Method for constructing a string of series insulators and a string of series insulators

Abstract

The application is suitable for the field of power transmission, and provides a construction method of a series insulator string and a series insulator string. The method comprises the following steps: obtaining a simulation model of an initial insulator string; according to the simulation model, taking the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator as variables, taking the minimization of the maximum surface field strength of the composite insulator as an objective function, and taking the internal maximum field strength of each porcelain insulator as a constraint condition, constructing and solving an optimization problem to obtain an optimal solution of the optimization problem; and constructing a target insulator string according to the target number and the target dielectric constant. The target insulator string constructed by the method can not only minimize the maximum surface field strength of the composite insulator, but also ensure that the internal maximum field strength of each porcelain insulator does not exceed the preset safety field strength threshold, thereby improving the reliability of the insulator string.

Description

Technical Field

[0001] This application belongs to the field of power transmission technology, and in particular relates to a method for constructing a series insulator string and the series insulator string. Background Technology

[0002] Composite insulators are widely used in high-voltage, ultra-high-voltage, and extra-high-voltage transmission lines due to their light weight, high mechanical strength, and excellent resistance to flashover. However, in actual operation, because composite insulators have low inherent capacitance, they are susceptible to stray capacitance from fittings, towers, and other sources, leading to significant non-uniformity in axial potential distribution. Electric field distortion and excessively high local field strength often occur near the high-voltage end fittings. Even with measures such as equipotential ring arrangement and optimized shed structure, the local field strength may still approach or exceed the corona initiation field strength threshold, inducing continuous corona discharge, local temperature rise, and accelerated aging of the silicone rubber material, seriously threatening the long-term safe operation of the transmission line.

[0003] Connecting porcelain insulators in series at the high-voltage end of composite insulators, utilizing their voltage-dividing effect to move the ends of the composite insulators away from strong electric field regions, is an effective way to improve the electric field distribution at the ends. However, the design of existing series connection schemes mainly relies on engineering experience to determine the number of porcelain insulators and generally uses standard porcelain insulators with fixed dielectric constants, failing to systematically consider the comprehensive influence of the number of porcelain insulators and dielectric constants on the surface electric field strength of the composite insulator and the internal electric field strength of the porcelain insulator itself.

[0004] This design approach may result in the porcelain insulators being unable to effectively reduce the maximum electric field strength on the surface of the composite insulator, or may cause the electric field strength inside the porcelain insulator to exceed the safe range, creating new electrical stress hazards and reducing the reliability of the constructed insulator strings. Summary of the Invention

[0005] In view of this, the present application provides a method for constructing a series insulator string and a series insulator string to solve the technical problem of low reliability of insulator strings in the prior art.

[0006] In a first aspect, embodiments of this application provide a method for constructing a series-connected insulator string, comprising: A simulation model of the initial insulator string is obtained; the initial insulator string includes a grounding tower, a composite insulator connected to the grounding tower, a string of porcelain insulators adjacent to the composite insulator, and a high-voltage conductor adjacent to the string of porcelain insulators, wherein the string of porcelain insulators includes several porcelain insulators connected in series; Based on the simulation model, using the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator as variables, minimizing the maximum surface electric field of the composite insulator as the objective function, and ensuring that the maximum internal electric field of each porcelain insulator does not exceed a preset safe electric field threshold as a constraint, an optimization problem is constructed and solved to obtain the optimal solution to the optimization problem; the optimal solution includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator. Based on the target quantity and the target dielectric constant of each, construct the target insulator string.

[0007] Optionally, the maximum surface electric field strength of the composite insulator is determined in the following way: Based on the simulation model, the electric field of the composite insulator is calculated using the finite element method. In the process of finite element calculation of the electric field of the composite insulator, the maximum electric field is selected as the maximum surface field strength of the composite insulator within the interface between the target silicone rubber material of the composite insulator and the air; the target silicone rubber material is the silicone rubber material in the insulation structure area between the high-voltage end hardware of the composite insulator and the first shed of the high-voltage end of the composite insulator.

[0008] Optionally, the step of performing finite element calculations on the electric field of the composite insulator based on the simulation model includes: Determine the operating voltage of the high-voltage conductor based on the voltage level of the target transmission line; Using the structural parameters of the composite insulator, the structural parameters of each of the porcelain insulators, the working voltage of the high-voltage conductor, the structural parameters of the grounding tower, and the structural parameters of the high-voltage conductor as the input boundary conditions of the simulation model, the electric field of the composite insulator is calculated by finite element method.

[0009] Optionally, the safe field strength threshold is determined in the following way: Obtain the air breakdown field strength of the internal pores of the ceramic insulator; The margin factor is determined based on the user's reliability requirements for the target insulator string; The safe field strength threshold is determined based on the air breakdown field strength and the margin coefficient.

[0010] Optionally, the optimization problem can be solved in the following ways: Based on the degree of impact of the number of porcelain insulators in the porcelain insulator string on the manufacturing cost and installation difficulty of the porcelain insulator string, and in combination with the limit on the number of porcelain insulators in the porcelain insulator string, several candidate quantities are determined; For each candidate quantity, construct and solve the sub-optimization problem corresponding to that candidate quantity, determine the optimal objective function value corresponding to that candidate quantity, and obtain the optimal objective function value corresponding to each candidate quantity. Among the candidate quantities, the candidate quantity with the smallest corresponding optimal objective function value is selected as the target quantity, and each dielectric constant corresponding to the target quantity is determined as the target dielectric constant.

[0011] Optionally, the step of constructing and solving the sub-optimization problem corresponding to the number of candidates, and determining the optimal objective function value corresponding to the number of candidates, includes: Using the dielectric constant of each porcelain insulator corresponding to the number of candidates as variables, minimizing the maximum surface electric field of the composite insulator as the objective function, and ensuring that the maximum internal electric field of each porcelain insulator does not exceed the safe electric field threshold as a constraint, the sub-optimization problem corresponding to the number of candidates is constructed. Within a preset range of manufacturable dielectric constants, the sub-optimization problem corresponding to the number of candidate quantities is solved using a preset algorithm to obtain the optimal objective function value corresponding to the number of candidate quantities; the preset algorithm is different for different numbers of candidate quantities.

[0012] Optionally, after solving the sub-optimization problem corresponding to the number of candidates using a preset algorithm, the method further includes: If the sub-optimization problem corresponding to the number of candidates has no solution, then the range of manufacturable dielectric constants is adjusted, and / or the number of candidates is increased to resolve the sub-optimization problem corresponding to the number of candidates.

[0013] Optionally, constructing the target insulator string based on the target quantity and each of the target dielectric constants includes: Each of the target dielectric constants is used to obtain a finished porcelain insulator. If no finished porcelain insulator exists for any of the target dielectric constants, a pre-set porcelain substrate is used as the base, and strontium titanate powder is added to the substrate according to the target doping ratio to obtain a doped porcelain insulator. The target doping ratio is determined according to the corresponding target dielectric constant, and the sum of the number of finished porcelain insulators and the number of doped porcelain insulators is the target quantity. Based on the target dielectric constants corresponding to the finished porcelain insulator and the doped porcelain insulator, the finished porcelain insulator, the doped porcelain insulator, the grounding tower, the composite insulator, and the high-voltage conductor are connected in series to obtain the target insulator string.

[0014] Optionally, the grounding tower in the target insulator string is connected to the composite insulator, the finished porcelain insulator and / or the doped porcelain insulator with the lowest target dielectric constant is adjacent to the composite insulator, and the finished porcelain insulator and / or the doped porcelain insulator with the highest target dielectric constant is adjacent to the high-voltage conductor. Furthermore, each of the finished porcelain insulator and / or the doped porcelain insulator is connected in series in order of the magnitude of the target dielectric constant.

[0015] Secondly, embodiments of this application provide a series insulator string, which is constructed by the method for constructing a series insulator string as described in any of the first aspects.

[0016] Thirdly, embodiments of this application provide 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 method for constructing a series insulator string as described in any of the first aspects above.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method for constructing a series insulator string as described in any of the first aspects above.

[0018] Fifthly, embodiments of this application provide a computer program product that, when run on a display device, causes the display device to perform the steps of the method for constructing a series insulator string as described in any of the first aspects above.

[0019] The beneficial effects of the method for constructing a series insulator string provided in this application embodiment are as follows: In the method for constructing a series insulator string provided in this application embodiment, a simulation model of an initial insulator string is first obtained. The initial insulator string includes a grounding tower, a composite insulator connected to the grounding tower, a string of porcelain insulators adjacent to the composite insulator, and a high-voltage conductor adjacent to the porcelain insulator string. The porcelain insulator string includes several porcelain insulators connected in series. Then, based on the simulation model, the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator are used as variables. The objective function is to minimize the maximum surface electric field of the composite insulator, and the constraint is that the maximum internal electric field of each porcelain insulator does not exceed a preset safe electric field threshold. An optimization problem is constructed and solved to obtain the optimal solution to the optimization problem. The optimal solution includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator. Finally, the target insulator string is constructed based on the target number and the target dielectric constants.

