length module 205 is used to determine the target length of the cable based on a first length range and a second length range.

[0090] The system provided by this invention, being used to implement the high-temperature superconducting cable length planning method in all the above embodiments, therefore includes all the advantages of the above-described high-temperature superconducting cable length planning method.

[0091] An embodiment of the third aspect of the present invention provides an electronic device. In some embodiments of the present invention, such as... Figure 10 As shown, an electronic device is provided, which may include: a desktop computer, a laptop, a handheld computer, and a cloud server, etc. The electronic device 3 may include, but is not limited to, a processor 301 and a memory 302. Those skilled in the art will understand that... Figure 10 This is merely an example of electronic device 3 and does not constitute a limitation on electronic device 3. It may include more or fewer components than shown, or different components.

[0092] Processor 301 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), or field-programmable gate arrays (FPGAs). Programmable Gate Array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0093] The memory 302 can be an internal storage unit of the electronic device 3, for example, a hard disk or memory of the electronic device 3. The memory 302 can also be an external storage device of the electronic device 3, for example, a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on the electronic device 3. The memory 302 can also include both internal and external storage units of the electronic device 3. The memory 302 is used to store computer programs and other programs and data required by the electronic device.

[0094] An embodiment of the fourth aspect of the present invention provides a computer-readable storage medium. In some embodiments of the present invention, a computer-readable storage medium is provided that, when executed by processor 301, implements the steps of the above-described method. Therefore, the computer-readable storage medium provided in the fourth aspect of the present invention has all the technical effects of the above-described steps, which will not be repeated here.

[0095] If integrated modules / units are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program may include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. A computer-readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM). Computer-readable media may include ROM (ROM only), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media. It should be noted that the content of computer-readable media may be appropriately added to or subtracted from the content required by the legislation and patent practice of a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media may not include electrical carrier signals and telecommunication signals.

[0096] The above embodiments are only used to illustrate the technical solutions of this disclosure, and are not intended to limit them. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. The above modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be included within the protection scope of this disclosure.

Claims

1. A method of planning a length of a high temperature superconducting cable, characterized by, The method comprises the following steps: determining the length range of the cable through multiple construction schemes; calculating the fault current of each phase under the fault condition for each candidate length in the length range, and calculating the temperature change curve according to the fault current and the resistance parameter; determining the temperature rising time required for the temperature of each phase to rise to the evaporation temperature of the liquid nitrogen in which the cable is located under the current candidate length according to the temperature change curve; determining the first length range in which the temperature of each phase of the cable does not reach the evaporation temperature according to the temperature rising time and the starting time required for the power grid protection system to remove the cable fault; calculating the maximum fault current passed by the adjacent cable running in parallel with the cable under the fault condition, obtaining the bearable fault current of the power grid, and determining the second length range of the cable under which the maximum fault current does not exceed the bearable fault current; determining the target length of the cable through the first length range and the second length range.

2. The high temperature superconducting cable length planning method of claim 1, wherein, The step of calculating the fault current of each phase under the fault condition for each candidate length in the length range comprises: constructing an equivalent circuit model of the cable according to the self-inductance of each conductor layer in the cable, the mutual inductance between each conductor layer, and the conductor resistance; calculating the fault current of each phase under the set fault condition according to the equivalent circuit model of the cable.

3. The high temperature superconducting cable length planning method of claim 2, wherein, The equivalent circuit model of the cable is associated with the current candidate length of the cable.

4. The high temperature superconducting cable length planning method of claim 1, wherein, The step of determining the temperature rising time required for the temperature of each phase to rise to the evaporation temperature of the liquid nitrogen in which the cable is located under the current candidate length comprises: determining the evaporation temperature of the liquid nitrogen according to the pressure of the liquid nitrogen when the cable is running, and determining the stable temperature of the liquid nitrogen when the cable is running under the current candidate length; determining the corresponding points of the evaporation temperature and the stable temperature in the temperature change curve, and determining the temperature rising time according to the abscissa of the corresponding points in the temperature change curve.

5. The high temperature superconducting cable length planning method of claim 4, wherein, The step of determining the first length range in which the temperature of each phase of the cable does not reach the evaporation temperature comprises: obtaining the temperature rising time under all candidate lengths, and drawing a first curve of the temperature rising time changing with the candidate length; recording all temperature rising times higher than the starting time on the first curve; determining the first length range through the candidate length corresponding to the recorded temperature rising time.

6. The high temperature superconducting cable length planning method of claim 1, wherein, The step of calculating the maximum fault current passed by the adjacent cable running in parallel with the cable under the fault condition comprises: calculating the fault current range of the adjacent cable running in parallel with the cable under the fault condition according to the voltage, resistance and load parameters of the cable; and taking the maximum value in the fault current range as the maximum fault current.

7. The high temperature superconducting cable length planning method of claim 6, wherein, The step of determining the second length range of the cable under which the maximum fault current does not exceed the bearable fault current comprises: obtaining the maximum fault current under all candidate lengths, and drawing a second curve of the maximum fault current changing with the candidate length; recording all maximum fault currents higher than the bearable fault current on the second curve; determining the second length range through the candidate length corresponding to the recorded maximum fault current.

8. A system for implementing the method for planning the length of a high temperature superconducting cable according to any one of claims 1-7, characterized in that, The method comprises the following steps: a length determination module configured to determine the length range of the cable through multiple construction schemes; a fault calculation module configured to calculate a fault current of each phase under a fault condition for each candidate length in the length range, and calculate a temperature change curve according to the fault current and a resistance parameter; a temperature rise judgment module configured to determine a temperature rise time required for a temperature of each phase to rise to an evaporation temperature of liquid nitrogen in which the cable is located according to the temperature change curve, and obtain a first length range; a current judgment module configured to calculate a maximum fault current passed by an adjacent cable under the fault condition, obtain a bearable fault current of a power grid, and obtain a second length range; a target length module configured to determine a target length of the cable according to the first length range and the second length range.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The processor executes the computer program to implement the steps of the high-temperature superconducting cable length planning method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to implement the steps of the high-temperature superconducting cable length planning method according to any one of claims 1 to 7.

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