[0020] Since this scheme uses minimizing the maximum surface electric field of the composite insulator as the objective function and ensuring that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold as the constraint, the optimization problem is constructed and solved to obtain the target insulator string. Therefore, the target insulator string constructed by this scheme can not only minimize the maximum surface electric field of the composite insulator, but also ensure that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold, thus improving the reliability of the insulator string. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating the implementation of a method for constructing a series-connected insulator string, as provided in an embodiment of this application; Figure 2 This is a schematic diagram of the structure of an initial insulator string provided in an embodiment of this application; Figure 3 A comparison diagram of the internal electric field strength of various ceramic insulators under different dielectric constant arrangements is provided for embodiments of this application. Figure 4 Comparison of electric field distribution cloud maps before and after series connection for the three embodiments provided in this application; Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0023] It should be noted that the terminology used in the embodiments of this application is only for explaining specific embodiments of this application and is not intended to limit this application. In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, "at least one" or "one or more" means one, two or more. The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature.

[0024] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0025] Traditional composite insulators, when applied to high-voltage, ultra-high-voltage, and extra-high-voltage transmission lines, suffer from extremely uneven axial potential distribution due to their small inherent capacitance and the influence of stray capacitance from fittings and towers. This results in widespread electric field distortion and excessively high local electric field strength near the high-voltage end fittings, potentially inducing persistent corona discharge, localized heating, and accelerated aging of the silicone rubber material, severely threatening the long-term safe operation of the transmission line. Existing solutions that improve the end electric field by connecting porcelain insulators in series rely on empirically determined numbers and the use of conventional single-dielectric-constant porcelain insulators, failing to adequately address the electrical stress issues inherent in the series-connected porcelain insulator sections.

[0026] To address this issue, this application proposes a method for constructing a series-connected insulator string, aiming to solve the aforementioned technical problems through optimized design. The method for constructing the series-connected insulator string provided in this application can be implemented by an electronic device, which may include, but is not limited to, mobile phones, computers, and tablets.

[0027] For ease of understanding, the following explains some key terms in this embodiment: A simulation model is a mathematical model that uses computer software to simulate a physical system in order to predict its behavior or performance. In this method, the simulation model is used to simulate the electric field distribution of an insulator string, thereby evaluating its electrical performance.

[0028] The dielectric constant is a physical quantity that measures the ability of a dielectric material to store electrical energy in an electric field. Different insulating materials have different dielectric constants, and their magnitudes directly affect the potential distribution and electric field strength of the material in an electric field.

[0029] Electric field strength refers to the intensity of the electric field at a specific point in an electric field, representing the electric force exerted on a unit charge at that point. In insulator design, electric field strength is a key parameter for assessing the electrical stress of insulating materials; excessively high electric field strength may lead to insulation breakdown.

[0030] An optimization problem is a mathematical problem that, under given constraints, seeks the optimal combination of variables that maximizes or minimizes the objective function. In this method, the optimization problem is used to determine the number and dielectric constant of porcelain insulators to achieve specific electrical performance objectives.

[0031] Please see Figure 1 , Figure 1 The flowchart illustrates a method for constructing a series-connected insulator string according to an embodiment of this application. This method may include steps S101 to S103, as detailed below: In S101, the simulation model of the initial insulator string is obtained; the initial insulator string includes a grounding tower, a composite insulator connected to the grounding tower, a porcelain insulator string adjacent to the composite insulator, and a high-voltage conductor adjacent to the porcelain insulator string. The porcelain insulator string includes several porcelain insulators connected in series.

[0032] In this embodiment, the electronic device can first acquire a simulation model of an initial insulator string. This initial insulator string typically includes a grounding tower, a composite insulator connected to the grounding tower, a string of porcelain insulators adjacent to the composite insulator, and a high-voltage conductor adjacent to the porcelain insulator string. The porcelain insulator string is composed of several porcelain insulators connected in series. This simulation model can be acquired in various ways. For example, it can be established by manually inputting parameters such as the geometric dimensions and material properties of the insulator string, or by selecting standard components from a pre-set insulator component database for combination.

[0033] Please see Figure 2 , Figure 2 This is a schematic diagram of the structure of an initial insulator string provided in an embodiment of this application. Figure 2 The initial insulator string may include 1—grounding tower; 2—composite insulator; 3-1—No. 1 porcelain insulator (adjacent to the composite insulator); 3-2—No. 2 porcelain insulator; 3-N—No. N porcelain insulator (adjacent to the high-voltage conductor); 5—high-voltage conductor, where N is a positive integer.

[0034] Optionally, the initial insulator string may also include 4 connecting fittings.

[0035] In S102, based on the simulation model, the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator are used as variables. The objective function is to minimize the maximum surface electric field of the composite insulator, and the constraint is that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold. The optimization problem is constructed and solved to obtain the optimal solution of the optimization problem. The optimal solution includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator.

[0036] In this embodiment, after obtaining the simulation model of the initial insulator string, the electronic device can construct and solve an optimization problem based on the simulation model. This optimization problem uses the number of porcelain insulators in the string and the dielectric constant of each porcelain insulator as variables. The objective function is set to minimize the maximum surface electric field strength of the composite insulator, while the constraint condition is that the maximum internal electric field strength of each porcelain insulator does not exceed a preset safe electric field strength threshold. By solving this optimization problem, the optimal solution can be obtained, which includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator.

[0037] Since this optimization problem uses the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator as variables, the variable x satisfies:

[0038] Wherein, εri is the dielectric constant of the i-th porcelain insulator, and its value is within the manufacturable range [εrmin, εrmax]. The lower limit εrmin and the upper limit εrmax of the relative dielectric constant of the porcelain insulator are determined by the physical structure and manufacturing constraints of the porcelain insulator.

[0039] The core objective of this scheme is to reduce the dielectric constant of porcelain insulators by adjusting the variable x, i.e., changing the number of porcelain insulators in the string and the dielectric constant of each individual insulator. Figure 2 The maximum surface electric field strength E0_max(x) of the composite insulator (component 2). Here, the unit of E0_max(x) can be set to kV / cm, and the specific value can be obtained through finite element analysis (FEM) of the electric field of multiple series-connected composite insulators, i.e.

[0040] Based on this, in one possible implementation, this application further proposes that the maximum surface electric field of the composite insulator be determined in the following way: finite element calculation of the electric field of the composite insulator is performed according to the simulation model; during the finite element calculation of the electric field of the composite insulator, the maximum electric field is selected as the maximum surface electric field of the composite insulator within the interface between the target silicone rubber material of the composite insulator and the air; the target silicone rubber material is the silicone rubber material in the insulation structure area between the high-voltage end fitting of the composite insulator and the first shed of the high-voltage end of the composite insulator.

[0041] Specifically, determining the maximum surface electric field strength of a composite insulator first relies on finite element analysis (FEM) of its electric field. FEM is a numerical analysis method that discretizes a complex geometric model into a finite number of elements and solves the electric field equations within each element to obtain a detailed distribution of the electric field across the entire region. After constructing a simulation model of the series-connected insulator string, this model includes the composite insulator's geometry, material properties, and relative position to its surrounding environment (such as high-voltage conductors and grounding towers). Based on this simulation model, specialized finite element analysis software can accurately simulate the electric field distribution of the composite insulator under operating voltage, providing a detailed data foundation for subsequent field strength assessment.

[0042] In the finite element method (FEM) calculation of the electric field of composite insulators, the key lies in accurately identifying and selecting the maximum surface electric field. This application explicitly states that the maximum electric field should be selected as the maximum surface electric field of the composite insulator at the interface between the target silicone rubber material and air. The selection of this interface is crucial because surface discharge and flashover of composite insulators typically originate at the interface between the insulating material and air, and the electric field strength in this region is often a key factor determining the insulation performance. Through finite element method calculations, the electric field strength values ​​at various points on this interface can be obtained, and the maximum value can be identified as the maximum surface electric field of the composite insulator.

[0043] Furthermore, this application precisely defines the "target silicone rubber material" as the silicone rubber material within the insulation structure region between the high-voltage end fittings and the first shed of the high-voltage end of the composite insulator. The high-voltage end of the composite insulator, particularly the region near the high-voltage conductor connecting fittings and the first shed, is typically the area with the highest electric field strength in the entire insulator string due to electric field distortion and stress concentration effects. Precisely limiting the evaluation scope to the interface between the silicone rubber material and air in this region ensures that the determined maximum surface electric field strength accurately reflects the most critical and stress-prone areas of the composite insulator, thus making the optimization target more targeted and practically meaningful.

[0044] Failure to fully consider actual operating conditions and key structural parameters during the finite element method calculation of the electric field may lead to discrepancies between the simulation results and the actual situation, thereby affecting the accuracy of the optimization problem and causing the final insulator string to fail to meet the expected performance or reliability requirements.

[0045] In this regard, this application further proposes the following steps for performing finite element calculations on the electric field of composite insulators based on the simulation model: determining the operating voltage of the high-voltage conductor according to the voltage level of the target transmission line; and performing finite element calculations on the electric field of composite insulators using the structural parameters of the composite insulators, the structural parameters of each porcelain insulator, the operating voltage of the high-voltage conductor, the structural parameters of the grounding tower, and the structural parameters of the high-voltage conductor as input boundary conditions of the simulation model.

[0046] One key step is determining the operating voltage of the high-voltage conductor based on the voltage level of the target transmission line. This step aims to provide accurate excitation source conditions for the electric field simulation. The voltage level of the target transmission line is a core parameter determining the electrical stress borne by the insulator string. The operating voltage can be determined based on the rated operating voltage of the transmission line, or it can consider transient or transient voltage peaks that may occur under specific operating conditions (such as overvoltage or fault conditions) to ensure the comprehensiveness and conservatism of the simulation results. For example, the highest operating voltage of the line can be used, or a certain overvoltage coefficient can be considered to determine the operating voltage.

[0047] Using the structural parameters of the composite insulator, the individual porcelain insulators, the operating voltage of the high-voltage conductor, the structural parameters of the grounding tower, and the structural parameters of the high-voltage conductor as input boundary conditions for the simulation model ensures that the finite element calculation accurately reflects the electric field distribution of the insulator string in the actual installation and operating environment. The structural parameters of the composite insulator include its geometric dimensions (e.g., skirt diameter, inter-laminar spacing, creepage distance, core diameter), material properties (e.g., dielectric constant and conductivity of silicone rubber), and the geometry and material of the fittings. The structural parameters of each porcelain insulator include its geometric dimensions (e.g., skirt diameter, inter-laminar spacing, creepage distance, porcelain height), material properties (e.g., dielectric constant and conductivity of the porcelain material), and the geometry and material of the fittings. The structural parameters of the high-voltage conductor include its diameter, cross-sectional area, material, and connection method and distance to the insulator string. The structural parameters of the grounding tower include its geometry, dimensions, material, relative position to the insulator string, and grounding method. These parameters collectively define the geometric model and material distribution of the simulation region, as well as the potential boundary conditions required for the electric field calculation (e.g., the operating voltage applied to the high-voltage conductor, with the grounding tower set to zero potential). By accurately inputting these parameters, a simulation environment that closely matches the actual physical model can be constructed, thereby improving the accuracy of electric field calculations.

[0048] In some of the embodiments described above in this application, the optimization problem is constrained by the condition that the maximum internal electric field strength of each porcelain insulator does not exceed a preset safe electric field strength threshold. However, if this safe electric field strength threshold is set improperly, the optimization results may fail to adequately guarantee the long-term operational reliability of the porcelain insulator, or cause unnecessary material waste and cost increases, thereby affecting the actual application performance and economy of the target insulator string.

[0049] In response, this application further proposes that the safe field strength threshold be determined by the following method: obtaining the air breakdown field strength of the pores inside the porcelain insulator material; determining the margin coefficient based on the user's reliability requirements for the target insulator string; and determining the safe field strength threshold based on the air breakdown field strength and the margin coefficient.

[0050] Specifically, obtaining the air breakdown field strength of the internal pores in a porcelain insulator refers to determining the minimum electric field strength required for partial discharge or breakdown of tiny pores or defects within the porcelain insulator material under the influence of an electric field, through experimental testing, consulting material handbooks, or theoretical calculations. For example, the air breakdown field strength of the internal pores can be calculated by fabricating a sample with simulated pores on a specific porcelain insulator material and conducting a breakdown voltage test under a controlled electric field. Alternatively, the specified values ​​for the air gap breakdown field strength of different insulating materials in relevant national standards or industry specifications can be consulted. This air breakdown field strength is a fundamental physical parameter for measuring the internal insulation performance of a porcelain insulator, directly reflecting the dielectric strength of the material at internal defects.

[0051] Based on this, the margin factor is determined according to the user's reliability requirements for the target insulator string. The margin factor is a safety factor that considers various uncertainties in actual engineering applications, such as batch variations in materials, manufacturing tolerances, changes in environmental conditions (e.g., temperature, humidity, pollution), long-term aging effects, and potential operating overvoltages. Users can set different reliability levels based on factors such as the voltage level of the transmission line, the severity of the operating environment (e.g., highly polluted areas, high-altitude regions), expected lifespan, economic losses from power outages, and maintenance costs. For example, for critical transmission lines in the State Grid or applications in extreme environments, extremely high reliability may be required, in which case the margin factor can be 1.5 to 2.0 or even higher.

[0052] Finally, the safe field strength threshold is determined based on the air breakdown field strength and the margin factor. Typically, the safe field strength threshold can be obtained by dividing the air breakdown field strength by the margin factor, i.e.: Safe field strength threshold =

[0053] Where Ecrit is the air breakdown field strength of the pores inside the porcelain insulator material, i.e., 30kV / cm; k is the margin factor, selected as 1~2.

[0054] Furthermore, since the core constraint in this scheme is the maximum electric field strength inside the porcelain insulator, it must not cause partial discharge or insulation breakdown during long-term service (i.e., the maximum electric field strength inside each porcelain insulator must not exceed the preset safe electric field strength threshold). Therefore, the following constraints apply:

[0055] in, This represents the maximum value of the maximum electric field strength inside each porcelain insulator.

[0056] Based on the above description, the optimization problem constructed in this embodiment can be represented in the following way:

[0057]

[0058]

[0059] In some embodiments described above, this application proposes determining the target number of porcelain insulators and the target dielectric constant of each porcelain insulator by constructing and solving an optimization problem, in order to minimize the maximum surface electric field of the composite insulator. However, in actual solving of this optimization problem, since the number of porcelain insulators is a discrete variable, and its number not only affects the electric field distribution but also directly relates to the manufacturing cost and installation difficulty of the insulator string, directly optimizing the number as a continuous variable may lead to a complex optimization process, difficulty in convergence, or solutions that do not conform to practical engineering applications and economic benefits. Furthermore, the limitation on the number of porcelain insulator strings needs to be considered during the optimization process to ensure the feasibility of the solution.

[0060] To address this, this application further proposes a solution to the optimization problem as follows: Based on the impact of the number of porcelain insulators in the porcelain insulator string on the manufacturing cost and installation difficulty of the string, and considering the limitation on the number of porcelain insulators in the string, several candidate quantities are determined; for each candidate quantity, a sub-optimization problem is constructed and solved to determine the optimal objective function value corresponding to that candidate quantity, thus obtaining the optimal objective function value for each candidate quantity; among all candidate quantities, the candidate quantity with the smallest corresponding optimal objective function value is selected as the target quantity, and the dielectric constants corresponding to the target quantity are determined as the target dielectric constants.

[0061] Specifically, when determining several candidate quantities, a series of potentially reasonable quantities of porcelain insulators can be pre-screened based on factors such as engineering experience, design specifications, cost budgets, and installation conditions. For example, the length range of porcelain insulator strings can be initially determined based on the voltage level of the transmission line, environmental conditions, and existing insulator string design experience, thereby calculating the possible quantity range of porcelain insulators. Simultaneously, considering manufacturing costs (higher costs with larger quantities) and installation difficulty (more quantities lead to more complex and time-consuming installation), reasonable limits can be imposed on the quantity, such as setting a minimum and a maximum quantity, or excluding certain uneconomical or inconvenient quantities for installation. These candidate quantities can be a portion of a continuous integer sequence or discrete values ​​selected based on specific rules.

[0062] For each candidate number, the number is fixed. Then, with the dielectric constant of each porcelain insulator as the variable, the objective function is to minimize the maximum surface electric field of the composite insulator, and the constraint is that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold. The sub-optimal problem is constructed and solved to determine the optimal objective function value corresponding to the candidate number.

[0063] This application further proposes to construct and solve the sub-optimization problem corresponding to the candidate number, and determine the optimal objective function value corresponding to the candidate number, including: using the dielectric constant of each porcelain insulator corresponding to the candidate number as a variable, minimizing the maximum surface electric field of the composite insulator as the objective function, and constraining that the maximum internal electric field of each porcelain insulator does not exceed the safe electric field threshold, to construct the sub-optimization problem corresponding to the candidate number; within a preset range of manufacturable dielectric constants, solving the sub-optimization problem corresponding to the candidate number using a preset algorithm to obtain the optimal objective function value corresponding to the candidate number; the preset algorithm is different for different candidate numbers.

[0064] Specifically, when constructing the sub-optimization problem corresponding to this number of candidate insulators, the dielectric constant of each porcelain insulator corresponding to this number of candidate insulators is used as the optimization variable. These dielectric constants are key parameters affecting the electric field distribution of the insulator string; by adjusting them, the electric stress distribution of the entire insulator string can be changed. Minimizing the maximum surface electric field strength of the composite insulator is used as the objective function. The aim is to effectively reduce the electric field stress on the surface of the composite insulator by optimizing the dielectric constant configuration of the porcelain insulators, thereby improving its operational reliability and preventing partial discharge and flashover. Simultaneously, the constraint that the maximum internal electric field strength of each porcelain insulator does not exceed a preset safe electric field strength threshold ensures that while optimizing the external performance of the composite insulator, the internal insulation performance of the porcelain insulator itself is also fully guaranteed, preventing insulation breakdown caused by internal defects.

[0065] When solving the sub-optimization problem corresponding to the number of candidate dielectric constants, the search is first limited to a pre-defined range of manufacturable dielectric constants. This range is typically determined based on the existing material manufacturing processes and performance limitations to ensure the optimization results are practically feasible and avoid obtaining theoretically optimal but impractically unproducible dielectric constant configurations. The solution process is completed using a pre-defined algorithm. It is worth noting that different pre-defined algorithms can correspond to different numbers of candidate dielectric constants. For example, when the number of candidate dielectric constants is 1, a one-dimensional parametric scan is used; when the number of candidate dielectric constants is 2, a two-dimensional full-factor parametric scan is used; when the number of candidate dielectric constants is ≥3, a full-factor simulation sampling is first performed on the candidate dielectric constant combinations, a polynomial response surface surrogate model is fitted, and then a sequence-constrained optimization algorithm (SLSQP) or a genetic algorithm is used on the surrogate model to find continuous optimal solutions, which are then cross-validated with the results of discrete sample screening.

[0066] Through the above technical solution, when optimizing for each candidate number of porcelain insulator strings, a clear mathematical model for the sub-optimization problem can be defined. This model uses the dielectric constant of the porcelain insulator as a variable, aims to minimize the maximum surface electric field of the composite insulator, and is constrained by ensuring that the maximum electric field inside the porcelain insulator does not exceed a safety threshold. This precise modeling method ensures the clarity of the optimization direction and the reliability of the results. Simultaneously, by limiting the search to a pre-defined range of manufacturable dielectric constants during the solution process, the practical feasibility of the optimization results is guaranteed. Furthermore, selecting different pre-defined algorithms based on different candidate numbers (i.e., problem size) can significantly improve solution efficiency and optimization accuracy, avoiding the limitations of a single algorithm on problems of different scales. This makes the entire insulator string optimization design process more efficient and accurate, ultimately yielding an optimized design scheme that balances the external flashover performance of the composite insulator and the internal insulation performance of the porcelain insulator, effectively improving the overall operational reliability and economy of the series-connected insulator strings.

[0067] In the actual solution process, there may be a situation where the sub-optimization problem corresponding to a certain number of candidate quantities cannot find a solution that satisfies all constraints within the preset range of manufacturable dielectric constants. This "no solution" state will cause the optimization process to stagnate, making it impossible to continue determining the optimal design under that number of candidate quantities, thus affecting the construction of the final target insulator string.

[0068] In response, this application further proposes that if the sub-optimization problem corresponding to the number of candidates has no solution, the range of manufacturable dielectric constants shall be adjusted, and / or the number of candidates shall be increased to resolve the sub-optimization problem corresponding to the number of candidates.

[0069] Specifically, when, within a preset range of manufacturable dielectric constants, a preset algorithm is used to solve the sub-optimization problem corresponding to the number of candidate quantities, and it is found that the sub-optimization problem has no solution, it means that within the currently set parameter space, there is no solution that can both meet safety requirements and optimize performance. To solve this problem, two strategies, or a combination thereof, can be adopted.

[0070] The first strategy is to adjust the range of manufacturable dielectric constants. This typically means widening the range, for example, allowing the use of materials with higher or lower dielectric constants, to increase the solution space and thus improve the likelihood of finding a feasible solution. Adjusting the range requires comprehensive consideration of material availability, manufacturing costs, and the potential impact on insulation performance. For example, the upper or lower limit of the dielectric constant can be appropriately expanded based on market research or the latest advances in materials science to incorporate more potential material options.

[0071] The second strategy is to increase the number of candidate insulators. In an insulator string, increasing the number of insulators can usually distribute the voltage, thereby reducing the electric field strength of a single insulator. When the existing number of porcelain insulators cannot meet the safe field strength threshold constraint, increasing their number can effectively reduce the electric field stress borne by each porcelain insulator, making it easier to find a combination of dielectric constants that satisfies all constraints with the new number of insulators.

[0072] After adjusting the range of manufacturable dielectric constants or increasing the number of candidate insulators, the sub-optimization problem corresponding to that number of candidate insulators needs to be solved again. This solution will be based on the new parameter settings (the adjusted range of dielectric constants or the increased number of insulators) in order to find a feasible and optimal solution under expanded search space or more relaxed physical conditions. This process may need to be iterated until an optimal solution that satisfies all conditions is found.

[0073] After obtaining the optimal objective function values ​​corresponding to all candidate quantities, these optimal objective function values ​​are compared. The candidate quantity corresponding to the smallest optimal objective function value is selected and determined as the final target quantity of porcelain insulators. Simultaneously, the dielectric constants of each porcelain insulator obtained when solving its sub-optimization problems with this target quantity are determined as the final target dielectric constants.

[0074] The above technical solution decomposes the original complex mixed-integer nonlinear optimization problem into a series of relatively simple continuous-variable optimization sub-problems, greatly reducing the difficulty and computational complexity of the optimization solution. First, by pre-considering manufacturing costs, installation difficulty, and quantity limitations, several candidate quantities are determined, allowing the optimization process to incorporate actual engineering constraints earlier and avoiding unrealistic optimization results. Second, solving the sub-optimization problem independently for each candidate quantity efficiently finds the optimal dielectric constant configuration for that quantity, thus obtaining the optimal electric field distribution. Finally, by comparing the optimal objective function values ​​under different candidate quantities, the insulator string design scheme that minimizes the maximum electric field strength on the composite insulator surface while meeting safety requirements and engineering constraints can be systematically selected. This ensures that the constructed target insulator string has a more uniform electric field distribution, higher reliability, and significant advantages in terms of economy and feasibility.

[0075] In S103, target insulator strings are constructed based on the target quantity and the dielectric constant of each target.

[0076] In some embodiments described above in this application, a method for constructing series insulator strings by optimizing the number and dielectric constant of porcelain insulators is proposed to reduce the maximum surface electric field of composite insulators. However, in practical applications, the target dielectric constant of each optimized porcelain insulator may not be fully met by commercially available finished porcelain insulators.

[0077] In response, this application further proposes a specific method for constructing the target insulator string, including: obtaining finished porcelain insulators corresponding to each target dielectric constant; if no finished porcelain insulator corresponds to any target dielectric constant, then using a preset porcelain as the substrate, and adding strontium titanate powder to the substrate according to the target doping ratio to obtain a doped porcelain insulator; the target doping ratio is determined according to the corresponding target dielectric constant, and the sum of the number of finished porcelain insulators and the number of doped porcelain insulators is the target quantity; and connecting the finished porcelain insulators, doped porcelain insulators, grounding towers, composite insulators, and high-voltage conductors in series according to the target dielectric constants corresponding to the finished porcelain insulators and doped porcelain insulators to obtain the target insulator string.

[0078] Specifically, when constructing the target insulator string, the first step is to obtain the target dielectric constant of each porcelain insulator obtained from the optimization problem, and then attempt to find matching finished porcelain insulators. Finished porcelain insulators refer to porcelain insulator products that have been mass-produced according to specific specifications and performance requirements and are ready for direct purchase or use. They typically have standardized dimensions, shapes, and dielectric properties. By consulting insulator manufacturers' product catalogs, technical specifications, or communicating with suppliers, it is possible to match the target dielectric constant in the optimization results with the dielectric constant of existing finished porcelain insulators.

[0079] If a target dielectric constant cannot be met by existing finished porcelain insulators (i.e., no corresponding finished porcelain insulator exists), a customized production method is adopted. Using a pre-defined porcelain substrate, strontium titanate powder is incorporated into the substrate according to the target doping ratio, resulting in a doped porcelain insulator. A doped porcelain insulator refers to a porcelain insulator whose dielectric properties are artificially adjusted to achieve a specific target dielectric constant by precisely controlling the proportion of specific additives (such as strontium titanate powder) incorporated into the basic porcelain material. The pre-defined porcelain substrate can be high-alumina porcelain, alumina porcelain, or silicate porcelain, depending on the required mechanical strength, heat resistance, insulation performance, and compatibility with the dopant. Strontium titanate powder is a commonly used high-dielectric-constant ceramic material, and its incorporation amount can effectively adjust the dielectric constant of the composite material.

[0080] Determining the target doping ratio typically requires a combination of experimental verification and theoretical calculations. A curve or model relating the doping ratio to the dielectric constant can be established beforehand, allowing the required doping ratio to be derived from the target dielectric constant. The doping process usually involves uniformly mixing, molding, and sintering strontium titanate powder with the ceramic matrix powder to ensure material densification and the formation of the desired crystalline structure, thereby achieving stable dielectric properties. It is important to note that the sum of the number of finished ceramic insulators and the number of doped ceramic insulators in the final constructed target insulator string must match the target number of ceramic insulators obtained from the optimization problem solution.

[0081] In one possible implementation, the target doping ratio can be determined using the following formula:

[0082] Where f is the target doping ratio, εm is the dielectric constant of the matrix, and εi is the dielectric constant of the doped phase strontium titanate. The dielectric constant of the composite ceramic is... is the relative permittivity of the doped filler phase.

[0083] In practical applications, the above formula can be transformed into the following formula:

[0084] Substituting εm=5.5 and εf=330 into the above formula, we can obtain the doping ratio corresponding to each dielectric constant involved in this embodiment (mass fraction is calculated based on the density of strontium titanate 5.11 g / cm³ and the density of electrical porcelain 2.4 g / cm³), as shown in Table 1.

[0085] Table 1 Target dielectric constant and strontium titanate doping ratio

[0086] In practical applications, the preparation process of doped porcelain insulators can be as follows: weigh strontium titanate powder and porcelain powder according to Table 1, mix them by wet ball milling, dry and sieve, dry press or isostatic press to form umbrella disc blanks, sinter according to the porcelain firing regime (firing temperature of about 1250-1350℃, with the upper limit taken as the doping amount increases), grind, glaze, glue metal accessories, and measure the dielectric constant and breakdown field strength.

[0087] More specifically, the firing process can be as follows: slowly increase the temperature from room temperature to 600℃ at a rate of 1-2℃ / min to remove structural water and forming agent; after 600℃, accelerate to 1050℃; then enter the liquid phase sintering section at a rate of 2-3℃ / min, and hold at 1250-1350℃ for 1-3 hours (the lower limit is used for low doping levels, and the upper limit is used for levels with a doping amount exceeding 30% by volume, and 0.5%-2% by mass of B2O3 or CuO sintering aids can be added to promote densification); slow cooling in the furnace to prevent cracking.

[0088] After obtaining all finished porcelain insulators and / or doped porcelain insulators that meet the target dielectric constant, they can be connected in series with grounding towers, composite insulators, and high-voltage conductors according to their respective target dielectric constants to obtain the target insulator string. The series connection process must comply with power industry standards and specifications to ensure reliable connections, sufficient mechanical strength, and electrical clearances conforming to design requirements. This typically involves using insulator string connection fittings and ensuring the robustness of the electrical and mechanical connections between the various components.

[0089] However, even if the optimal porcelain insulator parameters are obtained, if these porcelain insulators with different dielectric constants are not arranged in a reasonable spatial manner when constructing the target insulator string, local electric field concentration may still occur inside the insulator string or in the connection area, thereby affecting the overall uniformity of the electric field distribution of the insulator string and reducing its insulation performance and operational reliability.

[0090] In response, this application further proposes that when constructing the target insulator string, the grounding tower in the target insulator string is connected to the composite insulator, the finished porcelain insulator and / or doped porcelain insulator with the lowest target dielectric constant is adjacent to the composite insulator, and the finished porcelain insulator and / or doped porcelain insulator with the highest target dielectric constant is adjacent to the high-voltage conductor. Furthermore, each finished porcelain insulator and / or doped porcelain insulator is connected in series in order of the magnitude of the target dielectric constant.

[0091] Specifically, the grounding tower in the target insulator string is connected to the composite insulator. This connection marks the starting point of the insulator string, linking the entire insulation system to the earth potential and providing reliable insulation support for the high-voltage conductor. This is typically achieved through mechanical fixing and electrical connections to ensure structural stability and effective grounding.

[0092] Simultaneously, the finished porcelain insulators and / or doped porcelain insulators with the lowest target dielectric constant are placed adjacent to the composite insulators. In an insulator string, the electric field distribution typically weakens gradually from the high-voltage side to the grounding side. Placing porcelain insulators with relatively low dielectric constants adjacent to composite insulators helps to achieve a smooth transition of the electric field distribution in the transition region between the composite and porcelain insulator strings, avoiding localized electric field distortion caused by excessive differences in material dielectric properties. This connection is typically achieved through standard insulator connection methods such as ball-and-socket connections, U-ring connections, or tongue-and-plate connections.

[0093] Furthermore, the finished porcelain insulators and / or doped porcelain insulators with the highest target dielectric constant are placed adjacent to the high-voltage conductors. The high-voltage conductor is the component with the highest potential in the entire insulator string, and the electric field intensity around it is most concentrated. Insulating materials with higher dielectric constants have stronger electric field tolerance, effectively dispersing the electric field stress near the high-voltage conductor, reducing the local electric field intensity, and thus improving the withstand capability of the insulator string in high-potential regions. The connection between the high-voltage conductor and the insulator string is usually achieved through clamps, crimped tubes, or pre-twisted wires to ensure a firm and reliable connection with good electrical contact.

[0094] Furthermore, the finished porcelain insulators and / or doped porcelain insulators are connected in series sequentially according to the target dielectric constant. This ordered arrangement aims to create an insulator string with a gradient in dielectric constant. By gradually changing from a low dielectric constant to a high dielectric constant (or vice versa), the potential distribution and electric field intensity changes within the entire porcelain insulator string are smoother, avoiding abrupt electric field jumps between adjacent insulators, thereby reducing partial discharge and corona discharge, and improving the overall insulation performance of the insulator string. For example, if the connection proceeds from the composite insulator side to the high-voltage conductor side, the dielectric constant of the porcelain insulators should show an increasing trend.

[0095] Through the above technical solution, the construction of the target insulator string not only considers the optimization of the number and dielectric constant of porcelain insulators, but also further refines the arrangement order within the porcelain insulator string, resulting in a more rational electric field distribution among the grounding tower, composite insulators, porcelain insulator strings, and high-voltage conductors. Specifically, placing the finished porcelain insulators and / or doped porcelain insulators with the lowest target dielectric constant adjacent to the composite insulators helps to smooth the electric field transition at the ends of the composite insulators and avoid local electric field concentration. Simultaneously, placing the finished porcelain insulators and / or doped porcelain insulators with the highest target dielectric constant adjacent to the high-voltage conductors effectively disperses the high electric field intensity near the high-voltage conductors and reduces electric field stress at the connection points. Furthermore, by connecting the finished porcelain insulators and / or doped porcelain insulators sequentially according to their target dielectric constants, a smooth transition of the electric field distribution from the grounding side to the high-voltage side is achieved, avoiding electric field distortion and partial discharge risks caused by abrupt changes in dielectric constant. This refined arrangement makes the electric field distribution of the entire insulator string more uniform, effectively reducing the maximum electric field strength on the surface of the composite insulator and the maximum electric field strength inside the porcelain insulator. This significantly improves the overall insulation performance, operational reliability and service life of the target insulator string, and further optimizes the insulator string's anti-pollution flashover and withstand voltage capabilities.

[0096] Through the above technical solution, this application can flexibly select and obtain finished porcelain insulators or custom-doped porcelain insulators based on the target dielectric constant of each porcelain insulator obtained from the optimization results. This combination method effectively solves the problem that the target dielectric constant cannot be fully met by existing finished insulators, ensuring the accurate implementation of the optimization scheme. Specifically, when there are finished porcelain insulators that match the target dielectric constant, they can be purchased directly, thereby reducing manufacturing costs and production cycle; when there are no matching finished porcelain insulators, they are custom-produced by doping with strontium titanate powder, ensuring the precise adjustability of the dielectric constant. This allows the constructed target insulator string to strictly follow the optimized design, thereby effectively minimizing the maximum electric field strength on the surface of the composite insulator and ensuring that the maximum electric field strength inside the porcelain insulator does not exceed the safety threshold, significantly improving the electrical performance and operational reliability of the insulator string, while also taking into account economy and manufacturability.

[0097] As can be seen from the above, since this scheme takes minimizing the maximum surface electric field of the composite insulator as the objective function and the constraint that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold, the optimization problem is constructed and solved to obtain the target insulator string. Therefore, the target insulator string constructed by this scheme can not only minimize the maximum surface electric field of the composite insulator, but also ensure that the maximum internal electric field of each porcelain insulator does not exceed the preset safe electric field threshold, thus improving the reliability of the insulator string.

[0098] In some embodiments described above in this application, a method for constructing a series-connected insulator string is proposed. This method aims to minimize the maximum surface electric field strength of the composite insulator by optimizing the number and dielectric constant of porcelain insulators, while ensuring that the internal electric field strength of the porcelain insulator meets safety requirements. However, the final output of this method is optimized design parameters. How to translate these theoretical optimization results into practically usable physical insulator strings and ensure that they possess the expected electric field performance and reliability is a key aspect that needs further clarification and demonstration in practical applications.

[0099] To address this issue, this application proposes a series-connected insulator string. The unique feature of this series-connected insulator string is that it is not arbitrarily assembled, but rather constructed using the aforementioned method. Specifically, this construction method first obtains a simulation model of an initial insulator string, which includes a grounding tower, a composite insulator connected to the grounding tower, a string of porcelain insulators adjacent to the composite insulator, and a high-voltage conductor adjacent to the porcelain insulator string. The porcelain insulator string comprises several porcelain insulators connected in series. Then, based on the simulation model, using the number of porcelain insulators in the string and the dielectric constant of each porcelain insulator as variables, and minimizing the maximum surface electric field strength of the composite insulator as the objective function, with the constraint that the maximum internal electric field strength of each porcelain insulator does not exceed a preset safe electric field strength threshold, an optimization problem is constructed and solved to obtain the optimal solution. The optimal solution includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator. Finally, based on the target number and the target dielectric constants, the series-connected insulator string is constructed.

[0100] The insulator string constructed using this optimization method has carefully designed and selected parameters for each component (such as the number of porcelain insulators and the dielectric constant) to achieve optimal overall performance. For example, during the construction process, finished porcelain insulators corresponding to each target dielectric constant are obtained. If no finished porcelain insulator exists for any target dielectric constant, a pre-set porcelain substrate is used as the base, and strontium titanate powder is added to the substrate according to the target doping ratio to obtain a doped porcelain insulator. The target doping ratio is determined based on the corresponding target dielectric constant, and the sum of the number of finished porcelain insulators and the number of doped porcelain insulators is the target quantity. Subsequently, based on the target dielectric constants of the finished porcelain insulators and the doped porcelain insulators, the finished porcelain insulators, doped porcelain insulators, grounding towers, composite insulators, and high-voltage conductors are connected in series to obtain the target insulator string. During series connection, the grounding tower in the target insulator string is connected to the composite insulator, the finished porcelain insulator and / or doped porcelain insulator with the lowest target dielectric constant is adjacent to the composite insulator, and the finished porcelain insulator and / or doped porcelain insulator with the highest target dielectric constant is adjacent to the high voltage conductor. Furthermore, each finished porcelain insulator and / or doped porcelain insulator is connected in series in order of the magnitude of the target dielectric constant.

[0101] Through the aforementioned technical solution, the series-connected insulator string provided in this application, based on a rigorous optimization construction method, ensures excellent electric field performance and high reliability in actual operation. Specifically, this insulator string effectively controls the maximum surface electric field strength of the composite insulator to a low level, thereby significantly reducing the risk of flashover and extending its service life. Simultaneously, by strictly controlling the maximum electric field strength inside the porcelain insulator, internal discharge is avoided, further improving the overall insulation performance and operational stability of the insulator string. This physical product, obtained through optimized design, transforms theoretically optimal performance into a practically usable engineering entity, providing a safer, more reliable, and economical insulation solution for high-voltage transmission lines.

[0102] To further illustrate the construction method of the series insulator string provided in the embodiments of this application, three embodiments are given below.

[0103] In the first embodiment, when the number of candidates is N=1, the corresponding sub-optimization problem only uses the dielectric constant εr1 of the first porcelain insulator as a variable, which is a one-dimensional optimization problem. There is no need to use response surface or iterative algorithms. It can be solved directly by one-dimensional parameterized scanning.

[0104] Finite element simulation calculations were performed point-by-point within the pre-set candidate set of manufacturable dielectric constants {5, 7.5, 10, 12.5, 15}, resulting in a total of 5 sets of simulation working condition data. Then, based on the constraint condition that the maximum electric field strength EN_max inside the porcelain insulator is ≤30 kV / cm, feasible solutions were screened for all simulation working conditions. The working condition with the minimum maximum electric field strength on the surface of the composite insulator was selected as the optimal solution from the feasible solutions that satisfy the constraint.

[0105] Table 2 Simulation scan results of Example 1 (number of candidates N=1)

[0106] The results and dielectric constant constraints in Table 2 show two sets of monotonic variation patterns in the simulation results: the maximum electric field strength on the surface of the composite insulator gradually increases with increasing εr1, rising from 4.69 kV / cm to 5.88 kV / cm; the maximum electric field strength inside the porcelain insulator gradually decreases with increasing εr1, decreasing from 53.15 kV / cm to 27.01 kV / cm. Therefore, under the condition of only one porcelain insulator connected in series, there is a direct conflict between the objective function of minimizing the surface electric field strength of the composite insulator and the constraint condition of the electric field strength inside the porcelain insulator. There is no solution that simultaneously achieves ideal levels for both indicators. The solution process follows the principle of constraint priority in the selection process.

[0107] Using the discrete field strength data in Table 2 for interpolation, when the maximum field strength inside the porcelain insulator is taken as the safe field strength threshold of 30 kV / cm, the corresponding dielectric constant εr1≈13. Therefore, under the condition of N=1 candidate, the range of the dielectric constant of the porcelain insulator is constrained to εr1 ∈ [13, 15]. Among the discrete candidate dielectric constants selected in this study, only εr1=15 satisfies all the conditions.

[0108] Optimization result: εr1 =15. Under this condition, the maximum electric field strength on the surface of the composite insulator is 5.88 kV / cm, which is about 13.5% lower than the control group of 6.80 kV / cm without series porcelain insulators. The maximum electric field strength inside the porcelain insulator is 27.01 kV / cm, which is lower than the safe electric field strength threshold of 30 kV / cm, leaving a safety margin of about 10%. This result shows that when the number of candidates N=1, the improvement of the electric field at the end of the composite insulator is strongly limited by the constraint of the electric field strength inside the porcelain insulator, but it is already able to avoid the breakdown risk induced by internal defects of the porcelain insulator.

[0109] To prepare and assemble a porcelain insulator with a target dielectric constant of 15, it was determined that no matching finished porcelain insulators were available. Therefore, doping modification was performed. The initial doping ratio was 38.4% strontium titanate by volume (approximately 57% by mass), obtained according to the formula. Using a pre-designed porcelain as the matrix, strontium titanate powder was incorporated in the corresponding proportion. Following the sintering process described in this application, the blank was formed, sintered, ground, glazed, and metal fittings were glued. The dielectric constant was repeatedly measured and the doping ratio was iteratively adjusted until the dielectric constant of the porcelain insulator reached εr1 = 15 ± 0.5. The prepared doped porcelain insulator was then assembled in the target insulator string sequence: grounding tower, composite insulator, No. 1 porcelain insulator, and high-voltage conductor. After the string was completed, a three-dimensional electric field finite element simulation was performed on the assembled insulator string to verify the maximum electric field strength on the surface of the composite insulator and the maximum electric field strength inside the porcelain insulator. Both indicators were confirmed to meet the design requirements.

[0110] In the second embodiment, when the number of candidates is N=2, the corresponding sub-optimization problem uses a two-dimensional vector (εr1, εr2) as the design variable and is solved using a two-dimensional full-factor parameterized scan. Within the Cartesian product set {5, 7.5, 10, 12.5, 15}×{5, 7.5, 10, 12.5, 15} of the candidate dielectric constant set {5, 7.5, 10, 12.5, 15}, finite element simulation calculations are performed on all 25 combinations of dielectric constants. The maximum electric field strength on the surface of the composite insulator and the maximum electric field strength inside each of the two porcelain insulators are extracted under each working condition. The larger value between the maximum electric field strength inside the two porcelain insulators is taken as the constraint observation EN_max.

[0111] Table 3. Feasible Combinations for Example 2

[0112] Note: The unit of electric field strength is kV / cm. Of the 25 scanning combinations, the remaining 22 were deemed infeasible because the maximum electric field strength inside at least one porcelain insulator exceeded 30 kV / cm. For example, although the surface electric field strength of the composite insulator in combination (5, 15) was only 4.16 kV / cm, the maximum electric field strength inside the No. 1 porcelain insulator reached 42.2 kV / cm, which did not meet the constraint conditions.

[0113] Simulation results reveal the constraint coupling mechanism between porcelain insulators in a double-segment series structure: Porcelain insulator No. 2 is the last segment adjacent to the high-voltage conductor, and its maximum internal electric field is mainly affected by its own dielectric constant. The larger the value of εr2, the lower the internal electric field of porcelain insulator No. 2; however, increasing εr2 will increase the internal electric field of porcelain insulator No. 1. Therefore, the dielectric constant εr1 of porcelain insulator No. 1 cannot be too low. The discrete constraint range can be obtained from 25 sets of discrete simulation data: εr2 is taken as the upper limit of the candidate dielectric constant, 15, while simultaneously satisfying εr1≥10. Feasible combinations account for only 3 / 25 of all scanned conditions, which is more stringent than the constraint conditions for N=1, but the maximum electric field on the surface of the composite insulator corresponding to the feasible solution is significantly reduced.

[0114] Optimization result: ε = (10, 15). Under this condition, the maximum electric field strength on the surface of the composite insulator is 4.70 kV / cm, which is about 30.9% lower than the 6.80 kV / cm of the control group without series-connected porcelain insulators. The constraint observation EN_max = 28.6 kV / cm, which appears in porcelain insulator No. 2, further confirming that the last section of porcelain insulator adjacent to the high-voltage conductor is the main control part of the constraint condition. The optimized dielectric constant combination shows an increasing gradient distribution of εr1 < εr2, which is consistent with the aforementioned mechanism analysis conclusions.

[0115] Preparation and Assembly: Porcelain insulators with target dielectric constants of 10 and 15 were obtained respectively. The specifications of the finished porcelain insulators were checked. If no perfectly matching finished porcelain insulators were found, doping modification was carried out. According to the formula, the target dielectric constant of 10 for porcelain insulator No. 1 corresponds to a volume fraction of approximately 22.5% and a mass fraction of approximately 38.2% for strontium titanate; the target dielectric constant of 15 for porcelain insulator No. 2 corresponds to a volume fraction of approximately 38.4% and a mass fraction of approximately 57.0% for strontium titanate. After preparation, the dielectric constant needs to be measured and the doping ratio iteratively corrected. The two doped porcelain insulators were assembled in series in the following order: grounding tower, composite insulator, porcelain insulator No. 1, porcelain insulator No. 2, and high-voltage conductor. After assembly, a three-dimensional electric field finite element simulation was performed on the entire string of insulators to verify that the maximum electric field strength on the surface of the composite insulator and the maximum electric field strength inside each porcelain insulator met the design specifications.

[0116] In the third embodiment, when the number of candidates is N=3, the corresponding sub-optimization problem uses a three-dimensional vector (εr1, εr2, εr3) as the design variable and is solved in two steps. First, within the cubic Cartesian product set {5, 7.5, 10, 12.5, 15}³ of the candidate dielectric constant set {5, 7.5, 10, 12.5, 15}, full-factor three-dimensional finite element simulation sampling of all 125 dielectric constant combinations is completed. Second, a cubic polynomial response surface surrogate model is fitted based on the obtained 125 sets of simulation sample data, where the goodness of fit R² for the maximum electric field strength on the composite insulator surface is 0.9999, and the goodness of fit R² for the maximum electric field strength inside the porcelain insulator is 0.9875. A continuous optimal solution is obtained by using the Sequence Constraint Optimization (SLSQP) algorithm on this surrogate model; simultaneously, discrete optimal feasible solutions are directly selected from the 125 sets of discrete simulation samples, and the continuous optimal solution and the discrete optimal feasible solution are mutually verified.

[0117] Table 4 Feasible Combinations for Example 3

[0118] Note: All electric field strength units are kV / cm. Of the 125 simulation combinations, the remaining 116 combinations do not meet the constraints and are therefore deemed infeasible. The globally unconstrained optimal solution without applying electric field strength constraints to the porcelain insulator is combination (5, 5, 5). Under this condition, the maximum electric field strength on the surface of the composite insulator is 2.72 kV / cm, but the maximum electric field strength inside the No. 3 porcelain insulator reaches 49.7 kV / cm, significantly exceeding the safe electric field strength threshold.

[0119] Based on the results and the dielectric constant constraints, a statistical analysis was conducted on feasible combinations. The feasible solutions exhibit a very clear distribution characteristic: εr3 in all nine feasible solutions is taken as the upper limit of the candidate dielectric constant, 15, while also satisfying εr2≥10 and εr1≥7.5. This indicates that the No. 3 end section porcelain insulator, adjacent to the high-voltage conductor, is consistently the most stringent control point, while the front section porcelain insulator near the composite insulator side has greater freedom in material selection. The discrete optimal feasible solution is ε = (7.5, 10, 15), under this condition the maximum electric field strength on the surface of the composite insulator is 3.74 kV / cm, which is about 45.0% lower than the control group of 6.80 kV / cm without series porcelain insulators; the constrained observation EN_max = 28.0 kV / cm, the maximum electric field strength inside the three porcelain insulators are 26.8 kV / cm, 27.4 kV / cm and 28.0 kV / cm respectively, and the electric field strength distribution inside each section of porcelain insulator is balanced.

[0120] The continuous fine-optimal solution obtained based on the response surface surrogate model is ε. = (6.9, 10.4, 15), the predicted maximum electric field strength on the surface of the composite insulator is 3.71 kV / cm, and the predicted EN_max value is 30.0 kV / cm, which falls exactly on the safe electric field strength constraint boundary. This continuous solution is in high agreement with the calculated results of the discrete optimal feasible solution (7.5, 10, 15), verifying that the polynomial response surface surrogate model constructed in this study has good computational accuracy. Considering that actual material preparation needs to be carried out according to the dielectric constant range in Table 1, the discrete optimal feasible solution is preferred for engineering applications, while the continuous optimal solution can serve as a reference for fine-tuning the doping formula of ceramic insulators.

[0121] It should be noted that both the discrete optimal feasible solution and the continuous fine optimal solution spontaneously form a monotonically increasing dielectric gradient structure of εr1 < εr2 < εr3: the first porcelain insulator uses a lower dielectric constant to achieve a smooth transition in dielectric properties with the composite insulator; the third porcelain insulator, located near the high-voltage conductor, uses a high dielectric constant to suppress its internal field strength peak. This gradient arrangement is not pre-set, but rather an optimized output driven by the objective function of "minimizing the maximum field strength on the surface of the composite insulator" and the constraint condition of "the maximum field strength inside the porcelain insulator does not exceed the safe field strength threshold," providing a technical basis for the dielectric gradient series insulator string structure of this application.

[0122] Preparation and Assembly: Porcelain insulators with target dielectric constants of 7.5, 10, and 15 were obtained respectively. The specifications of the finished porcelain insulators were checked. If no perfectly matching finished porcelain insulator was found, doping modification was carried out. According to the formula, the target dielectric constant of 7.5 for porcelain insulator No. 1 corresponds to a volume fraction of approximately 11.4% and a mass fraction of approximately 21.4% for strontium titanate; the target dielectric constant of 10 for porcelain insulator No. 2 corresponds to a volume fraction of approximately 22.5% and a mass fraction of approximately 38.2% for strontium titanate; and the target dielectric constant of 15 for porcelain insulator No. 3 corresponds to a volume fraction of approximately 38.4% and a mass fraction of approximately 57.0% for strontium titanate. After preparation, the dielectric constant needs to be measured and the doping ratio iteratively corrected.

[0123] The three doped porcelain insulators prepared were assembled in series in the following order: grounding tower, composite insulator, porcelain insulator No. 1, porcelain insulator No. 2, porcelain insulator No. 3, and high-voltage conductor. After assembly, a three-dimensional electric field finite element simulation was carried out on the entire string of insulators to verify the maximum electric field strength on the surface of the composite insulator and the maximum electric field strength inside each porcelain insulator, confirming that all design specifications were met.

[0124] Please see Figure 3 , Figure 3 This is a comparison diagram of the internal electric field strength of various porcelain insulators under different dielectric constant arrangements, provided for embodiments of this application. Figure 3The figure shows a bar chart comparing the maximum electric field strength inside each porcelain insulator under the conditions of Comparative Example 1 and Example 3. Comparative Example 1 uses a uniform dielectric constant combination (5,5,5), Comparative Example 2 uses a reverse gradient dielectric constant combination (15,10,5), and Example 3 uses an incremental gradient dielectric constant combination (7.5,10,15) optimized in this application. The dashed line in the figure represents the safety threshold of 30kV / cm for the maximum electric field strength inside the porcelain insulator.

[0125] from Figure 3 Simulation results show that under the existing conventional uniform dielectric constant scheme (Comparative Example 1), the electric field strength inside the porcelain insulator rises rapidly along the series towards the high-voltage conductor end. The maximum electric field strength inside the No. 3 porcelain insulator, which is close to the high-voltage conductor, is as high as 49.7 kV / cm, which greatly exceeds the safety threshold of 30 kV / cm. If a reverse gradient arrangement is adopted (Comparative Example 2), the electric field strength inside the porcelain insulator on the high-voltage side deteriorates further, reaching 57.1 kV / cm, which will bring extremely high risks of internal partial discharge and insulation breakdown.

[0126] After adopting the monotonically increasing dielectric constant scheme optimized in this application (Example 3), the maximum electric field strength inside porcelain insulators No. 1, No. 2, and No. 3 are 26.8kV / cm, 27.4kV / cm, and 28.0kV / cm, respectively, all of which are controlled within the safety threshold of 30kV / cm. The distribution of electric stress inside each section of porcelain insulator tends to be balanced, eliminating the hidden danger of excessive electric field strength inside the high-voltage porcelain insulator.

[0127] Therefore, this application does not only focus on reducing the surface electric field strength of composite insulators, but also incorporates the internal electric field strength of porcelain insulators as a hard constraint into the optimization. By optimizing the output dielectric gradient structure that increases from the composite insulator end to the high-voltage conductor end, it can effectively suppress the phenomenon of internal electric field concentration in series porcelain insulators, especially the insulators near the high-voltage conductor, avoid the risk of partial discharge induced by pore defects inside the porcelain components, and significantly improve the electrical reliability of the entire series insulator string during long-term operation.

[0128] The optimization results of the three embodiments described above are compared below.

[0129] Table 5 Comparison of Optimization Results of Examples 1 to 3

[0130] As can be seen from the comparison in Table 5, as the number of series connections increases from N=1 to N=3, the marginal improvement in the maximum electric field strength on the surface of the composite insulator is approximately 1.2 kV / cm → 1.0 kV / cm, and the marginal improvement effect shows a decreasing trend. All three examples satisfy the safety field strength constraint condition that the maximum electric field strength inside the porcelain insulator is no greater than 30 kV / cm.

[0131] Please see Figure 4 , Figure 4 A comparison of the electric field distribution cloud maps before and after series connection in the three embodiments provided for this application. Figure 4 In the figure, Figure (a) shows the electric field distribution cloud map corresponding to the control group (without series connection); Figure (b) shows the electric field distribution cloud map corresponding to Example 1 (εr1=15); Figure (c) shows the electric field distribution cloud map corresponding to Example 2 (10, 15); Figure (d) shows the electric field distribution cloud map corresponding to Example 3 (7.5, 10, 15); and Figure (e) shows the electric field distribution cloud map corresponding to the continuous solution of Example 3 (6.9, 10.4, 15). It can be seen that after series connection, the high field region at the end of the composite insulator is significantly weakened, and the hot spot is transferred to the porcelain insulation section and thinned.

[0132] In practical applications, when selecting engineering solutions, if the requirements for electric field improvement are general, or if there are strict limitations on the total length of the insulator string, the design scheme of Example 1 can be selected. If a significant end voltage equalization effect is desired, and site conditions allow for the addition of 1-2 extra porcelain insulators, Example 2 or Example 3 should be preferred. For the case where N≥4, the optimization calculation can continue using the solution process of enumerating the number of candidates in the outer layer of this application, but the marginal benefit of field strength improvement will further decrease, and it is generally not preferred in engineering.

[0133] As can be seen from the above, compared with the existing technology that determines the number of insulators in series based on experience and uses porcelain insulators with a single dielectric constant, this method, by constructing and solving an optimization problem that considers minimizing the surface electric field strength of the composite insulator and the safety threshold of the internal electric field strength of the porcelain insulator, can systematically determine the optimal number of porcelain insulators and the optimal dielectric constant of each porcelain insulator. This method avoids the risks of incomplete optimization of the electric field strength at the high-voltage end of the composite insulator or the breakdown of the series-connected porcelain insulators themselves, which may occur in traditional methods. By optimizing the configuration of porcelain insulators with different dielectric constants, the electric field distribution of the entire insulator string is made more uniform, reducing the local electric field strength at the high-voltage end of the composite insulator, while ensuring the electrical safety of the series-connected porcelain insulators themselves, thereby improving the long-term operational reliability of the transmission line.

[0134] Please see Figure 5 , Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 5 As shown, the electronic device 5 provided in this embodiment may include: a processor 50, a memory 51, and a computer program 52 stored in the memory 51 and executable on the processor 50, such as a program corresponding to the method for constructing a series insulator string. When the processor 50 executes the computer program 52, it implements the steps described above in the embodiment of the method for constructing a series insulator string, for example... Figure 1 S101~S103 are shown.

[0135] For example, computer program 52 may be divided into one or more modules / units, one or more of which are stored in memory 51 and executed by processor 50 to complete this application. One or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of computer program 52 in electronic device 5.

[0136] Those skilled in the art will understand that Figure 5 This is merely an example of electronic device 5 and does not constitute a limitation on electronic device 5. It may include more or fewer components than shown, or combine certain components, or use different components.

[0137] Processor 50 can be a central processing unit (CPU), a graphics processing unit (GPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0138] The memory 51 can be an internal storage unit of the electronic device 5, such as a hard disk or RAM. The memory 51 can also be an external storage device of the electronic device 5, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, or flash card. Furthermore, the memory 51 can include both internal and external storage units of the electronic device 5. The memory 51 is used to store computer programs and other programs and data required by the electronic device. The memory 51 can also be used to temporarily store data that has been output or will be output.

[0139] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units is merely an example. In practical applications, the above functions can be assigned to different functional units as needed, that is, the internal structure of the electronic device can be divided into different functional units to complete all or part of the functions described above. The functional units in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0140] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps in the various method embodiments described above.

[0141] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0142] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, refer to the relevant descriptions of other embodiments.

[0143] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0144] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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. Such 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 application, and should all be included within the protection scope of this application.

Claims

1. A method for constructing a series-connected insulator string, characterized in that, include: A simulation model of the initial insulator string is obtained; the initial insulator string includes a grounding tower, a composite insulator connected to the grounding tower, a string of porcelain insulators adjacent to the composite insulator, and a high-voltage conductor adjacent to the string of porcelain insulators, wherein the string of porcelain insulators includes several porcelain insulators connected in series; Based on the simulation model, using the number of porcelain insulators in the porcelain insulator string and the dielectric constant of each porcelain insulator as variables, minimizing the maximum surface electric field of the composite insulator as the objective function, and ensuring that the maximum internal electric field of each porcelain insulator does not exceed a preset safe electric field threshold as a constraint, an optimization problem is constructed and solved to obtain the optimal solution to the optimization problem; the optimal solution includes the target number of porcelain insulators and the target dielectric constant of each porcelain insulator. Based on the target quantity and the target dielectric constant of each, construct the target insulator string.

2. The method according to claim 1, characterized in that, The maximum surface electric field strength of a composite insulator is determined in the following way: Based on the simulation model, the electric field of the composite insulator is calculated using the finite element method. In the process of finite element calculation of the electric field of composite insulator, the maximum electric field in the interface between the target silicone rubber material of composite insulator and air is selected as the maximum surface electric field of composite insulator. The target silicone rubber material is the silicone rubber material in the insulation structure area between the high-voltage end fittings of the composite insulator and the first shed of the high-voltage end of the composite insulator.

3. The method according to claim 1, characterized in that, The step of performing finite element calculations on the electric field of the composite insulator based on the simulation model includes: Determine the operating voltage of the high-voltage conductor based on the voltage level of the target transmission line; Using the structural parameters of the composite insulator, the structural parameters of each of the porcelain insulators, the working voltage of the high-voltage conductor, the structural parameters of the grounding tower, and the structural parameters of the high-voltage conductor as the input boundary conditions of the simulation model, the electric field of the composite insulator is calculated by finite element method.

4. The method according to claim 1, characterized in that, The safe field strength threshold is determined in the following way: Obtain the air breakdown field strength of the internal pores of the ceramic insulator; The margin factor is determined based on the user's reliability requirements for the target insulator string; The safe field strength threshold is determined based on the air breakdown field strength and the margin coefficient.

5. The method according to claim 1, characterized in that, The optimization problem is solved in the following way: Based on the degree of impact of the number of porcelain insulators in the porcelain insulator string on the manufacturing cost and installation difficulty of the porcelain insulator string, and in combination with the limit on the number of porcelain insulators in the porcelain insulator string, several candidate quantities are determined; For each candidate quantity, construct and solve the sub-optimization problem corresponding to that candidate quantity, determine the optimal objective function value corresponding to that candidate quantity, and obtain the optimal objective function value corresponding to each candidate quantity. Among the candidate quantities, the candidate quantity with the smallest corresponding optimal objective function value is selected as the target quantity, and each dielectric constant corresponding to the target quantity is determined as the target dielectric constant.

6. The method according to claim 5, characterized in that, The process of constructing and solving the sub-optimization problem corresponding to the number of candidates, and determining the optimal objective function value corresponding to the number of candidates, includes: Using the dielectric constant of each porcelain insulator corresponding to the number of candidates as variables, minimizing the maximum surface electric field of the composite insulator as the objective function, and ensuring that the maximum internal electric field of each porcelain insulator does not exceed the safe electric field threshold as a constraint, the sub-optimization problem corresponding to the number of candidates is constructed. Within a preset range of manufacturable dielectric constants, the sub-optimization problem corresponding to the number of candidate quantities is solved using a preset algorithm to obtain the optimal objective function value corresponding to the number of candidate quantities; the preset algorithm is different for different numbers of candidate quantities.

7. The method according to claim 5, characterized in that, After solving the sub-optimization problem corresponding to the number of candidates using a preset algorithm, the method further includes: If the sub-optimization problem corresponding to the number of candidates has no solution, then the range of manufacturable dielectric constants is adjusted, and / or the number of candidates is increased to resolve the sub-optimization problem corresponding to the number of candidates.

8. The method according to claim 1, characterized in that, The step of constructing the target insulator string based on the target quantity and each of the target dielectric constants includes: Each of the target dielectric constants is used to obtain a finished porcelain insulator. If no finished porcelain insulator exists for any of the target dielectric constants, a pre-set porcelain substrate is used as the base, and strontium titanate powder is added to the substrate according to the target doping ratio to obtain a doped porcelain insulator. The target doping ratio is determined according to the corresponding target dielectric constant, and the sum of the number of finished porcelain insulators and the number of doped porcelain insulators is the target quantity. Based on the target dielectric constants corresponding to the finished porcelain insulator and the doped porcelain insulator, the finished porcelain insulator, the doped porcelain insulator, the grounding tower, the composite insulator, and the high-voltage conductor are connected in series to obtain the target insulator string.

9. The method according to claim 8, characterized in that, The grounding tower in the target insulator string is connected to the composite insulator. The finished porcelain insulator and / or the doped porcelain insulator with the lowest target dielectric constant is adjacent to the composite insulator. The finished porcelain insulator and / or the doped porcelain insulator with the highest target dielectric constant is adjacent to the high-voltage conductor. The finished porcelain insulator and / or the doped porcelain insulator are connected in series in order of the magnitude of the target dielectric constant.

10. A series-connected insulator string, characterized in that, The series insulator string is constructed by the method for constructing a series insulator string as described in any one of claims 1 to 9.

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